IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 03, 2015 | ISSN (online): 2321-0613

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Non-Dimensional Aerodynamic Design of Centrifugal Compressor for

Small Scale Samkit V Shah

1 Prof. Nilesh R.Sheth

2 Prof. Samip P.Shah

3

1ME Student

2,3Professor

1Department of Energy Engineering 1,2

GEC Valsad 3

C.K.P.C.E.T SuratAbstract— This paper investigates the development of a

preliminary design method for centrifugal compressors. The

analysis and design of Turbo-machines, at any level of

sophistication, must ultimately be based on an

understanding of the thermodynamics and fluid mechanics

processes which take place in the machine. On the simplest

level a preliminary design may consist of no more than the

application of the basic equations to estimate the magnitude

of overall design parameters, while on more complex level

the design methods will attempt to simulate more closely the

actual flow. The present work describes the simplified

approach to optimum design of centrifugal compressor stage

with the help of fundamental equations, which describe

thermodynamics, and aero-fluid dynamic flow process in

Turbo-machines.

Key words: Conceptual Design for Centrifugal Compressor

Impeller, aero-fluid dynamic flow

NOMENCLATURE:

1) SYMBOLS

A- Flow area section of impeller, diffuser & volute channels

a -Speed of sound

C- Absolute velocity of gas (Air)

W- Relative velocity of gas with respect to rotating element

D2 -Impeller exit (tip) diameter

i -Blade incidence angle

Mu -Blade Mach number

M, M’- Absolute & Relative Mach number

m -Mass flow rate

N - Rotational speed of Impeller

P - Fluid static pressure

PR - Stage total pressure ratio

Po - Fluid Stagnation pressure

R - Universal gas constant, Radius

tb - Impeller blade thickness

U2 -Blade tip speed

x- Meridional (axial) distance from axis of rotation

Zb - Number of Impeller blades

z -Axial meridional distance along axis of rotation

SPECIAL CHARACTERS

α - Absolute flow angle w.r.t meridional (flow) direction

β -Relative flow angle w.r.t flow direction

βB -Blade angle

λ -Work input coefficient

γ -Isentropic index for air

ν -Impeller eye hub to shroud diameter ratio

μ -Slip factor

η -Efficiency

φ -Flow co-efficient

2) SUBSCRIPT

I -Impeller Total to Total

S -Stage Total to Total

01-Stagnation state at inlet to eye

02 -Stagnation state at impeller exit

1 -Static state at impeller eye

2 -Static state at impeller exit

1s - State at shroud of impeller eye inlet

1h -State at hub of impeller eye inlet

1m -State at mean section of impeller eye inlet

a -Axial meridional component

m -Radial meridional component

θ -Tangential component

I. INTRODUCTION

Centrifugal compressor, also called radial compressor, are

critical equipment in a wide variety of application in the

chemical process industries, power plant etc. As their name

suggest, their primary process is to compress a fluid in to

smaller volume while simultaneous increasing pressure and

temperature of fluid. In other words, compressor accepts a

mass of gas at some initial pressure and temperature and rise

pressure and temperature of a gas. A Solid foundation for

turbo machinery design must comprise basic fundamentals

and useful experience. Both the basic principles of fluid

mechanics and thermodynamics on the one hand and

appropriate design data on the other hand are essential. If

these two resources are utilized effectively, very fine design

can be prepared for new application. There are, however

probably as many different design techniques as there are

designers in the world. Each designer undoubtedly uses

similar basic principles with a different combination of

experimental data to achieve the desire result.

II. CONCEPTUAL DESIGN FOR CENTRIFUGAL COMPRESSOR

IMPELLER

The main requirement from an impeller design procedure is

the computation of the overall principal dimensions and the

inlet and discharge blade angles. Impeller design procedure

is carried out applying non dimensional parameters

thermodynamic correlation which disregard actual size of

machine and more general compared to dimensional

quantities.

A. Impeller Design Steps:

Impeller design has been accomplished systematically for

complete control of aerodynamic parameters within

optimum recommended range. Input parameter are as

follows

Power (P)

Stagnation Pressure ratio (PR) from 1.5 to 5 bar[9]

Gas constant (R=287 kJ/kg. K)

Specific heat ratio (ϒ=1.4)

At inducer eye hub to shroud diameter ratio

(D1h/D1s) from 0.3 to 0.6[9]

shroud inlet diameter to Outlet diameter (D1s/D2)

from 0.4 to 0.9[9]

Impeller Total to Total Efficiency (ηI)

Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale

(IJSRD/Vol. 3/Issue 03/2015/203)

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Stage Total to Total Efficiency (ηS) Inlet blade angle at shroud (β1s) from 560 to 640

[9]

Inlet absolute Flow angle (α1)

outlet Blade angle (β2 ) from 00 to -600 [9]

outlet absolute flow angle (α2) from 600 to 700 [9]

1) Step: 1 Determination of Blade Mach number (Mu)

It is governing parameter to decide the size and rotational

speed of impeller. Correlation between Mu and stagnation

pressure ratio is given as

For radial impeller βB2 = 0o, So λ=μ= 0.8 to 0.9

[3]

For high speed compressor developing high

pressure ratio, maximum allowable value of Mu would be

under 2.[4]

2) Step 2: Determination of stagnation temperature

ratio and pressure ratio (To2/T01 & P02/P01)

Generally, inlet stagnation condition is known to

designer. So knowledge of Mu gives the value of

developed stage total stagnation temperature.

Fig. 2.1: Main Component Of Centrigugal Compressor With

Velocity Triangle At Inlet And Exit[9]

3) Step 3: Determination of Absolute Impeller Exit

Mach number (M2) It depends on Mu and absolute

exit flow angle α2.

Fig. 2.2: Velocity Triangle At Outlet

[5]

Johnston and Dean (1966) showed that an optimum

swirl angle α2, for design purposes, lies between 63 to 68

degrees. Similarly Rodger and Sapiro (1972) considered the

optimum flow angles to lie between 60 to 70 degrees w.r.t

radial direction. [9]

4) Step 4: Determination of Relative outlet Mach

number ( ) at shroud

'

2M

Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale

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5) Step 5: Determination of absolute and Relative

inlet Mach number ( M1s & ) at shroud

Fig. 2.3: Inlet Velocity Triangle At Hub Shroud And

Mean[5]

6) Step 6: Determination of Non-dimensional mass

flow rate, flow co-efficient Impeller Blade height

to outlet radius ratio.

Flow co-efficient:

Non-dimensional Mass flow rate ratio:

In actual case blade height at impeller exit (b2) is

higher than above calculated value due to consideration of

hub thickness of each vane, therefore let actual blade height

be found assuming b2 = 1.1 b2.

7) Step 7: Now specify the mass flow rate and inlet

stagnation condition to convert the Non-

dimensional geometry of impeller in to absolute

dimension

Density at inlet of impeller

Sound velocity at inlet

Outlet flow area from impeller

Outlet radius of impeller

s1

'M

Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale

(IJSRD/Vol. 3/Issue 03/2015/203)

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Width of impeller blade flow passage at outlet

Inlet shroud radius

Inlet hub radius

8) Step 8: Determination of Impeller blade numbers

and maximum hub thickness (Zb, tbh)

Various correlations for estimation of slip factor

(μ) have been developed by many researchers

applied for wider range of impeller vane no.(Zb),

vane exit angle (βB2) and radius ratio.

Stodala equation:[13,14]

Where βB2 = 0 for radial vane

Weisner equation[10]

Stanitz equation:[10,14]

Impeller blade hub thickness (tbh) can be

determined from exit flow area correlation based

on blade thickness consideration as,

Where, b2t = 1.1b2

9) Step 9: Impeller geometry for Centrifugal

Compressor Vanes [11]

Wallace (1975) represented impeller geometry by

means of Lame Ovals equation of general form:

Where, x is radius (r) for hub or shroud lines for

radial blade impeller. The coefficients a, b, c and d are

obtained from the end conditions (x1, z1) and (x2, z2) for

shroud and hub curve with assumption and axial inlet and

radial exit blade. p and q are indices and can be varied to get

series of analytic curves.

From an aerodynamic standpoint, Birdi [5] has

suggested correlation for optimal axial length- tip

diameter ratio.

Where, K1 = 0.28 and K2 = 0.8

For hub, a = -Z1h, b = Z2h (L)-Z1h, c = -X2h, d =

X1h- X2h

For shroud, a = -Z1s, b = Z2s-Z1s, c = -X2s, d = X1s-

X2s;

p 2 3 2 3

q 1 1 2 2

p = 3 and q = 2 value is applied as it gives slight

long axial path inducer without prewhirl.

Fig. 2.4: Impeller meridional geometry

REFERENCES

[1] Duccio Bonaiuti, Andrea Arnone and Mirco Ermini

“Analysis and Optimization of Transonic

Centrifugal Compressor Impellers Using the

Design of Experiments Technique” ASME Vol.

128, OCTOBER 2006.

[2] Hua Chen and Vai-Man Lei “Casing Treatment and

Inlet Swirl of Centrifugal Compressors” ASME

Vol. 135 JULY 2013.

[3] Abraham engeda and yunbae kim “ The inlet flow

structure of centrifugal compressor stage and its

influence on the performance” ASME journal of

engineering for power, 2003.

[4] Barend w. botha and andriaan moolman

“Determining the impact of the different losses on

Centrifugal compressor” R&D journal,2005.

[5] Pekka R¨oytt¨a, Aki Gr¨onman, Ahti Jaatinen,

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“Effects of Different Blade Angle Distributions on

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Publishing Corporation International Journal of

Rotating Machinery Volume 2009 23 November

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[6] Milesh coopinger “ Aerodynamic performance of

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guide vane system” Lough borough

university,1999,

[7] Nilesh paul murray “ Effect of impeller diffuser

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[8] James M. Sorokes, Cyril J. Borer ans Jay M. Koch

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Pressure Non-Uniformity Caused by a Centrifugal

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Olean, USA

Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale

(IJSRD/Vol. 3/Issue 03/2015/203)

All rights reserved by www.ijsrd.com 843

[9] Adnan Hamza Zahed and Nazih Noaman Bayomi

“Design Procedure of Centrifugal

Compressors” ISESCO JOURNAL of Science and

Technology Volume 10 - Number 17 - May

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[10] C. Xu and R. S. Amano “Meridional

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[11] Flore Crevel,Nicolas Gourdain and Xavier Ottavy

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[12] Flore Crevel,Nicolas Gourdain and St_ephane

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[13] D pan and A whitefield “Design consideration for

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[15] G. Naga Malleshwar Rao, Dr. S.L.V. Prasad and

Dr. S. Sudhakarbabu “A COMPUTER

PROGRAMMED DESIGN OPTIMISATION

AND ANALYSIS OF COMPRESSOR

IMPELLER” Volume 2, Issue 1, January 2014

International Journal of Research in Advent

Technology.

BOOKS:

[16] Whitefiled and N.C.Basines “Design of radial

turbomachines” Longman scientific and technical

publication.

[17] David Japikse “Centrifugal compressor Design and

performance” ETI.