Showing papers on "Supersonic speed published in 1979"

Artificial Compressibility Methods for Numerical Solutions of Transonic Full Potential Equation

Abstract: New methods for transonic flow computations based on the full potential equation in conservation form are presented. The idea is to modify slightly the density (due to the artificial viscosity in the supersonic region), and solve the resulting elliptic-like problem iteratively. It is shown that standard discretization techniques (central differencing) as well as some standard iterative procedures (SOR, ADI, and explicit methods) are applicable to the modified transonic mixed-type equation. Calculations of transonic flows around cylinders and airfoils are discussed with special emphasis on the explicit methods that are suitable for vector processing on the STAR 100 computer.

Sonic-boom minimization with nose-bluntness relaxation

Abstract: A procedure which provides sonic-boom-minimizing equivalent area distributions for supersonic cruise conditions is described. This work extends previous analyses to permit relaxation of the extreme bluntness required by conventional low-boom shapes and includes propagation in a real atmosphere. The procedure provides area distributions which minimize either shock strength or overpressure.

Experiments of shock associated noise of supersonic jets

Abstract: The paper examines the aeroacoustics associated with model nozzles operating supersonically. In particular, the shock structure and radiated shock noise of Mach 1.5 and 2.0 nozzles are compared with those of a convergent nozzle over a wide nozzle pressure ratio range corresponding to a fully expanded Mach number between unity and 2.37. The nozzles were operated unheated both with and without a tab for screech tone suppression. The measurements show differences between the shock cell spacing of convergent and convergent-divergent nozzles, and the scaling relation appears to be a function of the exit-to-throat velocity ratio of each nozzle type. The acoustic measurements indicate the extent of the pressure ratio range where a C-D nozzle achieves a noise reduction benefit. At the design point of the Mach 1.5 nozzle, the total integrated sound power from this nozzle is 6 dB less than a convergent nozzle operating at the same pressure ratio and thrust

Implicit Algorithm for the Conservative Transonic Full-Potential Equation Using an Arbitrary Mesh

Abstract: A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Comparison of Multiequation Turbulence Models for Several Shock Boundary-Layer Interaction Flows

Abstract: Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.

Criteria for self-ignition of supersonic hydrogen-air mixtures

Abstract: A correlation of available self ignition data for supersonic hydrogen-air mixtures in configurations representative of scramjet combustors was made. The correlation was examined in light of simplified ignition-limit models. The data and model included cases of injection from transverse fuel jets on walls, transverse jets behind swept and unswept steps, and transverse injection ahead of swept and unswept steps and strut bases. The results provide useful guidance for predicting self ignition in a variety of applications. The likely regions for self ignition in a combustor are given in order of merit.

Radiative amplification of sound waves in the winds of O and B stars

Abstract: The velocity perturbation associated with an outwardly propagating sound wave in a radiation-driven stellar wind gives rise to a periodic Doppler shifting of absorption lines formed in the flow. A linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow. Detailed calculations of the acceleration due to a large number of lines indicate that significant amplification can occur throughout the high-velocity portion of winds in which the dominant force-producing lines have appreciable optical depths. In the particular case of the wind of Zeta Pup (O4f), it is found that the e-folding distance for wave growth is considerably shorter than the scale lengths over which the physical properties of the flow vary. A qualitative estimate of the rate at which mechanical energy due to nonlinear waves can be dissipated suggests that this mechanism may be important in heating the supersonic portion of winds of early-type stars.

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

Abstract: A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

Estimation of Attainable Leading-Edge Thrust for Wings at Subsonic and Supersonic Speeds

Abstract: The factors which place limits on the theoretical leading edge thrust are identified. An empirical method for the estimation of attainable thrust is presented. The method is based on the use of simple sweep theory to permit a two dimensional analysis, the use of theoretical airfoil programs to define thrust dependence on local geometric characteristics, and the examination of experimental two dimensional airfoil data to define limitations imposed by local Mach numbers and Reynolds numbers. Comparisons of theoretical and experimental aerodynamic characteristics for a series of wing body configurations are examined.

Numerical Calculation of Transonic Potential Flow about Wing-Body Combinations

Abstract: A method is presented for numerically calculating the transonic potential flow about rather general geometries. It is based upon a particularly simple form of the usual quasilinear potential equations and is formulated in terms of local representations of the solution and the mapping functions used to generate the finitedifference grid. Thus, all derivatives are generated numerically and there is no need to transform the equation—a formidable task when using boundary-conforming coordinate systems for complex geometries. The solution is stabilized by adding upwind bias in supersonic regions, and the difference equations are solved by relaxation. Sample results for wing-cylinder and simple wing-fuselage combinations are presented.

Computation of three-dimensional turbulent separated flows at supersonic speeds

Abstract: Numerical solutions of the time-averaged Navier-Stokes equations employing a simple eddy-viscosity model have been obtained for three dimensional turbulent flow fields at supersonic speeds. The computer results are compared with a series of experimental test flows describing the interaction of a swept shock wave with a turbulent boundary layer for various shock-wave strengths. Very good agreement is obtained between the computed and experimental surface and flow-field results. The computed flow fields are examined in detail to investigate the physics of this type of flow field. Questions concerning the existence of a vortex and the relationship between converging surface oil streaks and the resulting flow field are addressed.

Applications of Laplace transform methods to airfoil motion and stability calculations

Abstract: This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Drag Reduction by Cooling in Hydrogen-Fueled Aircraft

Abstract: Drag reductions are possible for cryo-fueled aircraft by using fuel to cool selected aerodynamic surfaces on its way to the engines. This is because cooled laminar boundary layers in air at subsonic and low supersonic speeds are more stable than adiabatic boundary layers and therefore more resistant to transition to turbulent flow. Calculations for A/=0.85 hydrogen-fueled transport show that drag reductions in cruise of about 20% are within reason. The weight of the fuel saved is well in excess of the weight of the required cooling system. These results suggest that the hydrogen fueled aircraft employing surface cooling is quite attractive as an energy conservative aircraft and warrants more detailed study.

Tone noise of three supersonic helical tip speed propellers in a wind tunnel

Abstract: Three supersonic helical tip speed propellers were tested in the NASA Lewis 8- by 6-foot wind tunnel. This is a perforated-wall wind tunnel but it does not have acoustic damping material on its walls. The propellers were tested at tunnel through flow Mach numbers of 0.6, 0.7, 0.75, 0.8, and 0.85 with different rotational speeds and blade setting angles. The three propellers, which had approximately the same aerodynamic performance, incorporated different plan forms and different amounts of sweep and yielded different near field noise levels. The acoustically designed propeller had 45 deg of tip sweep and was significantly quieter at M = 0.8 cruise than the straight bladed propeller. The intermediate 30 deg tip sweep propeller, which was swept for aerodynamic purposes, exhibited noise that was between the other two propellers. Noise trends with varying helical tip Mach number and blade loading were also observed.

Supersonic, low drag tubular projectile

Abstract: A hollow tubular projectile is disclosed having about 30 percent less masshan conventional ammunition projectiles and considerably less drag, as a result of precise aerodynamic design details.

Supersonic inlet having variable area sideplate openings

Abstract: An inlet duct of generally rectangular configuration for supersonic aircraft in which a normal shock is produced in close proximity to the forward lip of the lower duct wall, and in which variable area sideplate openings are provided just upstream of the normal shock to achieve boundary layer control for the normal shock-boundary layer interaction during on-design operation and increasing flow area for spillage as the normal shock is moved forward during off-design operation.

Properties of two- and three-dimensional separation flows at supersonic velocities

Abstract: The results are given of experimental investigations into three-dimensional separation of a turbulent boundary layer in the neighborhood of oblique shock waves, wedge-shaped obstacles, and sweptback steps at Mach numbers M∞ = 2, 2.25, 2.5, 3, 4 and Reynolds numbers Re∞ = u∞/v = (30–36)· 106 m−1. The characteristic regimes of the separated flows are considered. There is a discussion of the results of comparison and generalization of the pressure distribution in the two- and three-dimensional separation regions, and empirical dependences are also given for determining some geometrical parameters of these regions. An analogy is found in the characteristic pressures, and pressure distribution for a number of two- and three-dimensional separation flows, which suggests that one could use some of the known methods of analysis of two-dimensional separation of a turbulent boundary layer to calculate estimates for the three-dimensional case. This is confirmed by a comparison of calculated and experimental data.

Shock Boundary Layer Interaction on High Turning Transonic Turbine Cascades

Abstract: In recent years, the increase in turbine entry temperature, coupled with the capability of higher blade speeds, has led to greater interest in the high work capacity single-stage transonic high pressure turbine. However, the transonic turbine has a performance penalty compared with an equivalent subsonic unit due mainly to shock induced losses. A cascade investigation into the influence of supersonic shocks on turbine blade performance is reported. Two different rotor profiles designed for the same duty were tested in the rectilinear cascade wind tunnel at DFVLR-AVA Goettingen. The results indicate the sensitivity of the cascade performance to shock boundary layer interaction. The importance of Schlieren optics flow visualization (including high-speed film to show the unsteady behavior of the flow) in evaluating the results is discussed.Copyright © 1979 by ASME

Numerical simulation of steady supersonic viscous flow

Abstract: A noniterative, implicit, space-marching, finite-difference algorithm is developed for the steady thin-layer Navier-Stokes equations in conservation-law-form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

The physics of weak waves in gases

Abstract: The properties of air at meteorological temperatures relevant to sound propagation and shock wave structure are reviewed. Of particular interest is the irreversible process of vibrational relaxation which describes the transfer of energy to or from the vibrational modes of the molecules and which dominates the absorption of audible sound in air. A detailed discussion of the structure and propagation of weak nonlinear waves in air shows that relaxation is again the dominant effect. As an alternative method to the usual approach of nonlinear acoustics the exact gas-dynamic equations are solved numerically for a number of simple flow situations and exact results are obtained for the structure of steady waves. Estimates are obtained for the propagation distances required for the development of waveforms into steady profiles, and these distances are found under some circumstances to be greater than the dimensions of the Earth's atmosphere. The results are confirmed by laboratory experiments in CO2 and N2O and applied to waves in the air with special reference to the sonic bangs of supersonic aircraft. Very recent results of applying the same alternative approach to periodic waves are reviewed briefly.

Computation of supersonic viscous flows over ogive-cylinders at angle of attack

Abstract: The parabolic Navier-Stokes (PNS) marching finite-difference method is applied to 3-D viscous flow over pointed ogive-cylinders, and to turbulent flow over a cone. Ogive computations were performed using the new technique recently reported by Vigneron, Rakich, and Tannehill. Comparison is made with experiment and inviscid computations. The present results show that this method, which neglects part of the pressure gradient in the x-momentum equation, is nevertheless valid for flows with a strong favorable pressure gradient. In addition, turbulent separated flow over a cone has been computed using the older PNS code due to Lubard and Helliwell. It is found that one must freeze the turbulent eddy-viscosity model upstream of 3-D separation to get agreement with experiment.

A Rational Analysis of Periodic Flow Perturbation in Supersonic Two-Dimensional Cascade

Abstract: An analytical formulation which can be applied to obtain unsteady aerodynamic solutions for a cascade of flat plate blades oscillating in subsonic or supersonic flow with either subsonic or supersonic axial velocity component is presented. In the analysis, the flow is assumed to be two-dimensional and isentropic and the blades are undergoing small amplitude harmonic oscillations. The method of superposition of basic wave solutions of the linearized unsteady flow equation is used to construct the flow field induced by the harmonic motion of blades in cascade. This method leads to an integral equation from which the unsteady loading on a blade can be determined. Since the equation applied to both subsonic and supersonic inlet conditions, the present approach provides a unified basis for analyzing and understanding the complex physical phenomena associated with flow past vibrating cascades. The technique used to determine a solution for an unsteady supersonic cascade is also described and the results obtained are shown to agree with those from previous solution.