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DESIGN METHODOLOGY FOR AERODYNAMIC DESIGN

OF CENTRIFUGAL COMPRESSOR

A Thesis Submitted in partial fulfillment of the requirements of the degree

Of

B.TECH MECHANICAL ENGINEERING

by

ANAND VIJAYKUMAR

03BME018

SCHOOL OF MECHANICAL AND BUILDING SCIENCES

VITU N I V E R S I T Y

(Estd. u/s 3 of UGC Act 1956)

Vellore-632014, Tamil Nadu, India

www.vit.ac.in

APRIL, 2007


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ACKNOWLEDGEMENT

I would like to thank my Institute, Vellore Institute of Technology for providing me with

the opportunity for carrying out my project in the area of Turbo machinery and providing

me with the necessary guidance and infrastructure through which I could make this

project a grand success. I would also like to thank- Honeywell Technology Solutions Lab

for giving me this unique opportunity for carrying out my academic project in their

esteemed organization and providing me with all the guidance and support which are

needed at this level. I would also like to thanks my mentor at VIT, MR. D.R.S

Raghuraman who, with his immense experience and technical know-how provided me

with valuable inputs and guidance which made my project a truly valuable learning

experience.I would also thank my guide at Honeywell, MR. Shraman Goswami who in

spite of his busy work schedule took time off to guide me and played a very inspirational

role and help me understand the nuances of the subject with his highly technical expertise.


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CERTIFICATE

This is to certify that the thesis titled Design Methodology for Aerodynamic Design

of Centrifugal Compressors is submitted by Mr. Anand Vijaykumar, 03BME018 to

the School of Mechanical and Building Sciences of VIT University, Vellore for the

award of the degree in B.Tech Mechanical Engineering is a bonafide record of work

carried out by him under supervision. The content of this thesis, in full or in parts

have not been submitted to any other institute or University for the award of any

degree or diploma.

Guide Dean

Internal Examiner External Examiner


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ABSTRACT

The project presents a one dimensional (mean-line) design methodology for a

medium pressure ratio Centrifugal Compressor. A computational procedure for

design of a Centrifugal Compressor is established. The numerical model is based on

the conservation principles of mass, momentum and energy conservation and has

been utilized to predict the operational and aerodynamic characteristics of a small

centrifugal compressor as well as determining the performance and geometry of

compressor blades, both straight and backswept. The design code provides a basis

on which the design of the Compressor can be modeled by varying the key

parameters which include both aerodynamic and geometric details. The code shall

then predict and give a first cut solution, which will further help in zeroing on to a

particular design for the given requirements. The design which models the flow in

an Impeller, Diffuser and an annular bend takes into consideration various loss

models occurring in the complex flow of a Centrifugal Compressor. It makes use of

a Jet-Wake Model i.e. it splits the flow into Primary and Secondary zone and

performs a Mixed flow Analysis. The Design also performs an inverse flow analysis

where in we get the geometry by specifying aerodynamic details. The design has

been exhaustively validated by using a number of Test Compressors from NASA

test reports. Based on the geometry computed by the code, an impeller model is

generated using ANSYS BLADEGEN-Tool.


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CONTENTS

Page No

Acknowledgement.4

Abstract..5

List of Tables.7

List of Figures/ Exhibits/ Charts8

Nomenclature.9

1 INTRODUCTION13

1.1 General Introduction .131.2 Background Information...141.3 Introduction to Project..141.4 Introduction to Design Process.171.5 Literature Review..20

2 DESIGN PROCEDURE

2.1 Design Process Flow Chart for Primary Calculations..222.2 Preliminary Design...242.3 Design of Diffuser and Bend292.4 Methodology.312.5 Method of Loss Analysis..32

3 PROCEDURE FOR PRIMARY FLOW CALCULATION373.1 Impeller Design Validation..373.2 Vaneless Diffuser Design Validation...413.3 Vaned Diffuser Design Validation...443.4 Bend Diffuser Design Validation......49

4 SECONDARY FLOW ANALYSIS.52

4.1 Secondary flow regime524.2 Recirculation and Disk Friction loss534.3 Impeller Boundary Layer Control54

4.4 Slip Factor554.5 Impeller Secondary Flow Calculations564.6 Mixing Calculations.........58

5 DESIGN VALIDATION

5.1 Compressor Design Validation- Test Compressor-1.......60


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6 INVERSE DESIGN

6.1 Approach...636.2 Methodology 646.3 Other Modes of Operations...67

7 ANSYS BladeGen..69

7.1 Introduction to BladeGen...707.2 Using BladeGen.....70

8 Performance Variation with Geometry...74

8.1 Impeller Loss variations with Geometry....748.2 Impeller Exit Pressure Variations..75

9 CONCLUSION ..76

9.1 Conclusion..769.2 Towards Better Design...779.3 Scope for Future work....78

A APPENDIX.80

A.181A.281A.38 2A.48 3A.58 4A.68 5A.78 6A.88 7A.98 8

BIBILOGRAPHY/REFERENCES.90 .


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LIST OF TABLES

Table No Title Page No

2.1 Calculation of Impeller Exit ConditionUsing Spread Sheet Program26

3.1 Input for Impeller Design ..373.2 Assumptions Made In Impeller Design.373.3 Calculation Performed in Impeller Design403.4 Inputs for Vaneless Diffuser Design..413.5 Assumptions Made in Vaneless Diffuser Design...413.6 Calculations Performed for Vaneless Diffuser Design..433.7 Inputs for Vaned Diffuser Design ..443.8 Assumptions Made in Vaned Diffuser Design...453.9 Calculations Performed for Vaned Diffuser Design..46.3.10 Best Combination of Blades, Width, and

Flow Angle for Maximum Pressure Rise in a Vaned Diffuser..473.11 Inputs for Bend Diffuser Design483.12 Assumptions Made in Bend Diffuser Design493.13 Calculations Made in Bend Diffuser Design.49

4.1 Secondary Flow Calculations.514.2 Mixing Flow Calculations..58

5.1 Comparison of CFD results with 1D code for Test Compressor-1605.2 Comparison of 1D code Results with Test Results for Test Compressor-2...615.3 Comparison of 1D code Results with Test Results for Test Compressor-3...62

6.1 Variations in Impeller Exit Conditions as a Function ofImpeller Inlet Tip Mach number65

6.2 Various Losses Tabulated as function of Impeller Inlet Tip Radius...656.3 Variation of Inlet Tip Mach number with Impeller Inlet Tip Radius..666.4 Plot of Impeller Losses as a Function of Impeller Tip Radius71.


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LIST OF FIGURES/EXHIBITS/CHARTS

Figure No. Title Page No

1.1 Activity Chart..................................................................................121.2 Meanline Diagram of the Centrifugal Compressor.......161.3 Meridional view of impeller..14

2.1 Impeller Design Flow Chart..242.2 Compressor Flow range Vs Mach number at Vane diffuser exit..36

3.1 Impeller Inlet Velocity Triangle........403.2 Impeller Exit Velocity Triangle.413.3 Vaneless Diffuser Exit Velocity Triangle..443.4 Vaned Diffuser Exit Velocity Triangle..463.5 Bend Exit Velocity Triangle..51

4.1 Mixed Flow Calculation Flow Chart.........56

6.1 Variation of Rotor Efficiency with Impeller Inlet Tip Mach number...65

8.1 Blade-Blade View, Meridional View and Meshed View..658.2 Meshed View of Impeller Blade........668.3 Shaded View of Impeller Blade71

7.1 Plot of Impeller Blade Exit Angle Vs Impeller Losses.........727.2 Plot of Blade Backsweep Angle Vs Stagnation Pressure at Impeller Exit737.3 From Aerodynamic Design of Blades to Blade Fabrication..74

8.1 Plot of Impeller Blade Exit Angle Vs Impeller Losses..748.2 Backsweep Vs Impeller Stagnation Pressure Ratio...748.3 Backsweep Vs Impeller Stagnation Pressure Rise.758.4

A.1 Impeller Input Text File...80A.2 Vaneless Diffuser, Vaned Diffuser and Bend Input Text File.....81A.3 Impeller Design Source Code..82A.4 Impeller Source Code For design of Hub, Mean and Tip Conditions.83A.5 Source Code for the Design of Impeller Losses..84A.6 Vaneless Diffuser Design Source Code...85A.7 Vaned Diffuser Design Source Code...86A.8 Bend Design Source Code...87A.9 .88


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Nomenclature

absolute velocity angle2b blade angle at exit of impellerbt blade thicknessc absolute velocity

Cd coefficient of dischargect tangential velocity

cm meridional component of velocityCpi pressure loss coefficient (ideal)

Dhyd hydraulic diameter

DF diffusion factori1, h incidence angle at hub

r1, t radius at tip

r1, h radius at hubLC loss coefficientmf mass flow rate

M mach no

N rpmnrdb no of diffuser blades

Po,P stagnation pressurep static pressure

densityr radius

T static tempTo stagnation temp

w blade widthW relative velocity

zb impellor blades

Suffix

t tip

h hubm meridional component

Constants

k gamma

cp specific heat


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R universal gas constant

Re Reynolds Number

BLADE LOADING LOSS

SKIN FRICTION LOSS

DISK FRICTION LOSS

RECIRCULATION LOSS

INCIDENCE LOSS

No station name

1- impeller inlet2- impeller exit3- vaneless diffuser exit4- vaned diffuser exit5- bend exit


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Activity Chart and Schedule of Project Work.

Fig :1- Activity Chart


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CHAPTER-1

INTRODUCTION

1.1Introductory Remarks/Outline

GENERAL INTRODUCITION:

Over the past decade , there has been a growing interest and need for miniature energy

conversions systems, such as portable power generation for consumer electronics and

propulsion for micro fuel cells and handheld analytical instruments, as well as miniature

cooling units for electronics. Meeting this need requires the implementation of traditional

thermodynamic cycles at small scale, along with required machinery. Among the core

energy conversion technologies common large scales, compressors, pumps and turbines

are often used to convert fluid power to mechanical used for high power density and

reliability as illustrated by its prevalence in aerospace (aircraft gas turbines engines) and

power generation industries. But fabrication of such complex machines at millimeter

scale can however prove to be challenging and expensive.

The objective of current work consists of creating a knowledge base for design and micro

Turbo Machinery with special emphasis on Centrifugal Compressors Compressors.This project focuses on the design process of single stage micros scale turbo machinery

along with CFD predictions of the key aerodynamic performance parameters required in

the design process. This work focuses on unique and unexplored design space defined by

the small scale and planar geometries characteristics of turbo pumps, compressors, gas

turbines and steam turbines, or other turbo machinery-based Microsystems.

Correlations are proposed for the loss coefficient, based on laminar- turbulent flow theory.

A critical Reynolds no is also identified, below which adjacent boundary layers merge,

inducing sharp increase in loss and deviation. This imposes practical limits on the

miniaturization of such microturbomachinery.


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1.2Background Information

Honeywell Technology Solutions Lab has taken a personal initiative in developing a

100N thrust Micro jet (Gas Turbine Engine). The Compressor design could be applied for

this Gas Turbine Engine which could eventually be used in a UAV (Un-Manned Aerial

Vehicle) or a Land based Generator.

1.3 INTRODUCTION TO PROJECT

Problem Definition:

To develop a design methodology for the Aerodynamic design of a medium pressure

ratio Centrifugal Compressor.

Scope of the Project:

Aerodynamic Design of a Centrifugal Compressor.

Secondary Flow Analysis and Mixed Flow calculations.

Validation of Results with Test Compressor taken from NASA reports.

Performing Inverse Mean-line design.

Creating an impeller Blade Model using ANSYS BladeGen-tool.

The objective of the project is to design and eventually develop a Centrifugal compressor

of medium to high pressure ratio for a Micro Jet Engine (Small Gas Turbine Engine).

The project deals with the design methodology for the design of a Centrifugal

Compressor. The 1D design gives an initial design solution on the basis of which it can

be decided if a complete CFD analysis of the compressor is required.


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The Micro jet is designed for a thrust of 100N. The engine consists of a centrifugal

compressor, reverse flow annular combustor; radial turbine and exhaust system.

Fig: 1.2- Meanline Diagram of the Centrifugal Compressor

The following components of the Compressor are designed using the 1D

code.

- backward swept impeller- vaneless space- vaned diffuser- 90 deg angular bend


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1.4INTRODUCTION TO DESIGN PROCESS

The design of modern centrifugal compressors involves several different disciplines,

considerable historical design experience, and usually a variety of design tools.

The classical turbo-machinery design process begins with mean line performance

modeling calculations, once a cycle specification has been set freezes the design

flow, speed and stage pressure ratio or head rise.

When basic mean-line velocity triangles have been suitable optimized then

blading methods are used to design the required blade shapes. They may involve,

either direct or inverse computational methods or they should involve both flow

solvers and fundamental design rules.

When appropriate passage contours and blade shapes, are obtained it is reasonable

to go for final levels of design optimization.

At final level, CFD is used to study the full three-dimensional (3D) flow field

within the impeller, and the designer can then focus on the fine detailed design

considerations like localized regions of backflow, unwanted secondary flows, so

on and so forth.

1.4.1 Mean Line Flow Modeling:

One Dimensional or Mean line flow modeling is the simplest and the quickest way of

looking at the flow state.

When considering mean line we are paying attention to the average to characteristics of

the flow at that location which, on a mass or energy average basis gives the correct

representation of the entire flow field. However for the impeller exit we see that this is a

considerable simplification which cannot be justified under all circumstances. Hence the

concept of Two- Zone modeling comes into the picture.

The mean line flow modeling is illustrated for the stage with the overall stage

performance data only. Some assumptions about the slip-factor and diffuser pressure

recovery coefficient are introduced. Subsequently other experimental results are

progressively introduced and using the data, these assumptions can be checked or

eliminated, thereby improving the basic consistency model considerably.


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The modeling is for a compressor which features an impeller with radial blades or

backswept vanes at exit, a vaneless or vaned diffuser and a 90 degree annular bend.

1.4.2 Importance of Meanline Design:

Fundamental importance of meanline design is to optimize the basic velocity

triangle at each distinct, basic station throughout a turbo machine flow path. The

basic stations would include, for example, an impeller inlet, an impeller exit,

diffuser inlet, diffuser exit, and so forth. It makes no sense to try to use higher

order codes to optimize the average velocity triangle at these stations. This is the

important role of a meanline performance code.

If proper meanline optimization is not done, no amount of subsequent

optimization will correct for the inappropriate starting parameters. These starting

parameters involve the passage width, (b), and the mean radius,(r), where the

passage height is centered at each meanline station. Likewise, the mean blade

angle must be chosen according to the expected flow direction and desired

incidence. Preferred exit angles must be set. The correct mass flow rate and work

input (U2C2) level is nearly assured by these steps.

Basic stall criteria usually are assessed on a meanline level and should be

evaluated to assure adequate stable operating range or the compressor. In short,

most of the truly critical design criteria that must be met for a product to be

acceptable in the marketplace have a very important meanline design requirement.


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To meet these requirements, good meanline modeling is essential in order to start a

design optimization process with any real hope of a cost-effective, market-competitive,

product. Additionally, most diffusers and return channels are 2D in form so most of the

design process is complete at the meanline level. After the meanline optimization work is

completed, blades are designed to assume the intended deviation and, in turn, the work

input required and to turn the flow through desired angles either before or after the

impeller.

Fig: 1.3 Meridional view of impeller.


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1.5 Literature Review

1.)FORTRAN Program for Predicting Off- Design Performance of Centrifugal

Compressors

Provided the off design Characteristics of Centrifugal Compressor with aExample of a Compressor built by a commercial engine manufacturer to

demonstrate the effectiveness of the correlation with limited experimental Data.

Individual Losses are Computed Using Analytical Correlations which relates loss

Levels to Velocity Diagram Characteristics and Overall Geometry.

It Provides Valuable Information about Efficiency decrements through Use ofPlots and Tabulates Performance details for Validation.

2.) A Method of Performance Prediction of Centrifugal Compressors

Provides a huge database of Experimental data and by means of Extensive

Utilization of Correlations tests Results with predicted data.Provides correlations for finding variations in Gamma, Specific Heat andViscosity with variations in temperature and pressure

By means of a extensive availability of Measured data provides Tabulated Valuesfor finding out Loss Coefficients in Vaned Diffuser by suitably interpolating the

data.

Provides important correlations for finding Area Ratio (AR) in Vaned Diffuser.Also provide correlations for Loss Modal like Recirculation Loss and Leakage

Losses occurring in Impeller Section.


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Results and calculations

P1, T1, Po2, To2, P2, T2,

M1, M2,1 (deg)

OUTLET CALCULATIONS:

U2= (2*pi ()*r2*N)/60

ct2=U2+Cm2m*tan2b=U2 since 2b=0 (radial outlet

=1-(cos 2b) 0.5 /z 0.7 using Wiesners Correlationho =U2*ct2T02m=T01+(k-1)/(kR)* hoPo2/Po1= (1+ (nrotor *ho)/(Cp*T01))^k/ (k-1)cm2m and M2m are calculated as before.

W2m= (U2-ct2m) ^2+cm2m

2m=-cos-1(Cm2m/W2m)

2m= tan -1 (Ct2m/Cm2m)

Calculation of rotor

efficiency

Vaneless Diffuser Design

Output from Code

Results and Calculations of

Po3, To3, P3, T3, M3

Iteration on C3 till error in C3


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No

Error in C4


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2.2 PRELIMINARY DESIGN:

This report consists of evaluation of impeller and diffuser configuration that exhibits the

potential for high efficiency and adequate operating range. These configurations will be

selected for detailed aerodynamic design and fabrication.

The impeller configuration considered in this section includes radial and backward

curved impeller with conventional blading.

The diffuser configuration includes a vaneless diffuser, single-row vaned diffuser

(conventional vaned diffuser). Also included will be initial screening of possible

boundary layer control methods for adaptation to these configurations.

2.2.1 Conventional impeller

A particular operating speed is selected for conventional impeller. The tip Mach number

was limited to subsonic range to avoid shock losses.

A loss optimization study with a fixed speed and hub diameter was conducted and

included consideration of the following losses:

Impeller friction and turbulence

Impeller dump (mixing)

Impeller disk friction

Impeller axial clearance

Impeller efficiency is given by:

rotor= h Aero- h BL- h SF- h RC- h IN-h mixing

h Aero


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2.2.2Impeller Design Flow Chart

Fig :2.1-Impeller Design Flow Chart

The impeller exit back angle (backward sweep) was fixed or could be made variable.

Design of centrifugal section was a cut and try process where in the meridional shape

and the blade angles were varied to produce a desirable blade loadings. Initial

estimates of blade angle distribution, meridional shape, blockage, and loss

distribution were based on a previous 4:1 pressure ratio conventional impeller design.


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2.2.3 Preliminary Design Performed using Spread Sheet Program.

Table No: 2.1- gives the Impeller Exit conditions by Performing 3 design iterations.


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2.2.4 Boundary Layer Formation:

In any flow through a passage, a layer of low velocity, so called a boundary layer,

grows along the wall due to wall friction, where velocity varies from zero on the wall

to the main flow velocity.

In flow through a diverging passage, the pressure gradient balances with a moderate

change of velocity in the main flow, but the pressure gradient is too steep for the slow

flow in the boundary layer to keep the profile of velocity distribution. As a result the

profile of velocity in the boundary layer is distorted further and the layer gets thick

absorbing a part of the main flow, in worst case a reverse flow occurs near the wall,

and the pressure hardly increases downstream.

Rate of growth of the boundary layer and distortion of the velocity profile depends on

the pressure gradient, and the rate of growth is also proportional to the initial

thickness of the boundary layer. In cases of flow through curved ducts with

rectangular cross section, there is pressure gradient perpendicular to the curved wall,

and in the boundary layer on the flat side-walls cross-flow is induced toward the

lower pressure zone and slow flow accumulates.

2.2.5 Analysis of Impeller Boundary Layer:

Analysis of impeller boundary layer was done with use of calculations. This program

computed the characteristic parameters of two dimensional boundary layer including

compressibility effects and heat transfer to the wall.

The following sections discuss the preliminary and detailed design of the compressor

together with the methods of calculation and assumptions used in the compressor

design. Design point velocity diagrams and state conditions are given for various

stations throughout the stage. The velocity diagrams are deduced from the effective

flow areas dictated by assumed loss at various stations. Blade and Vane geometry and

surface velocity distribution are given for impeller channel diffuser, and bend.


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2.2.6 Impeller Flow Physics:

The flow from the impeller is steady with respect to the rotating system, and a jet

zone and a slow flow zone exist side by side in a pitch of vanes. If the flows, flow out

independently keeping the respective angular momentum, the backward leaning angle

of the slow flow is larger than that of the jet flow, because the radial velocity

component of the slow flow is smaller than that of the jet flow while their

circumferential velocity components are nearly equal. The slow flow or wake flow

and the jet flow must share a common border in the rotating system. Therefore, the jet

flow pushes the slow flow perpendicular to the border, i.e. outward and forward. As a

result the slow flow components are increased. Losing its width it gradually unifies

with jet flow to finally form a uniform flow at impeller exit.

The wake flow with increased circumferential/tangential velocity highly affected a

larger friction force exerted by walls of the stationery diffuser; the pressure loss

becomes larger unless the diffuser is very wide.


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2.3 DESIGN OF DIFFUSER AND BEND

The initial impeller meridional contour was constructed using mathematical curves

for the hub and shroud. An Initial blade shape was constructed by matching blade

angles at the inlet and exit to those required by part-power incidence and blade back

sweep with numerically smoothed curves between line endpoints. Near zero

incidence from free stream to blade mean camber line along the inducer span was

specified at design point to obtain more favorable incidence and consequently,

additional surge margin at part power operation.

A meridional plane flow solution was obtained using computer program. Iterations on

meridional shape, and blade angle distributions along the blade surface were obtained.

In the meridional analysis, the primary objectives were to obtain near-uniform

loading along the shroud meridional length with most of the diffusion occurring

within the inducer. High initial diffusion was considered acceptable because the

boundary layer is most able to withstand the adverse pressure gradient without

separating. Light diffusion along the shroud downstream of the inducer was used in

an attempt to minimize the potential for flow separation, which is most likely to occur

first at shroud section. Velocity peaks and shroud suction surface diffusion ware also

minimized to promote flow stability.

Detailed blade geometry and flow path information output from the final meridional

plane solution were used as input for a blade to blade solution as described. The final

blade angle distribution for the hub, mean and tip sections are shown and blade

surface velocity distributions from the blade to blade solutions for these three sections

are shown.

2.3.1 Vaneless Diffuser

The Vaneless Diffuser is frequently employed in process compressors, and

turbocharger compressors. A reasonable level of static pressure recovery can beachieved with a properly designed vaneless diffuser, which is also inherently

inexpensive. It comprises essentially of two parallel walls forming an open radial

annular passage from the impeller tip to some limiting outer radius. The most

common type of vaneless diffuser is the pinched or reduced area, vaneless diffuser


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which provides a necessary stabilization of the flow. The flow through the Vaneless

diffuser follows the conservation of mass and momentum equations

2.3.2 Channel Diffuser

The primary considerations in the detailed design of the channel diffuser wereincidence for adequate surge margin and throat area required for the design mass flow.

The wall spacing was equal to the impeller exit blade height plus the axial clearance

at impeller exit. At low flow rates the stream tubes diverge providing increased

available flow area, and diffusing flow field results. At high flow rates however due

to acceleration in the inlet region is sufficient to overcome most of diffusion in the

subsequent passage portion, and thus is hard choke and diffuser works like a nozzle.

The static pressure recovery in the Vaned diffuser section is a function of the diffuser

AR (Area Ratio) and throat blockage which measured by the boundary layer

thickness.

2.3.3 Turning Duct

The turning duct geometry is completely specified by two circular surfaces of

revolution, the inner wall radius and outer wall radius. The inlet annulus is specified

at a radial distance from the axis of rotation. Inlet static conditions are those which

correspond to exit of channel diffuser. A particular degree of swirl still remains in the

flow just inside the channel diffuser exit. Rapid expansion, assumed to occur at

constant total pressure, around the channel diffuser trailing edges result in a absolute

flow angle measured from radial direction.

Angular momentum remains relatively constant throughout the turning duct although

the slight increase in the duct streamline radius. The flow solution for the turning duct

was computed using the meridional plane analysis.


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2.4METHODOLOGY:

A C-language program for calculating the off-design performance of centrifugal

compressors with vaneless, channel diffuser and bend is presented. Use of the program

requires complete knowledge of the overall impeller and diffuser geometries.

Individual losses are computed using analytical equations and empirical correlations

which relate loss levels to velocity diagram characteristics and overall geometry. At flow

rates between surge and choke, individual efficiency decrements, compressor overall

efficiency and compressor total pressure ratio are tabulated.

An example case of performance comparison with a compressor built by a commercial

engine manufacturer is presented to demonstrate the correlation with limited

experimental data.

2.4.1 off Design Characteristics

The off-design performance characteristics of centrifugal compressors are of interest

because of the large effects that compressor component performance has on overall

cycle performance and because the compressor is required to operate at off-design

conditions much of the time. These losses become more pronounced at part-power

settings. In addition to good performance at off-design flow rates it is important that

the compressor operate stably over the range of flows and speeds required by the

engine operating envelope.

The usable range of the compressor pressure ratio-mass flow characteristic is

bounded by the surge and choke mass flow rates. Operation at flows less than the

surge point flow should be avoided because of potentially dangerous vibrations

induced by the intermittent flow reversals and power loss. Operation with the

compressor choked is generally avoided because of the poor compressor

efficiency and pressure ratio at the choke point. The problem undertaken in this

analysis is to determine the centrifugal compressor performance characteristics

over a range of rotative speeds and flow rates and predict the usable range of flow

rates at which the compressor can operate.


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The method of analysis uses the loss correlations and surge and choke criteria

added to predict compressor operating range.

The program predicts centrifugal compressor performance through utilization of

empirical correlations which are related to the compressor geometry and velocity diagram

characteristics.

A complete knowledge of the compressor overall geometry and working fluid inlet total

conditions is required for its use. Working fluid state conditions and flow properties are

calculated using a mean streamline one-dimensional analysis.

The program is limited to centrifugal compressors with channel diffusers operating up to

their choke point. A comparison of calculated and experimental performance is given to

demonstrate the correlation with limited experimental data.

The experimental data presented for comparison were obtained from a compressor

developed by NASA Research Centrerefernce [].

Shock losses in the rotor are neglected. Clearance losses are considered to be inherent in

the impeller losses since good performance correlation is achieved on compressors

operating with reasonable clearances.

2.5 METHOD OF LOSS ANALYSIS

Individual losses are calculated using velocity diagram characteristics and empirical

correlations determined by the input absolute velocity level and compressor geometry.

Overall compressor efficiency, total pressure ratio, and mass flow rate are tabulated for

each operating point inside the predicted range for each speed line that is input.


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2.5.1 CALCULATED LOSSES:

Blade loading loss - Boundary layer growth in the impeller is highly dependent on the

diffusion of the working fluid internal to the impeller itself. Equation for calculating the

diffusion factor of the impeller based on a uniform velocity loading along the blade chord.

This equation is used to calculate the impeller diffusion factor for impellers without

splitters. A modified form, with reduced penalty due to aerodynamic work input, is used

for impellers which have a set of splitter blades. With the diffusion factor calculated by

these methods the blade loading loss was expressed

Skin friction loss- In addition to the losses resulting from the aerodynamic loading

Of the impeller blades, the impeller incurs losses due to skin friction of the impeller

and shroud wetted areas. Developed an equation for this loss based on fully

Developed turbulent pipe flow. In the case of impellers with splitter blade rows, the

Empirical constant appearing in the equation is modified to account for the higher mean

Channel relative velocity caused by the addition of splitters. The general equation used

For skin friction loss is

Where KSF = 5.6 for conventional impellers and KSF = 7.0 for impellers with tandem

Blades.


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Disk friction loss- The specific loss due to windage on the compressor back face

is calculated using the equation

Recirculation loss- Losses resulting from work done on the working fluid due to

Backflow into the impeller are expressed as

Vaneless diffuser loss

Vaned diffuser loss - Curves of maximum static pressure recovery coefficient at

Given area ratio were extrapolated from the test data for square throat diffusers reported

For various combinations of vaned diffuser throat Mach number, aerodynamic blockage,

and area ratio. These data were recorded for channel diffusers with symmetrical pressure

Loadings about the channel centerline. The vaned diffuser in a Centrifugal compressor is

loaded with a pressure gradient across the channel. In this Analysis it was assumed that

the difference in the loadings between the test diffusers of and the compressor diffusers

would have no effect on calculated diffuser recovery. A one-seventh power velocity

distribution in the boundary layer along the vaneless space endwalls is used to calculate

the displacement thickness representing vaned diffuser throat blockage. The value ofstatic pressure recovery coefficient Cp corresponding to the vaned diffuser geometric

area ratio, inlet Mach number, and aerodynamic blockage is extrapolated from the test

data. The vaned diffuser exit critical velocity ratio is calculated using one-dimensional

continuity. Vaned diffuser loss is then calculated using the equation


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Calculation of Compressor choking Flow Two criteria are used in the prediction of

compressor choking flow:

(1) Inducer choke.

(2) Vaned diffuser choke.

Vaned diffuser choke is predicted from one-dimensional continuity using the computed

Values of weight flow, total temperature, total pressure, aerodynamic blockage, and the

geometric throat area. The maximum value of the one-dimensional weight flow function

is calculated from the equation

Calculation of Surge:

The vaned diffuser is assumed to be the component which governs the location of the

compressor surge point. Based on a database of a number of compressors covering a

range of pressure ratios indicates that the compressor flow range can be expressed as a

function of vaned diffuser leading edge mach number.


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Fig: 2.2-Compressor Flow range Vs Mach number at Vane diffuser exit

2.5.2 CONCLUDING REMARKS

This section summarizes the pertinent characteristics of the prediction method, discusses

the limitations of the method, and notes the effect of the limitations on the results. For

inducers with relative Mach numbers appreciably in excess of unity the predicted

compressor total pressure ratio and efficiency are greater than that attainable

experimentally. This is a result of neglecting shock losses in the inducer inlet. Predicted

static pressure recovery for vaned diffusers with throat Mach numbers greater than unity

will be too large. Extrapolation of the channel diffuser data used in the program is valid

only in the subsonic flow regime. Compressor total pressure ratio and efficiency are not

adequately predicted with the one-dimensional correlations when the compressor mass

flow rate is limited by the impeller rather than the vaned diffuser. The predicted total

pressure ratio and efficiency levels are higher than those measured experimentally.

Predicted surge point efficiencies are considerably lower than those measured on the

example compressor. This may be due in part to the difficulty encountered in making

precise measurements at this flow condition.

Overall Compressor Efficiency:

h aero- (h incidence+ h blade loading+ h skinfriction Loss

+ h vanelessdiffuser loss+ h vaned diffuser loss+ h bend loss)

h aero+ h recirculation+ h diskfriction loss

=


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CHAPTER-3

Step By Step Procedure for Primary flow calculation

3.1 Impeller Design Validation-

The calculations are performed 4:1 Rc, 404-III single stage Centrifugal Compressor for

use in regenerative gas turbine applications. Its is an Allison Engine Company Design

and details are taken fromReference [1]

Inputs:

Name Location Value

Total Pressureimpellerinlet 101.3 kpa

Total Temperature

impeller

inlet 288.166 K

N impeller 21789 rpmmass flow rate

(mf1)

impeller

inlet 4.391incidence at hub,

tip impeller 50

Radius at tipimpellerinlet 0.105 m

Radius at hubimpellerinlet 0.041 m

Radius impeller exit 0.216 m

Blade width (w2) impeller exit 0.017 mBlade Number impeller 15 blades , 15 splitters

exit clearance impeller exit 0.00023 m

Table No: 3.1-Inputs to Impeller

Assumptions:

Name Location Value

Mach no (initial)impellerinlet 0.3

2b impeller exit 500rotor (initial) impeller 0.86

Mach no (iterated)impellerinlet 0.392

rotor (iterated) impeller 0.918Mach no (initial) impeller exit 0.6Machno(interated) impeller exit 0.919

Table No: 3.2- assumptions made in impeller design


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Calculations:

Impellor inlet mean diameter = D1 = 0.146 m

Impellor exit tip diameter = D2 = 0.432 m

Impellor exit width = W2 = 0.017 m

Rotor speed (design) = N = 21789 RPM

Overall Compressor Pressure ratio = PR = 4

Compressor efficiency = = 0.859

Number of impellor blades = Zb = 30

Blade thickness at the impellor at mean = bt = 0.001 m

Compressor inlet mass flow = mf1 = 4.391 kg/s

Compressor inlet pressure (Total) = Po1 = 101300 Pa

Compressor inlet temperature = To1 = 288.166 K

Impellor exit blade angle = b2 = 500

Compressor inlet enthalpy (determined) = ho1 = 288577.2993 J/kg

Compressor exit enthalpy (determined) = h02 = 467329.6959 J/kg

Discharge coefficient = Cd = 0.97

P02 = P01*(1+(nrotor*ho)/(Cp*T01))k/(k-1)

= 467.253 Pa

nrotor = 0.918 (from loss models)

Area at the impeller exit (Area2) = *D2*W2Zb*W2*bt2 / cos ( b2)

= 0.0228169 m2

Calculation of Impeller exit parameters (Station 2)

Ae2 = Area2 * Cd

= 0.0228169*0.97

= 0.022132393 m2

h = h02h01

= 175894.318 J/kg

U2 = *D2*N/60

= 2* *0.216 * 21789 / 60


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39

= 492.280 m/s

h = U2 * ct2U1 * ct1

h = U2 * ct2

ct2 = 356.888 m/s

Slip factor = SF = ct2 / ct2i

= 1 / (1 + ( cos ( b2) / 2*Zb*(1-

(D1/D2))))

= 0.926

ct2i = ct2 / SF

= 372.445 / 0.926

= 385.408 m/sSlip = ct2ict2

= 385.408356.88

= 28.528 m/s

mf2 = 2 * Ae2 * Cm2

cm2 = mf2/ 2 * Ae2

= 4.391 / 2.37 *0.022= 84.2155 m/s m/s

c2 = ( cm22+ ct2

2)

= (84.21552 +356.882)

= 366.51 m/s

h2 = h02- c22/2

= 467329.6959-(366.51^2/2)

= 400164.9059 J/kg K

Static temperature at rotor exit (t2 ) = 395.148 K

CP2 = 1011.2866 J/kg K

2 = 1.391

a2 = Sonic speed = ( 2R t2)

= 397.17728 m/s


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Absolute Mach No. M2 = c2 / a2

= 0.92

Static pressure at impellor exit (P2 ) = P02/ (1+ (( 2-1) M22/2))

(

2/

2 -1)

= 269154

Pa

2 = P2/ R t2

= 260968/ 287 *397.498

= 2.37334 kg/m3

2 = tan-1

(ct2 / cm2)=

= 76.842

2 = Relative flow angle at impellor exit

= tan-1

(Vt2 / cm2)

= -58.466 ( 2 is

negative

)

Table No: 3.3-Impeller Inlet Exit Calculations

Impeller Inlet Velocity Triangle

Fig:3.1-Inlet Velocity Triangle

1 (deg): 901(deg): 38.4211b (deg): 33.421


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Impeller Exit velocity triangle

Fig: 3.2- Exit Velocity Triangle2 (deg): 13.1582 (deg): 31.5452b (deg): 40

3.2 Vaneless Diffuser Design Validation:

The flow is assumed to befree vortex flowand based on this condition the tangential

component of velocity (ct3) is determined. An initial assumption of absolute velocity (c3)

is made based on the diffusion factor (DF1). Iterations are performed on the absolute

velocity (c3) and Vaneless diffuser exit conditions are determined.

Inputs:

Name Location value

diameter vaneless exit d2*1.08=0.46656 m

width vaneless exit b2*0.98=0.01666 m

mass flow ratevanelessentry mf3=mf2=mf1

Table No: 3.4- Inputs to Vaneless Diffuser

Assumptions:Name Location value

diameter vaneless exit d2*1.08=0.46656 m

width vaneless exit b2*0.98=0.01666 m

mass flow rate

vaneless

entry mf3=mf2=mf1

Table No: 3.5- Assumptions made in Vaneless Diffuser Design


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Absolute Mach No.M3 = c3 / a3

= 0.873

P3 = P03/ (1+ (( 3-1) M32/2))

(

3/

3 -1)

= 276769 Pa

3 = P3/ R t3

= 2.4081 kg/m3

Area3 = *D3*W3

= 0.0237 m2

ae3 = Area3* Cd

= 0.02377

From continuity equation,

mf3 = 3*ae3*cm3

cm3 = 4.391*0.0237*2.4081

= 79.1624 m/s

ct3 = ct2*D2/D3

= 339.894 m/s

mf2 = mf3

ALPHA3 = tan-1

(Ct3/Cm3)

= 76.7703

Angle of radial diffuser blade

leading edge for zero incidence ( 3)

= tan-1

(cm3/ct3)

= 13.11

Table No: 3.6- Calculations made in Vaneless Diffuser Design


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Vaneless Diffuser Pressure Loss

PdrMMaaecfdp ****)sec(*)(cos*

BTcpgUUrrTRhg cos*))***2/()*(1(******

Vaneless Diffuse exit velocity triangle

Fig :3.3- Vaneless Diffuser Velocity Triangle3 (deg): 13.2297

3.3 Vaned Diffuser Design Validation:

The absolute flow angle (4) is fixed from blade geometry. An initial guess of the

absolute velocity (c4) is made based on a value of diffusion factor (DF2). Iterations are

performed on the absolute velocity and vaned diffuser exit conditions are determined.

The loss coefficient is as function of area ratio, length width ratio (LWR) and blockage.

Inputs:

Name Location Value

no of diffuser blades(nrdb) vaned diffuser 24

blade thickness (bt4) vaned diffuser 0.038 mdiameter (d4) vaned diffuser exit 0.72644 m

width (w4) vaned diffuser exitw3=w4 (nopinching)=0.01666 m

mass flow rate (mf4) vaned diffusermf4=mf3=mf2=const=4.391kg/s

absolute angle ( 4) vaned diffuse exit 39.5 calculated from paper

Mach no (m4n) vaned diffuser exit 0.193

Table No: 3.7- Inputs toVaned Diffuser


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Assumptions:

Name Location Value

loss coefficient (LC2)-initial vaned diffuser exit 0.2

coefficient of discharge vaned diffuser exit 0.97

Table No: 3.8- Assumptions Made in Vaned Diffuser Design

Calculations:

DF2=Diffusion factor = 2.265 initial guess

nrdb =number of radial diffuser

blade

= 24

bt3=diffuser blade thickness atentry

= 0.00 mm

bt4=diffuser blade thickness at exit = 0.038 mm

W4=Diffuser width = .01666 mm

mf4=mass flow rate = 4.390 kg/s

ALPHA4=exit blade angle = exit flow

angle desired = 39.5

D4=diffuser exit diameter = 0.726

P04 = P03LC2 (P03-P3)- (reference 1)

= 418062.4516 Pa

C4 = C3/DF2 (initial guess)

h04 = h03

= 467329.6959 J/kg

c4 =

= 82.1176 (iterated) m/s

h4 = h04- c42/2

= 467329.695982.11762/2

= 463958.0458 J/kg

t4 Static temperature at exit for h4 = 453.537 K

a4 = ( 4R t4)

=


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= 453.53 m/s

M4(Absolute flow Mach number) = c4 / a4

= 0.193

P4 = P04/ (1+ (( 4-1) M42/2))

(

4/

4 -1)

= 407393.91 Pa

4 = P4/ R t4

= 3.12 kg/m3

Area4 = *D4*W4nrbd*W4*bt4

= 0.0228 m2

ae4 = Area4* Cd

= 0.02216 m2

Cm4 = mf4 / 4ae4

= 4.391 / 3.02 * 0.02216

= 63.4103 m/s

ct4 = (c42Cm42)

= 52.176 m/s

Table No: 3.9- Vaned Diffuser Calculations

Vaned diffuser exit velocity triangle

Fig: 3.4-Vaned Diffuser Velocity triangle

4 (deg): 50.5


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3.3.1 Best Combination of No of diffuser blades, blade width, flow angle to get

highest Pressure Ratio.

The table below gives the combination of diffuser blades (nrdb), blade width (w) and flow

angle (alpha) for the maximum rise in static pressure ratio in radial diffuser and the compressor

as a whole.

Table No: 3.10- Best Combination of Blades, Width, and Flow Angle for MaximumPressure Rise in a Vaned Diffuser

No ofblades

blade width(m)

Alpha(alp4) P4/P1 (static pressure ratio) P5/P1 (static pressure ratio)

Vaned diffuser exit/impeller inlet Compressor exit/impeller inlet

24 0.038 30 4.20478 4.25476

24 0.038 40 4.17654 4.2011324 0.038 50 4.12072 4.0959

24 0.038 60 3.99098 3.8569

No of bladesblade width

(m)alpha(alp4) p4/p1 p5/p1

18 0.038 30 4.23132 4.28715

20 0.038 30 4.22382 4.278

22 0.038 30 4.21508 4.26732

24 0.038 30 4.20478 4.25476


(inch)alpha(alp4) p4/p1 p5/p1

18 1 30 4.24827 4.30782

18 1.2 30 4.24225 4.3005118 1.4 30 4.23517 4.29186

18 1.6 30 4.22677 4.28159


(inch)alpha(alp4) p5/p1

18 1 30 4.30782 Best Combination


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3.3.2 Calculation of Static Pressure recovery coefficient:

Table 1 is used to calculate Static pressure recovery coefficient (Cpr) Based on the Area

Ratio (AR) and Length/width (LWR) ratio which are obtained from geometric details.

Throat Blockage and other details known, Cpr can be found out.For LWR and AR not matching with the values in column, method of linear

interpolation is used.

Loss Coefficient (LC) = Cpi (Ideal Pressure Recovery)-Cp (static Pressure Recovery)

For calculation of static Pressure recovery coefficientReference[1]

Table No: 3.11-Estimating the Value of Vaned Diffuser Static Pressure Rise Coefficient

by interpolation and Approximation.


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3.4 Bend Desig n Validation:

Primary flow equations:

The flow in the bend is assumed to be free vortex. An initial guess of the absolute

velocity (c5) is made on the basis of diffusion factor (DF3). Iterations are performed onthe absolute velocity (c5) and bend exit conditions are found. A 25% pressure loss

coefficient is assumed.

Inputs:

Name location value

blade width (w5) bend 0.01673606 m

diameter (d5) bend exit d4+0.05*2+w5/2*2 m =0.809 m

inlet radius bend 0.389001

outlet radius bend 0.40432736

mass flow (mf5) bend exit mf4=mf3=mf2stagnation enthalpy bend h05=ho2

mach no bend exit 0.147

Table No: 3.12-Inputs to Bend Design

Assumptions:

Name location value

loss coefficient (LC3)-initial bend exit 0.25coefficient of discharge(cd5) bend exit 0.97

Table No: 3.13-Assumptions made in Bend Design

Calculations:

DF3=Diffusion factor = 1.1

W5=Diffuser width=W4 = 0.01666 mm

mf5=mass flow rate = 4.390 kg/s

D5=vane less diffuser exit diameter = D5 out-0.809, D5 in-0.778 m

LC3=Loss coefficient = 0.25h05=h04 = 467329.6959 J/kg

P05=P04LC3*(P04- P4) = 414862 Pa

ct5 = ct4D4/ D5

= 50.3971 m/s


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c5 = c4 / DF3 (initial assumption)

= 62.7661 m/s

h5 = h05c52/2

= 463390.1126 J/kg

T5 Static temperature

corresponding to h5

= 454.817 K

CP5 = 1020.55 J/kg K

5 = 1.3933

a5 = ( 5R t5)=

= 426.14 m/s

M5 = c5/ a5

= 0.147

P5 = P05/ (1+ (( 5-1) M52/2))

(

5/

5-1

)

= 414861.891 Pa

5 = P5/ R t5

= 3.178 kg/m3

Area5 = *D5*W54

= 0.0386 m2

ae5 = Area5* Cd

= 0.0386 * 0.97

= 0.037 m2

cm5 = mf5 / 5ae5

= 37.4127 m/s

c5new 62.7661 (iterated) m/s


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4W4 / tan (ALPHA4) = 5W5/ tan (ALPHA5)

Since W4 =W5

ALPHA5 = tan-1

( 5/ 4 * tan (ALPHA4))

= 39.0501

Table No: 3.14- Bend Design Calculations

Velocity triangle at bend

Fig: 3.5-Bend Velocity Triangle

5 (deg): 50.94


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Second is the leakage loss referred to as "recirculation", which exists where there

is throughflow, whereby a small proportion of the fluid returns from rotor outlet

to inlet. When there is no rotating shroud, cataloguing of losses becomes much

More confusing. A similar recirculation path exists as mentioned above and also

similar "disc-friction on the rear face (only) of the rotor. But it is no longer

obvious how to treat the remaining effects. Growth of a boundary layer on the

outer side of the flow passage combines in some manner with the zero-through

flow friction on the casing, and additional loss takes place due to peripheral

leakage around the blade tips. The latter is primarily associated with blade loading

and hence with through-flow, so that as noted earlier, tip leakage and

recirculation losses could not readily be distinguished in any experiment.

4.2 Modeling of Recirculation and Disk Friction Loss

For want of a better approach, the method adopted here is to assume that the losses from

boundary layer growth and friction together are the same for an unshrouded rotor as for a

shrouded one. Hence boundary layer growth on the passage outer side is treated in the

same way as on the other sides, additional friction is included corresponding to a double-

sided disc, and a clearance loss is added according to the best available correlation. The

question then arises how to treat the work represented by parasitic losses.In the case of a shrouded rotor, "recirculation loss" can be regarded as involving an

unchanging mass of fluid equal to a small proportion of the through flow, which is

continuously following a cycle of compression in the rotor, expansion along the leakage

path with some heat loss to the casing and rotor, and final cooling by giving up heat to

the through flowing air.

"Disc friction" also heats the casing and rotor. Much of the heat passing to the rotor from

these sources is then absorbed by the through-flowing air progressively throughout its

passage within the rotor. This violates the normal adiabatic state during compression

upon which conservation of rothalpy is based, and leads to an some heat loss to the

casing and rotor, and final cooling by giving up heat to the through flowing air.

"Disc friction" also heats the casing and rotor. Much of the heat passing to the rotor from

these sources is then absorbed by the through-flowing air progressively throughout its


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passage within the rotor. This violates the normal adiabatic state during compression

upon which conservation of rothalpy is based, and leads to a stagnation temperature rise

unmatched by any increase in Euler work additionally there is a quasi-instantaneous

increase in rotor inlet enthalpy due to cooling of recirculation fluid.

4.3 Impeller Boundary Layer Control:

Analysis of the impeller boundary layer was accomplished through the use of a

calculation method. A program computed the characteristics parameters of a two

dimensional boundary layer including compressibility effects and heat transfer. Both

laminar and turbulent flow was handled by the program as well as prediction of

transitions from laminar to turbulent boundary layer conditions. The basic program

required specification of free stream velocity as a function of flow path length. Flow

separation was predicted by a rapid drop off in friction coefficient with length. A wide

variety of test data was used to check program results and agreement in all cases was

excellent.

When examining the impeller, several boundary layer conditions had to be considered.

In the neighborhood of the shroud, a shroud boundary layer was calculated based on the

mean absolute velocity component and corresponding path length. Relative velocities

along the suction and pressure surface at impeller tip were used to define tow additional

boundary-layer conditions along the shroud. In the hub region, suction and pressure

surfaces as well as the mean relative velocities were employed in boundary layer analysis.

The boundary layer on the impeller tended to migrate to the tip and then to the shroud

wall as a result of centrifugal forces. Therefore flow separation on the pressure surface of

the impeller tip would extend into the shroud region and possibly trigger flow separation

across the entire area between blades.


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4.4 Slip Factor:

The slipfactor helps in estimating the energy transfer between the impeller and fluid.

Models of slip factor have been suggested in the past as a function of blade numbers,

flow coefficients, blade angles,etc. The flow pattern in an impeller is very complex due tothe development of secondary flow from the impeller. Eisner slip factor correlation is

most often used.

Weisner Sli p Factor Correlation: =sqrt (1-(cos 2b)) /z 0.7reference []

The slip factor decreases with flow rate. However, the measured and calculated values a

show a contrasting effects which was explained by Eckardt(1980) on account of inertia

effect. i.e. blade design of the impeller, guides the flow nearly to the radial direction until

the backsweep starts downstream between the planes. The increased inertia of a high flow

rate keeps the flow to maintain the strength of the secondary flow up to the impeller exit.

Therefore, the effects of the backsweep on the flow at high flow rate become small. The

deviation angle reduces at impeller exit and the slip factor increases with flow rate.


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4.5 Mixed Flow Calculation Flow Chart:

Fig: 4.1- Mixed Flow Calculation Flow Chart

Solve Secondary Zone equations

considering regions of Secondary flowlosses

Solve primary zone calculations

considering isentropic core flow

Solve Mixing Calculations

Input geometry, N, m

Once Geometry and aerodynamic Inputs constrained create Blade

Model using BladeGen Tool.

Perform Inverse Mean line optimization where in

aerodynamic parameters are fixed and geometry is obtained.

Perform Design Optimization and verify Aerodynamic

inputs/Assumptions


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4.5.1 Impeller Secondary flow calculations:

These calculations are performed on a Test Compressor- HPCC-Reference-[]

= ms/m (20% of core flow)

row2s = row2*1.2 (initial)

= 1-(m(1- )/(cos2b*Ageo*w2*row2))= 0.679

Cm2s = [m/ae2-row2*cm2(1-)]/row2s*

=87.5684

m/s

Ct2s =Ct2s=u2-(cm2s/tan(cos2b)-(1-sf)*u2

= 364.65 m/s

W2s = Sqrt((u2-ct2s)^2*cm2s^2)= 155.25 m/s

hT2s = hT+ disk friction loss

hs2 = hT2s-(2s^2/2)(2^2/2)

= 406919.964 Joules

T2s = h2s/Cp

= 402.29 m/s

row2snew = p2/R/T2s (iterated) m/s

=

= 2.332 Kg/m3

2s = cos(cm2s/w2s) J/kg K

= -55.665 deg

C2s= sqrt(cm2s^2+ct2s^2) K

= 375.01 m/s

To2s = T2s+(c2s^2)/(2*cp2)) J/kg K

= 471.81 m/s

po2s = p2*(To2s/T2)^(g2/(g2-1))

= 496215.63 pascal

Table No: 4.1-Secondary Flow Calculations


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4.6 Mixing Calculations:

Row2m = Row2*1.2 (initial)

Ct2m = (((m-ms)*ct2)+(ms*ct2s))/m;

= 366.2681m/s

cm2m = m/(ae2*row2m)

= 86.44m/s

p2m = p2+((((m-ms)*cm2)+(ms*cm2s)-(m*cm2m))/(area2))

c2m= sqrt (pow(ct2m,2)+pow(cm2m,2));

=376.33 m/s

To2m(((m- ms)*cp2*To2)+(ms*cp2*To2s)+

((diskloss+recir)*ms))/(cp2*array[11]);

= 469.44 KT2m = To2m-(pow(c2m,2)/(2*cp2))

= 399.44 K

row2mnew = p2m/R/T2m (iterated)

= 2.3491po2m = p2m*pow(To2m/T2m,(g2/(g2-1)));

sf=pnunew*((lamdanew-tan(array[7]*torad))/lamdanew);

= 475814.99

= ct2m/cm2m

= 4.23

= ct2m/u2

= 0.74

sf = *(( -tan(cos2b)/ );

= 0.9521

Table No: 4.2-Mixing Flow Calculations


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The mixing process has been realistically computed in order to deduce the levels of

discharge mixing losses and to have basis upon which one can estimate the loss in kinetic

energy due to formation of secondary flow.

The above two equations give the description of impeller flow process on a two zone one

dimensional basis. Computing the mixing process is important. It provides a closure to

the system of equations. Based on the mass averaged total pressure entering the mixing

control volume and the mixed-out total pressure leaving the control volume gives a

measure of the mixing loss. Secondary flow has been modeled as a low momentum or

wake-flow, and its presence at a relative velocity less than isentropic core flow relative

velocity implies a loss in kinetic energy on formation of secondary flow.


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CHAPTER-5

DESIGN VALIDATION

5.1Compressor Design Validation:

The geometric input for the impeller is taken from HPCC input. The incidence angle at

the inlet is kept constant at -5 (deg) from which blade angles are determined.

The Mach no is initially assumed as 0.3 at inlet and 0.6 at exit and iterated to get the

correct value of Mach no.

Impeller efficiency is determined by calculating losses and by subsequent iterations.

Validation Results: Comparison of CFD results with 1D design for HPCC

Reference-[ ]1 2 3 4 5

Total Pressure po(Kpa)

impellerinlet

impellerexit

vanelessdiffuser exit

vaneddiffuser exit bend Pr Ratio

30 blades (1Dcalculation) 101.3 467.253 453.386 418.062 414.862 4.09

(CFD) 101.129 458.936 445.861 420.949 414.328 4.097024592

Total TemperatureTo (K) 1 2 3 4 5 Temp Ratio

30 blades (1Dcalculation) 288.166 462.115 460.626 456.847 456.747 1.5850

(CFD) 288.22 453.91 453.93 454.03 453.99 1.575150926

Static Pressure p(Kpa) 1 2 3 4 5 Pr Ratio

30 blades (1 Dcalculation) 91.0855 269.154 276.769 407.394 408.661 4.48656

(CFD) 89.767 272.875 293.038 397.862 400.453 4.461026881

Static TemperatureT (K) 1 2 3 4 5 Temp Ratio

30 blades (1 Dcalculation) 279.52 395.148 400.46 453.537 454.817 1.627

(CFD) 278.382 392.117 402.448 446.718 449.68 1.615334325Mach No(M) 1 2 3 4 530 blades (1 Dcalculation) 0.392 0.919 0.87124 0.193 0.147

(CFD) 0.421 0.89 0.805 0.273 0.214

Table No: 5.1-Comparision of CFD results With 1D code for Test Compressor-1


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Validation carried out on Test Compressor 1:

Mean Line Flow Modeling based on a compressor tested by Eckardt (1980) available in

the book Introduction to Turbo Machinery by David Japikse.

The Compressor Features an impeller with radial blades at the exit.

The design is Validate by comparing results with the measured results obtained from test

compressor tested by Eckardt.

Table No: 5.2-Comparision of CFD results With 1D code for Test Compressor-2


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Validation carried out on Test Compressor -2:

Compressor design validation by comparing results of design Code with (NASA-TM-

71719) Test Compressor Developed for Energy Research Centre and Development

Agency Automotive Gas Turbine program NASA

Table No: 5.3-Comparision of Test Data Results with Results from 1D code for

Test Compressor-3


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CHAPTER -6

Inverse Design for Centrifugal Compressor using Meanline

6.1 Approach:

This approach is used for determining the optimum geometric parameters of centrifugal

compressor stages given specific performance requirements. This is commonly known as

inverse design approach.

The opposite process, which of calculating the performance parameters based on

geometric details is usually called analysis, or direct calculation. An algorithm and

computer code implementing the inverse approach is described.

As an alternative to commercially available inverse design codes, this program

uses a trusted database of loss models for individual stations, such as impellers,

vaned diffusers, etc.

This algorithm extends applicability of the inverse code by ensuring energy

conversation for any working medium, like imperfect gases. The concept of loss

coefficients for rotating impellers is introduced for improved loss modeling.

The governing conservation equations for each component of a stage are

presented and then described in terms of an iterative procedure which calculates

the required one-dimensional geometry.

A graphical user interface which facilitates user input and presentation of results

is also described. The visibility and re-usability of the code is highlighted as a

platform which easily provides for maintainability and future extensions.

The one-dimensional codes for centrifugal compressor stages have typically solved the

problem of analyzing geometry rather than doing inverse design. Furthermore, many of

these codes have no generalized loss models, but have instead past compressor

performance data tabulated to indicate performance of the machine under study. This

technique works for all cases where the new design is similar to an existing one, but

poorly when the new design differs significantly.


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6.2 Methodology

These codes are used for the design in an iterative manner, that is, the designer inputs the

geometry and sees if the code predicts the desired performance. A final design is thus

arrived at when the desired performance is arrived at. A more direct route to the final

design was thus desired.

These codes use a generalized set of loss models; it was desired to incorporate the basic

idea of these codes with the specific loss models capabilities.

6.2.1 Variation in Aerodynamic Parameters with Impeller Inlet Tip

Radius for an In-house Test Compressor

R1tip(m)

Po2Kpa P2 Kpa To2 K T2 K alpha2 deg M2

rotorEfficiency M1t

0.0265 368199 224121 444.544 386.048 65.89 0.8755 0.82745 0.822

0.027 376191 228825 445.463 386.774 66.4131 0.876255 0.8391 0.722

0.0275 379951 231036 445.891 387.111 66.65 0.876615 0.844575 0.658

0.028 381841 232144 446.133 387.286 66.7694 0.876 0.8472 0.607

0.0285 382593 232586 446.21 387.63 66.8164 0.87688 0.8483 0.567

0.02886 382645 232619 446.228 387.379 66.82 0.876885 0.84845 0.541

0.02886 396248 240552 447.644 388.461 67.6323 0.8783 0.8676 0.541

Table No: 6.1-Variations in Impeller Exit Conditions as a Function of Impeller Inlet Tip

Mach number.


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6.2.2 The plot below shows the variation of impeller inlet tip radius Vs impeller

efficiency

Based on the plot below we can make a reasonable estimate of how much we can twitch

the inlet radius (reduce space) without causing much reduction in efficiency

impeller inlet tip radius Vs rotor efficiency

0.815

0.82

0.825

0.83

0.835

0.84

0.845

0.85

0.855

0.0265 0.027 0.0275 0.028 0.0285 0.02886

impeller inlet tip radius

rotorefficiency

Fig: 6.1-Variation of Rotor Efficiency with Impeller Inlet Tip Mach number

6.2.3 The plot below shows the variation of Impeller inlet tip radius as a function of

impeller inlet tip mach no.The radius at tip should be varied in such a way that the tip mach no at inlet does not go

beyond a critical value of 0.7

impeller inlet tip radius Vs inlet tip mach no

0.0000.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

0.0265 0.027 0.0275 0.028 0.0285 0.02886

impeller inlet tip radius

imp

ellerinlettipmachno

Fig: 6.2- Variation of Inlet Tip Mach number with Impeller Inlet Tip Radius


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6.2.4 The Table Below shows the variation of losses as a function of Imepeller Inlet

Tip Radius.

R1 tipskin loss(joules)

Recirculation(joules)

blade loss(joules)

Disk frictionloss (joules)

incidence loss(joules)

0.0265 19036.4 4151.99 5959.91 2828.17 524.681

0.027 17512.1 4254.82 6116.82 2882.39 145.212

0.0275 16641.1 4344.69 6274.48 2907.88 22.9929

0.028 16072.7 4429.19 6440.35 2920.69 0.69

0.0285 15690.2 4510.3 6612.34 2925.82 30.1134

0.02886 15495.8 4567.22 6739.52 2926.2 72.3906

0.02886 11838 4608.42 7013.33 3017.84 533.209

Table No: 6.2-Various Losses Tabulated as function of Impeller Inlet Tip Radius.

6.2.5 The plot below shows the variation of impeller losses as a function of impeller

tip radiusThe loss distribution can be seen and its variation and dependence on the geometry is

clearly visible

Impeller Loss Vs Impeller Tip Radius

0

2000

4000

6000

8000

10000

12000

1400016000

18000

20000

0.0265 0.027 0.0275 0.028 0.0285 0.0289

Impeller Tip Radius

ImpellerLosses

Skin Loss

Recirculation

Blade Loss

Incidence loss

Fig: 6.3 Plots of Impeller Losses as a Function of Impeller Tip Radius.


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6.3 Other Modes of Operation:

The fundamental purpose of the algorithm presented here is to perform a design

calculation that is to find the geometry given performance.

However, the code can also be run in the analysis mode where performance parameters

are found given geometry.

A mixed mode of calculation, where a combination of some geometry and some

performance are given resulting in a mixture of geometry and performance, is also

possible.

This mode is particularly useful for designers who are trying to modify an existing

machine and have access to some of the geometric information, and some of the

performance conditions. The output is always the full set of geometry, velocities and

thermodynamic properties.

The following describes how each component offers the user the choice of design or

performance parameters.

To begin, for the overall stage the user may input either the power or outlet total

pressure. The user may input either the power or outlet total pressure. The user

may also enter both, but if this is done it is equivalent to setting the stage

efficiency, so efficiency will not be calculated independently through loss models.

For the inlet (station 00), the user may input, in addition to the total conditions,

either the static pressure, cross sectional flow area, or velocity (meridional). The

same is true for the outlet when it is a discharge cone.

For the inlet guide vane, the user may choose either the angle of the vane, or the

preswirl coefficient. Of course the user may also choose a vaneless inlet.


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For the impeller the user chooses either the diameter or the work input coefficient,

either the diffusion factor or outlet width, and either the mass flow rate or the

outlet blade angle. Of the latter, the user may choose both, but doing so is

equivalent to setting the slip so it will not be computed by a slip model.

For a vaneless diffuser, as discussed, the user may choose any tow of outlet

diameter, width, or diffusion factor. For a vaned diffuser any three of diameter,

width, diffusion factor, or outlet angle are chosen.

The basic conservation equations shown above naturally do not change when

code is run in various modes. The iterative algorithm does not change, however,

and must take into account the great many combinations of inputs the user may

wish to run.


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CHAPTER-7

ANSYS-BladeGen

7.1 Introduction to ANSYS BladeGen

BladeGen is a component of ANSYS Blade Modeler. The Blade Modeler software is a

specialized, easy to use tool for rapid 3D design of rotating machinery components. The

software is used to Design mixed flow and radial blade components of Compressor and

Diffusers.

BladGen with its rich set of tools and functionalities for designing a turbo machinery

blade from scratch, using industry-specific tools, workflow, and language that the blade

designer expects.

With BladeGen, the user can re-design existing blades to achieve new design goals orcreate completely new blade designs from scratch. Re-designing or evaluating existing

blade design, BladeGen facilitates the import of blade geometry interactively or through

user supplied files.

Blades were created using Angle-Thickness view and by choosing a radial blade

impeller. Input geometric details were provided in a radial vs. axial plot.

BladeGen allows sculpted or ruled element blades with linear or compound lean

leading or trailing edges.

Over/Under-Filing can be applied and leading and trailing edge shapes are easily

specified as a full radius, an ellipse ratio, or a simple cutoff. BladeGen allows

sculpted or ruled element blades with linear or compound lean leading or trailing

edges. Over/under-Filling was applied and trailing edge shapes are easily

specified at full radius, and ellipse ratio, or a simple cutoff.

With its provision for seamless path to both structural and fluid analysis, which enables

the user to efficiently transition from preliminary blade design, to full 3D viscous flow

analysis, and finally to users native CAD system.


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7.2 Using BladeGen

This BladeGen introduces a method of designing blades that is interactive, allows for

blade section development familiar to the aero-designer.

All the available inputs are geometric in nature but are represented as familiar

aerodynamic parameters. Any preprocessing, separate analysis, or designer experience is

easily communicated to blade model through a robust interface. General stream surfaces

are used to allow for stream surface generation and editing. These curves can be read in

from a file to allow for compatibility with existing flow analysis codes.

7.3 ANSYS BladeGenBlade Pictures

Three Views are made available of the blade generated using BladeGen:

Figure 1

The left most section shows the blade profile and in the blade to blade view. The

Shape and the NACA thickness distribution is clearly visible.

The middle section shows the meridional view of the impeller blade in a

R (radial) Vs (Axial Plot).

The last section shows the Grid View of the Compressor- impeller. The hub and

shroud are clearly visible In this view.

Figure 2

This view shows the impeller in the Grid Form.

Figure 3

This gives the shaded view of the Impeller Blades.


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Fig: 7.1-Blade-Blade View, Meridional View and Meshed View


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Fig: 7.2- Meshed View of Impeller Blade


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Fig: 7.3- Shaded View of Impeller Blade


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CHAPTER-8

Compressor Performance Based on impeller Geometry

8.1 Plots showing Loss Distributions as a function of Geometry.

impeller exitbacksweep angle

skinLoss

Recirculationloss

disk frictionloss

blade loadingloss

incidenceloss

(deg) (joules) (joules) (joules) (joules) (joules)

20 13245.6 5093.72 3075.67 9114.72 72.3906

25 13829.3 4932.69 3036.26 8370.47 72.3906

30 14604.1 4753.58 2985.6 7560.05 72.3906

35 15621.8 4541.79 2917.67 6630.04 72.3906

40 16962 4274.74 2822.77 5519.8 72.3906

45 18761.7 3899.83 2675.54 4097.11 72.3906

50 21311.9 3244.59 2392.66 2057.2 72.3906

Table No: 8.1- Variations of Impeller Losses with Impeller Blade Backsweep

The plot below shows the Variations of individual losses as a function of impeller blade

backswept angle.

Impeller Blade Exit angle VS Impeller Losses

0

5000

10000

15000

20000

25000

20 25 30 35 40 45 50

Impeller Blade Exit angle

ImpellerLosses

(Enthalpyloss)

Skin Friction Loss Recirculation Loss Disk Fricition Loss

Blade Loading Loss Incidence Loss

Fig: 8.1- Plot of Impeller Blade Exit Angle Vs Impeller Losses


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8.2 Plots showing Variation of Impeller Exit Pressure as a function of

Geometry.

Table No: 8.2- Values of Stagnation Pressure are tabulated for Variations in Blade Backsweep

Variation in stagnation pressure rise across impeller plotted as a function of blade

backsweep angle

Blade Backsweep Angle Vs Stagnation Pressure Ratio

0

0.5

1

1.5

2

2.53

3.5

4

4.5

25 30 35 40 45 50

Blade Backsweep

StagnationPressureRatio

Impeller exit

Stagnation Pressure

Ratio

Fig: 8.2- Blade Backsweep Vs Impeller Stagnation Pressure Ratio


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Blade Backsweep Angle Vs Stagnation Pressure Rise

0

100000

200000

300000

400000

500000

25 30 35 40 45 50

Impeller Exit Backsweep Angle

ImpellerExitStagnation

Pressure

Impeller Exit

Stagnation Pressure

Fig: 8.3- Blade Backsweep Vs Impeller Stagnation Pressure Rise


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Fig: 8.1

Rotor

Dynamic

Seals

Bearing-(2)

Computer

aided

Drafting-(1)

Rapid Prototyping-(10)

Numerical M/c

Casting/Molding

CFD PostProcessor-(3)

3D flow

Modeling-(4)

CFDPreprocessor-(5)

3D Geometry

Generation andThrough Flow

Analysis-(6)

CompressorMeanline

Design

Optimization

-(7)Synthesis-(8)

(9)

ComponentDevelopment-1

Product Development-2

Electronic Laboratory-3 Designers

Planning for Product

life, Maintenance and

Support

Design Principles

and Educational Aid

Operational Database

CYCLS CODES

Gas Turbines, Compressors

From Aerodynamic Design of Blades to Blade Fabrication


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CHAPTER-9

9.1 CONCLUSIONS:

The present 1D code correctly predicts the pressure ratio, total temperature

increase and efficiency of centrifugal compressor impeller over a wide range ofoperating conditions.

The loss models used are generalized and can be applied to a number ofcompressors with out modifications.

The flow in the Vaneless, Vaned Diffuser and Bend has been modeled based onCertain Values of Loss Coefficients which have been obtained from Experimental

Plots and Empirical Correlations and hence may not be very accurate.

The Design Validation successfully suggests that the design process has reachedreasonable levels of accuracy but has scope for improvements like theimplementation of Shock Losses when Mach No reaches values > 1.2.

The predicted flow development through the impeller is in good agreement withthe measured data.

The code reasonably simulates the evolution of secondary flow in the impellerwhich affects the jet-wake formation and location. The core of wake region at theimpeller exits near the suction side for the near stall flow rate, and the

shroud/suction side corner for the design and near choke flow rates.

The predicted values of slip factor increase with the flow rate for backsweptEckardt impeller and are in good agreement with measured values.

The mixed out velocity vectors are in good agreement with the values obtainedfrom code except for small differences in the calculated total conditions at the

vaned and Bend exit.

The Generalizations of the correlations imposes restriction on the robustness ofthe code, as the generalizations make reasonable assumptions and hence the

accuracy of the code may be affected slightly.

The exhaustive Testing of the design using Test Compressors from Openliterature implies that the code is robust and generalized and can be used for awide range of compressors.


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9.2 Towards a Better Design:

A plot of various parameters like clearance, incidence angle, Back sweep angle, Bladenumber should be plotted against rotor efficiency to determine the best value of the

parameter to give highest rotor efficiency.

The accuracy of the design depends on the how effectively the losses aremodeled.

Knowing the blade profile and thickness variations of blades will help produce amore efficient design.

The angle of incidence (i=b-) be so chosen that the incidence loss is minimum.The blade backflow angle effects the rotor efficiency, hence a optimum value ofback flow should be used.

The secondary flow and mixing should be considered for more efficient design.

Considerable area blockage would occur in impeller and diffuser blades, henceblockage factor should be considered in the design.

The number of blades and splitters cause variation in impeller pressure rise and

rotor efficiency hence should be appropriately chosen.The pressure loss coefficient is a function of length/width (L/W) ratio, blockageand Area Ratio hence appropriate plots or contours be chosen in its determination.

Slip factor depends on the blade geometry and no of blades and is a critical

component in determining rotor efficiency and stage pressure rise hence for the

determinations of slip factor the best formula should be chosen.

The loss models should be as exhaustive as possible considering all the losses likeblade loading, skin friction, disk friction, recirculation and leakage losses.

There will be considerable loss in the dynamic head during energy transferprocesses like impeller and diffuser, hence the pressure loss coefficients should be

appropriately chosen.

There will be variation in the values of constants like K and Cp; hence appropriateequations should be used to study their variations.

When the Mach no is >1.2 shock losses will occur and the loss models for shockwaves should be incorporated in the design.

The mass flow is assumed constant but there will be slight variations in the massflow rate across the compressor.

9.3 Scope for Future Work

The Design can be made more robust with provision to include Shock Losses.

The accuracy of the design could be improved by using Integration Methods andNumerical Methods.

The number of Stations could be increased to average the flow at these stations togather more comprehensive information about the flow field.

CFD analysis could be carried out in a later stage to ascertain the validity of thedesign.

Inverse Meanline design could be employed to get rough estimates of geometryby aerodynamically constraining it with critical parameters.


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APPENDIX-ASNAPSHOTS:

The following figures show how input is fed on a text file which is read by the Impeller

and Compressor Code:

A.1 Impeller I nputs

The input details to the Impeller are fed in Impeller_inputs.txt. The impeller code readsthe details from this file and performs iterations. The results of the impeller code are

written into a fileimpeller_diffuser_micro.txt.

Fig: A.1-Impeller Input Text File


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A.2 Vaneless ,Vaned and Bend Inputs

The inputs for diffuser and bend calculation are appended on the file created by

the impeller code which has impeller exit conditions already written on the file.The Diffuser (Vaneless & Vaned), Bend geometry are furnished in this file andthe file is read by the compressor code, which performs design iterations to getthe complete compressor details.

Fig:A.2-Vaneless, Vaned Diffuser and Bend Input File


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A.3 VIEW SOURCE CODE:

Fig: A.3-Impeller Source Code


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A.5 Figure below shows the code written for Loss Calculations:

Fig: A.5- Source Code Showing Correlations of Loss Models


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A.6 Figure Below shows the Code for Vaneless diffuser Design:

Fig: A.6- Source Code Showing Correlations For Vaneless Diffuser Design


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A.7 Figure below shows the code for Vaned Diffuser Design:

Fig: A.7- Source Code Showing Correlations For Vaned Diffuser Design


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SNAPSHOTS OF OUTPUT:

A.8 Impell er Output

Fig: A.8- Output of Impeller Design Code


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Reference:

1) Analytical correlation of centrifugal compressor design geometry for maximumefficiency with specific speed by Michael R Galvas, Lewis Research Centre Cleveland-Ohio, March 1972, NASA

2)Coordinates for High Performance 4:1 Pressure Ratio Centrifugal Compressor Ted FMcKain, Greg J Holbrook, Detroit Diesel Allison, Lewis Research Centre NASA, July1997

3) Microjet_design_document, compressor_code-Honeywell

4) Introduction to Turbo machinery- David Japikse, Nicholas C.Baines.

5) Centrifugal Compressor Surge and Speed Control- Jan Tommy Gravdahl,Member,IEEE, and Olav Egeland,Member, IEEE, 5th sept, 1999

6) Method of Performance Prediction for Centrifugal Compressors-M.V Herbert-National Gas Turbine Establishment.

8) Laser Anemometer Measurements of the Flow Field in a 4:1 Pressure RatioCentrifugal Impeller-G.J. Skoch U.S. Army Research Laboratory Lewis ResearchCenter Cleveland, Ohio, June 2-5, 1997

9) Michael R Galvas , A Fortron Program for predicting the Off Design Charactersitics of

a Centrifugal Compressor, November 1973,Lewis Research Centre and US Army Air

sistema de difusor

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