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TECHNICAL PAPERS

Calculation of the Mixed-Out State in Turbomachine Flows

[+] Author and Article Information
Anil Prasad

Aerodynamics Division, Pratt & Whitney Aircraft Engines, East Hartford, CT 06108

J. Turbomach 127(3), 564-572 (Mar 01, 2004) (9 pages) doi:10.1115/1.1928289 History: Received October 01, 2003; Revised March 01, 2004

A systematic and rational methodology for the calculation of an equilibrium state from an initial nonuniform flow field, is presented with particular emphasis on the underlying assumptions and their attendant justifications. The imposed conservation criteria that are used to define a final state from the initial one depend on the coordinate system and flow configuration being analyzed. The imposition of these criteria for flow in parallel-walled annular ducts defines a state of complete (mechanical and thermal) equilibrium, for which radial profiles of the velocity components, static pressure and temperature assume a specific form for a perfect gas. A robust method for solving the system of equations that define the state of complete equilibrium (or mixed-out state) is presented using an efficient algorithm. The procedure is applied to the swirling flow exiting an isolated transonic compressor, and comparisons are made with other available methods of averaging flow fields.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Conceptual schematic of the procedure to extract the equivalent state of complete equilibrium from an initial nonuniform state

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Figure 2

Schematic of computational geometry of NASA Rotor-35. Initial states are defined on axial planes indicated by the broken lines

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Figure 3

Radial profile of (a) axial velocity, vx, and (b) tangential velocity, vθ, normalized by the tip speed U, at ξ=0.2. The circumferentially-averaged profiles shown are: Dring–Oates method (×), area-weighted (– ∙ – ∙) and approximated planar mixing (– – –). The mixing out procedure that yields the state of complete equilibrium is shown by the solid line (—)

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Figure 4

Radial profile of normalized (a) static pressure (b) static temperature, (c) total pressure, and (d) total temperature at ξ=0.2. The circumferentially averaged profiles shown are: Dring–Oates method (×), area-weighted (– ∙ – ∙) and approximated planar mixing (– – –). The mixing out procedure that yields the state of complete equilibrium is shown by the solid line (—)

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Figure 5

Difference in loss coefficient relative to the entropy-averaged value as a function of mass flow rate at (a) ξ=0.2 and (b) ξ=0.45. Legend, SA: entropy-average, MA: mass-average, AA: area-average, and MX: mixed-out to state of complete equilibrium.

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Figure 6

Schematic of compressor geometry with long duct possessing slip walls shown as shaded regions in (a). Variation of loss coefficient with downstream distance is shown in (b), with the legend SA: entropy-averaged, MA: mass-averaged, MX: mixed-out to state of complete equilibrium

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