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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Acoustic resonances and sound scattering by a shear layer

The reflection and transmission characteristics of plane waves scattered by a finite-thickness shear layer having a linear velocity profile and bounded by two otherwise uniform parallel flows is examined using the pressure perturbation equation solutions in the shear layer shown previously to be in terms of Whittaker M functions. In addition to the angle of plane wave incidence and the relative Mach number of the flows bounding the shear layer, it is found that the scattering properties of the shear layer depend crucially upon a parameter tau in such a manner that the case tau approaching zero characterizes the long wavelength properties of the layer and the case tau approaching infinity characterizes the short wavelength properties of the layer. In contrast to the region of ordinary reflection in the cases where the corresponding vortex sheet does not have a Brewster angle, the values of the reflection coefficient up to tau of 2 follow those of the vortex sheet; for the case for which the corresponding vortex sheet has a Brewster angle, the magnitude of the reflection coefficient may be sensitive to even small changes in tau in certain cases.

Koutsoyannis, S. P.↗
NASA NTRS1989

A linear shock cell model for jets of arbitrary exit geometry

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Morris, P. J.↗
NASA NTRS1939

Downwash and Wake Behind Plain and Flapped Airfoils

Extensive experimental measurements have been made of the downwash angles and the wake characteristics behind airfoils with and without flaps and the data have been analyzed and correlated with the theory. A detailed study was made of the errors involved in applying lifting-line theory, such as the effects of a finite wing chord, the rolling-up of the trailing vortex sheet, and the wake. The downwash angles, as computed from the theoretical span load distribution by means of the Biot-Savart equation, were found to be in satisfactory agreement with the experimental results. The rolling-up of the trailing vortex sheet may be neglected, but the vertical displacement of the vortex sheet requires consideration. By the use of a theoretical treatment indicated by Prandtl, it has been possible to generalize the available experimental results so the predictions can be made of the important wake parameters in terms of the distance behind the airfoil trailing edge and the profile-drag coefficient. The method of application of the theory to design and the satisfactory agreement between predicted and experimental results when applied to an airplane are demonstrated.

Silverstein, Abe↗
NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗
NASA NTRS1995

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.

Messiter, A. F.↗
NASA NTRS1974

An Analytical Investigation of Wing-Jet Interaction

The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.

Lan, E. C.↗
NASA NTRS1980

On the swelling of rolled up vortex surfaces and the breakdown of the vortex core for slender wings

Simplified models of the vortex distribution over cylindrical surfaces are developed. The effect of a change of vortex strength was analyzed quantitatively by menas of potential theory. The considerable bulging of the cylindrical vortex sheet as a consequence of the change of the vortex strength is discussed. The coiling-up of the vortices rotation in opposite directions over the cylindrical surface renders the condition for instability and the subsequent large spreading of the vortex core. These processes occur without a positive pressure gradient being necessary in the field of flow surrounding the coiled up vortex sheet.

Das, A.↗
NASA NTRS1993

Effect of ground and ceiling planes on shape of energized wakes

Energized wakes expelled by devices like thrust augmentors, propellers and rotors are studied theoretically in order to explore how their shape changes as they interact with ground and ceiling planes. It is found that when the airstream is stationary and the vehicle in hover, the presence of a ceiling plane causes an energized wake to constrict even more than when in an unbounded medium. The presence of a ground plane is found to cause the wake to constrict less than in free space. The computations also show that the vortex sheets first move inward before moving downward. Along their trajectory, the vortex sheets that separate the energized fluid from the ambient fluid have a nearly constant strength and velocity which indicates that the velocity just inside the wake is approximately constant. When a velocity is given to the wind tunnel airstream, the forward edge of the wake first rises and then descends so that it spends more time in the vicinity of the actuator disk. Implications of these results on measurements obtained in wind tunnels are discussed.

Rossow, Vernon J.↗
NASA NTRS1979

Application of the AMI C sub l sub max prediction method to a number of airfoils

A method for calculating the flow about airfoils up to and beyond the stall is described. It is an iterative procedure between potential flow and boundary layer solutions. The separated region is modeled in the potential flow analysis using free vortex sheets which require an inner iteration to establish their shapes. The free vortex sheet length is an important parameter in the potential flow calculation. Results so far indicate a possible correlation between wake length and airfoil thickness/chord ratio. Calculated and experimental results are compared for a series of airfoils.

Dvorak, F. A.↗
NASA NTRS1987

Fundamental issues in the calculation of rotor wakes

The structure of a helicopter rotor wake and its effects on the aircraft aerodynamics and aeroacoustics are characterized, reviewing the results of recent analytical investigations. The focus is on the role of vortex structure and stability, and consideration is given to Lagrangian computational approaches, two-dimensional and three-dimensional representations of rotor wakes, vortex-sheet rollup computations, and the role of flow instability in the calculation of three-dimensional vortex sheets. Sample results from the author's studies (Sugioka and Widnall, 1985; Kantelis and Widnall, 1986) are presented in graphs and briefly discussed.

Widnall, Sheila↗
NASA NTRS1985

Computation of transonic vortex flows past delta wings Integral equation approach

The steady full-potential equation is written in the form of Poisson's equation, and the solution of the velocity field is expressed in terms of an integral equation. The solution consists of a surface integral of vorticity distribution on the wing and its free-vortex sheets and a volume integral of source distribution within a volume around the wing and its free-vortex sheets. The solution is obtained through successive iteration cycles. The source distribution is computed by using a mixed finite-difference scheme of the Murman-Cole type. The method is applied to delta wings. Numerical examples show that a conical shock is captured on the suction side of the wing. It is attached to the lower surface of the leading-edge vortex but does not necessarily reach to the wing surface.

Kandil, O. A.↗
NASA NTRS1950

Downwash in Vortex Region Behind Rectangular Half-wing at Mach Number 1.91

Results of an experimental investigation to determine downwash and wake characteristics in region of trailing vortex system behind a rectangular half-wing at Mach number 1.91 are presented. The wing had a 5-percent thick symmetric diamond cross section beveled to a knife edge at the tip. At small angles of attack, downwash angles were in close agreement with predictions of linearized theory based on the assumption of an undistorted vortex sheet. At higher angles of attack, the flow was greatly influenced by the rolling up of the vortex sheet.

Cummings, John L↗
NASA NTRS1940

A generalized vortex theory of the screw propeller and its application

The vortex theory as presented by the author in earlier papers has been extended to permit the solution of the following problems: (1) the investigation of the relation between thrusts and torque distribution and energy loss as given by the induction of helical vortex sheets and by the parasite drag; (2) the checking of the theorem of Betz of the rigidly behaving helical vortex sheet of minimum induced energy loss; (3) the extension of the theory of the screw propeller of minimum energy loss for the inclusion of parasite-drag distribution along the blades. A simple system of diagrams has been developed to systematize the design of airplane propellers for a wide range of parasite-drag distribution along the blades.

Reissner, Hans↗
NASA NTRS1976

A submerged singularity method for calculating potential flow velocities at arbitrary near-field points

A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices).

Maskew, B.↗
NASA NTRS1989

Evaluation of VSAERO in prediction of aerodynamic characteristics of helicopter hub fairings

A low-order panel code, VSAERO, was used to predict the aerodynamic characteristics of helicopter hub fairings. Since the simulation of this kind of bluff body by VSAERO was not documented before, the VSAERO solutions were correlated with experimental data to establish their validity. The validation process revealed that simulation of the aerodynamic environment around a hub fairing was sensitive to several modeling parameters. Some of these parameters are body and wake panels arrangement, streamwise and spanwise separation location, and the most prominent one-the wake modeling. Three wake models were used: regular wake, separated wake, and jet model. The regular wake is a wake with negligible thickness (thin wake). It is represented by a single vortex sheet. The separated wake and the jet model in the present application are wakes with finite thickness (thick wake). They consist of a vortex sheet enclosing a region of low-energy flow. The results obtained with the reqular wake were marginally acceptable for sharp-edged hub fairings. For all other cases under consideration, the jet model results correlated slightly better. The separated wake, which seemed to be the most appropriate model, caused the solution to diverge. While the regular wake was straight-forward to apply in simulations, the jet model was not. It requires the user to provide information about the doublet strength gradient on wake panels by guessing the efflux velocities at the wake shedding location. In summary, VSAERO neither predicts accurately the aerodynamic characteristics of helicopter hub fairings nor was cost effective.

Louie, Alexander↗
NASA NTRS1979

Acoustic resonances and sound scattering by a shear layer

The energy reflection coefficient is evaluated numerically for plane waves incident on a plane shear layer having a linear velocity profile. The shear layer is found to exhibit no resonances and no Brewster angles. The behavior of the reflection coefficient depends crucially on the parameter tau, a nondimensional measure of the disturbance Strouhal number with respect to the disturbance Mach number in the mean flow direction. For moderate values of tau, the amplified reflection regime degenerates into the total reflection one, whereas in the ordinary reflection regime the variation of the reflection coefficient with tau depends on whether or not the corresponding vortex sheet has a Brewster angle. The results indicate that caution should be exercised in uncritically modeling a finite thickness shear layer by a corresponding vortex sheet.

Koutsoyannis, S. P.↗
NASA NTRS1987

Spanwise pressure distribution on delta wing with leading-edge vortex flap

The aerodynamic characteristics of a highly swept planar delta wing employing conical leading edge flaps are numerically investigated, using a free vortex sheet method that is based on an advanced, three-dimensional inviscid flow panel method employing quadratic doublet distributions to represent the wing surface and the rolled-up vortex sheet and wake. Upward flap deflection shifts the negative pressure peak inboard of the basic wing and develops a significant suction pressure on the flap that then produces thrust component in the direction of flight; overall drag is thereby reduced.

Reddy, C. S.↗
NASA NTRS1981

Effect of leading-edge vortex flaps on aerodynamic performance of delta wings

The effect of leading-edge vortex flaps on the aerodynamic characteristics of highly swept-back wings is analytically investigated, using the free vortex sheet method. The method, based on a three-dimensional inviscid flow model, is an advanced panel type employing quadratic doublet distributions to represent the wing surface, rolled-up vortex sheet and wake and is capable of computing forces, moments and surface pressures.

Reddy, C. S.↗