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At least 109 records · Page 6

An experimental investigation of the effect of boundary layer refraction on the noise from a high-speed propeller

Models of supersonic propellers were previously tested for acoustics in the Lewis 8- by 6-Foot Wind Tunnel using pressure transducers mounted in the tunnel ceiling. The boundary layer on the tunnel ceiling is believed to refract some of the propeller noise away from the measurement transducers. Measurements were made on a plate installed in the wind tunnel which had a thinner boundary layer than the ceiling boundary layer. The plate was installed in two locations for comparison with tunnel ceiling noise data and with fuselage data taken on the NASA Dryden Jetstar airplane. Analysis of the data indicates that the refraction increases with: increasing boundary layer thickness; increasing free stream Mach number; increasing frequency; and decreasing sound radiation angle (toward the inlet axis). At aft radiation angles greater than about 100 deg there was little or no refraction. Comparisons with the airplane data indicated that not only is the boundary layer thickness important but also the shape of the velocity profile. Comparisons with an existing two-dimensional theory, using an idealized shear layer to approximate the boundary layer, showed that the theory and data had the same trends. Analysis of the data taken in the tunnel at two different distances from the propeller indicates a decay with distance in the wind tunnel at high Mach numbers but the decay at low Mach numbers is not as clear.

Dittmar, J. H.↗

Massive separation and dynamic stall on a cusped trailing-edge airfoil

The cross-over from a predominantly attached two-dimensional flow to the bluff body form of separation is modeled via the interacting boundary layer approximation. The initial breakdown of the predominantly attached flow on a cusped trailing edge airfoil is examined using the Hilbert integral form of the unsteady interacting boundary layer equations. In addition, an interacting boundary layer technique is developed for calculating bluff body separation. This new model eliminates the severe scaling problems associated with bluff body separation through the use of a realistic inviscid eddy model, based on the infinite eddy Kirchhoff free-streamline description of separation. Brief consideration is given to the cross-over from bluff body separation to a predominantly attached flow, the extension to finite eddies and cascade flows, and the possible coupling with full, or parabolized, Navier-Stokes calculations.

Rothmayer, A. P.↗

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.

Abarbanel, Saul↗

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

Effect of nose shape on three-dimensional stagnation region streamlines and heating rates

A new method for calculating the three-dimensional inviscid surface streamlines and streamline metrics using Cartesian coordinates and time as the independent variable of integration has been developed. The technique calculates the streamline from a specified point on the body to a point near the stagnation point by using a prescribed pressure distribution in the Euler equations. The differential equations, which are singular at the stagnation point, are of the two point boundary value problem type. Laminar heating rates are calculated using the axisymmetric analog concept for three-dimensional boundary layers and approximate solutions to the axisymmetric boundary layer equations. Results for elliptic conic forebody geometries show that location of the point of maximum heating depends on the type of conic in the plane of symmetry and the angle of attack, and that this location is in general different from the stagnation point. The new method was found to give smooth predictions of heat transfer in the nose region where previous methods gave oscillatory results.

Hassan, Basil↗

Boundary control of parabolic systems - Finite-element approximation

The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.

Lasiecka, I.↗

Influence of test configuration on the combustion characteristics of polymers as ignition sources

The experimental evaluation of polymers as ignition sources for metals was accomplished at the NASA White Sands Test Facility (WSTF) using a standard promoted combustion test. These tests involve the transient burning of materials in high-pressure oxygen environments. They have provided data from which design decisions can be made; data include video recordings of ignition and non-ignition for specific combinations of metals and polymers. Other tests provide the measured compositions of combustion products for polymers at select burn times and an empirical basis for estimating burn rates. With the current test configuration, the detailed analysis of test results requires modeling a three-dimensional, transient convection process involving fluid motion, thermal conduction and convection, the diffusion of chemical species, and the erosion of sample surface. At the high pressure extremes, it even requires the analysis of turbulent, transient convection where the physics of the problem are not well known and the computation requirements are not practical at this time. An alternative test configuration that can be analyzed with a relatively-simple convection model was developed during the summer period. The principal change constitutes replacing a large-diameter polymer disk at the end of the metal test rod with coaxial polymer cylinders that have a diameter nearer to that of the metal rod. The experimental objective is to assess the importance of test geometries on the promotion of metal ignition by testing with different lengths of the polymer and, with an extended effort, to analyze the surface combustion in the redesigned promoted combustion tests through analytical modeling of the process. The analysis shall use the results of cone-calorimeter tests of the polymer material to model primary chemical reactions and, with proper design of the promoted combustion test, modeling of the convection process could be conveniently limited to a quasi-steady boundary layer analysis where the economical solution of parabolic equations is involved. The products for the summer period are: (1) a conceptual-level redesign of the test apparatus, and (2) the development and use of an approximate integral boundary layer analysis to demonstrate the influence of geometry changes prior to testing. A computer code STAN5, an accurate numerical boundary layer model whose earlier versions were developed for the NASA Lewis Research Center by the Fellow, also was installed and validated on the WSTF and New Mexico State University computer systems as a starting point in the development of a more detailed fluid mechanics and combustion model.

Julien, Howard L.↗

An experimental study of three-dimensional shock wave/boundary layer interactions generated by sharp fins

The interaction between a turbulent boundary layer and a shock wave generated by a sharp fin with leading edge sweepback was investigated. The incoming flow was at Mach 2.96 and at a unit Reynolds number of 63 x 10 to the 6th power 0.1 m. The approximate incoming boundary layer thickness was either 4 mm or 17 mm. The fins used were at 5 deg, 9 deg and 15 deg incidence and had leading edge sweepback from 0 deg to 65 deg. The tests consisted of surface kerosene lampblack streak visualization, surface pressure measurements, shock wave shape determination by shadowgraphs, and localized vapor screen visualization. The upstream influence lengths of the fin interactions were correlated using viscous and inviscid flow parameters. The parameters affecting the surface features close to the fin and way from the fin were also identified. Essentially, the surface features in the farfield were found to be conical.

Lu, F. K.↗

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Funaro, Daniele↗

Application of a Reynolds stress model to separating boundary layers

Separating turbulent boundary layers occur in many practical engineering applications. Nonetheless, the physics of separation/reattachment of flows is poorly understood. During the past decade, various turbulence models were proposed and their ability to successfully predict some types of flows was shown. However. prediction of separating/reattaching flows is still a formidable task for model developers. The present study is concerned with the process of separation from a smooth surface. Features of turbulent separating boundary layers that are relevant to modeling include the following: the occurrence of zero wall shear stress, which causes breakdown of the boundary layer approximation; the law of the wall not being satisfied in the mean back flow region; high turbulence levels in the separated region; a significant low-frequency motion in the separation bubble; and the turbulence structure of the separated shear layer being quite different from that of either the mixing layers or the boundary layers. These special characteristics of separating boundary layers make it difficult for simple turbulence models to correctly predict their behavior.

Ko, Sung HO↗

Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing

An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength; which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other studies, it is found that the breaking waves undergo "self-acceleration," such that the zonal-mean intrinsic frequency remains approximately constant in spite of large changes in the background wind. It is also shown that many of the features obtained in the calculations can be understood in terms of linear wave theory. In particular, linear theory provides insights into the wavelength of the waves that break at high altitudes, the onset and evolution of breaking. the horizontal extent of the breaking region and its position relative to the forcing, and the minimum and maximum altitudes where breaking occurs. Wave breaking ceases at the altitude where the background dissipation rate (which in our model is a proxy for molecular diffusion) becomes greater than the rate of dissipation due to wave breaking, This altitude, in effect, the model turbopause, is shown to depend on a relatively small number of parameters that characterize the waves and the background state.

Prusa, Joseph M.↗

Aerothermodynamic Measurement and Prediction for Modified Orbiter at Mach 6 and 10

Detailed heat-transfer rate distributions measured laterally over the windward surface of an orbiter-like configuration using thin-film resistance heat-transfer gauges and globally using the newly developed relative intensity, two-color thermographic phosphor technique are presented for Mach 6 and 10 in air. The angle of attack was varied from 0 to 40 deg, and the freestream Reynolds number based on the model length was varied from 4 x 10(exp 5) to 6 x 10(exp 6) at Mach 6, corresponding to laminar, transitional, and turbulent boundary layers; the Reynolds number at Mach 10 was 4 x 10(exp 5), corresponding to laminar flow. The primary objective of the present study was to provide detailed benchmark heat-transfer data for the calibration of computational fluid-dynamics codes. Predictions from a Navier-Stokes solver referred to as the Langley aerothermodynamic upwind relaxation algorithm and an approximate boundary-layer solving method known as the axisymmetric analog three-dimensional boundary layer code are compared with measurement. In general, predicted laminar heat-transfer rates are in good agreement with measurements.

Micol, John R.↗

Coupled electromechanical response of composite beams with embedded piezoelectric sensors and actuators

Unified mechanics are developed with the capability to model both sensory and active composite laminates with embedded piezoelectric layers. A discrete-layer formulation enables analysis of both global and local electromechanical response. The mechanics include the contributions from elastic, piezoelectric, and dielectric components. The incorporation of electric potential into the state variables permits representation of general electromechanical boundary conditions. Approximate finite element solutions for the static and free-vibration analysis of beams are presented. Applications on composite beams demonstrate the capability to represent either sensory or active structures and to model the complicated stress-strain fields, the interactions between passive/active layers, interfacial phenomena between sensors and composite plies, and critical damage modes in the material. The capability to predict the dynamic characteristics under various electrical boundary conditions is also demonstrated.

Saravanos, D. A.↗

Self-consistent steady state model of the low-latitude boundary layer

Results are presented from a steady state numerical model of the low-latitude boundary layer (LLBL) on closed field lines and its coupling to the dayside auroral ionosphere. In the model the boundary layer approximation is used, the result being that inertial forces are taken into account only in the main flow direction (-x) where they are balanced by pressure forces, j x B forces, and viscous forces. Motion in the transverse directions (y and z) is treated kinematically, the force balances in these two directions being purely static. Computationally, the model is two dimensional, describing the motion of plasma and frozen-in magnetic field in the equatorial (xy) plane but allowing for lowest-order polynomial variation of some quantities with the coordinate (z) perpendicular to that plane. The plasma expands and compresses isentropically; the magnetic field is calculated self-consistently, which leads to approximately parabolic field line shape in planes parallel to the magnetopause (the xz plane), with maximum field curvature near the magnetopause edge of the LLBL. Coupling to the ionosphere via region 1 field-aligned currents is included. The effects of the ionosphere are represented by two parallel resistive plates at fixed height above and below the equatorial plane. The model can be used to investigate the influence of various physical parameters, for example, viscous and magnetic Reynolds numbers, and of boundary conditions at the magnetopause and in the magnetosphere on the LLBL development in the -x direction. Special attention is given to viscous effects which, under suitable circumstances, lead to a region 1 current that first increases and then reduces with increasing longitude away from local noon. Asymptotic matching of the antisunward motion of the cool LLBL plasma to sunward convection of hot plasma in the magnetosphere is illustrated along with the entrainment of magnetospheric plasma by the antisunward LLBL flow.

Drakou, E.↗

Perturbation solutions of combustion instability problems

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Googerdy, A.↗

Propagation of quasiplane waves along an impedance boundary

The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a time harmonic plane wave at grazing incidence to a finite impedance boundary. The resulting equations possess a solution which may be expressed in terms of the complementary error function. Asymptotic expansion of this solution for field points near the boundary provides results compatible with those for a point source on the boundary for both the soft boundary (finite impedance) and hard boundary (the limit in which the impedance becomes infinite) cases. The presence of a surface wave in the solution is also established.

Mcaninch, G. L.↗