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Mach Number Effects on Rough-Wall Turbulent Boundary Layers

  • Author(s): Alvarez, Morad;
  • Advisor(s): Kim, John;
  • Eldredge, Jeffery D.
  • et al.

The effects of surface roughness on compressible turbulent flow have not been studied as closely as the effects of surface roughness on incompressible flow.

To date, our knowledge of fully-rough high-speed turbulent flows comes from experiments, large eddy simulations, or direct numerical simulations of rough-wall channel flows.

This dissertation seeks to extend our understanding of rough-wall boundary layers by examining the effect of the freestream Mach number.

A previously-verified fifth-order hybrid weighted essentially non-oscillatory scheme with geometries imposed by a third-order cut-stencil method was modified to handle turbulent inflow boundary conditions and spanwise periodicity. The turbulence capabilities of the code were then validated against published results of a Mach 2.5 smooth-wall turbulent boundary layer.

Two direct numerical simulations of different freestream Mach numbers, 2.5 and 5.0, were conducted.

The results show that scaling the root mean square (RMS) of velocity and vorticity fluctuations with the local density accounts for the difference in magnitude.

Scaling the RMS of non-dimensionalized temperature fluctuations by the ratio of wall temperature and freestream temperature, provides reasonable collapse between both simulations.

Similarly, scaling by the ratio of wall density and freestream density offers reasonable collapse for the RMS of density fluctuations.

Both of these scalings offer good collapse regardless of the surface topology.

The Favre-averaged Reynolds shear stresses exhibit increased magnitude in regions with local compression.

Conversely the Favre-averaged Reynolds shear stresses decreased in regions with increased expansion.

A similar trend was observed for the wall-normal Favre-averaged Reynolds stress, but is not as pronounced.

The location of the expansion and compression waves from the edges of the roughness is directly affected by the local Mach angle.

For the \mf case, the Mach angles varied much more resulting in regions of decreased dilatation.

The freestream Mach number plays an indirect role in setting the shift in the log-layer.

The compressible results from both Mach numbers do not compare well to incompressible results.

This could be due to the different topologies.

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