Studies of the boundary layer, with natural induced turbulence, in the case of supersonic flow along a flat plate
Dynamic and thermal characteristics of natural and induced turbulent layers in supersonic flow along flat plates
Dorand, J.-F.↗
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Supersonic flow development in slotted wind tunnels
The development of test section slot shapes for achieving smooth supersonic Mach number distribution without overexpansion or waviness has, in the past, been largely an experimentally iterative or 'cutand try' procedure for each wind tunnel. To overcome the obvious disadvantages of time and expense involved in such an experimental approach, a simple analytical method has been developed to predict the supersonic flow development in a two-dimensional slotted tunnel given only the variation of open area ratio with downstream distance and the Mach number corresponding to the plenum static pressure. The well known method of characteristics is used with the constraint that it be compatible with the quadratic cross-flow pressure drop boundary condition at the slotted wall. The predicted results from this method agree remarkably well with the experimental calibration data available for some of the existing facilities. The flow mechanism responsible for causing overexpansion in the centerline Mach number distribution with some slot shapes has been brought to light.
Ramaswamy, M. A.↗
Numerical simulations of supersonic flow through oscillating cascade sections
A finite difference code has been developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model 'real' airfoils that have thickness and camber. Sample predictions are presented for a cascade of loaded airfoils and show appreciable differences in the unsteady surface pressure distributions when compared with the flat plate results.
Huff, Dennis L.↗
Theoretical characteristics in supersonic flow of two types of control surfaces on triangular wings
Methods based on the linearized theory for supersonic flow were used to find the characteristics of two types of control surfaces on thin triangular wings. The first type, the constant-chord partial-span flap, was considered to extend either outboard from the center of the wing or inboard from the wing tip. The second type, the full-triangular-tip flap, was treated only for the case in which the Mach number component normal to the leading edge is supersonic. For each type, expressions were found for the lift, rolling-moment, pitching-moment, and hinge-moment characteristics.
Tucker, Warren A↗
Analysis of supersonic flows using k-epsilon model and the RPLUS code: Progress towards high speed combustor analysis
The problem of interest here is the analysis of chemically reacting flow inside of supersonic ramjet combustors. Two key parameters need to be determined: mixing/combustion efficiency and kinetic energy efficiency. In order to determine these parameters, several potential loss mechanisms must be modeled correctly, including mixing, shear, turbulence, vorticity, shock waves, heat transfer, fuel injector drag, poor wall pressure integral, and chemical dissociation. This document discusses k-epsilon turbulence models for use in the RPLUS code for numerical modeling of combustor flow fields.
Lee, J.↗
Numerical calculation of flow fields about rectangular wings of finite thickness in supersonic flow
The calculation of the outer inviscid flow about a rectangular wing moving at supersonic speeds is reported. The inviscid equations of motion governing the flow generated by the wing form a set of hyperbolic differential equations. The flow field about the rectangular wing is separated into three regions consisting of the forebody, the afterbody, and the wing wake. Solutions for the forebody are obtained using conical flow techniques while the afterbody and the wing wake regions are treated as initial value problems. The numerical solutions are compared in the two dimensional regions with known exact solutions.
Vogel, J. M.↗
Conformal mappings for computations of steady, three-dimensional, supersonic flows
The evaluation of steady, supersonic, three-dimensional inviscid flows is considered, taking into account the construction of suitable grids on the basis of a simple conformal mapping. A description is presented of an analytical mapping technique. The technique is illustrated with the aid of examples of mappings, involving nontrivial geometries. Attention is given to a wing-fuselage cross section, a FORTRAN program for the basic mapping, the coupling of mappings, and the equations of motion.
Moretti, G.↗
Hypersonic engine component experiments in high heat flux, supersonic flow environment
A major concern in advancing the state-of-the-art technologies for hypersonic vehicles is the development of an aeropropulsion system capable of withstanding the sustained high thermal loads expected during hypersonic flight. Even though progress has been made in the computational understanding of fluid dynamics and the physics/chemistry of high speed flight, there is also a need for experimental facilities capable of providing a high heat flux environment for testing component concepts and verifying/calibrating these analyses. A hydrogen/oxygen rocket engine heat source was developed at the NASA Lewis Research Center as one element in a series of facilities at national laboratories designed to fulfill this need. This 'Hot Gas Facility' is capable of providing heat fluxes up to 450 w/sq cm on flat surfaces and up to 5,000 w/sq cm at the leading edge stagnation point of a strut in a supersonic flow stream. Gas temperatures up to 3050 K can also be attained. Two recent experimental programs conducted in this facility are discussed. The objective of the first experiment is to evaluate the erosion and oxidation characteristics of a coating on a cowl leading edge (or strut leading edge) in a supersonic, high heat flux environment. Macrophotographic data from a coated leading edge model show progressive degradation over several thermal cycles at aerothermal conditions representative of high Mach number flight. The objective of the second experiment is to assess the capability of cooling a porous surface exposed to a high temperature, high velocity flow environment and to provide a heat transfer data base for a design procedure. Experimental results from transpiration cooled surfaces in a supersonic flow environment are presented.
Gladden, Herbert J.↗
Comparison of Experimental and Theoretical Static Aeroelastic Loads and Deflections of a Thin 45 deg Delta Wing in Supersonic Flow
Wind tunnel tests showing the effects of static aeroelasticity for a thin 45 degree delta wing in supersonic flow are presented and compared with theory in the Mach number range 1.30 t o 4.00. Calculated deformations, normal-force coefficients, and pitching-moment coefficients based on a linearized potential theory for subsonic leading edges at a Mach number of 1.30 and a linearized potential theory for supersonic leading edges at Mach numbers of 1.64, 3.00, and 4.00 are shown to compare favorably with the wind-tunnel results. Calculations of these same deformations and coefficients based on piston theory are shown to compare satisfactorily with experiment at a Mach number of 4.00 but not so well at a Mach number of 3.00. A factor modification of piston theory is suggested which improves the correlation of these results with experiment and also with the potential-theory results.
Bennett, Floyd V.↗
Problem of oscillating cone in supersonic flow is solved by small perturbation techniques
Small perturbation technique solves the problem of an oscillating cone in supersonic flow. The logic of the program is straightforward, as reflected in the actual instructions for solving the problem.
Pao, T.-H.↗
Effect of angle of attack and injection pressure on jet penetration and spreading from a delta wing in supersonic flow
Effect of angle of attack and injection pressure on jet penetration and spreading from delta wing in supersonic flow
Hersch, M.↗
Tables for Supersonic Flow of Helium Around Right Circular Cones at Zero Angle of Attack
The results of the calculation of supersonic flow of helium about right circular cones at zero angle of attack are presented in tabular form. The calculations were performed using the Taylor-Maccoll theory. Numerical integrations were performed using a Runge-Kutta method for second-order differential equations. Results were obtained for cone angles from 2.5 to 30 degrees in regular increments of 2.5 degrees. In all calculations the desired free-stream Mach number was obtained to five or more significant figures.
Sims, J. L.↗
Constant-temperature hot-wire anemometer practice in supersonic flows. I - The normal wire
The performance of a constant-temperature normal hot-wire in a supersonic flow is critically examined. It is shown that this instrument is inherently unsuitable for measuring turbulent temperature correlations because of the highly nonlinear response to temperature fluctuations, particularly at low overheat ratios. The instrument is therefore limited to measurements of mean and fluctuating mass-flow rates. Suitable calibration procedures, as well as the limits on spatial and temporal resolution are discussed, and corrections for mean stagnation temperature changes are suggested.
Smits, A. J.↗
Base pressure in laminar supersonic flow.
An asymptotic description is proposed for supersonic laminar flow over a wedge or a backward-facing step, for large Reynolds number and for a base or step height which is small compared with the boundary-layer length. The analysis is carried out for adiabatic wall conditions and a viscosity coefficient proportional to temperature. In a particular limit corresponding to a very thick boundary layer, a similarity law is obtained for the base pressure. For a thinner boundary layer an asymptotic form for the base pressure is obtained which shows the dependence on the parameters explicitly and which permits good agreement with experiment. This latter result is based on an inviscid-flow approximation for the corner expansion and for reattachment with viscous forces important primarily in a thin sublayer about the dividing streamline. A prediction of the pressure distribution at reattachment is given and the result is compared with experimental pressure distributions.
Messiter, A. F.↗
Computation of multi-dimensional viscous supersonic flow
A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.
Buggeln, R. C.↗
Aeroelastic characteristics of a cascade of mistuned blades in subsonic and supersonic flows
An investigation of the effects of mistuning on flutter and forced response of a cascade in subsonic and supersonic flows is presented. The aerodynamic and structural coupling between the bending and torsional motions and the aerodynamic coupling between the blades are included. It is shown that frequency mistuning always has a beneficial effect on flutter. Additionally, the results indicate that frequency mistuning may have either a beneficial or an adverse effect on forced response, depending on the engine order of the excitation and Mach number.
Kielb, R. E.↗
Numerical analysis of supersonic flow through oscillating cascade sections by using a deforming grid
A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.
Huff, Dennis L.↗
Numerical analysis of supersonic flow through oscillating cascade sections by using a deforming grid
A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.
Huff, Dennis L.↗