I am having some trouble in applying boundary conditions for the turbulence quantities.
Let's take the case of a duct. I know the velocity profile at the inlet. I could estimate the values of the turbulent quantities at the inlet. But, I do not know the profiles for the turbulent quantities.
Won't it be erroneous to set fixed values for the turbulent quantities while specifying a velocity profile at the inlet?
Suppose, I were to specify a fixed value for velocity at the inlet, it should be o.k. to have a single number for the turbulent quantities at the inlet. In this case, shear stress would be zero at the inlet and there would no creation of turbulent kinetic energy at the inlet and hence the problem would be well defined in this case.
What do you all think?
Thanks for your feed backs,
Re: Boundary Conditions
(1). The inlet is the place where you specify the conditions so that the problem can be defined and the solution obtained. You will have to supply or simulate the inlet conditions in order to define the problem uniquely. (2). There are several ways to approach this problem: (a). measure everything at the current inlet and use the measured data as the inlet boundary condition,(that is the reason why inlet profile measurement is required in test data bank type project) (b). measure portion of the flow variables and derive the rest of the flow variables using similar flow models,(when measurement is difficult) (c). Assume the inlet conditions based on analytical models,(pure simulation) (d). move the inlet location further upstream such that the inlet condition will develop by itself. For example, you can specify the condition at the begining of a long pipe, so that the flow will develop naturally to give the right condition entering the computational domain. This is the easiest way to do. (3). Simulation of flow does not have to be identical to the real thing, and it requires a lot of experience to simulate the boundary conditions so that you can get the information you are looking for.
Re: Boundary Conditions
When you say fixed velocity at the inlet, I take it that you want to use a plug flow profile for axial velocity. Even if the velocity profile is a constant at the inflow, the no-slip walls would create shear immediately downstream of the inlet. With high enough Reynolds number and white noise (which gives constant profiles for the turbulent quantities), you should be able to predict transition (if you are using a LES ro a DNS) and turbulent flow eventually. Since you have to predict transition before the turbulent flow becomes fully developed, you have to provide enough axial length for the flow to develop into a fully developed state. Because of the high axial length, such a computation is not likely to be very efficient.
Here is a bit more sophisticated and sound solution to your problem. You can use a temporally developing turbulent flow in a duct to feed your spatial simulation of turbulent flow in a duct of same size. Here is how it works.
Temporal simulation :
i) No-slip walls
ii) Periodic boundary conditions for velocity components.
iii) Step periodic pressure B.C. in the axial direction, i.e., P(L+x) = P(x) + "DP" where L is the length of your duct.
The step periodic pressure B.C. means that your are simulating a pressure driven flow. The pressure gradient balances the frictional forces at the walls (which depend on Reynolds number).
iv) The bulk velocity would depend on "DP" (and shear stresses at walls). Once the flow has reached a stationary state, you can use the bulk velocity to compute the Reynolds number and if it is higher than the required Reynolds number, reduce "DP" till the bulk velocity is lowered to give you the required Re. If the Reynolds number is lower than required Re, then increase "DP" till you reach the appropriate Re. You might have to set up a Newtons iteration to change "DP" at every 10 time steps to move your flow Re to the required Re.
Once you have the turbulent flow setup at the required Re, take a single plane of this flow and use it for inflow conditions to a spatial simulation. This approach requires two simulation and so it some what expensive but quite accurate.
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