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CERTIFICATE This is to certify that the Dissertation entitled “CFD ANALYSIS OF PUMP INTAKE SUMP FLOW PATTERN - EFFECTS OF CHANGES IN SUMP GEOMETRYand 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 : ____________________ __________________________________ _____
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CFD Analysis of CW Pump Sump

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CFD Analysis of a CW intake system
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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 : 2012hd91507@wilp.bits-pilani.ac.inEMPLOYING ORGANISATION : Development Consultants Private LimitedSUPERVISORS NAME : Dr. Ranjan GangulySUPERVISORS EMAIL ADDRESS : ranjan@pe.jusl.ac.inDISSERTATION 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