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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Studies on the interference of wings and propeller slipstreams

The small disturbance potential flow theory is applied to determine the lift of an airfoil in a nonuniform parallel stream. The given stream is replaced by an equivalent stream with a certain number of velocity discontinuities, and the influence of these discontinuities is obtained by the method of images. Next, this method is extended to the problem of an airfoil in a nonuniform stream of smooth velocity profile. This model allows perturbation velocity potential in a rotational undisturbed stream. A comparison of these results with numerical solutions of Euler equations indicates that, although approximate, the present method provides useful information about the interaction problem while avoiding the need to solve the Euler equations.

Prabhu, R. K.↗
NASA NTRS1986

A comparison of global FGGE analyses and energetics (GLA vs ECMWF) for January 1979

The differences and similarities between ECMWF and NASA/Goddard Laboratory for Atmospheres (GLA) analyses and resultant energetics for the South Pacific Convergence Zone and the South Atlantic Convergence Zone are studied, as well as the global circulation patterns. The horizontal wind components, temperature, geopotential height, vertical p-velocity, velocity potential, streamlines, and mean sea level pressure derived from ECMWF and GLA analyses at different pressure levels are compared. It is observed that the mean sea level pressure, temperature, streamlines, and vertical velocity are nearly identical, and the least correlation is detected for the vertical velocity patterns. The energy contents and conversion obtained using the two analyses are examined, and the correlations between the data sets are described.

Huang, Huo-Jin↗
NASA NTRS1978

An efficient finite element technique for sound propagation in axisymmetric hard wall ducts carrying high subsonic Mach number flows

The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.

Tag, I. A.↗
NASA NTRS1976

A new unified approach for analyzing wing-body-tail configurations with control surfaces

A general theory for steady and unsteady, subsonic and supersonic potential aerodynamics for complex configurations is presented. Special attention is given to the theoretical formulation and the corresponding numerical implementation for coplanar interfering surfaces. Applying the Green's function method to the equation of the velocity potential and discretizing the spatial problem by using the finite-element technique, yields a set of differential-delay equations in time relating the potential to the normal wash. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t less than or equal to 0 (steady state) and of small perturbations around the steady state for time t greater than 0; the solution is obtained in the Laplace domain. From the potential, the aerodynamic pressure and the generalized forces are evaluated. The program SOUSSA (Steady, Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) is briefly described. Numerical results obtained with SOUSSA are presented.

Tseng, K.↗
NASA NTRS1984

Relaxation and approximate factorization methods for the unsteady full potential equation

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Shankar, V.↗
NASA NTRS1944

On the general theory of thin airfoils for nonuniform motion

General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.

BIBLIOGRAPHY-WINGS↗
NASA NTRS1985

Numerical solution of the full-potential equation for rotors and oblique wings using a new wake model

A three-dimensional, full-potential, quasi-steady code TFAR1 is proposed for calculating the transonic flow past a lifting helicopter rotor blade and oblique wing. The TFAR1 uses a two-dimensional nonlinear wake-model that allows a jump in velocity potential to propagate with the local fluid flow in the wake. Rotor calculations were made for a single blade at an advance ratio of 0.3, a rotational tip Mach number of 0.7, and at 0-degree incidence. A 1/7-scale model of the Cobra Operational Load Survey (OLS) rotor blade is calculated, and the pressure distributions are compared to the measurements for azimuth angles 0, 30, 60, 90, 120, and 150 degrees at the 95 percent spanwise station of the OLS blade. Furthermore, an oblique wing with Korn airfoil was calculated at the high transonic free-stream Mach number of 0.9791, zero incidence, and yaw angle of 40 degrees. The TFAR1, coupled with a helicopter performance code CAMRAD (Johnson, 1981), provides a full-potential code for calculating the entire flow field for a multiple-bladed rotor in transonic lifting forward flight.

Chang, I.-C.↗
NASA NTRS1976

A brief description of the Jameson-Caughey NYU transonic swept-wing computer program: FLO 22

A computer program for analyzing inviscid, isentropic, transonic flow past 3-D swept configurations is presented. Some basic aspects of the program are: (1) the free-stream Mach number is restricted only by the isentropic assumption; (2) weak shock waves are automatically located wherever they occur in the flow; (3) the finite-difference form of the full equation for the velocity potential is solved by the method of relaxation, after the flow exterior to the airfoil is mapped to the upper half plane; (4) the mapping procedure allows exact satisfaction of the boundary conditions and use of supersonic free stream velocities; (5) the finite difference operator is locally rotated in supersonic flow regions so as to properly account for the domain of dependence; and (6) the relaxation algorithm was stabilized using criteria from a time-like analogy.

Jameson, A.↗
NASA NTRS1978

Steady, Oscillatory and Unsteady, Subsonic and Supersonic Aerodynamics (SOUSSA) for complex aircraft configurations

The Green's function method and the computer program SOUSSA (Steady Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed. The Green's function method is applied to the fully unsteady potential equation yielding an integro-differential-delay equation. This equation is approximated by a set of differential-delay equations in time using the finite element method. The Laplace transform is used to yield a matrix relating the velocity potential to the normal wash. The matrix of the generalized aerodynamic forces is obtained by premultiplying and postmultiplying the matrices relating generalized forces to the potential and the normal wash by the generalized coordinates. The program SOUSSA is compared with existing numerical results. Results indicate that the program is not only general, flexible, and easy to use, but also accurate and fast.

Morino, L.↗
NASA NTRS1980

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Morino, L.↗
NASA NTRS1974

Lifting surface theory of axial compressor blade rows. I - Subsonic compressor. II - Transonic compressor

A linearized three-dimensional lifting surface theory is considered, taking into account relations to axisymmetric 'through-flow' or actuator disk theories, general results for flow within the blade row, relations to two-dimensional cascade theory, and finite blade and wake effects. Numerical results are presented, giving attention to the problem of wakeless flow and of wake flow. Expressions for wake functions are given in an appendix. The lifting line velocity potential employed by Namba (1972) is used as a starting point in the discussion of the lifting surface theory. A study of subsonic conditions is supplemented by an investigation of a transonic compresso, taking into account the general three-dimensional solution, induced velocities, and the acoustic pressure field.

Okurounmu, O.↗
NASA NTRS1994

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗
NASA NTRS1995

Numerical solution of the full potential equation using a chimera grid approach

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Holst, Terry L.↗
NASA NTRS1944

The flow of a compressible fluid past a circular arc profile

The Ackeret iteration process is utilized to obtain higher approximations than that of Prandtl and Glauert for the flow of a compressible fluid past a circular arc profile. The procedure is to expand the velocity potential in a power series of the camber coefficient. The first two terms of the development correspond to the Prandtl-Glauert approximation and yield the well-known correction to the circulation about the profile. The second approximation, involving the square of the camber coefficient, improves the velocity and pressure fields but yields no new results with regard to the circulation, since the circulation about the profile is an odd function of the camber coefficient. The third approximation, involving the cube of the camber coefficient, permits the use of higher values of the camber coefficient and furthermore yields an improvement to the Prandtl-Glauert rule with regard to the effect of compressibility on the circulation of the circular arc profile. Numerical examples with tables and graphs illustrate the results of the analysis.

Kaplan, Carl↗
NASA NTRS1973

High speed flow past wings

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Norstrud, H.↗
NASA NTRS1976

Numerical simulation of low gravity draining

A boundary value problem was solved numerically for a liquid that is assumed to be inviscid and incompressible, having a motion that is irrotational and axisymmetric, and having a constant (5 degrees) solid-liquid contact angle. The avoidance of excessive mesh distortion, encountered with strictly Lagrangian or Eulerian kinematics, was achieved by introducing an auxiliary kinematic velocity field along the free surface in order to vary the trajectories used in integrating the ordinary differential equations simulating the moving boundary. The computation of the velocity potential was based upon a nonuniform triangular mesh which was automatically revised to varying depths to accommodate the motion of the free surface. These methods permitted calculation of draining induced axisymmetric slosh through the many (or fractional) finite amplitude oscillations that can occur depending upon the balance of draining, gravitational, and surface tension forces. Velocity fields, evolution of the free surface with time, and liquid residual volumes were computed for three and one half decades of Weber number and for two Bond numbers, tank fill levels, and drain radii. Comparisons with experimental data are very satisfactory.

Bizzell, G. D.↗
NASA NTRS1995

Phase space analysis in anisotropic optical systems

From the minimal action principle follows the Hamilton equations of evolution for geometric optical rays in anisotropic media. As in classical mechanics of velocity-dependent potentials, the velocity and the canonical momentum are not parallel, but differ by an anisotropy vector potential, similar to that of linear electromagnetism. Descartes' well known diagram for refraction is generalized and a factorization theorem holds for interfaces between two anisotropic media.

Rivera, Ana Leonor↗
NASA NTRS1952

Axisymmetric supersonic flow in rotating impellers

General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.

Goldstein, Arthur W↗