Turbulent kinetic energy production and flow structures in compressible homogeneous shear flow

2016 ◽  
Vol 28 (9) ◽  
pp. 096102 ◽  
Author(s):  
Zongqiang Ma ◽  
Zuoli Xiao
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Turbulent Kinetic Energy ◽  
Energy Production ◽  
Flow Structures ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

scholarly journals Bounded Energy States in Homogeneous Turbulent Shear Flow—An Alternative View

1992 ◽  
Vol 114 (1) ◽  
pp. 29-39 ◽  
Author(s):  
P. S. Bernard ◽  
C. G. Speziale
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Dissipation Rate ◽  
Numerical Experiments ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Exponential Time ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Energy States

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k–ε model modified to account for net vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The plausibility of this result is further supported by independent calculations of isotropic turbulence which show that when this vortex stretching effect is accounted for, a much more complete physical description of isotropic decay is obtained. It is thus argued that the inclusion of vortex stretching as an identifiable process may have greater significance in turbulence modeling than has previously been thought and that the generally accepted structural equilibrium for homogeneous shear flow, with unbounded energy growth, could be in need of re-examination.

Compressibility Effects on Turbulence Growth in High-Speed Shear Flows

1994 ◽  
Vol 47 (6S) ◽  
pp. S179-S183
Author(s):  
S. Sarkar
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
High Speed ◽  
Shear Flows ◽  
Length Scale ◽  
Homogeneous Shear ◽  
The Mean ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

Compressibility effects on the evolution of turbulence are obtained from direct numerical simulation of homogeneous shear flow. It is found that when the gradient Mach number - a parameter based on the mean shear rate, integral length scale and speed of sound - increases, the growth of turbulent kinetic energy is inhibited. The reduced ‘efficiency’ of production is shown to lead to the inhibited growth of turbulent kinetic energy. Implications for inhomogeneous shear flows are discussed.

scholarly journals Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow

2017 ◽  
Vol 827 ◽  
pp. 225-249 ◽  
Author(s):  
Atsushi Sekimoto ◽  
Javier Jiménez
Keyword(s):  
Shear Flow ◽  
Vertical Direction ◽  
Large Eddy Simulations ◽  
Small Scale ◽  
Box Dimension ◽  
Equilibrium Solutions ◽  
Vortical Structures ◽  
Homogeneous Shear ◽  
Large Eddy ◽  
Homogeneous Shear Flow

Unstable equilibrium solutions in a homogeneous shear flow with sinuous (streamwise-shift-reflection and spanwise-shift-rotation) symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_{S}$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_{z}$. The fraction $R_{S}=L_{z}/l_{S}$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $R_{S}$ increases, and that the flow structures resemble those in plane Couette flow with the same sinuous symmetry. The vortical structures of both lower- and upper-branch solutions become spontaneously localised in the vertical direction. The lower-branch solution is an edge state at low $R_{S}$, and takes the form of a thin critical layer as $R_{S}$ increases, as in the asymptotic theory of generic shear flow at high Reynolds numbers. On the other hand, the upper-branch solutions are characterised by a tall velocity streak with multiscale multiple vortical structures. At the higher end of $R_{S}$, an incipient multiscale structure is found. The LES turbulence occasionally visits vertically localised states whose vortical structure resembles the present vertically localised LES equilibria.

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

scholarly journals Anisotropic clustering of inertial particles in homogeneous shear flow

2009 ◽  
Vol 629 ◽  
pp. 25-39 ◽  
Author(s):  
P. GUALTIERI ◽  
F. PICANO ◽  
C. M. CASCIOLA
Keyword(s):  
Relaxation Time ◽  
Shear Flow ◽  
Large Scale ◽  
Inertial Particles ◽  
Spatial Homogeneity ◽  
Homogeneous Shear ◽  
Multi Scale ◽  
Angular Distribution Function ◽  
Homogeneous Shear Flow ◽  
Anisotropic Clustering

Recently, clustering of inertial particles in turbulence has been thoroughly analysed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particle configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles. This in turn results in a multi-scale distribution of local particle concentration and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large-scale velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function (ADF) of particle pairs, which allows to address the anisotropy content of particle aggregates on a scale-by-scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales in which the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine-scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two closeby particles at viscous-scale separation.

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