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Oscillation amplitude, oscillation frequencies, plate thickness and area as drag coefficients for flat, square plates oscillating normal to their planes in air
An investigation was made of the capability for computing internal pressures throughout flight for compartments located within space shuttle vehicles. A test program was conducted at a 6 x 6 foot supersonic wind tunnel to determine orifice efficiencies for the flow of air into a compartment from a flowing external stream. Measurements were made over a Mach number range of 0.7 to 1.9 for varying orifice geometry, vent orientation, vent plate thickness, flat plate boundary layer thickness, and pressure ratio across the vent plate. A computer program developed for outflow venting was modified for use in computing compartment pressures for inflow conditions. Results from both the outflow and inflow computer programs are included. A user's manual and program listing of the inflow venting program are also included.
An iteration difference method for the calculation of the incompressible laminar boundary layer is described. The method uses Prandtl's boundary layer equation and the boundary conditions directly and permits the attainment of an arbitrary accuracy. The method has been tested successfully in the continuation of the Blasius profile on the flat plate, on the circular cylinder investigated by Heimenz and on an elliptical cylinder of fineness ratio 1:4. The method makes possible the testing of previously developed methods, all of which contain important assumptions.
The behavior of two different models of gas-surface interactions is studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic forces and heat transfer between the Maxwell and the Cercignani-Lampis-Lord (CLL) models for flat plate configurations at freestream conditions corresponding to a 140 km orbit around Venus. The size of the flat plate represents one of the solar panels on the Magellan spacecraft, and the freestream conditions correspond to those experienced during aerobraking maneuvers. Results are presented for both a single flat plate and a two-plate configuration as a function of angle of attack and gas-surface accommodation coefficients. The two-plate system is not representative of the Magellan geometry but is studied to explore possible experiments that might be used to differentiate between the two gas-surface interaction models. The Maxwell and CLL models produce qualitatively similar results for the aerodynamic forces and heat transfer on a single flat plate. However, the flow fields produced with the two models are qualitatively different for both the single-plate and two-plate calculations. These differences in the flowfield lead to predictions of the angle of attack for maximum heat transfer in a two plate configuration that are distinctly different for the two gas-surface interactions models.
A summary is given of the background and present status of pure-planing theory. Data for models having sharp chines have been obtained for a rectangular flat plate and two V-bottom surfaces having constant angles of dead rise of 20 degrees and 40 degrees and also for rectangular-flat-plate surfaces having very slightly rounded chines. The theory presented in NACA Technical Note 3233 for a rectangular flat plate is revised and extended to include triangular flat plates planing with base forward and V-shaped prismatic surfaces having a constant angle of dead rise, horizontal chine flare, or vertical chine strips. The agreement between the results calculated by the proposed theory and the experimental data is satisfactory for engineering calculations of lift and center-of-pressure location.
Experimental investigations have been conducted to determine the surface-pressure distribution on a flat plate and a body of revolution with a jet issuing at a large angle to the free stream and to obtain a better understanding of the entrainment mechanism close to the jet exit by quantitative mean velocity surveys. Pressure data were obtained with a flat plate model at several nozzle injection angles using a single round nozzle. For the body of revolution model, data were obtained with a round jet exhausting perpendicular to the crossflow and with two round jets spaced two to six nozzle diameters apart. Mean velocity measurements were obtained with laser velocimeter surveys near the base of a round jet exhausting normal to a flat plate. For the flat plate model, the pressure field shifts downstream and the entrainment effect decreases with decreasing nozzle injection angle. For the body of revolution model with two jets, the jet-induced effect of the rear jet on the surface-pressure distribution was less than the front jet. The flow regions close to the jet are defined by the laser surveys, but further mean velocity surveys are required to understand the entrainment mechanism.
With a goal of reducing jet engine weight, simulations of a fan blade containment system with an alternate geometry were tested and analyzed. A projectile simulating a fan blade was shot at two alternate geometry containment case configurations using a gas gun. The first configuration was a flat plate representing a standard case configuration. The second configuration was a flat plate with a radially convex curve section at the impact point. The curved surface was designed to force the blade to deform plastically, dissipating energy before the full impact of the blade is received by the plate. The curved case was able to tolerate a higher impact velocity before failure. The computational model was developed and correlated with the tests and a weight savings assessment was performed. For the particular test configuration used in this study the ballistic impact velocity of the curved plate was approximately 60 m/s (200 ft/s) greater than that of the flat plate. For the computational model to successfully duplicate the test, the very high strain rate behavior of the materials had to be incorporated.
The effect of concentration level on the specific power for a deployable, thin, gallium arsenide cell array in geosynchronous orbit for 10 years in conjunction with a two dimensional flat plate trough concentrator (V trough) and also with a multiple flat plate concentrator was investigated as well as the effects for a conventional silicon cell array on a rigid substrate. For application to a thin GaAs array at 1 AU for 10 years, the V trough produces a 19% benefit in specific power and a dramatic reduction in array area, while the multiple flat plate collector design is not only of no benefit, but is a considerable detriment. The benefit it achieves by reducing array area is duplicated by the 2D design. For the silicon array on a rigid substrate, improvement in performance due to a concentrator with ordinary mirror coating is quite small: 9% increase in specific power, and 13% reduction in array area. When the concentrator mirrors are coated with an improved cold mirror coating, somewhat more significant results are obtained: 31% specific power improvement; and 27% area reduction. In both cases, a 10 year exposure reduces BOL output by 23%.
A flat plate and faired pod have been mounted on a NASA SR-71A aircraft for use as a supersonic flight experiment test bed. A test article can be placed on the flat plate; the pod can contain supporting systems. A series of test flights has been conducted to validate this test bed configuration. Flight speeds to a maximum of Mach 3.0 have been attained. Steady-state sideslip maneuvers to a maximum of 2 deg have been conducted, and the flow field in the test region has been surveyed. Two total-pressure rakes, each with two flow-angle probes, have been placed in the expected vicinity of an experiment. Static-pressure measurements have been made on the flat plate. At subsonic and low supersonic speeds with no sideslip, the flow in the surveyed region is quite uniform. During sideslip maneuvers, localized flow distortions impinge on the test region. Aircraft sideslip does not produce a uniform sidewash over the test region. At speeds faster than Mach 1.5, variable-pressure distortions were observed in the test region. Boundary-layer thickness on the flat plate at the rake was less than 2.1 in. For future experiments, a more focused and detailed flow-field survey than this one would be desirable.
Unit-mass system of derivation of equations determines the deflection, slope, and moments for thin, flat, circular plates subjected to either a uniform or a symmetrical variable load. The derived equations are computed, organized in tabular form, and graphically depicted.
An analysis of the steady-state aerodynamic heating problem at high-supersonic speeds is made for two-dimensional flows with laminar boundary layers. The aerodynamic heating is shown to be reduced substantially by injecting a small amount of coolant through a porous surface into the boundary layer. The analysis includes calculations of the cooling requirements and equilibrium surface temperatures for flat plates and for an equilibrium surface temperatures for flat plates and for flat porous surfaces with several rates of fluid injection at Mach numbers from 5 to 15 and altitudes from sea level to 200,000 feet. Some calculations of the skin friction are also included.
Numerical boundary conditions for mass injection/suction at the wall are incorporated in the thin-layer Navier-Stokes code, F3D. The accuracy of the boundary conditions and the code is assessed by a detailed comparison of the predictions of velocity distributions and skin-friction coefficients with exact similarity solutions for laminar flow over a flat plate with variable blowing/suction, and measurements for turbulent flow past a flat plate with uniform blowing. In laminar flow, F3D predictions for friction coefficient compare well with exact similarity solution with and without suction, but produces large errors at moderate-to-large values of blowing. A slight Mach number dependence of skin-friction coefficient due to blowing in turbulent flow is computed by F3D code. Predicted surface pressures for turbulent flow past an airfoil with mass injection are in qualitative agreement with measurements for a flat plate.
A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the load surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimental results agreed reasonably well with theoretical predictions of convective heat transfer of flat plate laminar boundary layers. The results indicate that this non-intrusive optical measurement technique has the potential to obtain high quality surface convective heat transfer measurements in high speed flowfields.
A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to the heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the local surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimentally determined convective heat transfer coefficients were generally higher than the theoretical predictions for flat plate laminar boundary layers. However, the results indicate that this nonintrusive optical measurement technique has the potential to measure surface convective heat transfer coefficients in high speed flow fields.
A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to the heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the local surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimentally determined convective heat transfer coefficients were generally higher than the theoretical predictions for flat plate laminar boundary layers. However, the results indicate that this nonintrusive optical measurement technique has the potential to measure surface convective heat transfer coefficients in high-speed flowfields.
A procedure for analyzing the vibrations of rotating turbomachinery blades has been previously developed. This procedure is based upon shallow shell theory, and utilizes the Ritz method to determine frequencies and mode shapes. However, it has been limited heretofore to blades of uniform thickness, uniform curvature, and/or twist and rectangular planform. The present work shows how the procedure may be generalized to eliminate the aforementioned restrictions. Nonrectangular planforms are dealt with by a suitable coordinate transformation. This, as well as variable thickness, curvature and twist, require using numerical integration. The procedure is demonstrated on four examples of cantilevered blades for which theoretical and experimental data have been previously published: (1) flat plate with spanwise taper, (2) flat plate with chordwise taper, (3) twisted plate with chordwise taper, and (4) cylindrical shell with chordwise taper.
Reducing aircraft noise is a major objective in the field of computational aeroacoustics. Acoustic liners are an effective tool for reducing aircraft noise and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model is discussed in which the liner impedance is specified along a wide range of frequencies. An impedance boundary condition is derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate. It is assumed the flat plate has surfaces treated with acoustic liners. The stability of the numerical algorithm is assessed using eigenvalue analysis.
Receptivity and stability of supersonic boundary layers over blunt flat plates and wedges are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. Computations are performed for a flat plate with leading edge thicknesses of 0.0001, 0.001, 0.005 and 0.01 inches that give Reynolds numbers based on the leading edge thickness ranging from 1000 to 10000. Calculations are also performed for a wedge of 10 degrees half angle with different leading edge radii 0.001 and 0.01 inches. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of two-dimensional boundary layers. The transition Reynolds number for a flat plate with a leading edge thickness of 0.01 inches is about 3.5 times larger than it is for the Blasius boundary layer. It was also revealed that boundary layers on blunt wedges are far more stable than on blunt flat plates.