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Journal of Turbomachinery | Volume 128 | Issue 1 | TECHNICAL PAPERS
TECHNICAL PAPERS

Averaging Nonuniform Flow for a Purpose

[+] Author and Article Information
N. A. Cumpsty

 Rolls-Royce plc, Derby, UK

J. H. Horlock

 Whittle Laboratory, .Cambridge, UK

J. Turbomach 128(1), 120-129 (Feb 01, 2005) (10 pages) doi:10.1115/1.2098807 History: Received October 01, 2004; Revised February 01, 2005
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Averaging nonuniform flow is important for the analysis of measurements in turbomachinery and gas turbines; more recently an important need for averaging arises with results of computational fluid dynamics (CFD). In this paper we show that there is a method for averaging which is “correct,” in the sense of preserving the essential features of the nonuniform flow, but that the type of averaging which is appropriate depends on the application considered. The crucial feature is the decision to retain or conserve those quantities which are most important in the case considered. Examples are given to demonstrate the appropriate methods to average nonuniform flows in the accounting for turbomachinery blade row performance, production of thrust in a nozzle, and mass flow capacity in a choked turbine. It is also shown that the numerical differences for different types of averaging are, in many cases, remarkably small.
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Copyright © 2006 by American Society of Mechanical Engineers
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+Two streams of perfect gas
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Two streams of perfect gas
Figure 1

Two streams of perfect gas

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+Hypothetical fan profile of pressure ratio and polytropic efficiency
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Hypothetical fan profile of pressure ratio and polytropic efficiency
Figure 2

Hypothetical fan profile of pressure ratio and polytropic efficiency

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+Circumferential average temperature out of a combustor
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Circumferential average temperature out of a combustor
Figure 3

Circumferential average temperature out of a combustor

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+Comparison of averaged pressures for sinusoidal variation in stagnation pressure. Temperature uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.
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Comparison of averaged pressures for sinusoidal variation in stagnation pressure. Temperature uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.
Figure 4

Comparison of averaged pressures for sinusoidal variation in stagnation pressure. Temperature uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.

Grahic Jump Location
+Comparison of averaged pressures for sinusoidal variation in stagnation temperature. Pressure uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.
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Comparison of averaged pressures for sinusoidal variation in stagnation temperature. Pressure uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.
Figure 5

Comparison of averaged pressures for sinusoidal variation in stagnation temperature. Pressure uniform. Case 1—mass average/work average, Case 2—availability average/work average, and Case 3—thrust average/work average.

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+Temperature-entropy diagrams showing a comparison between availability averaging and work averaging for two streams entering at Pa1, Ta1 and Pb1, Tb1; leaving at Pa2, Ta2 and Pb2, Tb2. Availability-average state points marked as B1 and B2, work-average state points marked as w1 and w2.
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Temperature-entropy diagrams showing a comparison between availability averaging and work averaging for two streams entering at Pa1, Ta1 and Pb1, Tb1; leaving at Pa2, Ta2 and Pb2, Tb2. Availability-average state points marked as B1 and B2, work-average state points marked as w1 and w2.
Figure 6

Temperature-entropy diagrams showing a comparison between availability averaging and work averaging for two streams entering at Pa1, Ta1 and Pb1, Tb1; leaving at Pa2, Ta2 and Pb2, Tb2. Availability-average state points marked as B1 and B2, work-average state points marked as w1 and w2.

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