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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.

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.

R. Voß - One of the best experts on this subject based on the ideXlab platform.

  • TDLM - A Transonic Doublet Lattice Method for 3-D Potential Unsteady Transonic Flow Calculation and its Application to Transonic Flutter Prediction.
    1993
    Co-Authors: R. Voß
    Abstract:

    In this paper, a Transonic Doublet Lattice Method (TDLM) for calculating unsteady transonic pressure distributions and airloads is developed. The flow around harmonically surfaces is described by superposition of a steady mean transonic flow and an unsteady harmonic flow. The unsteady flow component is modelled by acceleration doublets on the mean wing surface and a source distribution in the flow field near the wing. The time-linearized unsteady transonic Small Perturbation Equation is solved by an integral Equation method. The unsteady aerodynamic results for a rectangular wing, the Northrop F5 wing, and the LANN wing in pitching oscillation are presented. Comparison is made with experimental and other numerical results. Agreement with the experimental results is very good. The flutter boundary of the semi-span AMP flutter model is calculated. The results show that the flutter boundary compares well with the test results. A parametric study of the influence of panel numbers in chordwise and spanwise directions is made, showing a very good convergence. The computing time for a six-mode flutter calculation per each reduced frequency is about 10 minutes on an IBM 3090. All results show that the TDLM is an accurate and economic unsteady transonic aerodynamic tool for routine transonic flutter calculation.

  • TDLM - A Transonic Doublet Lattice Method for 3D Potential Unsteady Transonic Flow Calculation.
    1992
    Co-Authors: R. Voß
    Abstract:

    In this report, a Transonic Doublet Lattice Method (TDLM) for calculating unsteady transonic pressure distributions and airloads isdeveloped. The flow around harmonically oscillating surfaces is described by superposition of a steady transonic mean flow and an unsteady harmonic flow. The unsteady flow component is modelled by acceleration potential doublets on the mean wing surface and a source distribution in the flow field near the wing. The time-linearized unsteady transonic Small Perturbation Equation is solved by an integral Equation method. Results for a rectangular wing, the Northrop F-5 wing, and the LANN wing in pitching oscillation are presented. Comparisons are made with both experimental and other numerical results. Agreement with the experimental results is very good. The computing time on the IBM 3090 is less than ten minutes for one reduced frequency, and it shows that the TDLM can provide a sufficiently accurate and cost-effective procedure for routine transonic flutter calculations.

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.