Discrete potential theory for two-dimensional Laplace and Poisson difference equations
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Saltzer, Charles↗
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Numerical evaluation of the (epsilon)-integral occurring in the Theodorsen arbitrary airfoil potential theory
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AIRFOILS - CIRCULAR TRANSFORMATION↗
Navier-Stokes and potential theory solutions for ahelicopter fuselage and comparison with experiment
A thin-layer Navier-Stokes code and a panel method code are used to predict the flow over a generic helicopter fuselage. The computational results are compared with pressure data at four experimental conditions. Both methods produce results that agree with the experimental pressure data. However, separation patterns and other viscous flow features from the Navier-Stokes code solution are shown that cannot be easily modeled with the panel method.
Chaffin, Mark S.↗
Theory of a Potential for Satellite Motion About a Triaxially Ellipsoidal Planet
Potential theory for satellite motion about triaxially ellipsoidal planet
Maddox, S. J., Jr.↗
Thermal, field emission with a terminated image potential
Theory for thermal field emission with image potential terminated at Fermi level
IMAGE↗
Influence of thickness and camber on the aeroelastic stability of supersonic throughflow fans: An engineering approach
An engineering approach was used to include the nonlinear effects of thickness and camber in an analytical aeroelastic analysis of cascades in supersonic acial flow (supersonic leading-edge locus). A hybrid code using Lighthill's nonlinear piston theory and Lanes's linear potential theory was developed to include these nonlinear effects. Lighthill's theory was used to calculate the unsteady pressures on the noninterference surface regions of the airfoils in cascade. Lane's theory was used to calculate the unsteady pressures on the remaining interference surface regions. Two airfoil profiles was investigated (a supersonic throughflow fan design and a NACA 66-206 airfoil with a sharp leading edge). Results show that compared with predictions of Lane's potential theory for flat plates, the inclusion of thickness (with or without camber) may increase or decrease the aeroelastic stability, depending on the airfoil geometry and operating conditions. When thickness effects are included in the aeroelastic analysis, inclusion of camber will influence the predicted stability in proportion to the magnitude of the added camber. The critical interblade phase angle, depending on the airfoil profile and operating conditions, may also be influenced by thickness and camber. Compared with predictions of Lane's linear potential theory, the inclusion of thickness and camber decreased the aerodynamic stifness and increased the aerodynamic damping at Mach 2 and 2.95 for a cascade of supersonic throughflow fan airfoils oscillating 180 degrees out of phase at a reduced frequency of 0.1.
Ramsey, John K.↗
Influence of thickness and camber on the aeroelastic stability of supersonic throughflow fans
An engineering approach was used to include the nonlinear effects of thickness and camber in an analytical aeroelastic analysis of casecades in supersonic acial flow (supersonic leading-edge locus). A hybrid code using Lighthill's nonlinear piston theory and Lane's linear potential theory was developed to include these nonlinear effects. Lighthill's theory was used to calculate the unsteady pressures on the noninterference surface regions of the airfoils in cascade. Lane's theory was used to calculate the unsteady pressures on the remaining interference surface regions. Two airfoil profiles were investigated (a supersonic throughflow fan design and a NACA 66-206 airfoil with a sharp leading edge). Results show that compared with predictions of Lane's potential theory for flat plates, the inclusion of thickness (with or without camber) may increase or decrease the aeroelastic stability, depending on the airfoil geometry and operating conditions. When thickness effects are included in the aeroelastic analysis, inclusion of camber will influence the predicted stability in proportion to the magnitude of the added camber. The critical interblade phase angle, depending on the airfoil profile and operating conditions, may also be influenced by thickness and camber. Compared with predictions of Lane's linear potential theory, the inclusion of thickness and camber decreased the aerodynamic stiffness and increased the aerodynamic damping at Mach 2 and 2.95 for a cascade of supersonic throughflow fan airfoils oscillating 180 degrees out of phase at a reduced frequency of 0.1.
Ramsey, John K.↗
An equivalent potential vorticity theory applied to the analysis and prediction of severe storm dynamics
Potential vorticity theory is developed in a description of an equivalent potential temperature topography, and a new theory suited to the description of scale interaction is elaborated. Macroscale triggering of ageostrophic flow fields at the mesoscale, in turn leading to release of convective instability along narrow zones at the microscale, is examined. Correlation of appreciable decrease in potential vorticity with such phenomena as cumulonimbi, tornados, and duststorms is examined. The relevance of a multiscale energy-momentum cascade in numerical prediction of severe mesoscale and microscale phenomena from radiosonde data is reviewed. Hypotheses for mesoscale dynamics are constructed.
Paine, D. A.↗
Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses
An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.
Batina, John T.↗
Adiabatic thermal models for planetary bodies
In a number of recent experiments it was found that the logarithmic derivative with respect to volume of the adiabatic temperature increase with pressure P to be an approximately constant quantity n. It was found that n decreases slightly with temperature, to be virtually unaffected by increasing pressure and to take values between 4 and 8 for a wide variety of materials. It is shown that these findings can be substantiated from thermodynamic arguments, finite strain theory, atomic potential theory and experimental data on the thermal expansion coefficient and the bulk modulus B. It will be shown that n is independent of pressure if it is exactly equal to dB/dP + 1. For these materials d log gamma/d log v = -1, where gamma is the thermodynamic Gruneisenparameter. It will increase with P during an isothermal transformation if n dB/dP + 1 and decrease of n dB/dP + 1. For most materials n is close to dB/dP and the changes will be slight if pressures do not become too extreme. During an adiabatic transformation n is virtually constant. Adiabatic thermal models for planetary bodies were calculated and are presented.
Spohn, T.↗
The Boundary Layers in Fluids with Little Friction
The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve. The admissibility of this method is based on the fact that, at zero pressure, which is to prevail at the cited stream curve, the connection of the fluid, and with it the effect of adjacent parts on each other, is canceled. In reality, however, the pressure at these boundaries is definitely not zero, but can even be varied arbitrarily. Besides, Helmholtz's theory with its potential flows does not satisfy the condition of adherence nor explain the origin of the vortices, for in all of these problems, the friction must be taken into account on principle, according to the vortex theorem.
Blasius, H.↗
Use of potential flow theory to evaluate subsonic inlet data from a simulator-powered nacelle at cruise conditions
Incompressible potential flow theory corrected for compressibility effects, using the Lieblein-Stockman compressibility correction, was used to predict surface and flow field static pressures for a subsonic inlet at cruise conditions. The calculated internal and external surface static pressures were in good agreement with data at most conditions. The analysis was used to determine the capture stream-tube location and static-pressure distribution. Additive drag coefficients obtained from these results were consistently higher than those obtained using one-dimensional compressible flow theory. Increasing the distance between the inlet and boattail increased the cowl drag force. The effect of the boundary layer on internal and external surface static-pressure distributions was small at the design cruise condition. The analytical results may be used as an aid to data reduction and for predicting inlet mass flow, stagnation point location, and inlet additive drag.
Bober, L. J.↗
Comparison of Experimental and Theoretical Static Aeroelastic Loads and Deflections of a Thin 45 deg Delta Wing in Supersonic Flow
Wind tunnel tests showing the effects of static aeroelasticity for a thin 45 degree delta wing in supersonic flow are presented and compared with theory in the Mach number range 1.30 t o 4.00. Calculated deformations, normal-force coefficients, and pitching-moment coefficients based on a linearized potential theory for subsonic leading edges at a Mach number of 1.30 and a linearized potential theory for supersonic leading edges at Mach numbers of 1.64, 3.00, and 4.00 are shown to compare favorably with the wind-tunnel results. Calculations of these same deformations and coefficients based on piston theory are shown to compare satisfactorily with experiment at a Mach number of 4.00 but not so well at a Mach number of 3.00. A factor modification of piston theory is suggested which improves the correlation of these results with experiment and also with the potential-theory results.
Bennett, Floyd V.↗
The magnetic field structure in the active solar corona.
The structure of the magnetic field of the active solar corona is discussed with reference to optical and radio observations of the solar atmosphere. Eclipse observations provide evidence of fine scale structures in the solar atmosphere that appear to relate to the coronal magnetic field. The coronal magnetic field used for comparison is calculated from potential theory; the influence of solar activity upon the potential theory field is discussed with reference to observations of the Faraday rotation of a microwave signal from Pioneer 6 as it was occulted by the solar atmosphere. Evidence has been found suggesting the existence of expanding magnetic bottles located at 10 solar radii above flaring active regions. The dynamics of these events is discussed. It is further suggested that these magnetic bottles are an important component in the solar corona.
Schatten, K. H.↗
Potential flow theory and operation guide for the panel code PMARC
The theoretical basis for PMARC, a low-order potential-flow panel code for modeling complex three-dimensional geometries, is outlined. Several of the advanced features currently included in the code, such as internal flow modeling, a simple jet model, and a time-stepping wake model, are discussed in some detail. The code is written using adjustable size arrays so that it can be easily redimensioned for the size problem being solved and the computer hardware being used. An overview of the program input is presented, with a detailed description of the input available in the appendices. Finally, PMARC results for a generic wing/body configuration are compared with experimental data to demonstrate the accuracy of the code. The input file for this test case is given in the appendices.
Ashby, Dale L.↗
Optimal Multi-Agent Search and Rescue Using Potential Field Theory
This paper presents an algorithm for efficient search and rescue using a multi-agent system of vehicles. The algorithm uses an artificial potential field combined with a time-varying reward function for visiting various points within the search area. The reward function is used to weight the attractiveness of these points in the potential field, and collision avoidance terms are used to repel vehicles from each other, which has the additional effect of reducing duplication of searching efforts. The algorithm generates velocity commands in real-time based on communication with the other vehicles. This framework allows vehicles to react in a dynamic environment, which is a significant advantage to simply following a-priori defined trajectories. Simulation results are presented to demonstrate the ability of the algorithm to cover the search area effectively. The algorithm is also compared to an exhaustive lawn-mower search pattern. This comparison is done via a Monte Carlo simulation with randomized target initial conditions and trajectories. The time to find the target improved by 16 and 30% in the mean and median, respectively. Additionally, this paper presents a method for analyzing the upper bound for time to find a target under the potential field guidance algorithm assuming a radially expanding search area.
John R Cooper↗
Aerodynamic Characteristics of NACA RM-10 Missile in 8- by 6-foot Supersonic Wind Tunnel at Mach Numbers from 1.49 to 1.98 II : Presentation and Analysis of Force Measurements
Experimental investigation of aerodynamic forces acting on body of revolution (NACA RM-10 missile) with and without stabilizing fins was conducted at Mach numbers from 1.49 to 1.98 at angles of attack from 0 to 9 degrees and at Reynolds number of approximately 30,000,000. Comparison of experimental lift, drag, and pitching-moment coefficients and center of pressure location for body alone is made with linearized potential theory and a semiempirical method. Results indicate that aerodynamic characteristics were predicted more accurately by semiempirical method than by potential theory. Breakdown of measured drag coefficients into components of friction, pressure, and base-pressure drag is presented for body alone at zero angle of attack.
TAIL-BODY COMBINATIONS - MISSILES↗
Potential Flow Theory and Operation Guide for the Panel Code PMARC
The theoretical basis for PMARC, a low-order panel code for modeling complex three-dimensional bodies, in potential flow, is outlined. PMARC can be run on a wide variety of computer platforms, including desktop machines, workstations, and supercomputers. Execution times for PMARC vary tremendously depending on the computer resources used, but typically range from several minutes for simple or moderately complex cases to several hours for very large complex cases. Several of the advanced features currently included in the code, such as internal flow modeling, boundary layer analysis, and time-dependent flow analysis, including problems involving relative motion, are discussed in some detail. The code is written in Fortran77, using adjustable-size arrays so that it can be easily redimensioned to match problem requirements and computer hardware constraints. An overview of the program input is presented. A detailed description of the input parameters is provided in the appendices. PMARC results for several test cases are presented along with analytic or experimental data, where available. The input files for these test cases are given in the appendices. PMARC currently supports plotfile output formats for several commercially available graphics packages. The supported graphics packages are Plot3D, Tecplot, and PmarcViewer.
Ashby, Dale L.↗