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Direct Numerical Simulation (DNS) of compressible spatially-developing turbulent boundary layers (SDTBL) is performed at a Mach number of 2.5 and low/high Reynolds numbers over isothermal Zero-Pressure Gradient (ZPG) flat plates. Turbulent inflow information is generated via a dynamic rescaling-recycling approach (J. Fluid Mech., 670, pp. 581-605, 2011), which avoids the use of empirical correlations in the computation of inlet turbulent scales. The range of the low Reynolds number case is approximately 400-800, based on the momentum thickness, freestream velocity and wall viscosity. DNS at higher Reynolds numbers (~3,000, about four-fold larger) is also carried out with the purpose of analyzing the effect of Reynolds number on the transport phenomena in the supersonic regime. Additionally, low/high order flow statistics are compared with DNS of an incompressible isothermal ZPG boundary layer at similar low Reynolds numbers and the temperature regarded as a passive scalar. Peaks of turbulence intensities move closer to the wall as the Reynolds number increases in the supersonic flat plate. Furthermore, Reynolds shear stresses depict a much larger "plateau" (constant shear layer) at the highest Reynolds number considered in present study.
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Implicit Subgrid-Scale Modeling of a Mach 2.5 Spatially Developing Turbulent Boundary Layer
We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy (u′ vs. t′) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., Cf and UVD+). iLES significantly overpredicts the peak values of u′, and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers.
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- Award ID(s):
- 1849243
- PAR ID:
- 10322170
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 24
- Issue:
- 4
- ISSN:
- 1099-4300
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/e24040555
