Modeling The Turbulent Scalar Fluxes In An Internal Wave Breaking Region In Stratified Flow With Obstacle

2017 ◽  
Vol 12 (1) ◽  
pp. 79-90
Author(s):  
Sergey Yakovenko
Keyword(s):  
Internal Wave ◽  
Reynolds Stress ◽  
Diffusion Processes ◽  
Local Equilibrium ◽  
Turbulence Models ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Scalar Flux ◽  
Flux Transport ◽  
Diffusion Type

Based on averaging of the direct numerical simulation data obtained earlier, statistical moments are calculated in a turbulent patch arising after internal wave overturning in a flow with obstacle and stable stratification. Temporal evolution and spatial behavior of the turbulent-scalar-flux transport equation budget have been studied. A priori estimations of approximations for the pressure-scalar-gradient correlation and turbulent-diffusion processes in this equation have been carried out. The performed analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. It is shown that, in the global balance of the turbulent-scalar-flux equation, the mean-shear and buoyancy productions and the pressure-scalargradient correlation are roughly balanced, as for the shear Reynolds stress equation, and in contrast to the scalar variance and normal Reynolds stress equations. The algebraic turbulent-scalar-flux relations of the gradient diffusion type, as well as those derived in local-equilibrium and nonequilibrium assumptions are incorrect; therefore the use of the full turbulent-scalar-flux equation is justified.

Turbulent Scalar Flux Models for the Mixing of Hot Gases in the Swirling Flow of High-Temperature Reactor Lower Plenums

2008 ◽  
Author(s):  
Dominik von Lavante ◽  
Eckart Laurien
Keyword(s):  
High Temperature ◽  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Swirling Flow ◽  
Turbulence Models ◽  
Operating Conditions ◽  
Vortical Flow ◽  
Mixing Efficiency ◽  
Scalar Flux ◽  
Flux Transport

With recent progress in high-temperature pebble-bed reactor programs research focus has started to include more ancillary engineering issues. One very important aspect for the realisability is the mixing of hot and colder helium in the reactor lower plenum. Under nominal operating conditions, depending on core design, the temperature of hot gas leaving the core can locally differ up to 210° C. Due to material limitations, these temperature differences have to be reduced to at least ±15° C. Several reduced-size air experiments have been performed on this problem, but their applicability to modern commercially sized reactors is not certain. With the rise in computing power CFD simulations can be performed in addition, but advanced turbulence modeling is necessary due to the highly swirling and turbulent nature of this flow. The presented work uses the geometry of the German HTR-Modul which consists of an annular mixing channel and radially arranged ribs. Using the commercial CFD code ANSYS CFX, we have made detailed analyses of the complex 3D vortical flow phenomena within this geometry. Several momentum transport turbulence models, e.g. the classical k-e model, advanced two-equation models and Reynolds-Stress Models were compared with respect to their accuracy for this particular flow. In addition, the full set of turbulent scalar flux transport equations was implemented for modeling the three components of turbulent transport of enthalpy seperately and were compared with the standard turbulent Prandtl number approach. As expected from previous work in related fields of turbulence modeling, the differences in predicting the mixing performance between models were significant. Only the full Reynolds-Stress model coupled with the scalar flux equations was able to reproduce the experimentally observed reduction of mixing efficiency with increasing Reynolds number. The correct scaling of mixing efficiencies demonstrates that the utilized turbulence models are able to reproduce the physics of the underlying flow. Hence they could be employed for the scaling and optimization of the lower plenum geometry. The results also showed that the original geometry used for the HTR-Modul is insufficient to provide adequate mixing, and that hence a not sufficiently mixed coolant for future reactor designs might be an issue. Based on this work, an optimization for future lower plenum geometries has become feasible.

Budget of Equations for Reynolds Stresses in a Turbulent Patch Arising from Internal Wave Breaking

2012 ◽  
Vol 7 (4) ◽  
pp. 87-95
Author(s):  
Sergey Yakovenko
Keyword(s):  
Internal Wave ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Wave Breaking ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Mixing Efficiency ◽  
Reynolds Stresses ◽  
Local Isotropy ◽  
Reynolds Stress Tensor

Results of the direct numerical simulations are used to obtain statistical moments in a quasi-steady turbulent patch arising in a stably stratified flow above an obstacle after internal wave breaking. Temporal evolution and spatial behavior of the Reynolds-stress tensor components and budgets of the Reynolds-stress transport equations have been studied. Such an analysis is helpful to explore the turbulent patch and its energetic characteristics by means of statistical moments, to examine closure hypotheses in turbulence models, and to evaluate geophysically important quantites. In particular, the calculated global value of the mixing efficiency is about 0.2 as in oceanic applications. Moreover, simple algebraic relations are proposed between the turbulent kinetic energy and its dissipation rate. In the Reynolds stress tensor equation, the pressure-strain correlation term provides the redistribution of the normal stress components according to the linear returnto-isotropy approximation, whereas the dissipation tensor roughly follows the local-isotropy assumption

Budget Of The Scalar Variance Equation In A Turbulent Patch Arising From Lee Wave Breaking

2015 ◽  
Vol 10 (4) ◽  
pp. 85-94
Author(s):  
Sergey Yakovenko
Keyword(s):  
Wave Breaking ◽  
Diffusion Processes ◽  
Transport Model ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Scalar Dissipation ◽  
Algebraic Expression ◽  
Lee Wave ◽  
Scalar Variance ◽  
Variance Equation

Based on averaged data of the direct numerical simulations, statistical moments are obtained in a turbulent patch arising after lee wave overturning in a flow with stable stratification and obstacle. Temporal evolution and spatial behavior of the scalar-variance transport equation budget have been studied. A priori estimations of algebraic approximations for scalar dissipation, scalar variance and turbulent-diffusion processes in the scalar-variance equation have been carried out. Such an analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. In the global balance of the scalar-variance equation, the compensation of production by dissipation and advection is shown, as for the turbulent kinetic energy equation. The ratio of turbulent time scales of the scalar and velocity fields varies from 0.2 to 2.2 within the wave breaking region, and the global value of this parameter is close to unity during the quasisteady period. The algebraic expression derived from the assumption of production and dissipation balance is incorrect leading to unphysical negative values, therefore the use of the full scalarvariance equation in the turbulent transport model is justified.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

2001 ◽  
Vol 124 (1) ◽  
pp. 86-99 ◽  
Author(s):  
G. A. Gerolymos ◽  
J. Neubauer ◽  
V. C. Sharma ◽  
I. Vallet
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Equations ◽  
Near Wall

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

Measurement and modelling of homogeneous axisymmetric turbulence

1998 ◽  
Vol 374 ◽  
pp. 59-90 ◽  
Author(s):  
TORBJÖRN SJÖGREN ◽  
ARNE V. JOHANSSON
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Theoretical Description ◽  
Wind Tunnel Experiments ◽  
Third Order ◽  
Point Velocity ◽  
First Time ◽  
Rapid Pressure

A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.

Applications of EARSM Turbulence Models to Internal Flows

2012 ◽  
Author(s):  
O. Z. Mehdizadeh ◽  
L. Temmerman ◽  
B. Tartinville ◽  
Ch. Hirsch
Keyword(s):  
Reynolds Stress ◽  
High Performance ◽  
Eddy Viscosity ◽  
Computational Cost ◽  
Turbulence Models ◽  
Industrial Applications ◽  
Mean Flow ◽  
Viscosity Models ◽  
Stress Models ◽  
Corner Flows

Turbulence modeling remains an active CFD development front for turbomachinery as well as for general industrial applications. While DNS and even LES still seem out of reach within the typical industrial design cycle due to their high computational cost, RANS-based models remain the workhorse of CFD. Currently, the most widely used models are Linear Eddy-Viscosity Models (LEVM), despite their known limitations for certain flow complexities. Therefore, extending the reliability of eddy-viscosity models to more complex flows without significantly increasing the computational cost can immediately contribute to more reliable CFD results for wider range of applications. This, in turn, can further reduce the need for costly tests and consequently can reduce the product development cost. A promising approach to achieve this goal is using Explicit Algebraic Reynolds Stress Models (EARSM), obtained through a simplification of the full Differential Reynolds Stress Models (DRSM), and can be perceived as an extension of LEVMs by including the non-linear relation between the turbulence stress tensor, the mean-flow gradient and the turbulence scales. These models are thus less demanding than DRSM, yet capable of capturing more complex turbulence features, compared to LEVM, such as anisotropy in the normal stresses. This may be particularly important in corner flows, for instance, in the hub-blade regions or in diffusers. This work explores the application of EARSM models to a double diffuser and a high-performance centrifugal compressor stage (HPCC). The results are compared to available experimental data [1,2] showing the importance of including the anisotropy of turbulence in the model, particularly in presence of turbulent corner flows in a diffuser. Furthermore, the EARSM results are also compared to results from the commonly used SST turbulence model. The CFD comparison includes details of the flow structure in the diffuser, where the most noticeable impact from the use of EARSM turbulence models is expected.

Numerical Study of the Turbulent Flow Around a Square Cylinder Near a Wall

2002 ◽  
Author(s):  
Emmanuel Guilmineau ◽  
Patrick Queutey
Keyword(s):  
Reynolds Stress ◽  
Numerical Study ◽  
Turbulence Models ◽  
Equation Model ◽  
Stream Velocity ◽  
Periodic Case ◽  
Square Cylinder ◽  
Mean Velocity ◽  
The One ◽  
Adjacent Wall

Calculations are reported for the flow around a two-dimensional, square cylinder at Re = 22,000 (based on the prism side dimension, D, and the free-stream velocity) placed at various distances from an adjacent wall. The nominal boundary layer thickness is 1.5D. Experiments have indicated that unsteady vortex shedding is suppressed when the wall is relatively close to the cylinder. The turbulent fluctuations are simulated with three turbulence models: the one-equation model of Spalart & Allmaras (1992), the two-equations SST K–ω model (Menter, 1993) and a Reynolds stress Rij–ω closures (Deng & Visonneau, 1999). The paper consists in comparing simulation and experimental results for configurations S/D = 1 (periodic case) and S/D = 0.25 (stationary case). Predicted and measured distributions of the mean velocity, Reynolds stress tensor and surface pressures are compared. Although the agreement is very good in general, observed discrepancies are discussed.

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