scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

Twin Inclined Circular Jets Evolution Through a Cool Crossflow

2007 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub Sai¨d ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Vortical Structures ◽  
Circular Jets ◽  
Turbulent Closure ◽  
The Mean ◽  
Good Agreement

The aim of this paper is to examine experimentally as well as numerically the flowfield resulting from the interaction between a twin circular inclined hot jets emerging into a cooling crossflow. The resulting flowfield is quite complex due to the presence of different vortical structures including the kidney vortex, the horse-shoe vortex, etc... The evolution of the twin inclined jets through the crossflow could be depicted by tracking the mean-flow velocity field and its associated turbulence statistics by means of the PIV technique. This evolution can be influenced by many factors. Herein, we will deal with that resulted by the injection nozzles’ inclination and the jets’ spacing. Then, we performed a three dimensional sample of the studied configuration in order to simulate the evolution of the resulting flowfield. For that, the Navier Stokes equations were simulated with an RSM second order turbulent closure model. Then a non uniform meshing was applied. A good agreement was obtained between the experimental data and the numerical modeling. After validation we could represent in addition to the available results, the temperature distribution and the effects the variation of the injection inclination and that of the jets’ spacing bring on it (on its spatial evolution).

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1991 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodolgy. The fully three dimensional, compressible, Reynolds averaged Navier-Stokes equations with k-ε turbulence modelling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1992 ◽  
Vol 114 (3) ◽  
pp. 528-537 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier–Stokes equations with k–ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

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