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Research Papers: Fundamental Issues and Canonical Flows

One-Dimensional Unsteady Periodic Flow Model with Boundary Conditions Constrained by Differential Equations

[+] Author and Article Information
Nhan T. Nguyen

 NASA Ames Research Center, Moffett Field, CA 94035

J. Fluids Eng 131(6), 061201 (May 12, 2009) (15 pages) doi:10.1115/1.3130244 History: Received November 02, 2007; Revised April 13, 2009; Published May 12, 2009

This paper describes a modeling method for closed-loop unsteady fluid transport systems based on 1D unsteady Euler equations with nonlinear forced periodic boundary conditions. A significant feature of this model is the incorporation of dynamic constraints on the variables that control the transport process at the system boundaries as they often exist in many transport systems. These constraints result in a coupling of the Euler equations with a system of ordinary differential equations that model the dynamics of auxiliary processes connected to the transport system. Another important feature of the transport model is the use of a quasilinear form instead of the flux-conserved form. This form lends itself to modeling with measurable conserved fluid transport variables and represents an intermediate model between the primitive variable approach and the conserved variable approach. A wave-splitting finite-difference upwind method is presented as a numerical solution of the model. An iterative procedure is implemented to solve the nonlinear forced periodic boundary conditions prior to the time-marching procedure for the upwind method. A shock fitting method to handle transonic flow for the quasilinear form of the Euler equations is presented. A closed-loop wind tunnel is used for demonstration of the accuracy of this modeling method.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Closed-circuit wind tunnel (NASA Ames 11 ft TWT)

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Figure 2

Wind tunnel compressor

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NASA Ames 11 ft TWT Mach number envelope

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Figure 4

Closed-loop transport system

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Figure 5

Compressor pressure ratio

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Wind tunnel discretization

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Compressor speed and inlet guide vane flap angle responses

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Drive motor rotor resistance and inlet guide vane motor voltage

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Figure 9

Test section Mach number response

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Mach number distribution

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Mass flow distribution

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Stagnation pressure distribution

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Stagnation temperature distribution

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Test section Mach number comparison between midpoint discretization and current discretization

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Figure 15

Computed shock location

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Figure 16

Maximum shock location error versus number of grid points

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Figure 17

Initial and final Mach number variations

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