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At least 559 records · Page 31

Unsteady inviscid and viscous computations for vortex-dominated flows

The unsteady supersonic flow around a rigid sharp-edged delta wing is solved using the unsteady Euler and thin-layer Navier-Stokes equations. The problem is formulated relative to a moving frame of reference so that computation of the grid motion is not required. A three-dimensional, implicit, aproximately factored, central-differencing, finite-volume scheme is used to obtain the time-accurate, unsteady, locally conical flow. The inviscid and viscous results are compared during the periodic response of a wing undergoing forced rolling-oscillation motion. The results show substantial differences in the surface pressure results and other distributed flow characteristics. These differences are attributed to the inviscid and viscous flow predictions in the vortex-dominated regions. The results of the total loads do not show any significant differences.

Kandil, Osama A.↗

Multigrid solution of unsteady Navier-Stokes equations using a pressure method

A multigrid relaxation method is applied to a pressure-based implicit procedure to solve unseady, incompressible Navier-Stokes equations. The present multigrid method is a Correction Scheme according to Brandt. This method is used to solve the scalar matrices resulting from the finite-volume formulation and uses flux averaging as the restriction operator. The accuracy and computational efficiency are demonstrated with a steady state driven cavity flow and an unsteady flow over a circular cylinder case. The results are compared with single grid results using the OrthoMin conjugate gradient method and experimental data.

Jiang, Y.↗

Computational study for passive control of supersonic asymmetric vortical flows around cones

The unsteady, compressible, double and single thin-layer Navier-Stokes equations are used to numerically study for the passive control of steady and unsteady, supersonic asymmetric flows around circular and noncircular cones. The main computational scheme of the present study is the implicit upwind, flux-difference splitting, finite-volume scheme. Passive control of flow asymmetry is studied by using a vertical fin in the leeward plane of geometric symmetry and side strakes with and without thickness at different orientations. The study is focused on circular-section cones since they are the most potential section-shapes for strong flow asymmetry. Side-strakes passive control has been shown to be more efficient and practical than the vertical-fin passive control.

Liu, C. H.↗

Enthalpy damping for high Mach number Euler solutions

An improvement on the enthalpy damping procedure currently in use in solving supersonic flow fields is described. A correction based on entropy values is shown to produce a very efficient scheme for simulation of high Mach number three-dimensional flows. Substantial improvements in convergence rates have been achieved by incorporating this enthalpy damping scheme in a finite-volume Runge-Kutta method for solving the Euler equations. Results obtained for blended wing-body geometries at very high Mach numbers are presented.

Moitra, Anutosh↗

Numerical study of turbulent secondary flows in curved ducts

The pressure driven, fully-developed turbulent flow of an incompressible viscous fluid in curved ducts of square-section is studied numerically by making use of a finite volume method. A nonlinear Kappa - Iota model is used to represent the turbulence. The results for both straight and curved ducts are presented. For the case of fully-developed turbulent flow in straight and curved ducts, the secondary flow is characterized by an eight-vortex structure for which the computed flowfield is shown to be in good agreement with available experimental data. The introduction of moderate curvature is shown to cause a substantial increase in the strength of the secondary flow and to change the secondary flow pattern to either a double-vortex or a four-vortex configuration.

Hur, N.↗

Modeling supersonic combustion using a fully-implicit numerical method

A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.

Maccormack, Robert W.↗

Advances in fluid dynamics

Various papers on advances in fluid dynamics are presented. Individual topics addressed include: nonunique solutions of the Euler equations; numerical solution of the biharmonic equation using a spectral multigrid method; finite-volume shape and placement for efficiency, accuracy, and physics; NND schemes and their application to numerical simulation of complex plume flow problems; symbolic analysis and computational algorithm construction; and velocity and mass flux distribution measurements of spherical glass beads in air flow in a 90-deg vertical-to-horizontal bend. Also discussed are: hyperbolic solution adaptive mesh generation; progress and future directions in CFD; numerical simulation of shock focusing; microbubble formation and splitting in a turbulent boundary layer for turbulence reduction; numerical study of spherical Taylor-Couette flow, trajectories of vortex lines beneath a free surface or above a plane; and a mathematical model for response of the coronary circulation to high sustained gravitational force fields.

Ballhaus, W. F., Jr.↗

CFD spinoff - Computational electromagnetics for radar cross section (RCS) studies

A finite-volume discretization procedure derived from proven CFD methods is used to solve the conservation form of the time-domain Maxwell's equations, in order to compute EM scattering from layered objects. This time-domain approach handles both single-frequency/continuous wave and broadband-frequency/pulse incident excitation. Arbitrarily shaped objects are modeled by means of a body-fitted coordinate transformation; complex internal/external structures with many material layers are treated through the implementation of a multizone framework capable of handling any type of zonal boundary condition. Results are presented for various two- and three-dimensional problems.

Shankar, Vijaya↗

3D Euler analysis of ducted propfan flowfields

A numerical method is presented for predicting the steady inviscid flow through a ducted propfan based on a time-marching solution of the three-dimensional Euler equations. A four-stage multiple-block Runge-Kutta finite volume numerical technique, utilizing implicit residual smoothing and a blended second and fourth difference dissipation, is applied to predict the transonic flowfield about both single-rotation and counter-rotations ducted rotors. Counter-rotation predictions are based on an average-passage system of equations approach. Calculations are performed for both a single sheared H-type grid system and a multiple-block grid system incorporating a C-type grid about the cowl. Numerical results are compared with experimental data for two cases: a low speed ducted propeller and a 1.15 pressure ratio fan stage.

Hall, Edward J.↗

An upwind approach to unsteady flowfield simulation

A numerical method to determine unsteady solutions of the laminar, perfect gas Navier-Stokes equations has been developed. The structured finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the viscous terms are computed by central differencing. Comparisons of numerical, analytical, and experimental results are made in two and three dimensions. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing.

Atwood, Christopher A.↗

Calculations of gaseous H2/O2 thruster

Calculations were made for the gaseous H2/O2 thruster for the Space Station by using the RPLUS code which employs an implicit finite volume, LUSSOR scheme to solve the Navier-Stokes equations and the species equations. The combustion processes of hydrogen and oxygen are modeled by a 9 species and 18 step reaction mechanism and the turbulence is simulated by the Baldwin-Lomax turbulence model for the thruster wall boundary layer and the modified Prandtl's mixing length model for the reacting shear layer. Results are presented for different mixture ratios and fuel film cooling percents and compared with the experimental data. The calculated performance predictions for the thruster agree well with the experimental data and the results demonstrate that the RPLUS code can be used for design and analysis of thrusters and rockets.

Kim, S. C.↗

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗

Computation of vortex-dominated flow for a delta wing undergoing pitching oscillation

The conservative, unsteady Euler equations for the flow relative to a moving frame of reference are used to solve for the three-dimensional steady and unsteady flows around a sharp-edged delta wing. The resulting equations are solved by using an implicit, approximately factored, finite-volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in crossflow planes at the grid-chord stations. The computational applications cover a steady flow around a delta wing, whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack. The steady results are compared with the experimental data, and the unsteady results are compared with results of a flux-difference splitting scheme.

Kandil, Osama A.↗

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

Chang, I-Chung↗

Numerical computation of viscous flow about unconventional airfoil shapes

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Ahmed, S.↗

Interactive real time flow simulations

An interactive real time flow simulation technique is developed for an unsteady channel flow. A finite-volume algorithm in conjunction with a Runge-Kutta time stepping scheme was developed for two-dimensional Euler equations. A global time step was used to accelerate convergence of steady-state calculations. A raster image generation routine was developed for high speed image transmission which allows the user to have direct interaction with the solution development. In addition to theory and results, the hardware and software requirements are discussed.

Sadrehaghighi, I.↗

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗