Turbofan performance assessment: A new method of analysis and presentation

CRANFIELD R E P O R T S . M . E . N O . 2

Bibliotheek TU Delft \ I 3 ü t t . 1572 1 Faculteit der Luchtvaart-en Ruimtevaarttechniel'

Kluyverweg 1 2629 HS Delft

C R A N F I E L D

I N S T I T U T E OF T E C H N O L O G Y

TURBOFAN PERFORMANCE ASSESSMENT

A NEW METHOD OF ANALYSIS AND PRESENTATION

T . J. CORBISHLEY K. W. RAMSDEN

Srv^lin^iP

CRANFIELD REPORT S.M.E. No. 2 May, 1972.

CRANFIELD INSTITUTE OF TECHNOLOGY SCHOOL OF MECHANICAL ENGINEERING

TURBOFAN PERFORMANCE ASSESSMENT

-A NEW METHOD OF -AN-ALYSIS -AND PRESENT-ATION

by

T. J. Corbishley

and

K. W. Ramsden, B.Sc.(Eng), M.Sc, C.Eng., M.I.Mech.E., F.B.i.S.

B i b l i o t h e e k TU D e l f t /LR

C S075507 SUMMARY

A t the project design stage, conventional methods of turbofan performance analysis involve lengthy and time consuming computer calculations leading to extensive graphical representation.

An alternative method of analysis is described, introducing a dimensionless form for both thaist and specific fuel consumption. Each of the latter parameters are found to vary linearly with a new parameter, the In-pass Ratio, over a wide range of typical engine parameters.

The proposed method is shown to facilitate, with little loss of accuracy, considerable savings in both computer time and graphical presentation when compared with exact methods.

CONTENTS

Page No. SUMMARY

NOTATION

1.0 INTROOUCTION 1 2.0 THE IN-PASS RATIO - /? 2

3.0 THE IN-PASS METHOD OF PERFORMANCE ANALYSIS 2 4.0 COMPARISON OF COMPUTATION TIME AND GRAPHICAL

PRESENTATION BETWEEN THE IN-PASS METHOD AND AN

EXACT METHOD 4 5.0 CONCLUSIONS 4

REFERENCES 5

FIGURES

1. JET VELOCITY OF GAS GENERATOR NOZZLE FOR FULL EXPANSION

2. VELOCITY RATIO PARAMETER

3a. TURBOFAN NETT THRUST AND SPECIFIC FUEL CONSUMPTION RATIOS USING AN EXACT METHOD OF COMPUTATION

3b. EFFECT OF COMPRESSOR PRESSURE RATIO AND TURBINE ENTRY TEMPERATURE ON NETT THRUST AND SPECIFIC FUEL CONSUMPTION

RATIOS

NOTATION

SYMBOLS

b - jet velocity parameter (defined in text) sfc - specific fuel consumption

TET - turbine entry temperature Vp - fan nozzle exit velocity

V j - gas generator nozzle exit velocity W - mass flow

X|>j - nett thrust a - fuel/air ratio

/3 - in-pass r a t i o : - ratio of the gas generator mass f l o w t o the t o t a l f l o w entering the turbofan intake

(I - by-pass ratio:- ratio of the by-pass mass flow to the gas generator mass flow

SUFFICES

8 - relating to by-pass flow G - relating to gas generator flow

o - extrapolated reference condition for a pure jet (defined in text). ref - reference condition for a pure jet

1.0 INTRODUCTION

Conventional methods of turbofan performance analysis, particularly at the project stage, require extensive study involving numerous engine parameters for various flight conditions. These parameters may, for example, include by-pass ratio, fan and overall pressure ratio, turbine entry temperature, component efficiencies, flight Mach number, altitude and ISA condition. With so many degrees of freedom, project studies for a new engine are time consuming and expensive in computer utilisation and lead to extensive graphical represent-ation.

This report proposes a method of project performance analysis and presentation, called the "In-pass Method", which yields a four-fold reduction in computer time and considerable reductions in necessary graphical representation.

The method depends on the introduction of an "In-pass Ratio", uniquely related to by-pass ratio and defined as the ratio of the gas generator mass flow to the total flow entering the intake. In addition, specific thrust and specific fuel consumption are made non-dimensional by using reference values for a pure jet computed at the same overall pressure ratio, turbine entry temperature and total mass flow.

The resulting variation of dimensionless specific thrust and specific fuel consumption with in-pass ratio is substantially linear. This linearity is shown to extend over a range of by-pass ratios dependent only on turbine entry temperature. Furthermore, the slopes of these lines depend on turbine entry temperature but are virtually independent of overall pressure ratio. Once the reference data for the pure jet are computed, a further single calculation at one by-pass ratio and one overall pressure ratio for each turbine entry temperature furnishes performance data at all other by-pass ratios and overall pressure ratios.

For the purpose of illustration, comparison is made, at ISA sea level static conditions, between the in-pass method and a typical exact method for a turbofan engine with a fan pressure ratio of 1.25. Ranges of compressor pressure ratios from 6 to 14 and of turbine entry temperatures from 1200K to 1600K are considered.

In this particular case, at the lowest turbine entry temperature, the linearity referred to above is shown to extend to a by-pass ratio of 7. Further, at this value, the in-pass method is accurate to within 2% of the exact method, the accuracy improving progressively as by-pass ratio is reduced. A t the highest turbine entry temperature of 1600K, the in-pass method is shown to be very nearly exact, the linearity extending to a by-pass ratio of approximately 9. The effects of changes in flight condition and fan pressure ratio are not detailed in the present report. It has, however, been shown by the authors, that the in-pass method is applicable to a greater or lesser extent over typical ranges of these parameters. The work described in this report was conducted as part of the first named author's Master of Science Thesis (to be submitted in September 1972) and which, it is hoped, will be published later as a separate report.

The authors are considerably indebted to Mr. J. R. Palmer, Deputy Head of the School of Mechanical Engineering, for his much valued assistance in this work.

2

-2.0 THE IN-PASS RATIO - 0

In conventional turbofan analysis, by-pass ratio is defined

as:-fi = W B / W Q

In the proposed method, the in-pass ratio is defined as the ratio of the gas generator mass flow, W Q , to the total mass flow entering the intake, W J Q J .

a- WQ/WTOT

T O T = W B + W Q

Thus:-Since:- W

then:- /3 = 1 / ( 1 + M ) or M = ( 1 - ^ ) / / J

giving the following

table:-M

P

3.0 THE IN-PASS METHOD OF PERFORMANCE ANALYSIS

Corbishley (Ref. 1) shows that for complete nozzle expansion, at ISA sea level static conditions, the ratio of the nett thrust Xfg, of a turbofan engine of in-pass ratio, /3, to that of a pure jet, X M . (/3 = 1.0), with the same total mass flow, compressor ratio and

'^ref

turbine entry temperature is given

by:-X N / by:-X N „ . = (1 - ^ ) V F / ( 1 +a,ef)Vj^^^ + /3 V j / V j

'ref ref 'ref

and that

sfc/sfCref = ^ / ( X N / X f g J

(3.1)

(3.2)

To illustrate the proposed method, data are computed for a turbofan engine of 1.25 fan pressure ratio using a typical exact method, the Turbocode Scheme (Rets. 2 and 3), at ISA sea level static conditions.

Figure 1 shows the variation of computed values of non-dimensional gas generator jet velocity, over a range of by-pass ratios for a fixed turbine entry temperature of 1400K.

In fact, it is seen that the variation of V j / V j with /x is linear over most of the range, such that:- ''^'

V j / V j

ref IVI bM)/Vj ref

where b/Vj is the slope and V j / V j is the hypothetical jet velocity ratio obtained as

'ref 'ref

3

-For each of the compressor pressure ratios considered in Figure 1, the value of V i / V i *'o •'ref is very close to unity. The exact values, for this case are shown in the following table.

Compressor Pressure Ratio Vj / V J ^ ''o -^ref 6.0 0.9892 10.0 0.9901 14.0 0.9921

Thus with little error V j / V j . . , = i-0 and

V j / V j ^ „ , = 1 - bM/Vj 'ref ref and since V j / V j ref

^Ji=(^-m

0^)hiVj

Combining Equations 3.1 and 3.3 gives, after some

rearrangement:-•f /

^N/^Nref = ^ < ^ ^ F ^ + - ^ ^ l # - - ^ W j ^ ^ ^ m - ^ T ^ ^ (3.4)

Note:- the value of b may be calculated

from:-^^^Jref = <^Jref' "^-i^^^^^ei ^^^'^^ " ^> <^ " ^J^^^ref* '^•^' The velocity ratio parameter, (Vp/(1 + a^gf) — b ) / V j

is a function of compressor pressure ratio and turbine entry temperature. The variation of this parameter is shown in Figure 2 for the case being considered, using again computed values derived from the exact Turbocode method.

It is seen that the highest value for, and variation in the velocity ratio parameter occurs at the lowest turbine entry temperature considered. This variation, over the range of pressure ratios covered, amounts to approximately + 2.5% and — 1.5% of the value at a mid-range pressure ratio of 10. A t the highest turbine entry temperature considered, the magnitude of the velocity ratio parameter is significantly less, its variation over the range of compressor pressure ratios falling virtually to zero. The in-pass solution neglects these variations in the velocity ratio parameter.

Consideration of the in-pass solution of Equation (3.4) reveals that the variation of the nett thrust ratio is most nearly linear in in-pass ratio, when the term containing the velocity ratio parameter is small in comparison with in-pass ratio itself. This occurs at a combination of high values for both in-pass ratio (that is low by-pass ratio), and turbine entry temperatures. Futhermore, the in-pass solution is most nearly independent of pressure ratio, at a given in-pass ratio, when the variation of the velocity ratio parameter with pressure ratio is smallest. This again has been shown to occur at the higher turbine entry temperatures. Summarising therefore, the in-pass method is closest to the exact method when by-pass ratio

4

-is low and turbine entry temperature -is high. Figures 3a and 3b show the variation of

^ N / ^ N r e f ^ = /3/(sfc/sfCref) ]

with in-pass ratio, j3, over a range of compressor pressure ratios and turbine entry temperatures for the particular case being studied. The solid lines represent the exact solution, the dotted lines being the in-pass solution.

The slope of the in-pass solution for each turbine entry temperature is obtained by solving Equation (3.4) at a mid-range compressor pressure ratio of 10 and at one value for in-pass ratio of 0.2 (/u = 4.0). Thus, the computation for the in-pass method requires a complete cycle calculation for a pure jet using an exact method to produce the

reference values. A further cycle calculation is then necessary at one compressor

pressure ratio of 10, for each turbine entry temperature and at an in-pass ratio of 0.20, say.

Figure 3 reveals the usefulness of the in-pass method, particularly at low by-pass ratios and high turbine entry temperatures. A t the lowest turbine entry temperature, the in-pass solution predicts the nett thrust ratio to within 2% of the exact solution at a by-pass ratio of approximately 7 (/3 = 0.125). A t the highest turbine entry temperature the in-pass solution is very nearly exact extending to a by-pass ratio of 9.

In all cases the method becomes more nearly exact as by-pass ratio progressively falls.

4.0 COMPARISON OF COMPUTATION TIME AND GRAPHICAL PRESENTATION BETWEEN THE IN-PASS METHOD AND AN EXACT METHOD

Figure 4 shows, typically, the conventional method of turbofan performance presentation. These two sets of curves represent the performance for each of two engines, with different by-pass ratios. In each case 25 cycle calculations were necessary to provide the data, this figure being multiplied by the number of by-pass ratios ultimately considered in a per-formance evaluation study.

Using the in-pass method, however, a complete set of cycle calculations are necessary only for a pure jet and then for a turbofan engine at one compressor pressure ratio for each turbine entry temperature and at one by-pass ratio.The linearity between in-pass ratio and nett thrust and specific fuel consumption ratios then furnishes data at all other by-pass ratios.

If, for example, at given flight conditions and fan pressure ratio, 5 each of compressor pressure ratio, turbine entry temperature and by-pass ratio are to be evaluated, then 125 cycle calculations are necessary using an exact method, resulting in 5 graphs of the type shown in figure 4. For the same information using the in-pass method 30 cycle calculations are necessary resulting in one graph for the reference data (pure jet) of the type shown in figure 4 and the general curves of figure 3a.

I he factor of saving in this case in computer time is, then, over 4 to 1.

5.0 CONCLUSIONS

5

-obviate the need for extensive project study computer calculations typical of exact methods. Furthermore, the method introduces negligible error in predicting nett thrust and specific fuel consumption when compared with exact methods, being most nearly exact and independent of compressor pressure ratio, at low by-pass ratios and high turbine entry temperatures. In particular the method has been demonstrated for a fan pressure ratio of 1.25 at ISA sea level static conditions but is known t o be valid t o a greater or lesser extent at other conditions of flight speed and altitude and at other fan pressure ratios.

REFERENCES

1. Corbishley, T.J.

2. Palmer, J.R.

3. Palmer, J.R.

" A new method of turbofan performance prediction incorporating variable pitch fan studies." M.Sc. Thesis. (to be submitted, September 1972)

"The 'Turbocode' Scheme for the programming of thermodynamic cycle calculations on an electronic digital computer." (CoA Report Aero 198)

"Description of the Algol version of the "Turbocode" scheme for the programming of thermodynamic cycle calculations on an electronic digital computer." (CoA Report Aero 203).

FAN PRESSURE RATIO - 1.25. I.S.A SEA LEVEL STATIC

V s 0.9901 Jref

EXACT VARIATION

• VAEIATION ASSUMED BÏ IN-PASS METHOD 0.22 -0.2L 0.20 0.19 -' T p 1 * «ref ^Jref - 1> TET = 1200 K 1.56JJ 1W)0 K u.xo . 0.17 -1600 K

COMPEESSOa PHESSUBE RATIO

1 1 — 1 6 8 10

|„,

• T

FIG. 2. VELOCITY RATIO PARAMETER

FIG. 1. JET VELOCITY OF GAS G E N E R A T O R NOZZLE FOR FULL EXPANSION

IN-PASS RATIO - p

I 1 1 1 1 1 , 1 I ^ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

FAN PRESSURE RATIO = 1.25. I.S.A. SEA LEVEL STATIC WXN _ref ^Asfc/afc^j.) > EXACT KETHQD m - P A S S METHOD ( A T 1 0 : 1 COMPRESSOR PEESSÜRE RATIO)

FIG. 3b. EFFECT OF COMPRESSOR PRESSURE RATIO AND TURBINE ENTRY TEMPERATURE ON NETT THRUST AND SPECIFIC FUEL CONSUMPTION RATIOS

COMPRESSOR PRESSURE

RATIO

FAN PRESSURE RATIO = 1.25. I.S.A. SEA LEVEL STATIC ^^°° ^

1200 K 1400 K COMPRESSOR PRESSURE RATIO BY-PASS RATIO 2:1 TOT 32 (ibf. sec/lbm) -1 L. 36 40 4if 48