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An approximation method for three-dimensional axially symmetrical supersonic flows is developed; it is based on the characteristics theory (represented partly graphically, partly analytically). Thereafter this method is applied to the construction of rotationally symmetrical nozzles. (author)
A summary is presented of the various documents that discuss and describe the computer programs and analysis techniques which are available for rocket nozzle and exhaust plume calculations. The basic method of characteristics program is discussed, along with such auxiliary programs as the plume impingement program, the plot program and the thermochemical properties program.
Nozzle design codes developed earlier were modified and used in order to design a supersonic wind tunnel nozzle with square cross-sections. As part of the design process, a post-processing code that generates square nozzles from the output of the Sivells code was written. The method is based on the results of an axisymmetric method of characteristics code and an axisymmetric boundary layer code. These design codes are documented.
One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.
Multi-layer assemblies of polysilicon thin films having predetermined stress characteristics and techniques for forming such assemblies are disclosed. In particular, a multi-layer assembly of polysilicon thin films may be produced that has a stress level of zero, or substantially so. The multi-layer assemblies comprise at least one constituent thin film having a tensile stress and at least one constituent thin film having a compressive stress. The thin films forming the multi-layer assemblies may be disposed immediately adjacent to one another without the use of intermediate layers between the thin films. Multi-layer assemblies exhibiting selectively determinable overall bending moments are also disclosed. Selective production of overall bending moments in microstructures enables manufacture of such structures with a wide array of geometrical configurations.
A method is presented for obtaining numerical solutions to a certain class of two-point boundary value problems which arise in optimal control theory. The problems are characterized by systems of nonlinear ordinary differential equations with nonlinear boundary conditions.
Methods for calculating stability and response characteristics of elastic aircraft
Characteristic methods for nonstationary flows have been published only for the special case of the isentropic flow up until the present, althought they are applicable in various places to more difficult questions too. This report derives the characteristic method for the flows which depend only on the position coordinates and time. At the same time the treatment of compression shocks is shown.
A design study of axisymmetric hypersonic wind tunnel nozzles was initiated by NASA Langley Research Center with the objective of improving the flow quality of their ground test facilities. Nozzles for Mach 6 air, Mach 13.5 nitrogen, and Mach 17 nitrogen were designed using the Method of Characteristics/Boundary Layer (MOC/BL) approach and were analyzed with a Navier-Stokes solver. Results of the analysis agreed well with design for the Mach 6 case, but revealed oblique shock waves of increasing strength originating from near the inflection point of the Mach 13.5 and Mach 17 nozzles. The findings indicate that the MOC/BL design method has a fundamental limitation that occurs at some Mach number between 6 an 13.5. In order to define the limitation more exactly and attempt to discover the cause, a parametric study of hypersonic ideal air nozzles designed with the current MOC/BL method was done. Results of this study indicate that, while stagnations conditions have a moderate affect on the upper limit of the method, the method fails at Mach numbers above 8.0.
The sonic-wedge characteristics method has been used to obtain the shock shapes and surface pressure distributions on several blunt two-dimensional shapes in a hypersonic stream for several values of the ratio of specific heats. These shapes include the blunt slab at angle of attack and power profiles of the form yb = a)P, where 0 les than m less than 1, Yb and x are coordinates of the body surface, and a is a constant. These numerical results have been compared with the results of blast-wave theory, and methods of predicting the pressure distributions and shock shapes are proposed in each case. The effects of a free-stream conical-flow gradient on the pressure distribution on a blunt slab in hypersonic flow were investigated by the sonic-wedge characteristics method and were found to be sizable in many cases. Procedures which are satisfactory for reducing pressure data obtained in conical flows with small gradients are presented.
Highly underexpanded free jet boundary contours
Hyperbolic equation for infinite elastic plate under impact loading - structural dynamics
FORTRAN computer program for designing supersonic inlets by characteristic theory
Initial hydrodynamic phase of hypervelocity impact analyzed by computer program using eigenvector approach
Analysis of rarefied gas flow in axisymmetric jet exhausting into vacuum including Prandtl-Meyer expansion
Rarefied monatomic gas flow in axisymmetric jet exhaustion into vacuum, noting expansion to low densities at thermodynamic unequilibrium
A study of the compressive magneto-acousic waves in a guiding centre plasma shows that the wavefront that emerges point disturbance after a finite time is a simple oblate spheroid with the axis of revolution parallel to the field lines. Thus, in a steady three-dimensional supersonic flow of guiding centre plasma a simple analytic exprencan be obtained to represent the characteristic surfaces. From a proper linear combination of the governing macroscopic equations, the characteristic equation is obtained. It represents the propagation of disturbances on the characteristic surface. The characteristic theory can be used to study the interaction of the solar wind with the moon and possibly with other planetary bodies.
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