An Improved Model for the Return to Isotropy of Homogeneous Turbulence

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Hari Warrior ◽  
Sajo Mathews ◽  
Subhendu Maity ◽  
Kaushik Sasmal
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Experimental Results ◽  
Homogeneous Turbulence ◽  
Cfd Modeling ◽  
Present Formulation ◽  
Improved Model ◽  
Stress Models

In CFD modeling, the most widely used Reynolds stress models is the Speziale, Sarkar, Gatski (SSG) model. The present formulation, though similar in structure to the SSG model, is a mathematical variation assuming homogeneity of turbulence and is an improved model for the slow pressure strain of turbulence. The basic thrust is that anisotropy of dissipation tensor is not negligible when compared to the anisotropy of turbulent kinetic energy and affects the slow pressure strain rate. After an exhaustive survey of the available experimental results on return to isotropy, graphical plots reveal that the model performs as good as the SSG model.

scholarly journals Probing Reynolds stress models of convection with numerical simulations: III. Compressibility modelling and dissipation

2006 ◽  
Vol 2 (S239) ◽  
pp. 86-88 ◽  
Author(s):  
F. Kupka ◽  
H. J. Muthsam
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Simulation Study ◽  
Pressure Fluctuations ◽  
3D Numerical Simulation ◽  
Stellar Convection ◽  
Stress Models

AbstractWe provide results from an extended 3D numerical simulation study of Reynolds stress models of stellar convection and probe the modelling of compressibility, pressure fluctuations, and dissipation of turbulent kinetic energy.

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.

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

Large Eddy Simulation of Cylindrical Jet Breakup and Correlation of Simulation Results With Experimental Data

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Shashank S. Moghe ◽  
Scott M. Janowiak
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Kinetic Energy ◽  
Experimental Results ◽  
Eddy Simulation ◽  
Jet Breakup ◽  
Large Eddy ◽  
Oil Jet ◽  
Piston Cooling

Modern engines with increasing power densities have put additional demands on pistons to perform in incrementally challenging thermal environments. Piston cooling is therefore of paramount importance for engine component manufacturers. The objective of this computational fluid dynamics (CFD) study is to identify the effect of a given piston cooling nozzle (PCN) geometry on the cooling oil jet spreading phenomenon. The scope of this study is to develop a numerical setup using the open-source CFD toolkit OpenFoam® for measuring the magnitude of oil jet spreading and comparing it to experimental results. Large eddy simulation (LES) turbulence modeling is used to capture the flow physics that affects the inherently unsteady jet breakup phenomenon. The oil jet spreading width is the primary metric used for comparing the numerical and experimental results. The results of simulation are validated for the correct applicability of LES by evaluating the fraction of resolved turbulent kinetic energy (TKE) at various probe locations and also by performing turbulent kinetic energy spectral analysis. CFD results appear promising since they correspond to the experimental data within a tolerance (of ±10%) deemed satisfactory for the purpose of this study. Further generalization of the setup is underway toward developing a tool that predicts the aforementioned metric—thereby evaluating the effect of PCN geometry on oil jet spreading and hence on the oil catching efficiency (CE) of the piston cooling gallery. This tool would act as an intermediate step in boundary condition formulation for the simulation determining the filling ratio (FR) and subsequently the heat transfer coefficients (HTCs) in the piston cooling gallery.

Two-equation turbulence modeling of an oscillatory boundary layer under steep pressure gradient

2010 ◽  
Vol 37 (4) ◽  
pp. 648-656 ◽  
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Detailed Comparison ◽  
Stream Velocity ◽  
Oscillatory Boundary Layer

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k–ε model, one k–ω model and two versions of k–ε / k–ω blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k–ε model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k–ω model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k–ε model proposed by Sana et al. and the original k–ω model.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

scholarly journals Wind–Wave Misalignment Effects on Langmuir Turbulence in Tropical Cyclone Conditions

2019 ◽  
Vol 49 (12) ◽  
pp. 3109-3126 ◽  
Author(s):  
Dong Wang ◽  
Tobias Kukulka ◽  
Brandon G. Reichl ◽  
Tetsu Hara ◽  
Isaac Ginis
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Wind Wave ◽  
Stokes Drift ◽  
Scaling Analysis ◽  
Surface Boundary ◽  
Langmuir Turbulence ◽  
Near Surface ◽  
Momentum Budget

AbstractThis study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.

On Measuring the Terms of the Turbulent Kinetic Energy Budget from an AUV

2006 ◽  
Vol 23 (7) ◽  
pp. 977-990 ◽  
Author(s):  
Louis Goodman ◽  
Edward R. Levine ◽  
Rolf G. Lueck
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Vertical Velocity ◽  
Autonomous Underwater Vehicle ◽  
Temperature Fluctuations ◽  
Transverse Component ◽  
Vertical Flux ◽  
Vertical Shear ◽  
Statistical Uncertainty

Abstract The terms of the steady-state, homogeneous turbulent kinetic energy budgets are obtained from measurements of turbulence and fine structure from the small autonomous underwater vehicle (AUV) Remote Environmental Measuring Units (REMUS). The transverse component of Reynolds stress and the vertical flux of heat are obtained from the correlation of vertical and transverse horizontal velocity, and the correlation of vertical velocity and temperature fluctuations, respectively. The data were obtained using a turbulence package, with two shear probes, a fast-response thermistor, and three accelerometers. To obtain the vector horizontal Reynolds stress, a generalized eddy viscosity formulation is invoked. This allows the downstream component of the Reynolds stress to be related to the transverse component by the direction of the finescale vector vertical shear. The Reynolds stress and the vector vertical shear then allow an estimate of the rate of production of turbulent kinetic energy (TKE). Heat flux is obtained by correlating the vertical velocity with temperature fluctuations obtained from the FP-07 thermistor. The buoyancy flux term is estimated from the vertical flux of heat with the assumption of a constant temperature–salinity (T–S) relationship. Turbulent dissipation is obtained directly from the usage of shear probes. A multivariate correction procedure is developed to remove vehicle motion and vibration contamination from the estimates of the TKE terms. A technique is also developed to estimate the statistical uncertainty of using this estimation technique for the TKE budget terms. Within the statistical uncertainty of the estimates herein, the TKE budget on average closes for measurements taken in the weakly stratified waters at the entrance to Long Island Sound. In the strongly stratified waters of Narragansett Bay, the TKE budget closes when the buoyancy Reynolds number exceeds 20, an indicator and threshold for the initiation of turbulence in stratified conditions. A discussion is made regarding the role of the turbulent kinetic energy length scale relative to the length of the AUV in obtaining these estimates, and in the TKE budget closure.

Effects of Axial Casing Grooves on the Structure of Turbulence in the Tip Region of an Axial Turbomachine Rotor

2020 ◽  
Author(s):  
Huang Chen ◽  
Yuanchao Li ◽  
Subhra Shankha Koley ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Suction Side ◽  
Reynolds Stresses ◽  
Flow Rates ◽  
Tip Leakage ◽  
Anisotropy Tensor ◽  
Stress Models ◽  
Turbomachine Rotor ◽  
Mean Strain

Abstract Challenges in predicting the turbulence in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between the Reynold stresses and the corresponding mean strain rate components. The geometric complexity introduced by casing grooves exacerbates this problem. Taking advantage of a large database collected in the refractive index-matched liquid facility at JHU, this paper examines the evolution of turbulence in the tip region of an axial turbomachine with and without axial casing grooves, and for two flow rates. The semi-circular axial grooves are skewed by 45° in the positive circumferential direction, similar to that described in Müller et al. [1]. Comparison to results obtained for an untreated endwall includes differences in the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and dominant terms in the TKE production rate. The evolution of TKE at high flow rates for blade sections located downstream of the grooves is also investigated. Common features include: with or without casing grooves, the TKE is high near the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor demonstrating shifts from one dimensional (1D) to 2D and to 3D structures over small distances. Furthermore, the correlation between the mean strain rate and Reynolds stress tensor components is poor. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes much more complex. Turbulence is also high in the corner vortex that develops at the entrance to the grooves and in the flow jetting out of the grooves into the passage. Consistent with trends of production rates of normal Reynolds stress components, the grooves increase the axial and reduce the radial velocity fluctuations compared to the untreated endwall. These findings introduce new insight that might assist the future development of Reynolds stress models suitable for tip flows.

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