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Levy, L. L., Jr.

Publications and source records attributed to Levy, L. L., Jr..

Computation of airfoil buffet boundaries

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Levy, L. L., Jr.↗

Predicted and experimental steady and unsteady transonic flows about a biconvex airfoil

Results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million. The experiments were conducted in a transonic, slotted wall wind tunnel. The computer code included an algebraic eddy viscosity turbulence model developed for steady flows, and all computations were made using free flight boundary conditions. All of the features documented experimentally for both steady and unsteady flows were predicted qualitatively; even with the above simplifications, the predictions were, on the whole, in good quantitative agreement with experiment. In particular, predicted time histories of shock wave position, surface pressures, lift, and pitching moment were found to be in very good agreement with experiment for an unsteady flow. Depending upon the free stream Mach number for steady flows, the surface pressure downstream of the shock wave or the shock wave location was not well predicted.

Levy, L. L., Jr.↗

Turbulence Modeling for Unsteady Transonic Flows

Conditionally sampled, ensemble-averaged velocity measurements, made with a laser velocimeter, were taken in the flowfield over the rear half of an 18% thick circular arc airfoil at zero incidence tested at M = 0.76 and at a Reynolds number based on chord of 11 x 10(exp 6). Data for one cycle of periodic unsteady flow having a reduced frequency f of 0.49 are analyzed. A series of compression waves, which develop in the early stages of the cycle, strengthen and coalesce into a strong shock wave that moves toward the airfoil leading edge. A thick shear layer forms downstream of the shock wave. The kinetic energy and shear stresses increase dramatically, reach a maximum when dissipation and diffusion of the turbulence exceed production, and then decrease substantially. The response lime of the turbulence to the changes brought about by the shock-wave passage upstream depends on the shock-wave strength and position in the boundary layer. The cycle completes itself when the shock wave passes the midchord, weakens, and the shear layer collapses. Remarkably good comparisons are found with computations that employ the time-dependent Reynolds averaged form of the Navier-Stokes equations using an algebraic eddy viscosity model, developed for steady flows.

Marvin, J. G.↗

Turbulence Modeling for Unsteady Transonic Flows

Conditionally sampled, ensemble-averaged velocity measurements, made with a laser velocimeter, were taken in the flowfield over the rear half of an 18% thick circular arc airfoil at zero incidence tested at M = 0.76 and of a Reynolds number based on chord of 11 x 10(exp 6). Data for one cycle of periodic unsteady flow having a reduced frequency bar-f of 0.49 are analyzed. A series of compression waves, which develop in the early stages of the cycle, strengthen and coalesce into a strong shock wave that moves toward the airfoil leading edge. A thick shear layer forms downstream of the shock wave. The kinetic energy and shear stresses increase dramatically, reach a maximum when dissipation and diffusion of the turbulence exceed production, and then decrease substantially. The response time of the turbulence to the changes brought about by the shock-wave passage upstream depends on the shock-wave strength and position in the boundary layer. The cycle completes itself when the shock wave passes the midchord, weakens, and the shear layer collapses. Remarkably good comparisons are found with computations that employ the time-dependent Reynolds averaged form of the Navier-Stokes equations using an algebraic eddy viscosity model, developed for steady flows.

Marvin, J. G.↗

On turbulence modeling for unsteady transonic flows

A detailed examination of the turbulent field in an unsteady transonic flow undergoing shock-induced separation is conducted. Ensemble-averaged mean and fluctuating velocities, obtained from conditionally sampled laser velocimeter data, are described and analyzed to assess the applicability of modeling concepts usually employed in steady-flow problems. Some comparisons with computations employing the Reynolds averaged Navier-Stokes equations with a mixing length turbulence model are then presented to illustrate the status of current predictive capabilities. The results appear to imply that turbulence models developed for steady flows apply and that the model need not reflect all the fine details of the turbulent structure but rather account in an approximate way for the production and destruction of the turbulence.

Marvin, J. G.↗

Steady and unsteady transonic flow

An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

Seegmiller, H. L.↗

An experimental and computational investigation of the steady and unsteady transonic flow fields about an airfoil in a solid-wall test channel

An experimental and computational investigation of the steady and unsteady transonic flow field about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible Navier-Stokes equations for flow over airfoils was modified to include solid-wall, slipflow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady flow fields about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 to the 6th are predicted and compared with experiment. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

Levy, L. L., Jr.↗

An experimental and computational investigation of the flow field about a transonic airfoil in supercritical flow with turbulent boundary-layer separation

A combined experimental and computational research program for testing and guiding turbulence modeling within regions of separation induced by shock waves incident on turbulent boundary layers is described. Specifically, studies are made of the separated flow over the rear portion of an 18%-thick circular-arc airfoil at zero angle of attack in high Reynolds number supercritical flow. The measurements include distributions of surface static pressure and local skin friction. The instruments employed include high-frequency response pressure cells and a large array of surface hot-wire skin-friction gages. Computations at the experimental flow conditions are made using time-dependent solutions of ensemble-averaged Navier-Stokes equations, plus additional equations for the turbulence modeling.

Rubesin, M. W.↗

An experimental and computational investigation of the flow field about a transonic airfoil in supercritical flow with turbulent boundary-layer separation

A combined experimental and computational research program is described for testing and guiding turbulence modeling within regions of separation induced by shock waves incident in turbulent boundary layers. Specifically, studies are made of the separated flow the rear portion of an 18%-thick circular-arc airfoil at zero angle of attack in high Reynolds number supercritical flow. The measurements include distributions of surface static pressure and local skin friction. The instruments employed include highfrequency response pressure cells and a large array of surface hot-wire skin-friction gages. Computations at the experimental flow conditions are made using time-dependent solutions of ensemble-averaged Navier-Stokes equations, plus additional equations for the turbulence modeling.

Rubesin, M. W.↗

Transonic flow about a thick circular-arc airfoil

An experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported. Special attention is given to the shock-induced separation phenomenon in the turbulent regime. Measurements presented include surface pressures, streamline and flow separation patterns, and shadowgraphs. For a limited range of free-stream Mach numbers the airfoil flow field is found to be unsteady. Dynamic pressure measurements and high-speed shadowgraph movies were taken to investigate this phenomenon. Comparisons of experimentally determined and numerically simulated steady flows using a new viscous-turbulent code are also included. The comparisons show the importance of including an accurate turbulence model. When the shock-boundary layer interaction is weak the turbulence model employed appears adequate, but when the interaction is strong, and extensive regions of separation are present, the model is inadequate and needs further development.

Mcdevitt, J. B.↗

Simulation of turbulent transonic separated flow over an airfoil

A code developed for simulating high Reynolds number transonic flow fields of arbitrary configuration is described. This code, in conjunction with laboratory experiments, is used to devise and test turbulence transport models which may be suitable in the prediction of such flow fields, with particular emphasis on regions of flow separation. The solutions describe the flow field, including both the shock-induced and trailing-edge separation regions, in sufficient detail to provide the profile and friction drag.

Deiwert, G. S.↗

Safe atmosphere entry of an isotope heat source with a single stable trim attitude at hypersonic speeds

A theoretical investigation has been made to design an isotope heat source capable of satisfying the conflicting thermal requirements of steady-state operation and atmosphere entry. The isotope heat source must transfer heat efficiently to a heat exchange during normal operation with a power system in space, and in the event of a mission abort, it must survive the thermal environment of atmosphere entry and ground impact without releasing radioactive material. A successful design requires a compatible integration of the internal components of the heat source with the external aerodynamic shape. To this end, configurational, aerodynamic, motion, and thermal analyses were coupled and iterated during atmosphere entries at suborbital through superorbital velocities at very shallow and very steep entry angles. Results indicate that both thermal requirements can be satisfied by a heat source which has a single stable aerodynamic orientation at hypersonic speeds. For such a design, the insulation material required to adequately protect the isotope fuel from entry heating need extend only half way around the fuel capsule on the aerodynamically stable (wind-ward) side of the heat source. Thus, a low-thermal-resistance, conducting heat path is provided on the opposite side of the heat source through which heat can be transferred to an adjacent heat exchanger during normal operation without exceeding specified temperature limits.

Levy, L. L., Jr.↗