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Research Papers: Fundamental Issues and Canonical Flows

Semi Analytical Solution to Transient Start of Weakly Underexpanded Turbulent Jet

[+] Author and Article Information
Iman Chitsaz

Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering,  Sharif University of Technology, Tehran, Iran, P.O. Box 11155-9567; CAE Department IranKhodro Powertrain Co.(IP-CO), Tehran, Zip Code:1398813711, Iran

Mohammad Hassan Saidi1

Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering,  Sharif University of Technology, Tehran, Iran, P.O. Box 11155-9567Saman@sharif.edu

Ali Asghar Mozafari

Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering,  Sharif University of Technology, Tehran, Iran, P.O. Box 11155-9567

1

Corresponding author.

J. Fluids Eng 133(9), 091204 (Sep 08, 2011) (8 pages) doi:10.1115/1.4004835 History: Received December 20, 2010; Revised August 01, 2011; Published September 08, 2011; Online September 08, 2011

This study presents a semi analytical solution for the transient weakly underexpanded jet. Different polytropic processes are compared with available experimental data in the literature to assess the best process for steady and transient weakly underexpanded jets. The steady state results agree reasonably well with the experimental and analytical data. It is also shown that isentropic process evaluates steady injection better than other processes. Tip penetration of transient results was compared with available data in literature, and no exact agreement for isothermal and isentropic is observed. This appears due to the linearization of equation of state. It is suggested that more accurate linearization with a combination of process should be used for transient injection. Effects of pressure ratio and exit velocity on the pressure profile are shown. It is also concluded that during injection locations of shock cells do not vary with pressure ratios while are affected by exit velocity.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Schlieren photograph of initial development of underexpanded jet [2]. (a) Pe/P∞ = 1.45, Me = 2; r/De = 0.25. (b) Pe/P∞ = 1.45, Me = 2; r/De = 0.0.

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Figure 2

Comparison of analytical and experimental results. (a) Pe/P∞ = 1.45, Me = 694.3; r/De = 0.25. (b) Pe/P∞ = 1.45, Ue = 694.3; r/De = 0.0.

Grahic Jump Location
Figure 3

Comparison of different polytropic power with experimental data. (a) Pe/P∞ = 1.45, Me = 694.3; r/De = 0.25, (b) Pe/P∞ = 1.45, Me = 694.3; r/De = 0.0.

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Figure 4

Comparison of non dimensional tip penetration for different polytropic power, Pe/P∞ = 1.45, Me = 2.0

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Figure 5

Jet propagation in time for Pe/P∞ = 1.45, Me = 2.0; r/De = 0.0 in isentropic process

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Figure 6

Jet development for different polytropic power. (a) Pe/P∞ = 1.45, Me = 2.0; r/De = 0.0, time = 13 ms. (b) Pe/P∞ = 1.45, Me = 2.0; r/De = 0.0, time = 19 ms.

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Figure 7

Effect of exit pressure ratio on evolution of jet centerline for Me = 2, n = 1.4, r/De = 0.0. (a) pressure ratio for time = 10 ms. (b) tip penetration.

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Figure 8

Effect of exit velocity on evolution of jet centerline for Ptotal/P0 = 11.3453, n = 1.4, r/De = 0.0. (a) pressure ratio for time = 20 ms. (b) tip penetration.

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Figure 9

Pressure distribution at different radial locations for Pe /P0  = 1.445, n = 1.4, Ue = 491 m/s, time = 3ms

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