Solutions of the incompressible Navier-Stokes equations using an upwind -differenced TVD scheme

2008 ◽  
pp. 278-282 ◽  
Author(s):  
Joseph J. Gorski
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Navier Stokes Equations

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

SPONTANEOUS NONEQUILIBRIUM CONDENSATION IN SUPERSONIC JETS IMPINGING ON CAVITY

2014 ◽  
Vol 06 (06) ◽  
pp. 1450070
Author(s):  
M. M. A. ALAM ◽  
T. SETOGUCHI ◽  
H. D. KIM
Keyword(s):  
Stokes Equations ◽  
Supersonic Jets ◽  
Navier Stokes ◽  
Droplet Growth ◽  
Tvd Scheme ◽  
Growth Equation ◽  
Moist Air ◽  
Navier Stokes Equations ◽  
Homogeneous Condensation ◽  
Flow Features

Spontaneous condensation of moist air in supersonic jets is of considerable interest in a variety of natural and industrial processes. During impingement of supersonic moist air jets, the nonequilibrium homogeneous condensation can be experienced at the region between downstream of nozzle exit and an obstacle. The subsequent release of latent heat thus results in a deceleration of the flow and a rise in pressure, known traditionally as the condensation shock; likely have strong effect on the flow features. The present paper reported of the effect of spontaneous nonequilibrium homogeneous condensation of moist air on the aerodynamic and oscillatory flow features of supersonic jets impinging on cavity. A total variation diminishing (TVD) scheme was used to solve the time dependent Favre averaged Navier–Stokes equations, and the droplet growth equation of liquid phase production for simulating the condensing jets. Both qualitative and quantitative validations of the numerical model were accomplished, and the results showed a good agreement between the computed results and experimental data. Predicted flow and oscillatory features of jets were presented.

A Numerical Investigation of Vortex Induced Vibration on an Elastically Mounted Rigid Cylinder

2008 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos Levi
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Moving Cylinder ◽  
Frequency Phase

The Vortex-Induced Vibration on an elastically mounted circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds Averaged Navier-Stokes equations and results are compared with experimental data. The upwind TVD scheme of Roe – Sweby is used to solve the governing equations and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the cylinder. The cylinder is laterally supported by a spring and a damper and is free to oscillate in the transverse direction. Results for the lift coefficient amplitude, displacement amplitude, frequency, phase angle, and power absorbed by the system are presented and compared to experimental data. The code was tested for the fixed cylinder case, and for the moving cylinder. The comparison with experimental data obtained from the literature showed the good quality of the numerical results and validated the code for simulations of vortex-induced vibration.

Development of A Two-Equation Turbulence Model for Hypersonic Shock Wave and Turbulent Boundary Layer Interaction

2011 ◽  
Vol 66-68 ◽  
pp. 1868-1873
Author(s):  
Jing Yuan Liu ◽  
Chun Hian Lee
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Single Point ◽  
Turbulence Models ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Navier Stokes Equations ◽  
Boundary Layer Interaction ◽  
Artificial Diffusion

For hypersonic compressible turbulence, the correlations with respect to the density fluctuation must not be neglected. A Reynolds averaged K-ε model is proposed in the present paper to include these correlations, together with the Reynolds averaged Navier-Stokes equations to describe the mean flowfield. The K-equation is obtained from Reynolds averaged single-point second moment equations which are deduced from the instantaneous compressible Navier-Stokes equations. Under certain hypotheses and scales estimation of the compressible terms, the K-equation is simplified. The correlation terms of the fluctuation field appearing in the resulting K-equation, together with a conventional form of the ε-equation, are thus correlated with the variables in the average field. The new modeling coefficients of closure terms are optimized by computing the hypersonic turbulent flat-plate measured by Coleman and Stollery [J. Fliud Mech., Vol. 56 (1972), p. 741]. The proposed model is then applied to simulate hypersonic turbulent flows over a wedge compression corner angle of 34 degree. The predicting results compare favorably with the experimental results. Also, comparisons are made with other turbulence models. Additionally, an entropy modification function of Harten-Yee’s TVD scheme is introduced to reduce artificial diffusion near boundary layers and provide the required artificial diffusion to capture the shockwaves simultaneously.

Vectorizable Implicit Algorithms for the Flux-Difference Split, Three-Dimensional Navier-Stokes Equations

1988 ◽  
Vol 110 (3) ◽  
pp. 297-305 ◽  
Author(s):  
P-M. Hartwich ◽  
C-H. Hsu ◽  
C. H. Liu
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Approximate Factorization ◽  
Navier Stokes Equations ◽  
Spatial Direction ◽  
Upwind Schemes ◽  
Highly Nonlinear ◽  
Flux Difference

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computations of vortical flows over a sharp-edged, thin delta wing have been chosen as numerical test cases. The convergence performance of the algorithms is discussed, and the accuracy of the computed flow field results is assessed. The validity of the present results is demonstrated by comparisons with experimental data.

A Two-Dimensional Numerical Simulation of Roll Damping Decay of a FPSO Using the Upwind TVD Scheme of Roe-Sweby

2012 ◽  
Author(s):  
Gustavo O. Guarniz Avalos ◽  
Juan B. V. Wanderley
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Viscous Effects ◽  
Roll Damping ◽  
Navier Stokes Equations ◽  
Decay Test ◽  
Spurious Oscillations ◽  
Volume Method ◽  
Bilge Keel

The study of roll damping is investigated for a Floating Production Storage and Offloanding (FPSO). For this purpose, a roll decay test of FPSO is simulated by means of the numerical solution of the slightly compressible Navier-Stokes equations in 2D. The governing equations are solved using the finite volume method and the upwind TVD scheme of Roe-Sweby. The roll damping for rectangular hulls is dominated by viscous effects. Strong vortices are formed around the bilge keel. Hence, in this zone, there is a discontinuity of pressure that the TVD scheme will resolve and capture the physics of the phenomenon without spurious oscillations. The numerical results are compared with experimental data for validating the numerical scheme implemented.

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