scholarly journals A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence

1989 ◽  
Author(s):  
JEFFREY YOKOTA
Keyword(s):  
Stokes Equations ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations

Detached-Eddy Simulations Over a Simplified Landing Gear

2002 ◽  
Vol 124 (2) ◽  
pp. 413-423 ◽  
Author(s):  
L. S. Hedges ◽  
A. K. Travin ◽  
P. R. Spalart
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Flow Fields ◽  
Equation Model ◽  
Landing Gear ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
Navier Stokes Equations ◽  
Instantaneous Flow ◽  
Eddy Simulation

The flow around a generic airliner landing-gear truck is calculated using the methods of Detached-Eddy Simulation, and of Unsteady Reynolds-Averaged Navier-Stokes Equations, with the Spalart-Allmaras one-equation model. The two simulations have identical numerics, using a multi-block structured grid with about 2.5 million points. The Reynolds number is 6×105. Comparison to the experiment of Lazos shows that the simulations predict the pressure on the wheels accurately for such a massively separated flow with strong interference. DES performs somewhat better than URANS. Drag and lift are not predicted as well. The time-averaged and instantaneous flow fields are studied, particularly to determine their suitability for the physics-based prediction of noise. The two time-averaged flow fields are similar, though the DES shows more turbulence intensity overall. The instantaneous flow fields are very dissimilar. DES develops a much wider range of unsteady scales of motion and appears promising for noise prediction, up to some frequency limit.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

Velocity Characteristics of Confined Coaxial Jets With and Without Swirl

1980 ◽  
Vol 102 (1) ◽  
pp. 47-53 ◽  
Author(s):  
M. A. Habib ◽  
J. H. Whitelaw
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Laser Doppler Anemometry ◽  
Velocity Ratio ◽  
Equation Model ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Jet Flows ◽  
Mean Velocity ◽  
Navier Stokes Equations

Measured values of the velocity characteristics of turbulent, confined, coaxial-jet flows have been obtained, without swirl, for ratios of maximum annulus to pipe velocities of 1.0 and 3.0 and with a swirl number of 0.23 for a velocity ratio of 3.0. They were obtained by a combination of pressure probes, hot-wire and laser-Doppler anemometry. The results are compared with calculations, based on the solution of finite-difference forms of the steady, Navier-Stokes equations, and an effective-viscosity hypothesis. The measurements allow the influence of confinement and swirl to be quantified and show, for example, the increased tendency towards centerline recirculation which results from both. The results with the three types of instrumentation allow a comparison within the corner recirculation region which reveals that serious errors of interpretation of mean-velocity measurements need not arise. The two-equation model, although able to represent the non-swirling flow is less appropriate to the swirling flow and the reasons are indicated.

Analysis of Combustor Acoustic Resonances Using an Efficient Transient Solver

2007 ◽  
Author(s):  
Klaus Brun ◽  
Rainer Kurz ◽  
Harold R. Simmons ◽  
Marybeth G. Nored
Keyword(s):  
Stokes Equations ◽  
Field Testing ◽  
Acoustic Resonance ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operational Conditions ◽  
Viscous Losses ◽  
Resonance Frequencies ◽  
Euler Solver

To reduce combustion induced dynamic vibrations, a thorough understanding of a combustor’s acoustic characteristics at all operational conditions is imperative. Acoustic methods that rely on the solution of the wave equation are not adequate to accurately predict acoustic resonance in any real combustor with thermal gradient and velocities. Also, solutions of the 3-D transient Navier-Stokes equations are impractical, even with today’s fast computers. A method is described herein that utilizes an efficient one-dimensional transient Euler solver to determine all acoustic resonance frequencies of a combustor at a given operating condition. Area changes, viscous losses, local temperatures, and open/closed wall-boundaries are modeled with a two-equation model. The analysis method was utilized to determine the dynamic pressures of a 20 MW industrial gas turbine’s combustor. Results compared favorably to field testing results of the same gas turbine.

Influence of the Fillet Between Blade and Casing on the Aerodynamic Performance of a Transonic Turbine Vane

2004 ◽  
Author(s):  
P. Pieringer ◽  
W. Sanz
Keyword(s):  
Stokes Equations ◽  
Equation Model ◽  
Numerical Code ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Treatment ◽  
Turbine Vane ◽  
Flow Situation ◽  
Transonic Turbine ◽  
Volume Method

Results of CFD simulations always suffer from simplifications made in flow modeling and boundary treatment, and from imprecise modeling of the geometry. For instance, the fillet between blade and casing is usually not considered in numerical calculations, since the grid generations is much more intricate and the effects on the flow result are assumed to be small. Especially when the profile close to the casing tends to induce flow separation, neglecting the fillet can result in a considerable error. In this paper, the influence of the fillet between the blade and casing at the hub and tip of a transonic turbine vane is investigated by CFD, taking into account different fillet radii. The numerical code applied solves the Reynolds-averaged Navier-Stokes equations using a time-iterative finite volume method. Turbulence is modeled by Spalart and Allmaras’ one-equation model. Results show that, depending on the flow situation, varying the fillet radius can either increase or decrease efficiency.

Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling

2009 ◽  
Vol 62 (4) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Nonlinear Models ◽  
Turbulence Models ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linear And Nonlinear ◽  
Reynolds Averaged Navier Stokes

The approach of Reynolds-averaged Navier–Stokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.

Reynolds Stress Modeling for Drag Reducing Viscoelastic Flows

2003 ◽  
Author(s):  
Richard Leighton ◽  
David T. Walker ◽  
Todd Stephens ◽  
Gordon Garwood
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Equation Model ◽  
Navier Stokes ◽  
Viscoelastic Flows ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Conformation Tensor

A Reynolds-stress transport equation model for turbulent drag-reducing viscoelastic flows, such as that which occurs for dilute polymer solutions, is presented. The approach relies on an extended set of Reynolds-Averaged Navier-Stokes equations which incorporate additional polymer stresses. The polymer stresses are specified in terms of the mean polymer conformation tensor using the FENE-P dumbbell model. The mean conformation tensor equation is solved in a coupled manner along with the Navier-Stokes equations. The presence of the polymer stresses in the equations of motion results in additional explicit polymer terms in the Reynolds-stress transport equations, as well as implicit polymer effects in the pressure-strain redistribution term. Models for both the explicit and implicit effects have been developed and implemented in a code suitable for boundary layer, rectangular channel and pipe-flow geometries. Calibration and validation is has been carried out using results from recent direct numerical simulation of viscoelastic turbulent flow.

A three-equation model for thin films down an inclined plane

2016 ◽  
Vol 804 ◽  
pp. 162-200 ◽  
Author(s):  
G. L. Richard ◽  
C. Ruyer-Quil ◽  
J. P. Vila
Keyword(s):  
Stokes Equations ◽  
Random Noise ◽  
Mathematical Structure ◽  
Liquid Films ◽  
Equation Model ◽  
Navier Stokes ◽  
Neutral Stability ◽  
Inclined Plane ◽  
Navier Stokes Equations ◽  
Wave Limit

We derive a new model for thin viscous liquid films down an inclined plane. With an asymptotic expansion in the long-wave limit, the Navier–Stokes equations and the work–energy theorem are averaged over the fluid depth. This gives three equations for the mass, momentum and energy balance which have the mathematical structure of the Euler equations of compressible fluids with relaxation source terms, diffusive and capillary terms. The three variables of the model are the fluid depth, the average velocity and a third variable called enstrophy, related to the variance of the velocity. The equations are numerically solved by classical schemes which are known to be reliable and robust. The model gives satisfactory results both for the neutral stability curves and for the depth profiles of wavy films produced by a periodical forcing or by a random noise perturbation. The numerical calculations agree fairly well with experimental measurements of Liu & Gollub (Phys. Fluids, vol. 6, 1994, pp. 1702–1712). The calculation of the wall shear stress below the waves indicates a flow reversal at the first depth minimum downstream of the main hump, in agreement with experiments of Tihon et al. (Exp. Fluids, vol. 41, 2006, pp. 79–89).

Computational Analysis of Scroll Tongue Shapes to Compressor Performance by Using Different Turbulence Models

2007 ◽  
Author(s):  
Cheng Xu ◽  
R. S. Amano
Keyword(s):  
Turbulence Model ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Range ◽  
Performance Predictions ◽  
Compressor Performance ◽  
Compressor Efficiency

A scroll is used to collect and transport swirling fluid produced by impeller or diffuser. Scroll or volute is one of the key components of centrifugal compressors. Design of the scroll not only impacts compressor efficiency but also influences operating range of the compressor. In this study, navier-stokes equations combined with both an zero-equation turbulence model and the k-ε turbulence model were used to simulate the flows inside a single stage compressor. Detailed flow simulations for a large cut back tongue scroll were presented and discussed. Studies showed that a large cut back rounded tongue scroll provided good operating range without dropping compressor peak efficiency dramatically. The turbulence model influences to the calculation were discussed and some suggestions for scroll flow modeling were made. The numerical results obtained using two turbulence models were compared and showed agreement reasonably well with experiments. Although the k-ε model behaves well inside the boundary layer, it was not decisively better than the zero-equation model for the performance predictions.

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