THESlS

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thesis entitled

Generation Of Compressor And 'Ihrbine
Volute Casings Using Visual Basic 4.0

presented by;

Michael S. D'Souza

has been accepted towards fulfillment
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Master Of Seience degree in Mechanical Engineering

 

 

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GENERATION OF COMPRESSOR AND TURBINE VOLUTE CASINGS USING
VISUAL BASIC 4.0

By

Michael S. D’Souza

A THESIS

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

MASTERS OF SCIENCE

Department of Mechanical Engineering

1997

ABSTRACT

GENERATION OF COMPRESSOR AND TURBINE VOLUTE CASINGS USING

VISUAL BASIC 4.0

By

Michael S. D’Souza

Regarding compressor volutes, it is strongly believed that quite a substantial
additional pressure recovery and gain in efficiency can be obtained from a good volute
design. For an industrial or a turbocharger compressor stage with a well-designed volute,
typically, there is an efficiency loss of between 2 - 5 percent in the volute. Nearly, all
arising from the inability of the volute to use the radial kinetic energy out of the diffuser
and from secondary flows.

The objective of this work is to develop a design and analysis tool for compressor
volutes and turbine scrolls. The work will review volute and scroll technology, study
theoretical volute and scroll flow, and develop a design procedure for compressor volutes
and turbine scrolls. The major portion of the work is programming visual basic where the
major task is to create subroutines to generate the volute profile and cross-section details.
The objective of using visual basic is to make the software a windows based application

and easy to use.

This thesis is dedicated to my parents, Vincent and Shirley D’Souza.

ACKNOWLEDGEMENTS

I would like to express my gratitude and appreciation to several people whose
guidance and support made this work possible. I would first like to thank my advisor Dr.
A. Engeda for letting me pursue a subject I was interested in. His technical guidance and
support was invaluable and very much appreciated; to Dr. C. Somerton and Dr. H. Lee,
the other committee members for their time and supportive comments. I would like to
specially thank Mr. G. Bruce for his guidance and patience which has helped me gain a
vast amount of knowledge on the subject from an industrial point of view.

I must also express my appreciation to Schwitzer US Inc. for their support of this

project.

iv

TABLE OF CONTENTS

Page

CHAPTER 1 - INTRODUCTION TO VOLUTES .............................................. 1
1.1 Introduction ..................................................................... 1

1.2 Basic Elements of a Centrifugal Compressor ........................... 2

1.3 General Design Approach .................................................... 4

1.4 Elementary Volute Design ................................................... 6

1.5 Volute Performance ........................................................... 9

1.6 Secondary flow in volutes ................................................... 10

CHAPTER 2 — INTRODUCTION ................................................................ 12
2.1 Description ..................................................................... 12

2.2 Design Concepts .............................................................. 13

2.3 Constant Centroid and Constant Inner Diameter Compressor Cross-

sections .......................................................................... 14
A. Constant Centroid Circular Cross-section ........................ 14
B. Constant Centroid Elliptical Cross-section ....................... 15
C. Constant Centroid Rectangular Cross-section .................... 16
D. Constant Inner Diameter Circular Crosssection .................. 16

E. Constant Inner Diameter Elliptical Cross-section.... . . . . . 17

F. Constant Inner Diameter Rectangular Cross-section ............ 18
2.4 Open Flow Turbine Area of Cross-section ............................... 19
2.5 Twin Flow Turbine Area of Cross-section ............................... 21

2.6 Radius Of Centroid for various cross-sections ........................ 22

A. Open Flow ............................................................ 22

B. Twin Flow ............................................................ 23
CHAPTER 3 - DESCRIPTION OF VISUAL BASIC APPLICATION .................... 25
3.1 Drawing Form - (frmdrawing.Frm) ....................................... 25
3.1.1 End Command Button - (cmdend) ............................. 26

3.1.2 Compressor Command Button - (cmdcomp) ................. 26

3.1.3 Turbine Command Button - (cdeurbine) ................... 26

3.1.4 Picture Box - (picbox) ........................................... 27

3.2 Compressor Data Form - (frmComp_data.Frm) ......................... 27
3.2.1 Combo Box 1 - (combol) ....................................... 27

3.2.2 Combo Box 2 - (comb02) ....................................... 28

3.2.3 Cancel Command Button - (cdeancel) ...................... 28

3.2.4 Text Boxes 1 - 10 ................................................ 28

3.2.5 Labels 1 - 10 ...................................................... 29

3.2.5 OK Command Button - (cmeK) .............................. 30

3.3 Turbine Data Form - (frmTurb_data.Frm) ................................ 30
3.3.1 Combo Box 1 - (Comboboxl) .................................. 31

3.3.2 Cancel Command Button - (cdeancel) ...................... 31

3.3.3 Text boxes 1 - 12 ................................................. 31

3.3.4 Labels 1 - l2 ...................................................... 32

3.3.4 Labels 1 - 12 ....................................................... 33

vi

3.4 Compressor Module - (ModCompressor.Bas) ........................... 33

3.5 Turbine Module - (ModTurbine.Bas) ..................................... 35
3.6 Parameter Form - (frmpara.Frm) .......................................... 36
3.7 FillCells Procedure ........................................................... 37

CHAPTER 4 - DESCRIPTION OF COMPRESSOR VOLUTE AND CROSS-SECTION

GENERATION MODULE ........................................................................ 39
4.1 Compressor Module - (ModCompressor.Bas) ........................... 39
4.2 Reading Input Data .......................................................... 39

4.3 Dimension and Area check calculations .................................. 40
4.4 Plotting the Inner Circle ..................................................... 41
4.5 Plotting the Centroid ........................................................ 41
4.6 Plotting the Wet Surface of the Volute Profile .......................... 42
4.6.1 Constant Centroid ................................................ 42

4.6.2 Constant Inner Diameter ......................................... 42

4.7 Plotting the Diffuser ......................................................... 43
4.8 Plotting the straight line surfaces (Cross-section) ....................... 44
4.9 Plotting three-fourths of Cross-section View ........................... 44
4.10 Plotting Radius R3 and Rest of Cross-sectional View ................. 45
4.10.1 Constant Centroid ............................................... 45

4.10.2 Constant Inner Diameter ....................................... 46

CHAPTER 5 - DESCRIPTION OF TURBINE VOLUTE AND CROSS-SECTION

GENERATION MODULE ........................................................................ 47

vii

5.1 Turbine Module - (ModTurbine.Bas) ..................................... 47

5.2 Open Flow Area - (Area) ................................................... 48
5.3 Twin Flow Area — (Area_twin_flow) ...................................... 48
5.4 Open Flow Plot - (plot_Turbine_profile) ................................. 48

5.5 Twin Flow Plot - (plot_twin_flow_turbine) ............................. 50
5.6 Open Flow Main - (SubOpen_Flow) ...................................... 51

5.7 Twin Flow Main - (SubTwin_flow) ...................................... 53
5.8 Area Check Calculations .................................................... 55

CHAPTER 6 - USE OF BEZIER CURVES FOR SURFACE GEOMETRY

GENERATION ...................................................................................... 56
6.1 Introduction .................................................................. 56

6.2 Explicit, Implicit and Parametric Functions ............................. 56

6.3 Bezier Curves ................................................................ 60

6.4 Changing The Order Of The Bezier Polynomial ........................ 62

CHAPTER 7 - CONCLUSIONS AND RECOMMENDATIONS ............................ 63
7.1 Future Interfacing for varying Area Distribution ........................ 63

7.2 Area Check Calculation ..................................................... 63

7.2.1 Compressor ......................................................... 63

7.2.2 Turbine .............................................................. 64

7.3 Bezier Curves ................................................................. 64

7.4 Parameter Form ............................................................... 65

7.5 Approximations .............................................................. 66

viii

7.5.1 Centering ........................................................... 66

7.5.2 Diffuser ............................................................. 66
7.6 Recommendations ............................................................ 66
List Of References .................................................................................. 67

ix

LIST OF TABLES

Page
Table 5.1 Distribution of Parameter Ratios (Open Flow) ...................................... 52
Table 5.2 Distribution of Parameter Ratios (Twin Flow) ...................................... 54

LIST OF FIGURES

Page
Figure 1.1 Cross-section of a centrifugal compressor .......................................... 2
Figure 1.2 Basic Volute Geometry ................................................................ 6
Figure 2.1 Elliptical External Volute .............................................................. 12
Figure 2.2 Rectangular External Volute ......................................................... 13
Figure 2.3 Rectangular Internal Volute .......................................................... 13
Figure 2.4 Constant Centroid (Circular c/s) ..................................................... 14
Figure 2.4 Constant Centroid (Elliptical c/s) .................................................... 14
Figure 2.6 Constant Inner Diameter (Circular c/s) ............................................. 17
Figure 2.7 Constant Inner Diameter (Elliptical c/s) ............................................ 18
Figure 2.8 Dimension Details .................................................................... 19
Figure 2.9 Subdivision for area calculation ..................................................... 20
Figure 2.10 Open Flow Divider Wall Details ................................................... 21
Figure 3.1 Drawing Form .......................................................................... 26
Figure 3.2 Compressor Data Form ............................................................... 27
Figure 3.3 Turbine Data Form .................................................................... 30
Figure 3.4 Compressor Module .................................................................. 34
Figure 3.5 Turbine Module ....................................................................... 35
Figure 3.6 Parameter Form ....................................................................... 36
Figure 4.1 Diffuser Construction ................................................................. 43

xi

Figure 4.2 Straight Lines and 3%: Cross-section Plot ............................................ 44

Figure 4.3 Radius R3 for Constant Centroid ................................................... 45
Figure 4.4 Radius R3 for Constant Inner Diameter ............................................ 46
Figure 5.1 Profile Generation (Open Flow) ..................................................... 49
Figure 5.2 Profile Generation (Twin Flow) ..................................................... 50
Figure 6.1 Bezier Curve Example ................................................................. 61
Figure 7.1 Cross-section made up of Bezier Curves ........................................... 64

xii

b5

BCR

CL

Ph

Rc

LIST OF SYMBOLS

Major axis of an ellipse
Minor axis of an ellipse
Volute passage width
Base circle radius
Velocity

Center line

Mass

Pressure

Parabola height

Radius

Radius of centroid

Turbine base width

Angle through which R1 spans

Density

Angle of intersection for R1 and R2

xiii

CHAPTER 1

INTRODUCTION TO VOLUTES

1.1 Introduction

Most centrifugal compressor and radial turbine design requirements need
solutions to two major problems : stress and aerodynamics. For both, aerodynamic design
and stress analysis of a centrifugal compressor stage or component, a complete
geometrical modeling is necessary.

The basic elements of a centrifugal compressor are a stationary casing containing
a rotating impeller followed by a radial diffuser. The fluid is drawn in through the inlet
casing 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, which is marked in Figurel.l,
is usually referred to as the inducer. In order to increase the angular momentum, the
impeller whirls the fluid outwards and turns it into a 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 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 an additional pressure rise in

this part of the compressor.

Diffuser vanes

 

    

:— lnducer section

Figure 1.1 Cross-section of a centrifugal compressor
1.2 Basic Elements of a Centrifugal Compressor

Centrifugal compressors are reliable, compact, and robust; they have better
resistance to foreign object damage, and are less affected by performance degradation due
to fouling. They are found in small gas turbine engines, turbochargers, and refrigerators
and are used extensively in the petrochemical and process industry. Since the centrifugal
compressor finds a wide variety of application, each application places its own demands
on the design of the compressor. The problems usually can be categorized as stress or
aerodynamic related.

The stress problems are caused by material strength limitations, and the capability
to accurately predict, blade and rotor steady state and vibrational stress for complex
impeller shapes and at high rotational speeds.

The aerodynamic problem is to efficiently accomplish, large air deflections and
diffusion at high flow velocity, with the added difficulty of very small passage flow areas

required to give good efficiency and high pressure ratio. Even though the individual

components of the compressor are capable of achieving high efficiency, it is the
efficiency of the whole stage that is of great importance. Thus, component matching is an
essential aspect of design. It is often required to redesign one or more components of the
compressor due to improper matching and sometimes the efficiency of a component is
sacrificed to achieve good matching.

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 50% of the total pressure at impeller exit will be dynamic pressure and
50% 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 the engine valves. This recovery therefore must be attempted in the
diffuser after the impeller and in the volute.

Compressor volutes and turbine scrolls are widely used for turbochargers,
because of their simple structure, easy production and wide operating range. However,
there are only very few documented data on internal flow measurements on volutes and
scrolls, because of their complex geometry and form, detailed flow pattern have not been
obtained. Therefore, the effects of geometrical parameters on performance have not been

clarified enough.

The heart of the compressor is the impeller, where all the energy transfer takes
place; it would be the likely suspect for any short comings 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 current strong demand, by turbocharger users for turbochargers with good
range and efficiency, is forcing the turbocharger designer to review his aerodynamics.
Two fruitful sources for potential improvement in turbocharger performance are in:

0 proper diffuser and volute design and
0 good understanding of the factors affecting the stable operating range and pressure
recovery of diffusers and volutes.

Both theoretical and experimental investigations of centrifugal compressors are
very expensive and time consuming. Because the flow is unsteady, and flow separation is
inevitable even with the best of designs. In addition there is still no clear knowledge for
the flow mechanism, particularly at the rotor exit region, impeller-diffuser and impeller-

volute interactions.

1.3 General Design Approach

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
scroll then becomes elaborate. A full such analysis is given by Brown and Bradshow /l/.
This calculation procedure furnishes the cross-sectional area but gives no guidance as to
the shape. Brown and Bradshaw /1/ 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 /2/ showed that certain volute geometry are more efficient than
others.

Stiefel /3/ 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 10 to 15 per cent smaller than that which would be designed through the
frictionless flow assumption. By reducing the size of the volute by 30 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 to 1 to one of6 to 1.

For radial turbine scroll Chapple, Flynn and Mully /4/, developed a performance
prediction approach and performed design 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.

1.4 Elementary Volute Design

VOLUTE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.2 Basic Volute Geometry
Figure 1.2 shows typical volute geometry. Using simplified theory, volute flow
aims to collect the flow uniformly along the circumference from (p = O to (p = (pm

(usually 360o - 80:3520). The mass flow distribution can be described as:

m<<p>=—"i=—<p+m. (H)

(Pmax
where mC is the effective compressor flow and m0 is the recirculating flow through the
tongue gap. Rearranging eq(l . l ):

m(<p) — ‘9 +29 (1.2)

mc _ (Pmax me

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

m“- = uz recirculating mass flow
m
C

$122 = u((p) mass ratio

C

Mcp) =—(P- +112 (1.3)

max
To determine the optimum path for the outer radius ra as a function of the angle (p,

conservation of angular momentum is applied as:
2212
r.cu = constant = 2 -°uao (1.4)

which gives the magnitude of the velocity as dependent on the radius. Applying

continuity of mass through a cross-sectional area dA gives:

dm = dA.p.cu(r) (1.5)
= b(r).drp.-D-§1.E"r29- (1.6)

The total mass flow through A((p) is

D ’8 d
mm =—"‘" c.» g p.b<r).-r—' (1.7)
20

2
r:—
2

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

which gives:

D a (1
$3 = j” cuao- 2an o... b(r).7r = pop)
”-2-

 

«p
—+
I b(r) dr= (pm ”2
.2220» r 2312., P_(‘L)
_2 2 lQD'm
C

(1.8)

(1.9)

The solution to eq( 1 .9) describes the distribution of the outer radius r... as a function of the

angle (p.

A very simple solution is usually to assume constant density circumferentially:

p(<p) = constant = 920 = 90c
and a rectangular cross-sectional area:
b(r) = constant = bD

so that eq( 1 .9) simplifies to:

lnrl'ao Ania-=1-
“”3” 020 b” Pam
2 m0

(1.10)

(1.11)

 

)
| x I
1 lb Baronet: D |
r ' °
_L=_e\ 2 "'0 J (1.12)
D20 2

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

adiabatic, inviscid, and incompressible flow.

2

53; = constant (1.13)
2 2

easier)

_ 2

Lp922=9§1(1—52r11) (”5)

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

1.5 Volute Performance

Detailed published information on the performance of volutes is very limited.
Japikse /5/ presented an incompressible flow model for a turbocharger volute. He
established the volute losses through three modeling assumptions as :
(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.

10

Weber and Koronowski /6/ developed a meanline performance prediction for volutes.
Eckert /1/ probably made one of the first attempts to account for friction and secondary
losses in volutes. Furthermore Iverson et al f7/, Kurokawa /8/ and Badie et al /9/ 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.

1.6 Secondary flow in volutes

Secondary flows in volutes and scrolls are very little understood. 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
prediction of the circumferential pressure distortion and performance of three-
dimensional volutes.

In turbine scrolls, 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 scroll 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

11

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

TOIOI'.

CHAPTER 2

VOLUTE BASICS

2.1 Description

A volute is made up of a circumferential passage around the diffuser exit with
progressively increasing cross-sectional area. This area serves to flow fluid velocity and
increase static pressure recovery. A full-collection plane is the region where all the mass
flow from the diffuser collects. At this location the divider that separates the collected
flow from the uncollected flow is called the “tongue”. Flow then exits to the connected
piping from this location.

The shape of this cross-section can vary and is fundamentally dependent on fluid

dynamic principles. The commonly used cross-section are of either circular, elliptical or

rectangular type.

 

 

 

mT

Rc

 

 

 

b5 r5

....................................... CL

 

 

 

 

 

 

Figure 2.1 Elliptical External Volute

12

l3

Volutes can be classified as external, internal and intermediate. Figure 2.1 and figure 2.2
is an example of external volutes, where the entire passage area is outside the diffuser exit
radius. Figure 2.3 shows an internal volute. The difference is that an internal volute
locates as much of the passage area as possible inside the diffuser exit radius. Figure 2.5
shows an intermediate volute. This volute may appear to differ from that of figure 2.1
only by the fact that the diffuser wall is extended into the volute. As the area increases the

Re for the external volute will also increase.

2.2 Design Concepts

 

 

W W

4‘
w
A
V

 

 

 

 

 

 

 

 

 

 

 

 

CL ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, CL

 

 

 

 

 

 

Figure 2.2 Figure 2.3
Rectangular External Volute Rectangular Internal Volute
To obtain the geometry of cross-section it is necessary to define the
circumferential variation of Re and the cross-sectional area. [In this thesis we concentrate
on external volutes and therefore need to define the cross-sectional area variation] For

simplicity the cross-sectional area is assumed to be a function of 0 that ranges from 0 -

14

360 around the volute profile. For various types of cross-sections the area calculations are

different and are presented below.

2.3 Constant Centroid and Constant Inner Diameter Compressor Cross-sections
The two type of cross-sections concentrated on in this study are of the “constant
inner diameter” and the “constant centroid” type. Figure 2.4 and Figure 2.6 illustrate the

difference in cross-section amongst these two types.

 

 

 

 

 

 

 

 

Figure 2.4 Constant Centroid (Circular c/s)
A. Constant Centroid Circular Cross-section
As illustrated in Figure 2.4 the calculation of the area of cross-section depends on
the area of the circle and the radius R3. If we divide the circular cross-section into four
quadrants we see that the area of three quadrants (I, II, III) are the simple area of a circle.

The fourth quadrant (IV) however has to be calculated differently. From the figure we can

15

see that the area of the fourth quadrant can be broken down into two parts, i.e. the area of
a rectangle and the area outside of the curve with radius R3.
Area (rectangle) = R1* (R1 - b5 - e) (2.1)

Area (outside curve) = (R3) 2 * (171* n) (2.2)

Subtracting these two areas we obtain the area of the fourth quadrant. Adding up all four

quadrants we then get the area of cross-section.

Area = % 1t (R1) 2 + [Area (rectangle) - Area (outside curve)] (2.3)

B. Constant Centroid Elliptical Cross-section

 

2a

 

IN
V

2b

 

 

\!

 

 

b5—-)I |(-—-
Rc

.......................................................... CL

 

 

 

 

 

Figure 2.5 Constant Centroid (Elliptical cls)
The calculation for the cross-section area is similar to the circular cross-section. In
this case the major axis and minor axis of the ellipse are known. Again if we breakdown
the whole cross-section into four quadrants, we use the formula for the area of the ellipse

(Area = nab) to calculate the area of the first three quadrants. The fourth quadrant is

l6

calculated similarly as above for the circular cross-section. The area is broken down into

the area of a rectangle and area outside the curve R3.

Area (rectangle) = b * (a - b5 - e) (2.4)
Area (outside curve) = (R3) 2 * ( 1 — i— * tr) (2.5)

Again by subtracting these areas the area to the fourth quadrant is obtained. Adding up all
the areas of the various quadrants the area of the cross-section is thus calculated.

Area = [ 3%: 11: a b ] + [Area (rectangle) - Area (outside curve)] (2.6)

C. Constant Centroid Rectangular Cross-section

Although rectangular cross-section types are not often used in turbochargers,
using similar methods as in elliptical and circular type, different geometry’s were derived.
Again the calculation of the area of cross-section is done in the same manner. The area is
broken down into four quadrants and the first three are calculated by using simple
methods. The fourth quadrant is calculated the same way as in the circular and elliptical

cross-section.

D. Constant Inner Diameter Circular Cross-section

As in figure 2.6 we see that the circular cross-section can also be broken down
into various quadrants. First we calculate the area of the first three quadrants using the
three-fourths area of a circle. Then the fourth quadrant is broken up into three parts.

These three parts are the area of a square, rectangle and area outside the curve R3.

Area (square) = (R1) 2 (2.7)

17

Area (rectangle) = R3 * (b5 + e) (2.8)
Area (outside curve) = (R3) 2 * (1— i * it) (2.9)
Area (4th quadrant) = Area (square) - Area (rectangle) - Area (outside curve) (2.10)

Totaling up the areas of the four quadrants the area of the cross-section is obtained.

Area = 3%: 1: (R1) 2 + Area (4'h quadrant) (2.1 1)

 

 

 

 

 

 

 

 

Figure 2.6 Constant Inner Diameter (Circular cls)

E. Constant Inner Diameter Elliptical Cross-section

Again this calculation process is similar to the constant inner diameter circular
cross-section. The total area is sub-divided into 4 quadrants and the area of the first three
quadrants are calculated using the area of an ellipse formula (Area = nab). The fourth
quadrant is broken down into smaller areas which are similar to the calculation procedure
of the circular cross-section. The formulas differ slightly and are as follows.

Area (rectangle-1) = a * b (2.12)

18

Area (rectangle-2) = R3 * (b5 + e) (2.13)

Area (outside curve) = (R3) 2 * (1 - § * n) (2.14)

Area (4‘h quadrant) = Area (rectangle-1) - Area (rectangle-2) - Area (outside curve) (2.15)

where Area (rectangle-1) is the area of the rectangle using the sides as of the major and
minor axis. Totaling up all the quadrants the area of the cross-section is obtained.

Area = 3A n: a b + Area (4th quadrant) (2.16)

 

 

 

 

 

 

Rc

 

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, CL

 

 

 

Figure 2.7 Constant Inner Diameter (Elliptical cls)

F. Constant Inner Diameter Rectangular Cross-section

As in the constant centroid rectangular cross-section this type is not often used,
but an approximation was made using the existing circular and elliptical cross-section
drawings. The area is calculated similarly to the area of the circular and elliptical cross-

section where the area is broken down into various quadrants and calculated individually.

19

2.4 Open Flow Turbine Area of Cross-section

The open flow turbine internal volute passage is similar to the centrifugal passage
and differ only in cross-sectional shape. As described in figure 2.8, the cross-section is
defined by three dimensions which are R], R2, and S. The outline is developed by
tangentially intersecting two curves of radius R1, R2 and a parabola. Described below is
the method used to calculate the area of cross-section knowing R1, R2 and S. Since the
cross-section is symmetrical we can concentrate on the area of one side of the central
axis. This cross-section is broken down into 3 different regions and each of these are

determined separately.

 

 

 

     

 

s
R1 5
I A
R2 5
Ph
xii]:
‘, ; v
5 <——->
(——-—>
w

 

 

 

Figure 2.8 Dimension Details.
As in the figure 2.9 the cross-section is divided into 3 parts alphabetically as A, B,
and C. Section A is the shaded region and using geometric methods, the formula to

calculate the area is as below. The area is subdivided into three smaller regions which are

20

denoted by different shades in the figure below. The two regions can be described as a

circular segment of a circle and a rectangle

 

 

 

 

 

Figure 2.9 Subdivision for area calculation.

Area - A (rectangle): (B_width) * (2 * bw_A) (2.17)
Area - A (circular segment) = R2 * (G - l/2 Sin (26)) (2.18)
Area (A) = Area - A (rectangle) + Area - A (circular segment) (2.19)

Area B can be described as a circular segment and the area for region B is,

Area (B) = R2 * (01- V2 Sin (2a)) (2.20)
Area C can be subdivided into a rectangle and parabola. Using the formulas below the
area to this region are calculated.

Area - C (rectangle) = (B_width) * (Ph) (2.21)
Area - C (parabola): % * (B_width - W) * (Ph) (2.22)

Area (C) = [Area — C (rectangle)] - [Area - C(parabola)] (2.23)

21

Adding up all the areas ,

Area (Total) = Area (A) + Area (B) + Area (C) (2.24)

2.5 Twin Flow Turbine Area of Cross-section

The area of a twin flow turbine is similar to the open flow turbine. The only
addition to the open flow is the existence of a divider wall that separates the flows. Also
the construction of the cross-section is now dependent on an additional parameter which
is R3 (as detailed). To determine the area of the twin flow cross-section the area of the
divider wall has to be calculated. This divider wall is broken down into three different

area, Div(A), Div(B) and Div(C). The formulas used for these areas are,

 

 

Area Div(B)

 

 

 

Slant angle (4)) I

 

 

: t (——Rtip

i

 

 

 

Figure 2.10 Open Flow Divider Wall Details

Div(A) = [11: * (Rtip) 2 ] / 4 (2.25)

22

[(Tip Ungthf * Sin(¢)]
2

 

Div(B) = [Tip Length] * Rtip + (2.26)

The area for region C (as drawn in the figure) can be considered as the combination of a

rectangle and a sector of a circle having radius R3.

Div(C rectangle) = ([Tip Length] * Sin ((1)) + R3) * R3 (2.27)
Div(C sector) = [11: * (R3) 2 ] /4 (2.28)
Div(C) = Div(C rectangle) — Div(C sector) (2.29)

Adding up all the areas and using the formula described earlier the area for an open flow
turbine can be determined,
Area (Divider wall) = Div(A) + Div(B) + Div(C) (2.30)

Area (Twin flow) = Area (Open flow) - Area (Divider wall) (2.31)

2.6 Radius 01' Centroid for various cross-sections.

For compressor cross-section the calculation of the centroid radius is fairly
simple. As the detailed figures earlier denoted, it can be seen from the area of cross-
section that the centroid radius is considered to be at the central Y-axis of the volute
passage. But for the turbine open flow and twin flow a detailed method is to be used.

A. Open Flow

Again the cross-section area is subdivided into the same regions as for the area
calculation. Now only the centroid radius for these individual regions are needed for the
overall centroid radius. They are calculated as follows,

Rc Area (A) = Ph + bw_A (2.32)

23

R1 - (Ph + (bw_A * 2))
3

 

Rc Area (B) = Ph + (bw_A * 2) + [ ] (2.33)

Rc Area (C) = (-:—) * Ph (2.34)

Using this the overall centroid radius is given by

 

RC = Re Area(A) *Area(A) + Rc Area(B) * Area(B) + Rc Area(C) * Area(C) (2.35)
Area(total)

B. Twin Flow
In this case the centroid radius is calculated the same way except that the divider
wall is taken into consideration. As described earlier the divider wall is broken down into
three smaller part and the centroid radius for each of these are,
Rc Div(A) = 0 (2.36)

This is due to the fact that this region is below the base circle radius and hence not

 

 

 

considered.

Rc Div(B) = [mp Length] 203“ ' mm] (2.37)

. . R3
Rc DIV(C rectangle) = [Rc D1V(B) * 2] + (7) (2.38)

*
Rc Div(C sector) = [Re Div(B) * 2] + [(R3 4) ] (2.39)

(3 * 717)
Rc Div (C) =[Re Div(C rectangle) * Div(C rectar11)gle()C-)i- Rc Div(C sector) * Div(C sector)]
zv

(2.40)

The centroid radius of the divider wall is obtained by,

24

 

RC Div =[Rc Div(B) * Div(B) + Rc Div(C) * Div(C)] (241)
Area(Divider wall)

The overall centroid radius is determined by,

 

Rc _ RC (Open Flow) * Area (Open Flow) - Rc Div * Area (Divider wall)
Area (Twin Flow)

] (2.42)

Where Re is the radius of centroid for a twin flow cross-section.

CHAPTER 3

DESCRIPTION OF VISUAL BASIC APPLICATION

This chapter deals with detailed explanation of the Visual Basic Application and
all associated forms and procedures. The motivation for using Visual Basic 4.0 was the
fact that further interfacing might be possible with the existing Visual Basic application
currently used by Schwitzer. Also Visual Basic is windows based, graphical and easy to

1186.

Overview of the application
The Visual Basic Application uses various forms and procedures that are as listed
below.
1) Drawing Form - (frmdrawing.Frm)
2) Compressor Data Form - (frmComp_data.Frm)
3) Turbine Data Form - (frmTurb_data.Frm)
4) Compressor Module - (ModCompressor.Bas)
5) Turbine Module - (ModTurbine.Bas)

6) Parameter Form - (frmpara.Frrn)

3.1 Drawing Form - (frmdrawing.Frm)
This form is the main form and the backbone of the application. It consist of three

command buttons and a picture box as detailed in Figure 3.1. This form does no detailed

25

26

calculation but is used only to manage the Compressor data form and Turbine data form.
The picturebox also displays the existing drawing except on start up. A few details on its

individual operation are listed below.

3.1.1 End Command Button - (cmdend)

This command button ends the application and exits out of the run mode.

 

 

[Compressor] I Turbine 1 [Earn

 

 

 

 

 

 

 

 

 

Figure 3.1 - Drawing Form

3.1.2 Compressor Command Button - (cmdcomp)

This button pulls up the Compressor Data Form which list all compressor input
parameter details.
3.1.3 Turbine Command Button - (cdeurbine)

This button executes and displays the Turbine Data Form which in turn list all

input parameter details required for the turbine profile generation.

27

3.1.4 Picture Box - (picbox)
The picture box is used as a drawing sheet and displays the generated plots from

the compressor and turbine modules.

3.2 Compressor Data Form - (frmComp_data.Frm)
The compressor data form is used to list and display all assumed data needed for

the volute and cross-section plot generations.

 

Labels 1- 10
Combo box 1

  
   

l-IO
ID

..

 

 

 

EDDDDDDUDQ

 

 

Figure 3.2 - Compressor Data Form
3.2.1 Combo Box 1 - (combol)
This combo box lists the various types of cross-section that can be chosen. The
options are Circular, Ellipse and Rectangular. The default selection is the circular cross-
section and is displayed in the box during start up. After the first plot the compressor data

form is recalled then the existing selection is displayed in the combo box.

28

3.2.2 Combo Box 2 - (comb02)

This combo box list the various types of volute generations available. In this
project the two options are Constant Centroid and Constant Inner Diameter. The default
selection is the Constant Centroid and is displayed in the box after start up. Again, if the
compressor data form is recalled at any point the existing selection is displayed for

convenience.

3.2.3 Cancel Command Button - (cdeancel)
This command button disregards any changes made to the compressor data form

and then displays the Drawing Form with the existing plot.

3.2.4 Text Boxes 1 - 10

These textboxes define various input parameters for the volute and cross-section
generations. They display the most current values used in the last generated plots. These
textboxes also facilitate to make changes to the drawings and adjust various parameters
so as to obtain the desired output. The list of text boxes are as below,
1) “txtArth” defines the area at the throat.
2) “txtratio” defines the AIR ratio at the throat.
3) “txtGapwidth_factor” defines passage width leading into the volute passage.
4) “txtEdgewidth_factor” defines flat edge width on entry into the volute passage.

5) “txtInn_Radius” defines inner radius of the compressor.

29

6) “txtRadius_R3” defines radius R3.

7) “txtTolerance” defines the Tolerance limits for area calculation.

8) “txtDiff_length” defines diffuser length.

9) “txtDiff_area__ratio” defines the ratio of the areas of the diffuser and throat.

10) “txtVolute_scaIe_comp” defines the scale at which the volute profile needs to be

drawn.

3.2.5 Labels 1 - 10
The labels used are in accordance to the textboxes available and are used purely to
define each textbox. They have no other function other than labeling each textbox on the
Compressor Data form. The list of labels used are,
1) “LabArth” displays “Arth=”
2) “Labratio displays “A/R=”.
3) “LabGapwidth_factor” displays “Gap width factor-’1
4) “LabEdgewidth_factor” displays “Edge width factor=”.
5) “LabInn_Radius” displays “Inner radius=”.
6) “LabRadius_R3” displays “R3”.
7) “LabTolerance” displays “tolerance=”.
8) “LabDiff_length” displays “Diffuser length=”.
9) “LabDiff_area_ratio” displays “Area[diff]/Area[throat]=”.

10) “LabVolute_scale_comp” displays “Volute Scale=”.

30

3.2.5 OK Command Button - (cmeK)

This is the actual control code on the Compressor Data Form. The “Ok” command
first reads data from the text boxes and combo boxes into variables. It then uses “if”
statements to decide what procedure to call from the data obtained in the combo boxes. If
the data in the combo boxes do not match the existing available procedure then an error
message is displayed so the user can correct the data. Once the information from the
combo boxes are matched by the “if” statements, the required procedure is called. Along

with the call for the subroutine, the data read previously from the textboxes are also

submitted to the procedures and the calculation for the plot are initialed.

3.3 Turbine Data Form - (frmTurb_data.Frm)

This form is similar to the Compressor data Form with a few changes. The display

of the form is as below.

 

 

 

 

 

 

Twin Flow

 

 

[Labels 1012 ]

 

[:1
El

.. l:i

 

 

 

I Ok I [Cancel]

 

Textboxes

10- 12 ‘

 

 

Open Flow

 

\

DDDEEDDDE

 

 

_ Textboxes

1-10

 

 

 

Figure 3.3 Turbine Data Form

 

 

31

3.3.1 Combo Box 1 - (Comboboxl)

In the Turbine data form there is only one combo box. The options for the combo
box are Open Flow or Twin Flow type of turbine housing. The default selection on start
up is the Open Flow and is displayed in the combo box. Again as in the case of the

compressor data form combo boxes the recent selection is displayed after the first plot.

3.3.2 Cancel Command Button - (cdeanceI)
This works in the same way as the Compressor Data Form command button and
disregards any changes to the Turbine data form and recalls the Drawing Form with the

existing plot.

3.3.3 Text boxes 1 - 12

These textboxes work in a similar manner to the Compressor Data Form to define
all data needed to generate the turbine volute and cross-section plots. A difference in
these text boxes is that from one to nine is used for common data of both open and twin
flow while the last three are used exclusively for the twin flow procedure. The list of text
boxes used are as below,
1) “txtArth_tur ” defines the area at the throat of the turbine.
2) “txtRatio_turb” defines the AIR ratio at the throat.
3) “txtBase_circ_radius” defines the base circle radius.
4) “txtWidth” defines the width of the passage leading into the volute passage.

5) “txtTolerance_turb” defines the tolerance limits for area calculation.

32

6) “txtLower_base_radius” defines the radius at the lower width of the passage.
7) “txtDiff_Length_turb” defines the length of the diffuser.

8) “txtDiff_area_ratio_tur ” defines ratio of the area of diffuser outlet and throat.
9) “txtVolute_scale” defines the scale at which the volute profile is to be plotted.
These are used only for the Twin flow turbine housings,

10) “txtRadius_R3” defines radius R3

11) “txtRadius_tip” defines the radius at the tip of the divider wall.

12) “txtDivider_angle” defines the angle at which the divider wall is inclined at.

3.3.4 Labels 1 - 12
Again these labels are used to define each text box on the Turbine Data Form. The
labels used are listed below,
1) “LabArth_turb” displays “Arth=”.
2) “LabRatio_turb” displays “A/R=”.
3) “LabBase_circ_radius displays “BCR=”.
4) “LabWidth” displays “Width=”.
5) “LabTolerance_turb” displays “Tolerance=”.
6) “LabLower_base_radius” displays “LowerBCR=”.
7) “LabDiff_Length_turb” displays “Diffuser Length=”.
8) “LabDiff_area_ratio_turb” displays “Area[Diff]/Area[Throat]=”.
9) “LabVolute_scale” displays “Volute Scale=”.

These are used only for the Twin flow turbine housings,

33

10) “LabRadius_R3 displays “Radius R3=”.
1 1) “LabRadius_tip” displays “Tip Radius=”.

12) “LabDivider_angle” displays “Divider Slantz”.

3.3.5 OK Command Button - (cmeK)

Again this is the actual control code on the Turbine Data Form. The Ok command
first reads data from the text boxes and combo boxes into variables. It also reads in data
needed for only the twin flow whether that procedure is executed or not. It then uses “if “
statements to decide what procedure to call from the data obtained in the combo boxes. If
the data in the combo boxes do not match the existing available procedure then an error
message is displayed so the user can correct the data. Once the information from the
combo boxes are matched up by the “if” statements the required procedure is then called.
Along with the call for the subroutine the data read previously from the textboxes are also
submitted to the procedures and the calculation for the plot are initialed. It may also be
noted that the data needed for only the twin flow turbine housing is not submitted to the

open flow procedure.

3.4 Compressor Module - (ModCompressor.Bas)
This module houses all the codes used for the various types or combinations of
compressor housings plot generations. The module is executed by the OK command

button on the compressor data form. A schematic diagram of the layout is as figure 3.4,

34

 

Compressor Data Form

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I 0K l
Compressor
Module
(1) Circular c/s (3) Ellipse c/s (5) Rectangle c/s
Constant Centroid Constant Centroid Constant Centroid
(2) Circular c/s (4) Ellipse c/s (6) Rectangle c/s
Constant ID Constant ID Constant ID

 

 

 

 

 

 

 

 

 

Figure 3.4 Compressor Module

The Ok command button decides which procedure listed under the module is to be
called. The Compressor Module contains the procedures and also for general declarations
common for all procedures. The procedures are described in detail in the next chapters
and a list of the procedures contained in the compressor module is as below,
1) SubCircular_ConstCentroid
2) SubCircular_ConstID
3) SubEllipse_ConstCentroid
4) SubEllipse_ConstID

5) SubRectangle_ConstCentroid

35

6) SubRectangle_ConstID

7) FillCells

3.5 Turbine Module - (ModTurbine.Bas)
This module contains all the Turbine generation procedures but which are

different form the compressor module procedures. A schematic of the procedure control

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

is detailed below,
Turbine Data Form
I OK i

l

Turbine

Module
7.

(1) Open Flow (2) Twin Flow
Procedure Procedure
Area (Open) Plot (Open) Area (Twin) Plot (Twin)
(6) (b) (C) (d)
Figure 3.5 Turbine Module

The Ok command in the turbine data form calls the required procedure. The main
procedure are the Open Flow and the Twin Flow, these in turn use the Area and Plot
procedure to calculate the area of the cross-section and plot, respectively. A detailed
explanation of these subroutines are described in the later chapters. The actual names of
these procedures housed by the Turbine Module are as described,

1) SubOpen_Flow

a) Area

36

b) plot_Turbine_profile
2) SubTwin_flow
c) Area_twin_flow

d) plot_twin_flow_turbine

3.6 Parameter Form - (frmpara.Frm)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R1 R3 S R2
Throat
330
300
Done
Figure 3.6 Parameter Form

This form is a support form and is used for data output. This form was designed
so as to replicate the data tables used in the existing Schwitzer drawings. Also data can be
read off this form and therefore found to be a convenient interface the second part of the
project. In this form a “grid” is used and the tittles to this grid is specified under “Form

Loa ”. On the “click” event of the Dimension command button the form is displayed.

37

The data is entered in to the grid via calling the “Fillcells” procedure which is located in

the Compressor Module.

3.7 FillCells Procedure

This procedure writes data into the cells which were generated previously by the
main procedures. A loop is constructed in each of the main subroutines and the number of
loops is equal to the number of rows in the grid (12). These loops send data to the
“FillCells” procedure column by column and the function of the procedure is to read the
data from the “call” command and write it to their respective cells. The data is written
column by column and is terminated after all cross-sections of 30 degree intervals are

recorded.

CHAPTER 4

DESCRIPTION OF COMPRESSOR VOLUTE AND CROSS-SECTION

GENERATION MODULE

This chapter deals with detailed explanation of the compressor module, data
generation and methods used to plot the data. The various procedures were grouped into
one module so as to call them from other codes. Also having these in a subroutine form

makes it flexible for future mating with other Visual Basic applications.

4.1 Compressor Module - (ModCompressor.Bas)

The module consist of six different procedures and is as detailed in Chapter 3. The
“0k” command on the Compressor Data Form matches up the input data and decides
using “if" statements on which subroutine is to be called. In the “General Declarations”
all values from the input data textboxes are defined as real numbers and are made
available to all the procedures in the module. The list of available subroutines are,
1) SubCircular_ConstCentroid
2) SubCircular_ConstID
3) SubEllipse_ConstCentroid
4) SubEllipse_ConstID
5) SubRectangle_ConstCentroid

6) SubRectangle_ConstID

38

39

These procedures work very similar to each other with minor differences in cross-section
details. A list of procedures are listed and the visual basic application executes these in
the order displayed as below,

1) Reading Input Data

2) Dimension and Area check calculations

3) Plotting the Inner Circle

4) Plotting the Centroid

5) Plotting the Volute Profile

6) Plotting the Diffuser

7) Plotting the straight line surfaces (Cross-section)

8) Plotting three-fourths of Cross-section View

9) Plotting radius R3 and rest of Cross-sectional View

4.2 Reading Input Data

This is common for all procedures and is the area in which all the input variables
are defined. The various values assigned to the text boxes in the Compressor Data Form
are read by the “OK” command and then sent via the call command. These values are
then assigned to variables in the procedures. It can be seen in the code that all text boxes
as described in Chapter 3 are read. In addition to this, a constant value of center
coordinates “(center_x_vol, center_y_vol)” are also assigned. These values were selected
to center them for the current size of the picture box and were not provided in the Data
Form to be easily interfaced with the Autoscaling procedure currently used by Schwitzer.

The initial commands erase the previous plot and insert the current plot drawing tittle.

40

4.3 Dimension and Area check calculations

In this subgroup the area over a range of O - 360 of the volute passage is read and
the corresponding parameter that make up the cross-section is determined. For
convenience the Area distribution though the volute passage was assumed to be linear and

a simple formula to evaluate the area is used,

 

Area (angle) = Area (throat) * (aggée) (4.1)

where angle is the volute passage from O - 360 degrees. This formula was kept simple to
be modified later on for use in non-linear AIR distributions. Using the area at the throat
the diameter, minor axis and height for circular, ellipse and rectangular cross-sections,
respectively are determined. In case of the circular cross-section the diameter at all angles
of the volute passage can be determined as the area is known. In the case of the elliptical
and rectangular cross-sections the width to height ratio is needed. This is obtained using
the area, centroid radius at the throat. Keeping this width to height ratio constant the
required parameters from O - 360 can be determined.

After these areas and parameters are recorded, a check for the actual area is
carried out. Using the previously generated values the true value of the areas is
determined. This is done by using the methods as defined in Chapter 2. Now using this
value, a check is carried out against the required area and if the tolerance limits are met
then it proceeds to the next degree of volute passage. If the difference in the areas are
greater than the required tolerance then one of the parameters are increased or decreased

until the tolerance is met. In case of the circular cross-section it is the diameter while for

41

the elliptical and rectangular cross—sections it is the height. This is done for 0 - 360 of the

volute passage and the true dimensions at each degree of cross-section is recorded.

4.4 Plotting the Inner Circle
The inner radius of the volute is specified in the Compressor Data Form and this
data is read and transferred to the subroutine by the “OK” command. This radius is then
plotted over 360 degrees of the volute and since it is constant, the plot is circular. The
curve is plotted using the cylindrical coordinate method and using a loop of “theta”
varying from 1 to 360 the following X and Y coordinate points are plotted.
X (theta) = Radius * Sin (theta) / drawscale (4.2)
Y (theta) = Radius * Cos (theta) / drawscale (4.3)
This method is used regularly for all the plots with minor differences. The drawscale is
used so as to scale the drawing, as the volute profile at full scale is large as compared to
individual cross-sections at different angles. The drawscale value is also specified in the
data form. Using these data points obtained lines are drawn from the X and Y coordinate
of one angle to the next. As the angle interval is small the plot appears to be a smooth

curve.

4.5 Plotting the Centroid

The centroid values of each degree of volute passage are calculated during
“Dimension and Area Check” loops using methods described in Chapter 2. These values
are then plotted in a manner similar to the way the inner radius is plotted. The difference

is that the centroid radius is not a constant value in the Constant Inner Diameter type.

42

Again the drawscale is used for scaling and the curve is plotted as a number of lines

joining the X and Y coordinate point at each degree of cross-section.

4.6 Plotting the Volute Profile

As the centroid around the volute passage is already known and plotted, to get the
volute profile only one parameter is needed. In the case of circular cross-section it is the
diameter while for the elliptical and rectangular type it is the height. These profiles can be
defined as the “inner and outer radii” for convenience.

4.6.1 Constant Centroid

For the constant centroid type of profiles the centroid radius remains constant, so
by adding or subtracting the diameter or height previously determined from the centroid
radius value the wet surface radius of the volute profile is obtained. For the outer radius it
is added while for the inner radius it is subtracted.

4.6.2 Constant Inner Diameter

For these types, the Inner radius remains unchanged and this is considered the
inner radii. By adding the diameter or the height previously obtained to the inner radius
the outer radius is determined.

This is done for each degree of volute passage and these radii are then plotted in a
manner similar to the inner radius and centroid radius. The drawscale is used for scaling
and lines are plotted from one X and Y coordinate to the next and a volute profile is
generated. Also it may be noted that the diffuser is assumed to be tangential and to avoid

overlap with the 1 - 90 degrees of volute profile an “if “ statement is used. This logical

43

operator checks to see if the profile at various angles overlap the diffuser. All Y

coordinates higher than the inner radii coordinate at the throat are not plotted.

4.7 Plotting the Diffuser

The diffuser is assumed to be tangential and therefore the inner surface of the
diffuser is tangential to the inner radius at the throat. Two variables (X_diff_A,
Y_diff_A) are determined. Y_diff_A is dependent on the ratio of the diffuser outlet area
to the throat area. The square root of this ratio is multiplied to the height of the throat and

this value is then added to the outer wet surface Y coordinate at the throat.

 

(X_diff_A, Y_diff_A)

9“
\
\
Q
\
o.. ‘
‘Q

l

\
\

\
> ~, '\

Diffuser Length 2‘, 1|

 

 

 

Figure 4.1 Diffuser Construction
The X_diff_A coordinate is dependent on the diffuser length and is obtained by adding
that length the X coordinate of the inner radii at the throat. Using these coordinates the

diffuser is then plotted as the rest of the coordinates are known.

44

4.8 Plotting the straight line surfaces (Cross-section)

This part of the code deals with the cross-section generation at different angles of
cross-section. For this a new set of center coordinates (center_x_cross, center _y_cross)
are defined and these are used to position the cross-section plots. The straight lines are as
described in the figure 4.2 and these are used to define the passage leading into the
volute. These lines are broken down into two parts and are referred to as “Line” and
“Inner Line”. Also these plot make use of the Edge width and Gap width factor (diffuser

width, b5) which are as detailed in the figure.

 

(Center_x_cross, Center _y_cross)

 

 

Edge Width

 

 

 

[Vt Cross-section Plot I

 

 

 

 

Figure 4.2 Straight Lines and 3/4 Cross-section Plot

4.9 Plotting three-fourths of Cross-section View

In this part of the code only three-fourths of the cross-section is plotted. The
dashed curve in figure 4.2 is similar to what is carried out. As cross-section at 30 degree
intervals are needed a loop is generated from 1 to 360 with a step of 30. The cross-section

parameters (diameter, minor and major axis, height and width) at these intervals were

45

calculated earlier during the “Dimension and Area Check” loop. Using these values the
cross-section is then plotted. A cylindrical coordinate method is used to plot the circular
and elliptical cross-sections while in the rectangular cross-section it is plotted using
straight lines. It may also be noted that for the rectangular cross-sections to avoid the
display of sharp edges, radius of curvatures were used. These are a set of curves of a

constant radii plotted at the edges.

4.10 Plotting Radius R3 and Rest of Cross-sectional View
The method of plotting R3 differ between Constant Centroid and Constant Inner
Diameter. Hence it is better to describe them separately.

4.10.1 Constant Centroid

 

,c".-- --—'"‘.
' .
I. ‘
O ..

 

’.
’/ [End coordinates l \.

 

 

 

Vertical and Horizontal Lines

 

 

 

 

 

Figure 4.3 Radius R3 for Constant Centroid
This method of plotting is common to all cross-sections of the constant

centroid type. Using the end coordinates from the previous plots (Edge plot and three-

4o

fourth cross-section plot) a vertical and horizontal line is drawn taking into consideration
that these lines will then be tangential to the curve of radius R3. The radius R3 is
specified in the data form and this value is then used to connect these lines with smooth

CUTVC.

4.10.2 Constant Inner Diameter

 

B” i
x..\. i :
....... I |

f ' ‘
z I

i :

[Horizontal Ling]

 

 

 

 

Figure 4.4 Radius R3 for Constant Inner Diameter
As compared to the Constant Centroid this is a little different. As the height of the
edge is governed by the value of radius R3. Only a horizontal line is plotted as shown in
figure 4.4 from the end coordinates of the previous three-fourth cross-section plot. The
length of the line is fixed by a tangential intersection with the curve of radius R3. The

curve itself is then plotted after that.

CHAPTER 5

DESCRIPTION OF TURBINE VOLUTE AND CROSS-SECTION

GENERATION MODULE

This chapter describes the code used to generate all data needed to construct the
cross-section of the Open Flow and Twin Flow turbine. Again it was found convenient to
group these as subroutines and house them under a single module. The turbine
subroutines differ from the compressor module subroutines in the way that it uses
procedures to calculate the area and also to plot the cross-sections. Other motivation for
this type of construction was so that at a future stage it could be interfaced with other

visual basic applications.

5.1 Turbine Module - (ModTurbine.Bas)
This module contains a number of procedures and are as listed,
1) Open Flow Area - (Area)
2) Twin Flow Area - (Area_twin_flow)
3) Open Flow Plot - (plot_Turbine_profile)
4) Twin Flow Plot - (plot_twin_flow_turbine)
5) Open Flow Main - (SubOpen_Flow)

6) Twin Flow Main - (SubTwin_flow)

47

48

5.2 Open Flow Area - (Area)

This procedure is used to calculate the area at different cross-sections of the open
flow turbine. The inputs to these procedures are passed with the call command in the
open flow main procedure. The method used to achieve this is as described in chapter 2.
The area is subdivided into 3 parts, then each is individually determined and then added
up. After the area is calculated the radius of centroid for that particular cross-section is
also determined. This is also described in detail in chapter 2. This data is then passed

back to the main procedure for data recording and further generations.

5.3 Twin Flow Area - (Area_twin_flow)

This procedure works in the same way as the open area calculation procedure. The
method for area calculation are detailed in chapter 2. The only difference being the
divider wall. All input parameters are passed on by the call command, the area and the
radius of centroid is generated using these parameters. This is then passed back to the

main procedure for further generation.

5.4 Open Flow Plot - (plot_Turbine_profile)

This procedure is used solely for plotting the turbine cross-section using the given
input parameters. This procedure is called from the main subroutine and is used to plot
the cross-section at 30 degree intervals. As the cross-section is assumed symmetrical for
this part of the project (Bezier curves would be able to handle curves that are not
symmetric once the initial plot was obtained), it was found easier to plot the left half of

the cross-section first and then mirror the right half. For the radius R1 to be plotted, the

49

angle through which it spans (or) is needed. This is obtained by using simple geometry as
described in the figure 5.1. The value of 9 is assumed and this is to ensure that radii R1
and R2 meet tangentially. The angle “9” can be varied in the code for special cases. (It
was also found that variations in 6 did not change the plot or area calculation drastically.)
Once “or” is calculated the center coordinates are assumed so as to position the plot on the

sheet and then the radius R1 is plotted through an angle “or”.

 

 

h
.._\l.

 

\

Right half is a
mirror image of
[the Left half

 

 

 

 

 

................................................................... cL

 

 

 

Figure 5.1 Profile Generation (Open Flow)
After Radius R1 is plotted the last point is used to start of the plot of radius R2.
Using the input parameters (R1, R2 and S), the center of radius R2 is determined using
simple geometry. Using these coordinates radius R2 is plotted over a span of 20. Now
using the end point of the radius R2 plot and base circle radius (BCR) the dimensions of
the parabola are known. Using the start and end coordinates of the parabola, the parabola

equation is determined. With this equation the parabola is then plotted. This completes

50

the left hand side of the plot. Using all the X coordinates used to plot the profile a mirror
set of X coordinates are generated about the central axis. Using these new set of mirror

coordinates the right hand side of the profile is plotted.

5.5 Twin Flow Plot - (plot_twin_flow_turbine)
This plot is similar to the open flow plot described earlier, except now in addition

to the open flow profile, the divider wall is introduced.

 

 

At

 

Right half is a
mirror image of
the Left half

 

 

 

Tip 4)

 

 

BCR \. '
" ]Divider Wall o

 

 

.................................................................. C r
Figure 5.2 Profile Generation (Twin Flow)

 

In this procedure the divider wall is plotted first. The divider wall diameter is used
to obtain the tip radius of the divider wall. Then using the Tip radius a curve is plotted
through 90 degrees. Using the end point coordinates of this curve the divider wall is
constructed. The length is obtained by using simple geometry. From the end point of the

divider wall radius R3 is then plotted through 90 degrees. Then with these endpoints as

51

the start points for radius R1, the rest of the plot is generated similar to the open flow plot
described earlier. As the initial overlapping part of radius R1 is not needed to be plotted
an ‘if” statement is used to check it until the generation reaches the end point of the

radius R3 plot.

5.6 Open Flow Main - (SubOpen_Flow)

This procedure is the main manager for the open flow turbine profile plot. It
regularly calls the area and plot subroutines to do the major part of the calculation as all
these are repetitive. As the evaluation of the open flow parameters give only the area as
input is not as easy as the compressor evaluations, an excel spread sheet was constructed
so as to study the pattern of variation in the parameters.

This excel sheet is attached in the appendix C. The first part of this spread sheet
calculates the area and the radius of centroid for a given set of parameters. This method is
as described in chapter 2. The second part of the excel sheet is a detailed examination of
all needed parameters with respect to area and centroid radius variation. Data was used
from the existing drawing provided by Schwitzer and using this data (R1, R2, and S) the
area and radius of centroid was determined. This was done for different types of existing
turbine design at every 30 degree of cross-section. A check was carried out on the
variation of the ratios of different parameters and it was found that the ratios of (Rl/Rc),
(R2/R1) and (R2/S) varied least. These ratio were then calculated on the same excel
sheet. This was done for each 30 degree interval of cross-section and the average of these
for each interval was also determined. These averages are as listed in the table below. The

average (Rc/Rc-l) is the ratio of the centroid radius of the current cross-section to the one

52

before. Computing these values it was noted that for some intervals there was a linear
variance. From the throat to 210 degree of cross-section all of the above ratio could be
obtained using a linear equation. This maybe noted in the code and a loop is used for
sequential generation of the plots. Further to 210 degrees of cross-section a linear
variation of all ratios simultaneously was found to be a problem and to simplify the
procedure loops were constructed for every two 30 degree intervals. These intervals are
grouped together in the table below with a different background color. This process was

repeated using the ratios below and the profiles for the various cross-sections were plotted

Rl/Rc RflRI R2/S Rc/Rc-l

Throat

330

300

270

240

210

0.165 1.025

0.155 1.030

120

90

60 1.100 0.055 0.142 1.045

30 1.050 0.045 0.135 1.050

 

Table 5.1 Distribution of Parameter Ratios (Open Flow)

53

Using the already recorded parameter values at various intervals of cross-section
the intermediate points of the radius R1 and Rc were evaluated by interpolating between
each interval. In this manner a value for the above parameters for each degree of cross-
section was obtained. Using these values the volute profile for the open flow turbine was
generated and plotted using the cylindrical coordinate method from O - 360 degrees. The
diffuser was then drawn out as well and is done so as described earlier for the compressor

module.

5.7 Twin Flow Main - (SubTwin_flow)

This method is similar to the working of the open flow procedure, except in this
case an additional parameter is involved. Again this procedure regularly calls the
subroutines for area and plot generation as these task are repetitive. Since the number of
parameters involved are large, the determination of these parameters from only the area as
an input is not simple. An excel sheet was used again to examine the pattern in which
these parameters were varying. This excel sheet is attached in the appendix.

From the excel sheet it can be seen that first a calculation of area and centroid
radius was done as described in chapter 2. This was then used to generate the second part
of the excel sheet in which (like the one used for open flow) various ratios were
calculated. It was found that in addition to ratios (RI/Re), (R2/R1) and (R2/S) , the radius
R3 also varied on a pattern of its own. These are described as in the table 4.2. Examining
these ratios it is observed that the ratios vary linearly for throat - 270, 240 - 180, 150 - 90
and 60 - 30 degree intervals of cross-section. Using these linearly varying subgroups,

loops were constructed in the code so as to generate the parameters. These subgroups are

54

denoted by a common background color in the table. Using loops for the above intervals,
linear equations to generate the required ratios were constructed within these loops. After
respective parameters were detemrined, the area using these determined parameters is
calculated using the “area” subroutine and the actual radius of centroid is found and

redefined.

R1/Rc R2/Rl R2JS R3 Rc/Rc-l

Throat

330

300

270

240

210

180

150

 

Table 5.2 Distribution of Parameter Ratios (Twin Flow)
As in the case of open flow the already recorded parameter values at

various intervals of cross-section the intermediate points of the radius R1 and Rc were

55

evaluated by interpolating between each interval. A value for each degree from 0 - 360
was then obtained. Using these values of R1, Rc and BCR a cylindrical plot was carried

out and the volute profile for the twin flow turbine was generated.

5.8 Area Check Calculations

For every 30 degree interval it may be noted that the “call” command was used.
The main function of this is to calculate the area and the centroid radius using the
parameters generated by the ratios. The Area subroutines returns these values and a check
is carried out to see whether these parameters generated were in accordance with the
requirements. If the tolerances were not met then a minute increase/decrease is made in
radius R1 and all parameters are redefined. This is carried on till the tolerances are met.
Also it maybe noted that although the radius of centroid is determined initially by using
the ratio values from the spread sheet. Using this generated parameters, the actual radius
of centroid is determined by the Area Subroutine and this value is recorded. This ensures

that the correct radius of centroid is used which then governs all other parameters.

CHAPTER 6
USE OF BEZIER CURVES FOR SURFACE GEOMETRY GENERATION

6.1 Introduction

This thesis being the first part of the project a few details of future work to be
done is detailed in this chapter. The earlier chapters described the method in which the
geometric parameters are generated, now using these parameters Bezier curves are to be
constructed so as to enhance surface generation. In this chapter a review of a few basic
ideas of analytical geometry, introduction to the’Bezier polynomial technique and some
fundamental properties of Bezier polynomials are presented. The use of these
polynomials for flexible volute profile and turbine description can be used to generate
simple curves that form part of a volute or turbine cross section along with other

elementary geometry’s like line, ellipse, parabola and arc.

6.2 Explicit, Implicit and Parametric Functions
In this section a brief summary will be given of some of the classical geometry
description concepts which are important for an appreciation of the capabilities of Bezier
functions. A more detailed description is given in [1] which is a good introduction to
computational geometry, particularly Bezier polynomials.
y = f(x) (6.1)
The simplest way to define a plane curve is to use the explicit form, where f(x) is

a prescribed function of x, enabling us to tabulate and plot the function in a familiar way.

56

57

The explicit form is satisfactory when the function is single valued 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,

f(x, y) = 0 (6.2)
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 calculated
directly unless the equation can be reduced to an explicit equation for x or y. For example
the equation,

x2+y2- r2: 0 (6.3)
is the implicit function for the circle. 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

=+ (r —x2) forthe upperhalfand y=- (r —x2) forthelowerhalf.
y

An alternative way of describing lines and curves which 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 = x(u), y = y(u). For example the circle
x2 + y2 - r2 = 0 can be expressed parametrically by the equations:

x = r * Cos (u)

y = r * Sin (u) (6.4)

where u takes values in the range of 0 < u < 21: . Although we normally need to describe

the range of the parameter u, this can be an advantage if we want to describe only the

58

segment of a curve. The parametric equations enable us to plot points on the curve by
evaluating x(u) and y(u) for successive values of u.

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

equation is

N
r(u) = 2 u"a. (6.5)
n=0

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.

The use of quadratic and cubic (2“‘I and 3rd order) polynomial parametric functions
and the physical meaning of their vector coefficients will now be illustrated.

The segments of quadratic parametric curves and surfaces are described by an
equation of the form:

r(u)=aO +alu+a2u2 (6.6)

It can be seen that the three vectors a0, a1, and a; are required to define the
segment of a quadratic curve. The general n vectors are needed to describe a curve of
degree (n-l). It is usual to assign parameter values of u = O and u = 1 to the two ends of
the segment, with 0 < u < l in between. The simplest tool to determine the vector
coefficients a0, a), and a2 is to specify the values of r, dr/du and d2r/du2 at the beginning

of the segment. Thus,

59

a=d®

00 +611 +a2 =r(1) (6.7)
a] =Cb/au(0)

Solving for a0, a], and a; we get,

“0 = r(O)
a1 = drdu (0) (6.8)

a. = r(l)—r(0)-%,(O)
By direct substitution in equation (6.7), we can obtain r in terms of r(0), r(l) and

dr/du(0). Thus,

r: r(u) =r(0)(1—112)+I(1)u2 +dVah(0)(u-u2) (6.9)

Altemately we may write r = U . Q . S where, U, Q and _S_ denotes the product of

the three matrices given below:

1 0 O r(O)
r(u)=[1 u u2]* 0 o 1 r(l) (6.10)
—1 1 —1drdu(o

Cubic parametric equations for the definition of curves and surfaces in aircraft

design, can be described by the equations of the form:

r: ,(u) zao +alu+a2u2 +a3u3 (6.11)
Following a similar procedure as done above for the parametric quadratic equation
we can write equation (6.11) in terms of the boundary conditions r(0), r(l), dr/du(0) and

dr/du(1) as follows:

1 0 0 0 r(0)
0 0 1 0 r0)
-3 3 -2 —1d’du(0)
2 —2 1 1 drdu(0)

r(u)=]l u u2 u3]* (6.12)

 

 

 

 

6.3 Bezier Curves

The vector coefficients of the parametric curves described by the equation (6.5)
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 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 curves due to
the many cross couplings as can be seen from the non-diagonal elements in the coefficient
matrix in equation (6.12).

Bezier [1] has recombined the terms of the polynomial parameterisation 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 Beziers form

- we write equation (6.6) as follows:
r = r(u) = (1— u)2 r0 +2u(1-u)rl + uzr2 (6-13)
where again 0 < u < l for any given segment. It can be seen that this is a simple

rearrangement of the quadratic polynomial form of equation (6.5) with,

61

do ="o
at = 2(’i _ro)

a2 =ro-2r,+r2

The important consequence of this rearrangement is that:

r(0)= r0
r(l)=r2
d%1u(0) = 2(r1 — r0)
dyduO) = 2("2 - r1)

 

 

 

 

 

Figure 6.1 Bezier Curve Example

(6.14)

(6.15)

Thus the curve described by Beziers form passes through the points r0 and r1 has

P0 and P2.

Similarly equation (6.11) can be written as:

r(u) = (l -- u)3r0 + 3(1— u)2 url + 3(1-- u)u2r2 + u3r3

a tangent at r0 in the direction from r0 to r1 and has a tangent at r; in the direction from
r; to r2. The straight lines P0P] and P1P2 form a figure called the characteristic polygon of
the curve. In order to design a quadratic curve, we choose the points Po and P2 through

which we want the curve to pass and then place P1 so that we get the desired tangents at

(6.16)

62

where,
a0 = r0
01 = 3(rl - ’0)
(6.17)
(12 = 3(r2 - 2r1+ r0)
a3 =r3 —3r2 +3rl —ro
Thus the description of an r1th order Bezier polynomial equation is:

N j -n

r(u)= 21-N— u" (l—u)~ r" (6.18)

6.4 Changing The Order Of The Bezier Polynomial

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(N’fH):(NI-.-1)[ir‘(n1;1)+(N+1—n)r2(%)] (6.19)

for O<n<N+1

 

 

 

where r(%) represents the 11th order Bezier polygon vector of an N‘h degree Bezier

Polynomial.

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 Future Interfacing for varying Area Distribution

In this project a linear A/R distribution was considered. This was set up simply as
described in chapter 4. This may be modified in the future so as to link itself to a varying
Area distribution. This area distribution will be plotted on a chart using bezier curves so
if a change is needed to be made it can be done by clicking and dragging the bezier nodes.
This makes the area distribution very flexible and as this is an input to the profile and

cross-section generation, it will suitably alter the drawings.

7.2 Area Check Calculation.
7.2.1 Compressor

It may be noted that the area check calculation is used for all compressor drawings
so as to finalize the exact area at each cross-section and also evaluate the parameters for
these cross-sections. [As discussed in Section 3.3 “Dimension and Area Check
Calculation”.] It was observed that the difference in the actual and assumed area was
small and therefore fewer iterations [as detailed in Section 3.3] were needed to fit the
tolerances and evaluate the parameters. The output displayed on the “Parameter Form”
was checked against the tables existing on the Schwitzer drawings and found to match

quite accurately. The reason the word “quite” is used is because the AIR profile was

63

64

considered to be linear in this project while is not the actual case on the existing

drawings.

7.2 Turbine

It may be noted that in the case of the turbine generation codes an “Area Check
Calculation Loop” was used in the initial loops but not later on. The reason here being
that a linear AIR distribution was used for the Area values and if we refer to the chart in
appendix C of the actual AIR distribution of the existing turbine drawings we see that it is
not linear. It was found that running the “Area Check Calculation Loops” on all the
generations took a long time. This is blamed on the reason that the initial guess on the
parameters were way off from the linear AIR distribution (i.e. the formula described in
equation 4.1) that they were being checked with. This caused the time delay in meeting
the tolerance limits and hence the plot. Therefore to reduce the run time until a more

realistic AIR distribution is constructed so as to check the tolerances against.

7.3 Bezier Curves

 

 

 

 

 

65

Figure 7 .1 Cross-section made up of Bezier Curves

As this thesis was the first part of the main project, it dealt with the initial
methods to generate various cross-sections. These can be referred to as node points.
Using these node point an attempt can be made to plot the same profile using bezier
curves. For example the figure shows a simple cross-section which can be subdivided into
a number of different bezier curves. These curves are referred to as Bezier(l), Bezier(2),
Bezier(3) and Bezier(4). As the node points are available, we can now use this data to
plot it. Bezier (1) would be a straight line and would need only the start and end points.
Bezier(2) is a curve of some dimension and would need a number of node points for
accurate definition. Bezier(2) would share it start node point with the end node point of
Bezier(l). Again Bezier(3) and Bezier(4) are straight lines which would be generated by
knowing the start and end points of each. Although this might look simple, it is not as the
cross-section can get complicated and methods have to devised on obtaining respective
node points.

The main advantage of using bezier curves in cross-sections such as the figure 7.1,
is that these node points can be changed to alter the shape and hence the area and
parameters of the cross—section. An example for which this may be used is to fit housings

into engines with limited space by modifying certain sections.

7.4 Parameter Form
A detailed description of the “Parameter Form” is done in Chapter 3. The main
function of this is to display data that was generated by the code in a format similar to the

existing tables available on the drawings. It was also designed to be the interface for the

66

Bezier curve application and all needed input data for that application may be generated
and displayed in a similar format. Also if data was changed on the grid it might be
possible to automatically update the bezier curve generations. This would make it
manipulative. Also it may be possible to update the data in the grid if the bezier curves
were altered by the ‘click and drag’ method. A reverse calculation may be possible so as

to provide all parameters such as area, radii etc.

7.5 Approximations

All assumed data was included on the data forms and may be changed as needed.
Some more generations that were assumed and may be changed later are,
7.5.1 Centering

A manual method was provided to center the drawings on the form. This was kept
simple so as to take advantage of the existing scaling technique used by Schwitzer in their
Visual Basic application. The center coordinates if need to be changed have to done by
changing the data in the code. This data is well commented on in the code.
7.5.2 Diffuser

The diffuser was constructed by using simple techniques as a lot of data on
diffuser construction was not available and is not a priority on this project. The generation

of the diffuser may be reconstructed later on if needed and so it is kept simple.

7 .6 Recommendations
It maybe recommended that for generating the bezier curves it may be more

advantageous to have a single procedure to define the cross-sections and generate the

67

curve based on some input parameters like radius, width etc. Then for each of these cross-
sectional types the number of bezier nodes could be arbitrary. The bezier formulation
could be written by a summation procedure. Once the number of curves are fixed, a
separate code could be used to define each curve that makes up the whole cross-section.
This might have an advantage and disadvantage, the advantage being that a construction
of this type would give the user a powerful grip on the flexibility of the cross-sectional
shape. The disadvantage would be that any future unseen shapes that need more than the

number of curves available could cause a problem.

LIST OF REFERENCES

1. Brown W.B. and Bradshow G.R.: Design and performance of a family of diffusing

scrolls with mixed flow impeller and vaneless diffuser, NACA Report 936, 1949

2. Eckert B and Schnell E. : Axial - und Radialkompressoren, 2nd ed. Springer Verlag,

1980

3. Stiefel W. : Experiences in the development of radial compressors, Lecture Notes VKI

1972, Brussels

4. Chapple P.M. , Flynn RF. and Mulloy J .M.: Aerodynamic design of fixed and variable
geometry nozzleless turbine casing, ASME Journal of Engineering for Power, Vol. 102,

January 1980

5. Japikse D.: advanced diffusion levels in turbocharger compressor and component

matching. IME Conference on Turbochargers and Turbocharging, Paper C45/82, 1982

6. Weber CR. and Koronowski M.E. : Meanline performance prediction of volutes in

centrifugal compressors, ASME-IGTI 1986, Paper 86-GT-216

68

69

7. Iversen H., Rolling GR. and Carson J.: Volute pressure distribution, radial force on the
impeller and volute mixing losses of a radial flow centrifugal pump, ASME Journal of

Engineering for Power, Vol. 82, April 1960

8. Kurokawa J .: Theoretical determination of the flow characteristics in volutes, IAHR-

AIRH Symposium Tokyo 1980

9. Badie R., Jonker J.B. and Van Essen T.G.: Calculation on the time dependent potential

flow in a centrifugal pump, ASME Paper 92-Gt-151

10. Gurewich and Gurewich : Visual Basic 4.0, 3rd Edition.

11. Rothbart : Mechanical Design and Systems Handbook.

12. David F. Roger and J. Alan Adams : Mathematical Formulation for Computer

Graphics, 2"d Edition.

 

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