An Improved Model Including Length Scale Anisotropy for the Pressure Strain Correlation of Turbulence

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
J. P. Panda ◽  
H. V. Warrior ◽  
S. Maity ◽  
A. Mitra ◽  
K. Sasmal
Keyword(s):  
Linear Function ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Present Model ◽  
Quadratic Model ◽  
Length Scale ◽  
Mean Velocity ◽  
Velocity Gradients ◽  
Anisotropy Tensor ◽  
Improved Model

In this paper, we consider the evolution of decaying homogeneous anisotropic turbulence without mean velocity gradients, where only the slow pressure rate of strain is nonzero. A higher degree nonlinear return-to-isotropy model has been developed for the slow pressure–strain correlation, considering anisotropies in Reynolds stress, dissipation rate, and length scale tensor. Assumption of single length scale across the flow is not sufficient, from which stems the introduction of length scale anisotropy tensor, which has been assumed to be a linear function of Reynolds stress and dissipation tensor. The present model with anisotropy in length scale shows better agreement with well-accepted experimental results and an improvement over the Sarkar and Speziale (SS) quadratic model.

Velocity Characteristics of a Confined Coaxial Jet

1979 ◽  
Vol 101 (4) ◽  
pp. 521-529 ◽  
Author(s):  
M. A. Habib ◽  
J. H. Whitelaw
Keyword(s):  
Dissipation Rate ◽  
Numerical Solutions ◽  
Reverse Flow ◽  
Velocity Ratio ◽  
Isothermal Flow ◽  
Turbulence Energy ◽  
Hot Wire ◽  
Gradient Tensor ◽  
Mean Velocity ◽  
Velocity Gradients

The velocity characteristics of a turbulent, confined, coaxial-jet flow have been determined by measurement and by the solution of conservation equations in differential form. The ratios of maximum annulus to pipe velocity were 3 and 1 and, in both cases, the profiles were fully developed in the exit plane. The geometric arrangement corresponded to a model furnace and the investigation was undertaken to provide information, for isothermal flow, relevant to furnace flows. The measurements were obtained with a hot-wire anemometer and include distributions of the axial mean velocity and the components of the Reynolds-stress tensor. They show, for example, that the larger velocity ratio results in a larger region of recirculation, larger velocity gradients and larger turbulence intensities in the mixing region and downstream of the region of reverse flow. Numerical solutions of the time-averaged forms of the equations of conservation of mass and momentum, together with equations for turbulence energy and dissipation rate, provided results which are in close agreement with the measurements except in regions of more than one major component of the velocity-gradient tensor where they are substantially in error. The reasons for the discrepancies and the consequential value of the calculation method are discussed.

Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models

1998 ◽  
Vol 212 (3) ◽  
pp. 193-212 ◽  
Author(s):  
S P Yuan ◽  
R M C So
Keyword(s):  
Stress Tensor ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Rotating Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Anisotropic Stress ◽  
The Mean ◽  
Anisotropic Stress Tensor

The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.

Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach

1991 ◽  
Vol 227 ◽  
pp. 245-272 ◽  
Author(s):  
Charles G. Speziale ◽  
Sutanu Sarkar ◽  
Thomas B. Gatski
Keyword(s):  
Dynamical Systems ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Equilibrium Structure ◽  
Quadratic Model ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Closure Models ◽  
Anisotropy Tensor ◽  
Hierarchy Of Models

The modelling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - appears to yield improved results over the Launder, Reece & Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in five independent homogeneous turbulent flows. However, some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modelling of the pressure–strain correlation. Possible alternative approaches are discussed briefly.

scholarly journals Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Reynolds Stress ◽  
Network Architecture ◽  
Eddy Viscosity ◽  
Deep Neural Networks ◽  
Test Cases ◽  
Neural Network Architecture ◽  
Stress Anisotropy ◽  
Anisotropy Tensor

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Law of bounded dissipation and its consequences in turbulent wall flows

2021 ◽  
Vol 933 ◽  
Author(s):  
Xi Chen ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Dissipation Rate ◽  
Scaling Law ◽  
Random Variable ◽  
Energy Dissipation Rate ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Wall Flows ◽  
Maximum Value ◽  
Turbulent Wall ◽  
Promising Perspective

The dominant paradigm in turbulent wall flows is that the mean velocity near the wall, when scaled on wall variables, is independent of the friction Reynolds number $Re_\tau$ . This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, by extending our earlier work (Chen & Sreenivasan, J. Fluid Mech., vol. 908, 2021, p. R3) we present a promising perspective, and support it with data, that fluctuations displaying non-zero wall values, or near-wall peaks, are bounded for large values of $Re_\tau$ , owing to the natural constraint that the dissipation rate is bounded. Specifically, $\varPhi _\infty - \varPhi = C_\varPhi \,Re_\tau ^{-1/4},$ where $\varPhi$ represents the maximum value of any of the following quantities: energy dissipation rate, turbulent diffusion, fluctuations of pressure, streamwise and spanwise velocities, squares of vorticity components, and the wall values of pressure and shear stresses; the subscript $\infty$ denotes the bounded asymptotic value of $\varPhi$ , and the coefficient $C_\varPhi$ depends on $\varPhi$ but not on $Re_\tau$ . Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form $\langle \varphi ^{2q}\rangle ^{{1}/{q}}_{max}= \alpha _q-\beta _q\,Re^{-1/4}_\tau$ , where $\varphi$ represents the streamwise or spanwise velocity fluctuation, and $\alpha _q$ and $\beta _q$ are independent of $Re_\tau$ . Excellent agreement with available data is observed. A stochastic process for which the random variable has the form just mentioned, referred to here as the ‘linear $q$ -norm Gaussian’, is proposed to explain the observed linear dependence of $\alpha _q$ on $q$ .

scholarly journals Effect of the Flame Dome Depth and Improvement of the Pressure Loss in the Dump Diffuser

1998 ◽  
Author(s):  
Shinji Honami ◽  
Wataru Tsuboi ◽  
Takaaki Shizawa
Keyword(s):  
Velocity Profile ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Pressure Loss ◽  
Total Pressure ◽  
Flow Behavior ◽  
Sudden Expansion ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

This paper presents the effect of flame dome depth on the total pressure performance and flow behavior in a sudden expansion region of the combustor diffuser without flow entering the dome head. The mean velocity and turbulent Reynolds stress profiles in the sudden expansion region were measured by a Laser Doppler Velocitmetry (LDV) system. The experiments show that total pressure loss is increased, when flame dome depth is increased. Installation of an inclined combuster wall in the sudden expansion region is suggested from the viewpoint of a control of the reattaching flow. The inclined combustor wall is found to be effective in improvement of the diffuser performance. Better characteristics of the flow rate distribution into the branched channels are obtained in the inclined wall configuration, even if the distorted velocity profile is provided at the diffuser inlet.

scholarly journals A Novel Simplification of the Reynolds-Chou-Navier-Stokes Turbulence Equations of Incompressible Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flow ◽  
Velocity Fluctuation ◽  
Explicit Representation ◽  
Navier Stokes ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulence Formulations

Based on author's previous work [Sun, B. The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed. Preprints 2018, 2018060461 (doi: 10.20944/preprints201806.0461.v1)], this paper proposed an explicit representation of velocity fluctuation and formulated the Reynolds stress tensor in terms of the mean velocity field. The proposed closed Reynolds Navier-Stokes turbulence formulations reveal that the mean vorticity is the key source of producing turbulence.

Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence

1976 ◽  
Vol 74 (4) ◽  
pp. 593-610 ◽  
Author(s):  
K. Hanjalić ◽  
B. E. Launder
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Numerical Solutions ◽  
Low Reynolds Number ◽  
Transport Processes ◽  
Turbulent Shear ◽  
Turbulent Shear Stress ◽  
Low Reynolds

The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient$\overline{uv^2}/\overline{u^2}\overline{v^2} $is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.

Sign in / Sign up

Export Citation Format

Share Document