CERTIFICATE
This is to certify that the Dissertation entitled CFD ANALYSIS
OF PUMP INTAKE SUMP FLOW PATTERN - EFFECTS OF CHANGES IN SUMP
GEOMETRY and submitted by JAYDEV CHAKRABORTY having ID-No.
2012HD91507 for the partial fulfillment of the requirements of M.S.
Project Engineering and Management degree of BITS, embodies the
bonafide work done by him/her under my supervision.
______________________
Signature of the Supervisor
Place : ____________________
_______________________________________
Date : ____________________ Name, Designation, Organization
& Location.
Birla Institute of Technology & Science, PilaniOff-Campus
Work Integrated Learning ProgrammeFirst Semester 2014-2015DCPL
ZG629T: Dissertation
BITS ID No. : 2012HD91507NAME OF THE STUDENT : JAYDEV
CHAKRABORTYEMAIL ADDRESS :
[email protected] ORGANISATION :
Development Consultants Private LimitedSUPERVISORS NAME : Dr.
Ranjan GangulySUPERVISORS EMAIL ADDRESS :
[email protected] TITLE : CFD ANALYSIS OF PUMP
INTAKE SUMP FLOW PATTERN - EFFECTS OF CHANGES IN SUMP GEOMETRY.
ABSTRACT
This paper considers the use of computational fluid dynamics
(CFD) as a tool to assist the engineer in the hydraulic design of
pump intakes by comparing different cases and establishing the
actual need of the additional geometrical features, like the pump
compartments and baffles. Encouragingly, the results show CFD can
be utilised to produce qualitative statements regarding the overall
system performance. It is not yet claimed that CFD can replace
physical modelling, but, it can provide a powerful tool to
supplement the experience and hydraulic expertise of the pump
intake system designer.
Keywords: CFD, environmental, hydraulic, model, simulation,
sump, turbulence, vortex.
Signature of Student
Name: Jaydev ChakrabortyPlace: KolkataDate: 14/11/2014Signature
of SupervisorName: Dr. Ranjan GangulyPlace: KolkataDate:
14/11/2014
ACKNOWLEDGEMENTS
This dissertation work was carried out under the principal
supervision of Dr. Ranjan Ganguly, Associate professor, Department
of power engineering, Jadavpur University. I express my heartfelt
gratitude towards his continual support and valuable guidance
amidst his busy schedule.
I must also thank Mr. D. S. Mallick, Executive director and HOD
Mechanical Engineering,DCPL, and Mr. N.A. Chaudhuri, Executive
director, DCPL, for their encouragement and support.
TABLE OF CONTENTS
1.INTRODUCTION81.1.Motivation81.2.Problems associated with
aberrant CW flow.91.3.Importance of CFD analysis for studying flow
pattern of CW pump-intake.101.4.Literature
search.101.5.Objectives.112.PROBLEM DESCRIPTION122.1.System
description122.2.Geometry122.3.Flow Data132.4.Case setup and
configurations used143.SOLUTION METHODOLOGY153.1.Governing
Equations153.2.Boundary Conditions163.3.Method of
Solution163.4.Mesh173.5.Solution and Post-processing184.RESULTS AND
DISCUSSIONS194.1.General194.2.Particle Tracer
Pathlines194.3.Surface streamlines214.4.Velocity
contours234.5.Vorticity plots285.References29
LIST OF FIGURES
Figure 1 : CW and ACW sump drawing (Plan view)12Figure 2 : CW
Compartment (Elevation View)13Figure 3: ACW Compartment (Elevation
view)13Figure 4 : CASE 2 Sump with Compartments14Figure 5 : CASE 1
Basic Sump Geometry14Figure 6 : CASE 3 - Sump with Compartments and
Baffles14Figure 7 : Computational domain (Plan)17Figure 8 :
Computational domain (End view)17Figure 9 : ACW Bell18Figure 10 :
CW Bell18Figure 11 : Particle Tracers from inlet - Case1 (left) and
Case2 (right)19Figure 12 : Particle Tracers from inlet Case2 (left)
and Case3 (right)20Figure 13 : Particle tracers entering ACW bell
Case 1 (left) and Case 2 (right)21Figure 14 : Surface streamlines
Case122Figure 15 : Surface streamlines Case222Figure 16 : Surface
streamlines Case322Figure 17 : Streamlines at -6.2 M - Case 1 and
Case 323Figure 18 : Location of strategic Planes23Figure 19 : Case
1 Velocity Contour Plane A-A24Figure 20 : Case 2 Velocity Contour
Plane A-A24Figure 21 : Case 3 Velocity Contour Plane A-A25Figure 22
: Velocity contour comparison Plane A-A Case 1 (left) and Case 3
(right)25Figure 23 : Velocity contour comparison Plane B-B Case 1
(left) and Case 3 (right)26Figure 24 : Velocity Contours Plane C-C
Case 127Figure 25 : Velocity Contours Plane C-C Case 227Figure 26 :
Velocity Contours Plane C-C Case 327Figure 27 : CW1 Bell Vorticity
Case 128Figure 28 : CW2 Bell Vorticity Case 128Figure 29 : ACW1
Bell Vorticity Case 128Figure 30 : ACW3 Bell Vorticity Case
128Figure 31 : CW1 Bell Vorticity Case 229Figure 32 : CW2 Bell
Vorticity Case 229Figure 33 : ACW1 Bell Vorticity Case 229Figure 34
: ACW3 Bell Vorticity Case 229Figure 35 : CW1 Bell Vorticity Case
330Figure 36 : CW2 Bell Vorticity Case 330Figure 37 : ACW1 Bell
Vorticity Case 330Figure 38 : ACW3 Bell Vorticity Case 330
LIST OF TABLESTable 1 : Abbreviations used7Table 2: Flow
Data13
Table 1 : Abbreviations used
CWCirculating Water / Cooling Water
ACWAuxiliary Cooling Water
HISHydraulic Institute standards
ANSI
CFDComputational Fluid Dynamics
RANSReynolds Averaged Navier-Stokes equation
1. INTRODUCTION
1.1. Motivation
The basic hydraulic design of CW pump intake systems are done in
accordance with the guidelines provided by the Hydraulic Institute
Standards (ANSI/HI 9.8-1998).These standard designs are often
modified on an ad-hoc basis to incorporate different site specific
constraints. These modifications can impact upon approach flow
characteristics and result in underperformance of the CW and ACW
pumps. The function of CW system in a thermal power plant is to
dissipate thermal load of Steam Turbine Condenser, Plate Heat
Exchangers and other mechanical equipments in the turbine and
boiler area. This system rejects the heat to the atmosphere at
cooling towers and the cooled water is pumped backed to the CW
system by CW and ACW pumps. In a thermal power plant, CW pumps
handle by far the largest volume of fluid flow, albeit at a low
head.
CW Pumps are known to experience common operational problems
such as reduced flowrate and head, effects on power consumption and
increased vibration and noise. In many extreme cases pumps may
suffer erosion of the impeller due to cavitation, and excessive
wear of shafts, bearings, wear rings and couplings. This results in
severe deterioration of pump performance and reliability, and
corresponds to a significant increase in operation and maintenance
costs. These problems are sometimes associated with certain
undesirable approach flow characteristics and are caused primarily
by poor design of the pump intake structure. Poor intake sump
design may result in submerged or surface vortices, swirl of flow
entering the pump, non-uniform distribution of velocity at the pump
impeller and entrainment of air or gas bubbles. Laboratory
experiments on scale-models have been utilised to identify the
source of particular problems with a pump sump or intake and find
practical solutions to rectify them. Such investigations have
generally resulted in successful solutions to identified problems,
however, physical model studies are time consuming and
expensive.
Computational fluid dynamics (CFD) is a tool for solving fluid
flow problems. This paper considers the use of CFD as a tool to
assist in the design of pump intake structures and study the
importance of various sump geometrical features such as the CW
compartments, ACW compartments and the baffles. ANSYS FLUENT ver
13.0 has been used to solve the Reynolds Averaged Navier-Stokes
(RANS) equation for solution of the problem.
In this study correlation will be sought between cases and the
effects of different geometrical components will be studied.
1.2. Problems associated with aberrant CW flow.
For pumps to achieve their optimum hydraulic performance across
all operating conditions the flow at the impeller must meet
specific hydraulic conditions. Pump inlet conditions are often
overlooked while designing the pumping intake stations, yet they
may constitute the single reason for a pumping station failing to
meet its required design flow rate. Regardless of the type of
intake, whether pressurized, sump or forebay, pump performance is
dependent upon the provision of adequate hydraulic conditions at
the impeller. A number of problems in the CW intake system can be
associated with aberrant water flow. Undesirable vibrations,
reduction in flow rates, erosion of impeller, excessive wear of
bearings, shaft, couplings etc. are some of the problems which can
be associated with aberrant flow of water in the pump intake sump.
These problems usually lead to higher operation and maintenance
costs and affect the system adversely.
Ideally, the flow approaching the intake section of CW pumps
should be uniform and steady, with vortices at the pump suction
close to zero.
Pump intake design must satisfy the requirements for proper
approach flow patterns for the following specific hydraulic
conditions:
1. Surface vortices;2. Submerged vortices;3. Swirl of flow
entering the pump;4. Non-uniform distribution of velocity at the
pump impeller; and5. Entrained air or gas bubbles.
The negative impact of each of these hydraulic conditions varies
with pump specific speed and size. In general, axial flow pumps
(high specific speed) or large pumps are more susceptible to poor
performance under adverse conditions than radial flow pumps (low
specific speed) or small pumps[endnoteRef:2]. [2: CFD Modelling of
a Pump Intake - Barak Truasheim]
The geometric orientation of the sump or the forebay plays a
major role in determining the uniformity of the approach flow and
can be a source of vortex formations. The vortices, generated
particularly in separation zones, near the pump entrances, have the
tendency of getting advected to the pump intake before getting
dissipated due to viscous action. The presence of high vorticity at
the pump bell-mouth, adversely affects pump head and discharge and
thus, is always undesirable. Further, the call for frequent
maintenance due to wear and tear of parts, amplifies the operation
and maintenance costs of the pumps. Cavitations, fluctuations of
load, vibration and noise, higher inlet losses and reduced pumping
efficiency are some of the problems that these pumps can face
attributed mainly to the aberrant flow patterns in the intake sump
and forebay. Therefore, the design of the channels leading into the
sump, the forebays, the sump itself with all the necessary
structures, shape of the intake, and the relative locations of the
pumps should aim at producing such flow conditions that the angular
momentum about the point of intake is as low as possible.
1.3. Importance of CFD analysis for studying flow pattern of CW
pump-intake.
Analysis done by experimental testing of scaled down models
which goes through a number of modification cycles to arrive at a
satisfactory solution is both time consuming & expensive. With
development of Computational Fluid Dynamics (CFD) & enhancement
of computing capabilities, analysis can be done in much less time
& expense
In the present work an attempt has been made to simulate and
predict the flow conditions such as vortices and swirl for multiple
pump intakes in a single sump, with an aim to validate and
understand the need and importance of some of the geometrical
features like the pump compartments and the baffles using
commercially available computational fluid dynamic software ANSYS
FLUENT 13.0 [endnoteRef:3] as an important design optimization tool
for intake sumps. The time and cost involved in doing the pump sump
physical model studies for the variation of sump geometry and other
components is very high and may be impractical. Hence the present
study emphasises on studying the effect of change in pump-intake
geometry using CFD as the analysis tool. [3: ANSYS FLUENT Ver 13.0
- Manual]
1.4. Literature search.
1.5. Objectives.
The objectives of the present study will be the following:
3D Geometric modelling of CW pump-intake sump.The initial CFD
analysis will include a part of the CW Channel (upto 5 m upstream
of forebay), forebay and the pump suction bell mouths. Other
structural features viz. pump sump chambers, baffles etc. will be
subsequently added and their impact in the overall flow pattern
will be studied. Meshing (grid formation) of the 3D model as needed
for the finite-volume CFD analysis.
Simulating the flow in the pump sump using CFD software and
analysing the flow profile. Graphical representation of various
flow parameters.
Study the effects of changes in sump geometry namely CW and ACW
compartments and baffles on various flow parameters with the aim of
reduction or preferably no vortex formation at the pump inlet.
2. PROBLEM DESCRIPTION2. 2.1. System description
The present study has been made on the CW intake system ,
installed for 1270MW Coal based Power Plant at Nagpur, Maharashtra
of M/s Ideal Energy Projects Limited (IEPL) [endnoteRef:4]. The CW
and ACW pumps were supplied by M/s Worthington PumpsIndia Ltd
(WPIL). The system constitutes two (2) CW pumps and three (3) ACW
pumps. Under normal condition, both the CW and two out of the three
ACW pumps would be operating. For all practical purposes, the free
water surface has been treated to be horizontal. [4: IEPL DOC
No]
2.2. Geometry
The sump geometry along with the CW and ACW bell profile are as
per WPIL drawings and in line with the guidelines stipulated by
ANSI/HIS-1998[endnoteRef:5]. The computational domain starts with a
CW channel (up to 5 m upstream of forebay; additional length of 5 m
has been considered to have the flow fully developed), which ends
in an expanding forebay with vertically sloping section. After the
forebay, lies the rectangular portion of the sump consisting of two
CW pumps and three ACW pumps. Towards the ends of each of the bay,
is placed the suction pipes of the pumps at required clearances
from the boundaries. The suction pipes consist of pump suction bell
mouth and outlet pipes. The outlet pipe from the suction bell mouth
of each pump is extended vertically up to the free surface to
ensure a fully developed outflow. Initial study comprises the
pump-sump and forebay only. In the subsequent stages, the
separation compartments and the baffles were added and their effect
on the overall flow pattern was studied. [5: ANSI / HIS 1998]
Figure 1 : CW and ACW sump drawing (Plan view)2.3. Figure 2 : CW
Compartment (Elevation View)Figure 3: ACW Compartment (Elevation
view)Flow Data
For the present case, maximum volumetric flow rate of each of
the pumps are considered for the CFD simulation. Further, the
initial geometry is modelled consisting of the forebay, side-walls,
suction bell mouths and discharge pipes. The additional structural
items viz. compartment walls, baffles etc. were modelled
subsequently and their effect on the overall flow-pattern within
the computational domain was studied.Table 2: Flow DataCW PumpsACW
Pumps
No. of Pumps23
No. of Pumps Working22
Rated Vol. Flow Rate of Each Pump17,000 m3/h1250 m3/h
Max Vol. Flow Rate of Each Pump22,100 m3/h1625 m3/h
Suction Bell Diameter2043 mm584 mm
2.4. Case setup and configurations used
The simulations were performed on the following configurations
and the effect of introducing the additional geometrical features
(compartments and baffles) were studied and are reported in a
case-to-case basis. This ensured comparisons between the cases and
systematic approach to understand the effects of various
geometrical features in the pump intake sump.
Table 3 : Configuration usedCONFIGURATIONDETAILSFIGURE
REFERENCE
CASE 1Basic Sump geometry with forebay only.Figure 4: Basic Sump
Geometry
CASE 2Addition of CW and ACW compartments to Case 1.
CASE 3Further addition of baffle walls in front of the pump
chambers.
Figure 4 : CASE 2 Sump with CompartmentsFigure 5 : CASE 1 Basic
Sump Geometry
Figure 6 : CASE 3 - Sump with Compartments and Baffles
3. SOLUTION METHODOLOGY3. 3.1. Governing Equations
The flow through the CW pump sump is isothermal, incompressible
and fully turbulent. The conservation of mass and momentum for the
flow is represented by the Reynolds Averaged Navier-Stokes
Equations, which are:
(1)
,(2)where the effective turbulent momentum diffusivity is given
as
.(3)For turbulence modeling of the flow, standard k- method is
employed as follows:
,(4)
.(5)The rate of production of turbulent kinetic energy Gk is
expressed as
.(6)Typical constants for the Standard k- model are C=0.09,
C1=1.44, C2=1.92, k = 1.0, = 1.3.
3.2. Boundary Conditions
The fully elliptic nature of the governing equations require
boundary conditions to be specified at all the physical boundaries
of the computational domain. The inlet boundary condition is
applied at the entry of the computational domain in terms of the
total mass flow entering into the sump. A turbulent intensity of
10% and integral length scale have been considered at the inlet.
The boundary conditions at the outlet of pipes (at the downstream
of the bellmouths) are considered to be fully developed. All wetted
surfaces (channel walls, channel bottom, piers, baffle wall, and
the intake pipes of the pumps) are specified as walls with no slip
boundary condition. The top free surface has been treated as a
boundary with symmetry.
The boundary conditions at various physical boundaries of
computational domain are as follows :
Inlet boundary condition is applied at entry to the
computational domain in terms of total mass flow entering into the
sump
A turbulent intensity of 10% & integral length scale
considered at the inlet
Boundary conditions at outlet of pipes, downstream of the bell
mouth are considered to be fully developed
All wetted surfaces (channel walls, channel bottom, piers,
baffle wall and intake pipes of the pumps) are specified as walls
with no slip boundary condition
Top surface has been treated as a boundary with symmetry
3.3. Method of Solution
The governing equations are numerically solved using a finite
volume CFD code following SIMPLE algorithm [6]. More than 2.5
million tetrahedral computational meshes have been used to
discterize the computational domain. Finer grids are adopted at the
bellmouth inlet and in the pump compartments where the velocity
gradients are high (See Fig. 2). The field variables are
discretized using the Power Law scheme. An underrelaxation
parameter of 0.7 is used for the momentum equation and 0.8 for the
k and equations. The solution proceeds through a succession of
iterations till the residuals fell below a preset convergence value
of 10-5.
3.4. Mesh
To analyze fluid flows, flow domains are split into smaller
subdomains (made up of geometric primitives like hexahedra and
tetrahedra in 3D and quadrilaterals and triangles in 2D). The
governing equations are then discretized and solved inside each of
these subdomains. The aim of the simulation was to analyse the
fluid flow within the computational domain. Considering that the
quality and resolution of the mesh have a great impact on the
results, a fine hybrid tetrahedral element mesh of about 1.5
million cells were used. (Fig 7 to Fig 10 below).
Figure 7 : Computational domain (Plan)
Figure 8 : Computational domain (End view)
Figure 9 : ACW BellFigure 10 : CW Bell
3.5. Solution and Post-processing
The process of solving a complex system is inherently difficult
and requires high-end computing machines. For stability and
convergence several hundred iterations were performed in ANSYS
FLUENT 13.0 SOFTWARE. The post processing of results were done
using ANSYS CFD POST and other tools like MS EXCEL.
4. RESULTS AND DISCUSSIONS4. 4.1. General
The results presented within this section are obtained using the
commercially available FLUENT CFD modelling software. The
simulations of different cases are compared and the effects of
addition of the geometrical components are discussed. The major
criteria which are considered for the comparison of the flow
parameters in between the cases are: prediction of vortices, swirl
angle, velocity distribution and air entrainment. For the ease of
reference, Cases 1 to 3 will be referred to.
4.2. Particle Tracer Pathlines
Particles were released from the inlet surface and the pathlines
over the entire computational domain were captured (see figures 11
- 15 ).The figure below (fig.11) compares the pathlines of
particle-tracers, released from the inlet surface, between Case 1
(basic sump geometry) and Case 2 (addition of CW and ACW
compartments). The encircled area shows the formation of a
circulation zone in Case 1, which is eliminated due to the
inclusion of the pump compartments, in Case 2.
Figure 11 : Particle Tracers from inlet - Case1 (left) and Case2
(right)
Comparing Case 2 (addition of CW and ACW compartments) with Case
3 (with compartments and baffles), the particles are observed to
flow upto the top of the pump bellmouths and then dip inside to
enter the bellmouth, in Case 2, while due to the presence of
baffles in Case 3, the particles reach the bellmouths underneath
the baffle walls.(see fig 12 below)
Figure 12 : Particle Tracers from inlet Case2 (left) and Case3
(right)
The flow occurring in Case 1 and Case 2 is not desirable as the
fluid enters the bell of the pump from right above and may entrap
air with it. The probability of the presence of air core is higher
in these two cases ( Case 1 and 2) rather than in Case 3. This can
be illustrated by the following image (see figure 13 ).
Figure 13 : Particle tracers entering ACW bell Case 1 (left) and
Case 2 (right)
The particle tracer pathlines depict the betterment of overall
flow within the sump area with subsequent additions of compartment
walls and baffles. Similar comparative cases will be given in the
following sections and the qualitative development of flow
parameters will be discussed.
4.3. Surface streamlines
The surface streamlines (at symmetry) are plotted to understand
the pattern of flow, occurring at the free surface of the
computational domain. These images (see fig. 14 and 15 ) show that
vortices are created above the bell mouths in Case 1, while
addition of compartments in Case 2, eradicates this problem and
vortex is found outside the pump compartments. Further addition of
the baffle walls in Case 3, diminishes the number of streams
reaching the pump suction from the top (see fig. 16).
Figure 14 : Surface streamlines Case1
Figure 15 : Surface streamlines Case2
Figure 16 : Surface streamlines Case3Streamlines at a lower
elevation (horizontal plane at EL 6.2 m from top), also depicts the
betterment of flow from Case 1 (fig.16) to Case 3 (fig.17).
Figure 17 : Streamlines at -6.2 M - Case 1 and Case 3
4.4. Velocity contours
Velocity contours are another set of identifiers, which can be
used to predict flow abnormalities, within the computational
domain. The domain is cut into a number of planes at strategic
locations (see fig.18 below) in order to analyse and understand the
velocity profiles in those areas.
Figure 18 : Location of strategic Planes
Velocity Contours on Plane A-A
Possible zone of air coreFigure 19 : Case 1 Velocity Contour
Plane A-AIt is observed in the above figure (fig.19) that there is
a zone above the bellmouth, where the gradient of velocity from
top-to-bottom is positive. Moreover, the velocity vectors in this
zone are not axial to the plane and are rather tangential to it.
This is conducive for formation of air core, which might even reach
the pump suction and cause adverse effects to the impeller. On
addition of pump compartments, as in Case 2, it is observed that
the above problem is resisted. However, there exists a zone of high
re-cirulation, just behind the CW bell (see fig.20 below), which
again can be detrimental to the pump suction.
Figure 20 : Case 2 Velocity Contour Plane A-A
Zone of high recirculation
The velocity contour on the same plane for Case 3 shows a
gradual increase in velocity as the flow approaches the suction
bellmouth, underneath the baffle walls (see fig. 21 below). No
major aberrations in flow profile are observed.
Figure 21 : Case 3 Velocity Contour Plane A-AIn order to provide
a more comparative picture, particle tracers were added along with
the velocity contour lines for comparing the base case (Case 1) and
the final case (Case 2). The figure is given below.
Figure 22 : Velocity contour comparison Plane A-A Case 1 (left)
and Case 3 (right) Velocity Contours on Plane B-B
Figure 23 below, shows the velocity magnitude contours in y-z
direction at plane B-B. In the left side image (Case 1), the
velocity gradient is from top to bottom direction as shown by the
arrow while in the right side image ( Case 3), the gradient is from
the sides.
The flow profiles at the bellmouths of CW pumps 1 and 2 are
almost identical in Case 3 (right side image below), showing
evidence of nearly similar flow distributions, whereas in Case 1
(left image below) the absence of compartment walls on one side and
presence of the sump wall on the other side of the CW pumps, there
is a slight difference in the contour profiles.
Figure 23 : Velocity contour comparison Plane B-B Case 1 (left)
and Case 3 (right)
Velocity Contours on Plane C-C
Gradual betterment of flow is observed from Case 1 to Case 3 as
depicted by the below images. Flow irregularities tend to minimize
on addition of compartments and baffles.
Figure 24 : Velocity Contours Plane C-C Case 1Figure 25 :
Velocity Contours Plane C-C Case 2
Figure 26 : Velocity Contours Plane C-C Case 3
4.5. Vorticity plots
The z-vorticity distributions on x-y plane at the CW and ACW
pump bellmouth throats are shown in Figs. 7 and 8 respectively. For
the CW pump bellmouths, the z-vorticity distributions shows
positive and negative z regions on the top and the bottom halves
for each CW pump. This can be attributed to the inertia of the flow
entering the bellmouth from the direction of the forebay (see Fig.
4). Similar trend is found in the ACW bellmouths, too. Evaluation
of swirl angle following the method described in Section 2.5 shows
that the swirl angle for all the pumps remains well within the
permissible limit of 5o.The above flow profiles are drawn under
when ACW pump1 and 2 are in operation, along with two CW pumps. For
the other two combinations, viz., ACW pumps 1 and 3, and ACW pumps
2 and 3 in operation, qualitatively similar flow profiles are
obtained. However, depending upon the actual z-vorticity
distributions, the values of the swirl angles at the pump
bellmouths differ slightly. The values of swirl angles under
different combinations of ACW pump operation is listed in Table 2.
It is seen from Table 2 that the swirl angle
Case 1 :
Figure 27 : CW1 Bell Vorticity Case 1Figure 28 : CW2 Bell
Vorticity Case 1
Figure 29 : ACW1 Bell Vorticity Case 1Figure 30 : ACW3 Bell
Vorticity Case 1
Case 2:
Figure 31 : CW1 Bell Vorticity Case 2
Figure 32 : CW2 Bell Vorticity Case 2
Figure 33 : ACW1 Bell Vorticity Case 2
Figure 34 : ACW3 Bell Vorticity Case 2
Case 3:
Figure 35 : CW1 Bell Vorticity Case 3
Figure 36 : CW2 Bell Vorticity Case 3
Figure 37 : ACW1 Bell Vorticity Case 3
Figure 38 : ACW3 Bell Vorticity Case 3
5. References