The laminar boundary layer on spinning bodies of revolution
Laminar boundary layer on spinning bodies of revolution in oncoming stream, using implicit finite difference technique
SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Laminar boundary layer on spinning bodies of revolution in oncoming stream, using implicit finite difference technique
Liquid metals vapor drag and electromagnetic fields effects on laminar film condensation, using finite difference method
Three dimensional inviscid compressible flow past sharp shouldered blunt bodies at angle of attack, presenting time dependent finite difference technique
Poiseuille pipe flow stability from finite difference equations approximation to nonlinear axisymmetric Navier-Stokes equations under stream function perturbation
Two nonlinear coupled second order differential equations finite difference solution, using nonsquare and nonuniform grids for minimum error
Turbulent boundary layers calculation downstream of compressible relaxing slot injection flows, using finite difference method based on eddy viscosity model
Three dimensional elastic plastic solid, calculating stress and deformation with finite difference procedure
Symmetric and asymmetric dynamic buckling of shallow elastic arches under uniform loads, using nonlinear finite difference method
Ar arc plasma thermochemical nonequilibrium, using finite difference techniques for nonlinear integrodifferential equations
Extreme eigenvalues of Toeplitz matrices associated with Laguerre and Jacobi polynomials, using finite difference operators
Global numerical weather prediction model, using finite difference grid and operators with smoothing techniques
Governing differential equation, boundary conditions for the analysis on which computer program is based, and method of solution of resulting finite difference equations are discussed in the documentation.
Method for predicting nozzle performance of microthrust rockets is discussed. Method is numerical and uses simplified computer program on IBM 360/65 computer. Analysis is based on slender channel equations with slip boundary conditions at walls. Implicit finite difference scheme is used to calculate pressure and velocity profiles along channel.
A computer program was developed to do the calculations for two-dimensional or axisymmetric configurations from low speeds to hypersonic speeds with arbitrary streamwise pressure, temperature, and Mach number distributions. Options are provided for obtaining initial conditions either from experimental information or from a theoretical similarity solution. The transition region can be described either by an arbitrary distribution of intermittency or by a function based on Emmons' probability theory. Correlations were developed for use in estimating the parameters of the theoretical intermittency function. Correlations obtained from other sources are used for estimating the transition point. Comparisons were made between calculated and measured boundary layer quantities for laminar, transitional, and turbulent flows on flat plates, cones, cone flares, and a waisted body of revolution. Excellent agreement was obtained between the present theory and two other theories based on the method of finite differences. The intermittency required to reproduce some experimental heat transfer results in hypersonic flow was found to be quite different from the theoretical function. It is suggested that the simple probability theory of Emmons may not be valid for representing the intermittency of hypersonic transitional boundary layers and that the program could be useful as a tool for detailed study of the intermittency of the transition region.
Several aspects of the oscillating wedge are investigated to evaluate both the resulting trends for the wedge and methods of analyzing unsteady flows. An existing hypersonic small disturbance theory for an oscillating thin wedge is extended and applied. A perturbation method involving linearization about the known flow is then derived and discussed. Subsequently, a finite difference technique for calculating the complete unsteady flow field of the wedge in motion is presented and discussed in conjunction with some calculated quasi-static nonlinear trends.
A variational integral is formulated from Hamilton's Principle and is proved to be equivalent to the usual differential equations of low-gravity sloshing in ellipsoidal tanks. It is shown that for a zero-degree contact angle the contact line boundary condition corresponds to the stuck condition, a result that is due to the linearization of the equations and the ambiguity in the definition of the wave height at the wall. The variational integral is solved by a Rayleigh-Ritz technique. Results for slosh frequency when the free surface is not bent-over compare well with previous numerical solutions. When the free surface is bent over, however, the results for slosh frequency are considerably larger than those predicted by previous finite-difference, numerical approaches: the difference may be caused by the use of a zero degree contact angle in the present theory in contrast to the nonzero contact angle used in the numerical approaches.
This technique has been applied to study such effects on incompressible flow around cylinders at moderate to low Reynolds numbers and for compression ramps at hypersonic Mach numbers by employing a finite difference method to obtain numerical solutions. The results indicate that the technique can be applied successfully in both regimes and does predict the correct trend in regions of large curvature and displacement body effects. It was concluded that curvature corrections should only be attempted in cases where all displacement effects can be fully accounted for.
The unified small disturbance equations are numerically solved using the well-known Lax-Wendroff finite difference technique. The method allows complete determination of the inviscid flow field and surface properties as long as the flow remains supersonic. Shock waves and other discontinuities are accounted for implicity in the numerical method. This technique was programed for general application to the three-dimensional case. The validity of the method is demonstrated by calculations on cones, axisymmetric bodies, lifting bodies, delta wings, and a conical wing/body combination. Part 1 contains the discussion of problem development and results of the study. Part 2 contains flow charts, subroutine descriptions, and a listing of the computer program.