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Research Papers: Techniques and Procedures

A Novel 2D Incompressible Viscous Inverse Design Method for Internal Flows Using Flexible String Algorithm

[+] Author and Article Information
Mahdi Nili-Ahmadabadi

School of Mechanical Engineering, Center of Excellence in Energy Conversion, Sharif University of Technology, P.O. Box 14588-89694, Tehran, Irannili@mech.sharif.edu

Ali Hajilouy-Benisi

Qadr Aerodynamic Research Center, Imam Hossein University, P.O. Box 14588-89694, Tehran, Iranhajilouy@sharif.edu

Farhad Ghadak

Qadr Aerodynamic Research Center, Imam Hossein University, P.O. Box 14588-89694, Tehran, Iranfghadak@yahoo.com

Mohammad Durali

School of Mechanical Engineering, Center of Excellence in Design, Robotics and Automation, Sharif University of Technology, P.O. Box 14588-89694, Tehran, Irandurali@sharif.edu

J. Fluids Eng 132(3), 031401 (Mar 17, 2010) (10 pages) doi:10.1115/1.4001072 History: Received August 13, 2009; Revised January 16, 2010; Published March 17, 2010; Online March 17, 2010

In this investigation, the flexible string algorithm (FSA ), used before for inverse design of subsonic and supersonic ducts in compressible flows with and without normal shock, is developed and applied for inverse design of 2D incompressible viscous internal flow with and without separation. In the proposed method, the duct wall shape is changed under an algorithm based on deformation of a virtual flexible string in flow. At each modification step, the difference between current and target wall pressure distributions is applied to the string. The method is an iterative inverse design method and utilizes the analysis code for the flow field solution as a black-box. Some validation test cases and design examples are presented here, which show the robustness and flexibility of the method in handling complex geometries. In cases with separated flow pressure distribution, a unique solution for inverse design problem does not exist. The design algorithm is a physical and quick converging approach and can efficiently utilize commercial flow analysis software.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The string deformation in a 2D flow

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Figure 2

Free body diagram of an arbitrary link i of the chain: (a) kinematics and (b) forces

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Figure 3

Implementation of the inverse design algorithm

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Figure 4

(a) Geometry of the nozzle with initial guess, (b) wall pressure distribution of the initial guess and target shape, and (c) modification steps of the nozzle wall from the initial guess to the target shape

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Figure 5

(a) Geometry of the diffuser with initial guess, (b) wall pressure distribution of the initial guess and target shape, and (c) modification steps of the diffuser wall from the initial guess to the target shape

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Figure 6

(a) Geometry of the 90 deg bended diffuser with its grid, (b) wall pressure distribution of the 90 deg bended diffuser along the inner and outer walls, and (c) modification steps from the initial guess to the target shape

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Figure 7

(a) Flow field of the diffuser with area ratio of 1.4. (b) Final shape after 400 modification steps with corresponding streamlines.

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Figure 8

(a) Wall pressure and (b) wall shear stress distribution of the diffusers shown in Fig.  77

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Figure 9

Shape modification steps from the initial guess to the target shape

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Figure 10

(a) Diffuser with area ratio of 1.2 as the initial guess, (b) wall pressure profile of the initial diffuser and modified pressure profile as the target pressure distribution, and (c) modified shape after 420 modification steps

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Figure 11

(a) Changes in wall pressure profile. (b) Wall shape equivalent to the corresponding pressure profile.

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Figure 12

(a) Streamlines inside the S-shaped diffuser with area ratio of 1.92 as the initial guess, (b) wall pressure profile of the initial diffuser and modified pressure profile as the target pressure distribution, and (c) designed S-shaped diffuser with area ratio of 2.17 after 2200 modification steps

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Figure 13

(a) Generated grid and (b) pressure contour inside the designed S-shaped diffuser

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Figure 14

The difference between designed S-shaped diffuser in viscous flow and ideal flow

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Figure 15

Control volume inside an S-duct

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Figure 16

The grid study for design of S-shaped diffuser

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Figure 17

(a) Streamlines inside the 90 deg bended diffuser as the initial guess, (b) wall pressure profile of the initial diffuser and modified pressure profile as the target pressure distribution, and (c) designed 90 deg bended diffuser after 1300 modification steps

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Figure 18

The difference between exit velocity profile of the initial guess and the designed diffuser

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Figure 19

(a) Initial pressure distribution and modified TPD for 90 deg bended diffuser and (b) designed 90 deg bended diffuser without separation

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