Since von Karmen proposed the similar solution of rotating disk problems in 1921,why most of works focus on the incompressible field including experiments,theoretical analysis and numerical simulation? Is it beacuse compressible BEK boundary layer problem is too difficult to simulation and do experiments?
The reason why most research has focused on incompressible flow in rotating disk problems and other similar setups is indeed because compressible boundary layer problems are harder to handle both experimentally and numerically. The added complexity of compressible flows, from temperature and pressure variations to shockwave formation and more complex numerical methods, makes them more challenging. As a result, there has been a historical preference for the simpler incompressible flow models in many studies.
Soufyane Ladeg
Thank you for your insightful comment! So your opinion is the most prossible reason for this phenomeno is the difficulties on numericial method and experiments.But not the nature of this problem. Dose it means that there indeed has a large research gap and the compressible setup is worth to study?
The rotating disk term adds an acceleration term to the conservation equations and the friction interaction models (turbulence or viscous) need to be rewritten to include the added energy gradient. This has been done for ballistic objects (PhD by M Combrink) but if the acceleration is small enough (typically anything less than 10 - 15 g) the flow can be treated as pseudo steady as the variations in energy density/pressure are not significant.
Since the flow in the boundary layer is mostly subsonic, unless you have very high pressure gradients due to the rotation, it is not going to change the model significantly. Consequently, incompressible solutions give a good enough answer for most engineering problems.
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