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NASA NTRS1987

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗

NASA NTRS1987

Navier-Stokes computations of vortical flows over low aspect ratio wings

An upwind-biased finite-volume algorithm is applied to the low-speed flow over a low aspect ratio delta wing from zero to forty degrees angle of attack. The differencing is second-order accurate spatially, and a multigrid algorithm is used to promote convergence to the steady state. The results compare well with the detailed experiments of Hummel (1983) and others for a Re(L) of 0.95 x 10 to the 6th. The predicted maximum lift coefficient of 1.10 at thirty-five degrees angle of attack agrees closely with the measured maximum lift of 1.06 at thirty-three degrees. At forty degrees angle of attack, a bubble type of vortex breakdown is evident in the computations, extending from 0.6 of the root chord to just downstream of the trailing edge.

Thomas, J. L.↗

NASA NTRS1986

The final warming and polar vortex disappearance during the Southern Hemisphere spring

Seven years (1979-1985) of NMC data are used to analyze Southern Hemisphere middle stratosphere winter-to-summer circulation transitions. These transitions are classified into two extreme categories: (1) a mid-October final warming accompanied by a major mid-October wave event (1979 and 1982), and (2) a mid-November final warming with no strong October wave event (1980 and 1981). After the final warming a wave event in late November-early December results in the disappearance of the polar vortex. All of these wave events in conjunction with zonal mean mass motions act to reduce zonal mean gradients of potential vorticity and ozone through horizontal mixing, and hence they act to destroy the vortex and fill the ozone hole. Additionally, it is noted that the final warming and the vortex breakdown are two distinct events separated by 15-40 days. Finally, past studies show that the time of these events has not radically changed.

Newman, Paul A.↗

NASA NTRS1987

Numerical simulation of vortical flows over a strake-delta wing

The vortical flow fields over a double-delta wing with sweep angles 80 and 60 deg are investigated by means of numerical simulations based on the LU-ADI code of Fujii and Obayashi (1986) for the three-dimensional thin-layer Navier-Stokes equations. The results obtained using an 850,000-point grid at angle of attack alpha = 6-40 deg are presented graphically, compared with experimental data, and characterized in detail. Qualitatively accurate simulations are obtained for transition phenomena such as strake/wing-vortex interaction at alpha = 12 deg, bubble-type vortex breakdown near the trailing edge at alpha = 30 deg, and spiral-type breakdown at alpha = 35 deg. It is suggested that quantitative simulations can be achieved at higher grid resolution.

Fujii, Kozo↗

NASA NTRS1987

Arcjet thruster research and technology, phase 1

The objectives of Phase 1 were to evaluate analytically and experimentally the operation, performance, and lifetime of arcjet thrusters operating between 0.5 and 3.0 kW with catalytically decomposed hydrazine (N2H4) and to begin development of the requisite power control unit (PCU) technology. Fundamental analyses were performed of the arcjet nozzle, the gas kinetic reaction effects, the thermal environment, and the arc stabilizing vortex. The VNAP2 flow code was used to analyze arcjet nozzle performance with non-uniform entrance profiles. Viscous losses become dominant beyond expansion ratios of 50:1 because of the low Reynolds numbers. A survey of vortex phenomena and analysis techniques identified viscous dissipation and vortex breakdown as two flow instabilities that could affect arcjet operation. The gas kinetics code CREK1D was used to study the gas kinetics of high temperature N2H4 decomposition products. The arc/gas energy transfer is a non-equilibrium process because of the reaction rate constants and the short gas residence times. A thermal analysis code was used to guide design work and to provide a means to back out power losses at the anode fall based on test thermocouple data. The low flow rate and large thermal masses made optimization of a regenerative heating scheme unnecessary.

Knowles, Steven C.↗

NASA NTRS1987

Numerical simulation of three-dimensional unsteady vortex flow using a compact vorticity-velocity algorithm

A numerical algorithm is presented which is used to solve the unsteady, fully three-dimensional, incompressible Navier-Stokes equations in vorticity-velocity variables. A discussion of the discrete approximation scheme is presented as well as the solution method used to solve the resulting algebraic set of difference equations. Second order spatial and temporal accuracy is verified through solution comparisons with exact results obtained for steady three-dimensional stagnation point flow and unsteady axisymmetric vortex spin-up. In addition, results are presented for the problem of unsteady bubble-type vortex breakdown with emphasis on internal bubble dynamics and structure.

Gatski, T. B.↗

NASA NTRS1988

Navier Stokes computation of the flow field over delta wings with spanwise leading edge blowing

The concept of spanwise leading edge blowing, a means of controlling the position and strength of leading edge vortices, is analyzed by numerical solutions of the three-dimensional Thin-Layer Navier Stokes equations. The leading edge jet is simulated by defining a permeable boundary, corresponding to the jet slot, where suitable boundary conditions are implemented. Numerical results agree favorably with experimental measurements. It is found that the use of spanwise leading edge blowing not only magnifies the size and strength of the leading edge vortices, but also moves the vortex cores outboard and upward. As a result, the increase in lift comes primarily from the greater nonlinear vortex lift. The presence of the leading edge jet stream displaces the flow outboard, thereby increasing the effective aspect ratio of the delta wing. However, blowing causes earlier vortex breakdown, thus decreasing the stall angle.

Yeh, David T.↗

NASA NTRS1988

The breakup of the Southern Hemisphere spring polar ozone and temperature minimums from 1979 to 1987

The purpose of this study is to quantify the observations of the polar vortex breakup. The data used in this study consist of Total Ozone Mapping Spectrometer (TOMS) data, and National Meteorological Center (NMC) analyses. The final warming is diagnosed using the difference between zonal means at 80 degrees and 50 degrees S for temperature, ozone, and layer mean temperature. The polar vortex breakup can also be diagnosed by the onset of weak zonal mean zonal winds (i.e., u, overbar denotes a zonal average) at 60 degrees S. Computations of the polar vortex breakdown date using NMC meteorological data and TOMS total ozone data indicate that the breakdown is occurring later in the spring in the lowest portion of the stratosphere. At altitudes above 100 mb, the large interannual variance of the breakdown date renders any trend determination of the breakdown date difficult. Individual plots of TOMS total ozone indicate that the total ozone minimum remains intact for a longer period of time than is observed in earlier years.

Newman, Paul A.↗

NASA NTRS1988

Numerical simulation of the vortical flow over a round-edged double-delta wing

Simulations of three-dimensional vortical flows over a thin double-delta wing with an aspect ratio of 2.05 have been performed. Steady-state solutions to the unsteady incompressible Navier-Stokes equations are obtained using a new implicit upwind-relaxation finite-difference scheme. The method is second-order accurate spatially and naturally dissipative. Numerical results indicate that key features of both vortical interaction and vortex breakdown are successfully simulated. The computed lift coefficients and lateral trajectories of the vortical cores are in good agreement with the experimental data.

Hsu, C.-H.↗

NASA NTRS1988

Experimental study of isothermal swirling flows in a dump combustor

Detailed mean and turbulence data were obtained in a dump combustor with and without swirling inlet flow. A two-component LDV was used, and large samples were collected to resolve the second- and third-order correlations of velocity fluctuations with good accuracy. Large-amplitude well-organized oscillations were observed in the swirling flows and discussed. The swirling flows with and without vortex breakdown exhibited significantly different mean flow and turbulence field behavior.

Samimy, M.↗

NASA NTRS1989

An experimental study of shock wave/vortex interaction

The interaction of a supersonic streamwise vortices (of Mach number 2.2, 3.0, and 3.5) with a normal shock wave has been experimentally investigated, and is found to be highly unsteady. Five-hole pressure-probe and temperature measurements ahead of the interaction are used as initial conditions for an axisymmetric Navier-Stokes calculation. The numerical results supports the hypothesis that supersonic vortex breakdown is an important factor in the observed interaction flow pattern.

Metwally, O. M.↗

NASA NTRS1989

An experimental investigation of delta wing vortex flow with and without external jet blowing

A visual and quantitative study of the vortex flow field over a 70-deg delta wing with an external jet blowing parallel to and at the leading edge was conducted. In the experiment, the vortex core was visually marked with TiCl4, and LDA was used to measure the velocity parallel and normal to the wing surface. It is found that jet blowing moved vortex breakdown farther downstream from its natural position and influenced the breakdown characteristics.

Iwanski, Kenneth P.↗

NASA NTRS1989

The separated flow field on a slender wing undergoing transient pitching motions

The flow field surrounding a delta wing undergoing a transient pitching motion was studied experimentally. Of particular importance was the location of the leading edge vortices over the surface of the wing. The study was conducted on a 70-deg sweep flat-plate delta wing pitched about its one-half chord position. It is found that the maximum pitch rate is the key factor involved in the amount of lag experienced by the vortex breakdown during the transient pitching motion.

Thompson, S. A.↗

NASA NTRS1989

TranAir and Euler computations of a generic fighter including comparisons with experimental data

The TranAir full-potential code and the FLO57 Euler code were used to calculate transonic flow solutions over two configurations of a generic fighter model. The results were computed at Mach numbers of 0.60 and 0.80 for angles of attack between 0 and 12 deg for TranAir and between 4 and 20 deg for FLO57. Due to the fact that TranAir solves the full-potential equations for transonic flow, TranAir is only accurate to about alpha = 8 deg, at which point the experimental results show the formation of a vortex at the leading edge. Euler results show good agreement with experimental results until vortex breakdown occurs in the solutions.

Goodsell, Aga M.↗

NASA NTRS1988

Measurements of a supersonic turbulent vortex

Mean-flow measurements of a supersonic turbulent streamwise vortex are presented. This vortex was produced by the injection of a swirling flow along the centerline of a supersonic airstream at Mach 3. Directional Mach number distributions, obtained via a five-hole flow-angularity probe, reveal vortex characteristics similar to those of the incompressible case, even though rotational Mach numbers up to 0.8 were obtained. This work is the first step of a study of the supersonic vortex breakdown phenomenon.

Metwally, O. M.↗

NASA NTRS1989

The effect of asymmetric vortex wake characteristics on a slender delta wing undergoing wing rock motion

An experimental investigation into the fluid mechanisms responsible for wing rock on a slender delta wing with 80 deg leading edge sweep has been conducted. Time history and flow visualization data are presented for a wide angle-of-attack range. The use of an air bearing spindle has allowed the motion of the wing to be free from bearing friction or mechanical hysteresis. A bistable static condition has been found in vortex breakdown at an angle of attack of 40 deg which causes an overshoot of the steady state rocking amplitude. Flow visualization experiments also reveal a difference in static and dynamic breakdown locations on the wing. A hysteresis loop in dynamic breakdown location similar to that seen on pitching delta wings was observed as the wing was undergoing the limit cycle oscillation.

Arena, A. S., Jr.↗

NASA NTRS1989

Surface pressure distributions on a delta wing undergoing large amplitude pitching oscillations

Wind tunnel experiments were performed on a 70 deg sweep delta wing to determine the effect of a sinusoidal pitching motion on the pressure field on the suction side of the wing. Twelve pressure taps were placed from 35 to 90 percent of the chord, at 60 percent of the local semi-span. Pressure coefficients were measured as a function of Reynolds number and pitch rate. The pressure coefficient was seen to vary at approximately the same frequency as the pitching frequency. The relative pressure variation at each chord location was comparable for each case. The average pressure distribution through each periodic motion was near the static distribution for the average angle of attack. Upon comparing the upstroke and downstroke pressures for a specific angle of attack, the downstroke pressures were slightly larger. Vortex breakdown was seen to have the most significant effect at the 40 to 45 percent chord location, where a decrease in pressure was apparent.

Thompson, Scott A.↗

NASA NTRS1990

A transonic/supersonic CFD analysis of a generic fighter

Flow fields about a generic fighter model have been computed using FLO57, a three-dimensional, finite-volume Euler code. Computed pressure coefficients, forces, and moments at several Mach numbers - 0.6, 0.8, 1.2, 1.4, and 1.6 - are compared with wind tunnel data over a wide range of angles of attack in order to determine the applicability of the code for the analysis of fighter configurations. Two configurations were studied, a wing/body and a wing/body/chine. FLO57 predicted pressure distributions, forces, and moments well at low angles of attack, at which the flow was fully attached. The FLO57 predictions were also accurate for some test conditions once the leading-edge vortex became well established. At the subsonic speeds, FLO57 predicted vortex breakdown earlier than that seen in the experimental results. Placing the chine on the forebody delayed the onset of bursting and improved the correlation between numerical and experimental data at the subsonic conditions.

Goodsell, Aga M.↗