An analytical solution is obtained for flow and heat transfer in a three-dimensional porous medium. Coolant from a reservoir at constant pressure and temperature enters one portion of the boundary of the medium and exits through another portion of the boundary which is at a specified uniform temperature and uniform pressure. The variation with temperature of coolant density and viscosity are both taken into account. A general solution is found that provides the temperature distribution in the...

Topics: NASA Technical Reports Server (NTRS), FLOW DISTRIBUTION, HEAT TRANSFER, POROUS MATERIALS,...

Two cases are considered. The first is concerned with mean flows of the Blasius type wherein the instabilities are represented by Tollmien-Schlichting waves. It is shown that the latter are generated fairly far downstream of the edge and are the result of a wave length reduction process that tunes the free stream disturbances to the Tollmien-Schlichting wave length. The other case is concerned with inflectional, uni-directional, transversely sheared mean flows. Such idealized flows provide a...

Topics: NASA Technical Reports Server (NTRS), BLASIUS FLOW, KELVIN-HELMHOLTZ INSTABILITY, LEADING EDGES,...

Flutter analyses were developed to predict the onset of supersonic unstalled flutter of a cascade of two-dimensional airfoils. The first of these analyzes the onset of supersonic flutter at low levels of aerodynamic loading (i.e., backpressure), while the second examines the occurrence of supersonic flutter at moderate levels of aerodynamic loading. Both of these analyses are based on the linearized unsteady inviscid equations of gas dynamics to model the flow field surrounding the cascade....

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC LOADS, CASCADE FLOW, FLUTTER ANALYSIS, SUPERSONIC...

A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC NOISE, AXISYMMETRIC FLOW, JET FLOW, LIGHTHILL GAS...

There has been an ongoing debate about the role of linear instability waves in the prediction of jet noise. Parallel mean flow models, such as the one proposed by Lilley, usually neglect these waves because they cause the solution to become infinite. The resulting solution is then non-causal and can, therefore, be quite different from the true causal solution for the chaotic flows being considered here. The present paper solves the relevant acoustic equations for a non-parallel mean flow by...

Topics: NASA Technical Reports Server (NTRS), JET AIRCRAFT NOISE, NOISE PREDICTION (AIRCRAFT), SUPERSONIC...

The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free stream disturbances incident on a flat plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER TRANSITION, FREE FLOW, MACH NUMBER,...

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become 0(1/M exp 4 In M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics...

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC INSTABILITY, BOUNDARY LAYER FLOW, BOUNDARY LAYER...

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even...

Topics: NASA Technical Reports Server (NTRS), BLASIUS FLOW, BOUNDARY LAYER TRANSITION, FLOW STABILITY,...

A function integral equation governing the unsteady motion of a supersonic cascade is derived. Various representations of the Kernel function are derived and discussed.

Topics: NASA Technical Reports Server (NTRS), CASCADE FLOW, INTEGRAL EQUATIONS, LEADING EDGES, SUPERSONIC...

The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, NONLINEAR EVOLUTION EQUATIONS,...

For shallow lakes and seas such as the great lakes (especially Lake Erie) where the depth is not much greater than the Ekman depth, the usual Ekman dynamics cannot be used to predict the wind driven currents. The necessary extension to include shallow bodies of water, given by Welander, leads to a partial differential equation for the surface displacement which in turn determines all other flow quantities. A technique for obtaining exact analytical solutions to Welander's equation for bodies of...

Topics: NASA Technical Reports Server (NTRS), LAKES, OCEAN CURRENTS, WIND VELOCITY, AIR WATER INTERACTIONS,...

Aerodynamic noise prediction has been an important and challenging research area since James Lighthill first introduced his Acoustic Analogy Approach over fifty years ago. This talk attempts to provide a unified framework for the subsequent theoretical developments in this field. It assumes that there is no single approach that is optimal in all situations and uses the framework as a basis for discussing the strengths weaknesses of the various approaches to this topic. But the emphasis here...

Topics: NASA Technical Reports Server (NTRS), JET AIRCRAFT NOISE, AEROACOUSTICS, MATHEMATICAL MODELS, NOISE...

Researchers show how an initially linear spanwise disturbance in the free stream velocity field is amplified by leading edge bluntness effects and ultimately leads to a small amplitude but linear spanwise motion far downstream from the edge. This spanwise motion is imposed on the boundary layer flow and ultimately causes an order-one change in its profile shape. The modified profiles are highly unstable and can support Tollmein-Schlichting wave growth well upstream of the theoretical lower...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER FLOW, BOUNDARY LAYER STABILITY, FREE FLOW,...

A combined quadrupole-dipole model has been developed for the noise generated by inlet flow distortion in a subsonic fan. A formula is derived for the total upstream-radiated acoustic power in each tone as a function of the design parameters of the fan and the properties of the inlet flow distortion. Numerical results are obtained for values of the parameters corresponding to various quiet fans. The analysis is compared with noise measurements taken on a 51-cm (20-in.) diameter research fan as...

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC PROPERTIES, AERODYNAMIC NOISE, INLET FLOW, PROPELLER...

A flow visualization study showed that strong Karman vortices are developed behind the blunt trailing edge of a plate when the free stream velocities over both surfaces are equal. These vortices tend to disappear when the surface velocities are unequal. This observation provided an explanation for the occurrence and disappearance of the lip noise often present in coaxial jets. Vortex formation and lip noise occurred at a Strouhal number of about 0.2 based on the lip thickness and the average of...

Topics: NASA Technical Reports Server (NTRS), KARMAN VORTEX STREET, TRAILING EDGES, FLOW VISUALIZATION,...

A space-time filtering approach is used to divide an unbounded turbulent flow into its radiating and non-radiating components. The result is then used to clarify a number of issues including the possibility of identifying the sources of the sound in such flows. It is also used to investigate the efficacy of some of the more recent computational approaches.

Topics: NASA Technical Reports Server (NTRS), ACOUSTICS, TURBULENT FLOW, MATHEMATICAL MODELS, FLOW...

Noise can be predicted by solving Full (time-dependent) Compressible Navier-Stokes Equation (FCNSE) with computational domain. The fluctuating near field of the jet produces propagating pressure waves that produce far-field sound. The fluctuating flow field as a function of time is needed in order to calculate sound from first principles. Noise can be predicted by solving the full, time-dependent, compressible Navier-Stokes equations with the computational domain extended to far field - but...

Topics: NASA Technical Reports Server (NTRS), NOISE PREDICTION, TIME DEPENDENCE, NAVIER-STOKES EQUATION,...

This paper reviews Lilley s reformulation of Lighthill s equation and shows that it can be obtained as a special case of a much more general acoustic analogy. It also shows how this generalized analogy can be used to eliminate some of the difficulties that arise when more conventional parallel flow analogies are applied to high speed jets. And, finally, some recent applications of these ideas are discussed.

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, PARALLEL FLOW, TENSORS, HIGH SPEED, ENTROPY,...

A theory of aerodynamic noise is presented which differs from Lighthill's theory primarily in the way in which convection of the noise sources is treated. The sound directivity pattern obtained from the present theory agrees better with jet-noise directivity data than does that obtained from Lighthill's theory. The results imply that the shear-noise contribution to jet noise is smaller than previously expected.

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC MEASUREMENT, ACOUSTIC PROPERTIES, AERODYNAMIC NOISE,...

An analysis was carried out to determine analytically the effect of an island on the wind driven currents in a shallow lake (or sea). A general analysis is developed that can be applied to a large class of lake and island geometries and bottom topographies. Detailed numerical results are obtained for a circular island located eccentrically or concentrically in a circular lake with a logarithmic bottom topography. It is shown that an island can produce volume flow (vertically integrated...

Topics: NASA Technical Reports Server (NTRS), ISLANDS, LAKES, THREE DIMENSIONAL FLOW, TURBULENT FLOW, WATER...

This book is based on a course presented at the Lewis Research Center for engineers and scientists who were interested in increasing their knowledge of differential equations. Those results which can actually be used to solve equations are therefore emphasized; and detailed proofs of theorems are, for the most part, omitted. However, the conclusions of the theorems are stated in a precise manner, and enough references are given so that the interested reader can find the steps of the proofs.

Topics: NASA Technical Reports Server (NTRS), ANALYSIS (MATHEMATICS), DIFFERENTIAL EQUATIONS, PROBLEM...

A theoretical description is given of the sound emitted from an arbitrary point in a parallel or nearly parallel turbulent shear flow confined to a region near solid boundaries. The analysis begins with Lighthill's formulation of aerodynamic noise and assumes that the turbulence is axisymmetric. Specific results are obtained for the sound emitted from an arbitrary point in a turbulent flow within a semi-infinite, open-ended duct.

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC PROPERTIES, AERODYNAMIC NOISE, SOUND LOCALIZATION,...

A formula is obtained for the total acoustic power spectra radiated out the front of the fan as a function of frequency. The formula involves the design parameters of the fan as well as the statistical properties of the incident turbulence. Numerical results are calculated for values of the parameters in the range of interest for quiet fans tested at the Lewis Research Center. As in the dipole analysis, when the turbulence correlation lengths become equal to the interblade spacing, the...

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC NOISE, INLET FLOW, PROPELLER FANS, SOUND...

Fluid from a reservior at constant pressure and temperature is forced through a porous wall of uniform thickness. The boundary through which the fluid exits has specified variations in pressure and temperature along it in one direction so that the flow and heat transfer are two-dimensional. The local fluid and matrix temperatures are assumed to be equal and therefore a single energy equation governs the temperature distribution within the wall. The solution is obtained by transforming this...

Topics: NASA Technical Reports Server (NTRS), HEAT TRANSFER, POROUS WALLS, SWEAT COOLING, BOUNDARY...

An analysis was conducted to determine the properties of sound generated by aerodynamic forces or motions originating in a flow, such as the unsteady aerodynamic forces on propellers or by turbulent flows around an aircraft. The acoustics of moving media are reviewed and mathematical models are developed. Lighthill's acoustic analogy and the application to turbulent flows are analyzed. The effects of solid boundaries are calculated. Theories based on the solution of linearized vorticity and...

Topics: NASA Technical Reports Server (NTRS), ACOUSTIC MEASUREMENT, ACOUSTIC PROPERTIES, AERODYNAMIC NOISE,...

This paper is concerned with utilizing the acoustic analogy approach to predict the sound from unheated supersonic jets. Previous attempts have been unsuccessful at making such predictions over the Mach number range of practical interest. The present paper, therefore, focuses on implementing the necessary refinements needed to accomplish this objective. The important effects influencing peak supersonic noise turn out to be source convection, mean flow refraction, mean flow amplification, and...

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, SUPERSONIC JET FLOW, MATHEMATICAL MODELS,...

An analytical method is developed for determining the flow interaction when a two-dimensional jet is injected between two moving streams. The jet is flowing out of channel and is turned as it enters between the external streams. The local velocity variation resulting from the flow interaction provides a static pressure variation along the jet bounding streamlines that is a priori unknown. Hense, the flow must be obtained by coupling the three flow regions (the jet and the free stream on either...

Topics: NASA Technical Reports Server (NTRS), FLUID JETS, INJECTORS, JET MIXING FLOW, TWO DIMENSIONAL JETS,...

Aerodynamic noise prediction has been an important and challenging research area since James Lighthill first introduced his Acoustic Analogy Approach over fifty years ago. This talk attempts to provide a unified framework for the subsequent theoretical developments in this field. It assumes that there is no single approach that is optimal in all situations and uses the framework as a basis for discussing the strengths weaknesses of the various approaches to this topic. But the emphasis here...

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, AERODYNAMIC NOISE, JET AIRCRAFT NOISE, NOISE...

The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out.

Topics: NASA Technical Reports Server (NTRS), JET AIRCRAFT NOISE, LINEARIZATION, EULER EQUATIONS OF MOTION,...