Search NASA⌕ Search

SEARCH · Search NASA

Results for “EQUATIONS - BOUNDARY LAYER - PRANDTL”

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.

At least 127 records · Page 7

Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects

The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.

Pittman, C. M.↗

One-dimensional analysis of plane and radial thin film flows including solid-body rotation

The flow of a thin liquid film with a free surface along a horizontal plate which emanates from a pressurized vessel is examined by integrating the equations of motion across the thin liquid layer and discretizing the integrated equations using finite difference techniques. The effects of 0-g and solid-body rotation will be discussed. The two cases of interest are plane flow and radial flow. In plane flow, the liquid is considered to be flowing along a channel with no change in the width of the channel, whereas in radial flow the liquid spreads out radially over a disk, so that the area changes along the radius. It is desired to determine the height of the liquid film at any location along the plate of disk, so that the heat transfer from the plate or disk can be found. The possibility that the flow could encounter a hydraulic jump is accounted for.

Thomas, S.↗

A verification of unsteady Navier-Stokes solutions around oscillating airfoils

A finite difference solution code for the two dimensional Navier-Stokes equations was combined with a moving-grid system. The thin layer Navier-Stokes equations with a turbulence model are solved in a time-accurate manner in order to study the unsteady aerodynamics around airfoils undergoing small amplitude pitching or heaving motions in the transonic regime. The accuracy of the solutions obtained by the use of the present moving-grid technqiue is investigated. The effects of the minimum grid size and the integrating time-step size on the solutions are also checked. Some of the solutions obtained by the present method are compared with experimental results. It is demonstrated that the unsteady aerodynamics around oscillating airfoils can be predicted fairly well by the present code for cases in which the dynamic angle of attack or displacement is small.

Nakamichi, J.↗

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta winds.

Kandil, Osama A.↗

Efficient solution methods for the Navier-Stokes equations

Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed. The methods are demonstrated in fully vectorized codes for a Cray type architecture. The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used. The methods are either time accurate or accelerated non-time accurate steady state schemes. Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented. Two dimensional inviscid and viscous calculations (e.g., airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed.

Pulliam, T. H.↗

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Elmiligui, Alaa↗

Aerothermodynamic environment for Jovian entry conditions

Solutions are presented for the aerothermal heating environments about blunt probes entering the atmosphere of Jupiter. The analysis employs a novel prediction procedure in which finite differences versions of the thin layer fluid dynamic equations are solved simultaneously with, and coupled to, a fully detailed radiation flux model. Predictions are presented and compared with those of earlier investigators. Radiative blowing corrections are presented for on- and off-stagnation point conditions. The use of a blowing correlation based on the retained mass was found to be useful for off-stagnation point conditions.

Nicolet, W. E.↗

Morphology of the Venus ultraviolet night airglow

Images of the nightside of Venus in the (0,1)delta band of nitric oxide have been obtained by the Pioneer Venus orbiter ultraviolet spectrometer (OUVS). The emission, which is produced by radiative association of N and O, shows a bright spot reaching 5 kR and located at 2 a.m. local solar time just south of the equator. The emitting layer is at 111 + or - 7-km altitude. A one dimensional vertical transport model shows that the hemispheric average brightness of 0.8 kR is consistent with the orbiter neutral mass spectrometer (ONMS) measurements of N and O near 167 km, and that the altitude of the emitting layer is consistent with the eddy mixing model proposed to explain the dayside helium profile measured by the bus neutral mass spectrometer. In the model, N reaches a peak of 7 x 10 to the 8th per cu cm at 114 km, and O reaches a peak of 2.6 x 10 to the 11th per cu cm at 106 km. There is a fair degree of consistency between the ONMS, OUVS, and other airglow measurements, except as regards the local time dependence.

Stewart, A. I. F.↗

SHARP: Subsonic High Altitude Research Platform

The Universities Space Research Association is sponsoring an undergraduate program which is geared to designing an aircraft that can study the ozone layer at the equator. This aircraft must be able to satisfy four mission profiles. Mission one is a polar mission that ranges from Chile to the South Pole and back to Chile, a total range of 6000 n.mi. at 100,000 ft with a 2500 lb payload. The second mission is also a polar mission, with an altitude of 70,000 ft and an increased payload of 4000 lbs. For the third mission, the aircraft will takeoff at NASA Ames, cruise at 100,000 ft carrying a 2500 lb payload, and land at Puerto Montt, Chile. The final mission requires the aircraft to take off at NASA Ames, cruise at 100,000 ft with a 1000 lb payload, make an excursion to 120,000 ft, and land at Howard AFB, Panama. Three missions require that a subsonic Mach number be maintained due to constraints imposed by the air sampling equipment. The aircraft need not be manned for all four missions. Three aircraft configurations have been determined to be the most suitable for meeting the above requirements. In the event that a requirement cannot be obtained within the given constraints, recommendations for proposal modifications are given.

Beals, Todd↗

Modeling the seasonal cycle of CO2 on Mars: A fit to the Viking lander pressure curves

We have constructed a more accurate Mars thermal model, similar to the one used by Leighton and Murray in 1966, which solves radiative, conductive, and latent heat balance at the surface as well as the one-dimensional heat conduction equation for 40 layers to a depth of 15 meters every 1/36 of a Martian day. The planet is divided into 42 latitude bands with a resolution of two degrees near the poles and five degrees at lower latitudes, with elevations relative to the 6.1 mbar reference areoid. This estimate of the Martian zonally averaged topography was derived primarily from radio occultations. We show that a realistic one-dimensional thermal model is able to reproduce the VL1 pressure curve reasonably well without having to invoke complicated atmospheric effects such as dust storms and polar hoods. Although these factors may cause our deduced values for each model parameter to differ from its true value, we believe that this simple model can be used as a platform to study many aspects of the Martian CO2 cycle over seasonal, interannual, and long-term climate timescales.

Wood, S. E.↗

High-altitude reconnaissance aircraft

At the equator the ozone layer ranges from 65,000 to 130,000+ ft, which is beyond the capabilities of the ER-2, NASA's current high-altitude reconnaissance aircraft. This project is geared to designing an aircraft that can study the ozone layer. The aircraft must be able to satisfy four mission profiles. The first is a polar mission that ranges from Chile to the South Pole and back to Chile, a total range of 6000 n.m. at 100,000 ft with a 2500-lb payload. The second mission is also a polar mission with a decreased altitude and an increased payload. For the third mission, the aircraft will take off at NASA Ames, cruise at 100,000 ft, and land in Chile. The final mission requires the aircraft to make an excursion to 120,000 ft. All four missions require that a subsonic Mach number be maintained because of constraints imposed by the air sampling equipment. Three aircraft configurations were determined to be the most suitable for meeting the requirements. The performance of each is analyzed to investigate the feasibility of the mission requirements.

Yazdi, Renee Anna↗

Direct simulation of the stably stratified turbulent Ekman layer

The Navier-Stokes equations and the Boussinesq approximation were used to compute a 3D time-dependent turbulent flow in the stably stratified Ekman layer over a smooth surface. The simulation data are found to be in very good agreement with atmospheric measurements when nondimensionalized according to Nieuwstadt's local scaling scheme. Results suggest that, when Reynolds number effects are taken into account, the 'constant Froud number' stable layer model (Brost and Wyngaard, 1978) and the 'shearing length' stable layer model (Hunt, 1985) for the dissipitation rate of turbulent kinetic energy are both valid. It is concluded that there is good agreement between the direct numerical simulation results and large-eddy simulation results obtained by Mason and Derbyshire (1990).

Coleman, G. N.↗