ON THE METHOD OF CHARACTERISTICS AND ITS APPLICATION TO THE CALCULATIONS OF ANNULAR NOZZLE FLOWFIELDS (GAS DYNAMICS, NUMERICAL FLUID MECHANICS)
Abstract
There are two major parts to this thesis. The first part is concerned with the theoretical analysis of the Method of Characteristics (MOC). The second part is concerned with applying the MOC to the calculation of annular nozzle flowfields. A new, simple and effective approach to deriving the characteristic equations of gas dynamics was proposed. The compatibility equation was derived in vector form, which is valid for any coordinate system. The concepts of this derivation are clearer than previous derivations. A general form of the energy equation which contains the speed of sound directly was obtained. This form, which is valid for either ideal or real gases, is particularly useful for the method of characteristics. Coordinate transformation by algebraic methods was studied in detail. It was found that this method may be the only practical method for solving moving boundary problems, such as the free jet boundary problem. Using the basic concepts of coordinate transformations, all the viscous force terms and the dissipative terms in a curved coordinate system were obtained. Thus, the method of characteristics can be used to solve either real viscous flowfields or flowfields with artificial viscosity for smearing shock waves. All the analyses stated above were used to form a computer program to solve flowfields in annular nozzles with complex geometric shapes. From the calculations of four annual nozzle examples, it is seen that the methods chosen to obtain the numerical solutions, such as an algebraic coordinate transformation, smearing of shock waves by artificial viscosity, and the application of the method of characteristics, yield an efficient and accurate procedure for calculating annular nozzle flowfields.
Degree
Ph.D.
Subject Area
Mechanical engineering
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