What is the non-linear model........????

I am not sure. But I think it is related to a turbulence model. It is probably developed recently to improve the performance of a turbulence model. I have not used it, maybe you can do some digging for me. Sometimes, people use a name with a stronger flavor for certain reasons. In physics, people tend to do just that in elementary particle field. Well, since I am not using this non-linear model, you can safely ignore it. Maybe, those who invented would like to say something about it.

A non-linear model is a turbulence model which has a non-linear relation between the Reynolds stresses and the strain of the fluid. This is in contrast to the many classical linear models which are based on the Boussinesq assumption that the principal axes of the reynolds stress tensor are coincident with those of the strain tensor (ie that the reynolds stresses can be modeled with a linear relation to the strain). There are many different flavors of non-linear models.

Dear Daijen,

Nonliner Model was developed by Prof. Speziale, a person who has worked extensively on k-epsilon modelling. This is developed to account for anisotropy of turbulence. If you take a look on the difference of normal Reynold stresses in Parallel Plate Channel Flow, the linear k-epsilon model gives a zero difference while a non-linear model do give a difference in these stress values which agree well with the experiments of J. Laufer.

It is observed that this difference of normal stresses is resposible for the secondary flows in pipe bend. As linear k-epsilon model gives a zero difference it does not predict this secondary flow in pipe bend while nolinear k-epsilon model has predicted it reasonably well. In short for simulating flow in a curved geometries nonlinear will provide best results compared to liner model.

You could find a large information in the paper published by Spezial in Journal of Fluid Mechanics. The Details I'll provide latter.

With regards

Bipin

Dear Bipin,

I'm sure you meant to elaborate on this if you had enough time. I thought I could save your time by adding my two cents.

When it comes to secondary flows, there are largely two different kinds. I suppose you're talking about the secondary flow caused by anisotropy of normal stresses. This class of secondary flows due to turbulent stresses are often refered to in the literature as "Prandtl's second kind of secondary motion". They occur at the corners in ducts with having sharp corners and even in external flows with corners (e.g. at wing-body junction), often being used as a touchstone for testing "non-isotropic eddy viscosity models" such as nonlinear or anisotropic k-epsilon models and second-moment closure models. However, their scales are normally small and therefore

Perhaps more important, especially in industrial applications, are the secondary flows of non-turbulent origion. Often being tagged as "Prandtl's first kind of secondary motion", they are caused by pressure gradient, centrifugal force, etc, not by turbulence. Such secondary flows exist therefore even in laminar flows in curved ducts and pipes and others.

Since, regardless of the origin of secondary flows, turbulence will continue to affect evolution of the secondary flows from their birth throughout their lifetime, more advanced turbulence models that can better represent turbulence (anisotropy, transports and history effects, etc.) have better overall chance of predicting the secondary flows more accurately.

Best regards, Sung-Eun