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Alfred Kluwick - One of the best experts on this subject based on the ideXlab platform.

  • Steady and unsteady transonic nozzle flow of dense gases
    Journal of Applied Mathematics and Mechanics, 1996
    Co-Authors: Stefan Scheichl, Alfred Kluwick
    Abstract:

    Vapours of fluids with sufficiently large specific heats have the distinguishing property that a sonic state M = 1 is reached three times rather than a single time during isentropic expansion or compression. As a consequence, a shockfree expansion of such a vapour from subsonic to supersonic speeds can in general not be achieved by means of a classical convergent-divergent Laval nozzle. In order to obtain a lossless expansion specially designed nozzles with two throats have then to be used. The present study deals with unsteady flow phenomena in slender nozzles. Starting from the classical Euler Equations supplemented with non-classical constitutive relationships a modified transonic small Perturbation Equation is derived. This Equation is used to investigate the transition process from purely subsonic to subsonic-supersonic flow which sets in if the pressure at some distance downstream of the throat area is lowered.

  • Transonic nozzle flow of dense gases
    Journal of Fluid Mechanics, 1993
    Co-Authors: Alfred Kluwick
    Abstract:

    The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Xavier-Stokes Equations supplemented with realistic Equations of state for gases which have relatively large specific heats a novel form of the viscous transonic small-Perturbation Equation is derived. Evaluation of the inviscid limit of this Equation shows that three sonic points rather than a single sonic point may occur during isentropic expansion of such media, in contrast to the case of perfect gases. As a consequence, a shock-free transition from subsonic to supersonic speeds cannot, in general, be achieved by means of a conventional converging-diverging nozzle. Nozzles leading to shock-free flow fields must have an unusual shape consisting of two throats and an intervening antithroat. Additional new results include the computation of the internal thermoviscous structure of weak shock waves and a phenomenon referred to as impending shock splitting. Finally, the relevance of these results to the description of external transonic flows is discussed briefly.

M. P. Markakis - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Theory
    Mathematical Problems in Engineering, 1997
    Co-Authors: D. E. Panayotounakos, M. P. Markakis
    Abstract:

    We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small Perturbation Equation to a nonlinear time independent partial differential Equation (P.D.E.) concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first Equation are constructed, while solutions including one arbitrary function for the second Equation are extracted. As an application the evaluation of the small Perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.

  • Ad hoc closed form solutions of the two-dimensional non-linear steady small Perturbation Equation in fluid mechanics
    International Journal of Non-Linear Mechanics, 1995
    Co-Authors: D. E. Panayotounakos, M. P. Markakis
    Abstract:

    Making use of convenient ad hoc assumptions we construct closed-form solutions of the non-linear two-dimensional irrotational steady small Perturbation Equation appearing in fluid mechanics. The methodologies developed succeed in giving the above solutions expressed in the form of fewer arbitrary functions than needed for general solutions. As an application we specify the above mentioned solutions in the case of the simplified non-linear transonic Equation governing the boundary value problem of a two-dimensional flow past a wave shaped wall.

D. E. Panayotounakos - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Theory
    Mathematical Problems in Engineering, 1997
    Co-Authors: D. E. Panayotounakos, M. P. Markakis
    Abstract:

    We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small Perturbation Equation to a nonlinear time independent partial differential Equation (P.D.E.) concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first Equation are constructed, while solutions including one arbitrary function for the second Equation are extracted. As an application the evaluation of the small Perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.

  • Ad hoc closed form solutions of the two-dimensional non-linear steady small Perturbation Equation in fluid mechanics
    International Journal of Non-Linear Mechanics, 1995
    Co-Authors: D. E. Panayotounakos, M. P. Markakis
    Abstract:

    Making use of convenient ad hoc assumptions we construct closed-form solutions of the non-linear two-dimensional irrotational steady small Perturbation Equation appearing in fluid mechanics. The methodologies developed succeed in giving the above solutions expressed in the form of fewer arbitrary functions than needed for general solutions. As an application we specify the above mentioned solutions in the case of the simplified non-linear transonic Equation governing the boundary value problem of a two-dimensional flow past a wave shaped wall.

Wolf Bartelheimer - One of the best experts on this subject based on the ideXlab platform.

  • An inverse method for the design of transonic airfoils and wings
    Inverse Problems in Engineering, 1996
    Co-Authors: Wolf Bartelheimer
    Abstract:

    A design method for transonic airfoils and wings based on the solution of the Euler/Navier-Stokes Equations is described. The applied design strategy is an inverse design method based on the work of Takanashi. The difference between the computed pressure distribution of a given geometry and the prescribed target pressure distribution is iteratively reduced by the solution of an inverse formulated transonic small Perturbation Equation (TSP-Equation). In this design method an analysis code is required, such as the Euler/Navier-Stokes code CEVCATS/FLOWer developed at DLR. It is shown that Takanashi's method must be modified in order to ensure the convergence of the design in transonic flow. In addition a smoothing algorithm based on Bezier curves is used to obtain a smooth surface. In order to estimate the accuracy and convergence of the design method, a redesign of a known transonic airfoil and wing is conducted. In all designed cases very accurate results are obtained within a small number of design cycles.

  • An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings.
    1995
    Co-Authors: Wolf Bartelheimer
    Abstract:

    A design method for transonic airfoils and wings based on the solution of the Euler-/Navier-Stokes Equations is described. The applied design strategy is an inverse design method based on the work of Takanashi. The difference between the computed pressure distribution of a given geometry and the prescribed target pressure distribution is iteratively reduced by the solution of an inverse formulated transonic small Perturbation Equation (TSP-Equation). In this design method an analysis code is required, such as the Euler-/Navier-Stokes code CEVCATS developed at DLR. It is shown that Takanashi's method must be modified in order to ensure the convergence of the design in transonic flow. In addition a smoothing algorithm based on Bezier curves is used to obtain a smooth surface. In order to estimate the accuracy and convergence of the design method, a redesign of a known transonic airfoil and wing is.

K. Dau - One of the best experts on this subject based on the ideXlab platform.

  • Computation of Viscous Phenomena in Unsteady Transonic Flow
    1992
    Co-Authors: U. R. Muller, H. Henke, K. Dau
    Abstract:

    Abstract : Progress in the development towards a 30 viscous-inviscid strong interaction method for computing unsteady transonic wing flow is reported. In the current version, an ADI-technique for solving the 3D unsteady Transonic Small Perturbation Equation (TSP) has been extended by incorporating an unsteady 2D integral boundary layer method and then simultaneously solving the viscous and inviscid flow Equations in a stripwise fashion.