Extension of equilibrium turbulent heat flux models to high-speed shear flows

We investigate the fluctuations of thermodynamic state-variables in compressible aerodynamic wall-turbulence, using results of direct numerical simulation (DNS) of compressible turbulent plane channel flow. The basic transport equations governing the behaviour of thermodynamic variables (density, pressure, temperature and entropy) are reviewed and used to derive the exact transport equations for the variances and fluxes (transport by the fluctuating velocity field) of the thermodynamic fluctuations. The scaling with Reynolds and Mach number of compressible turbulent plane channel flow is discussed. Correlation coefficients and higher-order statistics of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables from a well-resolved DNS are analysed. Implications of these results both to the understanding of the thermodynamic interactions in compressible wall-turbulence and to possible improvements in statistical modelling are assessed. Finally, the required extension of existing DNS data to fully characterise this canonical flow is discussed.

Section: Temperature Variance and Heat-fluxesmentioning

confidence: 99%

Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow

Gerolymos

Vallet

2014

“…Models proposed for turbulent heat flux or energy flux can be used for this purpose. For example, Bowersox (2009) presents the following algebraic model for the streamwise energy flux in a zero-pressure-gradient boundary layer:…”

Section: Application To Shock-boundary Layer Interactionsmentioning

confidence: 99%

Evolution of enstrophy in shock/homogeneous turbulence interaction

Sinha

2012

Interaction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier-Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of k-equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock-boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

“…An algebraic closure model for the turbulent heat flux in high-speed shear flows has been developed by Bowersox (2009), and used to predict velocity and temperature profiles of supersonic and hypersonic boundary layers with high accuracy. Bowersox (2009) shows that large improvements in near-wall predictions can be made by using a sophisticated turbulent heat flux model and accounting for variable Pr t effects.…”

Section: Energy Equation Closuresmentioning

confidence: 99%

“…Bowersox (2009) shows that large improvements in near-wall predictions can be made by using a sophisticated turbulent heat flux model and accounting for variable Pr t effects.…”

Section: Energy Equation Closuresmentioning

confidence: 99%

“…For example, the thermal boundary condition at the wall -adiabatic versus constant temperature, cold versus heated -can have a major influence on the velocity field. The closure model for turbulent heat flux (or equivalently turbulent Prandtl number) plays a critical role, see Bowersox (2009). Furthermore, low-Reynolds-number and wall-reflection physics which are important in subsonic boundary layers may also play a vital role.…”

Section: Comparison Against Two-equation Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Toward second-moment closure modelling of compressible shear flows

Gómez

Girimaji

2013

Compressibility profoundly affects many aspects of turbulence in high-speed flows, most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. We develop a unified framework for modelling pressurerelated compressibility effects by characterizing the role and action of pressure in different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for pressure-strain correlation, pressure-dilatation and dissipation evolution equations. The closure coefficients are established using fixed-point analysis by requiring consistency between model and DNS asymptotic behaviour in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing layers and boundary layers. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing Mach number are all well captured. High-speed boundary-layer results are also adequately replicated even without the use of advanced thermal-flux models or low-Reynolds-number corrections.