Why Turbulence models are not universal.
 

Dear users

can any one guide in this regard.following is what i can answer for the question why turbulence models are not universal ?is this enough or i should add more.

Turbulence models:

1. Mixing Length Model :

This model is not suitable when convective and diffusive transport of turbulence are important .In channel flows turbulence is produced near the wall and is transported to the center line by diffusion. This model neglects diffusive transport and predicts zero turbulence near the center line.In recirculating flows,where convective transport is important, this model produces unrealistic results.

Anology between turbulent motion of fluid particles and random molecular motion, on the basis of which ,the equation for t is developed is not perfect. More generally this model is of little use in complex flows because of the difficulty in specifying lm.

2 .One equation Model : Like the mixing length model , this model also involves lm,that has to be specified . lm varies from one flow to other and it is difficult to specify lm in complex flows.

3. Two equation model:

k- model: This model assumes Production = dissipation .But this is not the case near the wall , where viscous diffusion also predominates.Thus this model does not work near the wall and it is valid only at high Re.Later modifications have been made to take care of curvature, pressure gradient ,etc but they are not universal.This model has not produced secondary motion in Square duct.

k- model: Does not work under curvature . Near free stream it does not predict correct results.

This model is unreliable for

1. Seperated flows

2. flow over curved surfaces

3. non circular ducts. The difficulty is traced to Boussinesq eddy-viscocity approximation.

4: RSM: Inorder to over come the isotropic eddy viscocity assumption this model uses separate equations for the Re stresses.( six equations for 6 RS).Thus this model is computationally intensive as it uses 11 equations.

Despite of complexity , this model produces good results in flows with

1.Curved stream lines

2. secondary motion.

3.system rotation.

5. ASM: This model is called so because it uses algebraic relations instead of differential relations for RS.Provides good prediction of

1. Curvature flows.

2. System rotation.

ADvance thanks. senthil k.

Re: Why Turbulence models are not universal.
 

(1).Stop eating the garbage! (2). Within the framework of Reynolds Averaged equations, there are Reynolds stresses terms in the averaged equations. (3). No one knows what to do with these terms(statistical average terms) in the equations. I guess, one can measure these terms for any flow field, point-by-point. (4). So, we have to come up with a way to obtain the Reynolds stresses terms, if we want to solve the Reynolds Averaged equations. (5). Therefore, we are forced to model these terms, using equations for each stresses terms, using eddy viscosity concept, through mixing length formula, solving tke (k) or k-and-epsilon equations, etc...etc... (6). This is simply because, so far, there is no way to know what to do with the Reynolds stresses term. (Unless you use the DNS). (7). So, you are free to use any turbulence model you like, as long as you are happy with the results. And there is no evidence that you will get better solutions if you solve more equations in the model. (8). But if you systematically refine your model and validate the results using the reliable test data, then you are likely to get improved solution for that particular problem. (9). And In the eddy viscosity concept, we shift the burden from the Reynolds stresses through velocity gradient field to the calculation of the eddy viscosity, which is basically an unknown scalar function. (10). For any flow problem, if you happen to know the distribution of the eddy viscosity in the flow field (zero at the wall to some finite values in the flow field),then you can plug it into the definition to compute the Reynolds stresses through the velocity gradient field. (10). If you don't know the eddy viscosity distribution (a length scale), you can further model it using 1-equation, 2-equation models. (11). Regardless of what you do, the goal is the same, that is to specify the eddy viscosity and/or to calculate the Reynolds stresses. (which are just the unknown statistical average terms) (12). It is similar to the integral-differential equations which contain differential terms as well as integral terms. Now the equation contains the averaged velocity terms and the statistical average terms. The Reynolds averaged equation is the end, not the begining. So, if one can obtain a solution, it must not be Universal. (The Reynolds equations say that there is no way you will be able to solve this equations. But, if, for a problem, we develop a model to replace those terms, we can solve another set of equations and obtain some solutions. If these solutions are validated for that problem, the results can be very useful.) (13). It is like developing a formula to calculate the winning lottery number combination. To be a winner, you must validate it. (it is no good if someone else is winning)

Re: Why Turbulence models are not universal.
 

Dear J.C.Chien

I feel that you are trying to make me know that i can use any model if iam satisfied with the result.But my motive was to know why people go for LES ,While we have this much good models ( conditions apply).What LES can do more than other models and what it can't do to meet the physics. Expecting your reply. Thanks in advance senthil k.

Re: Why Turbulence models are not universal.
 

(1). I don't know. (2). I don't read LES. (3). I don't use LES in my job. (4). I am open minded. I guess, if you have time, and computer resources, and don't know how to model the turbulence for design application purposes, then, one way to let the computer do the number crunching hard work is to try LES or DNS. (5). This same question was asked in a cfd short course almost 15 years ago, Dr. W. Rodi's answer was if it was going to take over six months to run a case, it was not practical approach. He was teaching the turbulence modeling in that short course. (6). I think, in the research field, the subject does not have to be practical. (7). On the other hand, if we start taking LES approach in design applications, cfd approach and results will definitely not be accepted in the design and analysis loop. (8). Even if the DNS becomes practical, you will still see people using inviscid equations. (8). Advantages of LES over Reynolds averaged turbulence models?, I don't know. I guess, it is a research field, and Journals love to publish something new. The two-equation k-epsilon model is almost 30 years old, and the Navier-Stokes equation is over 100 years old. (9). I think, you can read more LES papers to find out more about the LES. Remembering the printed information is not very useful, unless you can understand it and make use of it. (10). DNS and LES are still transient simulation approach , which require huge amount of computer resources and time. The usefulness is still problem dependent. (11). Using a super-super IBM computer to simulate nuclear explosion? Well, that's what I say, you are free to do anything you like, if you are happy with the results. I mean, if you have the time and resources to do something, you don't have to justify it, you simply do it.

Re: Why Turbulence models are not universal.
 

1)I agree with John Chien's idea. 2)LES should be more accurate if it's correctly applied(time marching step,filter are all appropriate). 3)LES is modelling only the very high friquency part of the turbulence spectrum, but RANS modelling the whole spectrum. 4)LES is expensive, because it require much more CPU time and huge computer resources.