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July 21, 1999, 18:16 
Use of Scaling in numerical Analyses?

#1 
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While scaling is commonly used in wind tunnel experiments, to my knowledge, it is not used with numerical analyses. Any comment.
I am a graduate student working on my mastes in mechanical engineering. I have been modeling 2D and 3D dual mode combustion chambers, primarily the japan national aerospace plane. I have found that this geometry has tremendous upstream interaction and the flow is dominated by the combustion heat release. In such a case, a 1/4 scale model accurately (?) predicts the flow field and the wall pressure. Of course many simplications have been made. But if anyone has any comments, i would greatly appreciate insight into the arena of scaling and numerical modeling. Oh forgive me but i am using a the commercial code fluent for the study. 

July 22, 1999, 09:06 
Re: Use of Scaling in numerical Analyses?

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In experiments, scaling have to be carried out very crrefully. For example there has been some development recently in the field of 'micro' flying machines: An Helicopter the size of an insect. At this scale the viscous effects are dominant (because the size l of the machine is so small, the Reynolds number R=l*v/nu is indeed very small too, unlike for real helicopters). Preliminary test were made with much bigger helicopter (say of the order of a feet or so) and the experiments were carried out in the water to simulate the low Reynolds number. So in short, when one is doing a scaling in the experiments, one has to change some parameters (temperature, density, viscosity, in order to change eventually the Reynolds number) so that the scaling is valid.
In the computer modeling, once a problem is chosen with given parameters, it can in fact represent any scaling of the real problem but it might also represent something else. For example if you scale the micro helicopter to the metersize one, then the flow does not represent air but water, etc... In most of the cases I am studying, the equations are in fact written in nondimensional form. So that the scaling is in fact not at the time of writing or solving the equations, the scaling is made when one has to interpret the results. Some experiments are being carried out in Los Alamos (LANL) on a scale of Laboratory experiments, to represent flows in Astrophysics on a scale of lightyears and beyond. So scaling is in fact a part of modeling. PG. 

July 25, 1999, 22:33 
Re: Use of Scaling in numerical Analyses?

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(1). The sole advantage of using the CFD approach over the wind tunnel testing is that the fullscale problem can be solved in CFD approach directly. (2). In the wind tunnel testing, one can change the pressure, the property of the gas, the temperature of the flow to match the Mach number, the Reynolds number etc, to some extent only. (3). When a small wind tunnel is used, a scaled model has to be used in order to fit the test section and obtain meaningful resutls. If one can not change the test section pressure, temperature to match the Mach number and the Reynolds number, then the data obtained will not match the fullscale conditions. This is why after the model testing is done, it is still necessary to conduct the fullscale flight test. (4). The problem exists in other field such as the turbomachinery testing, combustor testing, etc... (5). In the wind tunnel testing, normally one is trying to match first the Mach number. Then, there will be socalled Reynolds number effect because the data obtained will be at a different Reynolds number.( the nature of the boundary layer, laminar, transitional, turbulent, the viscous loss, etc... all will be different. this is especially a problem at a transonic speed) (6). There are additional problems associated with the reacting flows. It is not easy or possible to simulate the chemical reaction rate. In this case a subscale model results will be different from that of the fullscale testing. This also depends on the Mach number in the combustion chamber, whether it is subsonic, transonic, or supersonic. So, sometimes the flow fields are similar but the chemistry is different. (7). In the wind tunnel testing, the scale model problem is solved by moving the scale of the model up and test it in a larger wind tunnel or wind tunnels which can simulate the flight condition closer. (8). In the CFD analysis, the problem is even bigger in the turbulence modeling, reacting flow modeling, and mesh generation. I would say that the current state of the art in the reacting flow CFD is still a long way from the wind tunnel testing level of accuracy. But since the CFD simulation does not cost much except the machine and computing time, it is a short term solution, better than nothing. (9). As for the results from a commercial code, it is essential to validate the result first before one can intrepret the computed results. ( mesh quality, turbulence modelling, solution scheme,...all have important impact on the solution) It is like testing a small scale model in a transonic wind tunnel, the results obtained is likely to be quite different from that of the flight test. I don't want to say that it is wrong because that is normally the first step in the process to move on to a bigger wind tunnel or test cell. As for the reacting flow CFD, a better turbulence model and reacting flow model is required in order to make use of the computed results. Unfortunately,you can't get such models from a code or from a wind tunnel.


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