A three-dimensional incompressible Navier-Stokes flow solver using primitive variables
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Kwak, D.↗
Engineering topics
Kwak, D.
Publications and source records attributed to Kwak, D..
A numerical study of three-dimensional incompressible flow around multiple posts
The incompressible laminar flow around single and double rows of an infinite number of posts between two flat plates has been calculated numerically. A C-grid with periodic boundary conditions has been used. The angle of attack, measured from the line normal to the row of posts, was varied between zero and less than 90 deg. The pressure loading was computed for all of the posts in each of these cases. Most of these calculations have been carried out on the Numerical Aerodynamic Simulation Cray 2 at NASA Ames Research Center.
Rogers, S. E.↗
Numerical Solution of the Incompressible Navier-Stokes Equations in Three-dimensional Generalized Curvilinear Coordinates
Numerically solving the incompressible Navier-Stokes equations is known to be time consuming and expensive. Testing of the INS3D computers code, which solves these equations with the use of the pseudocompressibility method, shows this method to be an efficient way to obtain the steady state solution. The effects of the waves introduced by the pseudocompressibility method are analyzed and criteria are set and tested for the choice of the pseudocompressibility parameter which governs the artificial sound speed. The code is tested using laminar flow over a two dimensional backward-facing step, and laminar flow over a two dimensional circular cylinder. The results of the computations over the backward-facing step are in excellent agreement with experimental results. The transient solution of the flow over the cylinder impulsively started from rest is in good agreement with experimental results. However, the computed frequency of periodic shedding of vortices behind the cylinder is not in agreement with the experimental value. For a three dimensional test case, computations were conducted for a cylinder end wall junction. The saddle point separation and horseshoe vortex system appear in the computed field. The solution also shows secondary vortex filaments which wrap around the cylinder and spiral up in the wake.
Rogers, S. E.↗
On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations
The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.
Rogers, S. E.↗
Computations of internal turbulent flow with large separated flow regions
An implicit two-equation turbulence solver in generalized coordinates has been developed and is used in conjunction with the three-dimensional incompressible Navier-Stokes solver, INS3D, to calculate the internal flow in one channel and in an additional channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the kappa-epsilon turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations are integrated using wall functions. The latter approach yields a faster convergence to the steady state solution than the former. For the case of channel flow, both the wall function and wall boundary condition approaches yield results in good agreement with the experimental data. the back-step (sudden expansion) flow is calculated using wall function approach. The predictions are in reasonable agreement with the experimental data.
Kaul, U. K.↗
A three-dimensional incompressible flow simulation method and its application to the Space Shuttle main engine. II Turbulent flow
An implicit finite difference code cast in general curvilinear coordinates is further developed for three-dimensional incompressible turbulent flows. The code is based on the method of pseudocompressibility and utilizes the Beam and Warming implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is further extended to include composite-grids to overcome the excessive computer memory required for solving turbulent flows in complex three-dimensional geometries. A simple turbulence model is proposed for internal flows. The code is being used for the Space Shuttle Main Engine (SSME) internal flow analyses.
Chang, J. L. C.↗
A computational study of saddle point separation and horseshoe vortex system
Incompressible flow around a cylinder-end wall junction has been simulated by solving the incompressible Navier-Stokes equations in three dimensions. The equations, cast in generalized curvilinear coordinates, are solved in time as a hyperbolic system by adding a pressure term in the continuity equation and are marched to a steady state. Various physical quantities associated with the saddle point of separation and the horseshoe vortex system are calculated. Computational and experimental results are generally consistent. The skin friction and the pressure distribution on the end wall are consistent with the physics of the problem. Secondary flows both in front of the cylinder and behind it are predicted that are in qualitative agreement with flow visualization results. The calculations also indicate a strongly nonuniform pressure loading along the length of the cylinder. A new mechanism for the existence of the recirculation bubbles behind the cylinder-end wall with relatively low ratio of cylinder height to the approaching boundary layer thickness is observed which is markedly different from its two-dimensional counterpart.
Kaul, U. K.↗
A new consistent spatial differencing scheme for the transonic full-potential equation
Previously cited in issue 5, p. 585, Accession no. A83-16678
Flores, J.↗
A solution procedure for three-dimensional incompressible Navier-Stokes equation and its application
An implicit, finite-difference procedure is presented for numerically solving viscous incompressible flows. For convenience of applying the present method to three-dimensional problems, primitive variables, namely the pressure and velocities, are used. One of the major difficulties in solving incompressible flows that use primitive variables is caused by the pressure field solution method which is used as a mapping procedure to obtain a divergence-free velocity field. The present method is designed to accelerate the pressure-field solution procedure. This is achieved by the method of pseudocompressibility in which the time derivative pressure term is introduced into the mass conservation equation. The pressure wave propagation and the spreading of the viscous effect is investigated using simple test problems. The present study clarifies physical and numerical characteristics of the pseudo-compressible approach in simulating incompressible flows. Computed results for external and internal flows are presented to verify the present procedure. The present algorithm has been shown to be very robust and accurate if the selection of the pseudo-compressibility parameter has been made according to the guidelines given.
Kwak, D.↗
A computational method for viscous incompressible flows
An implicit, finite-difference procedure for numerically solving viscous incompressible flows is presented. The pressure-field solution is based on the pseudocompressibility method in which a time-derivative pressure term is introduced into the mass-conservation equation to form a set of hyperbolic equations. The pressure-wave propagation and the spreading of the viscous effect is investigated using simple test problems. Computed results for external and internal flows are presented to verify the present method which has proved to be very robust in simulating incompressible flows.
Kwak, D.↗
An incompressible Navier-Stokes flow solver in three-dimensional curvilinear coordinate systems using primitive variables
An implicit, finite-difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional, curvilinear coordinate system. The pressure-field solution is based on the pseudo compressibility approach in which the time derivative pressure term is introduced into the mass conservation equation to form a set of hyperbolic equations. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds stresses, that are uncoupled from the implicit scheme, are lagged by one time-step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computed, and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.
Kwak, D.↗
On the method of pseudo compressibility for numerically solving incompressible flows
Pseudo compressibility is used for numerically solving incompressible flows to achieve computational efficiency. The use of pseudo compressibility results in a system of hyperbolic-type equations of motion that introduce waves of finite speed. The interactions of the wave propagation and the vorticity spreading are analyzed. A criterion governing the dependence of the pseudo compressiblity on the Reynolds number and the characteristic length of the flow geometry is obtained that allows for a proper convergence. It is demonstrated that the solution does tend to the incompressible limit. External and internal viscous flow test problems are presented to verify the theory.
Chang, J. L. C.↗
A new consistent spatial differencing scheme for the transonic full-potential equation
A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.
Flores, J.↗
An implicit, transonic, full-potential code for cascade flow on H-grid topology
A transonic, full-potential code is developed for computing the flow through two-dimensional cascades using an H-type grid topology that employs an implicit approximate-factorization scheme. The body-conforming H-grid is generated numerically by solving Poisson's equation. The flow-solution algorithm at the coordinate mapping singularity associated with this grid is investigated using two different types of finite-difference schemes. The grid-geometry effect on these schemes is also studied by noting free-stream capturing properties. It is found that by implementing a consistent spatial differencing scheme, the mapping singularities can be resolved numerically, and the grid-geometry-induced error minimized. The code is verified by computing model cascade flow problems.
Kwak, D.↗
Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation
The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.
Kwak, D.↗
A comparative study of nonreflecting far-field boundary condition procedures for unsteady transonic flow computation
Various nonreflecting far-field boundary condition procedures are compared by implementing them in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small-disturbance equations for transonic flows about airfoils. The first- and second-approximate nonreflecting conditions, as proposed by Engquist and Majda, are compared with the condition derived from the full-characteristic equation. The far-field boundary conditions and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the full-characteristic equation produces the most effective results, thus allowing the far-field boundary to be located closer to the airfoil; this decreases the computer time required to obtain the solution because fewer mesh points are required.
Kwak, D.↗
Nonreflecting far-field boundary conditions for unsteady transonic flow computation
The approximate nonreflecting far-field boundary condition, as proposed by Engquist and Majda, is implemented in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer time required to obtain the solution through the use of fewer mesh points.
Kwak, D.↗
Three-dimensional time dependent computation of turbulent flow
The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.
Kwak, D.↗