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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

On the solution of integral equations with a generalized Cauchy kernel

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Kaya, A. C.↗
NASA NTRS1994

Electrohydrodynamic deformation and interaction of a pair of emulsion drops

The response of a pair of emulsion drops to the imposition of a uniform electric field is examined. The case studied is that of equal-sized drops whose line of centers is parallel to the axis of the applied field. A new boundary integral solution to the governing equations of the leaky dielectric model is developed; the formulation accounts for the electrostatic and hydrodynamic interactions between the drops, as well as their deformations. Numerical calculations show that, after an initial transient during which the drops primarily deform, the pair drift slowly together due to their electrostatic interactions.

Baygents, James C.↗
NASA NTRS1998

Transition in Turbine Flows

We have further developed our capabilities to analyze transition in turbine boundary layers from first principles by integrating the nonlinear parabolized stability equations (PSE) with improved initial and boundary conditions. With modified iteration schemes, we are able to proceed deeper into the transition region where skin friction coefficient and heat transfer coefficient significantly increase. Initial and boundary conditions at elevated turbulence levels can be derived by receptivity analysis. Test runs for ERCOFTAC test case T3A at 2.4\% turbulence level provide results in good agreement with the experimental data. The sharper minimum of the skin coefficient also shown by DNS results is likely due to the missing intermittency. The method has been applied to various experimentally studied turbine blades (UTRC, VKI, Zierke, Langston, Hippensteele, and others). The PSE results, though physically reasonable, do not agree as well as expected with the experimental findings. We have, therefore, performed an extensive search for the reasons of the seemingly systematic deviations. A first source of uncertainty has been found in the often insufficient documentation of the experiments (e.g. on blockage by end-wall boundary layers). However, variation of the relevant parameters does not lead to more satisfactory agreement. A second reason has been found in the "standard procedure" which considers a 2D flow at midspan and uses a panel code and subsequent boundary-layer code to obtain the laminar basic flow for the transition analysis. Comparison with the pressure distribution obtained with a 3D design code (RVC3D) shows significant three-dimensionality of the flow (e.g. in the UTRC experiments). The spanwise variation has been neglected in our original PSE code. To overcome this problem, we have developed the PSE/3D for fully 3D boundary layers to account for streamwise and spanwise variations. Since the design code does not provide the boundary-layer flow with sufficient resolution, we have generated the Euler solution and employed a 3D boundary-layer code to obtain the viscous basic flow. Although only the linear stability level of PSE/3D has been implemented so far, the discrepancies with the experiments change but do not disappear. We still find deviations between the computed and experimental variations of C(sub f), and St along the blade for laminar flow. The main reason can be seen by comparing the solution of the boundary-layer code with the viscous results of the design code. The conventional boundary-layer solution exhibits an asymptotic behavior appropriate in external aerodynamics but does not match the steep gradients of the inviscid flow through the passage and consequently provides biased results for C(sub f), and St. An attempt is currently being made to correct this deficiency. Before attempting to perform the transition analysis for the viscous flow provided by the design code, we have analyzed the implementation and "best possible" results. Code and results exhibit flaws that may negatively affect the design and are intolerable for transition analysis. Therefore, we have decided to develop a new code to obtain a reliable basis for stability and transition studies. We expect to report improved results by the time of the meeting.

Herbert, Thorwald↗
NASA NTRS1997

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

Edwards, S.↗
NASA NTRS2000

A Real-Time Method for Estimating Viscous Forebody Drag Coefficients

This paper develops a real-time method based on the law of the wake for estimating forebody skin-friction coefficients. The incompressible law-of-the-wake equations are numerically integrated across the boundary layer depth to develop an engineering model that relates longitudinally averaged skin-friction coefficients to local boundary layer thickness. Solutions applicable to smooth surfaces with pressure gradients and rough surfaces with negligible pressure gradients are presented. Model accuracy is evaluated by comparing model predictions with previously measured flight data. This integral law procedure is beneficial in that skin-friction coefficients can be indirectly evaluated in real-time using a single boundary layer height measurement. In this concept a reference pitot probe is inserted into the flow, well above the anticipated maximum thickness of the local boundary layer. Another probe is servomechanism-driven and floats within the boundary layer. A controller regulates the position of the floating probe. The measured servomechanism position of this second probe provides an indirect measurement of both local and longitudinally averaged skin friction. Simulation results showing the performance of the control law for a noisy boundary layer are then presented.

Whitmore, Stephen A.↗
NASA NTRS1983

End wall flow characteristics and overall performance of an axial flow compressor stage

This review indicates the possible future directions for research on endwall flows in axial flow compressors. Theoretical investigations on the rotor blade endwall flows in axial flow compressors reported here include the secondary flow calculation and the development of the momentum integral equations for the prediction of the annulus wall boundary layer. The equations for secondary vorticity at the rotor exit are solved analytically. The solution includes the effects of rotation and the viscosity. The momentum integral equations derived include the effect of the blade boundary layers. The axial flow compressor facility of the Department of Aerospace Engineering at The Pennsylvania State University, which is used for the experimental investigations of the endwall flows, is described in some detail. The overall performance and other preliminary experimental results are presented. Extensive radial flow surveys are carried out at the design and various off design conditions. These are presented and interpreted in this report. The following experimental investigations of the blade endwall flows are carried out. (1) Rotor blade endwall flows: The following measurements are carried out at four flow coefficients. (a) The rotor blade static pressures at various axial and radial stations (with special emphasis near the blade tips). (b) The hub wall static pressures inside the rotor blade passage at various axial and tangential stations. (2) IGV endwall flows: The following measurements are carried out at the design flow coefficient. (a) The boundary layer profiles at various axial and tangential stations inside the blade passage and at the blade exit. (b) Casing static pressures and limiting streamline angles inside the blade passage.

Sitaram, N.↗
NASA NTRS1972

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 2: Constant property turbulent boundary layer flow with simultaneous mass transfer and pressure gradient

An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.

Boccio, J.↗
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 NTRS1985

Corrections for attached sidewall boundary-layer effects in 2-dimensional airfoil testing

The problems of sidewall boundary-layer effects in airfoil testing is treated by considering the changes in the flow area due to boundary-layer thinning under the influence of the airfoil flowfield. Using von Karman's momentum integral equation, it is shown that the sidewall boundary-layer thickness in the region of the airfoil can reduce to about half the undisturbed value under the conditions prevailing in testing of supercritical airfoils. A Mach number correction due to this increased width of the flow passage is proposed. Using the small disturbance approximation, the effect of the sidewall boundary-layers is shown to be equivalent to a change in the test Mach number and also in the airfoil thickness. Comparison of the results of this approach with other similarity rules and correlation of the experimental data demonstrate the applicability of the analysis presented from low speeds to transonic speeds.

Murthy, A. V.↗
NASA NTRS1995

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Krishnamoorthy, S.↗
NASA NTRS1979

Theoretical determination of nozzle admittances using a finite element method

A finite element method (FEM) is used to predict the admittances of axisymmetric nozzles. The flow in the nozzle is assumed to be isentropic and the disturbances are assumed to be small so that linear analyses apply. An approximate two dimensional compressible flow model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear acoustic wave equation. This partial differential wave equation is transformed to an integral equation using Galerkin's method and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. A two dimensional finite element method using linear triangular elements is used to solve the integral acoustic equation. A one dimensional FEM is used to solve the reduced nozzle acoustic equation developed by Crocco and the solution is used to verify the sufficiency of the boundary residual formation. It is shown that agreement between predicted values of the admittance and experimental data is quite good.

Sigman, R. K.↗
NASA NTRS1984

The influence of a wind tunnel on helicopter rotational noise: Formulation of analysis

An analytical model is discussed that can be used to examine the effects of wind tunnel walls on helicopter rotational noise. A complete physical model of an acoustic source in a wind tunnel is described and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. The simplified physical model is then modeled as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. Details of generating a suitable Green's function and integral equation are included and the equation is discussed and also given for a two-dimensional case.

Mosher, M.↗
NASA NTRS1984

The influence of wind-tunnel walls on discrete frequency noise

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Mosher, M.↗
NASA NTRS1992

Stiffnesses by (TtN) ensemble molecular dynamics

Calculation of elastic constants requires initializing a lattice of atoms, an h matrix defining the computational cell boundaries, and the parameters defining the interatomic potentials, then numerically integrating the equations of motion for the atoms and the computational cell boundaries, calculating strains and stresses at each timestep, and updating at each timestep the average quantities required for calculation of fluctuations. Enforcements of the DYNAMO FORTRAN code included addition of documentation, improved memory management and data flow, and enabling use of several interatomic potentials. Documentation included headers for each subroutine, which document the parameters input to the routine, algorithms employed, and output.

Tibbits, Patrick↗
NASA NTRS1983

A computational method for subsonic compressible flow in diffusers

Integral methods are used to model subsonic flow in planar diffusers operating with or without stall. Turbulent boundary layers are computed with a lag-entrainment method employing new correlations for shape factor and skin friction, which are based on a Coles-Van Driest velocity profile. The inviscid flow is modeled as one dimensional and is easily coupled with the boundary layer method to yield equations that can be solved by integrating in the downstream direction. Analysis of the equations describing flow in a diffuser shows that the boundary layer separation singularity may not be eliminated by viscous-inviscid interaction; a modified interaction scheme is used to guarantee a non-singular equation set. The nature of this singularity offers an explanation for the apparent universality of asymmetric stall in planar diffusers. Results for several flows demonstrate the accuracy and range of applicability of the method.

Childs, R. E.↗
NASA NTRS1986

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and application

The Rai (1984,85) patch-boundary scheme for the Euler equations is described. The integration methods used to update the interior grid points are are discussed. Stability of patch-boundary schemes and the use of these schemes in Navier-Stokes calculations are mentioned. Results for inviscid, supersonic flow over a cylinder, blast wave diffraction by ramp, and the motion of a vortex in a freestream are presented. These test cases demonstrate the quality of solutions possible with the scheme.

Rai, M. M.↗