The effects of sideslip, aspect ratio, and Mach number on the lift and pitching moment of triangular, trapezoidal, and related plan forms in supersonic flow
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WINGS, DELTA↗
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The Load Distribution Due to Sideslip on Triangular, Trapezoidal, and Related Plan Forms in Supersonic Flow
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LIFT DISTRIBUTION - WINGS↗
Supersonic flow around circular cones at angles of attack
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FLOW, SUPERSONIC↗
Accuracy of approximate methods for predicting pressures on pointed nonlifting bodies of revolution in supersonic flow
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FLOW, SUPERSONIC↗
Plasma motion in the Venus ionosphere - Transition to supersonic flow
A remarkable feature of the ionosphere of Venus is the presence of nightward supersonic flows at high altitude near the terminator. In this paper it is shown that the relatively high pressure dayside plasma wells up slowly, and at high altitude it is accelerated horizontally through a relatively constricted region near the terminator toward the low-density nightside. In effect, the plasma flows through a 'nozzle' that is first converging, then diverging, permitting the transition to supersonic flow. The model plasma accelerates to supersonic speeds, reaching sonic speed just behind the terminator. The ion transport rates are sufficient to produce and maintain the nightside ionosphere.
Whitten, R. C.↗
Combustion in supersonic flow
A workshop on combustion in supersonic flow was held in conjunction with the 21st JANNAF Combustion Meeting at Laurel, Maryland on October 3 to 4 1984. The objective of the workshop was to establish the level of current understanding of supersonic combustion. The workshop was attended by approximately fifty representatives from government laboratories, engine companies, and universities. Twenty different speakers made presentations in their area of expertise during the first day of the workshop. On the second day, the presentations were discussed, deficiencies in the current understanding defined, and a list of recommended programs generated to address these deficiencies. The agenda for the workshop is given.
Northam, G. B.↗
Three dimensional boundary conditions in supersonic flow
A theoretical analysis of the flow pattern at a solid surface in three dimensional supersonic flow is presented. The additional information necessary to overcome the nonuniqueness associated with the body tangency condition in three dimensions was developed. The analysis is based on the fact that three dimensional waves propagate locally exactly as they do in axisymmetric flow when viewed in the osculating plane to the streamline. The supersonic flow over an infinite swept corner is examined by both the classical solution and the three dimensional solution in the osculating plane and the results are shown to be identical. A simple numerical algorithm is proposed which accounts for the three wave surfaces that interact at a solid boundary.
Rudman, S.↗
Numerical study of the effect of an embedded surface-heat source on the separation bubble of supersonic flow
A numerical study of the conjugated problem of a separated supersonic flow field and a conductive solid wall with an embedded heat source is presented. Implicit finite-difference schemes were used to solve the two-dimensional time-dependent compressible Navier-Stokes equations and the time-dependent heat-conduction equation for the solid in both general coordinate systems. A detailed comparison between the thin-layer and Navier-Stokes models was made for steady and unsteady supersonic flow and showed insignificant differences. Steady-state and transient cases were computed and the results show that a temperature pulse at the solid-fluid interface can be used to detect the flow direction near the wall in the vicinity of separation without significant distortion of the flow field.
Degani, D.↗
Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations
The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.
Osher, S.↗
The inviscid axisymmetric stability of the supersonic flow along a circular cylinder
The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary layer flow (i.e., the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so called doubly generalized inflexion condition is derived, which is a condition for the existence of so called subsonic neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two freestream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to rapidly disappear as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.
Duck, Peter W.↗
The inviscid axisymmetric stability of the supersonic flow along a circular cylinder
The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary-layer flow (i.e. the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so-called 'doubly generalized' inflexion condition is derived, which is a condition for the existence of so-called 'subsonic' neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two free-stream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to disappear rapidly as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.
Duck, Peter W.↗
Infinitesimal Conical Supersonic Flow
The calculation of infinitesimal conical supersonic flow has been applied first to the simplest examples that have also been calculated in another way. Except for the discovery of a miscalculation in an older report, there was found the expected conformity. The new method of calculation is limited more definitely to the conical case.
Busemann, Adolf↗
Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model
A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.
Sommer, T. P.↗
Equations for the kinetic modeling of supersonically flowing electrically excited lasers
The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.
Lind, R. C.↗
Interactive calculation procedure for supersonic flows
An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept.
Tassa, Y.↗
Flow Visualization by Elastic Light Scattering in the Boundary Layer of a Supersonic Flow
We demonstrate instantaneous flow visualization of the boundary layer region of a Mach 2.5 supersonic flow over a flat plate that is interacting with an impinging shock wave. Tests were performed in the Unitary Plan Wind Tunnel (UPWT) at NASA Langley Research Center. The technique is elastic light scattering using 10-nsec laser pulses at 532 nm. We emphasize that no seed material of any kind, including water (H2O), is purposely added to the flow. The scattered light comes from a residual impurity that normally exists in the flow medium after the air drying process. Thus, the technique described here differs from the traditional vapor-screen method, which is typically accomplished by the addition of extra H2O vapor to the airflow. The flow is visualized with a series of thin two-dimensional light sheets (oriented perpendicular to the streamwise direction) that are located at several positions downstream of the leading edge of the model. This geometry allows the direct observation of the unsteady flow structure in the spanwise dimension of the model and also allows the indirect observation of the boundary layer growth in the streamwise dimension.
Herring, G. C.↗
Supersonic flow and shock formation in turbine tip gaps
Shock formation due to overexpansion of supersonic flow at the inlet to the tip clearance gap of a turbomachine has been studied. As the flow enters the tip gap, it accelerates around the blade pressure-side corner creating a region of minimum static pressure. The 'free streamline' separates from the wall at the corner; and, for Mach numbers greater than about 1.3, it curves back to intersect the blade tip. At this point, the freestream flow is abruptly turned parallel to the surface, giving rise to an oblique shock. The results are consistent with compressible sharp-edged orifice flow calculations found in the literature and with the theory of oblique shock wave formation in supersonic flow over a wedge. For freestream Mach numbers of 1.4 to 1.8, wave angles are 43 to 54 deg, and turning angles are 9 to 20 deg; as the Mach number increases, the angle of turn also increases. It appears that in a turbine, after separating from the inlet corner, the flow reattaches on the blade tip and an oblique shock is formed at 0.4-1.4 tip gap heights into the clearance gap. The resulting shock-boundary layer interaction may contribute to further enhancement of already high heat transfer to the blade tip in this region. This in turn could lead to higher blade temperatures and adversely affect blade life and turbine efficiency.
Moore, John↗
On the Kernel function of the integral equation relating lift and downwash distributions of oscillating wings in supersonic flow
This report treats the Kernel function of the integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for harmonically oscillating wings in supersonic flow. The treatment is essentially an extension to supersonic flow of the treatment given in NACA report 1234 for subsonic flow. For the supersonic case the Kernel function is derived by use of a suitable form of acoustic doublet potential which employs a cutoff or Heaviside unit function. The Kernel functions are reduced to forms that can be accurately evaluated by considering the functions in two parts: a part in which the singularities are isolated and analytically expressed, and a nonsingular part which can be tabulated.
Watkins, Charles E↗