Meccanica

, Volume 17, Issue 4, pp 211–221 | Cite as

A comparison between the craig-cox and the kacker-okapuu methods of turbine performance prediction

  • Giovanni Lozza
Article

Summary

Two complete comprehensive loss correlations for estimating the efficienty of axial-flow turbines are examinated in this paper: the well-known Craig-Cox method, and the recent development of the Ainley-Mathieson method, presented by Kacker and Okapuu, which reproposes the validity of this approach.

Firstly, a comparison is done by evaluating the losses in a number representative cascades, having various solidities, aspect ratios, Reynolds and Mach numbers. It is shown that the two methods are in good agreement for subsonic cascades having high flow coefficients, while significant differences are found in high deflection blades, especially for the secondary losses.

In the second part, it is investigated how the choice of correlation affects the project of a turbine stage. A design procedure, automatically carried out by a computer program, was applied to a number of cases: the differences between the two solutions of the same project problem obtained by using the two correlations are discusses. Parameters like specific speed, expansion ratio and size parameter are used to generalize the results.

Keywords

Mach Number Performance Prediction Size Parameter Expansion Ratio Flow Coefficient 

Nomenclature

b

axial chord, m

bb

backbone lenght, m

c

blade chord, m

CR

contraction ratio, defined by C-C

D

mean diameter, m

e

blade back radius, m

Fl

lift coefficient, defined by C-C

FL

flaring angle, deg

h

blade height, m

Kis

head coefficient, 2(Δh is )/u2

ks

equivalent sand grain size, m

KP, KS

correction factors defined by K-O

M1

blade inlet Mach number

M2

blade isoentropic outlet Mach number

Ns

specific speed,RPS\(\sqrt {Vout/} \Delta h_{is} ^{3/4}\)

o

throat opening, m

om in

blade critical throat, m

Re

Reynolds number

RPS

speed of revolution, rps

r*

isoentropic degree of reaction

s

pitch, m

t

trailing-edge thickness, m

u

peripheral speed at mean radius, m/s

v

absolute velocity, m/s

VH

size parameter,\(\sqrt {V_{out} /} \Delta h_{is} ^{1/4}\), m

Vin

volumetric flow rate, at turbine inlet total conditions, m3/s

Vout

volumetric flow rate, at turbine isoentropic outlet static conditions, m3/s

VR

volume ratio,Vout/Vin

w

relative velocity, m/s

Y

total pressure drop

z

number of blades

α

relative gas angles, deg

γ

specific heats ratio

δr

tip clearance, m

Δβ

rotor deflection, deg

Δη

efficiency decay

Δhis

total-to-static isoentropic enthalpy drop relative to the whole turbine, J/kg

φE

utilization factor of leaving losses

ηts

total-to-static efficiency

ηtt

total-to-total efficienty

ψz

loading coefficient by Zweifel

ρ

density, kg/m3

ξ

energy drop coefficient, referred to the ideal kinetic outlet energy

ξ′

energy drop coefficient, referred to the real outlet kinetic energy

Subscripts

1

blade inlet

2

blade outlet

S

relative to the stator

R

relative to the rotor

T

total conditions

Sommario

In questo articolo vengono considerati due metodi per la valutazione completa delle perdite fluidodinamiche in turbine assiali: il primo, ben noto, è quello proposto da Craig e Cox, mentre il secondo rappresenta il recente sviluppo del metodo di Ainley e Mathieson, operato da Kacker e Okapuu a conferma della validità dell'approccio originale.

Un primo confronto è stato effettuato valutando le perdite in alcune schiere tipiche, con diversi numeri di Reynolds e di Mach. Viene mostrato che i due metodi sono in buon accordo per schiere subsoniche aventi elevati coefficienti di flusso, mentre si rilevano differenze significative in pale ad alta deflessione, specialmente per ciò che riguarda le perdite secondarie.

Nella seconda parte si è voluto indagare come la scelta di una o dell'altra correlazione di perdite possa influenzare il progetto di stadi di turbine. Un certo numero di stadi tipici è stato ottimizzato mediante un codice automatico: vengono discusse le differenze tra le due soluzioni dello stesso problema progettuale risultate dall'uso di ambedue le correlazioni. I risultati sono presentati in funzione di parametri quali il numero di giri caratteristico, il rapporto di espansione e il coefficiente di «taglia», nell'intento di generalizzare i risultati.

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References

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Copyright information

© Pitagora Editrice Bologna 1982

Authors and Affiliations

  • Giovanni Lozza
    • 1
  1. 1.Dept. of Energetics Politecnico di MilanoItaly

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