Velocity Correction Scheme Research Articles

Analysis of flow in the spiral casing using a streamline upwind Petrov Galerkin method

Numerical simulation of complex three-dimensional flow through the spiral casing has been accomplished using a finite element method. An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime. For spatial discretization, a streamline upwind Petrov Galerkin technique has been used. The velocity field and the pressure distribution inside the spiral casing corroborate the results available in literature. The flow structure reveals the fact that very strong secondary flow is evolved on the cross-stream planes. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of flow in the spiral casing using a streamline upwind Petrov Galerkin method

Numerical simulation of complex three-dimensional flow through the spiral casing has been accomplished using a finite element method. An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime. For spatial discretization, a streamline upwind Petrov Galerkin technique has been used. The velocity field and the pressure distribution inside the spiral casing corroborate the results available in literature. The flow structure reveals the fact that very strong secondary flow is evolved on the cross-stream planes. Copyright © 1999 John Wiley & Sons, Ltd.

Three-dimensional analysis of flow in the spiral casing of a reaction turbine using a differently weighted Petrov Galerkin method

A weighted residual based finite element method has been used to predict the flow structure and the head loss in the spiral casing of a reaction turbine. An explicit Eulerian velocity correction scheme has been employed to solve the complete Reynolds-averaged Navier-Stokes equations. A Differently Weighted Petrov Galerkin (DWPG) method has been used for spatial discretization. The simulation has been performed for high Reynolds numbers. The head loss in the spiral casing has been calculated for Re = 5 × 10 5 and Re = 10 6. The velocity field and the pressure distribution inside the spiral casing corroborate the trends available in literature. The velocity field reveals the existence of a free-vortex character of the global flow field. A strong secondary flow is evolved on the cross-stream plane due to the centrifugal forces which act at right angles to the main flow.

Finite element analysis of transient natural convection in an odd‐shaped enclosure

The transient natural convective flow and heat transfer in a combined vertical and horizontal enclosure have been studied. The Galerkin’s finite element method coupled with Eulerian velocity correction scheme for pressure prediction has been employed. A detailed parametric study has been undertaken for evaluating the effects of Rayleigh number (Ra), width ratio (WR), and prescribed boundary conditions. The results indicate that the flow and isothermal patterns are strongly dependent on Ra and WR. Comparison with the results of vertical and horizontal enclosures indicates that the flow and heat transfer phenomena inside complex shaped cavities may be approximated in terms of the processes within vertical or horizontal sub‐domains. This appears to be reasonably valid if opposite walls of the enclosure are parallel. It is also observed that for certain types of boundary conditions, steady solutions do not exist at high Rayleigh numbers.

An enthalpy method for convection/diffusion phase change

AbstractAn enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.

FINITE-ELEMENT SOLUTION PROCEDURES FOR SOLVING THE INCOMPRESSIBLE, NAVIER-STOKES EQUATIONS USING EQUAL ORDER VARIABLE INTERPOLATION

The conventional finite-element formulation of the equations of motion (written in pressure-velocity variables) requires that the order of interpolation for pressure be one less than that used for the velocity components. This constraint is inconvenient and can be argued to be physically inconsistent when inertial effects are dominant. The origins of the constraint are discussed and three new finite-element formulations are advanced that permit equal order representation of pressure and velocity. Of these, the velocity correction scheme, similar to that commonly used in finite-difference procedures, offers superior performance for the examples examined in this paper.

Finite-Element Solution Procedures for Solving the Incompressible, Navier-Stokes Equations Using Equal Order Variable Interpolation

Abstract The conventional finite-element formulation of the equations of motion (written in pressure-velocity variables) requires that the order of interpolation for pressure be one less than that used for the velocity components. This constraint is inconvenient and can be argued to be physically inconsistent when inertial effects are dominant. The origins of the constraint are discussed and three new finite-element formulations are advanced that permit equal order representation of pressure and velocity. Of these, the velocity correction scheme, similar to that commonly used in finite-difference procedures, offers superior performance for the examples examined in this paper.