Rotationally Symmetric Potential Flows
This paper includes the following topics: 1) Characteristic differential equations; 2) Treatment of practical examples; 3) First example: Diffuser; and 4) Second Example: Nozzle.
Schaefer, Manfred↗
Engineering topics
Schaefer, Manfred
Publications and source records attributed to Schaefer, Manfred.
Two-Dimensional Potential Flows
Contents include the following: Characteristic differential equations - initial and boundary conditions. Integration of the second characteristic differential equations. Direct application of Meyer's characteristic hodograph table for construction of two-dimensional potential flows. Prandtl-Busemann method. Development of the pressure variation for small deflection angles. Numerical table: relation between deflection, pressure, velocity, mach number and mach angle for isentropic changes of state according to Prandtl-Meyer for air (k = 1.405). References.
Schaefer, Manfred↗
Equations for Adiabatic but Rotational Steady Gas Flows without Friction
This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.
Schaefer, Manfred↗