experimental test parameters

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Methodology

• Guide to Experimental Design | Overview, Steps, & Examples

Guide to Experimental Design | Overview, 5 steps & Examples

Published on December 3, 2019 by Rebecca Bevans . Revised on June 21, 2023.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias , survivorship bias , and attrition bias as time passes.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, other interesting articles, frequently asked questions about experiments.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

Prevent plagiarism. Run a free check.

Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalized and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomized design vs a randomized block design .
• A between-subjects design vs a within-subjects design .

Randomization

An experiment can be completely randomized or randomized within blocks (aka strata):

• In a completely randomized design , every subject is assigned to a treatment group at random.
• In a randomized block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomization isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs. within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomizing or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimize research bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalized to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bevans, R. (2023, June 21). Guide to Experimental Design | Overview, 5 steps & Examples. Scribbr. Retrieved August 12, 2024, from https://www.scribbr.com/methodology/experimental-design/

Is this article helpful?

Rebecca Bevans

Other students also liked, random assignment in experiments | introduction & examples, quasi-experimental design | definition, types & examples, how to write a lab report, get unlimited documents corrected.

✔ Free APA citation check included ✔ Unlimited document corrections ✔ Specialized in correcting academic texts

Please enable JavaScript to view this site.

• Statistics Guide
• Curve Fitting Guide
• Prism Guide
• Zoom Window Out
• Larger Text  |  Smaller Text
• Hide Page Header
• Show Expanding Text
• Printable Version
• Save Permalink URL

Prism offers seven related tests that compare two groups. To choose among these tests, answer three questions in the Experimental Design tab of the t test parameters dialog:

Experimental design: unpaired or paired

Choose a paired test when the columns of data are matched. That means that values on the same row are related to each other.

Here are some examples:

• You measure a variable in each subject before and after an intervention.

• You recruit subjects as pairs, matched for variables such as age, ethnic group, and disease severity. One of the pair gets one treatment; the other gets an alternative treatment.

• You run a laboratory experiment several times, each time with a control and treated preparation handled in parallel.

• You measure a variable in twins or child/parent pairs.

Matching should be determined by the experimental design, and definitely should not be based on the variable you are comparing. If you are comparing blood pressures in two groups, it is OK to match based on age or postal code, but it is not OK to match based on blood pressure.

Assume Gaussian distribution?

Nonparametric tests , unlike t tests, are not based on the assumption that the data are sampled from a Gaussian distribution . But nonparametric tests have less power . Deciding when to use a nonparametric test is not straightforward .

Choose test

After defining the experimental design, and the general approach (parametric or nonparametric), you need to decide exactly what test you want Prism to perform.

Parametric, not paired

Decide whether to accept the assumption that the two samples come from populations with the same standard deviations (same variances). This is a standard assumption of the unpaired t test. If don't wish to make this assumption, Prism will perform the unequal variance (Welch) unpaired t test .

Parametric, paired

Choose the paired t test (which is standard in this situation) or the ratio t test (which is less standard). Choose the paired t test when you expect the differences between paired values to be a consistent measure of treatment effect. Choose the ratio paired t test when you expect the ratio of paired values to be a consistent measure of treatment effect.

Nonparametric, not paired

Prism offers two choices: The Mann-Whitney test and the Kolmogorov-Smirnov test . It is hard to offer guidelines for choosing one test vs. the other except to follow the tradition of your lab or field. The main difference is that the Mann-Whitney test has more power to detect a difference in the median, but the Kolmogorov-Smirnov test has more power to detect differences in the shapes of the distributions.

Nonparametric, paired

In this case there is no choice.  Prism will perform the Wilcoxon matched pairs test.

© 1995- 2019 GraphPad Software, LLC. All rights reserved.

Hypothesis Testing

Parametric tests — the t-test, one-stop shop for t-tests — from theory to python implementation.

Shubhangi Hora

Towards Data Science

In my previous article we went through the whats, hows and whys of hypothesis testing with a brief introduction on statistical tests and the role that they play in helping us determine statistical significance. In this article and the coming few, we’ll take a deeper look at statistical tests — the different types of tests, the tests themselves and which test should be used for which situation.

As mentioned before, statistical tests are statistical methods that help us reject or not reject our null hypothesis . They’re based on probability distributions and can be one-tailed or two-tailed, depending on the hypotheses that we’ve chosen.

There are other ways in which statistical tests can differ and one of them is based on their assumptions of the probability distribution that the data in question follows.

• Parametric tests are those statistical tests that assume the data approximately follows a normal distribution , amongst other assumptions (examples include z-test, t-test, ANOVA). Important note — the assumption is that the data of the whole population follows a normal distribution, not the sample data that you’re working with.
• Nonparametric tests are those statistical tests that don’t assume anything about the distribution followed by the data , and hence are also known as distribution free tests (examples include Chi-square, Mann-Whitney U). Nonparametric tests are based on the ranks held by different data points.

Every parametric test has a nonparametric equivalent, which means for every type of problem that you have there’ll be a test in both categories to help you out.

The selection of which set of tests is apt for the problem at hand is not this black and white, though. If your data doesn’t follow a normal distribution, nonparametric tests are not necessarily the right pick. The decision is dependent on other factors such as sample size, the type of data you have, what measure of central tendency best represents the data, etc. Certain parametric tests can perform well on non normal data if the sample size is large enough — for example, if your sample size is greater than 20 and your data is not normal, a one-sample t-test will still benefit you. But, if the median better represents your data then you’re better off with a nonparametric test.

In this article, we will be looking at parametric tests — particularly the t-test.

Parametric tests are those that assume that the sample data comes from a population that follows a probability distribution — the normal distribution — with a fixed set of parameters.

Common parametric tests are focused on analyzing and comparing the mean or variance of data.

The mean is the most commonly used measure of central tendency to describe data, however it is also heavily impacted by outliers. Thus it is important to analyze your data and determine whether the mean is the best way to represent it. If yes, then parametric tests are the way to go! If not, and the median better represents your data, then nonparametric tests might be the better option.

As mentioned above, parametric tests have a couple of assumptions that need to be met by the data:

• Normality — the sample data come from a population that approximately follows a normal distribution
• Homogeneity of variance — the sample data come from a population with the same variance
• Independence — the sample data consists of independent observations and are sampled randomly
• Outliers — the sample data don’t contain any extreme outliers

Degrees of Freedom.

Before we get into the different statistical tests, there is one important concept that should be discussed — degrees of freedom.

The degrees of freedom are essentially the number of independent values that can vary in a set of data while measuring statistical parameters.

Let’s say you like to go out every Saturday and you’ve just bought four new outfits. You want to wear a new outfit every weekend of the month. On the first Saturday, all four outfits are unworn, so you can pick any. The next Saturday you can pick from three and the third Saturday you can pick from two. On the last Saturday of the month though, you’re left with only one outfit and you have to wear it whether you want to or not, whereas on the other Saturdays you had a choice.

So basically, you had 4–1=3 Saturdays of freedom to choose an outfit — your outfit could vary.

That’s the idea behind degrees of freedom.

With respect to numerical values and the mean, the sum of the numerical values must equal the sample size times the mean, i.e. sum = n * mean, where n is the sample size. So if you have a sample size of 20 and a mean of 40, the sum of of all the observations in the sample must be 800. The first 19 values can be anything, but the 20th value has to ensure that the total of all the values adds up to 800, therefore it has no freedom to vary. Hence the degrees of freedom are 19.

The formula for degrees of freedom is sample size — number of parameters you’re measuring.

Comparing means.

If you want to compare the means of two groups then the right tests to choose between are the z-test and the t-test.

One-sample (one-sample z-test or a one-sample t-test): one group will be a sample and the second group will be the population. So you’re basically comparing a sample with a standard value from the population. We are basically trying to see if the sample comes from the population, i.e. does it behave differently from the population or not.

An example of this is the one we discussed in the previous article — the mean age of patients known to visit a dentist is 18, but we hypothesize it could be greater than this. The sample must be randomly selected from the population and the observations must be independent of one another.

Two-sample (two-sample z-test and a two-sample t-test): both groups will be separate samples. As in the case of one-sample tests, both samples must be randomly selected from the population and the observations must be independent of one another.

Two-sample tests are used when there are two variables involved. For example, comparing the mean money spent on a shopping site between the two sexes. One sample will be female customers and the second sample will be male customers. Since the means are being compared, one of the variables involved in the test has to be numerical (the money spent on a shopping site is the numerical variable).

Important note: don’t confuse one-sample and two-sample with one-tailed and two-tailed! The former is related to the number of samples being compared and the latter with whether your alternate hypothesis is directional. You can have a one-sample two-tailed test.

How do we choose between a z-test and a t-test though? By looking at the sample size and population variance.

• If the population variance is known and the sample size is large (greater than or equal to 30) — we choose a z-test
• If the population variance is known and the sample size is small (less than 30) — we can perform either a z-test or a t-test
• If the population variance is not known and the sample size is small — we choose a t-test
• If the population variance is not known and the sample size is large — we choose a t-test

As mentioned above, the t-test is very similar to the z-test, barring the fact that it works well with smaller samples and the population variance doesn’t need to be known.

The t-test is based on the t-distribution, which is a bell-shaped curve like the normal distribution, but has heavier tails.

As the sample size increases, the degrees of freedom also increase, and the t-distribution becomes similar to the normal distribution. It becomes less skewed and tighter around the mean (lighter tails). Why? We’ll find out in a bit.

There are three types of t-tests . Introductions for two have already been given above — one-sample and two-sample . Both of these come under the ‘unpaired t-test’ umbrella, and so the third type of t-test is the ‘paired t-test’ .

The concept of paired and unpaired is to do with the samples. Is the sample the same or are they two different samples? Are we monitoring a variable in two different groups or the same group? If the sample is the same, then the t-test should be paired, else unpaired.

For example, let’s say you want to test whether a certain medication increases the level of progesterone in women.

If the data you have is the progesterone levels of a group of women before the medication was consumed and the progesterone levels of the same group of women after the medication was consumed, then you would conduct a paired t-test since the sample is the same.

If the data you have is the progesterone level of two groups of women of different age groups after the medication was consumed, then you would conduct a two-sample unpaired t-test since there are two different samples.

Every statistical test has a test statistic which helps us calculate the p-value which then determines whether to reject or not reject the null hypothesis. In the case of the t-test, the test statistic is known as the t-statistic. The formula to calculate the t-statistic differs depending on which t-test you’re performing, so let’s take a closer look at them all.

The code and data used in all the below examples can be found here .

One-sample t-test.

The average height of women in India was recorded to be 158.5cm. Is the average height of women in India today greater than 158.5cm?

To test this hypothesis I asked 25 women their height.

• My hypotheses are —
• The significance level is 0.05.
• The sample mean is 162cm and sample standard deviation is 2.4cm.
• Since the sample size is 25, the degrees of freedom will be 24 (25–1).
• Since I’m comparing a sample mean with a population mean (standard value), this will be a one-sample test.
• Since my hypothesis has a direction — the average sample height is greater than the average population height — this will be a one-tailed test.

The formula to calculate the t-statistic is:

So the t-statistic in our case will be

Next we need to look up the critical value of the t-distribution where alpha is 0.05 and the degrees of freedom are 24 in the table for t-statistic values . The critical value for our scenario is 1.711. Our t-statistic is greater than the critical value, so we can reject the null hypothesis and conclude that the mean height of women in India is greater than 158.5 cm!

While it is better to calculate the p-value in hypothesis testing to reject or not reject the null hypothesis, the formula to calculate the p-value for a t-statistic is a bit tricky. You can either work with the t-distribution table values or simply use the critical value to reject or not reject the null hypothesis when performing hypothesis testing manually. Otherwise using a calculator or python functions will help you get the p-value. Let’s see how!

We’ll start off by reading our csv into a dataframe:

We have two columns — age and height. For this one-sample t-test, we only need height since we are comparing the mean height of this sample with the population mean — 158.5cm.

Let’s check the mean and standard deviation of the height column:

The assumptions of a t-test state that the sample data must come from a normal distribution. We can check if the height column is normally distributed or not by using a Probability Plot(also known as a QQ plot — Quantile-Quantile plot). In brief, a probability plot is a graphical method to check if a data set follows a particular distribution. It is essentially a plot of two data sets — one is the data whose distribution you want to check, and the other is data from that distribution itself. In our case, one set of data will be the height column and the distribution will be the normal distribution.

The red line represents the normal distribution and the blue dots represent our data of the height column. The graph above confirms that the height column comes from / follows a normal distribution since the height data points follow the path of the normal distribution line.

Now, we will perform the one-sample t-test using scipy’s stats method. We need to pass it our data and the population mean:

The p-value is ridiculously small! So we can reject the null hypothesis.

Two-sample t-test.

Is there a relationship between age and height of women in India?

To test this hypothesis I asked 50 women their age — 25 women are between 27 and 30 years of age (group A), 25 women are between 37 and 40 years of age (group B).

• The sample mean and standard deviation for group A are 162cm and 2.4cm respectively.
• The sample mean and standard deviation for group B are 158.6cm and 3.4cm respectively.
• Since I’m comparing the means of two samples, this will be a two-sample test.
• Since my hypothesis is nondirectional, this will be a two-tailed test.

It was mentioned earlier that parametric tests assume homogeneity of variance, i.e. the variance of both the samples should be the same. In the example mentioned here, the variance is definitely not the same — the standard deviation of group A is 2.4cm whereas it’s 3.4cm for group B. Does this mean we can’t perform a two-sample t-test? No, it doesn’t! Thankfully, there’s a variation of the t-test that allows for different variances and it’s called Welch’s t-test .

When the variance of both samples is equal, the denominator used in calculating the t-statistic is known as the pooled variance. If the sample sizes of both groups is different then the formula is:

If the sample sizes of both groups is equal then the formula is simply:

It finds the common variance of the two groups to be used in the t-statistic formula. The formula for the t-statistic is:

However, when the variance of both samples is not equal, the denominator compares both variances and the formula to calculate the t-statistic is:

Furthermore, the calculation of the degrees of freedom also differs between the two tests. If the variance of both groups in the current example were equal, the degrees of freedom would be 48 (25+25–2; we subtract 2 because we are measuring two parameters — the means of each sample).

In the case of Welch’s t-test, the degrees of freedom are fractional, always smaller than the degrees of freedom of Student’s t-test, and frankly a bit complicated to calculate.

Since our variances are not equal, we will be performing Welch’s t-test.

So the t-statistic in our case will be:

Let’s do this in python too.

Group A is the same csv we used for the one-sample t-test, so we already know its mean and standard deviation. Let’s check the same for Group B.

Now we perform the t-test! To perform Welch’s t-test we simply need to pass the equal_var parameter as False. By default it is true so if we were performing Student’s t-test we needn’t pass it at all.

The p-value is much smaller than 0.05 hence we can reject our null hypothesis.

Paired t-test.

Does nutritional drink xyz increase the height of women?

To test this hypothesis I measured the height of 25 women before they began the course of the nutritional drink and then after they completed the course.

• My hypotheses are -
• The sample mean and standard deviation for the women before the drink are 162cm and 2.4cm respectively.
• The sample mean and standard deviation for the women after the drink are 167cm and 3.4cm respectively.
• Since I’m comparing the means of the same sample but with an intervention in between, this will be a paired t-test.
• Since my hypothesis is directional, this will be a one-tailed test.

Fun fact — a paired t-test calculates the differences between the paired observations in the two sets of data (same sample, before and after) and then performs a one-sample t-test with the mean difference and mean standard deviation.

Let’s implement this directly in python:

Read the csv into a dataframe.

Use the describe() method to check the mean and standard deviations of both the before and after columns.

Perform the paired t-test using scipy stat’s ttest_rel method! We pass ‘greater’ in the alternative parameter since our alternate hypothesis is that the mean height after the nutritional drink will be greater than the height before the drink.

The p-value is greater than 0.05, hence we can’t reject our null hypothesis.

Now that we’ve seen all the types of t-tests and their formulae for calculating the t-statistic, we can understand why as the sample size increases the t-distribution becomes similar to the normal distribution. All the different t-tests involve the sample’s standard deviation / variance. This is simply an estimation of the population’s variance since that is unknown. Since the assumption in a t-test is that the sample data is from a population which follows the normal distribution, as the sample size increases and hence the degrees of freedom increase, there is a higher chance of this estimation of variance to actually be correct, i.e. to be the population’s variance. Additionally, the larger the sample size, the closer it is to being the population. Since the population is normally distributed, it makes sense that the t-distribution for this larger sample size with a higher number of degrees of freedom also resembles a normal distribution.

Written by Shubhangi Hora

A python developer working on AI and ML, with a background in Computer Science and Psychology. Interested in healthcare AI, specifically mental health!

Text to speech

Experimental Research Design — 6 mistakes you should never make!

Since school days’ students perform scientific experiments that provide results that define and prove the laws and theorems in science. These experiments are laid on a strong foundation of experimental research designs.

An experimental research design helps researchers execute their research objectives with more clarity and transparency.

In this article, we will not only discuss the key aspects of experimental research designs but also the issues to avoid and problems to resolve while designing your research study.

Table of Contents

What Is Experimental Research Design?

Experimental research design is a framework of protocols and procedures created to conduct experimental research with a scientific approach using two sets of variables. Herein, the first set of variables acts as a constant, used to measure the differences of the second set. The best example of experimental research methods is quantitative research .

Experimental research helps a researcher gather the necessary data for making better research decisions and determining the facts of a research study.

When Can a Researcher Conduct Experimental Research?

A researcher can conduct experimental research in the following situations —

• When time is an important factor in establishing a relationship between the cause and effect.
• When there is an invariable or never-changing behavior between the cause and effect.
• Finally, when the researcher wishes to understand the importance of the cause and effect.

Importance of Experimental Research Design

To publish significant results, choosing a quality research design forms the foundation to build the research study. Moreover, effective research design helps establish quality decision-making procedures, structures the research to lead to easier data analysis, and addresses the main research question. Therefore, it is essential to cater undivided attention and time to create an experimental research design before beginning the practical experiment.

By creating a research design, a researcher is also giving oneself time to organize the research, set up relevant boundaries for the study, and increase the reliability of the results. Through all these efforts, one could also avoid inconclusive results. If any part of the research design is flawed, it will reflect on the quality of the results derived.

Types of Experimental Research Designs

Based on the methods used to collect data in experimental studies, the experimental research designs are of three primary types:

1. Pre-experimental Research Design

A research study could conduct pre-experimental research design when a group or many groups are under observation after implementing factors of cause and effect of the research. The pre-experimental design will help researchers understand whether further investigation is necessary for the groups under observation.

Pre-experimental research is of three types —

• One-shot Case Study Research Design
• One-group Pretest-posttest Research Design
• Static-group Comparison

2. True Experimental Research Design

A true experimental research design relies on statistical analysis to prove or disprove a researcher’s hypothesis. It is one of the most accurate forms of research because it provides specific scientific evidence. Furthermore, out of all the types of experimental designs, only a true experimental design can establish a cause-effect relationship within a group. However, in a true experiment, a researcher must satisfy these three factors —

• There is a control group that is not subjected to changes and an experimental group that will experience the changed variables
• A variable that can be manipulated by the researcher
• Random distribution of the variables

This type of experimental research is commonly observed in the physical sciences.

3. Quasi-experimental Research Design

The word “Quasi” means similarity. A quasi-experimental design is similar to a true experimental design. However, the difference between the two is the assignment of the control group. In this research design, an independent variable is manipulated, but the participants of a group are not randomly assigned. This type of research design is used in field settings where random assignment is either irrelevant or not required.

The classification of the research subjects, conditions, or groups determines the type of research design to be used.

Advantages of Experimental Research

Experimental research allows you to test your idea in a controlled environment before taking the research to clinical trials. Moreover, it provides the best method to test your theory because of the following advantages:

• Researchers have firm control over variables to obtain results.
• The subject does not impact the effectiveness of experimental research. Anyone can implement it for research purposes.
• The results are specific.
• Post results analysis, research findings from the same dataset can be repurposed for similar research ideas.
• Researchers can identify the cause and effect of the hypothesis and further analyze this relationship to determine in-depth ideas.
• Experimental research makes an ideal starting point. The collected data could be used as a foundation to build new research ideas for further studies.

6 Mistakes to Avoid While Designing Your Research

There is no order to this list, and any one of these issues can seriously compromise the quality of your research. You could refer to the list as a checklist of what to avoid while designing your research.

1. Invalid Theoretical Framework

Usually, researchers miss out on checking if their hypothesis is logical to be tested. If your research design does not have basic assumptions or postulates, then it is fundamentally flawed and you need to rework on your research framework.

2. Inadequate Literature Study

Without a comprehensive research literature review , it is difficult to identify and fill the knowledge and information gaps. Furthermore, you need to clearly state how your research will contribute to the research field, either by adding value to the pertinent literature or challenging previous findings and assumptions.

3. Insufficient or Incorrect Statistical Analysis

Statistical results are one of the most trusted scientific evidence. The ultimate goal of a research experiment is to gain valid and sustainable evidence. Therefore, incorrect statistical analysis could affect the quality of any quantitative research.

4. Undefined Research Problem

This is one of the most basic aspects of research design. The research problem statement must be clear and to do that, you must set the framework for the development of research questions that address the core problems.

5. Research Limitations

Every study has some type of limitations . You should anticipate and incorporate those limitations into your conclusion, as well as the basic research design. Include a statement in your manuscript about any perceived limitations, and how you considered them while designing your experiment and drawing the conclusion.

6. Ethical Implications

The most important yet less talked about topic is the ethical issue. Your research design must include ways to minimize any risk for your participants and also address the research problem or question at hand. If you cannot manage the ethical norms along with your research study, your research objectives and validity could be questioned.

Experimental Research Design Example

In an experimental design, a researcher gathers plant samples and then randomly assigns half the samples to photosynthesize in sunlight and the other half to be kept in a dark box without sunlight, while controlling all the other variables (nutrients, water, soil, etc.)

By comparing their outcomes in biochemical tests, the researcher can confirm that the changes in the plants were due to the sunlight and not the other variables.

Experimental research is often the final form of a study conducted in the research process which is considered to provide conclusive and specific results. But it is not meant for every research. It involves a lot of resources, time, and money and is not easy to conduct, unless a foundation of research is built. Yet it is widely used in research institutes and commercial industries, for its most conclusive results in the scientific approach.

Have you worked on research designs? How was your experience creating an experimental design? What difficulties did you face? Do write to us or comment below and share your insights on experimental research designs!

Frequently Asked Questions

Randomization is important in an experimental research because it ensures unbiased results of the experiment. It also measures the cause-effect relationship on a particular group of interest.

Experimental research design lay the foundation of a research and structures the research to establish quality decision making process.

There are 3 types of experimental research designs. These are pre-experimental research design, true experimental research design, and quasi experimental research design.

The difference between an experimental and a quasi-experimental design are: 1. The assignment of the control group in quasi experimental research is non-random, unlike true experimental design, which is randomly assigned. 2. Experimental research group always has a control group; on the other hand, it may not be always present in quasi experimental research.

Experimental research establishes a cause-effect relationship by testing a theory or hypothesis using experimental groups or control variables. In contrast, descriptive research describes a study or a topic by defining the variables under it and answering the questions related to the same.

good and valuable

Very very good

Good presentation.

Rate this article Cancel Reply

Your email address will not be published.

Enago Academy's Most Popular Articles

• Industry News

Google Releases 2024 Scholar Metrics, Evaluates Impact of Scholarly Articles

Google has released its 2024 Scholar Metrics, assessing scholarly articles from 2019 to 2023. This…

Ensuring Academic Integrity and Transparency in Academic Research: A comprehensive checklist for researchers

Academic integrity is the foundation upon which the credibility and value of scientific findings are…

• Publishing Research
• Reporting Research

How to Optimize Your Research Process: A step-by-step guide

For researchers across disciplines, the path to uncovering novel findings and insights is often filled…

• Trending Now

Breaking Barriers: Sony and Nature unveil “Women in Technology Award”

Sony Group Corporation and the prestigious scientific journal Nature have collaborated to launch the inaugural…

Achieving Research Excellence: Checklist for good research practices

Academia is built on the foundation of trustworthy and high-quality research, supported by the pillars…

Choosing the Right Analytical Approach: Thematic analysis vs. content analysis for…

Comparing Cross Sectional and Longitudinal Studies: 5 steps for choosing the right…

Research Recommendations – Guiding policy-makers for evidence-based decision making

Sign-up to read more

Subscribe for free to get unrestricted access to all our resources on research writing and academic publishing including:

• 2000+ blog articles
• 50+ Webinars
• 10+ Expert podcasts
• 50+ Infographics
• 10+ Checklists
• Research Guides

We hate spam too. We promise to protect your privacy and never spam you.

• AI in Academia
• Promoting Research
• Career Corner
• Diversity and Inclusion
• Infographics
• Expert Video Library
• Other Resources
• Enago Learn
• Upcoming & On-Demand Webinars
• Peer-Review Week 2023
• Open Access Week 2023
• Conference Videos
• Enago Report
• Journal Finder
• Enago Plagiarism & AI Grammar Check
• Editing Services
• Publication Support Services
• Research Impact
• Translation Services
• Publication solutions
• AI-Based Solutions
• Thought Leadership
• Call for Articles
• Call for Speakers
• Author Training
• Edit Profile

I am looking for Editing/ Proofreading services for my manuscript Tentative date of next journal submission:

In your opinion, what is the most effective way to improve integrity in the peer review process?

Define Experiment Parameters

Last modified: December 19, 2019

Even if a metric was chosen for a new feature or product, important parameters about how that metric will be measured and evaluated might not be set.

One of the things that makes analysis hard is that there are so many things happening at once that might affect the metric you are monitoring. Determining what caused the metric to move is complicated – hence the need for a good experiment that tries to control for as many of the other things that may be influencing the outcomes as possible.

In a typical business context, there are three parameters that you should spend time defining:

Not setting these parameters in the beginning allows people to move these around at the analysis stage in order to find data that makes their product or feature look more successful than it actually is. And that is bad, very bad. We want to limit the ability for people to let their confirmation bias flare up and allow them to interpret data incorrectly. Being strict on these parameters prevents people from changing how they interpret the data after the results are in.

Let’s talk through each of these pieces and some important considerations.

If you are testing out a feature or product with a subset of your user base, make sure your sample is representative of those you are expecting to use the product or feature. Otherwise the results might be biased and the feature or product will not perform how you expect when you roll it out to everyone.

Questions to ask yourself:

• Is the cohort unique in any way?
• Am I picking this cohort out of convenience?

If the answer to either is yes, you need to find a different cohort.

People report good news too early and bad news too late. If day one after you launch there is a big spike in the metric you are tracking it is natural to feel excited and send out a message to the company. Yet, this can be dangerous, not only to your reputation of coming to conclusions prematurely but to what the company learns about your new feature. If the next day, the spike drops back down, you have to communicate all over again to try and undo the harm.

Before the product or feature launches, you should address the following two questions:

• When will we know if this is successful?
• When will we know if this is not successful?

Most launches inevitably have a bit of marketing surrounding them so the first day or first week data is not usually reliable. You do not want a spike and then a return to normal, you want a sustained increase. Pick a date before launch to review and share the impact of the data.

You need to account for a lot of different things when creating an experiment to test a feature or product within a company. Think through what other initiatives are going on at your company and what world events are coming up that may affect your metrics.

Common reasons your results were higher than expected:

• Marketing Campaign recently launched
• Internal usage is being factored into the data

Common reasons your results were lower than expected:

• Data isn’t being tracked correctly
• Bug in the code
• Broken links
• Weekends and National Holidays

Look at it from other people’s shoes

The unfortunate truth is that most products or features will not have a big impact. You should therefore be prepared for a modification or revision to have either no effect or a negative impact. People in your organization will almost always be skeptical of large positive results. You should prepare for this because the goal of your product or feature is not only to provide value to your customers but to create knowledge your company can build off of.

Ask yourself:

• What would make me skeptical of the results?

Take your answer to that question seriously and do your best to address that in your experiment design.

• Define the cohort who will be involved in your experiment, note any characteristics that make them unrepresentative
• Set a timeline for when you will evaluate the success of your experiment
• Do your due diligence when conducting an experiment to make sure your results won’t be affected by other peoples’ actions.

Written by: Matt David Reviewed by: Twange Kasoma , Blake Barnhill , Matthew Layne , Mike Yi

• Contributors
• Data Conversations
• Cloud Data Management
• How to Design a Dashboard
• How to Teach People SQL
• Avoid Misrepresenting Data
• SQL Optimization
• Fundamentals of Analysis

©2019 All Rights Reserved • Terms

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 08 August 2024

Optimization design of hydrocyclone with overflow slit structure based on experimental investigation and numerical simulation analysis

• Shuxin Chen 1 , 3 ,
• Donglai Li 1 ,
• Jianying Li 2 &
• Lin Zhong 1  

Scientific Reports volume  14 , Article number:  18410 ( 2024 ) Cite this article

82 Accesses

Metrics details

• Chemical engineering
• Mechanical engineering

This study aims to address the issue of high energy consumption in the hydrocyclone separation process. By introducing a novel slotted overflow pipe structure and utilizing experimental and response surface optimization methods, the optimal parameters were determined. The research results indicate that the number of slots, slot angles, and positioning dimensions significantly influence the performance of the hydrocyclone separator. The optimal combination was found to be three layers of slots, a positioning dimension of 5.3 mm, and a slot angle of 58°. In a Φ100mm hydrocyclone separator, validated through multiple experiments, the separation efficiency increased by 0.26% and the pressure drop reduced by 24.88% under a flow rate of 900 ml/s. CFD simulation verified the reduction in internal flow field velocity and pressure drop due to the slotted structure. Therefore, this study provides an effective reference for designing efficient and low-energy hydrocyclone separators.

Similar content being viewed by others

A novel strategy for comprehensive optimization of structural and operational parameters in a supersonic separator using computational fluid dynamics modeling

Investigation of novel passive methods of generation of swirl flow in supersonic separators by the computational fluid dynamics modeling

Numerical study on the stimulation effect of boundary sealing and hot water injection in marine challenging gas hydrate extraction

Introduction.

Hydrocyclones are commonly used rotary flow separation and classification devices in industrial applications, owing to their simple structure, high separation efficiency, small footprint, and large processing capacity 1 , 2 . However, hydrocyclone separation performance is affected by structural parameters, with the overflow pipe being particularly important and the major factor influencing pressure drop 3 . Overflow pipe design parameters include length, insertion depth, diameter, and dimensions 4 .

Previous research has made significant progress in hydrocyclone structural optimization and numerical simulation. Some studies focused on optimizing the overflow pipe, such as increasing the distance for short-circuiting flow to enter the bottom, which improved internal pressure distribution 5 , 6 . Additionally, computational fluid dynamics (CFD) simulation of a hydrocyclone with conical section and dual tapered inlet showed significantly increased tangential velocity and axial velocity. This enhances centrifugal force on particles and reduces misplaced particles 7 . Adding a conical top to the overflow pipe improved fine particle separation efficiency but did not affect pressure drop 8 .

Despite these advances, inherent fluid flow characteristics lead to imperfect separation and high energy loss regardless of geometry. To further enhance performance, various designs have been explored, including introducing a center body 9 , 10 , inner cone 11 , 12 , double overflow pipe 13 , 14 , 15 , 16 , overflow pipe with conical top 17 , overflow cap 18 , 19 , and slit cone 20 , 21 , 22 . By altering hydrocyclone geometry, these designs improved separation performance. The overflow cap reduced air core diameter, decreasing energy consumption while increasing tangential velocity and centrifugal force, and decreasing axial velocity 18 , prolonging particle separation time and improving efficiency.

Numerical simulation has also been utilized to study multiphase flow in hydrocyclones. Despite different models and methods, these simulations accurately described the complex phenomena, demonstrating the extensive application of numerical techniques in multiphase flow research 23 , 24 , 25 , 26 , 27 .

While previous studies have focused on the overflow pipe, optimization of other structural parameters has been inadequate. Moreover, past research primarily considered specific particulate types and concentrations rather than comprehensive optimization across operating conditions. To address these limitations and further enhance performance, this study aims to design a slit conical overflow pipe hydrocyclone and optimize multiple key structural parameters. The significance of this research is that it will provide new perspectives to improve hydrocyclone performance and application in industrial fields, holding promise for resource conservation and environmental protection.

The research will combine experimental investigation and numerical modeling to obtain separation data under different parameters. Accurate numerical simulation will be utilized to model internal multiphase flow and determine optimal designs. Through improved design and accurate modeling, this study will provide new perspectives to enhance hydrocyclone performance and application, holding promise for resource conservation and environmental protection in industrial fields.

Overflow pipe structural design scheme

Geometry and dimensions of the overflow pipe structure are crucial factors affecting the pressure drop of a hydrocyclone. In order to increase throughput and reduce flow losses, thus lowering pressure drop, enlarging the diameter of the overflow pipe can be adopted. However, it should be noted that excessively large overflow pipe diameter may increase the probability of solid particles entering the overflow pipe region, leading to reduced separation efficiency of the hydrocyclone 28 , 29 . In this study, we improved the overflow pipe structure of a conventional 100 mm hydrocyclone by incorporating a slotted design to ensure separation efficiency remains unaffected while enhancing throughput and reducing energy consumption.

The introduction of the slotted structure significantly reduces the pressure drop and energy consumption of the hydrocyclone. The main mechanism behind this improvement lies in the increased outlet area of the overflow pipe achieved through the slotted design, thereby reducing fluid kinetic energy losses. According to the Bernoulli energy conservation law, higher fluid velocities result in greater kinetic energy losses and lower pressures. Hence, the slotted structure reduces fluid velocity inside the overflow pipe, thereby increasing outlet pressure, effectively lowering the overall pressure drop of the hydrocyclone. Moreover, theoretically, the slotted structure helps reduce short-circuit fluid flow entering the bottom outer vortex of the hydrocyclone, thereby reducing kinetic energy losses in the bottom region and contributing to overall pressure drop reduction within the hydrocyclone. Properly setting the number of slots, angles, and positioning dimensions of the slotted structure decreases turbulence intensity in the internal flow field of the hydrocyclone, mitigating energy losses caused by turbulent states and facilitating pressure drop reduction.

In summary, the improvement of the hydrocyclone through the slotted design of the overflow pipe optimizes internal flow dynamics, reduces energy losses in each component, and significantly lowers the pressure drop and energy consumption. This study provides a strong theoretical basis for designing efficient and low-energy hydrocyclones.

The design involves the uniform distribution of 4 narrow slots along the circumferential direction of each layer, with each slot having a height of 2 mm. The inter-layer spacing is fixed at 6 mm. Concurrently, an optimization design is conducted for the number of slot layers, slot positioning dimensions, and slot angles. Figure  1 illustrates the schematic diagram of the conventional structure of the hydrocyclone, while Fig.  2 presents the schematic diagram of the cone overflow pipe with a slot structure.

Conventional schematic diagram of the hydrocyclone.

Schematic diagram of the cone overflow pipe with seam structure in the hydrocyclone. Note : The total height of the overflow pipe is 120mm, with a slotted design featuring four uniform slots per layer, each slot having a height of 2mm. The bottom inner diameter (φ) of the conical overflow pipe is 20mm, while the top outlet inner diameter (φ) is 28.8mm. The wall thickness of the overflow pipe is 5mm, with a layer spacing of 4mm.

By considering the variation characteristics of the flow field in the hydrocyclone, significant optimization results were achieved. The number of slot layers (n) for the cone overflow pipe was varied at 1 layer, 2 layers, and 3 layers, while the slot angle (θ) was set to 30°, 45°, 60° and 75°. The slot positioning dimension (a) was tested at 3 mm, 4 mm, 5 mm, and 6 mm. These parameters were systematically combined and organized with specific codes to comprehensively investigate the influence of slot structure parameters on the separation performance of the hydrocyclone. In the overflow pipe of a hydrocyclone separator, optimizing the design by increasing the number of slots, adjusting slot angles, and positioning dimensions effectively reduces the pressure drop of the hydrocyclone. Increasing the number of slots enlarges the open area of the overflow pipe, reducing fluid resistance as it passes through the pipeline. Additionally, this optimization helps to decrease local pressure at the bottom inlet of the overflow pipe and reduces dynamic pressure drop as fluid flows through the hydrocyclone. However, increasing the number of slots to 5 or 6 layers, while further increasing the open area of the overflow pipe, also introduces potential issues. Excessive layers may position the slots in the short-circuit flow area within the hydrocyclone, potentially causing coarser overflow and thereby impacting separation efficiency and performance. Therefore, in the design optimization process, it is crucial to balance the number and placement of slots to ensure improved efficiency of the hydrocyclone while mitigating potential adverse effects from excessive layering.

At the outset, distinct levels of the three variables, namely the number of slot layers, slot angle, and slot positioning dimension, were meticulously planned. Subsequently, an orthogonal experiment was carried out to investigate multiple combinations of these variables. For more detailed information, kindly refer to Tables 1 and 2 .

Experimental procedure and analysis

Experimental setup.

The experimental setup for the hydrocyclone mainly consists of a batching system including a stirrer, material tank, and a feed system comprising a centrifugal pump and material pipelines. The separation and testing system consist of various types of hydrocyclones and testing instruments. Under identical experimental conditions, separation experiments are conducted on different types of hydrocyclones. Overflow and underflow samples are collected three times and averaged to reduce experimental errors. Figure  3 illustrates the experimental equipment for the hydrocyclone separator, while Fig.  4 depicts the process flow diagram for the hydrocyclone separation experiments. In this study's evaluation of hydrocyclone performance, precision-engineered differential pressure sensors, specifically the Honeywell STD720-E1HC4AS-1-A-AHB-11S-A-10A0-F1-0000 model, were strategically installed at the hydrocyclone's inlet, overflow, and underflow points for meticulous pressure measurement. This strategic deployment facilitated the real-time surveillance of pressure shifts at pivotal junctures, enabling an accurate determination of the hydrocyclone's pressure differential. Rigorous calibration of each sensor ensured the reliability of the data captured. Employing high-frequency sampling, which exceeded ten instances per second, allowed for the documentation of transient pressure variations. Subsequent data analysis yielded the computation of the average pressure drop. To affirm the experiments' accuracy and reproducibility, each testing scenario was conducted in triplicate, bolstering the confidence in the outcomes and providing a robust dataset for hydrocyclone optimization efforts.In this study, the mixed fluid was extracted from the blending tank and delivered to the hydrocyclone feed inlet via a pump designed for handling flow rates ranging from 600 to 5000 ml per second. The pump's flow rate was precisely measured using an electromagnetic flow meter, ensuring accurate control and monitoring of the fluid dynamics processes within the hydrocyclone.Among them, in Fig.  4 , the 8-Centrifugal pump is used for liquid extraction, with a working flow rate ranging from 500 to 3500 ml/s.

Diagram of experimental apparatus.

The process flowchart of the hydrocyclone separation experiment.

Experimental method

The experiment utilized a mixture of 1% mass concentration of glass bead fine powder and water. The median particle size of the glass beads was measured as 41.52 μm using an Eyetech laser particle size analyzer. The true density of the glass beads was determined to be \(2.6\text{ g}/{\text{cm}}^{3}\) . Figure  5 presents the particle size distribution of the glass bead experimental raw material.

The particle size distribution chart of the glass bead experimental raw material.

To collect samples from the overflow and underflow outlets, the mixture was filtered and weighed. Subsequently, the collected samples were subjected to filtration, extraction, drying, and weighing processes.

During the experimental process, the overflow and underflow flow rates were measured using electromagnetic flowmeters. The inlet and outlet pressures were measured using pressure gauges, and the pressure drop across the hydrocyclone was calculated based on Eq. ( 1 ). The mass of the glass bead samples after drying was weighed, and the separation efficiency of the hydrocyclone was calculated using Eq. ( 2 ).

Pressure Drop Calculation Formula:

In the equation, \({\text{P}}_{\text{in}}\) represents the inlet pressure of the hydrocyclone, and \({\text{P}}_{\text{out}}\) represents the overflow outlet pressure of the hydrocyclone.

The efficiency calculation formula is as follows:

In the equation, \({\text{C}}_{\text{u}}\) represents the concentration before separation (the inlet concentration into the hydrocyclone); \({\text{C}}_{\text{o}}\) represents the concentration of the overflow material (the output of the hydrocyclone); and \({\text{C}}_{\text{f}}\) represents the concentration of the underflow waste material.

Numerical calculation method

Calculation model and grid generation.

Numerical simulations were conducted to study the internal flow of the hydrocyclone, and the computational domain was established. Firstly, three-dimensional models of the three types of hydrocyclones were constructed using SolidWorks software. Subsequently, the constructed three-dimensional models were imported into CFD mesh software for grid generation.

To better represent the fluid motion, a tetrahedral structured grid was used as the fluid domain model for the hydrocyclone. During the grid generation process, refinement was applied to regions such as the tangential inlet of the hydrocyclone to capture the flow characteristics more accurately. Grid independence tests were also performed to reduce the influence of grid quantity on the numerical simulation results. Taking Type A conventional hydrocyclone as an example, since the fluid domain models had the same diameter and length before and after improvement, different grid numbers (approximately 200,000, 400,000, 600,000, and 900,000) were used for numerical simulation. In numerical simulations of fluid flow, maintaining an aspect ratio of the grid within a moderate range is crucial for optimizing the balance between simulation accuracy and computational efficiency. This strategy not only ensures the precision of simulation outcomes and the stability of the computational process but also aids in managing the consumption of computational resources. In this simulation, the grid aspect ratio was set at 2.8. Such a selection allows for the accurate capture of fluid dynamics within the hydrocyclone, including velocity profiles, pressure fields, and the trajectories of solid particles, while avoiding the computational instability and unnecessary cost increases associated with higher aspect ratios.

Moreover, particular attention was devoted to the optimization of near-wall grid refinement in simulations to adjust wall shear stress (Y +) values, a critical aspect for ensuring simulation accuracy. The correct Y + values are imperative for selecting turbulence models and wall treatment strategies, as they accurately depict the flow characteristics within the boundary layer. This approach enables precise identification of flow separation and reattachment points. Through meticulously designed grids and suitable simulation strategies, this measure not only guarantees the quality of simulations but also enhances computational efficiency, providing reliable data support for the design and optimization of hydrocyclones.

Through these numerical simulations, the influence of different grid quantities on the simulation results was evaluated, and an appropriate grid number was determined to obtain accurate and reliable simulation results. This exploration is crucial for further analyzing the performance of the hydrocyclone and the effects of improvements.

Numerical calculation method and boundary conditions

ANSYS Fluent software was used to conduct numerical simulations for different types of hydrocyclones. For the simulation, the Reynolds Stress Model (RSM) was chosen as the turbulence model for the fluid in the hydrocyclone, and standard wall functions were adopted 29 . The Reynolds Stress Model adequately accounts for the stress tensor induced by fluid rotation and is particularly suitable for high-intensity turbulent flow, making it a suitable option in this study.

The Volume of Fluid (VOF) model was employed for multiphase flow simulations. The VOF model can be used to simulate the interface between two or more immiscible fluids and track the movement of the phase interface by solving the continuity equation. The Volume of Fluid (VOF) model is principally utilized for capturing the dynamics between the liquid and air phases within the hydrocyclone, notably including the formation of the air core. The simulated fluid does not include glass particles.This method enables the simulation and thorough analysis of intricate flow phenomena inside the hydrocyclone, such as the efficiency of solid–liquid separation and the pressure drop. In parallel, the experimental component assessed the separation performance of glass particles, with these observations being integrated with numerical simulation outcomes to refine the hydrocyclone's design.

This study meticulously investigates the fluid dynamics within hydrocyclones, focusing primarily on the interaction between water and air, and the pivotal role of air core formation in influencing hydrocyclone performance. Acknowledging the core objective to unravel the intricacies of liquid–gas interactions on hydrocyclone efficiency, and given the minimal concentration of solid particles, it is argued that while particles do exert an influence on separation efficacy, their effect is marginal relative to the principal phenomena of interest—flow dynamics and air core genesis. Consequently, the disturbance effects of particulate matter on fluid flow are considered negligible for the scope of this investigation. This targeted approach allows for a nuanced exploration of the interaction between water and air, facilitating a more refined analysis of their collective impact on the hydrocyclone's internal flow field.

The genesis of the air core is ascribed to the negative pressure generated by the fluid's rotational movement within the hydrocyclone, compelling air to be drawn into the vortex. This fluid dynamic-induced negative pressure zone is identified as the direct catalyst for air core formation, critically influencing the hydrocyclone's separation efficiency and flow characteristics. Through a focused examination of water–air interactions, this research endeavors to enhance the understanding of hydrocyclone operational mechanisms, specifically analyzing the air core's effect on performance.In the simulation of the hydrocyclone, the main phase was set as the mixture liquid, with a constant temperature, density of \({998.2\text{kg}/\text{m}}^{3}\) , and viscosity of \(0.001\text{Pa}\bullet \text{s}\) . The air phase was considered as the second phase, with a density of \({1.293\text{kg}/\text{m}}^{3}\) and viscosity at room temperature. The overflow and underflow outlets were set as pressure outlets, and the air backflow rate was set to 1.

In this study, the initial stage of the calculation used a mixture liquid calculation, and after convergence, it transitioned to two-phase calculation. The implicit transient pressure–velocity coupling method used the SIMPLEC method. To ensure computational stability, the pressure gradient was computed using the Green-Gauss Cell-Based method, the pressure discretization used the PRESTO! method, the momentum discretization used the Second Order Upwind method, and the turbulent kinetic energy and turbulent kinetic energy dissipation rate used the first-order upwind scheme. The convergence criterion was set at a residual tolerance of 1e-5, and the balance of mass flow rates at the inlet and outlet phases was used as the criterion for convergence judgment. In this simulation, the results were subject to temporal averaging to ensure they accurately reflect the mean state of the flow within the hydrocyclone. Three complete flow cycles were selected for the temporal averaging process, guaranteeing the precision and representativeness of the outcomes.

The validation process of CFD simulation credibility

In this investigation, a sequence of meticulous validation procedures was conducted to affirm the robustness and fidelity of the computational fluid dynamics (CFD) simulations. Figure  6 depicts the diagram of different cross-sectional positions of the hydrocyclone. The inaugural phase entailed a grid independence verification (refer to Fig.  7 ), aiming to ascertain the sensitivity of the results to the computational cell size. Through systematic refinement of the mesh and scrutiny of solution convergence, spatial resolution was confirmed as adequate to capture the flow dynamics with precision. The superposition of velocity profile curves across varying mesh densities indicates that additional refinement does not significantly modify the outcomes, thereby asserting grid independence. For computational efficiency, the mesh count was selected in the order of 600,000 cells.

Hydrocyclone cross-sectional position.

Mesh independence verification.

Upon establishing grid independence, a time-step independence verification was executed (refer to Fig.  8 ), ensuring the temporal discretization was sufficiently detailed to capture essential time-dependent characteristics of the fluid flow. The consistency of simulation results across varying time steps, paired with negligible variations in the velocity profiles at a time step of 1e-5, suggests that the simulation has attained a quasi-steady state, exhibiting insensitivity to further reduction in the time step. In this study, the selection of the time step adheres to the Courant-Friedrichs-Lewy (CFL) condition to ensure the numerical stability of Computational Fluid Dynamics (CFD) simulations. The CFL condition, a critical criterion, guarantees that the distance a fluid particle travels within a time step does not exceed the size of a computational cell 30 . Through preliminary simulations, the impact of various time steps on the outcomes was assessed, and the time step was adjusted to maintain the CFL number within a range of less than or equal to 1. This procedure ensures the accuracy and stability of the simulations.

Time-step independence verification for hydrocyclone simulations.

Conclusively, to solidify the accuracy of the simulations, a numerical simulation accuracy test was performed (refer to Fig.  9 ). This entailed juxtaposing simulation outputs with experimental data. The high congruence between simulated axial velocity profiles and experimental observations substantiates the numerical model's precision, especially in predicting peak velocities pivotal to the hydrocyclone's performance.

Model accuracy validation through comparison with experimental data.

To comprehensively elucidate the computational approach adopted in the investigation of hydrocyclone separator performance, Table 3 consolidates the pivotal simulation parameters employed within the study.

Overflow pipe slotted structure optimization

Impact of overflow pipe slotted structure on hydrocyclone separation performance.

In this study, solid–liquid separation experiments were conducted for the hydrocyclone. Firstly, based on the desired feed concentration and separation target, the concentration of the mixture liquid was adjusted to obtain a glass bead fine particle mass concentration of 1%. Subsequently, the mixture liquid was adequately covered by the stirrer, and the motor was adjusted to start the stirrer, initiating the mixing of the material and water.

Simultaneously, the centrifugal pump's rotational speed was controlled to achieve the experimentally preset initial reading of the electromagnetic flowmeter, which was set at an initial flow rate of 680 ml/s. During the experimental stage, after the mixture liquid was fully and uniformly mixed under the action of the stirrer, and the flow rates at the overflow and underflow outlets of the hydrocyclone stabilized, the beakers were quickly placed at the overflow and underflow outlets for sampling.

The collected samples were subjected to drying, and the dried samples were weighed using a precise balance. The mass data of the samples obtained from the experiment were recorded. Specifically, in the experiment, weighing equipment (as shown in Fig.  10 ) was used to ensure the accurate weighing of the samples, ensuring the accuracy and reliability of the data. The experimental protocol followed the established procedure of drying the specimens at 105 degrees Celsius for around 24 h. This method was employed to remove all moisture from the samples, guaranteeing that the weight measurements accurately represent the dry mass of the specimens collected.

The equipment diagram for accurately weighing the experimental samples of hydrocyclone separation efficiency.

The separation performance of the hydrocyclone with a single-layer slotted conical overflow pipe Type B hydrocyclone and the conventional Type A hydrocyclone under equivalent operating conditions is illustrated in Fig.  11 . The graph depicts the influence of different inlet flow rates on the separation efficiency (η) and pressure drop (ΔP) for both types of hydrocyclones. The x-axis represents the hydrocyclone inlet flow rate (Q), the left y-axis represents the separation efficiency (η) of the hydrocyclone, and the right y-axis represents the pressure drop (ΔP) across the hydrocyclone.

Flow rate-efficiency pressure drop relationship chart.

When the inlet flow rate is the same, the improved Type B hydrocyclone shows a slight decrease in separation efficiency compared to the conventional Type A hydrocyclone. However, it also achieves a certain degree of pressure drop reduction, resulting in energy-saving benefits. Under the operating conditions with inlet flow rates ranging from 680 to 920 ml/s, the improved Type B hydrocyclone exhibits a relatively small reduction in pressure drop. However, when the inlet flow rate exceeds 780 ml/s, the pressure drop reduction of the Type B hydrocyclone gradually increases, reaching its maximum at 860 ml/s. Compared to the conventional Type A hydrocyclone, the Type B hydrocyclone shows a pressure drop reduction of 6.8 units. The pressure drop for the conventional Type A hydrocyclone is 42.04 kPa, while it is 39.18 kPa for the Type B hydrocyclone.

Furthermore, after the slotted modification, the separation efficiency of the improved Type B hydrocyclone is slightly lower than that of the conventional hydrocyclone. When the inlet flow rate is greater than 760 ml/s, the separation efficiency of the Type B hydrocyclone approaches that of the conventional Type A hydrocyclone. At an inlet flow rate of 880 ml/s, the separation efficiency of the conventional Type A hydrocyclone is 97.96%, while the Type B hydrocyclone achieves a separation efficiency of 97.62%. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type B hydrocyclone decreases by 0.35 percentage points. Moreover, with the increase in inlet flow rate, the separation efficiency of the Type B hydrocyclone gradually approaches that of the conventional Type A hydrocyclone, while the pressure drop reduction increases.

Based on the experimental data, it can be observed that compared to the conventional Type A hydrocyclone, the slotted conical overflow pipe structure has a relatively minor impact on separation efficiency as the inlet flow rate increases. However, it has a significant effect on pressure drop reduction. The slots act as fluid passages, increasing the outlet area of the overflow pipe, reducing the axial velocity of the fluid inside the hydrocyclone, and thereby reducing the kinetic energy loss and pressure drop.

Optimization of slotted layer number

In order to further reduce the energy consumption of the Type B hydrocyclone, an optimization design of the slotted layer number was conducted. The slotted layer number was set from 1 to 4, with a layer spacing of 6 mm, slot angle of \(30^\circ \) , and slot position size of 3 mm. These were designated as Type B to Type E, and separation experiments were carried out for each design. The relationship curves between different slotted layer numbers, inlet flow rates, and the hydrocyclone's separation efficiency and pressure drop are shown in Fig.  12 .

Inlet flow rate—separation efficiency and pressure drop curves under different numbers of seams.

The separation efficiency of the five types of hydrocyclones is positively correlated with the inlet flow rate. With an increase in the number of slots, the overall trend of the separation efficiency in Type B to Type E hydrocyclones gradually decreases. Among them, Type B to Type D hydrocyclones (with 1–3 layers of slots) exhibit a slow decline in separation efficiency, with a small reduction. The Type E hydrocyclone (with 4 layers of slots) shows a relatively larger decrease in separation efficiency because the increased number of slots elevates the slot position, causing short-circuit flow in the overflow pipe region, leading to the entrainment of solid particles from the slots into the overflow pipe, thereby increasing the separation efficiency reduction.

Regarding the pressure drop, as the inlet flow rate increases, all five types of hydrocyclones show a gradual upward trend in pressure drop. With an increase in the number of slots, compared to the conventional Type A hydrocyclone, the pressure drop reduction in Type B to Type E hydrocyclones gradually increases. Type B and Type C hydrocyclones (with 1 to 2 layers of slots) experience minor changes in pressure drop reduction, while Type D and Type E hydrocyclones (with 3 to 4 layers of slots) demonstrate a significant increase in pressure drop reduction. The increase in the number of slots results in a larger slot area, which increases the flow rate entering the overflow pipe, reduces the local pressure at the bottom inlet of the overflow pipe, decreases the overall dynamic pressure of the internal swirling flow in the overflow pipe, and increases the outlet static pressure of the overflow pipe. According to fluid dynamics principles, the change in velocity has a significant impact on fluid kinetic energy, which is a key reason for the significant reduction in pressure drop after slot modification. Based on the analysis above, Type D hydrocyclone exhibits a remarkable pressure drop reduction while maintaining almost the same separation efficiency.

During the actual experimental process, at an inlet flow rate of 680 ml/s, the Type D hydrocyclone achieved a separation efficiency of 90.6% with a pressure drop of 36.31 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type D hydrocyclone decreased by 3.04%, and the pressure drop decreased by 1.83%.As the inlet flow rate reached the working condition of 900 ml/s, the Type D hydrocyclone showed a turning point in separation efficiency, reaching its maximum value. At this point, the separation efficiency and pressure drop for the conventional Type A hydrocyclone were 97.69% and 43.34 kPa, respectively, while for the Type D hydrocyclone, they were 97.53% and 38.65 kPa, respectively. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type D hydrocyclone decreased by 0.16%, and the pressure drop decreased significantly by 10.28%. These results indicate that the Type D hydrocyclone is more suitable for separation operations under high inlet flow rate conditions.

Optimization of slot position and angle

The different slot positions in the overflow pipe will have a certain impact on the separation efficiency and pressure drop of the hydrocyclone. An experiment was conducted to explore the effect of slot positions on the Type D hydrocyclone. The slot size "a" was set to 4 mm, 5 mm, and 6 mm, corresponding to Type T, Type Jj, and Type Zz, respectively. Figure  13 shows the flow rate-separation efficiency and flow rate-pressure drop curves for different types of hydrocyclones under inlet flow rates ranging from 680 to 920 ml/s.

Inlet flow rate—pressure drop curves at various seam positions.

At an inlet flow rate of 680 ml/s, the separation efficiency of the Type Jj hydrocyclone is 90.72%, with a pressure drop of 26.0 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type Jj hydrocyclone decreases by 1.91%, and the pressure drop decreases by 2.99%.

When the inlet flow rate reaches the working condition of 900 ml/s, the Type Jj hydrocyclone achieves its highest separation efficiency at 97.84%, with a pressure drop of 37.87 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency of the Type Jj hydrocyclone increases by 0.15%, and the pressure drop decreases by 12.62%.Regarding the other three types of hydrocyclones with different slot positions, the relationship between efficiency, pressure drop, and slot position changes is not very pronounced. However, for the Type Zz hydrocyclone, a relatively significant decrease in separation efficiency is observed. This is because the top slot position is close to the short-circuit flow region, allowing some particles to enter the overflow pipe through the slots along with the fluid motion, resulting in a reduction in the hydrocyclone's separation efficiency. On the other hand, the variation in the slot position below the short-circuit flow has little effect on the hydrocyclone's separation performance.

To achieve continuous analysis of different levels of various factors within the experimental conditions and obtain a more accurate optimal solution, the response surface optimization method was utilized. In this approach, the inlet flow rate (Q) and the slot size (a) were selected as the influencing factors. The ranges of these two factors were determined, and the experimental data corresponding to these two factors' levels were input into the Design-Expert design software. By employing central composite design, specific values for the three levels of each factor were obtained (as shown in Table 4 ). The three levels are lower limit, center point, and upper limit, respectively.

Regarding the experimental data, a response surface optimization design method was employed to conduct multivariate regression analysis. The experimental data was input into the Design-Expert software to establish the quadratic polynomial response surface regression equations for the target functions, separation efficiency ( \({\text{Y}}_{\text{e}}\) ) and pressure drop ( \({\text{Y}}_{\text{p}}\) ), with respect to the variables X1 and X2, as shown in Eqs. ( 3 ) and ( 4 ):

Figure  14 a,b illustrate the interaction effects of inlet flow rate and orifice size on the objective functions \({\text{Y}}_{\text{e}}\) and \({\text{Y}}_{\text{p}}\) . With other parameters kept constant, an increase in the inlet flow rate leads to higher pressure drop and separation efficiency. In this simulation, while maintaining the other dimensions of the hydrocyclone unchanged, increasing the orifice size initially enhances the separation efficiency but then causes a decrease, and the pressure drop shows a decreasing trend followed by an increasing trend. When the orifice size is set to 5.3 mm, a better balance between separation efficiency and pressure drop can be achieved.

The influence of flow rate and positioning dimension on separation performance.

To investigate the influence of orifice angle on the separation efficiency and pressure drop of the hydrocyclone, four different angles, namely \(30^\circ \) , \(45^\circ \) , \(60^\circ \) , and \(75^\circ \) , were designed, corresponding to the models Type Jj, Type Nn, Type Rr, and Type Vv, respectively. These models were compared with the conventional Type A hydrocyclone under the same inlet flow rate condition. The flow rate-separation efficiency and pressure drop curves of the five hydrocyclone models are shown in Fig.  15 .

Inlet flow rate-efficiency pressure drop curves at different seam angles.

Type Jj, Type Nn, and Type Rr hydrocyclones exhibit similar separation efficiencies, while Type Vv hydrocyclone experiences a more significant decrease in separation efficiency.The pressure drop reduction follows the order from the largest to the smallest: Type Vv, Type Rr, Type Nn, and Type Jj hydrocyclones.

As the orifice angle increases, the overflow flow rate gradually increases, leading to a decrease in the kinetic energy loss of the internal fluid. When solid particles are carried into the orifice, they need to change direction to enter the overflow pipe. Part of the particles experiences inertial impact with the pipe wall and undergo secondary separation. With the increase in orifice angle, the fraction of particles being impacted and re-separated decreases gradually, which significantly reduces the separation efficiency of the hydrocyclone. Among them, the Type Rr hydrocyclone experiences a substantial decrease in pressure drop while maintaining the separation efficiency nearly constant.

At an inlet flow rate of 900 ml/s, the Type Rr hydrocyclone achieves the highest separation efficiency of 97.75% and a pressure drop of 31.56 kPa. Compared to the conventional Type A hydrocyclone, the separation efficiency increased by 0.06%, and the pressure drop decreased by 24.85%.

Figure  16 a,b represent the interaction between inlet flow rate and orifice angle on the objective functions \({\text{Y}}_{\text{e}}\) and \({\text{Y}}_{\text{p}}\) , respectively. When other parameters remain constant, an increase in the inlet flow rate leads to a rise in both separation efficiency and pressure drop. In this simulation, with the hydrocyclone's other dimensions unchanged, increasing the orifice angle initially enhances the separation efficiency and subsequently decreases it, while the pressure drop exhibits a gradual decline. An orifice angle of \(58^\circ \) appears to strike a balance between separation efficiency and pressure drop, providing better performance for the hydrocyclone.

Influence of multiple factors on separation performance.

To further investigate the optimization scheme with three orifice layers, a 5.3 mm orifice size, and a \(58^\circ \) orifice angle, experimental research is conducted with an initial inlet flow rate of 800 ml/s. The results are compared with the conventional Type A hydrocyclone, as shown in Fig.  17 , illustrating the contrast in pressure drop and separation efficiency. The efficiency-related data were meticulously compiled and analyzed using SPSS Statistics 22 software, employing a one-way ANOVA to conduct significance tests with Student's t-test at a P < 0.05 significance level. Graphical representation was created using Origin 2021.

The separation efficiency and pressure drop of the hydrocyclone before and after optimization.

Figure  18 illustrates the comparison of particle size efficiency between the optimized and conventional hydrocyclones at an inlet flow rate of 900 ml/s. Based on the results from Fig.  17 and the comparative chart in Fig.  18 , it can be concluded that within the range of inlet flow rates from 900 to 920 ml/s, the optimized hydrocyclone exhibits higher separation efficiency compared to the conventional type. However, as the inlet flow rate increases, the improvement in separation efficiency gradually diminishes, while the pressure drop also increases. At an inlet flow rate of 900 ml/s, the optimized hydrocyclone achieves the highest separation efficiency, reaching 97.77%, representing a 0.26% improvement compared to the conventional hydrocyclone. The corresponding pressure drop is 32.98 kPa, resulting in a reduction of 24.88%.Within the particle size range larger than 30 µm, the optimized hydrocyclone's particle size efficiency remains essentially unchanged compared to the conventional hydrocyclone.

Comparison of particle efficiency before and after optimization in hydrocyclone.

These results indicate that the optimized hydrocyclone can achieve higher separation efficiency and relatively smaller pressure drop within a certain range of inlet flow rates. This is of great significance for improving the hydrocyclone's performance and efficiency.

Numerical simulation analysis

Numerical simulation analysis is conducted on the optimized hydrocyclone, referred to as Type I, with three orifice layers, an orifice size of 5.3 mm, and an orifice angle of \(58^\circ \) . Numerical simulations are performed at an inlet flow rate of 900 ml/s and compared with the conventional Type A hydrocyclone. By comparing the two hydrocyclones in terms of fluid axial velocity, tangential velocity, pressure distribution, and other aspects, this numerical simulation analysis provides deeper insights into the improvement achieved by Type I hydrocyclone, thereby serving as a reference for further research and optimization.

Grid independence and numerical method validation

By examining the average tangential velocity at different sections of the hydrocyclone, it was observed that the average tangential velocity remained relatively constant when the grid size increased to approximately 600,000 cells. To validate the numerical simulation of the Type A hydrocyclone, the tangential velocities at various cross-sections were compared with experimental values. The results from the numerical simulations were found to be in close agreement with the experimental values, indicating that the numerical model used in this study can reasonably predict the solid liquid separation performance of the hydrocyclone. Therefore, the grids for Type A and Type I hydrocyclones were set to similar orders of magnitude, with 643,541 and 674,512 cells, respectively.

Pressure analysis

Based on the pressure distribution analysis, it was observed that as both types of hydrocyclones approached the center radially, the pressure gradually decreased, forming negative pressure regions. Figures  19 and 20 illustrate the pressure distribution at different cross-sectional positions. Compared to the Type A hydrocyclone, the modified hydrocyclone exhibited significantly reduced overall pressure, with an increased diameter of the air column and a noticeable decrease in pressure drop along the column. This indicates that the modified overflow pipe had a significant impact on the pressure distribution along the hydrocyclone column. The improved overflow pipe possessed a larger equivalent diameter, resulting in increased fluid discharge within the overflow pipe, thereby reducing the internal pressure of the hydrocyclone.

Pressure contour maps of hydrocyclones with different cross-sectional designs before and after improvement.

Before and after improvement, axial cross-sectional pressure contour maps of the hydrocyclone.

Based on the pressure distribution curves at different axial cross-sections in the hydrocyclone, as shown in Fig.  21 , it can be observed that the overall pressure trend exhibits an approximate "V" shape, and the negative pressure region at the axis of both hydrocyclones shows similar pressure values. The pressure is positively correlated with the radial position. Compared to the Type A hydrocyclone, the improved Type I hydrocyclone shows a gentler pressure curve in the external region of the overflow pipe, resulting in a significant overall pressure reduction.

Pressure distribution curves in different axial sections of the hydrocyclone before and after improvement.

Furthermore, the pressure of both hydrocyclone types is negatively correlated with the axial position. Specifically, in the axial positions ranging from the Y = − 0.015 m cross-section to the Y = − 0.04 m cross-section, the pressure variation in the Type I hydrocyclone is greater than that in the Type A hydrocyclone. Additionally, the pressure at the column cross-section located at Y = 0.01 m is higher than the pressure at the overflow pipe cross-section. The improved design of the overflow pipe in the Type I hydrocyclone reduces internal frictional resistance, leading to a notably lower pressure at the overflow pipe cross-section compared to the column cross-section. However, the Type I hydrocyclone adopts a tapered slotted design, resulting in a rapid increase in fluid velocity as it enters the overflow pipe, leading to localized turbulence and increased energy loss. As a consequence, the Type I hydrocyclone exhibits a slightly higher pressure drop compared to the TypeA hydrocyclone.

In summary, the optimization of the hydrocyclone's overflow pipe design in the Type I hydrocyclone reduces the overall pressure and improves the pressure distribution compared to the conventional Type A hydrocyclone.However, due to the introduction of the tapered slotted structure, the Type I hydrocyclone experiences a slightly higher pressure drop, indicating a trade-off between pressure reduction and energy loss in the design optimization.

The changes in the internal pressure distribution of the hydrocyclone before and after the optimization of the slotted structure are jointly presented in Figs. 19, 20 and 21.The results demonstrate that the pressure distribution of the optimized hydrocyclone is more reasonable and symmetrical in multiple cross-sections and axial profiles compared to the original hydrocyclone, and the pressure level is noticeably reduced. Specifically, the slotted structure leads to a reduction in pressure in the region near the outlet, a gradual decrease in the axial pressure gradient, and an overall pressure reduction across the hydrocyclone. The combined information from the three figures indicates that the introduction of the slotted structure significantly improves the internal pressure distribution of the hydrocyclone, which explains the observed phenomenon of reduced pressure drop from the perspective of the flow field. Therefore, the regulatory effect of the slotted structure on the internal pressure field is one of the key reasons for achieving the optimization of the hydrocyclone's performance.

Axial velocity analysis

In the analysis of axial velocity, detailed distribution simulations of the axial velocity were conducted at axial cross-section positions (Y = 0.04 m and 0.08 m) for both hydrocyclone types, and the results are presented in Fig.  22 .By observing the axial velocity distribution of the two hydrocyclone types, it can be seen that the velocity gradually increases from the wall to the axis and sharply rises to its maximum value in the central region, presenting a generally symmetrical profile.

Comparison of axial velocity distribution before and after improvement in the hydrocyclone.

The improved symmetry in the pressure and velocity distributions of the optimized hydrocyclone compared to the original hydrocyclone confirms the effectiveness of the slotted structure optimization in achieving a more balanced and stable flow field inside the hydrocyclone. The changes in pressure and velocity distributions provide valuable insights into the flow behavior, contributing to the understanding of the improved separation performance and reduced pressure drop observed in the experimental results.

It is noteworthy that, compared to the Type A hydrocyclone, the Type I hydrocyclone exhibits a slight decrease in its axial velocity. In the Type I hydrocyclone, the reduction in axial velocity is more pronounced in the inner swirling region than in the outer swirling region. The optimized hydrocyclone with overflow slits shows a significant decrease in axial velocity in the inner swirling region near the overflow outlet. Specifically, at the Y = 0.04 m section, the maximum axial velocity of the prototype hydrocyclone is approximately 3.2 m/s, while the optimized version only reaches 2.8 m/s. Similarly, at the Y = 0.08 m section, the maximum axial velocity decreases from 2.9 to 2.6 m/s. This reduction in axial velocity is attributed to the enlargement of the outlet area by the overflow slits, which weakens the intensity of the inner swirling vortex flow, leading to a decrease in the axial velocity of the vortex flow.

The increase in the number of overflow slits will further expand the outlet area and cause a further decrease in the axial velocity of the inner swirling flow. However, excessive slit numbers may lead to a saturation effect. Additionally, the opening angle of the slits affects the outlet flow rate, where too large an angle can result in excessively low axial velocities. On the other hand, the height of the slit controls its range of influence and directly determines the distribution pattern of the axial velocity field.

Figure  23 provides a visual representation of the X-direction velocity (axial velocity component) distribution in the axial section of the two hydrocyclones. From the figure, it is evident that the optimized hydrocyclone with overflow slits exhibits a more uniform and symmetric axial velocity distribution within its interior, especially in the region near the overflow outlet, where the velocity field distribution appears more reasonable. Specifically, after the slit optimization, the maximum axial velocity near the overflow outlet reduces significantly from the original 3.2–2.8 m/s. This indicates that the introduction of the overflow slits weakens the intensity of the vortex flow in the overflow tube region, leading to a notable reduction in the axial velocity component.

Comparison of axial section x velocity distribution before and after improvement in the hydrocyclone.

The Type I hydrocyclone can effectively control the distribution of axial velocity to match the tangential velocity field, thereby achieving the goal of improving the hydrocyclone's separation efficiency. The axial velocity distribution plays a crucial role in optimizing the hydrocyclone's performance.

In addition, after introducing the overflow slit in the hydrocyclone, the axial velocity of the outer swirling region near the hydrocyclone wall shows a slight decrease, although this effect is relatively minor. However, as the radial position moves towards the axis, the axial velocity in the inner swirling region experiences a significant reduction, with the impact of the overflow slit becoming more pronounced. This phenomenon can be explained by the fact that, under the same inlet flow conditions, the overflow slit structure enlarges the equivalent diameter of the overflow outlet. As a result, the rotational speed of the fluid around the central axis decreases, causing the zero-velocity envelope surface to move inward. This process increases the time for medium and large particles in the outer swirling region to participate in the separation, resulting in a more thorough separation effect. Additionally, the overflow slit structure also reduces the likelihood of coarse particles in the outer swirling region re-entering the inner swirling flow. Therefore, the influence of the overflow slit on hydrocyclone performance is mainly manifested in the reduction of axial velocity in the inner swirling region and the enhancement of solid–liquid separation efficiency. The optimized combination of the overflow slit parameters in Type I hydrocyclone satisfies the separation requirements of the axial velocity field, thereby improving the overall separation performance of the hydrocyclone.

Tangential velocity analysis

In this study, the tangential velocity of the fluid in the hydrocyclone with an inlet flow rate of 900 ml/s was analyzed. The comparison of the tangential velocity distribution curves at different cross-sectional positions for both hydrocyclone types is shown in Fig.  24 .Overall, the tangential velocity distribution curve exhibits an "S"-shaped trend. As the distance from the hydrocyclone wall decreases, the tangential velocity increases with decreasing radius. It reaches its maximum value near the hydrocyclone wall and then gradually decreases with further reduction in radius. When approaching the vicinity of the air core, the tangential velocity drops sharply, eventually becoming zero at the central axis.

Velocity distribution curves of different axial sections in the hydrocyclone before and after improvement.

The design of overflow slit in the hydrocyclone reduces the internal fluid velocity, causing small-sized solid particles to lack sufficient centrifugal force to enter the outer swirling region for separation. Instead, they are eventually discharged through the overflow outlet, leading to a decrease in the hydrocyclone's particle size efficiency for small particles. However, large-sized particles, due to their larger volume and mass, can still overcome the reduced centrifugal force and enter the outer swirling region, thus their particle size efficiency remains unaffected. Compared to Type A hydrocyclone, the overall tangential velocity in Type I hydrocyclone slightly decreases, resulting in a reduction of the centrifugal force experienced by solid particles.

Additionally, when observing the tangential velocity above the overflow slit (Y = − 0.04 m) in Fig.  25 , it is evident that the decrease in tangential velocity above the overflow slit is more significant compared to the cylinder and cone sections, with the cone section experiencing a larger reduction than the cylinder section. This phenomenon is attributed to the greater influence of diameter size on the tangential velocity, and the impact of the overflow slit structure becomes more pronounced above the overflow slit level.

Comparison of tangential velocity distribution at the upper section of the overflow pipe.

As a result, the overflow slit design in the hydrocyclone has selective effects on particle size efficiency. It reduces the separation efficiency for small-sized particles due to reduced centrifugal force, while having limited impact on the efficiency of large-sized particles. Moreover, the influence of the overflow slit structure on tangential velocity is more evident above the overflow slit level, especially in the cone section.

Based on the combined analysis of the axial velocity distribution in Fig.  24 and the tangential velocity distribution in Fig.  25 at different axial cross-sections, it is evident that the Type I hydrocyclone, after optimization with the slotted structure, exhibits a more symmetrical and stable tangential velocity distribution compared to the Type A hydrocyclone. Specifically, at multiple cross-sections in Fig.  24 , the tangential velocity near the hydrocyclone wall is reduced by 0.2–0.4 m/s in the optimized hydrocyclone compared to the Type A hydrocyclone, and the negative tangential velocity in the central region is also decreased. In Fig.  25 , the tangential velocity distribution above the slotted structure shows an overall reduction of 0.3–0.5 m/s, with a smaller slope in the curve. This indicates that the introduction of the slotted structure weakens the internal vortex, resulting in a decrease in the tangential velocity component. Moderating the tangential velocity can contribute to achieving a more stable separation performance. Therefore, the regulation of the tangential velocity field through the slotted structure is one of the significant factors in optimizing the hydrocyclone's performance.

Furthermore, the proportion between axial and tangential velocities directly influences the hydrocyclone's separation efficiency. According to the above analysis, the velocity matching between the two components needs to be adjusted according to the particle size of different materials. For fine or low-density particles, increasing the axial velocity is necessary to rapidly remove them from the hydrocyclone wall and prevent excessive fine particles from entering the underflow. At the same time, providing a higher tangential velocity allows light particles to obtain sufficient centrifugal force to enter the overflow outlet. For coarse or high-density particles, reducing the axial velocity appropriately can increase their residence time inside the hydrocyclone for adequate separation. The tangential velocity can also be adjusted accordingly to reduce turbulence losses inside the hydrocyclone. For materials with a wide particle size distribution, a moderate combination of axial and tangential velocities should be chosen to achieve good separation performance for particles of different sizes. The axial velocity should not be too high or too low, and the tangential velocity needs to be controlled within an appropriate range. By adjusting the proportion between these two velocities when the operating conditions change, customized separation of materials can be achieved, thus expanding the hydrocyclone's applicability range.

The comprehensive experimental study with multiple factors reveals that the interaction of overflow slit design parameters, including positioning size, number of slits, and angle, significantly affects the separation performance of the hydrocyclone under identical operating conditions.

The number of overflow slits has a considerable impact on the pressure drop of the hydrocyclone. As the number of slits increases, the pressure drop also gradually increases. However, this is accompanied by a decrease in the hydrocyclone's separation efficiency. After optimizing the number of slits to three layers, a better compromise between separation efficiency and pressure drop is achieved.

Changing the positioning size of the overflow slits has a minor effect on the separation performance of the hydrocyclone. Excessively increasing the positioning size can lead to a sharp decrease in the separation efficiency. The positioning size of 5.3 mm provides a good balance between separation efficiency and pressure drop.

Altering the angle of the overflow slits has a significant impact on the hydrocyclone's separation performance. An excessively large angle causes a drastic reduction in separation efficiency. At an inlet flow rate of 900 ml/s, compared to the conventional hydrocyclone, the hydrocyclone with three layers of slits, a positioning size of 5.3 mm, and an angle of \(58^\circ \) exhibits an increase in separation efficiency of 0.26% and a substantial reduction in pressure drop, reaching 24.88%. This demonstrates that the optimized design of the conical overflow slits enables the hydrocyclone to maintain its separation efficiency under high inlet flow conditions while significantly reducing pressure drop. This results in remarkable energy savings and achieves the goal of optimized design, providing valuable reference for the development of new hydrocyclones.

The findings from this study provide essential insights into the impact of overflow slit design on the performance of hydrocyclones, offering valuable guidance for the development and optimization of hydrocyclone separators.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Ding, J. et al. Research progress on the application of hydrocyclone separators in water treatment. Environ. Eng. 39 (08), 1–6 (2021) ( (in Chinese) ).

Google Scholar  

Chen, T. W. et al. Effect of cyclone split ratio on carbon release performance of excess sludge. Chin. J. Chem. Eng. 72 (11), 5761–5769 (2021) ( (in Chinese) ).

CAS   Google Scholar  

Martínez, L. F., Lavín, A. G., Mahamud, M. M. & Bueno, J. L. Improvements in hydrocyclone design flow lines stabilization. Powder Technol. 176 (1), 1–8 (2007).

Article   Google Scholar  

Song, M. H. et al. Discussion on the deep improvementof separation efficiency of liquid-liquid hydrocyclone. Prog. Chem. Ind. 40 (12), 6590–6603 (2021) ( (in Chinese) ).

Li, F., Liu, P., Yang, X., et al. Purification of granular sediments from wastewater using a novel hydrocyclone. Powder Technol. 393 (2021).

Li, F., Liu, P., Yang, X., et al. Numerical simulation on the effects of different inlet pipe structures on the flow field and seperation performance in a hydrocyclone. Powder Technol . 373 (2020).

Wakizono, Y., Maeda, T., Fukui, K. & Yoshida, H. Effect of ring shape attached on upper outlet pipe on fine particle classification of gas-cyclone. Sep. Purif. Technol. 141 , 84–93 (2015).

Article   CAS   Google Scholar  

Wakizono, Y. et al. Effect of ring shape attached on upper outlet pipe on fine particle classification of gascyclone. Sep. Purific. Technol. 141 , 84–93 (2015).

Huang, L. et al. Numerical analysis of a novel gas-liquid pre-separation cyclone. Sep. Purific. Technol. 194 , 470–479 (2018).

Jiayu, Z. et al. Study on the influence of central cone structure on flow field and separation efficiency of hydrocyclone. Mineral Conserv. Util. 4 (6), 65–69 (2018).

Lixin, Z. et al. Flow field analysis and structural optimization of internal cone-type oil removal hydrocyclone. Chem. Eng. Mach. 38 (02), 202–205 (2011).

Xiao, X. U. et al. Dissolved gas separation using the pressure drop and centrifugal characteristics of an inner cone hydrocyclone. Sep. Purific. Technol. 161 , 121–128 (2016).

Chen, B. et al. Experimental study on separation performance of dual overflow pipe hydrocyclone. Light Metals 475 (05), 9–13 (2018).

Peikun, L. et al. Numerical simulation and experimental study on separation performance of dual overflow pipe hydrocyclone. Coal Mine Machinery 41 (02), 40–43 (2020).

Showalter S, Kosteski Edward G. Three-phase cyclonic fluid separator: US, US007288138B2[P]. 2007-10-30

Zhang, Y. et al. The study on numerical simulation and experiments of four product hydrocyclone with double vortex finders. Minerals 9 (1), 23 (2019).

Article   ADS   Google Scholar  

Hongyan, L. et al. Effect of Hydrocyclone Overflow Pipe Structure on Fine Particle Separation. Journal of Chemical Engineering 68 (05), 1921–1931 (2017).

Hongyan, L. et al. Influence of novel outlet baffle structure on separation performance of hydrocyclone. J. Chem. Eng. 69 (05), 2081–2088 (2018).

Peikun, L. et al. Study on flow field characteristics and separation performance of hydrocyclone with overflow cap structure. Fluid Machinery 49 (01), 1–6 (2021).

Jihai, D. et al. Influence of conical slot on solid-liquid separation performance of hydrocyclone. J. Chem. Eng. 70 (05), 1823–1831 (2019).

Xiulin, L. et al. Experimental study on structural optimization of PV type cyclone separator. China Powder Sci. Technol. 25 (05), 72–77 (2019).

Xiulin, L. et al. Experimental study on structural optimization of cyclone separator. Modern Chem. Industry 39 (12), 205–209 (2019).

Ghodrat, M. et al. Numerical analysis of hydrocyclones with different vortex finder configurations. Minerals Eng. 63 , 125–138 (2014).

Liu, H., Jia, X. & Wang, B. Simulation study on the influence of overflow pipe structural parameters on cyclone separator performance. Fluid Machinery 48 (11), 6–10 (2020).

Jianxiang, Z. & Tianhe, Z. Numerical simulation of optimizing the convergent nozzle radius of cyclone separator exhaust pipe. Fluid Machinery 43 (12), 28–32 (2015).

Huang, Q., Xiao, H., Chen, A., et al. Hydraulic cyclone with conical slot structure. Patent No. CN109225687B, Shandong Province, 19 Mar 2021.

Ren, L. et al. Scheme design of filtration-type hydrocyclone. J. Southwest Pet. Inst. 01 , 82–85 (2005).

Yamei, L. et al. Analysis of the influence of cyclone separator structural parameters on its performance. Chem. Eng. Machinery 48 (05), 678–682 (2021).

Yang, L. & Zhenbo, W. Research progress on factors affecting separation efficiency of hydrocyclone. Fluid Machinery 44 (02), 39–42 (2016).

Zhang, W. et al. Study on flow field characteristics and separation performance of conical overflow pipe slotted hydrocyclone. Fluid Machinery 51 (08), 64–72 (2023).

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (U2031142) and Heilongjiang Provincial Natural Science Foundation of China (LH2023F050).Technology Innovation Center of Agricultural Multi-Dimensional Sensor Information Perception, Heilongjiang Province (DWCGQKF202107) This work was supported by the Tianjin Research Innovation Project for Postgraduate Students (No. 2021KJ088).

Author information

Authors and affiliations.

School of Mechanical and Electrical Engineering, Qiqihar University, Qiqihar City, 161006, Heilongjiang Province, China

Shuxin Chen, Donglai Li & Lin Zhong

School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin City, 150080, Heilongjiang Province, China

Jianying Li

Tianjin Ren’ai College, Tianjin City, 300000, China

Shuxin Chen

You can also search for this author in PubMed   Google Scholar

Contributions

C.S.: Designed and led the research project, responsible for overall project planning, contributed important ideas and theoretical support in paper writing. L.D.: Responsible for data collection and preprocessing. Provided detailed descriptions and analysis of the experimental section for paper writing. Conducted data analysis and statistical processing, offering strong support for interpreting the paper's results. L.J.: Provided significant insights in the discussion section. Supervised and guided the entire research process, offering valuable professional opinions. Made important revisions and additions in the literature review and conclusion sections. L.Z.: Responsible for data collection and graphical representation. All authors collaborated actively, contributing to different stages of the research task, and collectively played essential roles in completing the paper.

Corresponding author

Correspondence to Shuxin Chen .

Ethics declarations

Competing interests.

We, Chen Shuxin, Li Donglai, Li Jianying, and Zhong Lin, hereby declare that during the process of writing and submitting this paper, we have no financial or non-financial competing interests. We do not have any direct or indirect financial relationships or other interests that could potentially lead to conflicts of competing interests with any institutions, organizations, or individuals. The design, data collection, analysis, and interpretation of results for this study have been conducted with objectivity and integrity, unaffected by any competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .

Reprints and permissions

About this article

Cite this article.

Chen, S., Li, D., Li, J. et al. Optimization design of hydrocyclone with overflow slit structure based on experimental investigation and numerical simulation analysis. Sci Rep 14 , 18410 (2024). https://doi.org/10.1038/s41598-024-68954-y

Download citation

Received : 06 August 2023

Accepted : 30 July 2024

Published : 08 August 2024

DOI : https://doi.org/10.1038/s41598-024-68954-y

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

A study of the effect of experimental test parameters on data scatter in microbond testing

Pandey, g.; kareliya, c.h.; singh, r.p., journal of composite materials 46(3): 275-284, article emailed within 1 workday.

Related References

Experimental test parameters.

Context in source publication

Similar publications.

• Luke Spaulding
• Jared C. Dunlap

• Gino Iannace

• Build Acoust

• Siu O’Young

• Olha Haponenko

• Recruit researchers
• Join for free
• Login Email Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google Welcome back! Please log in. Email · Hint Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google No account? Sign up

Surface roughness assessment of ABS and PLA filament 3D printing parts: structural parameters experimentation and semi-empirical modelling

• ORIGINAL ARTICLE
• Published: 12 August 2024

Cite this article

• John D. Kechagias   ORCID: orcid.org/0000-0002-5768-4285 1  

As a typical 3D printing process, fused filament fabrication still has disadvantages when operating on manufacturing lines due to the non-uniform textures of the oriented surfaces of the 3D-printed components. This work investigates the effects of structural parameters, i.e., orientations angle, ABS and PLA materials, three different layer thicknesses, three different perimeters, and three different infill rates utilizing a balanced modified Taguchi experimental design and 63 different parametric combinations to characterize the surface roughness parameters: average Ra, mean roughness depth Rz, root mean square Rq, skewness Rsk, and kurtosis Rku. The analysis of the experimental results, i.e., the levels mean values analysis plots and linear residual analysis of variances, showed that the layer thickness strongly influences all surface parameters and interacts considerably with all orientations. In contrast, material type, number of perimeters, and infill rate had insignificant impacts on surface roughness parameters. Finally, the additive linear modelling approach was utilized and validated for proper predictions, making it helpful for surface engineering applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Data availability

All data generated or analyzed during this study are included in the manuscript.

Code availability

Not applicable.

Şirin Ş, Aslan E, Akincioğlu G (2023) Effects of 3D-printed PLA material with different filling densities on coefficient of friction performance. Rapid Prototyp J 29:157–165. https://doi.org/10.1108/RPJ-03-2022-0081

Article   Google Scholar  

Lanzotti A, Grasso M, Staiano G, Martorelli M (2015) The impact of process parameters on mechanical properties of parts fabricated in PLA with an open-source 3-D printer. Rapid Prototyp J 21:604–617. https://doi.org/10.1108/RPJ-09-2014-0135

Ait-Mansour I, Kretzschmar N, Chekurov S, Salmi M, Rech J (2020) Design-dependent shrinkage compensation modeling and mechanical property targeting of metal FFF. Prog Addit Manuf 5:51–57. https://doi.org/10.1007/s40964-020-00124-8

Loh GH, Sotayo A, Pei E (2021) Development and testing of material extrusion additive manufactured polymer–textile composites. Fash Text 8:2. https://doi.org/10.1186/s40691-020-00232-7

Adisa AO, Colon AR, Kazmer DO, Peterson AM (2023) Interrelationships between process parameters, cross-sectional geometry, fracture behavior, and mechanical properties in material extrusion additive manufacturing. Polym Eng Sci 63:3906–3918. https://doi.org/10.1002/pen.26495

Hasanzadeh R, Mihankhah P, Azdast T, Bodaghi M, Moradi M (2024) Process-property relationship in polylactic acid composites reinforced by iron microparticles and 3D printed by fused filament fabrication. Polym Sci Eng 64:399–411. https://doi.org/10.1002/pen.26556

Ali S, Abdallah S, Devjani DH, John JS, Samad WA, Pervaiz S (2023) Effect of build parameters and strain rate on mechanical properties of 3D printed PLA using DIC and desirability function analysis. Rapid Prototyp J 29:92–111. https://doi.org/10.1108/RPJ-11-2021-0301

Bodaghi M, Mobin M, Ban D, Lomov SV, Nikzad M (2021) Surface quality of printed porous materials for permeability rig calibration. Mater Manuf Process 37:548–558. https://doi.org/10.1080/10426914.2021.1960994

Galati M, Minetola P (2020) On the measure of the aesthetic quality of 3D printed plastic parts. Int J Interact Des Manuf 14:381–392. https://doi.org/10.1007/s12008-019-00627-x

Spahiu T, Canaj E, Shehi E (2020) 3D printing for clothing production. J Eng Fiber Fabr 15:155892502094821. https://doi.org/10.1177/1558925020948216

Srivastava M, Rathee S (2022) Additive manufacturing: recent trends, applications and future outlooks. Prog Addit Manuf 7:261–287. https://doi.org/10.1007/s40964-021-00229-8

Dave HK, Patel BH, Rajpurohit SR, Prajapati AR, Nedelcu D (2021) Effect of multi-infill patterns on tensile behavior of FDM printed parts. J Braz Soc Mech Sci 43:23. https://doi.org/10.1007/s40430-020-02742-3

Campbell RI, Martorelli M, Lee HS (2002) Surface roughness visualisation for rapid prototyping models. Comput Aided Des 34:717–725. https://doi.org/10.1016/S0010-4485(01)00201-9

Shakeri Z, Benfriha K, Zirak N, Shirinbayan M (2022) Mechanical strength and shape accuracy optimization of polyamide FFF parts using grey relational analysis. Sci Rep 12:13142. https://doi.org/10.1038/s41598-022-17302-z

Reeves PE, Cobb RC (1995) Surface deviation modeling of LMT processes–a comparative analysis. In: 5th European Conference on Rapid Prototyping and Manufacturing. University of Nottingham, Nottingham, pp 59–76

Chryssolouris G, Kechagias JD, Kotselis JL, Mourtzis DA, Zannis SG (1999) Surface roughness modelling of the Helisys laminated object manufacturing (LOM) Process. 8th Eur. Conf. Rapid Prot. Manuf. University of Nottingham, Nottingham, pp 141–152

Google Scholar  

Mukhtarkhanov M, Perveen A, Talamona D (2020) Application of stereolithography based 3D printing technology in investment casting. Micromachines (Basel) 11:946. https://doi.org/10.3390/mi11100946

Charoo NA, Barakh Ali SF, Mohamed EM, Kuttolamadom MA, Ozkan T, Khan MA, Rahman Z (2020) Selective laser sintering 3D printing – an overview of the technology and pharmaceutical applications. Drug Dev Ind Pharm 46:869–877. https://doi.org/10.1080/03639045.2020.1764027

Pandey P, Nayak A, Taufik M (2022) Evaluation of mathematical models for surface roughness prediction of PolyJet 3D printed parts. Adv Mater Process Technol 10:89–98. https://doi.org/10.1080/2374068X.2022.2097416

Turner BN, Gold SA (2015) A review of melt extrusion additive manufacturing processes: II. Materials, dimensional accuracy, and surface roughness. Rapid Prototyp J 21:250–261. https://doi.org/10.1108/RPJ-02-2013-0017

Jain R, Nauriyal S, Gupta V, Khas KS (2021) Effects of process parameters on surface roughness, dimensional accuracy and printing time in 3D printing. In: Pandey PM, Kumar P, Sharma V (eds) Advances in production and industrial engineering. Lecture notes in mechanical engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5519-0_15

Selvam A, Mayilswamy S, Whenish R, Naresh K, Shanmugam V, Das O (2022) Multi-objective optimization and prediction of surface roughness and printing time in FFF printed ABS polymer. Sci Rep 12:16887. https://doi.org/10.1038/s41598-022-20782-8

Butt J, Bhaskar R, Mohaghegh V (2022) Investigating the effects of ironing parameters on the dimensional accuracy, surface roughness, and hardness of FFF-printed thermoplastics. J Compos Sci 6:121. https://doi.org/10.3390/jcs6050121

Sardinha M, Vicente CMS, Frutuoso N, Leite M, Ribeiro R, Reis L (2021) Effect of the ironing process on ABS parts produced by FDM. Mater Des Process Commun 3:e151. https://doi.org/10.1002/mdp2.151

Caputo M, Rashwan O, Waryoba D, McDade K (2022) Surface texture and thermo-mechanical properties of material extruded and ironed polylactic acid. Addit Manuf 59:103084. https://doi.org/10.1016/j.addma.2022.103084

Saad MS, Nor AM, Baharudin ME, Zakaria MZ, Aiman AF (2019) Optimization of surface roughness in FDM 3D printer using response surface methodology, particle swarm optimization, and symbiotic organism search algorithms. Int J Adv Manuf Technol 105:5121–5137. https://doi.org/10.1007/s00170-019-04568-3

Kandananond K (2021) Surface roughness prediction of FFF-fabricated workpieces by artificial neural network and Box-Behnken method. Int J Metrol Qual Eng 12:17. https://doi.org/10.1051/ijmqe/2021014

Mushtaq RT, Iqbal A, Wang Y, Cheok Q, Abbas S (2022) Parametric effects of fused filament fabrication approach on surface roughness of acrylonitrile butadiene styrene and nylon-6 polymer. Materials 15:5206. https://doi.org/10.3390/ma15155206

Butt J, Bhaskar R, Mohaghegh V (2022) Investigating the influence of material extrusion rates and line widths on FFF-printed graphene-enhanced PLA. J Manuf Mater Process 6:57. https://doi.org/10.3390/jmmp6030057

Singh S, Singh M, Prakash C, Gupta MK, Mia M, Singh R (2019) Optimization and reliability analysis to improve surface quality and mechanical characteristics of heat-treated fused filament fabricated parts. Int J Adv Manuf Technol 102:1521–1536. https://doi.org/10.1007/s00170-018-03276-8

Chaidas D, Kitsakis K, Kechagias J, Maropoulos S (2016) The impact of temperature changing on surface roughness of FFF process. IOP Conf Ser: Mater Sci Eng 161:012033. https://doi.org/10.1088/1757-899X/161/1/012033

Chaidas D, Kechagias JD (2022) An investigation of PLA/W parts quality fabricated by FFF. Mater Manuf Process 37:582–590. https://doi.org/10.1080/10426914.2021.1944193

Aslani K-E, Chaidas D, Kechagias J, Kyratsis P, Salonitis K (2020) Quality performance evaluation of thin walled PLA 3D printed parts using the Taguchi method and grey relational analysis. J Manuf Mater Process 4:47. https://doi.org/10.3390/jmmp4020047

Biglete ER, Christian E, Manuel M, Dela Cruz JC, Verdadero MS, Diesta JMB, Niko G, Miralpez D, Javier RAC, Ian C, Picato J (2020) Surface roughness analysis of 3D printed parts using response surface modeling. In: 2020 11th IEEE Control and System Graduate Research Colloquium (ICSGRC), Shah Alam, Malaysia, pp 191–196. https://doi.org/10.1109/ICSGRC49013.2020.9232561

Rakshit R, Ghosal A, Paramasivan K, Podder S, Misra D, Panja SC (2022) An experimental investigation of surface roughness and print duration on FDM printed polylactic acid (PLA) Parts. In: 2022 Interdisciplinary Research in Technology and Management (IRTM), Kolkata, India, pp 1–5. https://doi.org/10.1109/IRTM54583.2022.9791603

Vyavahare S, Kumar S, Panghal D (2020) Experimental study of surface roughness, dimensional accuracy and time of fabrication of parts produced by fused deposition modelling. Rapid Prototyp J 26:1535–1554. https://doi.org/10.1108/RPJ-12-2019-0315

el Magri A, el Mabrouk K, Vaudreuil S, Chibane H, Touhami ME (2020) Optimization of printing parameters for improvement of mechanical and thermal performances of 3D printed poly(ether ketone) parts. J Appl Polym Sci 137:49087. https://doi.org/10.1002/app.49087

Pazhamannil RV, Jishnu Namboodiri VN, Govindan P, Edacherian A (2022) Property enhancement approaches of fused filament fabrication technology: a review. Polym Eng Sci 62:1356–1376. https://doi.org/10.1002/pen.25948

Tiwary VK, Arunkumar P, Deshpande AS, Rangaswamy N (2019) Surface enhancement of FDM patterns to be used in rapid investment casting for making medical implants. Rapid Prototyp J 25:904–914. https://doi.org/10.1108/RPJ-07-2018-0176

Francis V, Garg S, Saxena KK, Jain PK, Lade J, Kumar D (2022) Effect of chemical and heat treatment on 3D printed parts: nanoparticles embedment approach. Adv Mater Process 8:2277–2288. https://doi.org/10.1080/2374068X.2022.2037876

Fuss FK (2011) The effect of surface skewness on the super/postcritical coefficient of drag of roughened cylinders. Procedia Eng 13:284–289. https://doi.org/10.1016/j.proeng.2011.05.086

Hansson KN, Hansson S (2011) Skewness and kurtosis: important parameters in the characterization of dental implant surface roughness—a computer simulation. ISRN Mater Sci 2011:1–6. https://doi.org/10.5402/2011/305312

Petropoulos GP, Pandazaras CN, Davim JP (2010) Surface texture characterization and evaluation related to machining. Surface Integrity in Machining. Springer London, London, pp 37–66

Chapter   Google Scholar  

Phadke MS (1989) Quality engineering using robust design. Prentice Hall PTR, Englewood Cliffs, New Jersey, p 07632

Costa N (2019) Design of experiments – overcome hindrances and bad practices. The TQM Journal 31:772–789. https://doi.org/10.1108/TQM-02-2019-0035

Montgomery DC (2012) Design and analysis of experiments, 8th edn. Wiley, Hoboken, NJ, USA

Kechagias JD, Zaoutsos SP (2023) An investigation of the effects of ironing parameters on the surface and compression properties of material extrusion components utilizing a hybrid-modeling experimental approach. Prog Addit Manuf. https://doi.org/10.1007/s40964-023-00536-2

Download references

No funding was received for conducting this study.

Author information

Authors and affiliations.

University of Thessaly, 43100, Karditsa, Greece

John D. Kechagias

You can also search for this author in PubMed   Google Scholar

Contributions

JK: methodology, conceptualization, resources, data curation, data analysis, software, visualization writing (draft and editing); writing (review and editing), supervision.

Corresponding author

Correspondence to John D. Kechagias .

Ethics declarations

Ethics approval.

No human participants or animals involved.

Consent to participate

Consent for publication.

The author has read and agreed to the published version of the paper.

Competing interests

The author declares no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 45 KB)

Rights and permissions.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Kechagias, J.D. Surface roughness assessment of ABS and PLA filament 3D printing parts: structural parameters experimentation and semi-empirical modelling. Int J Adv Manuf Technol (2024). https://doi.org/10.1007/s00170-024-14232-0

Download citation

Received : 06 April 2024

Accepted : 31 July 2024

Published : 12 August 2024

DOI : https://doi.org/10.1007/s00170-024-14232-0

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Fused filament fabrication
• 3D printing
• Surface roughness
• Find a journal
• Publish with us
• Track your research

Optimisation of friction surfacing process parameters for a1100 aluminium utilising different derivatives of palm oil based on closed forging test

• Syahrullail, S.
• Hamid, M. K. A.

Nowadays, cold forging is one of the most commonly utilised methods in industrial manufacturing, and most metal-forming lubricants are not ecologically friendly; in some cases, these chemicals may produce large chemical emissions and pose a risk to the community. Bio-oil lubricants have garnered increasing attention as potential alternatives for mineral oil-based lubricants, since they are critical in resolving existing obstacles. This article intends as a case study and demonstrating the usage of different derivatives of palm oil as a bio-lubricant in the closed forging test (CFT). As an outcome of the friction, wear behaviour and deformation, the closed forging test is important in the knowledge of materials and engineering studies. In this test, aluminium (A1100) was utilised to compare the formation of the workpiece using palm oil based and commercial metal-forming oil as a benchmark lubricant. During the forging process, these components' material flow patterns are analysed at intermediate phases of the die stroke level. Using the experimental data, the finite element approach will be used to predict the workpiece friction, effective stress and metal flow. By developing a Coulomb–Tresca friction model, a cold forging test also was used to do studies on the interaction between the Coulomb friction coefficient (CFC) and Tresca shear friction (TSF). From the results, certain types of palm oil-based lubricants perform better than mineral oil-based lubricants in terms of friction coefficient, with palm stearin having the lowest friction coefficient (m = 0.33/µ = 0.139), followed by palm kernel oil and palm mid olein (m = 0.39/µ = 0.159). The palm oil-based lubricant, on the other hand, has generated poor performance in terms of surface texture and surface roughness (R a ) with a high rate of wear compared to the no sample lubricant and commercial metal-forming oil (m = 0.42/µ = 0.1675).

• Finite element method;
• Material flow pattern

LimbNET: collaborative platform for simulating spatial patterns of gene networks in limb development

• Find this author on Google Scholar
• Find this author on PubMed
• Search for this author on this site
• ORCID record for Antoni Matyjaszkiewicz
• For correspondence: [email protected]
• Info/History
• Preview PDF

Successful computational modelling of complex biological phenomena will depend on the seamless sharing of models and hypotheses among researchers of all backgrounds - experimental and theoretical. LimbNET, a new online tool for modelling, simulating and visualising spatiotemporal patterning in limb development, aims to facilitate this process within the limb development community. LimbNET enables remote users to define and simulate arbitrary gene regulatory network (GRN) models of 2D spatiotemporal developmental patterning processes. Researchers can test and compare each others' hypotheses - GRNs and predicted spatiotemporal patterns - within a common framework. A database of previously created models empowers users to simulate, explore, and extend each others' work. Spatiotemporally-varying gene expression intensities, derived from image-based data, are mapped into a standardised computational description of limb growth, integrated within our modelling framework. This enables direct comparison not only between datasets but between data and simulation outputs, closing the feedback loop between experiments and simulation via parameter optimisation. All functionality is accessible through a web browser, requiring no special software, and opening the field of image-driven modelling to the full scientific community.

Competing Interest Statement

The authors have declared no competing interest.

View the discussion thread.

Thank you for your interest in spreading the word about bioRxiv.

NOTE: Your email address is requested solely to identify you as the sender of this article.

Citation Manager Formats

• EndNote (tagged)
• EndNote 8 (xml)
• RefWorks Tagged
• Ref Manager
• Tweet Widget
• Facebook Like
• Google Plus One

Subject Area

• Systems Biology
• Animal Behavior and Cognition (5514)
• Biochemistry (12534)
• Bioengineering (9410)
• Bioinformatics (30773)
• Biophysics (15825)
• Cancer Biology (12890)
• Cell Biology (18469)
• Clinical Trials (138)
• Developmental Biology (9982)
• Ecology (14939)
• Epidemiology (2067)
• Evolutionary Biology (19134)
• Genetics (12722)
• Genomics (17513)
• Immunology (12649)
• Microbiology (29656)
• Molecular Biology (12347)
• Neuroscience (64613)
• Paleontology (479)
• Pathology (1998)
• Pharmacology and Toxicology (3449)
• Physiology (5320)
• Plant Biology (11065)
• Scientific Communication and Education (1728)
• Synthetic Biology (3059)
• Systems Biology (7679)
• Zoology (1728)

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Study on chassis leveling control of a three-wheeled agricultural robot, 1. introduction, 2. the structure of the three-wheeled chassis leveling system, 3. mathematical modelling, 3.1. force model of the three-wheeled chassis, 3.2. attitude model of the three-wheeled chassis, 3.3. single-wheel suspension system model, 3.3.1. single-wheel suspension model, 3.3.2. hydraulic servo system model of the suspension actuator, 3.3.3. state equation of the single-wheel suspension, 4. chassis leveling control, 4.1. chassis stepwise leveling method, 4.2. adaptive dual-loop composite control strategy (adlccs), 4.2.1. design of the outer-loop controller, 4.2.2. design of the inner loop controller, 4.2.3. adaptive optimization of control parameters, 5. simulation study, 5.1. simulation setup, 5.2. comparison with baseline methods, 5.3. discussion, 6. test verification, 6.1. test setup, 6.2. comparison with baseline methods, 6.3. discussion, 7. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest, appendix a. derivation of the suspension structure principle, appendix b. hydraulic servo system model of the suspension actuator.

• Dettù, F.; Corno, M.; D’Ambrosio, D.; Acquistapace, A.; Taroni, F.; Savaresi, S.M. Modeling, control design and experimental automatic calibration of a leveling system for combine harvesters. Control. Eng. Pract. 2023 , 132 , 105411. [ Google Scholar ] [ CrossRef ]
• Hu, J.; Pan, J.; Dai, B.; Chai, X.; Sun, Y.; Xu, L. Development of an attitude adjustment crawler chassis for combine harvester and Experiment of adaptive leveling system. Agronomy 2022 , 12 , 717. [ Google Scholar ] [ CrossRef ]
• Peng, H.; Ma, W.; Wang, Z.; Yuan, Z. Leveling Control of Hillside Tractor Body Based on Fuzzy Sliding Mode Variable Structure. Appl. Sci. 2023 , 13 , 6066. [ Google Scholar ] [ CrossRef ]
• Lü, X.; Liu, Z.; Lü, X.; Wang, X. Design and study on the leveling mechanism of the tractor body in hilly and mountainous areas. J. Eng. Des. Technol. 2024 , 22 , 679–689. [ Google Scholar ] [ CrossRef ]
• Jin, X.; Wang, J.; Yan, Z.; Xu, L.; Yin, G.; Chen, N. Robust vibration control for active suspension system of in-wheel-motor-driven electric vehicle via μ-synthesis methodology. J. Dyn. Syst. Meas. Control. 2022 , 144 , 051007. [ Google Scholar ] [ CrossRef ]
• Liu, S.; Zheng, T.; Zhao, D.; Hao, R.; Yang, M. Strongly perturbed sliding mode adaptive control of vehicle active suspension system considering actuator nonlinearity. Veh. Syst. Dyn. 2022 , 60 , 597–616. [ Google Scholar ] [ CrossRef ]
• Han, S.-Y.; Dong, J.-F.; Zhou, J.; Chen, Y.-H. Adaptive fuzzy PID control strategy for vehicle active suspension based on road evaluation. Electronics 2022 , 11 , 921. [ Google Scholar ] [ CrossRef ]
• Jayaraman, T.; Thangaraj, M. Standalone and interconnected analysis of an independent accumulator pressure compressibility hydro-pneumatic suspension for the Four-Axle Heavy Truck. Actuators 2023 , 12 , 347. [ Google Scholar ] [ CrossRef ]
• Chen, H.; Gong, M.; Zhao, D.; Zhu, J. Body attitude control strategy based on road level for heavy rescue vehicles. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 2021 , 235 , 1351–1363. [ Google Scholar ] [ CrossRef ]
• Liu, S.; Zhang, L.; Chen, M.; Yang, C.; Zhang, J.; Wang, J. Multiple Suspensions Coordinated Control for Corner Module Architecture Intelligent Electric Vehicles on Stepped Roads. IEEE Trans. Intell. Veh. 2024 . [ Google Scholar ] [ CrossRef ]
• Zhang, N.; Yang, S.; Wu, G.; Ding, H.; Zhang, Z.; Guo, K. Fast distributed model predictive control method for active suspension systems. Sensors 2023 , 23 , 3357. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Hamza, A.; Ben Yahia, N. Artificial neural networks controller of active suspension for ambulance based on ISO standards. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 2023 , 237 , 34–47. [ Google Scholar ] [ CrossRef ]
• Fu, B.; Liu, B.; Di Gialleonardo, E.; Bruni, S. Semi-active control of primary suspensions to improve ride quality in a high-speed railway vehicle. Veh. Syst. Dyn. 2023 , 61 , 2664–2688. [ Google Scholar ] [ CrossRef ]
• Li, J.; Wang, J.; Chen, Y.; Si, E. Optimization of Suspension Active Control System Based on Improved Genetic Algorithm. In Proceedings of the 2023 7th International Conference on Electrical, Mechanical and Computer Engineering (ICEMCE), Xi’an, China, 25–27 October 2024; pp. 737–740. [ Google Scholar ]
• Jin, X.; Wang, J.; He, X.; Yan, Z.; Xu, L.; Wei, C.; Yin, G. Improving vibration performance of electric vehicles based on in-wheel motor-active suspension system via robust finite frequency control. IEEE Trans. Intell. Transp. Syst. 2023 , 24 , 1631–1643. [ Google Scholar ] [ CrossRef ]
• Ding, R.; Wang, R.; Meng, X.; Chen, L. Research on time-delay-dependent H∞/H2 optimal control of magnetorheological semi-active suspension with response delay. J. Vib. Control. 2023 , 29 , 1447–1458. [ Google Scholar ] [ CrossRef ]
• Maciejewski, I.; Blazejewski, A.; Pecolt, S.; Krzyzynski, T. A sliding mode control strategy for active horizontal seat suspension under realistic input vibration. J. Vib. Control. 2023 , 29 , 2539–2551. [ Google Scholar ] [ CrossRef ]
• Chen, G.; Jiang, Y.; Tang, Y.; Xu, X. Revised adaptive active disturbance rejection sliding mode control strategy for vertical stability of active hydro-pneumatic suspension. ISA Trans. 2023 , 132 , 490–507. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Nguyen, T.A. A novel approach with a fuzzy sliding mode proportional integral control algorithm tuned by fuzzy method (FSMPIF). Sci. Rep. 2023 , 13 , 7327. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Wu, L.; Zhao, D.; Zhao, X.; Qin, Y. Nonlinear adaptive back-stepping optimization control of the hydraulic active suspension actuator. Processes 2023 , 11 , 2020. [ Google Scholar ] [ CrossRef ]
• Nguyen, H.L.T. Lyapunov-based Design of a Model Reference Adaptive Control for Half-Car Active Suspension Systems. Meas. Control. Autom. 2024 , 5 , 22–29. [ Google Scholar ]

Click here to enlarge figure

Share and Cite

Zhao, X.; Yang, J.; Zhong, Y.; Zhang, C.; Gao, Y. Study on Chassis Leveling Control of a Three-Wheeled Agricultural Robot. Agronomy 2024 , 14 , 1765. https://doi.org/10.3390/agronomy14081765

Zhao X, Yang J, Zhong Y, Zhang C, Gao Y. Study on Chassis Leveling Control of a Three-Wheeled Agricultural Robot. Agronomy . 2024; 14(8):1765. https://doi.org/10.3390/agronomy14081765

Zhao, Xiaolong, Jing Yang, Yuhang Zhong, Chengfei Zhang, and Yingjie Gao. 2024. "Study on Chassis Leveling Control of a Three-Wheeled Agricultural Robot" Agronomy 14, no. 8: 1765. https://doi.org/10.3390/agronomy14081765

Article Metrics

Further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals