## Application of the Method of Coordinate Perturbation to Unsteady Duct Flow

Description: The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics. Himmel, Seymour C. September 1, 1958 UNT Libraries Government Documents Department National Advisory Committee for Aeronautics Collection Technical Report Archive and Image Library Total Uses: 28 Past 30 days: 5 Yesterday: 0
Creator (Author): Creation: September 1, 1958 The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics. fluid mechanics and thermodynamics Originator : Case Inst. of Tech. NACA Technical Memorandums UNT Libraries Government Documents Department National Advisory Committee for Aeronautics Collection Technical Report Archive and Image Library URL: http://hdl.handle.net/2060/20030065117 REP-NO: NACA-TM-1439 CASI: 20030065117 ARK: ark:/67531/metadc63897 Report Text Access: Public License: Public Domain Statement: No Copyright, Unclassified, Unlimited, Publicly available