An implicit finite volume nodal point scheme for the solution of two-dimensional compressible navier-stokes equations

An implicit finite volume nodal point scheme has been developed for solving the two-dimensional compressible Navier-Stokes equations. The numerical scheme is evolved by efficiently combining the basic ideas of the implicit finite-difference scheme of Beam and Warming (1978) with those of nodal point schemes due to Hall (1985) and Ni (1982). The 2-D Navier-Stokes solver is implemented for steady, laminar/turbulent flows past airfoils by using C-type grids. Turbulence closure is achieved by employing the algebraic eddy-viscosity model of Baldwin and Lomax (1978). Results are presented for the NACA-0012 and RAE-2822 airfoil sections. Comparison of the aerodynamic coefficients with experimental results for the different test cases presented here establishes the validity and efficiency of the method

Application of Program Laws to LCA Planforms

This report presents the results of the computational work carried out for the lift analysis of LCA wings in supersonic flows using a computer software called LAWS [1]. The lifting pressure distribution and the associated force coefficients have been obtained for three planforms specified by the LCA group

RANS Computations for flow through a variable mach number flexible nozzle at a mach 4

Numerical simulation of flow through a Variable Mach number Flexible Nozzle (VMFN) at Mach 4 is carried out using the CFD code IMPRANS to validate the design of the nozzle based on the method of characteristics with boundary layer correction. The CFD analysis for the contour uses an implicit Reynolds-averaged Navier-Stokes (RANS) solver with Baldwin-Lomax turbulence model.Detailed flow characteristics like the centerline Mach number distribution and Mach contours of the steady flow through the converging x2013; diverging nozzle are obtained to study and assess the suitability of the design

Viscous unsteady flow around a helicopter rotor blade in forward flight

The unsteady three dimensional Reynolds averaged Navier-Stokes equations are solved for the moving domain in an inertial frame of reference to obtain time-accurate solution for the flow past a helicopter rotor blade in forward flight.The method uses an implicit dual time stepping procedure,a finite volume nodal point spatial discretisation and baklwin-Lomax turbulence model.Results are presented for nonlifting and lifting cases.For the first case,the surface pressure distributions are found to be in good agreement with the experimental results at 89% of the rotor radius,except near the shock which is predicted to lie closer to the leading edge.In the lifting case,the surface pressure distributions compare well with the inviscid solution,both methods predicting the presence of a shock in the outboard region at the azimuth angle of 90 degree.However,the effect of viscosity here turns out to be to weaken the shock as well as to shift the shock position upstream

Implicit boundary condition procedure - Application to 1-D euler solver

An implicit boundary condition procedure is employed in the.solution of one-dimensional Euler equations by the implicit finite dixA3;erence scheme of Beam and warming. The implicit boundary point trecitment is-based on the method of characteristics. Implementation of the procedure is illustrated using the subsonic inflow and outflow conditions for a quasi-one-dimensional Laval nozzle flow. Results show that implicit application of boundary conditions. enhances the potential of the implicit algori thrn by permitting the use of large time steps

Computation of compressible flows: Implicit methods 13; 13;

The present lecture is mainly concerned with the implicit finite difference technique of Beam and Warming and some of the many variants of this popular and widely used implicit method. The Euler and Navier-Stokes equations for 2-D compressible flows and the implicit time differencing formulae are presented in sections 2 and 3. The implicit, noniterative, approximate factorization, central difference algorithm in delta form is derived in section 4 while section 5 deals with stability and convergence considerations. Next, some salient features of implicit upwind schemes based on flux-vector splitting, and TVD schemes are discussed in section 6. The unfactored implicit relaxation method due to Hanel et al is outlined in section 7. Finally, an implicit finite volume nodal point scheme is presented in section 8. Section 9 presents some examples and results for certain flow problems while section 10 contains some concluding remarks.13; 13

LAWS-Lift analysis of wings in supersonic flows

A computer program 'called LAWS has been developed for the Lift Analysis of Wings In Supersonic flows. The program Is based on supersonic linearized theory integral equations and the Mach box method of wing representation Given the planform and the free stream Mach number, the code computes the lifting pressure distribution over the wing . surface and the associated force coefficients. The methodology used here is valid for flat wings with any complex planform. Comparison of the results for flat delta and arrow wings show good agreement with the -exact solutions . The Input and output information for program LAWS is . available in the help file of code NALSOF0507 of the SOFFTS library at NAL

Computational requirements for the solution of navier-stokes equations

An overview of the computational requirements for the13; application of Navier-Stokes equations in the design of a13; flight vehicle is presented. Estimates given in different13; references are summarised. The pacing items in accomplishing the numerical simulation of the flow around a flight vehicle are also outlined

Solution of one-dimensional euler-equations by the implicit finite difference technique of beam and warming

A computer program has been developed for the solution of13; one-dimensional Euler equations by the implicit finite difference method of Beam and Warming. The initial and boundary conditions of a given one-dimensional inviscid flow problem form the basic input for the l-D Euler solver. Two test cases - (i) propagating shock wave and (ii) shock tube flow - are considered. Results obtained show fairly good agreement with exact solutions

An implicit navier-stokes solver for the steady laminar supersonic flow past a semi-infinite flat plate at zero incidence

An implicit Navier-Stokes solver has been developed for simulating the steady laminar supersonic flow past a semi-infinite flat plate at zero incidence. The implicit finite difference technique of Beam and Warming is employed for solving the two-dimensional compressible Navier-Stokes equations. Computations have been carried out for the test case of Mach number = 2.0 and .6. Reynolds number = 10. The velocity profile in the boundary layer compares well w:ith the similar solution profile. The 2-D Navier-Stokes code is capable of capturing the leading edge shock as well. About 300 time steps are needed to yield the time asymptotic steady state solution