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The newly improved three-dimensional method of characteristics program has been applied successfully to the calculation of flow fields over a variety of bodies including slab delta wings and shuttle orbiters. Flow fields over fuselage shapes for Mach numbers as low as 1.5 have been calculated. Some typical results are presented.
A computational technique was developed for the method of characteristics solution of a one-dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method, it was possible to compute the unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operation engine was achieved in the calculation of both the third octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The method computes the precise paths on the x-t plane of a finite number of C(sub +), C(sub -) and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and the radiated noise.
Intermediate thrust sub-arcs analyzed by method of characteristic constants for optimum retrothrust program in inverse-square-law force field
The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.
Method of characteristics for flow field analysis on elliptical winged body
Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.
The influence of molecular transport is included in the computation by treating viscous and thermal diffusion terms in the governing partial differential equations as correction terms in the method of characteristics scheme. The development of a production type computer program is reported which is capable of calculating the flow field in a variety of axisymmetric mixed-compression aircraft inlets. The results agreed well with those produced by the two-dimensional method characteristics when axisymmetric flow fields are computed. For three-dimensional flow fields, the results agree well with experimental data except in regions of high viscous interaction and boundary layer removal.
The Method of Characteristics (MOC) is a classic technique for designing supersonic nozzles. An interactive computer program using MOC has been developed to allow engineers to design and analyze supersonic nozzle flow fields. The program calculates the internal flow for many classic designs, such as a supersonic wind tunnel nozzle, an ideal 2D or axisymmetric nozzle, or a variety of plug nozzles. The program also calculates the plume flow produced by the nozzle and the external flow leading to the nozzle exit. The program can be used to assess the interactions between the internal, external and plume flows. By proper design and operation of the nozzle, it may be possible to lessen the strength of the sonic boom produced at the rear of supersonic aircraft. The program can also calculate non-ideal nozzles, such as simple cone flows, to determine flow divergence and nonuniformities at the exit, and its effect on the plume shape. The computer program is written in Java and is provided as free-ware from the NASA Glenn central software server.
The calculation procedure is based on the method of characteristics for steady three-dimensional flow. The bow shock wave and the internal shock wave system were computed using a discrete shock wave fitting procedure. The general structure of the computer program is discussed, and a brief description of each subroutine is given. All program input parameters are defined, and a brief discussion on interpretation of the output is provided. A number of sample cases, complete with data deck listings, are presented.
A study has been performed to determine an estimate of the accuracy of rocket exhaust plume induced spacecraft environments calculated with the more widely used computational methods. Calculations of plume flowfields and plume induced environments using Method of Characteristic (MOC) based models are compared with both experimental results and direct simulation Monte Carlo (DSMC) results to determine the applicability and accuracy of Method of Characteristic models.
Method of characteristics solution for equations governing unsteady flow of liquids in closed systems
A computational code for solving two-dimensional, time-dependent MHD equations by the method of characteristics is presented. Its capabilities are demonstrated by solving two very different problems for which analytical solutions exist: linearized, standing MHD wave motions in a magnetized cylindrical plasma, and nonlinear self-similar expansion of a magnetized plasma ball. The nonlinear development of standing MHD wave solutions in a cylindrical plasma is also studied. The method can be naturally embedded in the computational architecture of massively parallel processors.
Unified approach to propagation of plane, cylindrical and spherical dilation waves in elastic media, using method of characteristics
Unified approach to propagation of plane, cylindrical and spherical dilation waves in elastic media, using method of characteristics
Digital computer program for solution of unsteady flow fields in expansion or shock tunnels by method of characteristics
This report details the development of a 2D and 3D Method of Characteristic (MOC) tool for the design of complex nozzle geometries. These tools are GUI driven and can be run on most Windows-based platforms. The report provides a user's manual for these tools as well as explains the mathematical algorithms used in the MOC solutions.
The method of characteristics has been applied for the determination of the supersonic-flow properties around bodies of revolution at a small angle of attack. The system developed considers the effect of the variation of entropy due to the curved shock and determines a flow that exactly satisfies the boundary conditions in the limits of the simplifications assumed. Two practical methods for numerical calculations are given. (author)
A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.