Hello,

Has anyone done a SYSTEMATIC investigation of predicted heat transfer coefficients when yplus is out of the suggested ranges? (And more importantly, is willing to talk about it!)

Years ago I (carefully) did a flat plate benchmark and found my commercial code matched the DB correlation well. However, that model was carefully done - two layer, enough cells in the sublayer, hod.

What I wish I had was that data, and then the following cases also:

Half as many points in the sub-layer 1/10 as many points in the sub-layer 2 points in the sub-layer etc.

cases without two-layer model: non-two layer with yplus of 1 non-two layer with ylpus of 10 non-two layer with yplus of 30 (typical minimum of where it is supposed to be) non-two layer with yplus of 100 non-two layer with yplus of 200 non-two layer with yplus of 300 (typical maximum of where it is supposed to be) non-two layer with yplus of 500 non-two layer with yplus of 1000 etc.

What happens to all of the above cases when you run the various differencing schemes? How important is is to use variable fluid properties? What happens when you run other turbulence models?

I know my code works well when you do everything you are supposed to do to get heat transfer coefficients correct, but I don't know how far the code is off if you don't do what you need to do. This information would be useful for evaluating models where wall heat transfer has been included, but not in the detail it should have. (Do my h's change by 10% for a high yplus, or is it 3000%? etc.)

Thanks

Andrew

Dear Andrew

There is a study on turbulence modelling application on internal cooling system for gas turbine engine. The study also include the effect of y+ on high Reynolds number k-epsilon model on windage moment(shear stress on the rotating disc) and heat transfer rate on simplified model of rotating disc system. Comparisons of two layer model due to Wolfstein are also included.

Virr,G.P., Chew, J.W. and Coupland, J., 1994, Application of computational fluid dynamics to turbine disk cavities, J. Turbomachinery, 116, pp 701-708

From my understanding, on some cases of rotating disc system at certain flow conditions, the heat transfer rate on the wall may be related to heat transfer rate. In that case, increasing shearing stress may increase heat transfer rate.

(1). A good question. and here are simple answers. (2). When using a wall function approach, as long as Y+ is in the region ,say Y+ => 100 and still inside the boundary layer, the results are not sensitive to the first Y+ value. (3). When using a low Reynolds number model, even with small enough Y+, the computed heat transfer coefficient, most of the time ,is not accurate when compared with test data. ( In this case, it is repeatable but not accurate.) (4). When using a low Reynolds number model, with irregular coarse mesh, the result can be anything but repeatable. The accuracy depends on both the turbulence model , the numerical method and the formulation. (5).A couple of years ago, I computed several cases of flow over a flat plate with non-uniform cell distributions in x direction using triangular cells, the results showed that you can get almost any answer you want. The results obtained were a function of cell stretching in x direction. ( The code used was a widely used commercial code.) This strange behavior gradually disappeared when the cell sizes next to the wall all became less than the size of the linear velocity region. In other words, when you represent a linear curve by several non-uniform cells, the results are the same ( you have accurate solution). When the first cell size is outside the linear profile region, the result can be anything ( you don't have accurate solutions) because of the rapid changing profile. So, it is essential that you put enough number of cells in the computation to guarantee all flow variables are independent of the mesh. Remember that the shear stress, the TKE, the TKE dissipation, the velocity, the temperature, the eddy viscosity all have different profiles. Satisfication of continuity , momentum and energy equations does not guarantee that these profile distribution will be correct. So, my suggestion is: write a simple laminar flow code over a 2-D channel entrance, set the free stream and the wall temperature, and monitor the wall heat transfer distribution as a function of cell size and distribution. Even in this simple case, the cell size must be small enough and must be at the right location to give the correct answer.( try to divide the x distance into several segments and then use different stretched x cell distributions for each segment.)

Dear Andrew

With regard to discussion given by Mr John C. Chien, I have another paper by

Morse, A.P 1988 Numerical prediction of turbulent flow in rotating cavities J. Turbomachinery vol 113 pp 131-131

The paper discuss application of a low Reynold number k-e model on rotating disc system, and again the size of near-wall region goes to size such y+ < 0.5 ( laminar sublayer) to give the 'best' windage moment as well as the heat transfer rate

A. Aziz Jaafar

Gentlemen,

Thank you for your input. Perhaps I will crank through some of the cases I described and let you know what I find. I am particularly interested in the result when yplus is too high. (I hate reinventing the wheel, but sometimes it is necessary to get exactly what you want.)

Andrew