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A procedure to study the local stability of planar shock waves is presented. The procedure is applied to a Rankine-Hugoniot shock in a divergent/convergent nozzle, to an isentropic shock in a divergent/convergent nozzle, and to Rankine-Hugoniot shocks attached to wedges and cones. It is shown that for each case, the equation governing the shock motion is equivalent to the damped harmonic oscillator equation.
The transonic flow theory has been considerably improved in recent years. The problems at subsonic speeds of a moving body concern chiefly the drag and the problems at supersonic speeds, the detached and attached shock waves. Inasmuch as the literature contains some information that is valuable and some other information that is misleading, the purpose of this paper is to discuss those analytical methods and their applications which are regarded as reliable in the transonic range. After these methods are reviewed, a short discussion without details and proofs follows to round out the picture. (author)
The numerical method involving both the method of integral relations and the method of characteristics have been applied to investigate the steady flow phenomena associated with the accurrence of Mach reflection and Mach disc from nozzle flows. The solutions of triple-shock intersection are presented. The regime where Mach configuration appears is defines for the inviscid analysis. The method of integral relations developed for the blunt body problem is modified and extended to the attached shock wave and to internal nozzle flow problems.
A user's manual is presented for a program that calculates the supersonic flow on the windward side of conical delta wings with shock attached at the sharp leading edge by the method of lines. The program also has a limited capability for computing the flow about circular and elliptic cones at incidence. It provides information including the shock shape, flow field, isentropic surface-flow properties, and force coefficients. A description of the program operation, a sample computation, and a FORTRAN 4 program listing are included.
A simple dynamic systems analysis is used to give examples of strong, weak overdriven, and weak underdriven oblique detonations. Steady oblique detonations consisting of a straight lead shock attached to a solid wedge followed by a resolved reaction zone structure are admitted as solutions to the reactive Euler equations. This is demonstrated for a fluid that is taken to be an inviscid, calorically perfect ideal gas that undergoes a two-step irreversible reaction with the first step exothermic and the second step endothermic. This model admits solutions for a continuum of shock wave angles for two classes of solutions identified by a Rankine-Hugoniot analysis: strong and weak overdriven waves. The other class, weak underdriven, is admitted for eigenvalue shock-wave angles. Chapman-Jouguet waves, however, are not admitted. These results contrast those for a corresponding onestep model that, for detonations with a straight lead shock, only admits strong, weak overdriven, and Chapman-Jouguet solutions.
Program LRCDM2 was developed for supersonic missiles with axisymmetric bodies and up to two finned sections. Predicted are pressure distributions and loads acting on a complete configuration including effects of body separated flow vorticity and fin-edge vortices. The computer program is based on supersonic panelling and line singularity methods coupled with vortex tracking theory. Effects of afterbody shed vorticity on the afterbody and tail-fin pressure distributions can be optionally treated by companion program BDYSHD. Preliminary versions of combined shock expansion/linear theory and Newtonian/linear theory have been implemented as optional pressure calculation methods to extend the Mach number and angle-of-attack ranges of applicability into the nonlinear supersonic flow regime. Comparisons between program results and experimental data are given for a triform tail-finned configuration and for a canard controlled configuration with a long afterbody for Mach numbers up to 2.5. Initial tests of the nonlinear/linear theory approaches show good agreement for pressures acting on a rectangular wing and a delta wing with attached shocks for Mach numbers up to 4.6 and angles of attack up to 20 degrees.
Dorodnitsyn's integral method is used to obtain an approximate solution to the supersonic nonequilibrium flow over pointed bodies with attached shock waves. The partial differential equations governing the flow are converted to an approximate set of ordinary equations, which are solved by numerical integration starting at the body tip. Detailed analytical and numerical results for the first approximation are presented, considering the vibrational relaxation of a diatomic gas over a wedge or cone. It is shown that the first approximation yields: (1) The exact flow-variable gradients at the wedge tip (2) Expressions for the flow-variable gradients at the cone tip which are in agreement with extrapolations of characteristics calculations (3) A good approximate algebraic solution for frozen or equilibrium conical flow (4) An approximate expression for the nonequilibrium-flow stream function which affords a means of obtaining variations across the shock layer of the temperature and vibrational energy. Numerical results for both the wedge and cone compare favorably with identical cases computed by the method of characteristics.
Flow swallowing enthalpy probes for low density plasma gas flows in constricted arc heated facility, discussing attached shock system
Results are presented of an experimental investigation on a nonconical wing which supports an attached shock wave over a region of the leading edge near the vertex and a detached shock elsewhere. The shock detachment point is determined from planform schlieren photographs of the flow field and discrepancies are shown to exist between this and the one calculated by applying the oblique shock equations normal to the leading edge. On a physical basis, it is argued that the shock detachment has to obey the two-dimensional law normal to the leading edges. From this, and from other measurements on conical wings, it is thought that the planform schlieren technique may not be particularly satisfactory for detecting shock detachment. Surface pressure distributions are presented and are explained in terms of the flow over related delta wings which are identified as a vertex delta wing and a local delta wing.
The evolution of reusable surface insulation is described, with attention to the mullite and other aluminosilicates, zirconia, and silicon carbide-coated carbon compositions experimented with in the late 1960s and early 1970s. Evaluation and development concentrated in this period on such aspects of design and material properties as cold soak performance, attachment, shock impingement, surface coating cracks, and tile gap design and heating. In addressing the central problem of heat-shield thermal conductivity, it was found that for a given density, silica fibers had a lower conductivity than those of mullite. This was due to the one-micron, as opposed to 4.7-micron, diameter of the silica fibers, which resulted in smaller pores and therefore less convective and radiative heat transfer. Attention is also given to tile coating materials and the high-temperature processes by which they were applied.
Molecular flow velocity (one component), translational temperature, and static pressure of N2 are measured in a supersonic wind tunnel using inverse Raman spectroscopy. For velocity, the technique employs the large Doppler shift exhibited by the molecules when the pump and probe laser beams are counterpropagating (backward scattering). A retrometer system is employed to yield an optical configuration insensitive to mechanical vibration, which has the additional advantage of simultaneously obtaining both the forward and backward scattered spectra. The forward and backward line breadths and their relative Doppler shift can be used to determine the static pressure, translational temperature, and molecular flow velocity. A demonstration of the technique was performed in a continuous airflow supersonic wind tunnel in which data were obtained under the following conditions: (1) free-stream operation at five set Mach number levels over the 2.50-4.63 range; (2) free-stream operation over a range of Reynolds number (at a fixed Mach number) to vary systematically the static pressure; and (3) operation in the flow field of a simple aerodynamic model to assess beam steering effects in traversing the attached shock layer.
The instability of a compressible flow past a wedge is investigated in the hypersonic limit. Particular attention is given to the Tollmien-Schlichting waves governed by triple-deck theory though some discussion of inviscid modes is given. It is shown that the attached shock has a significant effect on the growth rates of Tollmien-Schlichting waves. Moreover, the presence of the shock allows for more than one unstable Tollmien-Schlichting wave. Indeed, an infinite discrete spectrum of unstable waves is induced by the shock, but these modes are unstable over relatively small but high frequency ranges. The shock is shown to have little effect on the inviscid modes considered by previous authors and an asymptotic description of inviscid modes in the hypersonic limit is given.
The instability of a compressible flow past a wedge is investigated in the hypersonic limit. Particular attention is paid to Tollmien-Schlichting waves governed by triple-deck theory though some discussion of inviscid modes is given. It is shown that the attached shock can have a significant effect on the growth rates of Tollmien-Schlichting waves. Moreover, the presence of the shock allows for more than one unstable Tollmien-Schlichting wave. Indeed an infinite discrete spectrum of unstable waves is induced by the shock, but these modes are unstable over relatively small but high frequency ranges. The shock is shown to have little effect on the inviscid modes considered by previous authors and an asymptotic description of inviscid modes in the hypersonic limit is given.
Hypersonic waverider design has become an important concern in the aerospace industry. As one part of an inverse design effort for waveriders, work has been done to apply existing Euler and Navier-Stokies flow solvers to hypersonic geometries with sharp leading edges. Previously, calculations were done on bodies with rounded leading edges or with conical solutions for the nose initial conditions. In this paper, solutions are computed about waveriders and conical shapes with sharp leading edges without resorting to either shortrcut. All solutions show attached shocks with fully supersonic flows at the nose and along the leading edges. Flows about several waverider shapes are shown, as well as a preliminary cone with inlet calculation to study the shock/inlet interaction.
The nonlinear stability of a compressible flow past a wedge is investigated in the hypersonic limit. The analysis follows the ideas of a weakly nonlinear approach. Interest is focussed on Tollmien-Schlichting waves governed by a triple deck structure and it is found that the attached shock can profoundly affect the stability characteristics of the flow. In particular, it is shown that nonlinearity tends to have a stabilizing influence. The nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits.
The longitudinal and lateral stability derivatives of caret-wing waveriders flying on-design are calculated using linear piston theory. The experimental work of Kipke is used to validate the lift and pitch stiffness coefficients. Comparison is also made to the analytical work done by Hui. The calculations are extended to off-design conditions with an attached shock wave using tangent wedge theory. The stability derivatives of a Mach 6 waverider are computed and conclusions about its stability are drawn.
A computational study was conducted to better understand experimental results obtained from wind tunnel tests of a Mach 4 waverider model and a comparative reference configuration. The experimental results showed that the performance of the reference configuration was slightly better than that of the waverider model. These results contradict waverider design theory, which suggests that a waverider optimized for maximum lift-to-drag should provide better performance than any other non-waverider configuration at a given design point, especially at hypersonic speeds. The computational results showed that the predicted surface pressure values and the integrated lift and drag coefficients from the pressure distributions were much lower for the reference model than for the flat-top model, due to the reference model bottom surface having a slight expansion. The lift-to-drag ratios for the flat-top model were higher due to a relatively low drag for the same amount of lift. These results indicate that the performance advantage of the reference model was due to the shape of the bottom surface and not due to the flat top surface. The results also showed that the reference model exhibited the same shock attachment characteristics as the waverider because the planform shapes were identical. CFD predictions show that the planform shape gives the waverider an advantage in performance over conventional hypersonic vehicles and that altering the bottom surface of a waverider does not cause significant performance degradation.
The integration of a class of hypersonic high-lift configurations known as waveriders into hypersonic cruise vehicles was evaluated. Waveriders offer advantages in aerodynamic performance and propulsion/airframe integration (PAI) characteristics over conventional hypersonic shapes. A wind-tunnel model was developed which integrates realistic vehicle components with two waverider shapes, referred to as the 'straight-wing' and 'cranked-wing' shapes. Both shapes were conical-flow-derived waveriders at a design Mach number of 4.0. The cranked-wing shape was designed to provide advantages in subsonic performance and directional stability over conventional waveriders. Experimental data and limited computational fluid dynamics (CFD) predictions were obtained over a Mach number range of 2.3 to 4.63 at a Reynolds number of 2.0x10(exp 6) per foot. The CFD predictions and flow visualization data confirmed the shock attachment characteristics of the baseline waverider shapes and illustrated the waverider flow-field properties. Both CFD predictions and experimental data showed that no significant performance degradations occur at off-design Mach numbers for the waverider shapes and the integrated configurations. The experimental data showed that the effects of adding a realistic canopy were minimal. The effects of adding engine components were to increase the drag and thus degrade the aerodynamic performance of the configuration. A significant degradation in aerodynamic performance was observed when 0 degree control surfaces were added to close the blunt base of the waverider to a sharp trailing edge. A comparison of the fully-integrated waverider models to the baseline shapes showed that the performance was significantly degraded when all of the components were added to the waveriders. The fully-integrated configurations studied here do not offer significant performance advantages over conventional hypersonic vehicles, but still offer advantages in air-breathing propulsion integration. Additionally, areas are identified in this study where improvements could be made to enhance the performance. Both fully-integrated configurations are longitudinally unstable over the Mach number range studied for unpowered conditions. The cranked-wing fully-integrated configuration provided significantly better lateral-directional stability characteristics than the straight-wing configuration.