Showing papers on "Supersonic speed published in 1977"

A finite volume method for transonic potential flow calculations

Abstract: It is proposed to solve the exact transonic potential flow equation on a mesh constructed from small volume elements, which can be conveniently packed around any reasonably smooth configuration. The calculation is performed on two sets of interlocking cells. The velocity and density are calculated in the primary cells, and a flux balance is then established in the secondary cells. The scheme is desymmetrized by the addition of artificial viscosity in the supersonic zone. Some results are included for a swept wing and a wing-cylinder combination.

Prediction of static aerodynamic characteristics for slender bodies alone and with lifting surfaces to very high angles of attack

Abstract: An engineering-type method is presented for computing normal-force and pitching-moment coefficients for slender bodies of circular and noncircular cross section alone and with lifting surfaces. In this method, a semi-empirical term representing viscous-separation crossflow is added to a term representing potential-theory crossflow. For many bodies of revolution, computed aerodynamic characteristics are shown to agree with measured results for investigated free-stream Mach numbers from 0.6 to 2.9. The angles of attack extend from 0 deg to 180 deg for M = 2.9 from 0 deg to 60 deg for M = 0.6 to 2.0. For several bodies of elliptic cross section, measured results are also predicted reasonably well over the investigated Mach number range from 0.6 to 2.0 and at angles of attack from 0 deg to 60 deg. As for the bodies of revolution, the predictions are best for supersonic Mach numbers. For body-wing and body-wing-tail configurations with wings of aspect ratios 3 and 4, measured normal-force coefficients and centers are predicted reasonably well at the upper test Mach number of 2.0. Vapor-screen and oil-flow pictures are shown for many body, body-wing and body-wing-tail configurations. When spearation and vortex patterns are asymmetric, undesirable side forces are measured for the models even at zero sideslip angle. Generally, the side-force coefficients decrease or vanish with the following: increase in Mach number, decrease in nose fineness ratio, change from sharp to blunt nose, and flattening of body cross section (particularly the body nose).

Reynolds Number Dependence in Supersonic Jet Noise

Abstract: An experimental study of the noise production by high speed jets over a wide range of Reynolds numbers has been performed. Two jets of nominal Mach numbers 1.5 and 2.3 were run over a Reynolds number range from 5300 to 107,000. Microphone measurements of the radiated noise and hot-wire measurements of the flow fluctuations demonstrate that at low Reynolds numbers coherent flow instabilities produce a dominant portion of the noise. In the nominal Mach number 2.3 jet these instability waves convect downstream supersonically with respect to the ambient air. In the nominal Mach number 1.5 jet the instabilities convect downstream subsonically. In both cases however, sound pressure level amplitude contours show that the low Reynolds number jets radiate noise comparable to intermediate and high Reynolds number jets. These measurements constitute substantial evidence that a flow instability model of the dominant noise generators may be appropriate for conventional high Reynolds number supersonic jets. a0 C D d M m n r Re St u U Nomenclature speed of sound outside jet wavespeed in the downstream direction diameter of the jet effective diameter of the jet Mach number of the jet at the exit normalized mass velocity fluctuations = azimuthal mode number = radial distance from jet centerline = Reynolds number = p Ud/n. = Strouhal number =fd/ (/(/is frequency) = local velocity =mean centerline velocity of the jet at the nozzle exit

Profile modifications and plateau formation due to light pressure in laser-irradiated targets.

Abstract: A steady-state spherical model has been used in this Letter to study the influence of light pressure on plasma flow and density profile modifications. Whereas in former investigations transitions from subsonic to sonic or supersonic flow and the concomitant formation of density septs have been studied in plane models, this paper treats the transition from supersonic to supersonic flow; and the new phenomenon of density plateau formation just below the critical density is found.

Separation ahead of Protuberances in Supersonic Turbulent Boundary Layers

Abstract: The data were obtained using the optical-surface indicator technique of visualizing the flow; its accuracy and reproducibility are discussed. The proturberances are immersed in the boundary layer on the wall of a supersonic wind tunnel. The relative importance of various nondimensional groups is evaluated. The variation of primary separation distance is presented as a function of obstacle dimensions, Mach number, and Reynolds number, the last being the least significant. These results do not support some scaling laws found in the literature. An alternative correlation is proposed which applies to both small and large cylindrical protuberances.

On the Mechanics of High Speed Liquid Jets

Abstract: Both experimental and theoretical methods are used to investigate the mechanics of the emergence and flight of a liquid jet travelling at speeds supersonic relative to the sound speed of the liquid. The experimental work uses an Imacon image converter camera to follow the mechanical events at micro-second framing intervals. The theoretical investigation employs similarity arguments and the Tschaplygin transformation to investigate the role of liquid overcompression in the process of the jet emergence. In addition, simple theoretical arguments are used to examine the effects of Stokes drag on the small liquid particle shround surrounding the jet and Taylor instability effects in the late time history of the jet's flight. An evacuated chamber is used to verify the theoretical prediction that subsonic (relative to the liquid sound speed) jets will not undergo the violent decompression process predicted for supersonic jets. The experimental and theoretical evidence are synthesized into an overall picture of the jet's history from initial decompression of an overdense supersonic jet to the breakup of the resulting liquid slugs by deceleration and Taylor instability.

Unsteady flow in a supersonic cascade with strong in-passage shocks

Abstract: A model for a supersonic blade row with two in-passage shock waves is developed. It accounts for three-dimensional effects in real flows by using an altered blade shape in a two-dimensional cascade. There is enough flexibility in the choice of blade shape to accommodate a desired entrance angle, exit angle, boundary-layer thickness and stage pressure ratio at a given entrance Mach number. The model divides the mean flow into regions of uniform or one-dimensional flow in which the solutions for the unsteady flow may be formed successively. The analysis makes use of previous solutions for unsteady flow in cascades and over an oscillation wedge. Six flow conditions are chosen in the range of parameters for which the two-shock model is valid for studies of flutter in torsion and bending. It is found, in keeping with previous results from a single-shock model, that in each case there is increasing instability with decreasing frequency.

On the prediction of two-dimensional supersonic viscous interactionsnear walls

Abstract: An existing iterative finite-difference prediction method for the solution of the elliptic differential equations governing incompressible flowfields is adapted to handle compressible fields in which both subsonic and supersonic regimes may be present. The basic procedure and its adaptation are described. The modified method is tested against known analytic solutions for some inviscid supersonic flows, and against experimental data for some laminar, and one turbulent, boundary-layer/wave interactions near walls. The method performs tolerably well. The inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment.

Departures from classical beam theory in laminated, sandwich, and short beams

Abstract: where Eq. (12) holds on y= [Br/F(Br) ] f [ F ( B r ) x ] , exactly as before, F being arbitrary. Equation (8) for the pressure coefficient still holds, except that the freestream Mach number of the affinely related flow (instead of being zero) is now V2, and (3 is replaced by B. This supersonic flow is exactly the canonical wave problem treated by Heaslet and Lomax, in which supersonic sources and doublets were introduced, with the conormal replacing the geometric normal. Thus the tools of classical supersonic and subsonic analysis are applicable immediately if the approximation given in Eq. (4) is used.

Fluctuating Pressure Environment of a Drag Reduction Spike

Abstract: Wind-tunnel measurements have been made of the fluctuating pressure environment in a region of spikeinduced flow separation. Extremely large pressure fluctuations (30% of freest ream dynamic, pressure) were measured on the sides of the spike base at transonic speeds which are related to the nonaxisymmetric, vortical nature of the separated flow at a>0. Even higher (42% of freestream dynamic pressure) pressure fluctuations were observed on the windward side of the nose cap at supersonic speeds and a>7 deg. This is the result of an intermittent shock-shock interaction. The method of Coe et al. of normalizing the spectral data with the local separated flow height was moderately successful in collapsing the data into a manageable number of characteristic spectra. However, the spectra for the spike-induced separation at supersonic speeds agreed better with the results of Speaker and Ailman for two-dimensional step-induced separation than they did with the threedimensional ramp-induced separation of Coe et al. Spectral peaks were observed which corresponded to Roberts' critical subsonic wake flapping frequency.

Oscillating delta wings with attached shock waves

Abstract: An unsteady flow theory is presented for studying the flowfield in the compression side of an oscillating flat delta wing with attached shock waves. Regular perturbation methods are used to analyze the in-phase and outof-phase flow components for small amplitudes and reduced frequencies. In particular, the out-of-phase flow is found to be "quasiconical," thus a pressure formulation can be realized. In the outboard region, where the crossflow is supersonic, exact solutions are found representing parallel surfaces of isobars. In the central region where the crossflow is subsonic, the problem is reduced to that of an ordinary-differential equation by a spanwise integration technique. Closed-form solutions are obtained for all cases. Numerical examples are presented to exhibit the dependence of the damping derivatives on several flow and geometrical parameters. Neutral damping boundaries are also given. It is found that the damping derivatives are generally less sensitive to the sweepback-angle and the freestream Mach number variations than to the mean-incidence variations, except near the shock detachment. Critical assessments, improvement schemes and future extensions were also discussed.

Supersonic aerodynamic characteristics of a Sparrow 3 type missile model with wing controls and comparison with existing tail-control results

Abstract: An experimental investigation was conducted on a model of a wing control version of the Sparrow III type missile to determine the static aerodynamic characteristics over an angle of attack range from 0 deg to 40 deg for Mach numbers from 1.50 to 4.60.

Secondary Gas Injection into a Supersonic Conical Nozzle

Abstract: N experimental survey of the flowfield induced by secondary gas injection into a supersonic conical nozzle is presented. The aim is to clarify the structure of the flowfield and to supply the necessary information for making a model of it. Two different types of pressure probes, Pitot tube and cone-surface pressure tube (cone probe), were used to deduce flow properties over a cross section. Wall pressure distribution was also measured. The results of the measurement indicate that the flowfield downstream of the injection port was composed of some elementary parts which were discerned due to their physical features. The effect of injection pressure on the structure of the flowfield was investigated at one axial location in the symmetrical plane of the flow. The test nozzle was conical with 9.6° half-angle and had a 26.0-mm-diam. throat. The secondary injector was a singleport-type converging nozzle and was drilled normal to the main nozzle wall. The injector port diameter, di9 was 4.0 mm. Both the main stream and the secondary jet were supplied by the same high-pressure air reservoir. Mach number and Reynolds number of the main stream at the injection location without injection were 2.1 and 8.7xl0 6, respectively. The cone probe had a 10° half-angle conical nose tip. It was considerably sensitive to probe angulation, especially at a high Mach number. Therefore we measured the flow direction at first and then set the cone probe axis in this direction and measured the cone surface pressure, pc. The Mach number, M, and the ratio of pc to Pitot pressure, pp, were correlated as M = 0.1612 (p c /p p )-°- 6541 f or 0.1

Numerical Simulation of Supersonic and Hypersonic Turbulent Compression Corner Flows

Abstract: A relaxation turbulence eddy viscosity model is incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensiona l compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of the relaxation process are studied. In general, using the relaxation model, the eddy viscosity value in the outer layer of the separation region is reduced substantially, and good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96 and Reynolds number of 10 7, with wedge angle of 25°. However, the application of the relaxation model to hypersonic flow at Mach number 8.66 and Reynolds number of 22 x 106, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.

Calibration of transonic and supersonic wind tunnels

Abstract: State-of-the art instrumentation and procedures for calibrating transonic (0.6 less than M less than 1.4) and supersonic (M less than or equal to 3.5) wind tunnels were reviewed and evaluated. Major emphasis was given to transonic tunnels. Continuous, blowdown and intermittent tunnels were considered. The required measurements of pressure, temperature, flow angularity, noise and humidity were discussed, and the effects of measurement uncertainties were summarized. A comprehensive review of instrumentation currently used to calibrate empty tunnel flow conditions was included. The recent results of relevant research are noted and recommendations for achieving improved data accuracy are made where appropriate. It is concluded, for general testing purposes, that satisfactory calibration measurements can be achieved in both transonic and supersonic tunnels. The goal of calibrating transonic tunnels to within 0.001 in centerline Mach number appears to be feasible with existing instrumentation, provided correct calibration procedures are carefully followed. A comparable accuracy can be achieved off-centerline with carefully designed, conventional probes, except near Mach 1. In the range 0.95 less than M less than 1.05, the laser Doppler velocimeter appears to offer the most promise for improved calibration accuracy off-centerline.

Maintained detonation waves in an annular channel: A hypothesis which provides the link between classical acoustic combustion instability and detonation waves

Abstract: This paper is an account of a part of a research programme carried out at Rolls-Royce Limited. The programme was directed at evaluating the benefits which may acerue by using detonation waves as the heat addition process in an airbreathing gas turbine power plant. The concept of a maintained detonation wave moving around an annulus which is continuously replenished with fresh combustibles is well known. The work is largely experimental and is directed at the attainment of a demonstration of such a maintained moving detonation wave in ethylene/oxygen/air mixtures. The detonation wave moves into fresh combustibles which are introduced through continuous inlet slits in the annular chamber wall at right angles to the direction of the propagation of the wave. The design has no moving mechanical parts, and the valving of the gas flow is achieved gas-dynamically by matching the pressure profiles behind the detonation wave to the pressure of the inflowing combustibles. The two or three supersonic combustion waves which propagate in a stable fashion have pressure ratios between 2 and 10 and velocities between 1100 and 1500 m/s. These results are functions of the energy content of the incoming combustibles and the gas dynamics of the scavenging and refilling processes. Consideration of all these results has led to the conclusion that all such waves propagating with constant velocity around a continuously replenished annular channel obey the Chapman-Jouguet hypothesis for stable detonations; the unusually low pressure ratios and velocities are accounted for by consideration of the conditions of the gas upstream of the wave which results from incomplete scavenging with fresh combustibles of the hot combustion products of the pressure wave. This explanation provides the link between maintained rotating detonation waves and classical acoustic instability.

Interaction between a supersonic boundary layer and acoustic disturbances

Abstract: The development of disturbances in a boundary layer that have been induced by an external acoustic field are investigated. The problem is considered in the linear formulation. It is shown that the oscillations inside the supersonic boundary layer can have several times the intensity of the external disturbances. The susceptibility of the boundary layer to the acoustic disturbances increases with increasing Mach number. Cooling of the surface leads to a small decrease in the intensity of the longitudinal velocity oscillations in the layer. The effect of the parameters of the acoustic wave is considered, i.e., the effect of the frequency and phase velocity on the development of the disturbances.

Freely interacting transonic boundary layers

Abstract: Transonic free interactions for compressive and expansive boundary‐layer flows are studied numerically and analytically. The results are qualitatively the same as those in supersonic interacting flows. However, it is found that the upstream decay is either algebraic or exponential, depending on whether the transonic interaction parameter is zero or not. The asymptoptic structure of the singularity in expansive free interactions is derived and comparison with the numerical computations shows good agreement.

Nozzle arc interruption in supersonic flow

Abstract: The general arc boundary layer equation is used to derive partial differential equations in arc radius and heat flux potential which account for the temporal and spatial variations of density,velocity, enthalpy, radiation, and electrical conductivity in a Laval nozzle. The model accounts for arc turbulence and permits the cooling "time constant" to vary with position and time. The model has been solved for linear current and voltage ramps subject to the conditions that the interrupting ability varies as (dI/dt)-2and that the nozzle flow is supersonic. Curves show the transient variations of arc radius, temperature, resistance, time constant and post arc current. The calculations indicate that a Cassie arc exists after current zero and that the Cassie-Mayr transition time can exceed 1 µ s.

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

Abstract: The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

Finite-Element Panel Flutter in Three-Dimensional Supersonic Unsteady Potential Flow

Abstract: A finite-element formulation and solution procedure are developed for flutter prediction of rectangular panels with one surface exposed to three-dimensi onal supersonic unsteady potential flow. Each element is divided into several Mach boxes. The aerodynamic influence coefficients between each pair of sending and receiving boxes are computed by the method of Gaussian quadrature. The aerodynamic matrix is based on the numerically computed velocity potentials for all boxes. The effect of in-plane force is included. This development is particularly useful in the low supersonic range for panels with chord-span ratio less than about one, where the piston theory does not give satisfactory accuracy. Examples are demonstrated by using the 16 d.o.f. rectangular plate element. Results for flutter boundaries for the unstressed panels agree well with an alternative Galerkin's modal solution. The examples demonstrate that flutter boundaries are dominated by higher modes for panels with higher chord-span ratio. They also demonstrate that the dominating flutter boundaries abruptly change modes as the Mach number is varied. The beneficial effect of in-plane tension is demonstrated.