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.

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 A Compressible Turbulence Model for Pressure—Strain

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 34
Author(s):  
Hechmi Khlifi ◽  
Adnen Bourehla
Keyword(s):  
Mach Number ◽  
Shear Flow ◽  
Turbulent Flows ◽  
High Speed ◽  
Turbulence Models ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

This work focuses on the performance and validation of compressible turbulence models for the pressure-strain correlation. Considering the Launder Reece and Rodi (LRR) incompressible model for the pressure-strain correlation, Adumitroaie et al., Huang et al., and Marzougui et al., used different modeling approaches to develop turbulence models, taking into account compressibility effects for this term. Two numerical coefficients are dependent on the turbulent Mach number, and all of the remaining coefficients conserve the same values as in the original LRR model. The models do not correctly predict the compressible turbulence at a high-speed shear flow. So, the revision of these models is the major aim of this study. In the present work, the compressible model for the pressure-strain correlation developed by Khlifi−Lili, involving the turbulent Mach number, the gradient, and the convective Mach numbers, is used to modify the linear mean shear strain and the slow terms of the previous models. The models are tested in two compressible turbulent flows: homogeneous shear flow and the newly developed plane mixing layers. The predicted results of the proposed modifications of the Adumitroaie et al., Huang et al., and Marzougui et al., models and of its universal versions are compared with direct numerical simulation (DNS) and experiment data. The results show that the important parameters of compressibility in homogeneous shear flow and in the mixing layers are well predicted by the proposal models.

scholarly journals A compressibility corrections of the pressure strain linear part models

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 453-466
Author(s):  
Hechmi Khlifi
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
High Speed ◽  
Linear Part ◽  
Characteristic Parameter ◽  
Stress Equation ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Stress Models ◽  
Compressibility Effects

The main focus of this paper is the analysis of the compressibility effects and the validation of some recent Reynolds stress models for computing compressible turbulent flows. The pressure strain correlation is one of the several terms appearing in the Reynolds stress equation which directly reflect the compressibility effects on the turbulence. For this reason, a special attention is paid to the modeling of this term in order to account for compressibility effects at high-speed. The models developed by Speziale Sarkar and Gatski (SSG) and Fu, Launder and Tselepidakis (FLT) for the pressure strain correlation are examined to be extended to compressible turbulent flows. A compressibility corrections of these models using the turbulent Mach number are proposed. The calculations have been performed for the compressible homogeneous shear flow and the turbulent plate mixing-layers. The comparison of the proposed compressibility modifications of the SSG and FLT models with its universal version shows some important ameliorations in results for the majority characteristic parameter of the structural compressibility effects. It?s found that the predicted results from the modified SSG and FLT models are in reasonable agreement with the accepted data.

The formulation of the RANS equations for supersonic and hypersonic turbulent flows

2020 ◽  
pp. 1-31
Author(s):  
H. Zhang ◽  
T.J. Craft ◽  
H. Iacovides
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
High Speed ◽  
Mean Flow ◽  
Rans Equations ◽  
Flow Equations ◽  
The Mean ◽  
The Impact

Abstract Accurate prediction of supersonic and hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged Navier–Stokes (RANS) approach in general, and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (k) appear explicitly in the RANS equations through the modelling of the Reynolds stresses in such approach, and similar terms appear in the mean total energy equation. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one- or two-equation models. The omission of these terms may not be appropriate under hypersonic conditions. Nevertheless, this is a widespread practice, even for very high-speed turbulent flow simulations, because many software packages still make such approximations. To quantify the impact of ignoring these terms in the RANS equations, two linear two-equation models and one non-linear two-equation model are applied to the computation of five supersonic and hypersonic benchmark cases, one 2D zero-pressure gradient hypersonic flat plate case and four shock wave boundary layer interaction (SWBLI) cases. The surface friction coefficients and velocity profiles predicted with different combinations of the turbulent kinetic energy terms present in the transport equations show little sensitivity to the presence of these terms in the zero-pressure gradient case. In the SWBLI cases, however, comparisons show that inclusion of k in the mean flow equations can have a strong effect on the prediction of flow separation. Therefore, it is highly recommended to include all the turbulent kinetic energy terms in the mean flow equations when dealing with simulations of supersonic and hypersonic turbulent flows, especially for flows with SWBLIs. As a further consequence, since k may not be obtained explicitly in zero-equation, or certain one-equation, models, it is debatable whether these models are suitable for simulations of supersonic and hypersonic turbulent flows with SWBLIs.

scholarly journals Diurnal Dynamics of the Umov Kinetic Energy Density Vector in the Atmospheric Boundary Layer from Minisodar Measurements

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1347
Author(s):  
Alexander Potekaev ◽  
Nikolay Krasnenko ◽  
Liudmila Shamanaeva
Keyword(s):  
Energy Density ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Flux ◽  
Wind Effect ◽  
Kinetic Energy Density ◽  
Near Surface ◽  
Density Vector ◽  
The Mean ◽  
Umov Vector

The diurnal hourly dynamics of the kinetic energy flux density vector, called the Umov vector, and the mean and turbulent components of the kinetic energy are estimated from minisodar measurements of wind vector components and their variances in the lower 200-meter layer of the atmosphere. During a 24-hour period of continuous minisodar observations, it was established that the mean kinetic energy density dominated in the surface atmospheric layer at altitudes below ~50 m. At altitudes from 50 to 100 m, the relative contributions of the mean and turbulent wind kinetic energy densities depended on the time of the day and the sounding altitude. At altitudes below 100 m, the contribution of the turbulent kinetic energy component is small, and the ratio of the turbulent to mean wind kinetic energy components was in the range 0.01–10. At altitudes above 100 m, the turbulent kinetic energy density sharply increased, and the ratio reached its maximum equal to 100–1000 at altitudes of 150–200 m. A particular importance of the direction and magnitude of the wind effect, that is, of the direction and magnitude of the Umov vector at different altitudes was established. The diurnal behavior of the Umov vector depended both on the time of the day and the sounding altitude. Three layers were clearly distinguished: a near-surface layer at altitudes of 5–15 m, an intermediate layer at altitudes from 15 m to 150 m, and the layer of enhanced turbulence above. The feasibility is illustrated of detecting times and altitudes of maximal and minimal wing kinetic energy flux densities, that is, time periods and altitude ranges most and least favorable for flights of unmanned aerial vehicles. The proposed novel method of determining the spatiotemporal dynamics of the Umov vector from minisodar measurements can also be used to estimate the effect of wind on high-rise buildings and the energy potential of wind turbines.

Analysis of Turbulent Thermal Convection Between Horizontal Plates

1983 ◽  
Vol 105 (4) ◽  
pp. 789-794 ◽  
Author(s):  
M. Kaviany ◽  
R. Seban
Keyword(s):  
Temperature Distribution ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Thermal Convection ◽  
Equation Model ◽  
Experimental Results ◽  
Mixing Length ◽  
Mean Temperature ◽  
The Mean ◽  
The One

The one-equation model of turbulence is applied to the turbulent thermal convection between horizontal plates maintained at constant temperatures. A pseudo-three-layer model is used consisting of a conduction sublayer adjacent to the plates, a turbulent region within which the mixing length increases linearly, and a turbulent core within which the mixing length is a constant. It is assumed that the Nusselt number varies with the Rayleigh number to the one-third power. As a result, the steady-state distributions of the turbulent kinetic energy and the mean temperature are obtrained and presented in closed forms. These results include the effects of Prandtl number. The predictions are compared with the available experimental results for different Prandtl and Rayleigh numbers. Also included are the predictions of Kraichnan, which are based on a less exact analysis. The results of the one-equation model are in fair agreement with the experimental results for the distribution of the turbulent kinetic energy and the mean temperature distribution. The predictions of Kraichnan are in better agreement with the experimental results for the mean temperature distribution.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

Uncertainty analysis of CFD and performance prediction for an pumpjet propulsor

2020 ◽  
pp. 2150083
Author(s):  
Chao Liu ◽  
Hongxun Chen ◽  
Zhengchuan Zhang ◽  
Zheng Ma
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Uncertainty Analysis ◽  
Turbulent Kinetic Energy ◽  
Guide Vane ◽  
Outer Region ◽  
Turbulence Models ◽  
Operating Conditions ◽  
Operating Characteristics ◽  
Standard Formula

In order to reveal the operating characteristics of the pumpjet propulsor, standard [Formula: see text]–[Formula: see text], standard [Formula: see text]–[Formula: see text], RNG [Formula: see text]–[Formula: see text] and SST [Formula: see text]–[Formula: see text] turbulence models were used to conduct steady calculation for the whole flow channels. By comparing the calculation results with experimental data, it was found that the calculation errors were very large in some operating conditions. Therefore, the uncertainty analysis was carried out at all operating conditions of the pumpjet propulsor and the error source was finally determined that it is mainly derived from the model error. Then, the applicability of different turbulence models was analyzed to numerical simulation for the pumpjet propulsor by comparing the internal and external characteristics. It can be seen that the strong turbulent kinetic energy in the guide vane will inevitably cause energy loss, but not necessarily in the impeller. In this area, the increase of turbulent kinetic energy will enhance the mixing and transport of fluids, and the impeller makes the fluids get more energy. In addition, a modified hybrid Reynolds Average Numerical Simulation/Large Eddy Simulation (RANS/LES) model was proposed for unsteady calculation, and the performances, internal flow states and the interaction between the pump and the outer region were further revealed under various conditions of the pumpjet propulsor, which provides some references for predicting accurately and selecting conditions optimally in the future.

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