Turbulence Modeling - Science topic

Different turbulence models have different requirements and guidelines for the appropriate range of y+ values. Usually for the standard high Reynolds k-epsilon model,a y+ value between 30 and 200 is typically recommended.

A while back I got suggestion from my seniors that I have very fine mesh at interface than adjacent domain and is the reason for large courant number. But is this issue having significant effect on the torque after stall point?

Hi Armin and All,

In my research on turbulence modeling for blood flow simulations in hemodialysis cannulae (Salazar et al., 2008, found in ResearchGate at: ), I explored the impact of turbulence modeling on predicting hemolysis (red blood cell damage). This work might be relevant to the query about turbulence values affecting reattachment length in bluff body simulations.

The paper highlights the importance of accurate turbulence modeling since blood flow in cannulae is often turbulent, and turbulence significantly impacts hemolysis. I discuss the selection of an appropriate turbulence model for accurate flow predictions.

We validated our approach using a benchmark case of a coaxial jet array, which shares similarities with cannula flow. The findings suggest that the Shear Stress Transport (SST) model with Gamma-Theta transition yielded the best results compared to standard k-ε and k-ω models.

Here's how this research might be helpful to your situation:

While my paper focuses on hemolysis in cannulae, it offers valuable considerations for turbulence modeling in general. It highlights the importance of validation and suggests a potentially suitable turbulence model for your bluff body simulation.

I hope this information is helpful!

Best regards,

Luis

I am interested in your question but it needs a lot more explanation. Let me explain what I'm wondering about that I'd need to know to think about your question: If you are solving a F(u)=b, the residual is

Residual = b-F(u_approximate).

This is a vector with a lot of components so plots are usually some sort of aggregate statistic.

So what is your system?? Sometimes, people solve F(u)=b by time stepping: (u_n+1 - u_n)/k + F(u_n)=b then the residual means the discrete time derivative. Sometimes codes are written to be very memory efficient so they calculate something they call a residual that is just some easy to get data that serves as an optimistic proxy.

Maojin Gong This AI response is not false as it could be sufficient for a reader Lamda. However, it is not scientifically accurate as we are on a research thread. Furthermore, it does not display the mentioned references...

Maciej: The short answer to your question is no (as far as i know). The main challenge is defining a proper length scale in Re, and the sensible solution is to use some hydraulic diameter for internal flows, and the local position for external flows (flat plates, aerofoils, tubes etc). The main thing is that Re in some way should relate to the boundary layer thickness, which can be difficult (This is why the Nu and Cf for developing flows must be corrected with a d/L-expression for internal flows). Some attempts have been made at using the momentum thickness as length scale, which has showed some success in estimating the transition to turbulence.

Hi Nishidh Shailesh Naik Burye ,

If you have a constant, uniform, fixed shear stress field, OpenFOAM does have a "fixedShearStress" boundary which takes as input the vector value of \tau (assuming its constant over the entire boundary).

If you have anything more complicated (like a non-uniform shear stress field), you will unfortunately have to get your hands dirty coding a custom boundary condition. The easiest way would be to make a copy and modify the existing fixedShearStress boundary in OF. It imposes a Dirichlet boundary based on the velocity normal gradient field (from tau) and the cell-centred values of the velocity field from cells neighbouring the boundary. If you do follow this approach, it is important to just make sure you cancel out any velocity in the boundary normal direction, to make sure you don't accidentally, while converging, introduce inlet or outlet flow across the boundary.

Regards

CFD softwares are based on numerical methods or techniques to predict the fluid behavior for various conditions e.g. LES and RANS turbulence modelling etc. Unlike exact solutions , the numerical methods involve approximations of the governing fluid parameters which cannot be evaluated at once and thus need iterative computational solvers.

During this process several types of errors are introduced while approximating variable property e.g round off errors ( machine precision) , truncation errors depending on the type of numerical scheme used.

However , according to the nature of fluid and it's interaction with surrounding environment , ( in your e.g yplus wall function which is measure of the fluid friction resistance near wall ) the solutions obtained through numerical schemes present a significant source of error which can interpret the fluid behavior in entirely different manner.

Therefore, the solution is often tested by repeating the process using better approximations and schemes with a focus to obtain the exactness of parameter value leading to iterations.

During iteration process , the error can amplify or reduce ( which is indicative of the stability of solution ) depending on boundary conditions used to obtain solution. So, often an error tolerance is introduced as condition in numerical algorithm to make the solution more meaningful and realistic which closely approximates the fluid behavior. In your case wall shear stress is being approximated using wall units in logarithmic boundary layer.

Once that condition is satisfied, the process stops and proceeds further by evaluating the next dependent variable and so on until complete solution is obtained.

Is this boundary condition correct for this simulation?

Nishidh Shailesh Naik Burye

if you work by prescribing the Re_tau number of your non dimensional solution, you have the y+ at the first cell known.

Since y+ = u_tau*y/ni = Re_tau *y/L you just scale your non dimensional first cell height by Re_tau.

If you encounter the mentioned error in COMSOL Multiphysics with a RANS turbulence model, ensure proper initialization of the Reciprocal Wall Distance variable in study steps. Confirm correct settings for turbulence model and wall treatment, validate boundary conditions, and check solver settings. Consult COMSOL documentation for model-specific guidance. If issues persist, contact COMSOL support for assistance. Review and ensure proper definition and initialization of all required variables in accordance with RANS turbulence model requirements.

Desta,

I am puzzled - you seem to have answered your own question.

Are you honestly looking for help?

See these Chapters in French:

First question: where could have ChatGPT taken the relative information for training? Honestly, if you're going to use that, I can't see how you could not want to know about that.

Second question: why ChatGPT? This is not some complex information we can't extract from complicated data. It's just exactly there for you to learn or to search trough. Also, it could be better done by making a new net from scratch just about that, than using a LLM that really has nothing to do with this.

My general comment is that engineers and scientists should not look for answers in a tool that is not even tought to be what they want. ChatGPT just spits out words following a prompt and a statistical model. That is not different from a bad student that just goes by memory without understanding. ChatGPT is actually worst, as it never assumes it could not know something. You wanna ask that about turbulence models? Oh my...

I don’t use RANS formulation, I can just address some general questions:

1) use at least 3-4 nodes within y+<1

2) Are you comparing your solution to experimental measurements? Are you sure to be congruent with the experimental inflow conditions?

3) have you assessed you are able to reproduce the results for the classic test-case of the backward facing step at high Re number?

I am interested to learn if it is possible "Ram Chandra Pageni" since I am doing research in Space Science.

In computational fluid dynamics (CFD), the y+ value is used to determine the appropriate treatment of the near-wall region in turbulence modeling. It represents the non-dimensional distance of the first grid cell from the wall, normalized by the viscous length scale.

Different turbulence models have different requirements and guidelines for the appropriate range of y+ values. Here's a general overview of how y+ values are used with different types of turbulence models:

It's important to note that these are general guidelines, and the appropriate y+ range can vary based on the specific turbulence model and the flow conditions. Additionally, advancements in meshing techniques and solver capabilities have reduced the sensitivity to y+ values in some cases. It's always recommended to consult the documentation or literature specific to the turbulence model and software you are using for more accurate guidance on y+ values.

Ilya Lichadeev What I mean that it depends how you verify your numerical model (point-wise, using integral values, etc.), and which experimental data is used. For some setups it is not possible to get a perfect quantitative match, but it is enough if your model follows the trends observed in the experiment.

As you can see, the RANS solution produces an averaged field over the sphere also for laminar vortex shedding.

However, if you have a fully laminar flow, simply solve for it. If You think to have transitional conditions, Depending on you computational power, use LES or DNS.

Hi Naveen,

I have the same question; has your issue been resolved ?

Alin

Hongxiang Yu

In general, for dynamic mesh simulations, models that involve additional terms in the turbulence kinetic energy equation, such as WALE (Wall-adapting Local Eddy-Viscosity) or dynamic Smagorinsky, may be more suitable. These models account for the effects of mesh deformation on the turbulence field and can improve the accuracy of the simulations.

WALE model includes additional terms in the eddy-viscosity calculation that account for the effects of rotation rate, strain rate, and dissipation rate. This model can be more accurate for complex flows with high strain rates and rotation rates, such as flows with vortices or swirling motions.

On the other hand, the Smagorinsky model is a popular choice for LES simulations in OpenFOAM and is widely used for a range of flows. This model uses a constant eddy viscosity coefficient that is proportional to the grid size, which means that it can be computationally efficient for large-scale simulations. However, it may not be as accurate for complex flows or when mesh deformation effects are significant.

When choosing an LES model for dynamic mesh simulations, it is important to consider the specific characteristics of the flow and the desired level of accuracy. It is also recommended to perform sensitivity studies to investigate the effect of different LES models on the results and to validate the simulations against experimental data or other established methods.

Possibly you should have a look at

Baumert, H. Z., Universal equations and constants of turbulent motion,

Physica Scripta, T155, 014,001 (12pp), doi:10.1088/0031-8949/2013/T155/014001, 2013.

Also have a look at the attachments.

Feel free to ask specific questions!

Best,

Helmut

Forget this k-eps model. While k is a so-called conserved variable, eps ist not. Eps is a colored mix of variables. I recommend for turbulence the k-Omega-model. It allows in my interpretation (2009) e.g. the derivation of the von-Karman constant as 1/sqrt(2*pi)~0.3989... as well as also other constants of this model. Cheers, Helmut

Here is a sample UDF code for the k-e-v2-f turbulence model in ANSYS Fluent:

This code defines a UDF for the k-e-v2-f turbulence model in ANSYS Fluent. The UDF computes the turbulent kinetic energy (k), the turbulent dissipation rate (eps), and the second moment of the velocity fluctuations (v2). It also computes the turbulent viscosity (mu_t) and the constants C1, C2, and C3, which are used to compute the wall function values of epsilon and f. The UDF then sets the values of k, epsilon, and f in the turbulent and laminar regions of the flow, and updates these values in the solver.

#include "udf.h"

DEFINE_K_EPSILON(k_e_v2_f, c, t, dS, eqn) { real k, eps, f; real v2, S; real mu; real rho; real Cmu, C1, C2, C3; real sigma_k, sigma_e, sigma_f; real f_wall, eps_wall;

k = C_K(c, t); eps = C_EPSILON(c, t);

v2 = 2.0k/3.0; S = sqrt(2.0k)/C_MU(c, t);

mu = C_MU(c, t); rho = C_R(c, t); Cmu = 0.09; mu_t = rhoCmukeps/(muS);

C1 = 1.44; C2 = 1.92; C3 = 1.0;

eps_wall = C2sqrt(k)pow(C_DIST(c, t), 2.0/3.0); f_wall = C3(1.0 - exp(-C1pow(C_DIST(c, t), 1.5)));

sigma_k = 1.0; sigma_e = 1.3; sigma_f = 1.0;

if (C_DIST(c, t) < 1.0e-10) { eps = eps_wall; f = f_wall; }

else { k = sigma_kmu_tfv2/(epsC_MU(c, t)); eps = sigma_emu_tfv2/(kC_MU(c, t)); }

f = sigma_fmu_tfv2/(kC_MU(c, t));

if (S < 1.0e-10) { k = 0.0; eps = 0.0; }

dS[eqn] = 1.0; C_K(c, t) = k; C_EPSILON(c, t) = eps; }

Hi,

In my reasearch project, I have completed recently; a research for a typical turbocharger compressor optimisation. It has been studied air turbulent flow simulated the K-Omega SST turbulence model. My numerical simulations has been validated and I wrote some papers. Please have a look into my papers, hopefully it can help.

Regards,

It is possible to calculate Taylor microscale and macroscale. Taylor microscale can be calculated using the fitting of the parabola at the origin. One may find details within this paper:

Chuychai, P., Weygand, J. M., Matthaeus, W. H., Dasso, S., Smith, C. W., & Kivelson, M. G. (2014). Technique for measuring and correcting the Taylor microscale. Journal of Geophysical Research: Space Physics, 119(6), 4256-4265. Available on:

I recommend you the previous links because you can easily copy and paste values from there, but you find theory, airfoil geometry and experimental data here: https://aeroknowledge77.files.wordpress.com/2011/09/58986488-theory-of-wing-sections-including-a-summary-of-airfoil-data.pdf

Also I recommend to search for experimental data here in RG.

The conservation equations for the turbulence kinetic energy (TKE), k (m2 s-2) and its rate of dissipation ε (m2 s-3) are calculated using k-ε standard model.

These two quantities are used to calculate the effect of the turbulence fluctuation components on the averaged conservation equations. The standard k-ε model is simple and proves to be stable in predicting flow in turbocharger compressor or other applications. In my research, although k-ε model has been used in most of the simulations, the results using RNG k-ε and k-omega models have also been examined.

The K-omega turbulence model has superior performance in terms of numerical stability in the viscous sublayer of wall-bounded flows. However, it is very sensitive to the free stream turbulence parameters, thus it is unsuitable for certain complex applications.

Standard k-epsilon The baseline two-transport-equation model solving for kinetic energy k and turbulent dissipation ε. Turbulent dissipation is the rate at which velocity fluctuations dissipate. This is the default k–ε model. Coefficients are empirically derived; valid for fully turbulent flows only. In the standard k-e model, the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature.

Standard k-omega A two-transport-equation model solving for kinetic energy k and turbulent frequency ω. This is the default k–ω model. This model allows for a more accurate near wall treatment with an automatic switch from a wall function to a low-Reynolds number formulation based on grid spacing. Demonstrates superior performance for wall-bounded and low Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free shear, and compressible flows. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Solves one equation for turbulent kinetic energy k and a second equation for the specific turbulent dissipation rate (or turbulent frequency) w. This model performs significantly better under adverse pressure gradient conditions. The model does not employ damping functions and has straightforward Dirichlet boundary conditions, which leads to significant advantages in numerical stability. This model underpredicts the amount of separation for severe adverse pressure gradient flows. Pros: Superior performance for wall-bounded boundary layer, free shear, and low Reynolds number flows. Suitable for complex boundary layer flows under adverse pressure gradient and separation (external aerodynamics and turbomachinery). Can be used for transitional flows (though tends to predict early transition). Cons: Separation is typically predicted to be excessive and early. Requires mesh resolution near the wall.

So, K epsilon is best suited for flow away from the wall, say free surface flow region, whereas k-omega model is best suited for near the wall flow region, where adverse pressure gradient is developed.

I hope this helps.

If the size t is less than 8-12 distances to the bottom surface, the drag force will be determined, among other things, by the added masses of the liquid reflected from the bottom surface. If this is not important, then in the model you need to specify a distance of more than 12.

The number of wall layers is enough 5.

From above on a free surface, the wind has a speed and direction?

Hi

I tried to run an ANSYS FLUENT simulation with SST Model and it was hard to converge. The laminar model should converge, I'd suggest using a better quality mesh.

In some cases the SST will resolve to low/zero turbulence, but that is not always the case. The SST model will have turbulent fluid coming in the inlet, as set by your boundary condition. This would take time/distance to convert to laminar using the SST model. Check your Viscosity ratio in your results, see how turbulent the SST model is showing your flow to be. Laminar flows can have problems converging where they are actually turbulent flows, or where transient laminar flow structures exist. (This is assuming you have a good quality mesh and the simulation is correctly set up.) If you say the flow should be laminar then it is still quite possible that a laminar steady state simulation will not converge because of transient flow structures. This is very common in heat transfer simulations with natural convection - the natural convection tends to have transient laminar structures. If this is the case the only way to proceed is to do a transient laminar simulation. If you solve a laminar simulation with a turbulence model you are adding extra dissipation to the model. This dissipation is not real, it is a product of the turbulence model you are using, but it can have the effect of damping out these transient flow structures and apparently converging. The SST turbulence model is better than most turbulence models as when the turbulent kinetic energy goes to zero (it is exactly zero in a laminar flow, by definition) the turbulent viscosity also goes to zero, so SST does not add much dissipation to the model and you might get away with it. But k-epsilon based models are well known to have far too much dissipation in the low Reynolds number regimes because as k goes to zero the turbulent viscosity goes to a finite value, and this is false additional dissipation. This is why the k-e model is a bad choice for low Reynolds number flows, and you either need to modify it or use a k-omega based model like SST which does give zero turbulent viscosity at zero turbulent kinetic energy. However, if your flow is steady state laminar and you use the SST turbulence model the turbulence model is likely to give effectively zero turbulent viscosity, meaning that your answer probably will be reasonably accurate (only with a small amount of extra dissipation). If your flow is transient laminar and you use the SST turbulence model there is a good chance the turbulence model will generate too much dissipation and damp out the transient flow, which is wrong. You are likely to get a big error in this case. In this case using the SST turbulence model is wrong. A transient laminar model is correct. Note you will need to do time step, mesh and convergence criteria sensitivity studies to work out what you need for time step and mesh size, and convergence criteria.

Hopefully that explains things a bit.

In such cases, modifying the BC or mesh configuration may be beneficial.

Hi Somenath, It should be possible with ANSYS as I have made it possible in STARCCM+ for my flat plate simulations. I will let you know the procedure in STARCCM+ and probably the same steps can be followed in ANSYS too.

1. Make a line probe where vertical measurements can be taken at the location or position where you want to have U+ vs Y+ plot.

2. Go for an XY plot where Y-axis is U+ and X-axis is a log scale of Y+.

3. Now the input part to this plot should be the earlier line probe.

4. Most of the software has Y+ defined so you just need to recall the expression for Y+ from the software database and assign it on the x-axis.

5. U+ may not be defined in most software. Hence create a custom field scalar function defining U+. (You will get a standard expression for U+ from any Fluid Mechanics Text Book, I follow Frank M White and it has expressions for U+ too).

6. Finally assign this newly defined U+ to the Y-axis.

Hope you too will get the same on ANSYS.

In general, for internal flows with curvature and rotations, k-Omega SST model performs the best. While k-epsilon models are used widely, they are not able to capture the near-wall effects (performs weakly under adverse pressure gradients and along curvatures). While k-Omega-SST model uses a blending function and allows us to go to y+ ~ 1, without having the adverse problems like in k-epsilon. In essence, it functions like the k-Omega model near the walls, and like a k-epsilon model in the far-fields.

Hello Mr Jayathilake,

the kOmegaSSTt is suitable for this problem in my opinion, especially when computational limits are low. With adequate refinement in the critical regions you might achieve good results. I don't know which code you are using for your simulations but, if available, you can also try the kOmegaSSTSAS approach. This "Scale Adaptive Simulation" approach is able to resolve turbulent length scales more precisely. It falls back to kOmegaSST if the mesh is coarse. But if you apply some further refinement you should get a more detailed results. Timesteps should be limited to CFL<=1. Compared to LES or DES mesh and solution order requirements are still lower I guess.

Computational effort for this model is not really higher than for the kOmegaSST.

You may have a look e.g. at these publications of the model developer Mr. F. Menter:

and many more.

I hope this helps.

Best Regards

David

it may be caused by grid.

First - changing two things in a simulation at the same time is obvious not a good approach (mesh AND turbulence model).

Further I need to say, that first you would need to find out, where your simulation comes to a mesh-independente solution (this question can be anbswered with no regard to which turbulence model you are using, if properly implemented in the CFD solver), and only on a mesh level, where the CFD solution is independent from the mesh resolution you can start to make judgements about model errors or about which turbulence model is more suitable for your particular application.

In contrary, if your solution is not yet mesh independent, i.e. the mesh is still too coarse, you are looking on a not known mix of discretization errors and model errors. This can mislead you to a misjudgement about a particular physical model and on the next following refinded mesh the situation (with the two models in question) might be reversed in comparison to what you have observed on the coarser mesh.

This CFD methodology has been outlined almost 22 years ago in the so-called "CFD best practice Guidelines for Industrial CFD".

The report can be ordered on this page from ERCOFTAC.

The methodology says, that the following hierachy of CFD error quantification and elimination should be observed:

1) round-off error

2) iteration error (cut-off error with respect of stopping a solution process at a certain iteration number or by matchig a certain quantitative convergence criterion)

3) spatial and time discretization error

...and only afterwards you can investigate model errors of physical models.

Any attempt to investigate more than just one error source at the same time or to change the order of investigation of the errors from this error hierarchy potential will lead to erroneous CFD result.

Best regards,

Dr. Th. Frank.

WMLES or SBES model with a well thought (and validated) mesh resolution.

Regards,

Dr. Th. Frank.

PS : Your question did not involve any limitations on the computational time of the proposed turbulence modeling approach. Therefore a scale-resolving simulation would clearly deliver the best possible results (I'm not proposing a diret numerical simulation, since you asked for turbulence modeling approaches; DNS is resolving turbulence, but not modeling it).

Pradyumn Chiwhane I am posting here a previous answer I provided on submerged oscillating bodies in quiescent fluid. The total force exerted by the fluid on the cylinder, you should consider besides the drag the added mass force. Academic references are provided within the following research projects:

Pradyumn Chiwhane I am not used to performing calculations with CFX. Researchers in my group do.

If this is the total force exerted by the fluid on the cylinder, you should in my opinion deduce the added mass force to obtain the net Drag. You may consult academic references within the following research projects:

Academic resources on fluid Mechanics are provided on the project references:

SINGLE PHASE AND MULTIPHASE TURBULENT FLOWS (SMTF) IN NATURE AND ENGINEERING APPLICATIONS | Jamel Chahed | 3 publications | Research Project (researchgate.net)

The SST k-ω model is a hybrid of the best of k-ω and k-ε. This model uses the k-ω model near walls, and transitions to k-ε model in the open flow field. It’s popular in aerospace and turbo-machinery applications.

So SST is the most effective model for young computational fluid dynamists.

Flows with greater anisotropy in the turbulence stress tensor render standard one equation and two equation RANS models not great as they make assumptions about the turbulent shear stresses which turn out to be untrue for specific cases. This anisotropy is commonly present in flows with large separations etc. Reynolds stress models remedy this by solving transport equations for each component of the stress tensor but these too have limitations and haven't proven to be of much advantage. If high accuracy is desired, LES or DNS are the only way. But for most engineering flows of interest, one equation and two-equation eddy viscosity models provide sufficient engineering accuracy with results in a reasonable time.

Resources, and academic tools on turbulent single-phase and multiphase flows are availble on the project:

Mohamed Bounouib please follow the links attached herewith and follow the steps for the flow simulation in an axial pump. That will be easier for you

Regards

Ahmed Gharib Yosry Thanks for your assistance. i tried to reverse the boundary conditions, replace the inlet and outlet with each other. but the torque doesn't goes down the optimum value.

In the COMSOL documentation the no-slip BC is indicated to be (u,v)=(0,0).

What you described is slip condition. You can consult the COMSOL team for more clarification. You can also run a test simulation to see how the code performs.

Dear Fellows,

We are all choosing a Turbulence Model for our flows. We are already creating decision chart in our heads. So, why not put these decision steps together and create a real chart? Please do not think so complicated. At the end of the chart there won't be only one Turbulence Model for relevant case, there will be list (at end of different decision steps same model could be listed too). After that you can do some literature search to select the best model in the list.

Please consider that.

Best regards,

Güven

Güven Nergiz please follow the following links below :

i hope it will help you.

The Reynolds Stress Model is the most complete turbulence model with regards to representing turbulent flow.

I would add that the meaning of y+ is very very simple. It is nothing but that the local Reynolds number measured along a normal-to-wall direction. That is, y+=0 is the wall position and then the value increases according to y+=(u_tau/vi)*y.

The Reynolds number is not high, and accuracy can mean saving of lives. Do not use a turbulence model, perform a direct simulation (DNS) resolving all temporal and spatial scales with an appropriate function for the viscosity (shear thinning character). This can be done with any numerical code solving the Navier-Stokes equations, and the numerical costs will be affordable.

I think it may be due to BCs. Can you please your problem in detail, so that I may help you in diverg. Issue

Dear Vinay,

I would recommend you to follow the video lecturer on Computational Fluid Dynamics by Prof. Suman Chakraborty according to me it is one of the best.

You can also follow Prof. Fillipo Maria Denaro's technical report/ppt on CFD, available in the ResearchGate.. He is one the famous researcher in computational physics and CFD.

Dear Prof. Th. Frank

Thank You very much for your explanation and suggestions on my error.

Hi Nehal,

If you have refined the mesh and used the appropriate turbulence model, then I suggest you to please check the convergence of the result.

Hi,

this is not an easy to setup simulation, also it may look like this on the first glance.

Why?

1) Vortices leading to air entrainment are rather small flow structures of thin diameter and having substantial velocity gradients over the diameter of the vortex. This velocity gradients need to be fairly good resolved in order to resolve the low pressure occuring in the center of the vortex leading to the air entrainement. For that a very fine mesh resolution is required.

2) Usually such vortices - if they are not artificially and by geometric design measures stabilized - are not stationary in space. So the vortex is moving around / precessing and that makes it even harder to establish a well resolved numerical mesh with fine mesh resolution at the vortex center. It might be suitable to use adaptive mesh refinement, but without a coarsening algorithm there is the danger, that the geometrical space more and more fills with refined mesh cells, making the simulation rather very expensive.

3) Standard 2-equation turbulence models are by default not capable of capturing the strong velocity gradients in flows with strong streamline curvature / rotation. A SST k-omega-based turbulence model with curvature correction is at least recommended.

4) It has to be made sure, that the turbulence conditions at the free surface between liquid and air are capturing the physical valid conditions. Usually a fine mesh resolution at the free surface is required for that in addition with turbulence model damping terms at the free surface, i.e. the turbulent kinetic energy at the free surface needs to be dampended to zero or small values.

Regards,

Dr. Th. Frank.

I try to address better the question. If the flow problem admits a statistically steady state you start from an initial condition and run until you flow variables are statistically steady, that is you see them oscillating in time around a constant value. From that moment the solution is physically correlated.

Conversely, if you have a problem that has an unsteady behavior also in the mean values, you need to simulate at least the largest time period of your problem.

This approach is typical for DNS/LES formulations, sice you are using a URANS approach the real physical meaning of your unsteady simulation can be debated. If your flow problem is statistically steady, your URANS shouldn't be somehow different from a RANS solution.

The key is that you cannot fix arbitrarily a number of time steps without knowing the nature of your flow problem.

I suggest to monitor in time the mean values

it may help you:

Best

The problem I faced while using SST I need to put the value of turbulence intensity at the entrance, and if I specify it to zero then my solution does not converge.

If you want to use the RANS formulation you should assume your flow field is totally developed. That means you can set the inflow profile according to a statistically mean velocity in a channel

Can provide more information

simply you can save your case and data file at the current time step , and then reopen it and procced the calculation again . the error at each time step will disappear.