[modest_may]

Recently, flow and heat transfer simulations for the ribbed-duct model of Acharya et.al [1] are conducted based on k-ω turbulence model in CFX. Results indicate that the range of separation regions after the rib is over-predicted, as presented in the uploaded Figure 2. This results in higher wall temperature and thus lower Nusselt number. Meanwhile, it is also observed that the eddy viscosity around the rib is under-estimated.
I would like to modify the k-ω turbulence equations using Cel routines or by adjusting some parameters related to this model. Can anyone give me some advises?

PS: The SST and k-e turbulence models are also employed, the former gets the same results as k-ω model, while the latter obtains extremely larger Nu value than experiments. This is exhibited in Figure 2, where the black circles are experimental data. What I really want to do is modifying the k-ω turbulence equations.

Hope to get some replies, thanks.
[1] Acharya S, Dutta S, Myrum TA. Heat transfer in turbulent flow past a surface-mounted two-dimensional rib. ASME Journal of Turbomachinery, 1998,120:724-734

[ghorrocks]

Attempting to adjust a turbulence model to get a better fit to experimental results is a very brave thing to do. Fixing up the area which it gets wrong while keeping everything else working problem requires much more courage than I have. Most people leave adjusting turbulence models to turbulence experts.

You have access to all the fundamental model constants through the "Advanced Turbulence Control" switch in CFX-Pre. You can also overwrite the eddy viscosity entirely. But I say again, adjusting these parameters is rarely a good idea.

It is well known that two equation turbulence models do not predict separations very well. If there was a simple way to fix it, it would already be in the model. The usual approach for accurate models of separations is to use a LES based model. Have you considered using an LES model?

[modest_may]

Thank you for your reply, sir.

The reason why i want to modify the k-ω turbulence model is due to an ongoing study which uses source models to simulate flow and heat transfer. The idea in this study is similar to that in Immersed Boundary Method, which uses a single domain to predict flow and heat transfer.

In order to realize this, source terms are added into the momentum, energy and turbulence model equations. For the ribbed-duct model shown in the above Figure 1, i have conducted actual and source model based simulations. Mesh details for these two methods are presented in the following Figure 4. Meanwhile, Figure 5 depicts predicted distributions of Nu using actual CFD with k-ω turbulence model(A-k-ω), source method CFD without (S) and with (S+k-w-s) adding sources into k-ω turbulence equations.

It is interesting that when k-ω equations are not modified, predicted Nu is nearly the same as measured value (EXP). However, when source terms, which depend on material properties of fluid or solid, there's almost no difference between predictions using actual CFD (A-k-ω) and source method (S+k-w-s).

This result may be case dependent, but it implies that the numerical precision can be improved if the turbulence equations are corrected. In addition, it also suggests that the way to improve numerical precision for the source model method, which considers source terms in k-ω turbulence equations, lies in increasing accuracy for the simulation of CFX itself. That's the reason why i want to modify the turbulence model. However, it seems that i lost the direction to move on.

LES is an excellent method, but it is not the major choice for my current study.

Nevertheless, thank you again for your advises.

[ghorrocks]

I do not see how the results you show then suggest that modifying the turbulence equations will help the situation. No matter, it is not my research so I will just answer the question you asked.

You can either do adjustments of existing turbulence models by adjusting the model constants, or you can develop your own entire turbulence model by using the eddy viscosity setting. If you develop your own model you will probably need to use additional variables to convect the turbulence variables around and source terms to create and destroy turbulence.

[modest_may]

Yes, for now, developing new turbulence model as you suggested may be an appropriate way, i just feel that this is an interesting topic.
Thank you, sir, for your kind advice.

[Gert-Jan]

- For the situation with the Immersed Boundary method, can you show temperature and velocity contour in a plane crossing the rib?
- I assume you use water.......
- Do your properties depend on temperature?
- What is your Y-plus?
- I think Yplus is very small. Then why still use an epsilon based model?

[modest_may]

1 Contour of the temperature is displayed in Figure 6，where the lines with squares and circles are predicted and measured distributions of the velocity respectively. As noted before, Actual CFD is the simulation for real ribbed-duct model, while source CFD and source CFD plus k-ω sources represent source model based predictions without and with k-ω source terms.

Temperature near the downstream surface of the rib is higher in Figures 6 (a) and (c) than that in Figure 6 (b). This results in lower Nu value for actual (A-k-ω) and source plus sources (S+k-ω-s)cases in Figure 5.

2. The material used is air, its properties is not changed with temperature, but the thermal conductivity is interpolated depending on the fluid or solid material.
(..Maybe i should consider temperature-dependent properties..).

3. The Y-plus is lower than 1 for ω-based and low-Re k-e turbulence models, while it is about 12 for the standard k-epsilon turbulence model. I just want to examine effects of various turbulence models on heat transfer simulations.

I reckon that the problem now does not lie in the source method, it has a need in improving the precision of the k-ω turbulence model of CFX for heat transfer predictions. So this is my core question. Besides, do you have proper suggestions for turbulence modeling of IBM?

Thank your for your concern.

[modest_may]

Also, I am sorry for replying you late, this is due to time difference, :-)

[ghorrocks]

The answer to your question is in my previous post - you can do your own turbulence model using additional variables and the eddy viscosity setting.

A side question - Are your models 2D or 3D? That might make a difference.

[modest_may]

Originally Posted by ghorrocks

The answer to your question is in my previous post - you can do your own turbulence model using additional variables and the eddy viscosity setting.

A side question - Are your models 2D or 3D? That might make a difference.

Dear sir, sorry to reply late, the last post is answering the question of Gert-Jan. :-).
The domain is 2D, since two dimensional condition can be satisfied in experiments.
Besides this problem, can you give me some tips to calculate the bulk temperature, Tb? Honestly, i cannot find an unified definition for Tb, some researchers use the inlet temperature, while some use the mass averaged temperature at the interested location along the stream-wise direction (for this ribbed-duct model).

[ghorrocks]

Are you sure this flow is 2D? It will be a major source of error if that assumption is not correct.

There is no universal definition of bulk temperature. If you are comparing to literature Nusselt number values then you have to use the definition used in the literature you can comparing to. If you are comparing to many results you might need to use several definitions.

[modest_may]

Originally Posted by ghorrocks

Are you sure this flow is 2D? It will be a major source of error if that assumption is not correct.

There is no universal definition of bulk temperature. If you are comparing to literature Nusselt number values then you have to use the definition used in the literature you can comparing to. If you are comparing to many results you might need to use several definitions.

Since the ratio of the channel width (w=0.3m) to the rib height (h=6.35mm) is relatively large, i.e., w/h is about 47.24, two dimensional flow condition can be assumed. Some numerical studies of Acharya also use two-dimensonal domain, and in fact, i have ever performed 3D simulations, results indicate small differences between 2D and 3D predictions.

Thank your for your carefulness and for your explanation of the bulk temperature.

Thank you, sir. :-),:-),:-)

[ghorrocks]

I assume the width (w) is the dimension in the z direction. If w is small then won't there be strong viscous effects from the close proximity of the walls? Or was something done to make these frictionless walls?

[modest_may]

Originally Posted by ghorrocks

I assume the width (w) is the dimension in the z direction. If w is small then won't there be strong viscous effects from the close proximity of the walls? Or was something done to make these frictionless walls?

Yes, the width (w) is the dimension in the z direction, and it is about 47.24 times the rib height. The ratio of w to h is relatively large so that three-dimensional effects can be regarded as negligible. Archaya et al [1] and other researchers, for example, the LES study of Yan et.al[2], also conducted 2D simulations for this rib model.

I performed another calculation using k-ω and SST turbulence models in CFX for the rib model of Rau[3], differences in the Nu between predictions and measurements of this model are relatively smaller than that of the above Archaya's rib model. This really puzzles me. Maybe the boundary condition has some inappropriateness, as you noted before.

Additionally, in the study on pipe expansion case of Baughn[4], the author denoted that difference between the wall and bulk temperature should be high enough that uncertainties of temperature differences (wall to bulk fluid) would be small. Since smaller errors in the wall temperature could lead to a significant degree of uncertainty in the Nusselt number, especially at the higher heat fluxes. I think this idea is also a valuable guidance.

:-).
PS: The time on this cfd-online web site also puzzles me, it seems that you are always here. I really appreciate you spending so many efforts to help me. Thank you very much.

[1] Acharya S, Myrum T, Qiu X and Sinha S. Developing and periodically developed flow, temperature and heat transfer in a ribbed duct. International Journal of Heat and Mass Transfer, 1997, 40(2):461-479.
[2] Yan L, Pau GT, G.Lo I. Comparison of zonal RANS and LES for a non-isothermal ribbed channel flow. International Journal of Heat and Fluid Flow, 2006, 27:391-401.
[3] Rau G, Cakan M, Moeller D, Arts T. The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel. ASME Journal of Turbomachinery, 1998,120:368-375.
[4] Baughn JW, Hoffman MA, Takahashi RK, Launder BE. Local Heat Transfer Downstreamof an Abrupt Expansion in a Circular Channel With Constant
Wall Heat Flux. ASME Journal of Turbomachinery, 1984,106:789-796.

[ghorrocks]

A well researched answer! I must admit that when I look at my last post the question was prompted by me not noticing that the width was in metres but the height was in mm.

Yes, I check the forum all sorts of weird times. Maybe I am an addict.

[modest_may]

Originally Posted by ghorrocks

A well researched answer! I must admit that when I look at my last post the question was prompted by me not noticing that the width was in metres but the height was in mm.

Yes, I check the forum all sorts of weird times. Maybe I am an addict.

also, more attention to rest...:-), :-), :-)
Have a nice day, sir, and wish you happy every second.

[modest_may]

I examined flow and heat transfer conditions for the ribbed-duct model of Archaya [1] in past few days, and conducted some simulations for the ribbed model of Rau et.al [2]. Some results are presented here to finish this thread.

1. The single rib model displayed in the first post is the same as the ten ribs model in Ref.[1]. Therefore, periodic conditions should be considered in simulations. Figure 1 depicts predicted and measured Nu using a domain containing ten ribs. Discrepancies between numerically simulated values using k-ω turbulence model in CFX and tested data become smaller.

2. Figure 2 plots Nu-distributions for the rib model of Rau et.al [2]. Since no details of the inlet velocity, temperature and wall heat flux were provided in the original paper [2]. Three inlet velocity values are examined here. The wall heat flux is specified as 500 [W m^-2]. It can be observed from Fig.2 that increasing inlet velocity helps to enlarge the Nu value. When the inlet velocity is 37 [m/s], currently predicted Nu using k-ω turbulence model are in the best accordance with measured data, especially at locations downstream the rib.

Hope this helpful.

Min.

PS: The bulk temperature (Tb) is assumed to be linearly increased, formulations for Tb can be referred to the definition in Ref.[3]. In addition, Menter et.al [4], who are from Ansys CFX Germany, also simulated flow and heat transfer for Rau et.als' rib model using k-ω and SST turbulence models. Results in Fig.2 are similar to theirs.

[1] Acharya S, Myrum T, Qiu X and Sinha S. Developing and Periodically Developed Flow, Temperature and Heat Transfer in a Ribbed Duct. International Journal of Heat and Mass Transfer, 1997, 40(2):461-479.
[2] Rau G, Cakan M, Moeller D, Arts T. The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel. ASME Journal of Turbomachinery, 1998,120:368-375.
[3] Baughn JW, Hoffman MA, Takahashi RK, Launder BE. Local Heat Transfer Downstreamof an Abrupt Expansion in a Circular Channel With Constant Wall Heat Flux. ASME Journal of Turbomachinery, 1984,106:789-796.
[4] Menter F, Carregal Ferreira J, Esch T, Konno B. The SST Turbulence Model with Improved Wall Treatment for Heat Transfer Predictions in Gas Turbines. Proceedings of the International Gas Turbine Congress 2003 Tokyo, 2003, 11.2-11.7, IGTC2003-TS-059.