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Results for “EQUATIONS - STRESSES PLATES”

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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1958

On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field

The use of a magnetic field to control the motion of electrically conducting fluids is studied. The incompressible boundary-layer solutions are found for flow over a flat plate when the magnetic field is fixed relative to the plate or to the fluid. The equations are integrated numerically for the effect of the transverse magnetic field on the velocity and temperature profiles, and hence, the skin friction and rate of heat transfer. It is concluded that the skin friction and the heat-transfer rate are reduced when the transverse magnetic field is fixed relative to the plate and increased when fixed relative to the fluid. The total drag is increased in all of the areas.

Rossow, Vernon J↗
NASA NTRS1984

Reduction of astrographic catalogues

An automatic program for the reduction of overlapping Carte du Ciel plates is described. The projection and transformation equations are given and the RAA subprogram flow is outlined. The program was applied to two different sets of data, namely to nine overlapping plates of the Cape Zone of the CdC, and to fifteen plates taken with the CIDA-refractor of the open cluster Tr10.

Stock, J.↗
NASA NTRS1932

Transmission of heat from a flat plate to a fluid flowing at a high velocity

The writer, starting with the consideration of the hydrodynamic and thermodynamic equations for the turbulent boundary layer of a flat plate when it is necessary to take into account the heat produced by friction, arrives at the conclusion that the transmission of the heat follows the same law that is valid when the frictional heat is negligible, provided the temperature of the fluid is considered to be that which the fluid would reach if arrested adiabatically. It is then shown how the same law holds good for faired bodies, and some applications of the law are made to the problems of flight at very high speeds.

Crocco, Luigi↗
NASA NTRS2016

Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers

Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.

Balakumar, P.↗
NASA NTRS1979

Acoustic plane waves normally incident on a clamped panel in a rectangular duct

The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.

Unz, H.↗
NASA NTRS1972

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

Dow, J. W.↗
NASA NTRS1978

Transitional Boundary-Layer Solutions Using a Mixing-Length and a Two-Equation Turbulence Model

Boundary-layer solutions were obtained using the conventional two-layer mixing-length turbulence model and the Wilcox-Traci two-equation model of turbulence. Both flatplate and blunt-body geometries were considered. The most significant result of the study is development of approximations for the two-equation model which permit streamwise stepsize comparable to that used in mixing-length computations. Additionally, a set of model-equation boundary conditions derived which apply equally well to both flat-plate and blunt-body geometries. Solutions obtained with the two-equations turbulence model are compared with experimental data and/or corresponding solutions obtained using the mixing-length model. Agreement is satisfactory for flat-plate boundary layers but not for blunt body boundary layers.

Anderson, E. C.↗
NASA NTRS1977

Over-relaxation applied to the MacCormack finite-difference scheme

An over-relaxation procedure is applied to the MacCormack finite-difference scheme in order to reduce the computation time required to obtain a steady-state solution. The implementation of this acceleration procedure to an existing computer program using the regular MacCormack method is extremely simple and does not require additional storage. The over-relaxation procedure does not alter the steady-state solution, which is second-order accurate. The method is first applied to Burgers' equation. A stability condition and an expression for the increase in the rate of convergence are derived. The method is then applied to the calculation of the hypersonic viscous flow over a flat plate, using the complete Navier-Stokes equations, and the inviscid flow over a wedge. Reductions in computing time by factors of 3 and 1.5, respectively, are obtained by over-relaxation.

Desideri, J.-A.↗
NASA NTRS1943

The Heat Transfer to a Plate in Flow at High Speed

The heat transfer in the laminar boundary layer of a heated plate in flow at high speed can be obtained by integration of the conventional differential equations of the boundary layer, so long as the material values can be regarded as constant. This premise is fairly well satisfied at speeds up to about twice the sonic speed and at not excessive temperature rise of the heated plate. The general solution of the equation includes Pohlhausen's specific cases of heat transfer to a plate at low speeds and of the plate thermometer. The solution shows that the heat transfer coefficient at high speed must be computed with the same equation as at low speed, when it is referred to the difference of the wall temperature of the heated plate in respect to its "natural temperature." Since this fact follows from the linear structure of the differential equation describing the temperature field, it is equally applicable to the heat transfer in the turbulent boundary layer.

Eckert, E.↗
NASA NTRS1986

Convective diffusion in protein crystal growth

A protein crystal modeled as a flat plate suspended in the parent solution, with the normal to the largest face perpendicular to gravity and the protein concentration in the solution adjacent to the plate taken to be the equilibrium solubility, is studied. The Navier-Stokes equation and the equation for convective diffusion in the boundary layer next to the plate are solved to calculate the flow velocity and the protein mass flux. The local rate of growth of the plate is shown to vary significantly with depth due to the convection. For an aqueous solution of lysozyme at a concentration of 40 mg/ml, the boundary layer at the top of a 1-mm-high crystal has a thickness of 80 microns at 1 g, and 2570 microns at 10 to the -6th g.

Baird, J. K.↗
NASA NTRS1969

Nonlinear flutter of curved plates.

Nonlinear Galerkin analysis of curved plate flutter, using shallow shell/von Karman equations and quasi-steady aerodynamic theory

Dowell, E. H.↗
NASA NTRS1980

Calculation of oblique-shock-wave laminar-boundary-layer interaction on a flat plate

A finite difference solution to the problem of the interaction between an impinging oblique shock wave and the laminar boundary layer on a flat plate is presented. The boundary layer equations coupled with the Prandtl-Meyer relation for the external flow are used to calculate the flow field. A method for the calculation of the separated flow region is presented and discussed. Comparisons between this theory and the experimental results of other investigators show fairly good agreement. Results are presented for the case of a cooled wall with an oncoming flow at Mach number 2.0 without and with suction. The results show that a small amount of suction greatly reduces the extent of the separated region in the vicinity of the shock impingement location.

Goldberg, U.↗
NASA NTRS1988

A general explicit solution of the central overlap problem

The matrix of the normal equations of a central overlapping-plate solution with general models for frame parameters and the star parameters is inverted explicitly in terms of the inverses of the matrices in the isolated systems for the frame and star parameters. This makes it possible to calculate from explicit formulas the numerical estimates of the star and frame parameters which would follow from a rigorous overlapping-plate solution. Also, the covariance matrix of the adjustment parameters are calculated.

Eichhorn, Heinrich↗
NASA NTRS1991

A numerical method for unsteady aerodynamics via acoustics

Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.

Hodge, Steve↗
NASA NTRS1990

Models of space averaged energetics of plates

The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.

Bouthier, O. M.↗
NASA NTRS1958

A Theoretical and Experimental Study of Planing Surfaces Including Effects of Cross Section and Plan Form

A summary is given of the background and present status of the pure-planing theory for rectangular flat plates and v-bottom surfaces. The equations reviewed are compared with experiment. In order to extend the range of available planing data, the principal planing characteristics for models having sharp bottom surfaces having constant angles of dead rise of 20 degrees and 40 degrees. Planing data were also obtained for flat-plate surfaces with very slightly rounded chines for which decreased lift and drag coefficients are obtained.

Shuford, Charles L , Jr↗
NASA NTRS2003

Electromagnetic Scattering From a Polygonal Thin Metallic Plate Using Quadrilateral Meshing

The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.

Deshpande, Manohar D.↗