I hope somebody can explain a few things to me.

I'm just looking at some CFD turbulence modeling texts and I've got some basic (?) questions. Considering the difference between algebraic and two-equation models it seems that the algebraic approach obtains tubulence quantities from only local influences. If this is so, how is the effect of a turbulent freestream modeled. Surely the presence of far-field turbulence plays a part in the behavior of the flow when it attaches to some surface. Along these same lines, it seems, then, that for two-equation models, inflow boundary conditions must be known for the turbulence quantities. What's the trick here? Even if the inflow kinetic energy level is known in the freestream, how does it behave as a wall is approached? Are Neumann boundary conditions appropriate? Turbulent energy seems like something that would be pretty much convected into a domain, i.e. with primarily upstream influences.

Secondly, how is turbulent transition on a body surface enforced? I see occasions where transition is specified along a predetermined line on a body. (I assume such a prespecified line must arise experimentally) Upstream of this line is the turbulent viscosity simply set to zero in spite of the model's (algebraic or whatever) results?

Lastly, if the inflow has a non-zero turbulence level, will the boundary layer forming on a surface in the flow be immediately turbulent?

Sorry if these questions are goofy. I appreciate any responses. Thanks.

Your questions are very relevant. I'll try to answer them one by one briefly:

1. difference between algebraic and two-equation models?

An algebraic model is based on the local flow and geometry - usually it is an algebraic formula which gives the eddy-viscosity as a function of strain, distance to wall etc. This means that, as you point out, these models can not account for any history effects associated with the turbulence, like for example the inlet turbulence level. The inlet turbulence level can be accounted for by using ad-hoc correlations which relate constants etc. to the inlet turbulence level. Another common thing you see is that the inlet turbulence level only comes in in the transition criteria.

A 2-eqn model solves two extra transport eqations for the turbulence (usually turbulent kinetic energy, k, and a lenghth-scale/time-scale in the form of dissipation, epsilon). This means that you to some extent can account for history effects, like the inlet turbulence level. Naturally you also need to know the inlet level of these properties, or at least have some clue about their level.

1b. Surely the presence of far-field turbulence plays a part in the behavior of the flow when it attaches to some surface

Algebraic models are usually only used in wall-bounded flows. When you have separation and re-attachment these models often fail... but as always there are exceptions.

2. Even if the inflow kinetic energy level is known in the freestream, how does it behave as a wall is approached?

Close to the wall it goes to zero. The behaviour further out in the boundary layer is more complex. Please check a good turbulence book and you'll find lots of details.

3. Are Neumann boundary conditions appropriate?

No, the wall-boundary condition is Dirichlet (k=0). You might use Neuman at the outlet, but that depends entirely on what kind of solver you are using. Note that you can't just use a common high-Re k-epsilon model down to wall by only applying a dirichlet bounday condition on k - you have to either fit the solution to a wall-law or use special damping functions to assure correct profiles in the boundary layers.

4. Turbulent energy seems like something that would be pretty much convected into a domain, i.e. with primarily upstream influences?

Simply speaking, as long as you don't have any shearing in the flow you don't have any production of turbulence, hence the turbulence is just convected downstream, but of course the turbulent energy decays as you come further downstream.

5. how is turbulent transition on a body surface enforced?

There are as many tricks as there are researchers I guess. Some people use advanced intermittency models to make a smooth transition from laminar to turbulent flow, others just switch on the turbulence model at a specific location. Transition prediction is a large research subject and it is impossible to give a more exact answer. There are no techniques which are general - you have to use something which is suitable for your specific application.

6.if the inflow has a non-zero turbulence level, will the boundary layer forming on a surface in the flow be immediately turbulent?

No, you usually have a laminar region followed by transition and a turbulent region. For very high turbulence levels and certain flows the laminar region can be very small though. If the transition is caused by convection and diffusion of free-stream turbulent energy into the boundary layer it is usally called a by-pass transition. This kind of tranistion is very different from a natural transition where growing instabilities and turbulent spots cause the transition.

>A 2-eqn model solves two extra transport eqations for the turbulence (usually turbulent kinetic energy, k, and a
>lenghth-scale/time-scale in the form of dissipation, epsilon). This means that you to some extent can account for history
>effects, like the inlet turbulence level. Naturally you also need to know the inlet level of these properties, or at least have
>some clue about their level.

The calculation of turbulent viscosity is based on transported quantaties but the Reynolds stresses are then modelled using only local flow conditions. The only slightly confusing thing is that we've already transported turbulent kinetic energy then we go and recalculate the effects of the stresses based on isotropic turbulent viscosity and local gradients.

True. The Boussinesq assumption is a big weakness in these models. It fails terribly on flows with large normal strain (stagnation regions, flows with strong acceleration etc.) and these models have difficult to account for curvature effects etc. If anisotrpy plays an important role in your flow you can't use these models directly off the shelf.

You can also use different variants (NLEVM, EARSM ..) of non-linear stress-strain relations and thereby account for local anisotropy effects, but then you wont get any history effects included of course. You can go one step further and use a 3-eqn model like for example the Craft, Launder, Suga k-epsilon model, which has a third transport equation to for the anisotropy. Finally you have the full RSM approach, where you transport all components of the reynolds stress tensor, and thereby also transport information about anisotropuy etc. For most application this approach is too expensive, too unreliable and too difficult to use though.

Turbulence modeling is fun - you can always critsise other models, nothing works well for all cases anyway ;-)