Ehlers, F. Edward
Overview
Works:  36 works in 61 publications in 1 language and 490 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Other 
Classifications:  TL521.3.C6, 536.2 
Publication Timeline
.
Most widely held works by
F. Edward Ehlers
Development and application of a program to calculate transonic flow around an oscillating threedimensional wing using finite
difference procedures by Warren H Weatherill(
Book
)
1 edition published in 1989 in English and held by 74 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 74 WorldCat member libraries worldwide
Development and application of algorithms for calculating the transonic flow about harmonically oscillating wings by
F. Edward Ehlers(
Book
)
2 editions published in 1984 in English and held by 74 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 74 WorldCat member libraries worldwide
The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings by Warren H Weatherill(
Book
)
3 editions published in 1978 in English and held by 72 WorldCat member libraries worldwide
3 editions published in 1978 in English and held by 72 WorldCat member libraries worldwide
A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils by
F. Edward Ehlers(
Book
)
3 editions published in 1982 in English and held by 66 WorldCat member libraries worldwide
3 editions published in 1982 in English and held by 66 WorldCat member libraries worldwide
A method for computing the leadingedge suction in a highrorder panel method by
F. Edward Ehlers(
Book
)
2 editions published in 1984 in English and held by 63 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 63 WorldCat member libraries worldwide
Proceedings of the 1962 Heat Transfer and Fluid Mechanics Institute, held at University of Washington, June 13, 14, 15, 1962 by
Heat Transfer and Fluid Mechanics Institute(
Book
)
5 editions published in 1962 in English and held by 22 WorldCat member libraries worldwide
5 editions published in 1962 in English and held by 22 WorldCat member libraries worldwide
A finite difference method for the solution of the transonic flow around harmonically oscillating wings by
F. Edward Ehlers(
Book
)
5 editions published in 1974 in English and held by 19 WorldCat member libraries worldwide
5 editions published in 1974 in English and held by 19 WorldCat member libraries worldwide
Computation of the transonic perturbation flow fields around two and threedimensional oscillating wings by
W. H Weatherill(
Book
)
5 editions published in 1975 in English and held by 17 WorldCat member libraries worldwide
5 editions published in 1975 in English and held by 17 WorldCat member libraries worldwide
An investigation by the hodograph method of flow through a symmetrical nozzle with locally supersonic regions by
F. Edward Ehlers(
Book
)
4 editions published in 1951 in English and held by 7 WorldCat member libraries worldwide
To study the flow of a compressible fluid through a channel having locally supersonic regions, the Tricomi equation is used in the hodograph variables as an approximation in the sonic region to the equation of flow of an irrotational, inviscid gas. A oneparameter family of solutions of the Tricomi equation is used which provides symmetrical acceleratedecelerated flows. Variation of this parameter alters the Mach number at the center of the throat, the velocity distribution and gradient along the center streamline, as well as the shape of the channel, that is the curvature of the bounding streamline. Other solutions to the Tricomi equations are discussed which may be used to formulate channel flows
4 editions published in 1951 in English and held by 7 WorldCat member libraries worldwide
To study the flow of a compressible fluid through a channel having locally supersonic regions, the Tricomi equation is used in the hodograph variables as an approximation in the sonic region to the equation of flow of an irrotational, inviscid gas. A oneparameter family of solutions of the Tricomi equation is used which provides symmetrical acceleratedecelerated flows. Variation of this parameter alters the Mach number at the center of the throat, the velocity distribution and gradient along the center streamline, as well as the shape of the channel, that is the curvature of the bounding streamline. Other solutions to the Tricomi equations are discussed which may be used to formulate channel flows
Proceedings ... held at University of Washington, June 1315, 1962 by Heat Transfer and Fluid Mechanics Institute(
Book
)
3 editions published in 1962 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1962 in English and held by 3 WorldCat member libraries worldwide
Influence of acceleration on combustion in a rocket engine(
Book
)
2 editions published in 1966 in English and held by 2 WorldCat member libraries worldwide
The influence of acceleration was analyzed under the following assumptions: The velocity distribution of the quasionedimensional steady state flow through the nozzle is linear in the axial variable. Combustion occurs at a fixed point in the nozzle and at a constant temperature. Burning rate for a solid propellant is proportional to a power n of the chamber pressure. For a liquid propellant with injection rate unaffected by the acceleration, the ratio of burning rate to injection rate is equal to the power of n of the ratio of the instantaneous pressure and the pressure at an earlier time determined by the time lag in the combustion process. For the liquid propellant with time lag, instability occurs for some values of time lag and of the burning rate parameter n. From the linearized solutions, a stability diagram was drawn in the plane of the time lag and burning rate parameter n. Increasing either time lag or the combustion rate exponent from neutrally stable values produces instability. The effect of increasing the magnitude of acceleration appears to shift the neutral curve to lower values of time lag and the burning rate exponent. (Author)
2 editions published in 1966 in English and held by 2 WorldCat member libraries worldwide
The influence of acceleration was analyzed under the following assumptions: The velocity distribution of the quasionedimensional steady state flow through the nozzle is linear in the axial variable. Combustion occurs at a fixed point in the nozzle and at a constant temperature. Burning rate for a solid propellant is proportional to a power n of the chamber pressure. For a liquid propellant with injection rate unaffected by the acceleration, the ratio of burning rate to injection rate is equal to the power of n of the ratio of the instantaneous pressure and the pressure at an earlier time determined by the time lag in the combustion process. For the liquid propellant with time lag, instability occurs for some values of time lag and of the burning rate parameter n. From the linearized solutions, a stability diagram was drawn in the plane of the time lag and burning rate parameter n. Increasing either time lag or the combustion rate exponent from neutrally stable values produces instability. The effect of increasing the magnitude of acceleration appears to shift the neutral curve to lower values of time lag and the burning rate exponent. (Author)
The equilibrium flow of an ideal dissociating gas over a cone(
Book
)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
The ordinary differential equations are derived for the axiallysymmetric flow over a cone of the Lighthill ideal dissociating gas under thermodynamic equilibrium. By means of trigonometric transformations, the equations are simplified to forms containing only rational functions. The equations are integrated numerically by a fourth order RungeKutta method and a program listing in Fortran is included in the appendix. Tables of pressure, temperature, fraction of dissociation, and cotangent of the local Mach angle on the solid cone boundary are tabulated for free flight at Mach numbers of 8, 10, 12, and 14 in an atmosphere of pure oxygen corresponding to altitudes of 20,063; 32,163; and 47,350 meters and for shocks having a tangent of the cone half angle varying from 0.4 to 1.22. The results are compared with calculations for the ideal perfect gas with a ratio of specific heats = 4/3. (Author)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
The ordinary differential equations are derived for the axiallysymmetric flow over a cone of the Lighthill ideal dissociating gas under thermodynamic equilibrium. By means of trigonometric transformations, the equations are simplified to forms containing only rational functions. The equations are integrated numerically by a fourth order RungeKutta method and a program listing in Fortran is included in the appendix. Tables of pressure, temperature, fraction of dissociation, and cotangent of the local Mach angle on the solid cone boundary are tabulated for free flight at Mach numbers of 8, 10, 12, and 14 in an atmosphere of pure oxygen corresponding to altitudes of 20,063; 32,163; and 47,350 meters and for shocks having a tangent of the cone half angle varying from 0.4 to 1.22. The results are compared with calculations for the ideal perfect gas with a ratio of specific heats = 4/3. (Author)
The slow viscous flow of an incompressible fluid through a constriction(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
An approximate solution is given for the slow viscous flow of an incompressible fluid through a constricting channel consisting of one straight and one curved wall. The flow assumed to be laminar and the pressure to be constant throughout each cross section. The inertial terms in the momentum equations are neglected in comparison with the viscous friction terms. Specific formulae are given for the volumetric rate of flow through a channel whose curved wall is either a parabolic or a circular arc. Graphs of the dimensionless volumetric rate of flow for a practical range of the geometric parameters are also included. (Author)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
An approximate solution is given for the slow viscous flow of an incompressible fluid through a constricting channel consisting of one straight and one curved wall. The flow assumed to be laminar and the pressure to be constant throughout each cross section. The inertial terms in the momentum equations are neglected in comparison with the viscous friction terms. Specific formulae are given for the volumetric rate of flow through a channel whose curved wall is either a parabolic or a circular arc. Graphs of the dimensionless volumetric rate of flow for a practical range of the geometric parameters are also included. (Author)
On the gas layer surrounding a projectile being fired from a smooth bore gun(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
An analysis of the gas envelope surrounding a projectile being fired from a smooth bore gun is presented. By reducing the equations of stress and strain in an accelerated body to dimensionless form and examining the dimensionless parameters, it is shown that the strains in an accelerated body do not increase with increasing acceleration if the pressure surrounding the body is increased proportionately, provided Poisson's ratio remains constant and Young's modulus increases with the applied pressure. A simple analysis on the assumption of parallel flow is given for the flow in the gap between the moving projectile and the gun barrel. For constant gas properties, the shear stress on the projectile and on the gun barrel and the pressure gradient are constant. For isothermal flow in the slot, the shear stress on the projectile increases toward the low pressure end approaching asymptotically the Couette flow value. For mass flow rate in the slot below a certain value, the shear stress acts as a thrust on part of the projectile near the high pressure end and a drag on the leading edge or low pressure end. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
An analysis of the gas envelope surrounding a projectile being fired from a smooth bore gun is presented. By reducing the equations of stress and strain in an accelerated body to dimensionless form and examining the dimensionless parameters, it is shown that the strains in an accelerated body do not increase with increasing acceleration if the pressure surrounding the body is increased proportionately, provided Poisson's ratio remains constant and Young's modulus increases with the applied pressure. A simple analysis on the assumption of parallel flow is given for the flow in the gap between the moving projectile and the gun barrel. For constant gas properties, the shear stress on the projectile and on the gun barrel and the pressure gradient are constant. For isothermal flow in the slot, the shear stress on the projectile increases toward the low pressure end approaching asymptotically the Couette flow value. For mass flow rate in the slot below a certain value, the shear stress acts as a thrust on part of the projectile near the high pressure end and a drag on the leading edge or low pressure end. (Author)
Method for Solving NonLinear Simultaneous Equations Using the Gradient Vectors(
Book
)
1 edition published in 1959 in English and held by 1 WorldCat member library worldwide
Occasionally, it becomes necessary to solve a complicated set of nonlinear simultaneous equations. The problem may arise when those design parameters are sought which must satisfy a number of nonlinear restraint or when the maxima or minima of a nonlinear function are required. The stationary values of such a function are given by the values of the variables which make the partial derivatives of the function vanish. These solutions usually are difficult to obtain by simple means, and one can not always be certain that other solutions in the range of interest are not being overlooked. In this note, methods using the gradient vectors are developed for solving the nonlinear simultaneous equations f(x, y) = g(x, y) = O and also the equations f(x, y, z) = g(x, y, z) = h(x, y, z) = O. (Author)
1 edition published in 1959 in English and held by 1 WorldCat member library worldwide
Occasionally, it becomes necessary to solve a complicated set of nonlinear simultaneous equations. The problem may arise when those design parameters are sought which must satisfy a number of nonlinear restraint or when the maxima or minima of a nonlinear function are required. The stationary values of such a function are given by the values of the variables which make the partial derivatives of the function vanish. These solutions usually are difficult to obtain by simple means, and one can not always be certain that other solutions in the range of interest are not being overlooked. In this note, methods using the gradient vectors are developed for solving the nonlinear simultaneous equations f(x, y) = g(x, y) = O and also the equations f(x, y, z) = g(x, y, z) = h(x, y, z) = O. (Author)
Application of the theory of hormander to finding the fundamental solution of hyperbolic linear partial differential equations(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A procedure following the theory of Hormander is explained for finding the fundamental solution to a hyperbolic linear partial differential equation with constant coefficients. The relevant theorems concerning hyperbolic operators are reviewed and the fundamental solutions are derived for the one and the two dimensional wave equations, and for the equation of small disturbances propagating in a uniform subsonic or supersonic stream. By means of these examples, it is demonstrated that Hormander's theory provides a clear and valuable procedure for obtaining the fundamental solution and for defining the region of integration of the convolution integral solution to the inhomogeneous partial differential equation. By the appropriate choice of inhomogeneous term, the solution to the Cauchy problem for the plane of initial time is easily found for each of the three partial differential equations considered. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A procedure following the theory of Hormander is explained for finding the fundamental solution to a hyperbolic linear partial differential equation with constant coefficients. The relevant theorems concerning hyperbolic operators are reviewed and the fundamental solutions are derived for the one and the two dimensional wave equations, and for the equation of small disturbances propagating in a uniform subsonic or supersonic stream. By means of these examples, it is demonstrated that Hormander's theory provides a clear and valuable procedure for obtaining the fundamental solution and for defining the region of integration of the convolution integral solution to the inhomogeneous partial differential equation. By the appropriate choice of inhomogeneous term, the solution to the Cauchy problem for the plane of initial time is easily found for each of the three partial differential equations considered. (Author)
A Numerical Method for Computing the Transonic Fan Duct Flow over a Centerbody into an Exterior Free Stream  Program Tea343(
Book
)
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
A theory and computer program are presented for computing the transonic fan duct and free jet flow exhausting over the centerbody of a turbofan engine and merging with an exterior stream flowing over a nacelle. This report presents a complete derivation of the theory, a description of the finite difference procedures employed, and several examples of calculated flow. A description of the computer program is given in the Appendices together with instructions for its use
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
A theory and computer program are presented for computing the transonic fan duct and free jet flow exhausting over the centerbody of a turbofan engine and merging with an exterior stream flowing over a nacelle. This report presents a complete derivation of the theory, a description of the finite difference procedures employed, and several examples of calculated flow. A description of the computer program is given in the Appendices together with instructions for its use
Flow through a cylindrical tube in the slip flow regime(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
By the introduction of a parabolic velocity profile, the boundary layer momentum and continuity equations were reduced to ordinary differential equations by integration across the tube. The coefficients in the velocity profile were determined to satisfy the slip boundary condition of Maxwell at the tube wall and the condition of zero shear at the edge of the boundary layer. In place of the energy equation, the total temperature in the inlet region was assumed to be a linear function of the velocity and the constants were determined to satisfy the temperature jump condition of Poisson at the wall. Similar formulae were developed for isothermal flow. Calculations of the inlet length for the flow to become fully developed viscous slip flow were made for both theories. For inlet Mach numbers above a critical value at small dimensionless inlet mean free paths, the flow does not become fully developed but the boundary layer thickness attains a maximum when the core velocity is about equal to the speed of sound. This critical Mach number increases rapidly with increasing inlet values of the mean free path, indicating that slip flow is more apt to become fully developed than continuum flow. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
By the introduction of a parabolic velocity profile, the boundary layer momentum and continuity equations were reduced to ordinary differential equations by integration across the tube. The coefficients in the velocity profile were determined to satisfy the slip boundary condition of Maxwell at the tube wall and the condition of zero shear at the edge of the boundary layer. In place of the energy equation, the total temperature in the inlet region was assumed to be a linear function of the velocity and the constants were determined to satisfy the temperature jump condition of Poisson at the wall. Similar formulae were developed for isothermal flow. Calculations of the inlet length for the flow to become fully developed viscous slip flow were made for both theories. For inlet Mach numbers above a critical value at small dimensionless inlet mean free paths, the flow does not become fully developed but the boundary layer thickness attains a maximum when the core velocity is about equal to the speed of sound. This critical Mach number increases rapidly with increasing inlet values of the mean free path, indicating that slip flow is more apt to become fully developed than continuum flow. (Author)
The influence of combustion oscillations on the jet in still air and in supersonic flight(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The equations of unsteady motion for compressible flow were linearized under the assumption of small perturbations in the uniform parallel jet and exterior streams. The equations were solved for a supersonic jet issuing into still air and for a supersonic jet into a supersonic stream by means of the Laplace transformation in the time and axial variables. The boundary conditions of continuous pressure and flow inclination along the jet and stream interface were satisfied on the undisturbed location of the interface and the perturbation pressure at the jet exit was assumed to be cosinusoidal. The shape of the jet boundary and density perturbation in the jet stream were computed for several two dimensional flows. Near the jet exit the jet boundary deflection has maximum and minimum amplitudes at the points where the two interior Mach lines from the edges of the jet exit and their reflections intersect the jet interface. The transform solutions for axially symmetric flow were also obtained, but only the shape of the jet boundary in still air was computed. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The equations of unsteady motion for compressible flow were linearized under the assumption of small perturbations in the uniform parallel jet and exterior streams. The equations were solved for a supersonic jet issuing into still air and for a supersonic jet into a supersonic stream by means of the Laplace transformation in the time and axial variables. The boundary conditions of continuous pressure and flow inclination along the jet and stream interface were satisfied on the undisturbed location of the interface and the perturbation pressure at the jet exit was assumed to be cosinusoidal. The shape of the jet boundary and density perturbation in the jet stream were computed for several two dimensional flows. Near the jet exit the jet boundary deflection has maximum and minimum amplitudes at the points where the two interior Mach lines from the edges of the jet exit and their reflections intersect the jet interface. The transform solutions for axially symmetric flow were also obtained, but only the shape of the jet boundary in still air was computed. (Author)
SPOT HEATING OF PLATES(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The heat equation was solved for the temperature distribution in an infinite plate with one surface insulated and with heat applied locally to the other surface. Two classes of boundary conditions on the heated surface were considered: (1) A circle or a strip is heated at a rate to maintain it at a constant elevated temperature. (2) Heat is applied at a constant uniform rate to a circle or strip on one surface of the plate. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The heat equation was solved for the temperature distribution in an infinite plate with one surface insulated and with heat applied locally to the other surface. Two classes of boundary conditions on the heated surface were considered: (1) A circle or a strip is heated at a rate to maintain it at a constant elevated temperature. (2) Heat is applied at a constant uniform rate to a circle or strip on one surface of the plate. (Author)
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Related Identities
 Boeing Commercial Airplane Company
 Langley Research Center
 United States National Aeronautics and Space Administration Scientific and Technical Information Office
 United States National Aeronautics and Space Administration
 Weatherill, Warren H. Author
 Weatherill, W. H. Author
 United States National Aeronautics and Space Administration Scientific and Technical Information Branch
 Manro, Marjorie E.
 Yip, Elizabeth L.
 Sebastian, J. D.
Associated Subjects
Aerodynamics, SupersonicMathematical models Aerodynamics, TransonicComputer simulation Aerodynamics, TransonicMathematical models AirplanesWings Fluid mechanics Flutter (Aerodynamics) HeatTransmission Hodograph equations Leading edges (Aerodynamics) Oscillating wings (Aerodynamics) Oscillating wings (Aerodynamics)Computer simulation Unsteady flow (Aerodynamics) Unsteady flow (Aerodynamics)Computer simulation Vortexmotion
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