 

E .

 

 

 

 

 

 

 

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Michigan State
University

 

 

 

This is to certify that the

thesis entitled

GRID GENERATION OF VOLUTES USING VISUAL
BASIC

presented by

J oscelyn Wayne Pereira

has been accepted towards fulfillment
of the requirements for

MS degree in Engineering

 

 

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[\
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a] professor

Date December 15', 1998

 

0-7639 MS U is an Afﬁrmative Action/Equal Opportunity Institution

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1M clam-BM“

GRID GENERATION OF VOLUTES USING VISUAL BASIC

By

J oscelyn Wayne Pereira

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1998

ABSTRACT

GRID GENERATION OF VOLUTES USING VISUAL BASIC

By

J oscelyn Wayne Pereira

The design of most volutes, for centrifugal compressors and radial turbines are
based on a linear AIR (cross sectional area by centroid radius) distribution together with
some empirical experience of the designer. Depending on the particular conﬁguration, the
losses in volutes especially at off—design points can be signiﬁcantly high leading to poor
stage efﬁciency. It is strongly believed that volute performance improvements are
possible if an aerodynamic analysis aids the design process. The aerodynamic analysis
could be one-dimensional, two-dimensional or three-dimensional in a form of
computational ﬂuid dynamics (CFD). To analyze a volute aerodynamically, a geometric
model of the volute is required. This geometric model should allow the various volute
parameters to be systematically deﬁned and to be easily varied.

This thesis has developed the necessary mathematical model to deﬁne the
geometry of the volute. The model with its procedures has been programmed in Visual

Basic with the objective of serving as an aid for volute design and performance analysis.

iii

For Mama

ACKNOWLEDGEMENTS

I would like to express my gratitude and appreciation to several persons who have
helped me make this possible. Firstly to Dr. Abraham Engeda, my mentor and friend who
has helped me in pursuing a ﬁeld I was interested in. His technical guidance, support and
encouragement, throughout the course of this work were invaluable and very much
appreciated. To Dr Ranjan Mukherjee and Dr. John McGrath, the committee members for
their advice, suggestions and interest in this work, and for their help and support; and to

Mr. Craig Gunn at MSU for his help in preparing this thesis.

I would also like to specially thank Mr. Geoffrey Bruce and Mr. Jonathan
McGuire from Schwitzer Inc. for their guidance, support and criticism which has helped
me gain a vast amount of knowledge and experience. I also express my gratitude to

Schwitzer Inc. for their support of this project.

A special thank you also for Mr. Sandeep Rao for his numerous criticism,
assistance and friendship in painstakingly going through this thesis. Also to all the other

friendships and great people that have made my stay at Michigan State an enjoyable one.

Last, but certainly not the least, to all my family for their support, help and love,

and especially to mama, who still has her one hand behind me, pushing me all the way.

Friday November 13, 1998 Joscelyn Wayne Pereira

iv

TABLE OF CONTENTS

 

 

 

LIST OF TABLES vii
LIST OF FIGURES - viii
NOMENCLATURE x
CHAPTER 1: INTRODUCTION
1.1 INTRODUCTION ........................................................................................................... 1
1.2 THE NEED FOR A DESIGN TOOL. ................................................................................. 4
1.3 OBJECTIVES AND STRUCTURE OF THIS THESIS. ........................................................... 5
CHAPTERZ: VOLUTES
2.1 INTRODUCTION ........................................................................................................... 7
2.2 DESIGN APPROACH REVIEW ....................................................................................... 9
2.3 SIMPLE THEORETICAL COMPRESSOR VOLUTE DESIGN ............................................. 10
2.4 VOLUTE PERFORMANCE ............................................................................................ 13
2.5 SECONDARY FLOW IN VOLUTES ................................................................................ 14
CHAPTER 3: MATHEMATICAL ELEMENTS
3.1 BEZIER CURVES ........................................................................................................ 16
3.2 VOLUTE CROSS SECTIONS ......................................................................................... 27
3.3 VOLUTE CROSS-SECTIONS WITH BEZIER CURVES. .................................................... 31
3.4 DIFFUSERS/INLET SECTION. ...................................................................................... 37
3.5 GENERATING THE VOLUTE ........................................................................................ 42
3.5 AREA CALCULATIONS. .............................................................................................. 43
3.7 AREA/CENTROID RADIUS CALCULATION. ................................................................. 46
CHAPTER 4: VOLUTE DESIGN - THE PROGRAM
4.1 VOLUTE DESIGN FEATURES ...................................................................................... 47
4.2 FORMS ...................................................................................................................... 51
4.3 SAMPLE DESIGN ........................................................................................................ 79
CHAPTER 5: GEOMETRY VERIFICATION
5.1 INTRODUCTION ......................................................................................................... 85
5.2 GEOMETRY VERIFICATION: ....................................................................................... 86
5.3 DISCUSSIONS: ............................................................................................................ 93
CHAPTER 6: CONCLUSIONS AND FUTURE WORK
6.1 CONCLUSIONS ........................................................................................................... 94
6.2 FUTURE WORK .......................................................................................................... 95
REFERENCES - - 103

 

LIST OF TABLES

TABLE 5.1: VERIFICATION OF COMPRESSOR CIRCULAR CONST. ID ................................... 86
TABLE 5.2: VERIFICATION OF COMPRESSOR CIRCULAR CONST. CENTROID ....................... 87
TABLE 5.3: VERIFICATION OF COMPRESSOR ELLIPTICAL CONST. ID ................................. 88
TABLE 5.4: VERIFICATION OF COMPRESSOR ELLIPTICAL CONST. CENTROID ..................... 89
TABLE 5.5: VERIFICATION OF OPEN FLOW TURBINE .......................................................... 90
TABLE 5.6: VERIFICATION OF TWIN FLOW TURBINE .......................................................... 91

Vi

LIST OF FIGURES

FIGURE 1.1: CROSS SECTION OF CENTRIFUGAL COMPRESSOR ........................................... 03
FIGURE 2.1: TYPES OF VOLUTES ........................................................................................ 07
FIGURE 2.2: BASIC VOLUTE GEOMETRY ............................................................................ 10
FIGURE 3.1: BEZIER CURVE ............................................................................................... 20
FIGURE 3.2: FIRST DERIVATIVE CONTINUITY BETWEEN CUBIC BEZIER CURVES ............... 23
FIGURE 3.3: LINE WITH BEZIER CURVE .............................................................................. 24
FIGURE 3.4: ARC WITH BEZIER CURVE .............................................................................. 24
FIGURE 3.5: CIRCLE WITH BEZIER CURVE .......................................................................... 25
FIGURE 3.6: ELLIPSE WITH BEZIER CURVE ......................................................................... 25
FIGURE 3.7: PARABOLA WITH BEZIER CURVE .................................................................... 26
FIGURE 3.8: GEOMETRY COMPRESSOR CIRCULAR CONSTANT CENTROID .......................... 28
FIGURE 3.9: GEOMETRY COMPRESSOR CIRCULAR CONSTANT ID ...................................... 28
FIGURE 3.10: GEOMETRY COMPRESSOR ELLIPTICAL CONSTANT CENTROID ...................... 29
FIGURE 3.1 1: GEOMETRY COMPRESSOR ELLIPTICAL CONSTANT ID .................................. 29
FIGURE 3.12: GEOMETRY OPEN FLOW TURBINE ................................................................ 30
FIGURE 3.13: GEOMETRY TWIN FLOW TURBINE ................................................................ 30
FIGURE 3.14: SEGMENTS, COMPRESSOR CIRCULAR CONST. CENTROID ............................. 31
FIGURE 3.15: SEGMENTS, COMPRESSOR CIRCULAR CONST. ID ......................................... 32
FIGURE 3.16: SEGMENTS, COMPREZSSOR ELLIPTICAL CONST. CENTROID ......................... 33
FIGURE 3.17: SEGMENTS, COMPRESSOR ELLIPTICAL CONST. II) ....................................... 34
FIGURE 3.18: SEGMENTS, OPEN FLOW TURBINE ................................................................ 35
FIGURE 3.19: SEGMENTS, TWIN FLOW TURBINE ................................................................ 36
FIGURE 3.20: FIRST SECTION OF DIFFUSER FOR COMPRESSORS ......................................... 37
FIGURE 3.21: SECOND SECTION OF DIFFUSER FOR COMPRESSORS ..................................... 38
FIGURE 3.22: OPEN FLOW TURBINE CROSS SECTION AT THROAT ...................................... 39
FIGURE 3.23: OPEN FLOW TURBINE INLET ......................................................................... 39
FIGURE 3.24: TWIN FLOW TURBINE CROSS SECTION AT THROAT ...................................... 40
FIGURE 3.25: TWIN FLOW TURBINE INLET ......................................................................... 41
FIGURE 3.26: AREA, COMPRESSOR CIRCULAR CONSTANT ID ............................................ 43
FIGURE 3.27: AREA, COMPRESSOR CIRCULAR CONSTANT CENTROID ............................... 44
FIGURE 3.28: AREA, COMPRESSOR ELLIPTICAL CONSTANT ID .......................................... 44
FIGURE 3.29: AREA, COMPRESSOR ELLIPTICAL CONSTANT CENTROID .............................. 45
FIGURE 3.30: AREA, OPEN FLOW TURBINE ........................................................................ 45
FIGURE 3.32: AREA, TWIN FLOW TURBINE ........................................................................ 46
FIGURE 4.1: FORM PROFILE ................................................................................................ 51
FIGURE 4.2: FORM GEOMETRY, TAB GENERAL .................................................................. 58
FIGURE 4.3: FORM GEOMETRY, TAB SHAPES ..................................................................... 60
FIGURE 4.4: FORM GEOMETRY, TAB COMPRESSOR ............................................................ 61
FIGURE 4.5: FORM GEOMETRY, TAB TURBINE ................................................................... 63
FIGURE 4.6: FORM GEOMETRY, TAB AXIS ......................................................................... 65
FIGURE 4.7: FORM GEOMETRY, TAB DIFFUSER .................................................................. 66
FIGURE 4.8: FORM ADD NODE ........................................................................................... 68

Vii

FIGURE 4.9: FORM NEW DESIGN ........................................................................................ 69

FIGURE 4.10: FORM OPEN DESIGN ..................................................................................... 70
FIGURE 4.1 1: FORM THREE DIMENSION (SPLASH) ............................................................. 71
FIGURE 4.12: FORM VOLUTE VISUALIZATION [THREE DIMENSION] .................................. 72
FIGURE 4.13: FORM GENERATE FILES ................................................................................ 74
FIGURE 4.14: FORM QUICK VIEW ....................................................................................... 76
FIGURE 4.15: FORM DIMENSION ......................................................................................... 77
FIGURE 4.16: FORM GRAPHS .............................................................................................. 78
FIGURE 4.17: 2-D CROSS SECTION AT 3600 FOR SAMPLE COMPRESSOR DESIGN ................ 80
FIGURE 4.18: SOLID MODEL FOR SAMPLE COMPRESSOR DESIGN ......... 81
FIGURE 4.19: AREA GRAPHS FOR SAMPLE COMPRESSOR DESIGN ...................................... 81
FIGURE 4.20: 2-D CROSS SECTION AT 3600 FOR SAMPLE TURBINE DESIGN ....................... 83
FIGURE 4.21: SOLID MODEL FOR SAMPLE TURBINE DESIGN .............................................. 84
FIGURE 4.22: AREA GRAPHs FOR SAMPLE TURBINE DESIGN ............................................. 84
FIGURE 6.1: MULTI-BLOCK TWIN FLOW TURBINE MESH ................................................... 99
FIGURE 6.2: PRESSURE DISTRIBUTION ON THE WALLS ..................................................... 100
FIGURE 6.3: VELOCITY VECTORS AT A SURFACE .............................................................. 101

viii

waaa~va°v>

Greek

81313-6

Subscripts

noamrswto

RISE-OB

NOMENCLATURE

area

Width or distance along a quasi orthogonal
absolute velocity

mass ﬂow

pressure

radius

radius of volutes

radius of volutes

comer radius

Width of volute

angle along the volute
density

mass ratio

rotational Speed

impeller exit

diffuser inlet

diffuser exit

volute inner surface

volute outer surface

effective compressor mass ﬂow
centroid radius

maximum

recirculating mass flow

throat

tangential component of velocity
recirculating ﬂow

Chapter 1

INTRODUCTION

1.1 Introduction

A volute is used to either distribute or to collect ﬂuid from a rotor. Volute casings
are well established in turbocharger applications. They are cost effective to manufacture
and have an aerodynamic advantage of adapting to a wide operating range. However, the
Shape of such casings takes the role of vanes in guiding the ﬂow into the rotor, and
performance penalties are often paid for incorrect design. However, there is very little
documented data on internal ﬂow measurements in volutes. Because of their complex
geometry and form, detailed ﬂow patterns have not been obtained. Therefore, the effects
of geometrical parameters on performance have not been clariﬁed adequately.

In recent times, turbochargers and turbocharging technologies have progressed
signiﬁcantly. There has been a great deal of research into improvement of compressor
and turbine aerodynamic performance: new bearings, new materials, variable geometry
systems and new control systems. This has all contributed to efﬁcient turbocharged
engine performance.

In the interests of size, cost and response it is usual for automotive turbochargers
to be small, high speciﬁc speed units. The compressor impeller exit flow has high kinetic
energy, typically ﬁfty percent of the total pressure at the impeller exit will be dynamic
pressure and ﬁfty percent static pressure. The diesel engine cannot utilize this level of

kinetic energy and if good stage performance is to be achieved, then it must be recovered

and converted to static pressure before it reaches the engine valves. This recovery must
therefore be attempted in the diffuser after the impeller and in the volute.

The heart of the compressor is the impeller, where all the energy transfer takes
place; it would be the likely suspect for any shortcomings that could occur. Surprisingly,
the designer has had more success with the impeller than with the diffuser or volute
systems. The design of an appropriate diffusing and volute system to slow down the ﬂuid
efﬁciently has been for a long time and still is one of the main difﬁculties in centrifugal
compressor design. The strong demand, by turbocharger users for turbochargers with
good range and efﬁciency, is forcing the turbocharger designer to review the
aerodynamics. Two fruitful sources for potential improvement in turbocharger
performance are in:

0 Proper design of the diffuser and volute, and

0 Good understanding of the factors affecting the stable operating range and

pressure recovery of diffusers and volutes.

Taking the centrifugal compressor as an example, its basic elements are deﬁned as a
stationary casing containing a rotating impeller followed by a radial diffuser as illustrated
in Figure 1.1. The ﬂuid is drawn in through the inlet easing into the eye of the impeller
parallel to the axis of rotation. In a radial compressor for use in gas turbines or
turbochargers this axial portion is usually referred to as the inducer. In order to increase
the angular momentum, the impeller whirls the ﬂuid outwards and turns it in the direction
perpendicular to the rotation axis. As a result, the energy level is increased and both
higher pressure and velocity are achieved. The purpose of the following diffuser is to

convert the kinetic energy of the ﬂuid into additional pressure energy. Following the

Volute

 

K \
\R\\
g
5E

\
\\

\\\\\\\\

/I1‘

Impeller
Shroud
Eye \
——>
—v

 

 

 

 

\

 

A
W //////%‘

n—hduoerSoctlon

Flow

 

 

 

 

 

 

 

 

1N

Figure 1.1: Cross Section of Centrifugal
Compressor

diffuser is a scroll or volute whose function is to collect the ﬂow from the diffuser and
deliver it to the outlet pipe. It is possible to gain a further deceleration and thereby
additional pressures rise in this part of the compressor.

The ﬂow in turbine volutes is of a complex nature, due to the high degree of
turning and curvature, as well as due to the existence of a recirculation region around
what is commonly known as ‘the tongue’, where the ﬂow renters the volute and high
mixing occurs. The function of the volute will depend upon Whether the turbine has inlet
nozzle vanes. If it has, then the volute must simply deliver a uniform gas ﬂow ahead of
the rotor; if it has not, it must also guide the ﬂow ahead of the rotor.

Much of the early work on volute design employed one-dimension, inviscid,
incompressible analysis. This analysis assumed a constant angular momentum, which is
called free vortex ﬂow. Clearly these analysis were not realistic, as they do not take into

account the effects of the geometry, viscosity and compressibility.

1.2 The Need for a Design Tool.

It is seen from the preceding section that improvement in turbocharger component
efﬁciency is an important goal for all turbomachinery designs.

Most of the research work has been concentrated on rotors since they were
considered to have the main effect on turbomachinery efﬁciency. Recent research has
shown the need for new design techniques for the volutes to improve overall
performance.

Turbochargers are some of the smallest machinery that fall under the general
category of turbo machines. In these machines a change in a percentage point in the
efﬁciency is of great importance to the designer. One of the main areas where the
efﬁciency could be improved by efﬁcient and sufﬁcient design, are the volutes for
compressors and turbines.

At present the most common way of designing of volutes emperically, follows the
testing of the volute. The aerodynamic engineer speciﬁes the critical area and supplies
this to the drafting engineer. The draftsman uses the critical area and the linear
distribution of the area (or AIR), generates the cross section shapes, and wraps the volute
around the rotor. The volute casing is then manufactured and is tested. Overall stage
performance across the machine (including the volute) is measured.

Ideally, the test of the volute would like to be done only after a simulation has
proved a design. But this would be possible only if a suitable design tool were available
that would simulate a volute model, which could then be analyzed. The design tool

should then be capable of manipulating the geometry of the volute if an unfavorable

result was obtained. This iteration process is completed once an optimized design is
achieved.

Thus, the design process would be completed and proven analytically with the
analysis of the volute model on a computer before a test could be performed to verify the
expected results, thereby saving the designer, and hence industry valuable time and

TBSODI'CCS.

1.3 Objectives and Structure of this Thesis.

The objective of this thesis is to build a universal design tool applicable to a wide
variety of volute conﬁgurations that would be more powerful and more useful to
practicing design engineers. A design tool that could achieve this would meet the
following requirements.

(1) Easy to understand and use.

(2) Capabile of manipulating the geometry.

(3) Able to analyze the design with the help of necessary packages

(4) Able to export the volute to another package, for e. g. Drafting, Manufacturing etc.

A thoughtfully prepared approach is introduced in this thesis; concentrating on building
the design platform, being able to manipulate the geometry and exporting the volute to
other packages. The design tool is built in Visual Basic, a powerful interactive
programming language available for personal computers. Visual Basic allows for easy
graphical modeling of the volute cross sections through the use of Bezier polynomials. It
is capable of supporting well designed systems with boundless capabilities; and because

it is a Windows based system it is extremely user friendly.

This thesis is divided into six chapters;
Chapter 2, “Volutes”, presents a general overview of volutes, their types and the general
design procedure.
Chapter 3, “Mathematical Elements”, contains the main mathematical elements used to
generate the volute cross sections. This chapter gives detailed explanation of the curves,
the design of the different cross sections, and the various formulas required to calculate
these cross sections.
Chapter 4, “Volute Design — The Program”, is written as a manual for the program. This
provides the help to the terminology used describing different terms. It provides a
detailed description of each screen, their menus and functions.
Chapter 5, “Geometry Veriﬁcation”, attempts to verify the geometry external to Visual
Basic.
Chapter 6, “Conclusions and Future Work”, throws some light on the future course of this
project.
The appendices contain information important to the code. They contain a list of all

subroutines available from the code, as well as some sample ﬁles that the program uses.

Chapter 2

VOLUTES

2.1 Introduction

Volutes are mainly classiﬁed based on their shape. The most common shapes are

circular. Overhang volutes are those volutes where the centroid radius is lower than the

inner volute radius. Figure 2.1 illustrates a few common volutes.

 

 

 

 

 

 

 

 

 

 

 

 

(a) Circular Volute (b) Elliptical Volute (c) Rectangular Volute

~--
‘ -———---

      
 

“

 

 

 

 

(d) Overhang Volute

Figure 2.1: Types of Volutes

Past work has focused on the design of the rotor, while the impact of the volute
conﬁguration on the efﬁciency of a turbo-machine was often neglected. Recent research
work has shown the importance of volute design techniques in further improvement of
the turbo machine performance.

The main object for designing the volute is to provide a uniform distribution of
ﬂow parameters along the circumference at the outlet of the volute so that the blades of
the rotor or the vanes of the stator do not experience ﬂuctuating forces. Reduction or
elimination of such forces would signiﬁcantly increase fatigue life.

Until recently, analytical solutions of the ﬂow ﬁeld in the volute were limited to
one or two-dimensional ﬂow assumptions. Some one and two-dimensional analyses on
the volute cross section planes were performed with various through-ﬂow, velocity
proﬁles. Although these investigations provided some insight about the features of the
flow in the volute, they do not provide a solution for a real three-dimensional ﬂow. A true
three-dimensional analysis is needed since the through-ﬂow velocity proﬁle depends on
both the cross-sectional conﬁguration of the volute and its location along the
circumference.

At the present time, volute designs are still based on one-dimensional ﬂow
calculations. The inlet velocity distribution has been assumed to be uniform across the
volute. However, such assumptions are unrealistic; a variation in the inlet velocity
distribution exists and depends mainly on the volute effects.

To begin a design, the ﬂow within the volute is treated as one dimensional and
free of vortex. From this, the ﬂow area and its centroid at any azimuth angle can be

calculated. The exact shape of the cross section of the volute is, however, left undecided.

A designer must use personal experience in choosing the cross section. One problem
associated with such methods is that because the ﬂow equations are only satisﬁed at the
centroids of the ﬂow passage and not at the wall. The ﬂow at the wall is likely to have

different conditions and velocity vectors from those at the centroid.

2.2 Design Approach Review

In the design of a compressor volute, the main problem is to provide a constant
pressure along the circumference so that a point on the impeller does not experience a
ﬂuctuating force. A simple procedure is to design for constant velocity at volute inlet by
continuity, but for completeness it is necessary to account for frictional and density
effects. The calculation of the circumferential variation of the cross-sectional area of the
volute then becomes elaborate. A full analysis is given by Brown and Bradshow [3].
This calculation procedure furnishes the cross-sectional area but gives no guidance as to
the shape. Brown and Bradshaw [3] also investigated four typical volute forms and
showed that for these four types exactly the same compressor performance was obtained.
On the other hand, Eckert [4] showed that certain volute geometries are more efﬁcient
than others.
Stiefel [5] studied the optimization of the impeller, vaneless diffuser and volute. He
found that with a vaneless diffuser the optimum volute operation was achieved when the
volute was ten to ﬁfteen per cent smaller than that which would be designed through the
frictionless ﬂow assumption. By reducing the size of the volute by thirty percent, he

transformed an unstable performance characteristic to a stable one up to a pressure ratio

of 6.3. This was done by changing the design point of the volute from a pressure ratio of
3.8:1tooneof6:1.

For a radial turbine volute Chapple, Flynn and Mully [6] developed a
performance prediction approach and performed the designs based on it. The large
number of parameters inﬂuencing the performance of a centrifugal compressor volute
prohibit systematic experimental investigation because of the time and cost involved in

the manufacturing and testing of the complex three-dimensional geometry.

2.3 Simple Theoretical Compressor Volute Design

Figure 2.2 Shows typical volute geometry.

b (r)

 

 

la

————5
is
N
x,
N
ix

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.2: Basic Volute Geometry

10

Using simpliﬁed theory, volute ﬂow aims to collect the ﬂow uniformly along the
circumference from (p = 0 to (p = (pm (usually 90m = 3600 —80 = 3520 ).

The mass ﬂow distribution can be described as
m6

 

m(¢) = Wm. (2.1)

Where me is the effective compressor ﬂow and m0 is the recirculating ﬂow through the
tongue gap. Rearranging equation (2.1)

m(¢) = (p + 21. (2.2)
mt? ¢max mC

 

gives a deﬁnition for the recirculating mass ﬂow and for the mass ﬂow ratio as

The recirculating mass ﬂow and

 

m0
_ = #1
mC
The mass ratio
"’( (p ) = M w
mC
Thus
mm = l— + u
gm 2 (2.3)

To determine the optimum path for the outer radius r6 as a function of the angle a , the

conservation of angular momentum is applied as

D (2.4)

rc =—ic =Const
2 U5

ll

Which gives the magnitude of the velocity as dependent on the radius. Applying
continuity of mass through a cross-sectional area dA gives

dm=dAp cu(r) (2.5)

11

dm=b(r)drp Iii-€15- (2-6)
r

The total mass ﬂow through A ( a ) is

m((P)=-Dz—5cu5 j pb(r)-‘-1£ (2.7)

D, r

r:—

A ﬁrst simple solution is to assume that density in the cross-section A ( (p ) is constant,

which gives

 

 

map);i pm)
2

Cu5
mc mc r

] brag—aw») (2.8)
=2; r
2

Using equation (2.3), one of the basic equations of volutes can be obtained as

4’
-——+
" b(r)511_ 09.1,, #2
D5 D5 r D25 p(¢)
”7 7%—
m

C

 

(2.9)

The solution to equation (2.9) describes the distribution of the outer radius r6 as a
function of the angle (a .

A very simple solution is usually to assume constant density circumferentially

p( <0 ) = const = p. = p”. (2.10)

And a rectangular crOss-sectional area

 

 

b(r)=c0nst=bD (2-11)
So that equation (2.9) simpliﬁes to
(P
r, — + #2
I 5’: = 25. film... (2.12)
_05 r [)0 05 Cid
"T T m

12

And can be solved to give the solution

 

 

 

{/1
—+
’0 2'r6 1 ¢max #Z
In r ,5 =ln—=—————— (2.13)
'=_ 05 bD _D5_Cu5 p
2 mc iii
#4:. (2.14)
16“}... " 53"”
D5

The second basic equation for the volute is based on the equation of motion for an

adiabatic, inviscid, and incompressible ﬂow.

2
ﬂ+c— = const (215)
p 2
2
ﬁ+fi=£+ as.) (2'16)
p 2 p 2 r/
p p. c: ,__r_.) 9-1")
p 2 r j

where p, c, r and p are pressure, velocity, radius and density respectively.

2.4 Volute Performance
Detailed published information on the performance of volutes is very limited.
Japikse [7] presented an incompressible ﬂow model for a turbocharger volute. He

established the volute losses through three modeling assumptions as:

13

(a) The kinetic energy associated with the meridional component of velocity at volute
inlet is totally lost.

(b) When the ﬂow through the volute decelerates, the pressure loss is assumed to be
equivalent to that in a sudden expansion mixing loss.

(c) If the ﬂow accelerates through the volute, no pressure loss is assumed.

Weber and Koronowski [8] developed a meanline performance prediction for
volutes. Eckert [4] probably made one of the ﬁrst attempts to account for friction and
secondary losses in volutes. Furthermore, Iverson et a1 [9], Kurokawa [10] and Badie et
al [11] also attempted ﬂow prediction in volutes. A reliable prediction method will be of
great help in determining the inﬂuence of the different design parameters on the volute
ﬂow and losses. However, be it a simple or complex analysis tool, the starting point is a

simple ﬂexible geometry model of the volute cross section.

2.5 Secondary Flow in Volutes

Secondary ﬂows in volutes are understood very little. A large amount of losses in
these components is suspected to be associated with secondary ﬂows.

The ﬂow inside a compressor volute is highly three-dimensional with swirling
ﬂow. A swirling velocity component has an important inﬂuence on the cross-wise and
circumferential variation of the static pressure and velocity distribution. The volute ﬂow
is built up of layers of non-uniform total pressure and temperature in addition to the high
shear forces at the center of the volute, which results in a rotational ﬂow. One and two-

dimensional methods are therefore of limited interest, and are unable to provide a reliable

14

prediction of the circumferential pressure distortion and performance of three-
dimensional volutes.

In turbine volutes, although the accelerating ﬂow suppresses the boundary layer
growth, a strong secondary ﬂow is generated by centrifugal forces in a circulating ﬂow
ﬁeld and inﬂuences the volute internal ﬂow characteristics as well as nozzle exit ones.
The ﬂow is skewed axially and behaves in a complex three-dimensional character. This
three dimensional nature is closely related to the turbine performance when a wide axial
width nozzle is used with a high speciﬁc speed turbine. It is necessary to take the three-
dimensional nature into account in a design to match the nozzle ﬂow with the turbine

rotor. Again, this requires a simple ﬂexible geometry model of the volute cross section.

15

Chapter 3

MATHEMATICAL ELEMENTS

3.1 Bezier Curves
3.1.1 Explicit, Implicit and Parametric Functions.

In this section a brief summary is given of some of the elementary geometry
concepts that are important for an appreciation of the capabilities of Bezier Curves. A
more detailed description is given in reference [2], which is a good introduction to
computational geometry, in particular, Bezier Curves.

The simplest way to deﬁne a plane curve is to use the explicit form y = f ( x )
where f ( x) is a prescribed function of x , enabling us to tabulate and plot the function in
a familiar way.

The explicit form is satisfactory when the function is a single value and the curve
has no vertical tangents. However, this precludes many curves of practical importance
such as circles, ellipses and other conic sections. The general implicit form of a curve is
the equation
(3.1)

f(x.y)=0

where f ( x, y ) is a prescribed function of x and y. It can easily be determined whether
or not a point (x, y ) lies on the curve, but the points on the curve cannot be easily
calculated unless the equation can be reduced to an explicit equation for x or y. For
example, the equation

2 2_2=
x+y r 0 (3.2)

16

is the implicit function for the circle with a radius of r. The value of y is not described

directly as a function of x. If we require an explicit equation, the circle must be divided

into two segments with y = +m for the upper half and y = - r2 -x2 for the
lower half.

An alternative way of describing lines and curves that treats the coordinates x
and y symmetrically is the parametric form. The coordinates x and y are expressed as

functions of an auxiliary parameter u , so that x = f ( u ) and y = g( u ). For example the

circle x2 + y2 = r2 can be express parametrically by the equations

x = eros(u) (3'3)
y = rxSin(u)

where u takes values in the range of 0 S. u S 271 . Although we normally need to describe
the range of the parameter u , this can be of an advantage if we want to describe only a
segment of the curve. The parametric equation enables us to plot points on the curve by
evaluation x( u) and y( u ) for successive values of u.

Because in a design process one needs to determine tangents, normals, curvatures
etc., a parameterization is needed that makes differentiation easy. Polynomial functions
of the parameters are an obvious choice. The n‘“ order polynomial parametric equation is

N n
r(u)=n2=ou an (3.4)
Polynomials of high degree can describe complex curves, but they require a large number
of coefﬁcients whose physical signiﬁcance is difﬁcult to grasp. Thus, they are an
inappropriate tool for the designer. Moreover, the use of high degree polynomials may

introduce unwanted oscillations in the curve.

17

The use of quadratic and cubic (second and third order) polynomial parametric
functions and the physical meaning of their vector coefﬁcients will now be illustrated.
The segment of quadratic parametric curves and surfaces are described by an
equation of the form.
r(u)= a0 + alu + azu2 (3.5)
It can be seen that the three-vector a0 , a1 and a2 are required to deﬁne the segment of a

quadratic curve. In general It vectors are needed to describe a curve of degree (n —1). It

is usual to assign parameter values of u = O and u =1 to the two ends of the segment,

with 0 S u S1 in between. The simplest tool to determine the vector coefﬁcients a0 , al

and a2 is to specify the values of r, dz!“ and 61%“ at the beginning of the segment.
2

Thus
a. = r(0)
ao+al+a2=r(1) (3'6)
al = dr/du(0)
Solving for a0, a1 and a2 we get
a0 = r( O )
a. =(drdux0) (3.7)

a. = r(1)—r(01-(drdu)(0)

By direct substitution in equation (3.6), we can obtain r in terms of r( 0), r(1) and

d
”permits

=r(u)=r(0)(l—u2)+r(1)u2+drdu(0)(u—u2) (3.8)

18

Altemately, we may write the above equation in the form r = [U ][C][S] where U, C and

S denotes the product of the three matrices as given below.

1 O 0 r(0)
r(u)=[1 u u2 0 O 1 dr(l) (3.9)
—l 1 —1 ’du(0)

Cubic parametric equations for the deﬁnitions of curves, for e.g., surfaces in
aircraft design can be described by the equation of the form
(3.10)

2 3
r = r(u) = a0 +alu+a2u +a3u

Following a similar procedure as done above for the parametric quadratic equation we

can write equation (3.10) in terms of the boundary conditions r( O ) , r(1 ) , d’ du( 0 ) and

(1%“ 1) as follows:

 

 

 

1 o 0 o" r(0)
r(u)=[l u u2 u3 0 O l 0 dyrnzo)
—3 3 —2 —1 dd“ (3.11)
2 —2 l 1 b rdu(1)_

3.1.2 Bezier Curves

The vector coefﬁcients of the parametric curves described by the equation (3.4)
can be related to the position of the end points of the curve and to derivatives at these end
points with respect to the parameter u. However, the derivatives With respect to the
parameter u do not have an obvious meaning in the terms of curve geometry concepts
such as Slope and radius of curvature. Moreover, the relationship in terms of derivatives
with respect to the parameter u becomes complex for higher order polynomial curve due
to the many cross couplings as can be seen from the non diagonal elements in the

coefﬁcient matrix in equation (3.11).

19

Bezier [2] has recombined the terms of the polynomial parameterization in a way
that makes the physical meaning of the vector coefﬁcients more apparent. This is of
course most important if we wish to design curves rather than ﬁt them. In Bezier form we
write equation (3.5) as follows:

r=r(u)=(1—u)2r0+2u(l—u)rl +u2r2 (3,12)
where again 0 S u S 1 for any given segment. It can be seen that this simple
rearrangement of the quadratic polynomial form of the equation (3.4) with

do =r0

“1:2(rI-ro) (3.13)
a2 =r0 -2rl +r2

The important consequence of this rearrangement is that
r(0) = r0
r(1) =r2
6%,, (0) = 2(r. — r.)
6%,, (1) = 2(r. — r.)

(3.14)

Thus, the curve described by Bezier form passes through the points r0 , rl and r2 ,
has a tangent at r0 in the direction from r0 to r1 and has a tangent at r2 in the direction

from rI to r2. The straight lines P0P, and 19le form a ﬁgure called the characteristic

polygon P1 '1

P2 r2

P0 r0
Figure 3.1 Bezier Curve

20

of the curve. In order to design a quadratic curve we choose the points P0 and P2 through
which we want the curve to pass and then place Pl so that we get the desired tangents at
P0 and P2.

Similarly equation (3.10) can be written as

3.15
r(a)=(1—u)3ro+3(1—u)2ur,+3(1—u)u2r2+u3r3 ( )
where
a0 =r0
a. =3<r. —r.)
a2 =3(r2-2r,+r0) (3.16)

a3 = r3 —3r2 +3r1—r0

Thus the description of an n"l order Bezier polynomial equation could be written

N

l

r(u) = Emu" (l-u)”‘" r. (3.17)
3.1.3 Properties of Bezier Curves:
(1) The basis functions are real.
(2) The degree of the polynomial deﬁning the curve segment is one less than the number
of deﬁning polygon points.
(3) The curve generally follows the Shape of the deﬁning polygon.
(4) The ﬁrst and last points on the curve are coincident with the ﬁrst and last points of the
deﬁning polygon.
(5) The tangent vectors at the ends of the curve have the same direction as the ﬁrst and

last polygon spans, respectively.

21

(6) The curve is contained within the convex hull of the deﬁning polygon, i.e. within the
largest convex polygon obtainable with the deﬁning polygon vertices.
(7) The curve exhibits the variation diminishing property. Basically this means that the

curve does not oscillate about any straight line more often than the deﬁning polygon.

3.1.4 Changing the order of Bezier Polynomials.

When working interactively, it is often found that a particular curve segment is
not sufﬁciently powerful (that is, does not have sufﬁcient degrees of freedom) to adopt a
desired shape. There are two possible ways to resolve this difﬁculty; the segment may be
split into two or more segments, retaining initially the same shape or a higher order curve
segment, again of the same shape may be substituted. Curve splitting is simple
mathematically and may be advantageous where it is desired to use only curves of up to a
certain order. Increasing the order of a curve does not change the shape of the Bezier

curve. The following easily proved procedure increases the order from N to N +1 .

r*[ " ]= 1 [ir*("'1)+(N+1-n)r*(l]]
N+1 (N+1) N N

where O S n S N +1 and r*[%\ represents the 72'” order Bezier polygon vector of an
2

(3.18)

 

 

N ”' degree Bezier Polynomial.
This process of changing the order of the Bezier polynomial is visually
implemented by adding a control point to the Bezier curve. Thus, by adding a node to the

Bezier polynomial cross section we increase the order of the Bezier Polynomial.

22

3.1.5 Joining Bezier Segments

Additional ﬂexibility can be obtained by subdividing a curve into two or more
Bezier curves, which combined are identical to the original curve. However, slope and
curvature continuity has to be maintained when joining Bezier curves. Continuity
conditions between adjacent Bezier curves are simply speciﬁed. If one Bezier curve P( t )
of degree n is deﬁned by B, vertices and an adjacent Bezier curve Q( s ) of degree m is
deﬁned by C, vertices, then the ﬁrst derivative of continuity at the joint between the
curves is given by

P'(l)=Q'(0) (3.19)

Since positional continuity is implied at the joints, C0 = B". Thus, the tangent vector
directions are the same if the three vertices B“, B" = C0, C1 are collinear; i.e.

Bn( Co ) need only lie somewhere on the line between B and C1. If both direction and

n—1
magnitude of the tangent vectors at the joint are to be equal, then C0 = B" must be the

midpoint of the line joining B,,_l and C,.

Figure 3.2 illustrates this for n = m = 3 , i.e. for two Bezier curves.

B1 82

Prt) 0(1) C3

C1 (:2

Figure 3.2: First Derivative continuity between cubic Bezier curves

23

3.1.6 Lines and Arcs with Bezier Curves

As a Bezier curve is deﬁned by its deﬁning polygon, it is possible to generate
elementary geometrical shapes, such as lines and arcs with Bezier curves.

Thus, a line would require a minimum of two control points (nodes) to be deﬁned

in its entirety, as illustrated in Figure 3.3.

 

Figure 3.3: Line with Bezier curves

Similarly, an arc would be deﬁned by a control polygon consisting of a minimum of three

control points. This is illustrated in Figure 3.4.

 

Figure 3.4: Arc with Bezier curve

24

In a similar way the following have been deﬁned

 

 

 

 

 

Circle:
N6 N5
r ‘ . N4
mi R . N3
I —I— I
NB NS 1‘“ N2
9 ‘ R
Figure 3.5: Circle with Bezier curve
Ellipse:
NS NS
I I I N4 —-T-—

h'b

 

 

 

 

 

 

N9, N1 J 2

9’8 [I

Figure 3.6: Ellipse with Bezier curve

"F
9

T
.l + .
l

 

25

Parabola:

N1 N5

 

 

 

I I
N2 N3 N4

Figure 3.7: Parabola with Boner curve

It is seen from the above ﬁgures, Figure 3.5 for a circle and Figure 3.6 for an
ellipse, that when it is desired to draw a circle of radius R , it is necessary to deﬁne the
control points at g * R , where g is a scalar, also known as the correcting factor. The
‘circle’ thus generates not an exact circle but a close approximation to the circular arc, the

maximum deviation from the mean radius being i 0.5% .

26

3.2 Volute Cross Sections

The volutes for turbines and compressors are designed using Bezier curves. Each
cross section of the volute is made up of different segments comprising of arcs, straight
lines, sections of a circle and sections of parabolas. Each volute comprises of a set of
segments that vary only dimensionally across the volute. The different types of volute
cross sections designed are as listed below.

Compressors:
(1) Circular Constant Centroid
(2) Circular Constant Inner Diameter
(3) Elliptical Constant Centroid
(4) Elliptical Constant Inner Diameter

Turbines:
(5) Open Flow Turbines
(6) Twin Flow Turbines

Each cross section is deﬁned by certain parameters, such as the width of the

volute (S ), radii (R) of circles and arcs, etc. The values of these parameters vary for the

volute cross sections from a section at 300 to a section at 3600. However, the shape of the
cross sections remains unchanged. The values of these parameters are obtained from the
Area by Centroid radius distribution curve and the area at the throat [1].

Below are typical geometrical deﬁnitions that completely deﬁne the cross section

of the volute.

27

(1) Compressor Circular Constant Centroid:

L Widih S _]

Radius Fit

    
   

 

 

 

 

ﬁr’
Radius as g
1‘3
E
E Width p
Width

Figure 3.8: Geometry Compressor CCC -

(2) Compressor Circular Constant Inner Diameter:

r—ML—a

 

 

 

 

P
ll lWidth

Figure 3.9: Geometry Compressor Circular Constant ID

28

(3) Compressor Elliptical Constant Centroid:

Width S

L
‘7 Radius R1

____.L

 

/
Ra ius

 

E
Cent

 

 

 

5mm I. I" 'I Passage
Width
Figure 3.10: Geometry Compressor Elliptical Constant Centroid

(4) Compressor Elliptical Constant Inner Diameter:
’ Erratum...

EWHM
Width

 

 

 

 

 

 

Figure 3.11: Geometry Compressor Elliptical Constant ID

(5) Turbine Open Flow:

 

 

L Width 8 _J
Radius R1
< Radius R2
\ { I Base Circle Radius
j:
33—55mm" 1:: ,1 Lower Base Circle Radius

 

 

 

 

Figure 3.12: Geometry Open Flow Turbine

(6) Turbine Twin Flow:

Width 8

6

\
\‘s

F

 

 

 

 

 

K I Base Circle Radius
r I Divider Wall Radius
MES Width ,1] Lower Base Circle Radlus

 

 

 

 

Figure 3.13: Geometry Twin Flow Turbine

30

3.3 Volute Cross-Sections with Bezier Curves.

The volutes for compressors and turbines are designed using Bezier curves. Each
volute cross section is formed by joining different elementary components of geometry;
namely lines, circles, parabolas and ellipses. Each component is called a segment. These
segments are generated individually with Bezier curves (Refer Section 3.1 E) and the
required volute shape is obtained by joining these segments together. The points of
tangency are maintained between two adjacent segments such that all the segments taken
together appear as a single curve.

The formulation of each volute cross section from its segments using Bezier
Curves are as given below.

(1) Compressor Circular Constant Centroid.

 

 

 

 

 

 

Figure 3.14: Segments, Compressor Circular Const. Centroid

The proﬁle consists of the following segments:

Segment 1: Straight line

31

Segment 2: Span of 2700 of a circle of radius Rl
Segment 3: Straight line
Segment 4: Span of 900 of a circle of radius R3

Segment 5: Straight line
Segment 6: Straight line

Segment 7: Straight Line

(2) Compressor Circular Constant inner Diameter.

 

Se n 2
+ K genera 5
+
__am__t__Se an 3 . £22m;
S n 4
Segment 6

 

 

 

 

Figure 3.15: Segments, Compressor Circular Const. ID

The proﬁle consists of the following segments:

Segment 1: Straight line

Segment 2: Span of 2700 of a circle of radius RI

Segment 3: Straight line

32

Segment 4: Span of 900 of a circle of radius R3

Segment 5: Straight line

Segment 6: Straight line

(3) Compressor Elliptical Constant Centroid.

 

 

 

 

 

 

ﬁgment 3 ' Segment 1
Segment 4
Sggment 7

 

Figure 3.16: Segments, Compressor Elliptical Const. Centroid

The proﬁle consists of the following segments:

Segment 1: Straight line

Segment 2: Span of 2700 of an ellipse with width S and height 2 * Rl
Segment 3: Straight line

Segment 4: Span of 900 of a circle of radius R3

Segment 5: Straight line
Segment 6: Straight line

Segment 7: Straight Line

33

(4) Compressor Elliptical Constant Inner Diameter:

 

 

S ment 2
+ < Segment 5
+ (
Segment 3 . Sggmenti
Segment 4
m: 6

 

 

 

 

Figure 3.17: Segments, Compressor Elliptical Coust. ID

The proﬁle consists of the following segments:

Segment 1: Straight line

Segment 2: 270° of an ellipse with width 5 and height 2 * R,

Segment 3: Straight line

Segment 4: 900 of a circle of radius R3

Segment 5: Straight line

Segment 6: Straight line

34

(5) Turbine Open Flow:

Segment 4 Segment 3

 

 

Segment 5 Segment 2

 

 

Segment 6 Segment 1

1

Figure 3.18: Segments, Open Flow Turbine

 

 

 

 

The proﬁle consists of the following segments:

Segment 1: Half a parabola

Segment 2: Span of approximately 1200 of a circle of Radius R2
Segment 3: Span of approximately 300 of a circle of Radius R,
Segment 4: Span of approximately 300 of a circle of Radius R,

Segment 5: Span of approximately 1200 of a circle of Radius R2

Segment 6: Half of a parabola

35

(6) Turbine Twin Flow:

 

 

 

 

 

ment 4
ant 9
Segment 10
Segment 7
Se ment 11 Se ment 1
>ggr
Segment 6 /

 

 

 

Figure 3.19: Segments, Twin Flow Turbine

The proﬁle consists of the following segments:

Segment 1: Half a parabola

Segment 2: Span of approximately 1200 of a circle of Radius R2

Segment 3: Span of approximately 280 of a circle of Radius R,
Segment 4: One quarter of a circle of Radius R3

Segment 5: Straight line
Segment 6: Semi-circle of diameter equal to the divider wall thickness

Segment 7: Straight line

Segment 8: One quarter of a circle of radius R3
Segment 9: Span of approximately 280 of a circle of Radius R,

Segment 10: Span of approximately 1200 of a circle of Radius R2

Segment 11: Half of a parabola

36

3.4 Diffusers/Inlet Section.

For compressors the section through which the gas leaves the compressor is
known as the diffuser. This is used to diffuse the ﬂow, i.e., converting the kinetic head of
the ﬂuid into pressure head. Similarly, the section into which the gas enters a turbine is
called the Inlet Section. This is used to accelerate the ﬂow of the gas, which then
impinges on the blades of the turbine. The three general cases (i.e., compressors, open
ﬂow turbines and twin ﬂow turbines) are described below.

[Note:] The term ‘diffuser’ as used above should not be confused with the diffuser as in
the overall turbo-machine.
3.4.1 Compressors

We shall consider the case of a compressors ﬁrst. The diffuser section originates

0
from its ﬁrst cross section at 360 of the volute, which is as shown in Figure 3.21

 

 

Cross section at 360 deg.
ﬁrst section of Diffuser

 

 

 

 

Figure 3.20: First Section of Diffuser for Compressors

37

The second section, i.e. the exit of the diffuser is of a circular cross section of radius R ,

refer Figure 3.22

Exit Radius

Figure 3.21: Second Section of Diffuser for Compressors

The diffuser thus transforms from a cross section shape of Figure 3.21 to a circular cross
section as shown in Figure 3.22. This transformation is linear through the length of the

diffuser.

38

3.4.2 Turbine Open Flow

FIRST SECTION OF DIFFUSER

 

 

Tongue tip diameter 3 Base Circle Radius
THROAT

 

——zr
Lower Base Circle Radius

 

 

Figure 3.22: Open Flow Turbine Cross Section at Throat

For an open ﬂow turbine the base of the inlet section (at 3600) is designed up to
the base circle radius as illustrated in Figure 3.23. The ﬁrst section of the Inlet Section is

rectangular in shape and is dimensioned as in Figure 3.24, the inlet section is formed by

varying the cross section varies linearly from the cross section at 3600 (Figure 3.23) to the

ﬁrst section of the Inlet Section (Figure 3.24) over the length of the Inlet Section.

Corner Radius

 

49

Hal ht

 

 

CL D
L Width =l|

I‘
Figure 3.23: Open Flow Turbine Inlet

 

39

3.4.3 Turbine Twin Flow.
The Inlet Section for the Twin Flow turbines are slightly different. The inlet
section comprises of two passages whose cross sections are mirror images of each other

across the dividing plane. We shall consider just one of these two Inlet sections passages.

O
The second section of the Inlet Section i.e. at the cross section 360 of the volute, has the

same shape as the cross section of the volute, with the base at the Base Circle Radius.

 

 

 

 

This is as shown in Figure 3.25.
INLET SECTION INLET SECTION
. . I
Tongue tip diameter I 4 I Base Circle Radius
THROAT I Divider Wall Radius
ﬁr
I Lower Base Circle Radius

 

 

l

Figure 3.24: Twin Flow Turbine Cross Section at Throat

Each passage of the Inlet Section for the twin ﬂow turbines have a rectangular
cross-section at the inlet, the same as in open ﬂow turbines. The complete cross section

for the twin ﬂow turbine at the turbine inlet is as shown in Figure 3.26.

40

Here as well, the cross section transforms linearly for each passage from the cross
section as shown in Figure 3.25 to the section as shown in Figure 3.26 over the length of

the inlet section.

Divider Wall Thickness

 

Comer Radius

 

Heith

 

 

 

 

 

 

Width

7E
4L—

Figure 3.25: Twin Flow Turbine Inlet

41

3.5 Generating the Volute.

The volute is divided into three main regions
(1) The Diffuser (for compressors) or Inlet Section (for turbines)
(2) The Volute

(3) The Throat (only for turbines)
The volute spans from O0 to 3600 for compressors and from 300 to 3600 for turbines. At

every 300 interval, a 2-D cross-section is generated using Bezier curves. The 2-D Bezier
cross sections are generated by specifying the control points that are calculated from the
geometrical data. Thus, by deﬁning a cross section in 2-D and knowng its angle of
location on the volute, we generate the 3-D model of the volute. The region between

sections are then interpolated. The method of interpolation is such that the x and y

coordinates of the node points are interpolated between sections, depending on the
number of sections required (say it ). Thus, the angle between two adjacent sections
would be 360/ it. Using these interpolated values of the node points, a 2-D Bezier cross
section is generated. Its angle of location on the volute being the third axis, a 3-D model
of the volute is thus generated having n number of cross sections.

The diffuser/Inlet Section is generated in a similar way as the volute and is

deﬁned in the preceding article (i.e. Article 3.4)

The region between 00 and 300 for a turbine is known as the Throat. This is the
area that wraps under the Inlet section and back into the volute. The cross section at 300 is
the same as that generated in the volute. The section at 00 is obtained as explained. It is a

0
part of the cross section at 360 . The upper surface is at a position of the base circle

42

radius minus twice the tongue tip radius (Figure 3.23 and Figure 3.25). Thus knowing
these two sections in 2-D the sections between them are linearly interpolated to give 2-D
sections. Then with the angle at which each section lies, the 3-D model of the throat is
created.

Thus, these three regions put together (i.e. the Volute, Inlet Section/Diffuser and

Throat) deﬁne the volute in its entirety.
3.6 AREA CALCULATIONS:

The area is calculated numerically using Green’s Theorem, which is deﬁned as

Area = Ide + Ndy (3.20)
C

The area calculated for each type of volute is as shown below by the shaded section.

(1) Compressor Constant Inner Diameter.

Figure 3.26: Area, Compressor Circular Constant ID

 

 

 

 

43

(2) Compressor Circular Constant centroid.

 

 

 

 

Figure 3.27: Area, Compressor Circular Constant Centroid

(3) Compressor Elliptical Constant Inner diameter.

 

 

 

 

Figure 3.28: Area, Compressor Elliptical Constant II)

(4) Compressor Constant Centroid radius.

 

 

 

 

Figure 3.29: Area, Compressor Elliptical Comtant Centroid

(5) Turbine Open Flow

 

 

Figure 3.30: Area, Open Flow Turbine

45

(6) Turbine Twin Flow

/ /

 

 

 

 

Figure 3.31: Area, Twin Flow Turbine

3.7 Area/Centroid Radius Calculation.
From the above section we calculate the area. The centroid radius is calculated
numerically with the following formula. The centroid radius is about the ‘x’ axis.

.dm (3.21)
M

 

y CR = I
where:

M = mass
Y = Mean distance from the ‘x’ axis.

Thus, once the centroid radius is obtained, the ratio of area to the centroid radius is then

plotted for the cross sections from 300 to 3600 at 300 intervals.

46

Chapter 4

VOLUTE DESIGN - THE PROGRAM

4.1 Volute Design Features
(1) Drawing Bezier curves:

Each cross-section of the volute is generated using Bezier curves. As seen in the
previous article 3.1, Bezier curves give us a great deal of freedom in the shapes we
generate and the ease in increasing the degree of the equation. This program uses Bezier
curves to generate the 2-D cross sections for the different types of volutes.

(2) Specifying Geometry:

When we start a new design, we begin with some deﬁning parameters such as the
AIR ratio, the area at the throat, base circle radius, the passage width, wheel diameters,
corner radii, diffuser dimensions and overall width of the volute. The program provides a
user interface to input all the geometrical and other data, processes them and generates
the required volute.

(3) Changing Node Positions:

The shape of the Bezier curve is determined by its control polngn. The control
polygon is made up of control points also known as node points. Thus, when it is desired
to change the shape of the curve one has to change the node points. The program visually
implements this by allowing the user to manipulate the node points, which is done by the
user clicking the node point, dragging the cursor to the point desired, forming a new

control polygon and thus generating a new Bezier curve.

47

(4) Adding and Deleting Nodes:

Very often, it is desired to increase the degree of freedom of a curve. This is
achieved by increasing the control points in the control polygon for the Bezier curve. The
program allows the user to add a node point, increasing the order of the curve. However
increasing the order of the curve does not change the shape of the curve. Similarly, the
user is allowed to delete a node or control point. Deleting a control point decreases the
order of the curve, making a curve of order n , a curve of order n — I. This results in the
change of shape of the curve and thus the volute.

(5) Referencing Nodes:

While modifying the shape of the volute using Bezier curves, the user views only
one cross-section at a time. The user has a choice of referencing certain number of cross
sections collectively while modifying a selected cross section. These options are:

(a) Reference all cross sections.

This allows the user to simultaneously modify all the sections of the volute from

300 to 3600 while modifying any one cross-section between the two cross sections.
(b) Reference the current cross section.

This allows the user to reference only that cross-section on which one working.
The remaining sections are not affected by ones changes to the working cross section.
(c) Reference between sections.

The user speciﬁes the two outermost cross sections between which changes are to
be reﬂected in.
(6) Hiding/Showing Nodes:

The program allows the user to toggle the display of nodes, while working on a

48

cross-section on the screen.
(7) Area:

The program calculates the area of the displayed cross-section of the volute. The
boundaries and formula for the area calculated could be viewed from section 3.6.
(8) Area Curves:
The program plots two types of area curves and displays them on a new screen, which
could then be printed as output. The ﬁrst curve plotted is an area distribution curve,
which is the area against cross-section angle. The second curve is the plot of the ratio of
the area by centroid radius against the cross-section angle. These are important curves in
the design of a volute.

(9) Viewing Different Sections:

The program allows the user to switch between cross sections from 300 to 360°.
(10) Zooming:

The zoom feature allows the user to zoom into or out of a cross-section view to
enable one to make minor adjustments to the shape of the volute cross section.

(11) 3-D Views:

A three-dimensional object is created using the 2-D cross-section with its angular
location on the volute. Two forms of the 3-D model are available: a wire mesh model and
a solid view model. There are a few features with these models. The user can control the
grid size, view the model from a desired angle of projection, rotate the model with the
help of scrollbars and zoom into or out of the model. The model is also divided into the
Diffuser/Inlet section and Volute. Both these elements can be viewed together or

individually.

49

(12) Dimensions:

A list of the geometrical data that deﬁne the volute cross sections is tabulated for
the drafting or manufacturing of the volute.
(13) Files:

The program generates an output ﬁle of the model. This ﬁle is in a text format
that can be read by other programs. The output ﬁle contains the coordinates of the model,
which are speciﬁed either in rectangular, polar or in spherical coordinates
(14) Documenting a Design:

This feature allows the designer to document a design. Documenting means
saving all the necessary design and geometrical data that could be retrieved and modiﬁed
in the future. Thus, the designer could proceed to improve an already optimized design,
without losing the data of the optimized design.

(15) Open/NewIRun a Design:

This feature gives the user the option of starting a new design, in which all the
parameters are initialized to begin a new design. Alternatively, it can also allow the user
to open a previously documented design. Run is the same as documenting a design, as
described in (N).

(16) Status Panel:

This status panel is displayed at the bottom of the screen. It displays online help
and details about the current design project. Some of the information it displays about the
current project are the type of volute, node numbers, design run number, displayed volute

cross-section and the date and time.

50

4.2 Forms

4.2.1 Form PROFILE

Ele Qu'ckView Zoom ﬁennrehy View leechw yndow Heb
D Y

 

W: 1018“ 0:44PM

Figure 4.1: Form Proﬁle

The form proﬁle is the platform for the design tool Volute Design. It is the form
that supports the volute to be designed, allows for modiﬁcation of the volute cross-
section and is the general interface for the various features of the program. The form
consists of a working area (the grid) in which the volute cross sections are drawn. In this
area the volute can be generated, modiﬁed and documented. Rulers are placed on the two
axis of the grid. Above the grid lie the menu and the toolbar. On the far right of the
toolbar is a display panel. This panel displays the location of the cursor while moving
nodes and while zooming. It also displays some features like ‘Zooming’ or ‘Delete node’

etc. while those commands are executed. On the right of the grid lie the command

51

buttons. Below the grid lies the status bar, which displays the help, and detailed status of
a project design.

The menus command buttons and status bar are now discussed in detail.

4.2.1.1 Menus
1) File
K File

0 New
0 Open
0 Save
0 Redraw
0 Print
0 Exit

New: Starts a new design. Clears the screen and brings up the New Design form
Open: Opens an existing design. Brings up the Open Design form
Save: Saves the current design
Redraw: Clears and redraws the screen. Settings remain the same
Print: Prints the form
2) Quick View
Quick View is a text viewer that allows you to View the ﬁles related to the geometry and
the coordinate ﬁle of the volute. Hard copies (prints) could be taken of the ﬁles.
K Quick View
0 Geometry

0 Output File

52

’ Rectangular
’ Circular
’ Spherical
Geometry: View the geometry ﬁle
Rectangular: View the rectangular coordinate ﬁle
Circular: View the polar coordinate ﬁle
Spherical: View the spherical coordinate ﬁle
[NOTE:] The Output ﬁles can only be viewed after they have been generated i.e. by
running the Generate File, as explained later. Else, these menus are disabled.
3) Zoom

Enlarges or shrinks the screen size.

K Zoom
0 Zoom Box
0 Zoom In
0 Zoom Out
0 Restore

Zoom Box: The zoom box can be created by clicking down on the required top left comer
of the area to be zoomed and dragged till the required zoom box is drawn. Releasing the
mouse zooms the screen accordingly.

Zoom In: Zooms in the picture with a ﬁxed factor

Zoom Out: Zooms out the picture with a ﬁxed factor

Restore: Restore restores the original scale

53

4) Geometry
Displays the geometry form that is used to specify the geometrical and
aerodynamic data for the design of a volute.
5) View
K View
0 Cross Section At
’ 30 ~ 360

0 Dimensions
Cross Section At: (300 ~ 3600) Displays the cross-section of the volute at the desired

0 0
cross-section angle. That is any cross-section angle between 30 and 360 .

Dimensions: Displays the Dimension form. This is the form which you can View the
geometrical data (radii R ,, R2, R3 and width S) necessary for drafting or manufacturing

the volute.
6) TASCFlow

Displays the TASCFlow input form. This form is to be used as an interface to
TASCFlow or any other CFD (Computational Fluid Dynamics) package.
7) Window

Displays a list of all the open windows. When the desired window is clicked, it
becomes the active window.
8) Help

Contains the help ﬁles

54

4.2.1.2 Command Buttons
1) Add Node:

Brings up the Add Node form. This form is used for adding a node (a control point
in the Bezier polygon) to the existing cross-section proﬁle.
2) Del Node:

Deletes a node from the volute cross-section proﬁle. On clicking this command,
the mouse pointer changes to an ‘up’ arrow, which, when placed above the desired node
to be deleted, asks for a conformation before deleting the node.

[NOTE:] For the Add Node and Del Node commands, the changes in adding or deleting a
node is reﬂected in the all cross sections.
3) Add/Rem Node Num:

This button toggles between Add Node Num and Del Node Num. It is used for
displaying or removing the node numbers on the nodes.
4) Hide/Show Nodes:

This button toggles between Hide Nodes and Show nodes. It is used for displaying
the nodes (i.e. Show Nodes) or for removing the nodes from the screen (i.e. Hide nodes).
5) Area:

Calculates and displays the area in a message box for the current volute cross-
section on the screen.

6) Graphs:

Displays the two graphs that are calculated by the program, namely

(a) Area Vs the Cross Section Angle, and

(b) Area/Centroid Radius Vs Cross-Section Angle.

55

These graphs are for the current volute being designed.
7) 3-Dim:

This button displays the 3D View of the volute. It initially displays a splash screen
where the user speciﬁes the grid size. It then calculates the grid and plots the volute on
the Three Dimension form. The Splash form also acts as an update bar, informing the user
of the current progress of execution of the operation.

8) Gen Files:

This command is used for generating an output ﬁle of the coordinates of the
volute proﬁle. It gives the user the choice of the grid size and a choice of the ﬁle type (i.e.
rectangular coordinates, polar coordinates or Spherical coordinates) for the output ﬁle.

9) Run:

This is used for documenting a design. When this command is executed, the
program saves all the necessary data required to save the design. Thus, the same design
could be opened at a later date and modiﬁcations or output ﬁles generated, for the design.
[NOTE] Where executing the Run command, the program saves only the critical data,
thus if any or all output ﬁles are required, the design would have to be loaded using Open

on the ﬁle menu and then generate the output ﬁles.

4.2.1.3 Status Bar

The status bar is designed to provide the user with information related to the
design. It is divided into seven panels, each displaying information about the design
project.

Panel 1: Displays the help for the command buttons

56

Panel 2: Displays the Node Number above that which the mouse is

Panel 3: Describes the volute types (i.e. compressors or turbines)

Panel 4: Displays the shape and geometry of the volute. That is for compressors would
display either Circular or Elliptical and their geometry i.e. Constant Centroid or Constant
Inner Diameter for compressors, or for a turbine whether it is an Open Flow or a Twin
Flow turbine.

Panel 5: Displays the current cross-section being viewed

Panel 6: Displays the current run number of the design

Panel 7: Displays the current date and time

4.2.2 Form GEOMETRY

The Geometry form is the user interface that allows the user to specify the type
and geometrically deﬁne the volute to be designed. The geometry data consists of the
geometry for the volute as well as the diffuser/inlet section. This form is also used to set
certain parameters (such as dimensioning units, type of volute, axis-offset, etc.) that are
used in the design process. Overall, this form is divided into six sub screens (General,
Shape, Compressor, Turbine, Axis and Diﬁuser) that one navigates between with the use

of the Tab control. Each sub screen and its features Shall now be described.

57

4.2.2.1 General

 

Geometry B
General IShapeI Compressorl Ttrb'nel Axis] Diﬂ’userl

 

 

 

 

 

 

 

 

 

—Tvpe: —Referencho:
PWCM PAISections
“@EVE (”BetweenSections
(“BezierSufaces (O‘CtnentSection
ReferenchoBetweenSectlons:

InstSectionAt: 180 v SecondSectlonAt: 270 v

 

 

 

E3 _.m...__lei

Figure 4.2: Form Geometry, Tab General

 

 

 

1) type

This choice speciﬁes the type of curves that will be used to generate the volute
cross-section proﬁle. There are two choices:
(i) Generating the volute by Primitive Curves and
(ii) Generating the curve by Bezier Curves

Generating the volute cross-section proﬁles with Primitive Curves involves
drawing the cross-section using solid geometry. Here the cross sections are divided into
segments in the way as explained in section 3.2. These segments are then drawn by
equations that describe the corresponding circles, parabolas, arcs and straight lines.

However generating the volutes with Primitive Curves does not provide the user

58

with the freedom to modify the volute.

Generating the volute cross-section proﬁles with Bezier Curves involves drawing
the cross-section proﬁles with Bezier curves. The way each cross-section is drawn is
described in section 3.3 Bezier curves allow the user to repeatedly modify the cross
sections to obtain an optimized design.

2) Referencing
Referencing involves to what extent a modiﬁcation in the current cross section, should be
reﬂected in the remaining part of the volute.

When the choice selected is All Sections, the modiﬁcations made on the current
0
cross-section will be reﬂected in all cross sections i.e. between cross-section 30 and

0

cross-section 360 .
When the choice selected is Between Sections, the Between Sections frame gets
enabled, allowing the user to select the two limiting cross sections across which

modiﬁcations to one cross sections should be reﬂected. Thus for example, if a user
0 0 0
speciﬁes between sections 180 and 360 ; then when a cross-section between 180 and

0 0 0
360 is modiﬁed, modiﬁcations are reﬂected in all cross sections between 180 and 360 .
When the choice selected is Current Section, modiﬁcations are only reﬂected in
the current cross section.

3) View Cross Section At

0 0
To specify which cross-section (i.e. any cross-section between 30 and 360)
becomes the current cross section.
4) Dimensioning Units

To specify the dimension units of the design project i.e. Inches, ms or ems.

59

4.2.2.2 Shape

 

General Shape IConpressorI Tub'nel Axisl Diﬂiiserl

 

 

 

 

 

 

Volute:
(0‘ Compressor
r: rubric
-Shape Tatar-es:—
WCrcula (‘0pr
(”W (O‘Twhﬁow
C Ream
i-Geometry:

(3 Constantlmeroiameter

r Constatt Centroid

 

 

 

 

QK I canceII

Figure 4.3: Form Geometry, Tab Shape

 

 

 

Shape, allows the user to specify the type of volute required to be generated. With
a combination of the volute type, volute shape and volute geometry, the user can choose
one of six options of a volute to be generated. These six options are as listed below:
(1) Compressor Circular Constant Inner Diameter
(2) Compressor Circular Constant Centroid
(3) Compressor Elliptical Constant Inner Diameter
(4) Compressor Elliptical Constant Centroid
(5) Turbine Open Flow

(6) Turbine Twin Flow

60

4.2.2.3 Compressor
This sub form is used for inputting the geometrical data for the design of a
compressor.

[NOTE] Please refer to the Figures 38-3. 12 for the speciﬁc geometrical terms.

 

 

General | Shape Compressor | Turb'ne | Axis I Difﬁisa' I
Area at the "root: 524
Area I Centroid Reds: E91
Passage Wm. i Cer'itroid Redus: EB?—
Edge Witth I («hold Rm: 5025
[that Rm: Ikm
Radus R3: 510—
Aree Tolerance: 507
ALL DIIVENSIONS IN INC-ES
QK I Cancel I

 

 

 

Figure 4.4: Form Geometry, Tab Compressor

Area at the Throat: Deﬁnes the critical area at the throat. That is the cross-section at
O

360 .

Area / Centroid Radius: Deﬁnes the ratio of the area at the throat to the centroid radius.

For calculations, the centroid radius is obtained knowing this ratio and the critical area at

the throat.

Centroid Radius = Area at the throat X Area / Centroid Radius (41)

61

Passage Width / Centroid Radius: Deﬁnes the ratio of the passage width to the centroid
radius. For calculations, the passage width is obtained as:
(4.2)

Passage Width

Passage Width =
Centroid Radius

x Centroid Radius

 

Edge Width / Centroid Radius: Deﬁnes the ratio of the edge width to the centroid radius.

For calculations the edge width is obtained as:

Edge Width (4'3)

Edge Width 2 x Centroid Radius
Centroid Radius

 

Inner Radius: Deﬁnes the radius of the inner surface (the volute surface closest to the
centerline). This radius is used only for the geometry type of Constant Inner Diameter.
Radius R3: Deﬁnes the comer radius of the volute.

Area Tolerance: Area tolerance is the tolerance for the area calculated by the program to

the area speciﬁed.

62

4.2.2.4 Turbine
This sub form is used for inputting the geometrical data for the design of a
turbine.

[NOTE] Please refer to the ﬁgure 3.13 and ﬁgure 3.14 for the speciﬁc geometrical terms.

 

Gereral I Shane] Compressor Ttrb'ne IAxisI Diffuser]

Design Area (Area at the Throat):
Area I Centroid Radus:

Rotor Racks (Lower Baa Ode Radus): 1,7195
Tongue Racius (Base Ode Radus):

597'
IL?-
I.—
W
Aero Tb Witth (Passage With): 5175—
rm T'p Rm ﬁns—
Area Tolerance: W-
Divider Wal Rm: W
Divider Wal Tip Radus: 571—-
Divider an we (decrees): FT
Radus R3: EE—

MDINENSIONSININO'ES

 

1:
1g;

 

 

 

Figure 4.5: Form Geometry, Tab Turbine

Design Area (Area at the Throat): Deﬁnes the critical area at the throat. That is at the

O
cross-section at 360 .
Area / Centroid Radius: Deﬁnes the ratio of the area at the throat to the centroid radius.
For calculations, the centroid radius is obtained knowing this ratio and the critical area at

the throat.

Centroid Radius = Area at the throat x Area/ Centroid Radius (4'4)

63

Rotor Radius (Lower Base Circle Radius): Deﬁnes the radius of the rotor wheel. It is
also known as the lower base circle radius.
Tongue Radius (Base Circle Radius): Deﬁnes the base circle radius. This is the radius of
the location of the top surface of the tongue. It is deﬁned as:

Base Circle Radius 2 Togue RR x Rotor Radius + 2 x Tongue Tip Radius (4.5)
Aero Tip Width (Passage Width): Deﬁnes the aero tip passage also known as the passage
width.
Tongue Tip Radius: Deﬁnes the radius of the tongue tip.
Area Tolerance: Area tolerance is the tolerance for the area calculated by the program to
the area speciﬁed.
Divider Wall Radius: This is the radius of the bottom tip of the divider wall. It is also
calculated as

Divider Wall Radius = Divider Wall RR x Rotor Radius (4.6)

(Speciﬁed only for twin ﬂow turbines)
Divider Wall Tip Radius: Deﬁnes the radius of the divider wall tip. It is the equivalent of
the divider wall thickness at its bottom edge (if the Divider Wall Slant Angle is not equal
to zero) or the divider wall thickness, if the slant angle is zero. (Speciﬁed only for twin
ﬂow turbines)
Divider Wall Slant Angle: Deﬁnes the angle to which the walls of the divider wall are
tilted from the normal. It is measured in degrees. (Speciﬁed only for twin flow turbines)

Radius R3: Deﬁnes the corner radius. (Speciﬁed only for twin flow turbines)

4.2.2.5 Axis

 

 

General I Shape I Compressor] Tubine Axis IDiﬂ'user I

 

 

 

 

 

 

 

 

 

 

0 )
+Y l +Y
+Z
‘ x +X_ x +X
-Y .1 v
u 0
Mid X may : Fm Inches
Offset Y AXBBY : Fm Indies
Offset Z AxisBy : Fm Indies

 

LL20:

Figure 4.6: Form Geometry, Tab Axis

 

 

 

This sub form is used for the shifting of the axis. The volute is deﬁned with the
center of the coordinate system at the center of the volute. If required, the volute could be
mated with other components in the overall design layout by moving the center of the
volute (or shifting axis) to the desired location. The axis are offset individually i.e. the X-
axis, Y-axis and Z-axis.

[NOT E:] This is applicable only for designs using the rectangular coordinate system.

65

4.2.2.6 Diffuser

This sub form completely deﬁnes the diffuser. There are three types of diffusers:
one for the compressors (refer section 3.4 A), one for the open ﬂow turbine (refer section
3.4 B) and the split diffuser for the twin ﬂow turbine (refer section 3.4 C). There are two

ways of designing diffusers. These are as described below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ General I Shape] Compressor] Turbinel Axis Diffuser I
mammal: TYPE:Tthlow

~Di‘fuserDesim:
(‘UseAreaRatio GpseExpictGeanetryl
Tmlocationmdemeqees): ET
Di‘fuser Length: [425—
orrtsummmrrset: 53"

-AreaRan:
Area (om ; mt. (Thrall): [2T-
AspectRatio(thhﬁ-leidt): Er—

~ExplctGeomeUy:
fowerExtRadus W—
mum 5'45"—
ormmmm [Es—
fouserExtComer Radix: W

momsrousmmoa
_c_ati_|

 

 

 

Figure 4.7 : Form Geometry, Tab Diffuser
Diffuser Design: One way to design the diffuser is to specify an area ratio in which the

area of the diffuser is speciﬁed as a ratio of the area at the critical area (i.e. at the cross-

section 3600) to the area of the diffuser or by explicitly dimensioning the diffuser. The
option buttons Use Area Ratio calculates the dimensions from the speciﬁed area ratio,

whereas the option button Use Explicit Geometry uses the speciﬁed dimensions by the

66

user to calculate the diffuser geometry. If the option is Use Area Ratio then Use Explicit
Geometry is disabled and similarly vice-versa.

Diﬂ'user Length: Deﬁnes the length of the diffuser.

Diffuser (Flange) Offset: Deﬁnes the distance of the center of the ﬂange of the diffuser
from the Y-axis.

Area (Diﬂ) / Area (Throat): Deﬁnes the ratio of the area of the diffuser to the area at the

throat (i.e. the area at cross-section 360°)
Aspect Ratio: Deﬁnes the aspect ratio i.e. the ratio of the diffuser width to the diffuser
height. (Speciﬁed only for turbines)
Diﬁuser Exit Radius: It is the radius of the diffuser exit. (Speciﬁed only for
compressors)
Diffuser Exit Width: Width of the diffuser inlet. (Speciﬁed only for turbines)
Diffuser Exit Height: Height of the diffuser inlet. (Speciﬁed only for turbines)
Diffuser Exit Corner Radius: Deﬁnes the comer radius of the diffuser inlet. (Speciﬁed
only for turbines)

There are two command buttons on the form Geometry.
OK: This command accepts all the speciﬁed data, processes it and generates the volute.
Cancel: Cancel aborts the processing and returns to the currently active screen.
[NOTE] The term ‘Diffuser’ used above is used to indicate the diffusing element for the
compressor volute as well as the inlet section for turbines. It should not be confused with

the diffuser of the turbo-machine.

67

4.2.3 Form ADD NODE

This form adds a node or control point to the current volute proﬁle. Since one
cross-section is made up of multiple Bezier segments, it provides the user with the option
of the segment to which a node should be added. It provides two pictures. The one on the
left is of the current design screen and the second on the right is a picture of the default
segment breakup with different coloration for ease of the user. Only one node can be
added at a time. Adding a node does not change the shape of the curve; it only provides
the user with an increased degree of freedom.
[NOTE] This desired node point is simultaneously added in the same location across all

cross sections.

 

Add Node

 

Please click the wgment 'n which to add a node.

 

PSegnertl
r‘Segnontz
6W3
rm“
(‘Seonents
4 1| rm“.

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.8: Form Add Node

Segments: This gives the user the selection of the particular segment in which the node

should be added

OK: Takes the user inputs and adds a node to the desired segment

68

Cancel: Aborts adding of node and returns to currently active screen.

4.2.4 Form NEW DESIGN
The form New Design is for initiating a new design project. It obtains information

from the user regarding the name of the project and the path location of the project ﬁles.

 

I] New Design

 

Welcome to Volute Design.
Complete the folowing steps. It wil get you started with a

 

 

 

new design for a vohte.
Project Name : I
Project Path : [czxprogram FilesMcrosoft Visud Studiowasa
Drive : I D c: z]
Diectory : cg‘

 

   
   

Shogun Files
Silicosoft Visual Studo

Cornell uext I

 

 

 

 

Figure 4.9: Form New Design

Project Name: Name of the project

Project Path: Only a display box, displaying the project ﬁle path

Drive: Selection of drive in which the project ﬁles should reside

Directory: Selection of directory in which the project ﬁles should reside

Next: Is highlighted only after a valid project name has been entered. Displays the
Geometry form for the inputting of the geometrical data regarding the new design.

Cancel: Cancels the initialization of a new project

69

4.2.5 Form OPEN DESIGN
The form Open Design is for opening an existing design project. It obtains
information from the user regarding the location and name of the project.

Look for project in : [Q .3 LI

Directory: 801
Fies : (File Type *.svd) l 6305
lDefault.svd

 

 

 

 

 

 

 

 

Project Nunez IVoluteDesign

RmNunber: r-

Cancell Qpenl

 

 

 

 

Figure 4.10: rot-m Open Design

Look for Project in: Selection of the drive in which the project resides.

Directory: Selection of the directory in which the project resides.

Files: Displays a list of all the project ﬁles in the selected directory.

Project Name: Display box only. Displays the project name of the project ﬁle selected
form the Files box.

Run Number: Display box only. Displays the run number of the selected project.

Open: Opens the selected project.

Cancel: Aborts opening of a project and returns to currently active screen.

70

4.2.5 Form THREE DIMENSION
The form Three Dimension, is one of two forms for the viewing a 3-D model of
the volute. The ﬁrst form obtains user input regarding the size of the grid, while the

second form displays the volute model.

 

v'v lhiee Dimension

 

 

 

 

 

 

 

-Grid Size:

NumberofCrossSectlons: 36x11.9x11,9
__ 1 r
1 l I) 1 I g . L I 1 . ‘ I n l

12 180

NtmbaofPoitsonead'iCrossSection:

- 2. [m—

 

 

24 360

 

P' BeGenerate the Grid.

cmml

 

 

 

Figure 4.11: Form Three Dimension (Splash)
Number of Cross Sections: This deﬁnes the number of cross sections desired for the
volute. There are two methods of inputting this data. One, the slider bar could be moved
to the desired number of cross sections, which is constantly updated in the text box to the
right. Alternatively, the desired number of cross sections could be entered directly into
the text box. The limiting values are displayed below the slider bar.
Number of Points on each Cross Section: This is the total number of points that make up
a single cross section. The methods of inputting the data are similar to the Number of
Cross Sections.
ReGenerate the Grid: Checking this box forces the program to regenerate the grid each
time the 3-D model is desired to be viewed. If this is not checked, the last model in the

program’s memory would be displayed.

7]

Continue: Brings up the Volute Visualization — [Three Dimension] form that displays the
3-D model.

The form Volute Visualization — [Three Dimension] displays the 3-D model and
has the capabilities apart from viewing the model, to zoom in or out, to view different

parts of the volute, to View the volute at different projections and to rotate the model.

 

 

Figure 4.12: Form Three Dimension

4.2.5.1 Functions

1) Left Scroll Bar: This is the zoom bar. Moving the pointer up zooms in, while moving
it down zooms out.

2) Right Scroll Bar: The right scroll bar is for rotating the model about the X-axis.

3) Bottom Scroll Bar: The bottom is scroll bar is used for rotating the model about the Y-

axis.

72

4.2.5.2 Menu:

1) File
K File
0 Print
0 Close

Print: Prints the form
Close: Closes the Volute Visualization — [Three Dimension] form and returns to the
currently active window
2) View
The view menu is for viewing the model at different angles of projection. The
different available angles of projection are Front, Back, Side, Diffuser Down, Oﬁset
Front, Oﬂset Back and Offset Side.
3) Options
K Options
0 Show Volute Core
0 Show Diffuser
- Wiremesh Volute Core
0 Wiremesh Diffuser
Show Volute Core: Toggle button that displays or removes the volute core section
Show Diﬁ‘user: Toggle button that displays or removes the diffuser section
Wiremesh Volute Core: Toggle button that displays the volute core as a Wiremesh model

or as a solid model

73

Wiremesh Drﬁ’user: Toggle button that displays the diffuser section as a Wiremesh model

or as a solid model

4.2.6 Form GENERATE FILES
The form Generate Files is for generating the output coordinate ﬁles. The user
speciﬁes the grid size of the volute model, and the ﬁle type desired. The program assigns

the ﬁle name and generates the ﬁle.

 

5 Generate files B I

~HeType:

 

 

(0‘ Pectanqdar (X YZ) Coordinates}

 

t‘ Clyhdrical (R Theta 2) Coordinates.

t" Sphericd (R Theta no Coordinates. Outpttﬁu
lTest_O.xyz

 

 

 

36 x 11.7 x 11.7

 

 

\p
OI

 

 

 

 

l7 BeGenerate the Grid

 

 

 

Generate I Cancel

 

 

 

 

Figure 4.13: Form Generate Files
File Type: This is for the coordinate system of the output-generated ﬁle. The user
speciﬁes one of the three choices of coordinates namely, rectangular, cylindrical or

spherical coordinates.

74

Output File: Only a view box. Gives the name of the output ﬁle. The output ﬁle is saved
in the same directory as the project.

Number of Cross Sections: This is the number of cross sections desired for the volute.
There are two methods of inputting this data. One, the slider bar could be moved to the
desired number of cross sections, which is constantly updated in the text box to the right.
Alternatively, the desired number of cross sections could be entered directly into the text
box. The limiting values are displayed below the slider bar.

Number of Points on each Cross Section: This is the total number of points that make up
a single cross section. The methods of inputting the data are similar to the Number of
Cross Sections.

ReGenerate the Grid: Checking this box forces the program to regenerate the grid each
time the 3-D model is desired to be viewed. Otherwise, the last model in the programs
memory would be displayed.

Generate: Generates the output ﬁle.

Cancel: Aborts the operation to generate a ﬁle and returns to the currently active screen.

75

4.2.7 Form QUICK VIEW

This form is a text viewer and allows the user to view the geometry ﬁle or the

coordinate ﬁles generated.

GEOMETRY
Geometry Fam Vales ‘
ClIVB Type:

Bezier Ctrves

Refermchg:

Curmt Section

Between Secticne : Fret Section:

130

Between Sections : Second Section:

270

View Croce Secttm At:

:50

Dimenstnhg mils:

Vow:
Comm
Shape: :J

 

 

 

 

Figure 4.14: Form Quick View

Title: Name of the ﬁle being displayed

Print: Prints the form

Close: Closes the form and returns to last currently active screen

76

4.2.8 Form DIMENSIONS

This form displays a tabulated list of the geometrical data (radii R,, R2, R3 and
width S) necessary for to specify the volute. It displays the list at of radii and width at

0
every 30 cross-section interval. These dimensions are useful for the drafting of the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

volute.
% Dimensions
Velma IDiﬁ’userI Momensimshmo-Es
c. Section Radus R1 I Radius R2 I Radius R3 | width 5
30 ° 0.244 0.000 0.100 0.487
60 ° 0.345 0.000 0.100 0.689
90 ° 0.422 0.000 0.100 0.844
120 ° 0.487 0.000 0.100 0.975
150 ° 0.545 0.000 0.100 1.090
180 ° 0.597 0.000 0.100 1.194
210 ° 0.638 0.000 0.100 1.277
240 ° 0.683 0.000 0.100 1.365
270 ° 0.724 0.000 0.100 1.448
300 ° 0.755 0.000 0.100 1.511
330 ° 0.792 0.000 0.100 1.585
360 ° 0.828 0.000 0.100 1.655
_—————.____—_———-—-——-_____—
Erht I Close I
Figure 4.15: Form Dimension
Print: Prints the form

Close: Closes the form and returns to currently active screen

4.2.9 Form GRAPHS

This is an ‘output’ form. It displays the two graphs of the area distribution that are
necessary to design the volute. The ﬁrst graph (above) is the graph of the area against the
cross section. The second graph (below) is the graph of the ratio of the area by centroid

radius against the cross-section angle.

 

I@

 

 

 

 

 

 

 

 

 

 

 

 

FieOptions
AREAVS CROSS SECTIMMEPLOT
lllllllllllllllllllllllll
0 so so 9.0 no 12 LL 212 m m 32 no at
J AREA] CENTROID RADIUS Vs CROSS SECTICNMEPLOT
633
m
lllllllllllTlllllVlTlTll
o 30 s_0 8_0 120 in) i 210 240 270 :13 _ £0
Figure 4.16: Form Graphs
A)Menu:
l)File
K File
0 Print
0 Close

Print: Prints the form

Close: Closes the form and returns to the currently active screen

78

2) Options
K Options

0 Grid

Grid: Toggle switch that displays the grid or removes the grid

4.3 Sample Design

We shall now model two sample volutes. One for a compressor and the other for a

turbine. Their geometry, 2—D cross-section at 3600, their 3-D views (solid) and their area

graphs are given below. The geometry is the input data for the Geometry form.

4.3.1 Compressor
1) Geometry:
Curve Type:

Referencing:

View Cross Section At:

Dimensioning Units:
Volute:

Shape:

Compressor Geometry:

X offset:

Y offset:

Z offset:

Area at the Throat:

Area/Centroid Radius:

Bezier Curves
Current Section
360

Inches
Compressor
Circular
Constant Centroid
0.00

0.00

0.00

2.24

0.91

79

Passage Width/Centroid Radius: 0.05

Edge Width/Centroid Radius: 0.025

Inner Radius: 1.80

Radius R3: 0.10

Area Tolerance: 0.07

Diffuser Design Type: Use Explicit Geometry
Diffuser Exit Radius: 1.25

Diffuser Length: 4.25

Diffuser (Flange) Offset: 3.625

2) 2-D Cross Section:

 

 

 

0
Figure 4.17: 2-D Cross section at 360 for sample
compressor design

80

3) Solid Model:

 

Figure 4.18: Solid model for sample compressor design

4) Area Graphs:

 

Figure 4.19: Area graphs for sample compressor design

81

4.3.2 Turbine

1) Geometry:

Curve Type:
Referencing:

View Cross Section At:
Dimensioning Units:
Volute:

Turbine Geometry:

X offset:

Y offset:

Z offset:

Area at the Throat:
Area/Centroid Radius:
Base Circle Radius:
Passage Width:

Area Tolerance:

Lower Base Circle Radius:

Radius R3:

Divider Wall Tip Radius:
Divider Wall Slant Angle:
Divider Wall Radius:
Tongue Tip Radius:

Diffuser Design Type:

Bezier Curves
All Section
90

Inches
Turbine
Twin Flow
0.00

0.00

0.00

3.93

1.256
2.0977
0.6115
0.01
1.7198
0.50

0.1 l

0.00

1.884

0.06

Use Explicit Geometry

82

4.25

Diffuser Length

3.46

Diffuser Exit Width

2.38

Diffuser Exit Height

0.62

Diffuser Exit Corner Radius

3.625

Diffuser (Flange) Offset

2) 2-D Cross Section

.a... .. .....-...._.._......- *.,-_ _.., V
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. . . . H e _ .
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4»

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i
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- -+- - . A.........-..-' -.-.—..'--.-~-.-.-..... .. - -e._
~ ' ‘. : ‘ . i
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-C..._. ....»....,. --__.-- . .1

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0

Figure 4.20: 2-D Cross section at 360 section for sample turbine design

." . .
. w .
.1, ..1 .
e .a x
,. 111 4... 1
. . . ,, c H
.. h d a u .
n . H m . a. J u
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+. . .. .e .e 1 . 1.4. A 1:“... 1 . L s 1.
. . _ . . . a
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83

3) Solid Model:

 

Figure 4.21: Solid model for sample turbine design
4) Area Graphs:

 

Figure 4.22: Area graphs for sample turbine design

84

Chapter 5

GEOMETRY VERIFICATION

5.1 Introduction

This chapter, geometry veriﬁcation of the volute, is a check of the Visual Basic
program that has been developed to show that the program generates the volutes that
conform to existing standards. The procedure to verify the volutes compares a volute
generated by the Visual Basic program to the same volute that has been generated by
another software that could check the necessary dimensions. This calibration is
important, as the veriﬁcation should be made outside of the Visual Basic program. This is
due the fact that any errors generated by the Visual Basic program are not compounded
during the veriﬁcation.

The veriﬁcation is done using the software package FIELDVIEW. FIELDVIEW
is an interactive data visualization package that assists in the investigation of complex
three-dimensional ﬂuid dynamic data sets. FIELDVIEW is a leading visualization
package designed speciﬁcally for CFD data. Unlike most plotting applications,
FIELDVIEW is built upon a full 3D data handling capability, with comprehensive
support for both structured and unstructured grids.

The critical design criteria, namely the area and the centroid radius, are measured

at four cross section locations: 360°, 2700, 1800 and 90°. Measurements of area and

centroid radius at these locations are made in FIELDVIEW and then compared with the

85

results obtained from the visual basic program developed. The comparisons are made in a

tabular format that displays the percentage errors alongside.

5.2 Geometry Verification

The veriﬁcations have been performed for compressors as well as turbines, as listed

below:

(1) Compressor Circular Constant Inner Diameter:

Table 5.1: Verification of Compressor Circular Const. ID

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION
Volute Compressor
Type Constant Inner Diameter
Shape Circular
Area at Throat 1.63
Area Throat / Centroid Radius 0.6
Passage Width / Centroid Radius 0.05
Edge Width / Centroid Radius 0.025
Inner Radius 1.8
R3 0.1
Area Tolerance 0.01
RESULTS
Design Criteria Model VB Model % Error
(Inches) (Inches)
Area - 360° 1.6297 1.6203 0.58%
Area - 270° 1.2181 1.2103 0.64%
Area - 180° 0.8037 0.798 0.71%
Area - 90° 0.3971 0.3884 2.19%
Radius - 360° 2.4558 2.4601 «0.18%
Radius - 270° 2.3681 2.3722 -0.17%
Radius - 180° 2.2632 2.267 —0.17%
Radius - 90° 2.129 2.1368 -0.37%

 

86

 

(2) Compressor Circular Constant Centroid

Table 5.2: Verification of Compressor Circular Const. Centroid

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION
Volute Compressor
Type Constant Centroid
Shape Circular
Area at Throat 1.63
Area Throat / Centroid Radius 0.6
Passage Width / Centroid Radius 0.05
Edge Width / Centroid Radius 0.025
Inner Radius 1.8
R3 0.1
Area Tolerance 0.01
RESULTS
Desi Model VB Model
Criteﬁila (Inches) (Inches) % Error
Area - 360° 1.6208 1.6231 -0. 14%
Area - 270° 1.2047 1.206 -0.11%
Area - 180° 0.7878 0.788 -0.03%
Area - 90° 0.3729 0.3718 0.29%
Radius - 360° 2.6224 2.6226 -0.01%
Radius - 270° 2.6382 2.6384 -0.01%
Radius - 180° 2.6572 2.6568 0.02%
Radius - 90° 2.683 2.6825 0.02%

 

87

 

(3) Compressor Elliptical Constant Inner Diameter

Table 5.3: Verification of Compressor Elliptical Const. ID

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION
Volute Compressor
Type Constant Inner Diameter
Shape Elliptical
Area at Throat 1.63
Area Throat / Centroid Radius 0.6
Passage Width / Centroid Radius 0.05
Edge Width / Centroid Radius 0.025
Inner Radius 1.8
R3 0.1
Area Tolerance 0.01
RESULTS
Desi Model VB Model
(3171:; (Inches) (Inches) % Error
Area - 360° 1.6359 1.6226 0.81%
Area - 270° 1.2228 1.2115 0.92%
Area - 180° 0.8083 0.7998 1.05%
Area - 90° 0.3949 0.3897 1.32%
Radius - 360° 2.6362 2.6437 -0.28%
Radius - 270° 2.5244 2.5316 -0.29%
Radius - 180° 2.3912 2.3982 -0.29%
Radius - 90° 2.2178 2.2223 -0.20%

 

88

 

 

(4) Compressor Elliptical Constant Centroid

Table 5.4: Verification of Compressor Elliptical Const. Centroid

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION
Volute Compressor
Type Constant Centroid
Shape Elliptical
Area at Throat 1.63
Area Throat / Centroid Radius 0.6
Passage Width / Centroid Radius 0.05
Edge Width / Centroid Radius 0.025
Inner Radius 1.8
R3 0.1
Area Tolerance 0.01
RESULTS
Mi Model VB Model
Criteﬁila (Inches) (Inches) % Error
Area - 360° 1.6205 1.6228 -0.14%
Area - 270° 1.2047 1.2059 -0. 10%
Area - 180° 0.7891 0.7889 0.03%
Area - 90° 0.3737 0.372 0.45%
Radius - 360° 2.6001 2.6002 0.00%
Radius - 270° 2.6203 2.6204 0.00%
Radius - 180° 2.6447 2.6446 0.00%
Radius - 90° 2.678 2.6782 -0.01%

 

89

 

(5) Open Flow Turbine

Table 5.5: Verification of Open Flow Turbine

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION

Volute Turbine
Type Open Flow
Area at Throat 3.93
A/R 1.256
Rotor Radius (LBCR) 1.7198
Tongue Radius (BCR) 2.0977
Aero Width (Passage Width) 0.6115
Tongue Tip Radius 0.06
Area Tolerance 0.01
Diffuser Exit Width 3.46
Diffuser Exit Height 2.36
Diffuser Comer Radius 0.62
Diffuser Length 4.25
Flange Offset 3.625

RESULTS

Desi Model VB Model
Criteil'la (Inches) (Inches) % Error

Area - 360° 3.941 3.9411 0.00%
Area - 270° 2.9654 2.9655 0.00%
Area - 180° 1.9706 1.9705 0.01%
Area - 90° 0.9905 0.9906 -0.01%
Radius - 360° 3.33 3.3302 -0.01%
Radius - 270° 3.061 3.0616 -0.02%
Radius - 180° 2.772 2.772 0.00%
Radius - 90° 2.398 2.398 0.00%

 

 

90

l

(6) Twin Flow Turbine

Table 5.6: Veriﬁcation of Twin Flow Turbine

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESIGN INFORMATION
Volute Turbine
Type Twin Flow
Area at Throat 3.93
AIR 1.256
Rotor Radius (LBCR) 1.7198
Tongue Radius (BCR) 2.0977
Aero Width (Passage Width) 0.6115
Tongue Tip Radius 0.06
Area Tolerance 0.01
Diffuser Exit Width 3.46
Diffuser Exit Height 2.36
Diffuser Corner Radius 0.62
Diffuser Length 4.25
Flange Offset 3.625
Divider Wall Radius 1.884
Divider Wall Tip Radius 0.11
Slant Angle 0
Radius R3 0.5

 

 

91

 

Table 5.6 Continued...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESULTS
Model VB Model
Design Criteria (Radius (Radius % EI’I'OI'

Ratio) (Inches) Ratio) (Inches)
Inlet Area 7.0319 7.0513 -0.28%
Inlet Length 4.25 4.25 0.00%
Inlet Offset 3.625 3.625 0.00%
Critical Area(Area
Throat) 3.9251 3.93 012%
Critical Radius 3.0948 3.129 -l.09%
AIR 1.2683 1.256 0.98%
Wheel O/D 3.4396 3.4396 0.00%
Tip Width 0.6115 0.6115 0.00%
3:12;!“ wan Radms 1.0953 1.8837 1.0955 1.884 0.02%
Min. Divider Wall Thick 0.22 0.22 0.00%
“We Rad” Ram 1.2197 2.0977 1.2198 2.0978 0.00%
(Upper) . .
T°”g“° Ra‘hus Ram 1.1507 1.979 1.15 1.9778 0.06%
(Lower)

 

92

 

5.3 Discussions:

We see from the above volute models that the critical dimensions conform to the
existing model to within a maximum error of 1%. The errors mainly exist in the area
calculations, which in turn has a direct affect on the centroid radius. Some of the reasons
for the errors in the area calculations are:

(1) Bezier Curves:

As seen from the previous chapters, the volutes are generated using Bezier curves.
The Bezier polynomial deﬁnition of a circle, however, does not generate an exact circle.
It conforms to the circular arc with a maximum deviation of approximately :1: 0.05%
from the mean radius.

(2) Tolerance:

The program calculates the area to within the speciﬁed tolerance limit. There is a
minimum tolerance limit set, because the program uses an iterative process in calculating
the area; That is, it increases the dimensions (radii and width) incrementally until the
speciﬁed area has been reached within the tolerance limit. This minimum tolerance is
required (and set to 0.001) because program would oscillate about the speciﬁed area,
taking an extended time to converge.

(3) Numerical Integration:

The program calculates the area by numerical integration, following the

Trapezoidal rule. Even though a large number of points (typically 500) are taken on each

cross-section, a small error arises in the area calculation.

93

Chapter 6

CONCLUSIONS AND FUTURE WORK

6.1 Conclusions

We have seen from Chapter 1, “Introduction”, the need for having a good design
tool for volutes. This design tool should be ﬂexible to the different shapes of volutes,
should be user friendly in the exchange of data, should be ﬂexible to manipulate the
cross-sectional shapes and should be robust. Until recently, volute design has been the
neglected part of Turbochargers, with the emphasis on the rotor design. Most companies
designed their new volutes by sealing their successful predecessor, and most of the time
this scaling design method works. However, being able to design a turbocharger with
good performance characteristics, would only be realized if an effective volute is
designed.

To be able to design the volute, a good design tool is required. This design tool
would generate a model, test the ﬂow paths and manipulate the cross section shape to
achieve a good design. The starting point of this design tool is to generate the grid of the
volute model. Once the grid is obtained, an engineer can perform an analysis of the
volute, manipulating the geometry as and when required.

The Visual Basic Program — Volute Design, as described about in Chapter 4,
“Volute Design - The Program”, is a good ﬁrst step in this direction. It provides us with a

platform that could be expanded in the future to accommodate other features useful to the

94

 

design process. Visual Basic has an excellent development environment that one uses to
develop user friendly design tools. Bezier curves give the required ﬂexibility to
manipulate the volute cross section shapes. They are easy to implement especially by
visually implementing the control points in which one is able to move the control points
about, thereby changing the shape of the curve. We have also seen the various features of
the program. Not only is the program able to generate the volute based on certain design
speciﬁcations, but it is also able to change the geometry cross sections. The program is
also ﬂexible in the size of the grid generated and also the ﬁle coordinate system of the
output ﬁles.

Thus, the design tool Volute Design developed in this thesis would lead us in the

direction of designing and optimizing a volute with a favorable shape and ﬂow paths.

6.2 Future Work

The work for the future has been divided into two groups. Improvements to the
program and the work related to analyzing the volute with a CFD package are as follows.
6.2.1 The Program
(1) Tongue Deﬁnition:

The tongue is currently generated for turbines by the interpolation of the two

0 0
cross sections between 0 and 30 . By proper deﬁnition of the radius of curvature of the
tongue, it could be generated more accurately and we would have more control over this

region of the volute.

95

(2) Tongue Location Angle:

The tongue location angle is presently set at the cross section at 3600. If we are
able to move the location of the tongue across the volute, it would give us additional
ﬂexibility in designing different types of volutes for the turbine.

(3) Direct Speciﬁcation of the Geometry.
If the program could be modiﬁed to directly input the critical dimensions

(R1, R2, R3 and S) from the user, it would allow the designer by overriding the

programs default method of calculating these dimensions, the ability to create a speciﬁc
volute, thus giving greater ﬂexibility. At present the program calculates theses values
from the area and centroid radius speciﬁed at the throat [1].

(4) Modifying the AIR Ratio.

Future work could include being able to directly modify the. AIR ratio graph that
is plotted by the program. Changes in the AIR ratio would then be directly reﬂected in the
cross section area. This gives the designer additional ﬂexibility in the methods of design.
(5) Diffuser Deﬁnition:

The diffusers are currently generated by direct interpolation of the end cross
sections. If we specify the geometry at additional intermediate cross-sections, it would
give the designer better control over the design of the diffusers and thus the volute.

(6) Tongue Tip.

Generating the tongue tip and by proper control of its angle in the volute is of

signiﬁcance importance in directing the ﬂow. Proper control of the angle, radius and

length of the tongue tip would improve overall performance of the volute.

96

(7) Bezier Surface Patches:

If we implement the use of Bezier surface patches (these are two-dimensional
Bezier curves) it would result in a smoother grid.
(8) Rectangular Cross section for Compressors:

Generating rectangular cross sections allows for the testing and performance of
rectangular cross sectioned volutes, giving the designer a different type of volute to
experiment with.

(9) Viewing any Cross Section:
At present, the program displays cross sections only at 300 sections. However, it

may be desired to view a section that is not at a 300 interval. This could be implemented
by displaying the front view of the volute and allowing the user to pick the cross section
they would wish to view.

(10) DLL/OLE Links:

DLL (Dynamic LinkLibrary) and OLE (Object Linking and Embedding) give the
program addition ﬂexibility with Visual Basic to use shared code or directly link them to
other programs. These other software could be a drafting tool, a CFD analysis package
etc.

( l 1) Interface with TASCFlow:

TASCFlow is a software that would be used to run a computational ﬂuid dynamic
analysis on the turbine. All the input requirements in TASCFlow such as pressure,
temperature, mass ﬂow rate, etc. could be speciﬁed in the program and used when the

analysis is performed directly from the program.

97

6.2.2 TASCFLOW

The ﬂow inside of centrifugal compressors and turbines is highly three
dimensional. This makes the design of volutes a difﬁcult task. Most of the volute design
methods are based on inviscid ﬂow assumption, for example, Chapple [21], Baskharone
[20], Owarish [24], Chen [22] and so on. Meanwhile, however, we still can not fully
understand the ﬂow mechanism inside volutes; therefore, we can not design new models
aerodynamically. Recently, Computational Fluid Dynamics (CFD) is becoming a
powerful tool in both volute design and ﬂow analysis. It can give us the details of the
ﬂow, so we can understand the ﬂow mechanism better. Ayder and Van den
Braembussche [19] predicted the three-dimensional inviscid ﬂow ﬁeld inside a
centrifugal compressor volute using an Euler solver. To take the losses into account, a
loss model was incorporated. They gave a detail comparison between the numerical result
and the experiment data. Martinez—Botas, Pullen and Shi [23] analyzed the three-
dimensional ﬂow through a turbine volute with non-symmetric circular cross-section by
using a three-dimensional N avier-Stokes solver, and the results are satisfactory for most
part of the volute and much better than the free-vortex result.

A CFD analysis for the current project is being conducted. Some of the results of
a twin ﬂow turbine casing by using a commercial code TASCFlow are shown in the
following.

Figure 6.1 is the grid, which is a multi-block mesh. Using multi-block meshes
allowes us to build more orthogonal grid near the walls, thereby giving us a better result
near the wall.

Figure 6.2 shows the pressure proﬁle on the wall, including the exit surface.

98

The velocity vectors are in Figure 6.3. It can be seen that the ﬂow complies with
the free vortex assumption from the inlet to a quarter of the volute. Thereafter, the ﬂow
becomes fully three dimensional, and the free-vortex assumption is no longer valid.

From these results, it is proved that CFD analysis is a useful method in volute

design and should be implemented for the analysis of the ﬂow path in volutes.

99

 

 

 

 

Figure 6.1: Multi-block Twin Flow Turbine Mesh

 

 

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101

 

 

 

 

Figure 6.3: Velocity Vectors at a Surface

102

 

REFERENCES

REFERENCES

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103

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104

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105

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