Reynolds stress transport equations in a momentumless wake - Experiments and models

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 281-287
Author(s):  
Thierry M. Faure
Keyword(s):  
Reynolds Stress ◽  
Transport Equations ◽  
Momentumless Wake

Modeling Of Turbulent Transport Equations

1996 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Time Scales ◽  
Eddy Viscosity ◽  
Ad Hoc ◽  
Stokes Equations ◽  
Transport Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stress Models

The high-Reynolds-number turbulent flows of technological importance contain such a wide range of excited length and time scales that the application of direct or large-eddy simulations is all but impossible for the foreseeable future. Reynolds stress models remain the only viable means for the solution of these complex turbulent flows. It is widely believed that Reynolds stress models are completely ad hoc, having no formal connection with solutions of the full Navier-Stokes equations for turbulent flows. While this belief is largely warranted for the older eddy viscosity models of turbulence, it constitutes a far too pessimistic assessment of the current generation of Reynolds stress closures. It will be shown how secondorder closure models and two-equation models with an anisotropic eddy viscosity can be systematically derived from the Navier-Stokes equations when one overriding assumption is made: the turbulence is locally homogeneous and in equilibrium. A brief review of zero equation models and one equation models based on the Boussinesq eddy viscosity hypothesis will first be provided in order to gain a perspective on the earlier approaches to Reynolds stress modeling. It will, however, be argued that since turbulent flows contain length and time scales that change dramatically from one flow configuration to the next, two-equation models constitute the minimum level of closure that is physically acceptable. Typically, modeled transport equations are solved for the turbulent kinetic energy and dissipation rate from which the turbulent length and time scales are built up; this obviates the need to specify these scales in an ad hoc fashion. While two-equation models represent the minimum acceptable closure, second-order closure models constitute the most complex level of closure that is currently feasible from a computational standpoint. It will be shown how the former models follow from the latter in the equilibrium limit of homogeneous turbulence. However, the two-equation models that are formally consistent with second-order closures have an anisotropic eddy viscosity with strain-dependent coefficients - a feature that most of the commonly used models do not possess.

A Simulative Study on the Effects of Additional Inertia Force Exerting on the Water Dynamic Features of Damaged Vessels

2013 ◽  
Vol 634-638 ◽  
pp. 3727-3731
Author(s):  
Ang Li ◽  
Jin Yun Pu
Keyword(s):  
Reynolds Stress ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Transport Equations ◽  
Flow Coefficient ◽  
Inertia Force ◽  
Dynamic Features ◽  
High Turbulence

With the aid of “gambit” and Reynolds Stress Transport Equations, the residential cabin model and the turbulence model were established. By observing the effects of additional inertia force exerting on the water dynamic features of damaged vessels under different linear accelerations, the following conclusions could be obtained: (1) the inflow direction through square and round breaks is deviated from the heave, and contrary to the sailing direction; while that derivation of triangle breaks is comparatively smaller, less effected by inertia force (2) within high turbulence intensity areas, square breaks mainly appear in pre-inflow areas, and triangle and round breaks mainly occur in post-inflow areas (3) with the increase of acceleration, the flow coefficient of the three kind of break tends to decline, whereas that trend seems to be less noticeable with triangle breaks (4) under the effect of inertia force, the shrink coefficient of the three types of break incline to drop; the round breaks is less effected while a distinct variance could be observed in the cases of square and triangle shaped breaks.

Calculation of Turbulent Wall Jets With an Algebraic Reynolds Stress Model

1980 ◽  
Vol 102 (3) ◽  
pp. 350-356 ◽  
Author(s):  
M. Ljuboja ◽  
W. Rodi
Keyword(s):  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Transport Equations ◽  
Turbulent Shear ◽  
Wall Jet ◽  
Wall Jets ◽  
Mean Velocity ◽  
Empirical Constant ◽  
Turbulent Wall Jets ◽  
Turbulent Wall

A modified version of the k-ε turbulence model is developed which predicts well the main features of turbulent wall jets. The model relates the turbulent shear stress to the mean velocity gradient, the turbulent kinetic energy k, and the dissipation rate ε by way of the Kolmogorov-Prandtl eddy viscosity relation and determines k and ε from transport equations. The empirical constant in the Kolmogorov-Prandtl relation is replaced by a function which is derived by reducing a model form of the Reynolds stress transport equations to algebraic expressions, retaining the wall damping correction to the pressure-strain model used in these equations. The modified k-ε model is applied to a wall jet in stagnant surroundings as well as to a wall jet in a moving stream, and the predictions are compared with experimental data. The agreement is good with respect to most features of these flows.

A Reynolds stress model of turbulence and its application to thin shear flows

1972 ◽  
Vol 52 (4) ◽  
pp. 609-638 ◽  
Author(s):  
K. Hanjalić ◽  
B. E. Launder
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Energy Dissipation Rate ◽  
Solution Procedure ◽  
Transport Equations ◽  
Turbulent Shear ◽  
Turbulence Energy ◽  
Boundary Layer Flows

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor$\overline{u_iu_j}$and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components.For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress$-\overline{u_1u_2}$the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-layer flows including examples of flow remote from walls, those developing along one wall and those confined within ducts. Three of the flows are strongly asymmetric with respect to the surface of zero shear stress and here the turbulent shear stress does not vanish where the mean rate of strain goes to zero. In most cases the predicted profiles and other quantities accord with the data within the probable accuracy of the measurements.

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