AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac July 25, 2019

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Presentation transcript:

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac July 25, 2019 topic19b_nozzle_flow

Quasi One-Dimensional Nozzle Flow Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Quasi One-Dimensional Nozzle Flow Insert Nozzle Flow Schematic Schlieren pictures of the flow July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Non-dimensionalize the governing equations as follows: Conservation Form Non-dimensionalize the governing equations as follows: July 25, 2019 topic19b_nozzle_flow

Governing Equations in Non-dimensional Variables July 25, 2019 topic19b_nozzle_flow

Vector Elements July 25, 2019 topic19b_nozzle_flow

Relationship between U vector and F vector July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR An Example Problem Nozzle Shape: The nozzle is assumed to be of fixed shape. The following equation gives the desired properties of a supersonic convergent-divergent nozzle having a minimum area section. July 25, 2019 topic19b_nozzle_flow

In principle initial Conditions can be specified arbitrarily. Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR In principle initial Conditions can be specified arbitrarily. However, steady state solution can be reached faster by judiciously choosing the initial conditions. An obvious choice would be the close-form relations between area ratio and the flow properties, which would almost be the same as the numerical solution that one would expect. However, in order to test the robustness of a given numerical method, it would be preferable to choose the initial conditions that are not so close to the actual steady state solution. Anderson (1995) suggests the following linear variation. July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR July 25, 2019 topic19b_nozzle_flow

Program Completed University of Missouri-Rolla Copyright 2002 Curators of University of Missouri July 25, 2019 topic19b_nozzle_flow