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

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Presentation on theme: "AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac July 25, 2019"— Presentation transcript:

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

2 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

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

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

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

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

7 Vector Elements July 25, 2019 topic19b_nozzle_flow

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

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

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

11 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

12 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

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

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

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

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