Large-eddy simulation of a spatially-evolving supersonic turbulent boundary layer at
Introduction
The study of supersonic turbulent boundary layers (STBL) is crucial for understanding basic flow physics in turbulent wall-bounded flows. The study has also a great importance in many industrial applications, such as high speed external and internal aerodynamics [2], [3], [4], [5], combustion and detonation [6], [7]. For adiabatic STBL, and due to viscous heating, compressibility effects arise mainly from the large change in the fluid properties (variable-density flow). It is then commonly concluded that adiabatic supersonic turbulent boundary layers at moderate Mach numbers (typically ) can be studied using the same models as low-speed flows, as long as the variations in the mean flow properties are accounted for (see for example Morkovin [8], Bradshaw, [9] and Smits & Dussauge, [10]). Adiabatic supersonic turbulent boundary layers were first investigated through experiments, in order to validate the Morkovin’s hypothesis (for a large data compilation, see Fernholz & Finley, [11]).
Three-dimensional numerical simulations of turbulent boundary layer are usually classified as direct Navier–Stokes simulations (DNS) and large-eddy simulations (LES). In DNS, all relevant scales of motions are numerically resolved and therefore a detailed representation of a turbulent flow field can be obtained. In LES, only large energy-containing eddies are numerically resolved. This is accomplished by filtering-out the high-frequency component of the flow field and using the low-pass-filtered form of the Navier–Stokes equations to solve for the large-scale component only. The effects of the filtered-out small-scale fields on the resolved fields are accounted for through the so-called subgrid-scale (SGS) model. Many different LES approaches have been developed for the construction of SGS models; some of these are described in this paper, whose objective is to address their applicability in the case of supersonic turbulent flow over a flat plate at a zero-pressure-gradient. Our focus here is on developing a methodology for assessing LES approaches on a representative flow, which is the obvious pre-requisite before applying these models to more complex geometries.
Among others, Spyropoulos & Braisdell () [12] reported LES of spatially-evolving supersonic turbulent boundary layer at Mach number . Because of the low considered Mach number, the modeling of the isotropic part of the shear stresses was not found to have a considerable effect on the skin-friction coefficient, . The insufficient amount of turbulent transport was attributed to the use of the dynamic Smagorinsky model (DSM), in which the eddy viscosity is computed using the smallest resolved scales. Hadjadj et al. () [13] recently studied spatially-evolving STBL with cooled walls via well-resolved LES’s at low Reynolds numbers. Also, supersonic flat-plate boundary layers have been investigated by Yan et al. () [14] using monotonically integrated large-eddy simulation (MILES) approach. In this simulation, the numerical dissipation induced by the scheme substitutes the SGS eddy viscosity, mimicking from an energetic view-point the action of SGS terms on the flow dynamics. Their results indicate that the subgrid-scale effects can be adequately modeled using MILES without the need for the Smagorinsky model.
In LES, the accuracy of the resolved scales highly relies on the mesh size. Locally refined grids usually lead to more resolved turbulent energy but with costly CPU time and memory requirements. The strategy in LES is then to make the best compromise between accuracy and computational costs. Dissipation of a given SGS model may originate, in different proportions, either from the resolved velocity fluctuations or from the mean-averaged velocity gradients. In the recent work of Ben-Nasr et al. (2016) [15], we presented a detailed study of a spatially-evolving STBL over a flat plate at and . Different SGS models (namely the DSM, the wall-adapting local eddy-viscosity (WALE) model and the Coherent Structures model (CSM)) as well as grid resolutions were used in order to compare the contribution of the SGS modeling on turbulence. The advantage and superiority of CSM and WALE in resolving high-speed compressible turbulent boundary layer over flat plate is clearly established in that study over computationally costly DSM. It is also interesting to mention the performance of Implicit LES (ILES) with respect to other models. In the present study, we extend the previous work for higher , while using wider spanwise domain for various LES models. Much coarser grid resolutions have been employed to assess the effectiveness of the LES modeling compared to well-resolved LESs presented in Ben-Nasr et al., (2016) [15]. We further highlight the interesting features of these LESs in light of the near wall interactions of the fluctuating quantities as a natural sequel of the previous work. After a brief description of the numerical methodology and the problem setup in Section 2, we present the flow analysis in Section 3. Turbulence statistics up to fourth-order moments are reported in order to assess more specifically the near-wall behavior of the SGS models. Finally, the conclusions are drawn in Section 4.
Section snippets
Numerical methodology and SGS modeling
For sake of brevity, we restrict the description of the governing equations used for the present study. The details of the numerical methodology as well as the modeling aspect can be found in Ben-Nasr et al., (2016) [15]. The convective fluxes are discretized using a sixth-order locally-conservative skew-symmetric split-centered formulation [16]. The viscous fluxes are discretized using a fourth-order compact central differences scheme. Time advancement is assessed by a standard explicit
Basic flow organization
It is known that the inner part of the boundary layer is occupied by alternating streaks of high- and low-speed fluids. These streaks are presumed to derive from elongated, counter-rotating streamwise vortices near the wall. At , those streaks are shown to significantly contribute to the turbulence production, which occurs during the bursting process: low-speed streaks would gradually lift up from the wall, oscillate, and then break up violently, ejecting fluid away from the wall and into
Conclusion
In this paper, large-eddy simulations of a spatially-evolving supersonic turbulent boundary layer over a flat plate are performed using three different SGS models. An Implicit LES (a subset of under-resolved DNS) is also investigated to assess its applicability and to see whether small truncation terms of a sixth-order numerical scheme would themselves serve as SGS models. The results are compared to both DNS and theoretical considerations and showed an overall acceptable agreement. The study
Acknowledgments
This work was performed using HPC resources from GENCI [CCRT/CINES/IDRIS] (Grant 2016-0211640) and from CRIANN (Centre Régional Informatique et d’Applications Numériques de Normandie, Rouen. The authors acknowledge Prof. Sergio Pirozzoli, University of Rome La Sapienza, for providing his DNS data for validation.
References (39)
- et al.
Numerical investigations of transient nozzle flow separation
Aerospace Sci. Technol.
(2016) - et al.
Numerical study of shock/boundary layer interaction in supersonic overexpanded nozzles
Aerosp. Sci. Technol.
(2015) - et al.
Effect of wall temperature in supersonic turbulent boundary layers: A numerical study
Int. J. Heat Mass Transfer
(2015) Generalized conservative approximations of split convective derivative operators
J. Comput. Phys.
(2010)- et al.
Application of a local SGS model based on coherent structures to complex geometries
Int. J. Heat Fluid Flow
(2008) - et al.
Large-eddy simulation of turbulent channel flows with conservative iso scheme
J. Comput. Phys.
(2011) - et al.
A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulation
J. Comput. Phys.
(2003) - et al.
Statistical behavior of supersonic turbulent boundary layers with heat transfer at M=2
Int. J. Heat Fluid Flow
(2015) - et al.
Turbulence in supersonic boundary layers at moderate Reynolds number
J. Fluid Mech.
(2011) - et al.
Supersonic flow control
Shock Waves
(2015)
Unsteady flow conditions during dual-bell sneak transition
AIAA J. Propul. Power
Mean structure of one-dimensional unstable detonation with friction
J. Fluid Mech.
Computational study of detonation-wave propagation in narrow channels
Phys. Fluids
Effect of compressibility on turbulent flows
Compressible turbulent shear layers
Annu. Rev. Fluid Mech.
A critical compilation of compressible turbulent boundary layer data
AGARDograph
Large-eddy simulation of a spatially evolving supersonic turbulent boundary layer flow
AIAA J.
Large-eddy simulation of supersonic flat-plate boundary layers using the monotonically integrated large-eddy simulation MILES technique
J. Fluids Eng.
Cited by (12)
Heat transfer enhancement of Water-Al<inf>2</inf>O<inf>3</inf> nanofluid in an oval channel equipped with two rows of twisted conical strip inserts in various directions: A two-phase approach
2020, Computers and Mathematics with ApplicationsImprovement of the scale-adaptive simulation technique based on a compensated strategy
2020, European Journal of Mechanics, B/FluidsHybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence
2022, Acta Mechanica Sinica/Lixue XuebaoModelling and simulation of tidal energy generation system: a systematic literature review
2022, International Journal of Advanced Technology and Engineering Exploration