Investigation of Throughflow Hypothesis in a Turbine Cascade Using a Three-Dimensional Navier–Stokes Computation

1995 ◽  
Vol 117 (1) ◽  
pp. 126-132
Author(s):  
G. Perrin ◽  
F. Leboeuf
Keyword(s):  
Kinetic Energy ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Minor Role ◽  
Passage Vortex ◽  
Spatial Fluctuations ◽  
Flow Variables ◽  
A Minor

The results of a computation, performed with a three-dimensional Navier–Stokes computation at ONERA, have been averaged in the blade-to-blade direction; the spatial fluctuations around the averaged flow variables have also been determined. It has then been possible to estimate all terms in the average components of the momentum equations. The comparison of the two-dimensional balances of these three equations shows that the shear stress plays a minor role in the momentum balance, except on the dissipation of the passage vortex kinetic energy downstream of the blade trailing edges. The kinetic energy of the spanwise component of the velocity spatial fluctuations has a very strong influence on the radial pressure gradient; it introduces a convection effect. This is a key effect for all these balances.

Investigation of Through-Flow Hypothesis in a Turbine Cascade Using a 3D Navier-Stokes Computation

1993 ◽  
Author(s):  
G. Perrin ◽  
F. Leboeuf
Keyword(s):  
Kinetic Energy ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Minor Role ◽  
Passage Vortex ◽  
Spatial Fluctuations ◽  
Flow Variables ◽  
A Minor

The results of a computation, performed with a three-dimensional Navier-Stokes computation at ONERA, have been averaged in the blade-to-blade direction; the spatial fluctuations around the averaged flow variables have also been determined. It has then been possible to estimate all terms in the average components of the momentum equations. The comparison of the two-dimensional balances of these three equations shows that the shear stress play a minor role in the momentum balance, except on the dissipation of the passage vortex kinetic energy downstream of the blade trailing edges. The kinetic energy of the spanwise component of the velocity spatial fluctuations has a very strong influence on the radial pressure gradient; it introduces a convection effect. This is a key effect for all these balances.

scholarly journals Effect of the Radial Pressure Gradient on the Secondary Flow Generated in an Annular Turbine Cascade

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hesham M. El-Batsh
Keyword(s):  
Pressure Gradient ◽  
Secondary Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Navier Stokes ◽  
Pressure Probe ◽  
Passage Vortex ◽  
Flow Loss ◽  
Radial Pressure Gradient

This paper introduces an investigation of the effect of radial pressure gradient on the secondary flow generated in turbine cascades. Laboratory measurements were performed using an annular sector cascade which allowed the investigation using relatively small number of blades. The flow was measured upstream and downstream of the cascade using a calibrated five-hole pressure probe. The three-dimensional Reynolds Averaged Navier Stokes equations were solved to understand flow physics. Turbulence was modeled using eddy-viscosity assumption and the two-equation Shear Stress Transport (SST)k-ωmodel. The results obtained through this study showed that the secondary flow is significantly affected by the pressure gradient along blade span. The experimental measurements and the numerical calculations predicted passage vortex near blade hub which had larger and stronger values than that predicted near blade tip. The loss distribution revealed that secondary flow loss was concentrated near blade hub. It is recommended that attempts of reducing secondary flow in annular cascade should put emphasis on the passage vortex near the hub.

scholarly journals On the Transport of Spatial Fluctuation Correlations in a Turbine Stator

1994 ◽  
Author(s):  
G. Perrin ◽  
F. Leboeuf
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Test Case ◽  
Spatial Fluctuation ◽  
Turbine Stator ◽  
Passage Vortex ◽  
And Diffusion ◽  
Highly Loaded

When averaging the Navier-Stokes or Euler equations in the circumferential direction of a turbomachine, some so-called “spatial fluctuation terms” appear in the averaged conservation equations. We give the transport equations for these kinematic spatial fluctuation correlations. We evaluate the various terms in these equations, using the results of a three-dimensional Navier-Stokes computation. The test case is a highly loaded subsonic turbine stator. We discuss the magnitudes of the various terms. It is shown that blade force terms and diffusion terms have dominant effects, as respect to the production by the averaged field and the shear stress terms. The dissipation of the fluctuation kinetic energy occurs mainly in the passage vortex area, and in the blade wake.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

scholarly journals Numerical simulations of flow past an autonomous underwater vehicle at various drift angles

2012 ◽  
Vol 9 (2) ◽  
pp. 135-152 ◽  
Author(s):  
Sreekar Gomatam ◽  
S Vengadesan ◽  
S K Bhattacharyya
Keyword(s):  
Autonomous Underwater Vehicle ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Underwater Vehicle ◽  
Navier Stokes ◽  
Structure Variation ◽  
Flow Past ◽  
Computational Fluid Dynamics Cfd ◽  
Marine Engineering ◽  
Flow Variables

Three dimensional (3D) flow past an Autonomous Underwater Vehicle (AUV) is simulated using a Computational Fluid Dynamics (CFD) approach at a Reynolds (Re) number of 2.09x106. A non-linear k-? (NLKE) turbulence model is used for solving the Reynolds Averaged Navier-Stokes (RANS) equations. The effect of control surfaces over the flow, the flow interaction between the hull and the appendages at various Angles of Attack (AoA) and the effect of the symmetry plane is studied. Flow structure, variation of flow variables and force distribution for various AoA are presented and discussed in detail.DOI: http://dx.doi.org/10.3329/jname.v9i2.12567 Journal of Naval Architecture and Marine Engineering 9(2012) 135-152

Three-dimensional unsteady Navier—Stokes analysis of stator—rotor interaction in axial-flow turbines

2000 ◽  
Vol 214 (1) ◽  
pp. 13-22 ◽  
Author(s):  
L He
Keyword(s):  
Three Dimensional ◽  
Axial Flow ◽  
Navier Stokes ◽  
Time Stepping ◽  
Finite Volume Discretization ◽  
Dual Time Stepping ◽  
Passage Vortex ◽  
Speed Up ◽  
Time Marching ◽  
Grid Technique

A three-dimensional full Navier-Stokes method is developed and applied to calculations of unsteady flows through multiple blade rows in axial-flow turbomachinery. The solver adopts the cellcentred finite volume discretization and the four-stage Runge-Kutta time-marching scheme. Unsteady calculations are effectively accelerated by using a time-consistent multi-grid technique, resulting in a speed-up by a factor of 10–20 with adequate temporal accuracy. The computational efficiency and validity of the present multi-grid technique are illustrated by comparisons with the results of the conventional dual time-stepping scheme. Calculated unsteady pressures on blade surfaces for a turbine stage performances at different stator-rotor axial gaps reveals a marked three-dimensional behaviour of the interaction between incoming wakes and rotor passage-vortex structures. The time-averaged losses from unsteady calculations show a noticeable spanwise redistribution compared with the steady results. Two dimensional and three-dimensional calculations indicate opposite trends in stage efficiency variation when the stator—rotor gap is reduced.

scholarly journals NUMERICAL SIMULATION OF TURBULENT WAVE BOUNDARY LAYERS

1986 ◽  
Vol 1 (20) ◽  
pp. 119 ◽  
Author(s):  
J.H. Trowbridge ◽  
C.N. Kanetkar ◽  
N.T. Wu
Keyword(s):  
Velocity Field ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Second Order ◽  
Minor Role ◽  
Steady Streaming ◽  
Stokes Waves ◽  
A Minor ◽  
Wave Boundary

This paper reports numerical computations of fully rough turbulent boundary layers produced by first and second order Stokes waves. The computations are based on a mixing length turbulence closure and on a slightly more sophisticated turbulent kinetic energy closure. The first order results compare well with existing laboratory results. Reversal of the second order steady streaming under relatively long waves, which has been predicted analytically, is also predicted in the numerical results, The steady second order velocity field is found to become fully established only after a development time on the order of a few hundred wave periods. Both the first and second order results indicate that advection and diffusion of turbulent kinetic energy play a minor role in determining the Reynolds averaged velocity field.

scholarly journals Modelling of snow entrainment and deposition in powder-snow avalanches

1998 ◽  
Vol 26 ◽  
pp. 253-258 ◽  
Author(s):  
Dieter Issler
Keyword(s):  
Kinetic Energy ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Model Parameters ◽  
Momentum Exchange ◽  
Erosion And Deposition ◽  
Practical Applications ◽  
Suspension Layer ◽  
Dense Flow ◽  
Avalanche Formation

Following Norem’s description of powder-snow avalanche formation and structure, we propose a mathematical model that consists of a suspension layer and a so-called saltation layer. The latter is only a few meters deep and is modelled by depth-averaged mass and momentum balances. In the suspension layer, the mass and momentum balance equations for the mixture are supplemented by the snow mass balance and the transport equations for turbulent kinetic energy and dissipation. Mass and momentum exchange between the two layers is determined by particle settling, turbulent diffusion against the concentration gradient and aerodynamic shear forces. The net erosion or deposition rate is a function of the kinetic energy of the impacting particles. The saltation layer reacts on the suspension layer in that saltating particles extract momentum from the air flow. The preliminary estimates of the model parameters can be refined by means of saltation-trajectory simulations. Three-dimensional simulations with a simplified model have clearly shown the importance of snow erosion and deposition in practical applications. This approach is well suited for coupling to a dense-flow avalanche model.

scholarly journals Flow Topology of Three-Dimensional Spherical Flame in Shock Accelerated Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Yuejin Zhu ◽  
Lei Yu ◽  
Gang Dong ◽  
Jianfeng Pan ◽  
Zhenhua Pan
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Joint Probability ◽  
Reflected Shock Wave ◽  
Minor Role ◽  
Flow Topology ◽  
Reflected Shock ◽  
Compression And Expansion ◽  
Scale Turbulence ◽  
A Minor

The flow topologies of compressible large-scale distorted flames are studied by means of the analysis of the invariants of the velocity gradient tensor (VGT). The results indicate that compressibility plays a minor role in the distorted flame zone. And the joint probability density function (p.d.f.) of the Q-R diagram appears as a teardrop shape, which is a universal feature of turbulence. Therefore, the distorted flame exhibits the characteristic of large-scale turbulence combustion, especially behind the reflected shock wave, while the p.d.f. of the QS⁎-QW diagram implies that the dissipation is enhanced in the compression and expansion regions, where it is higher than that when P=0. Furthermore, we identify that the flame evolution is dominated by rotation by means of a quantitative statistical study, and the SFS topology is the predominant flow pattern. Not surprisingly, negative dilatation could suppress the unstable topologies, whereas positive dilatation could suppress the stable topologies.

scholarly journals Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1528
Author(s):  
Mads Kyed
Keyword(s):  
Kinetic Energy ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Periodic Forcing ◽  
Navier Stokes Equations ◽  
Whole Space ◽  
Time Periodic Solutions ◽  
Time Periodic

The existence of weak time-periodic solutions to Navier–Stokes equations in three dimensional whole-space with time-periodic forcing terms are established. The solutions are constructed in such a way that the structural properties of their kinetic energy are obtained. No restrictions on either the size or structure of the external force are required.

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