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Theoretical predictions and observations of incompressible viscous flow about body of revolution at angle of attack compared in report. Body consists of solid circular cylinder at downstream end and tapered in ogive of revolution to point on axis at upstream end. Study was test of modern numerical methods for solution of equations of fluid dynamics, conducted as step toward future work on more difficult problems.
The 3-D supersonic viscous flow in an experimental MHD channel has been numerically simulated. The experimental MHD channel is currently in operation at NASA Ames Research Center. The channel contains a nozzle section, a center section, and an accelerator section where magnetic and electric fields can be imposed on the flow. In recent tests, velocity increases of up to 40% have been achieved in the accelerator section. The flow in the channel is numerically computed using a new 3-D parabolized Navier-Stokes (PNS) algorithm that has been developed to efficiently compute MHD flows in the low magnetic Reynolds number regime. The MHD effects are modeled by introducing source terms into the PNS equations which can then be solved in a very e5uent manner. To account for upstream (elliptic) effects, the flowfield can be computed using multiple streamwise sweeps with an iterated PNS algorithm. The new algorithm has been used to compute two test cases that match the experimental conditions. In both cases, magnetic and electric fields are applied to the flow. The computed results are in good agreement with the available experimental data.
Rotational effects on laminar subsonic compressible viscous flow across shaft face seals, noting leakage rates and pressure profiles
A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
An improved hybrid method for computing unsteady compressible viscous flows is presented. This method divides the computational domain into two zones. In the outer zone, the unsteady full-potential equation (FPE) is solved. In the inner zone, the Navier-Stokes equations are solved using a diagonal form of an alternating-direction implicit (ADI) approximate factorization procedure. The two zones are tightly coupled so that steady and unsteady flows may be efficiently solved. Characteristic-based viscous/inviscid interface boundary conditions are employed to avoid spurious reflections at that interface. The resulting CPU times are less than 60 percent of that required for a full-blown Navier-Stokes analysis for steady flow applications and about 60 percent of the Navier-Stokes CPU times for unsteady flows in non-vector processing machines. Applications of the method are presented for a rectangular NACA 0012 wing in low subsonic steady flow at moderate and high angles of attack, and for an F-5 wing in steady and unsteady subsonic and transonic flows. Steady surface pressures are in very good agreement with experimental data and are essentially identical to Navier-Stokes predictions. Density contours show that shocks cross the viscous/inviscid interface smoothly, so that the accuracy of full Navier-Stokes equations can be retained with a significant savings in computational time.
Accurate prediction of surface skin friction and heat transfer for viscous flow applications using computational fluid dynamics tools necessitates thin wall-normal elements in the boundary layer. A tetrahedral adaptation process is extended to incorporate the advancing front local reconnection procedure. Thin boundary-layer grids are adapted from the solution, which governs the boundary-layer grid parameters such as first cell height off the wall. The process enables grid-converged steady-state results from a CAD file. Results are presented across the speed range from low subsonic flow over an airfoil to high-speed flows over blunt bodies and a rocket.
Accurate prediction of surface skin friction and heat transfer for viscous flow applications using computational fluid dynamics tools necessitates thin wall-normal elements in the boundary layer. A tetrahedral adaptation process is extended to incorporate the advancing front local reconnection procedure. Thin boundary-layer grids are adapted from the solution, which governs the boundary-layer grid parameters such as first cell height off the wall. The process enables grid-converged steady-state results from a CAD file. Results are presented across the speed range from low subsonic flow over an airfoil to high-speed flows over blunt bodies and a rocket.
The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.
The simulation of transonic viscous flow over a modified F-16A including inlet is presented. A zonal approach is utilized which allows appropriate clustering suitable for viscous calculations on all solid surfaces. Computational efficiency is enhanced by solving the thin-layer Navier-Stokes equations in viscous zones adjacent to the aircraft and the Euler equations on those coarse zones away from the aircraft. The flow conditions for this transonic case are freestream Mach number of 0.9, angle of attack of 4.12 deg, and a Reynolds number (based on root chord) of 4.5 million. A total of 19 zones are utilized yielding a total of 350,000 grid points. This case required about 3000 iterations to reduce the residual by three orders, which takes about 10 hr of CPU time on the Cray X-MP/48 computer. Pressure distributions on the wing and on cross sections through the inlet region compare favorably with the experimental data for this transonic case.
Research in aerodynamics is discussed. The development of equilibrium air curve fits; computation of hypersonic rarefield leading edge flows; computation of 2-D and 3-D blunt body laminar flows with an impinging shock; development of a two-dimensional or axisymmetric real gas blunt body code; a study of an over-relaxation procedure forthe MacCormack finite-difference scheme; computation of 2-D blunt body turbulent flows with an impinging shock; computation of supersonic viscous flow over delta wings at high angles of attack; and computation of the Space Shuttle Orbiter flowfield are discussed.
A space-marching method, developed to compute three-dimensional flows for internal geometries, has been utilized to predict viscous flows through a curved duct and over a swept wing. The Navier-Stokes equations have been posed as an initial value problem by neglecting the streamwise viscous diffusion terms and by treating the pressure gradient as a known source term. The resulting equations have been solved by a non-iterative (single pass) algorithm at each streamwise step. The results are compared with earlier computations (based on iterative methods) and the experimental data. The agreement between the present predictions, the experimental data, and the earlier predictions is good for the cases computed. The computation time is only a fraction of the iterative methods.
A computerized analytical model of a multi-component airfoil in viscous, subsonic flow has been developed. The model, representing attached flow, defines viscous pressure distributions, lift, moments, and local boundary-layer properties on each element of an arbitrarily arranged slotted airfoil. The final viscous solution is obtained by an iterative technique for successively combining an inviscid solution with boundary-layer displacement thicknesses. Ordinary boundary-layers include laminar, transition, and turbulent types. A significant feature of the program is an analytical model representing the merging of the upper surface boundary layer with the slot efflux. Typical correlations with experiment are provided and program applications are discussed.
The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.
Method developed to account for effects of compressibility in viscous flows through long, circular pipes of uniform diameter. Based on approximation of variations in density and velocity across pipe cross section by profile equations developed for boundary-layer flow between flat plates.
The primary project was the numerical simulation, by a finite element/finite difference method, of the viscous flow about an airfoil. The secondary project involved the numerical simulation of the three-dimensional separated and vortex-dominated flow about a hemispherically capped cylinder in the transonic regime. Preliminary calculations were started for the hemisphere-cylinder at 0 and 5 degree angle of attack. The solution of the flow field about airfoils and wings is required to determine the important parameters of lift, moment, and drag. Viscous effects must be accounted for if the drag is to be accurately calculated. At present there are basically two approaches to the numerical simulation of the flow field, the use of fully viscous models and the inviscid/viscous models. The fully viscous models require the solution of an approximation of the Navier-Stokes equations and therefore should simulate most of the physical mechanisms. A fast, accurate, and computationally efficient inviscid flow solver was recently developed by Hartwich. It is thought that Hartwich's program coupled to a fast, accurate, and computationally efficient boundary layer code, will make an excellent tool for airfoil design. The purpose of the primary project was to develop a compressible boundary layer code using the semidiscrete Galerkin finite element method. The numerical scheme employed used the combination of a Dorodnitsyn formulation of the boundary layer equations, with a finite difference/finite element procedure (semidiscrete Galerkin method), in the solution of the compressible two-dimensional boundary layer equations. A laminar compressible boundary layer code was developed and tested for a NACA 0012 airfoil at a Mach number of 0.5, a Reynolds number of 5000, and zero angle of attack. At present the boundary layer program solves up to, but not beyond, separation.