### Notes on "Review and assessment of turbulence models for hypersonic flows"

On the heels of the recent PECOS center announcement and my recent advisor choice, I'm taking some baby steps to prepare for my first summer of graduate research. On a recommendation from Prof Moser, I'm reading through a 2006 survey of hypersonic turbulence models by Roy and Blottner and cooking up naive questions/notes:

- What are the effects of "hypersonic mixing layers"?
- For a hypersonic flow result that uses ideal gas relations, what are the general effects of introducing non-ideal constitutive laws for gas behavior?
- What are the additional challenges behind predicting the natural transition to turbulence in hypersonic versus other flows?
- DNS is computationally expensive, and RANS/LES are comparatively cheap. How much cheaper are they for the same flow parameters and grid?
- The article sounds like many people cook incompressible turbulence models and then expand them with compressible terms. Does anyone work in reverse and treat the incompressible as a special case of a compressible model?
- What are the differences between the full Navier-Stokes, thin layer Navier Stokes, parabolized Navier-Stokes, viscous shock layer, and boundary layer equation formulations? When are each of them preferred? What are their effects on uncertainty in the simulation results?
- What is the reason for artificially limiting the production-to-dissipation ratio of turbulent kinetic energy? How could any model requiring this kneecapping give reasonable results?
- What's the background behind "... for computational fluid dynamics simulations, the residual reduction levels correlate quite well with the actual iterative error in the flow properties" ?
- Is there an open database of turbulence results in the way that the bioinformatics community makes its raw data available for consumptions? E.g. ERCOFTAC
- Which of the cases listed on pages 477-8 and in ERCOFTAC are of most interest to us in PECOS? Expect Holden reference 43 to be of interest.
- What are the particulars between Van Driest II theory? What causes Roy and Blottner to up the bound to 5% from 3%? See references 133 and 134.
- What is wall skin friction?
- What approaches are used to transform flat plate turbulence results to other geometries? E.g. sharp cone as mentioned on page 479.
- What are the differences between the "perfect gas model" and ideal gas model?
- Almost all of the experimental results discussed are under Mach 12. Will we run into problems with validating against lower Mach results and then simulating higher Mach numbers?
- Details surrounding "the elliptic mathematical character of the separated flow region, these pitot surveys should be used with caution".
- What is a turbulent Prandtl number?
- What are incompressible coordinates?
- I need to review concepts of fully developed boundary layers. And other concepts. Badly.
- What exists besides RANS/LES approaches to model turbulence effects? Are there other schools of thought around dealing with the computational complexity of the Navier-Stokes equations?
- Which of the models listed in Table 4 are relevant to the current PECOS efforts? Did any of the models/areas survive/persevere in the funding dry spell over the last decade?
- Is the distinction between one and two equation models primarily done for computational cost reasons?
- Any good background on general theory of turbulence from a lay perspective? Any historical reading on the evolution of turbulence research from both a mathematical and engineering point of view?
- Roy and Blottner require integration to the wall in all reviewed models and don't examine "wall functions"? Why?
- Lots of the two equation models are based on a k-epsilon or k-omega foundation. Are these classifications or common ancestors which then tend to be further specialized/improved? See reference 152 and the revised model in 153. See reference 159 and 6.
- There is lots of mention of "adverse pressure gradients" when talking about the advantages of k-omega over k-epsilon models. What qualifies as an adverse pressure gradient?
- In modeling turbulence, is the general goal to have the minimal error with respect to quantities of interest? Or is it to be bounding/conservative so that model results can be "safely" applied to engineering problems? Generally, do people take an engineering or a science mindset when constructing and using turbulence models?
- Can models be designed to emphasize accuracy of some quantities of interest? Or are they more of a try-it-out-and-see-what's-good approach?
- Why is grid refinement recommended as the next checkmark to add to model validation studies? What causes researchers to generally either not do it or to not report detailed results when they do?
- See reference 156 for Rodi's k-epsilon model, which seems to have good results according to the conclusions in section 4.6. What causes it to work well? What causes its weaknesses upstream of the interaction region?
- What is shock unsteadiness?
- What are the reasons for model sensitivity to y^{+} spacing?

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