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This paper describes the requirements, design, and prototype testing of the flex-section and hinge seals for the Laminar Flow Supersonic Wind Tunnel Primary Injector. The supersonic atmospheric primary injector operates between Mach 1.8 and Mach 2.2 with mass-flow rates of 62 to 128 lbm/s providing the necessary pressure reduction to operate the tunnel in the desired Reynolds number (Re) range.
Nonlinear aerodyanmic characteristics of missile bodies computed. Program NOZVTX calculates nonlinear aerodynamic characteristics and flow fields of missile bodies at various angles-of-attack and roll in supersonic flow. Output includes geometry, centroids, and surface pressure of source panels and positions, strengths, and velocity components of shed vortexes. NOZVTX written in FORTRAN IV for batch execution.
The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.
The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.
In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.
A nonlinear method based on the full potential equation in conservation form, cast in an arbitrary coordinate system, has been developed to treat predominantly supersonic flows with embedded subsonic regions. This type of flow field occurs frequently near the fuselage-canopy junction area and wing leading edge regions for a moderately swept fighter configuration. The method uses the theory of characteristics to accurately monitor the type-dependent flow field. A conservative switching scheme is developed to transition from the supersonic marching algorithm to a subsonic relaxation procedure, and vice versa. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. Results are shown for a few configurations, including a wing-body-wake realistic fighter model having embedded subsonic regions.
A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.
A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.
A numerical procedure has been developed for the computation of supersonic flows over complex conical geometries. The full potential equation is solved using a finite-volume method with a non-body-fitted rectangular grid. The only mapping done is the transformation of the spherical cross-flow plane to a flat surface using a stereographic projection. A new procedure for very thin fins is described which does not require the resolution of the fin thickness. Applications for simple cones, conical wing-bodies, wave riders and finned geometries compare favorably with existing solutions with body-fitted grids and available experimental data.
Linearized slender-body theory is applied to the computation of aerodynamic forces on an oscillating, or deforming, body in supersonic flow. The undeformed body is a body of revolution and the deformed body is represented by movement of a line through the centers of the cross sections which are assumed to remain circular. The time dependence is based on sinusoidal motion. For a body of vanishing thickness the slender-body theory yields the apparent mass approximation as it is obtained for incompressible crossflow around a cylinder. Both linearized slender-body theory and the apparent mass approximation are used to calculate the pitching-moment coefficients on a rigid slender body with a parabolic arc nose cone, and these coefficients are compared with some experimental results.
Three dimensional inviscid supersonic flow fields with primary and embedded shock and expansion waves determined over and behind wings and wing-body configurations
A recently reported parabolized Navier-Stokes code has been employed to compute the supersonic flow field surrounding an ogive-cylinder-boattail body at incidence. The computations were performed for flow conditions where an extensive series of experimental surface pressure and turbulent boundary-layer profile measurements had been obtained. Comparison between the computational results and experimental measurements for angles of attack up to 6 deg show excellent agreement. At angles greater than 6 deg discrepancies are observed which are tentatively attributed to three-dimensional turbulence modeling errors.
A nonlinear aerodynamic prediction technique based on the full potential equation in conservation form has been developed for the treatment of supersonic flows. The method uses the theory of characteristic signal propagation to accurately simulate the flow structure, which includes shock waves and mixed elliptic-hyperbolic crossflow. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. The necessary body-fitted grid system in every marching plane is generated numerically, using an elliptic grid solver. Results are shown for conical and nonconical wing-body combinations and compared with experimental data and Euler calculations. The method demonstrates an enormous savings in execution time and memory requirements over Euler methods.
In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.
The new Lagrangian method introduced by Loh and Hui (1990) is extended for 3-D steady supersonic flow computation. Details of the conservation form, the implementation of the local Riemann solver, and the Godunov and the high resolution TVD schemes are presented. The new approach is robust yet accurate, capable of handling complicated geometry and reactions between discontinuous waves. It keeps all the advantages claimed in the 2-D method of Loh and Hui, e.g., crisp resolution for a slip surface (contact discontinuity) and automatic grid generation along the stream.
A new finite-difference scheme has been developed to solve efficiently the unsteady Euler equations for three-dimensional inviscid supersonic flows with subsonic pockets. The technique utilizes planar Gauss-Seidel relaxation in the marching direction and approximate factorization n the crossflow plane. An 'infinitely large' time step is used in parts of the flowfield where the component of velocity in the marching direction is supersonic - here the Gauss-Seidel sweeps are restricted to the forward direction only, and the procedure reduces to simple space-marching; a finite time step is used in parts of the flowfield where the marching component of velocity is subsonic - here, backward and forward Gauss-Seidel sweeps are employed to allow for upstream and downstream propagation of signals, and a time-asymptotic steady state is obtained. The discretization formulas are based on finite-volume implementation of high accuracy (up to third-order) total variation diminishing formulations. Numerical solutions are obtained for an analytically defined forebody, a realistic fighter configuration, and the Space Shuttle. The results are in very good agreement with available experimental data and numerical solutions of the full-potential equation.
A user's manual for a computer program which calculates the supersonic flow about circular, elliptic, and bielliptic cones at incidence and elliptic cones at yaw by the method of lines is presented. The program is automated to compute a case from known or easily calculated solution by changing the parameters through a sequence of steps. It provides information including the shock shape, flow field, isentropic surface properties, entropy layer, and force coefficients. A description of the program operation, sample computations, and a FORTRAN 4 listing are presented.
Numerical results illustrating the capabilities of an advanced aerodynamic surface paneling method are presented. The method is applicable to both subsonic and supersonic flow, as represented by linearized potential flow theory. The method is based on linearly varying sources and quadratically varying doublets which are distributed over flat or curved panels. These panels are applied to the true surface geometry of arbitrarily shaped three dimensional aerodynamic configurations.