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

2014 ◽  
Vol 757 ◽  
pp. 701-746 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Correlation Coefficients ◽  
Statistical Modelling ◽  
Transport Equations ◽  
Wall Turbulence ◽  
State Variables ◽  
Turbulent Plane ◽  
Thermodynamic Variables ◽  
Plane Channel Flow

AbstractWe 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. Statistics and correlation coefficients of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables are analysed. The implications of these results, leading 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.

The Destruction-of-Dissipation Tensor εεij in Wall Turbulence

2017 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Plane Channel ◽  
Wall Turbulence ◽  
Scaling Relations ◽  
Pressure Term ◽  
Turbulent Plane ◽  
Plane Channel Flow ◽  
Production Mechanisms ◽  
Molecular Viscosity

The paper investigates the destruction-of-dissipation tensor εεij in low-Reynolds number turbulent plane channel flow. This tensor, which represents the destruction of the dissipation tensor εij (appearing in the budgets of the covariances of fluctuating velocities rij) by molecular viscosity, exhibits specific near-wall anisotropy and is not 2-C at the wall. The budgets of εεij (turbulent and viscous diffusion, pressure-term, various production mechanisms, and destruction by molecular viscosity εεεij) are studied and various scaling relations are examined.

scholarly journals Restricted nonlinear model for high- and low-drag events in plane channel flow

2019 ◽  
Vol 864 ◽  
pp. 221-243 ◽  
Author(s):  
Frédéric Alizard ◽  
Damien Biau
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Wall Turbulence ◽  
Asymptotic State ◽  
State Variables ◽  
Mean Flow ◽  
Quadratic Interaction ◽  
Maximum Drag Reduction ◽  
The Mean ◽  
Plane Channel Flow

A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.

scholarly journals The dissipation tensor in wall turbulence

2016 ◽  
Vol 807 ◽  
pp. 386-418 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Plane Channel ◽  
Transport Equations ◽  
Wall Turbulence ◽  
Reynolds Stresses ◽  
Turbulent Plane ◽  
Plane Channel Flow ◽  
Derivatives Of

The paper investigates the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$in wall turbulence. Available direct numerical simulation (DNS) data are examined to illustrate the differences in the anisotropy of the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$with respect to the anisotropy of the Reynolds stresses$\unicode[STIX]{x1D633}_{ij}$. The budgets of the transport equations of the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$are studied using novel DNS data of low Reynolds number turbulent plane channel flow with spatial resolution sufficiently fine to accurately determine the correlations of products of two-derivatives of fluctuating velocities$u_{i}^{\prime }$and pressure$p^{\prime }$which appear in various terms. Finally, the influence of the Reynolds number on the diagonal components of$\unicode[STIX]{x1D700}_{ij}$($\unicode[STIX]{x1D700}_{xx}$,$\unicode[STIX]{x1D700}_{yy}$,$\unicode[STIX]{x1D700}_{zz}$) and on the various terms in their transport equations is studied using available DNS data of Vreman and Kuerten (Phys. Fluids, vol. 26, 2014b, 085103).

Reduced-basis modeling of turbulent plane channel flow

2006 ◽  
Vol 35 (2) ◽  
pp. 189-207 ◽  
Author(s):  
P.S. Johansson ◽  
H.I. Andersson ◽  
E.M. Rønquist
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Reduced Basis ◽  
Turbulent Plane ◽  
Plane Channel Flow

Correlation coefficients of thermodynamic fluctuations in compressible aerodynamic turbulence

2018 ◽  
Vol 851 ◽  
pp. 447-478 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Isotropic Turbulence ◽  
Plane Channel ◽  
Correlation Coefficients ◽  
Building Blocks ◽  
Wall Turbulence ◽  
Turbulence Structure ◽  
Leading Order ◽  
Homogeneous Isotropic Turbulence ◽  
Exact Relations ◽  
Plane Channel Flow

Thermodynamic fluctuations of pressure, density, temperature or entropy $\{p^{\prime },\unicode[STIX]{x1D70C}^{\prime },T^{\prime },s^{\prime }\}$ in compressible aerodynamic turbulence, although generated by the flow, are fundamentally related to one another by the thermodynamic equation of state. Ratios between non-dimensional root-mean-square (r.m.s.) levels ($\text{CV}_{p^{\prime }}:=\bar{p}^{-1}\,p_{rms}^{\prime }$, $\text{CV}_{\unicode[STIX]{x1D70C}^{\prime }}:=\bar{\unicode[STIX]{x1D70C}}^{-1}\,\unicode[STIX]{x1D70C}_{rms}^{\prime }$, $\text{CV}_{T^{\prime }}:=\bar{T}^{-1}\,T_{rms}^{\prime }$), along with all possible 2-moment correlation coefficients $\{c_{\unicode[STIX]{x1D70C}^{\prime }T^{\prime }},c_{p^{\prime }\unicode[STIX]{x1D70C}^{\prime }},c_{p^{\prime }T^{\prime }},c_{s^{\prime }\unicode[STIX]{x1D70C}^{\prime }},c_{s^{\prime }T^{\prime }},c_{s^{\prime }p^{\prime }}\}$, represent, in the sense of Bradshaw (Annu. Rev. Fluid Mech., vol. 9, 1977, pp. 33–54), the thermodynamic turbulence structure of the flow. We use direct numerical simulation (DNS) data, both for plane channel flow and for sustained homogeneous isotropic turbulence, to determine the range of validity of the leading-order, formally $O(\text{CV}_{\unicode[STIX]{x1D70C}^{\prime }})$, approximations of the exact relations between thermodynamic turbulence structure parameters. Available DNS data are mapped on the $(\text{CV}_{\unicode[STIX]{x1D70C}^{\prime }}^{-1}\,\text{CV}_{T^{\prime }},c_{\unicode[STIX]{x1D70C}^{\prime }T^{\prime }})$-plane and their loci, identified using the leading-order approximations, highlight specific behaviour for different flows or flow regions. For the particular case of sustained compressible homogeneous isotropic turbulence, it is shown that the DNS data collapse onto a single curve corresponding to $c_{s^{\prime }T^{\prime }}\approxeq 0.2$ (for air flow), while the approximation $c_{s^{\prime }p^{\prime }}\approxeq 0$ fits reasonably well wall turbulence DNS data, providing building blocks towards the construction of simple phenomenological models.

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