Visualization of Fluid Flow Patterns in Horizontal Circular Pipe Ducts

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Visualization of Fluid Flow Patterns in Horizontal Circular Pipe Ducts Powered By Docstoc
					                                                            (IJCSIS) International Journal of Computer Science and Information Security,
                                                            Vol. 9, No. 6, June 2011



    VISUALIZATION OF FLUID FLOW PATTERNS IN
        HORIZONTAL CIRCULAR PIPE DUCTS
                    Olagunju, Mukaila,
             Department of Computer Science,                                                         Taiwo, O. A (Ph.D)
           Kwara State Polytechnic, Ilorin, Nigeria                                              Department of Mathematics
                 olamukaila@yahoo.com                                                            University of Ilorin, Nigeria.
                                                                                                  Oataiwo2002@yahoo.com


Abstract— This paper developed a visualization model for                      Visualization has a lot of definition which depend on it
determination of frictional Head loss in a circular pipe ducts. Head          application. Visualization according to [1], is the systematic
loss is due to friction when the liquid or gases come in contact with         and focus visual display of information in form of tables,
wall of the pipe. To determine the loss at each duct, modified Hagen          diagrams and graphs. Previous authors were concerned with
postulates equation was used in visualization. Frame work stages              representative and process of information by the brain in their
were developed which consists of data generation framework stages,
data enrichment framework stages, data rendering framework stages,
                                                                              definitions [2] where they tried to distinguish between Visual
visualization development stages and output representation                    perception as meaning the image, an object achieved and as it
framework stages. Based on the model of visualization stages,                 can be seen as visual imagery, the mental production of an
MATLAB program was used to determine head loss due to pressure                object in its absence and spatial imagery as represented by
drop and represented in tabular form and 2D representation. This              tactile meaning. A linkage was established between brain
model greatly assist the learners and instructors in determine the            activities with the uses of phrase “mental imagery” instead of
flow patterns especially the head loss of fluid in a pipe wall by             visual imagery [3].
considering different points or ducts, this model serve as a reusable                   Also [5], visualization is also described as internal,
for both learner and instructors by assist in determine the region            mental construct i.e. mental models, thought to be in the mind
along the wall of the pipe where the head loss is very great.
                                                                              and use in mental imagery and to solve problems.
 Keywords: Step Wise Visualization, Patterns, circular, pipe ducts,
fluid flow.                                                                   Visualization is also described as the act or process of
                                                                              interpreting in visual terms or putting into visual form [4.
Introduction                                                                             Fluid according to [5] is defined as a substance
For centuries, fluid flow researchers have been studying fluid                which cannot with stand a shear force or stress without
flows in various ways, and today fluid flow is still an                       moving as can a solid. It was further classified fluids as liquids
important field of research. The areas in which fluid flow                    or gases. A liquid has intermolecular forces which hold it
plays a role are numerous. Gaseous flows are studied for the                  together so that it possesses volume but no definite shape.
development of cars, aircraft and spacecrafts, and also for the               They also classified fluid by the types of their flow into
design of machines such as turbines and combustion engines.                   laminar and turbulent flow.
Liquid flow research is necessary for naval applications, such
as ship design, and is widely used in civil engineering projects
such as harbor design and coastal protection. In chemical                     Characteristics of Good Visualization.
engineering, knowledge of fluid flow in reactor tanks is                          Before visualization can be categorized as a good
important; in medicine, the flow in blood vessels is studied.                 Visualization, it must have these qualities:-
Numerous other examples could be mentioned. Fluid is always                       1. It serves a clear purpose
flow in pipe.                                                                     2 Show the data without distorting it.
The pipeline and pumping designers are always concern with                        3 Cause the viewer to think about the substance of the
flow patterns especially in preventing the losses of fluid in                          data.
when the pressure drop play major role                                            4 Present large quantities of data in smallest space.
As fluid flows inside the pipe, the pressure drop or losses
occur due to fluid contact with pipe wall and try lead to                         Materials and Methods
friction loss which also called the head loss velocity is one of                  The material use in this paper is based on data that ware
the factors loss in pipe the size of pipe diameter (inside) also                  generated from modify Hagen postulate equation. The
cause friction loss. There two factors mentioned about ,which                     method used is based on development of mathematical
can only be demonstrated as factors causing head loss or                          model and visualization by develop taxonomy framework
                                                                                  stages.
friction loss function, model, stimulation and visualization
approach which is the
Focus of this work. Visualization is hereby proposed to
predetermine the flow trends.                                                     Taxonomy of Visualization Model (TVM)




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                                                                                                            ISSN 1947-5500
                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                      Vol. 9, No. 6, June 2011


Taxonomy according to [7], in his paper title. “A principled of
taxonomy of software “ Defined taxonomy as a common
language or terminology that facilitates communication about            B = -pe2,where 0 < e < r
ideas or discoveries.                                                        4k
 “An early step towards understanding any set of phenomena              (2)


                                                                              =         +           −
is to develop taxonomy” [9].                                            Substitute 2 into 1 to get
The importance of taxonomy for visualization includes:
To make the thinking way and application goals clear
              1. To discover the shortage of visualization
                   research.
              In this work, in order to illustrate the Taxonomy         U=p ( r2-e2)
              of Visualization Model (TVM), the frame work                  4k
              stages were developed for visualization process.          (3)
              The frame work stages consist of different stages         3 can be rewritten as
              and these include:                                             Pe2 ( r2– e2)
              1. Data generation frame work stage.                            4k e2 e2 for a particular duct.
              2. Data Enrichment and Enhancement frame
                   work stage.                                          (4)


                                                                                  1−        −                           + ⋯−            1−
              3. Visualization mapping frame work stage.                Also the total velocity is given as
              4. Rendering frame work stage.                                                            2
                                                                                                             1-
              5. Display frame work stage.                                                          pe       1
                   Based on stages of visualization process,            (5)
                   different computer aided visualization
                   experiment can be develop with the
                   mathematical formulations.

                                                                                                         =
                                                                        Also Reynolds number along the ducts is given as


                                                                              =−                ∗
                                                                                                                                r
                                                                                                                      2          2
Mathematical formulations

                                                                                                                          1−
This work was developed based on Visualization process

                                                                                                                   4k           ei2
model and each stage is developed as follow:
Data generation:- For this work, the model equation to be                                 µ.
                                                                                                     =−
Visualized shall be based on Hagen’s equation
The derivation is as follows from Equation 1 below and the                                                    Where
assumptions before the model include:
    1. Flow starts from rest                                              = Kinematic viscosity
    2. The flow is taken place inside the boundary wall                 K= Dynamic viscosity
    3. Parameters A and B are constants                                 D= Diameter of the pipe
    4. The flow is taking place at a particular temperature
    e.g. 200c                                                                     And the total hand loss along the pipe is give as

The Heagen Equation which is equation is given as
    u=pr2+loge r+B
          4k
(1)
                                                                        Where
Where:                                                                            hf = head loss
P = Pressure of pipe                                                              λ = Frictional loss of the fluid
u = Velocity                                                                      l = Length of the pipe
e = Various point of eccentricity                                                 u = Velocity of the moving object in the pipe
r = Radius of the pipe                                                            g = Acceleration due to gravity
A = Parameter constant                                                            d = Diameter of the pipe when the fluid is moving
k= Dynamic viscosity

The Equation (1) above is modified with the following
assumptions
When u = 0, r = e, parameter constant A = 0
Then 0 = pe2+B
         4k




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                                                                                                                  ISSN 1947-5500
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                                                                       0.08                     688.05                       345.85                          251630.15

                                                                       0.10                     671.93                       337.75                          245732.57

                                                                       0.12                     652.22                       327.84                          238524.42
 Table 1:             HEAD LOSS ALONG THE WALL OF                      0.14                     628.92                       316.13                          230005.69
                          THE PIPE
               0
Output at 0 c                                                          0.16                     602.04                       302.62                          220176.38
Length of the pipe 4m
Radius of the pipe 0.4m                                                0.18                     571.58                       287.31                          209036.51

  Point of         Velocity   Discharge   Head lost                    0.20                     537.54                       270.20                          196586.06
eccentricity                     rate
                                                                       0.22                     499.91                       251.28                          182825.03
   -0.40            -0.00       -0.00       NaN
                                                                       0.24                     458.70                       230.57                          167753.44
   -0.38            69.88       35.13      2556.19
                                                                       0.26                     413.91                       208.05                          151371.26
   -0.36           136.18       68.45     49801.80
                                                                       0.28                     365.53                       183.73                          133678.52
   -0.34           198.89       99.97     72736.84
                                                                       0.30                     313.57                       157.61                          114675.20
   -0.32           258.02      129.69     94361.31
                                                                       0.32                     258.02                       129.69                          94361.31
   -0.30           313.57      157.61     114675.20
                                                                       0.34                     198.89                         99.97                         72736.84
   -0.28           365.53      183.73     133678.52
                                                                       0.36                     136.18                         68.45                         49801.80
   -0.26           413.91      208.05     151371.26
                                                                       0.38                      69.88                         35.13                         25556.19
   -0.24           458.70      230.57     167753.44
                                                                       0.40                      -0.00                         -0.00                           NaN
   -0.22           499.91      251.28     182825.03

   -0.20           537.54      270.20     196586.06
                                                                     Figure1:        Graphical representation of the velocity
   -0.18           571.58      287.31     209036.51                        versus varying points on the radius of 0.4m
                                                                                                              Velocity versus points of eccentricity
   -0.16           602.04      302.62     220176.38                                 800


   -0.14           628.92      316.13     230005.69                                 600

   -0.12           652.22      327.84     238524.42
                                                                              velocity




                                                                                    400
   -0.10           671.93      337.75     245732.57

   -0.08           688.05      345.85     251630.15                                 200


   -0.06           700.59      352.16     256217.16                                      0
                                                                                         -0.4   -0.3   -0.2       -0.1           0           0.1       0.2     0.3   0.4
   -0.04           709.55      356.66     259493.60                                                                   points of eccentricity


   -0.02           714.93      359.36     261459.46

   0.00             NaN         NaN         NaN

   0.02            714.93      359.36     261459.46

   0.04            709.55      356.66     259493.60

   0.06            700.59      352.16     256217.16




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                                                                                                               -0.14            351.98            176.93            72120.56

                                                                                                               -0.12            365.02            183.48            74791.69

                                                                                                               -0.10            376.05            189.02            77051.88
Figure 2:        Graphical representation of Reynolds
        constant versus points of eccentricities                                                               -0.08            385.08            193.56            78901.12
                      5            Reynolds constant Versus points of eccentricity
                   x 10                                                                                        -0.06            392.09            197.09            80339.42
               3
                                                                                                               -0.04            397.11            199.61            81366.78
          2.5
                                                                                                               -0.02            400.12            201.12            81938.20
               2
                                                                                                                0.00             NaN               NaN                NaN
   Head loss




          1.5                                                                                                   0.02            400.12            201.12            81983.20

               1                                                                                                0.04            397.11            199.61            81366.78

          0.5                                                                                                   0.06            392.09            197.09            80339.42

                                                                                                                0.08            385.08            193.56            78901.12
               0
               -0.4       -0.3   -0.2       -0.1           0           0.1      0.2   0.3       0.4
                                                points of eccentricity                                          0.10            376.05            189.02            77051.88

                                                                                                               0.012            365.02            183.48            74791.69

Table 2:                         HEAD LOSS ALONG THE WALL OF                                                    0.14            351.98            176.93            72120.56
                                      THE PIPE
                                  Output two at 200c                                                            0.16            336.94            169.36            69038.48
                                 length of the pipe 4m
                                 Radius of the pipe 0.4                                                         0.18            319.89            160.80            65545.46

                                                                                                                0.20            300.84            151.22            61641.50
  Point of                        Velocity                     Discharge               Head lost
eccentricity                                                      rate
                                                                                                                0.22            297.78            140.63            57326.60
   -0.40                                -0.00                       -0.00                    NaN
                                                                                                                0.24            256.72            129.04            52600.75
   -0.38                            39.11                           19.66                   8013.40
                                                                                                                0.26            256.72            129.04            47463.96
   -0.36                            76.21                           38.31               15615.85
                                                                                                                0.28            204.57            102.83            41916.22
   -0.34                           111.31                           55.95               22807.36
                                                                                                                0.30            175.49             88.21            35957.54
   -0.32                           144.40                           72.58               29587.92
                                                                                                                0.32            144.40             72.58            29587.92
   -0.30                           175.49                           88.21               35957.54
                                                                                                                0.34            111.31             55.95            22807.36
   -0.28                           204.57                          102.38               41916.22
                                                                                                                0.36            76.21              38.31            15615.85
   -0.26                           231.65                          116.44               47463.96
                                                                                                                0.38            39.11              19.66            8013.40
   -0.24                           256.72                          129.04               52600.75
                                                                                                                0.40             -0.00             -0.00              NaN
   -0.22                           279.78                          140.63               57326.60

   -0.20                           300.84                          151.22               61641.50

   -0.18                           319.89                          160.80               65545.46

   -0.16                           336.94                          169.36               69038.48




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Table 3:       HEAD LOSS ALONG THE WALL OF                 -0.28           1407.98           2830.81           721205.57
                    THE PIPE
                Output three at 200c                       -0.26           1435.01           2885.25           735074.91
                 length of pipe 4m
                                                           -0.24           1460.08           2935.66           747916.89
               Radius of the pipe 0.8
                                                           -0.22           1483.14           2982.03           759731.51
  Point of     Velocity   Discharge   Head lost
eccentricity                                               -0.20           1504.20           3024.37           770518.78
                            Rate
                                                           -0.18           1523.25           3062.68           780278.68
   -0.80        -0.00       -0.00       NaN
                                                           -0.16           1540.30           3096.96           789011.23
   -0.78        79.22      159.28     40580.66
                                                           -0.14           1555.34           3127.20           796716.41
   -0.76       156.44      314.53     80133.95
                                                           -0.12           1568.38           3153.41           803394.24
   -0.74       231.65      465.75     118659.89
                                                           -0.10           1579.41           3175.59           809044.71
   -0.72       304.85      612.94     156158.47
                                                           -0.08           1588.44           3193.74           81366.83
   -0.70       376.05      756.09     192629.69
                                                           -0.06           1595.45           3207.85           817263.58
   -0.68       445.24      895.21     228073.56
                                                           -0.04           1600.47           3217.93           819831.98
   -0.66       512.43      1030.30    262490.06
                                                           -0.02           1603.48           3223.98           821373.01
   -0.64       577.61      1161.36    295879.21
                                                            0.00            MaN               NaN                 NaN
   -0.62       640.79      1288.38    328241.00
                                                            0.02           1603.48           3223.98           821373.01
   -0.60       701.96      1411.37    359575.43
                                                            0.04           1600.47           3217.93           819831.98
   -0.58       761.13      1530.33    389882.50
                                                            0.06           1595.45           3207.85           817263.58
   -0.56       818.28      1645.26    419162.21
                                                            0.08           1588.44           3193.74           813667.83
   -0.54       873.44      1756.15    447414.57
                                                            0.10           1579.41           3175.59           809044.71
   -0.52       926.59      1863.01    474639.57
                                                            0.12           1568.38           3153.41           803394.24
   -0.50       977.73      1965.84    500837.20
                                                            0.14           1555.34           3127.20           796716.41
   -0.48       1026.87     2064.64    526007.48
                                                            0.16           1540.30           3096.96           789011.23
   -0.46       1074.00     2159.40    550150.41
                                                            0.18           1523.25           3062.68           780278.68
   -0.44       1119.12     2250.13    573265.97
                                                            0.20           1504.20           3024.37           770518.78
   -0.42       1162.25     2336.83    595354.17
                                                            0.22           1483.14           2982.03           759731.51
   -0.40       1203.36     2419.50    616415.02
                                                            0.24           1460.08           2935.66           747916.89
   -0.38       1242.47     2498.13    636448.51
                                                            0.26           1435.01           2885.25           735074.91
   -0.36       1279.57     2572.73    655454.64
                                                            0.28           1407.93           2830.81           721205.57
   -0.34       1314.67     2643.30    673433.41
                                                            0.30           1378.85           2772.34           706308.88
   -0.32       1347.76     2709.84    690384.82
                                                            0.32           1347.76           2709.84           690384.82
   -0.30       1378.85     2772.34    706308.88




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                                                                                     ISSN 1947-5500
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0.34   1314.67   2643.30   673433.41
                                               Figure3:                                  Graphical representation of head loss
0.36   1279.57   2572.73   655454.64                                                 versus points of eccentricities
0.38   1242.47   2498.13   636448.51                                      5               Reynolds constant Versus points of eccentricity
                                                                   x 10
                                                          10
0.40   1203.36   2419.50   616415.02

0.42   1162.25   2336.83   595354.17                           8

0.44   1119.12   2250.13   573265.97
                                                               6




                                                   Head loss
0.46   1074.00   2159.40   550150.41

0.48   1026.87   2064.64   526007.48                           4

0.50   977.73    1965.84   500837.20
                                                               2
0.52   926.59    1863.01   474639.57
                                                                0
0.54   873.44    1756.15   447414.57                           -0.8           -0.6      -0.4       -0.2           0           0.2      0.4   0.6   0.8
                                                                                                       points of eccentricity
0.56   818.28    1645.26   419162.21
                                             Discussion of the Results
0.58   761.13    1530.33   389882.50
                                             MATLAB (Matrix Laboratory) program version 2007a was
0.60   701.96    1411.37   359575.43         used to develop a Taxonomy of Visualization Model System
                                             (TVMS) for determination of flow patterns of water. Table 1,2
0.62   640.79    1288.38   328241.00         and 3 above show the tabular representation of points
                                             eccentricities (ducts), velocities, discharge rate and head losses
0.64   577.61    1161.36   295879.21         at zero and twenty degree centigrade respectively. It was
                                             discovered that velocity is higher at neighborhood of the
0.66   512.43    1030.30   262490.06         centre of and also the discharge rate and head loss follow the
                                             same pattern. The temperature effects was clearly shown that
0.68   445.24    895.21    228073.56
                                             at increase in temperature, the head loss, discharge rate are
0.70   376.05    756.09    192629.69         also reduce. Figure 1 to 3, shown the flow pattern of fluid
                                             especially water by consider velocity, discharge rate and
0.72   304.85    612.94    156158.47         Reynolds. The three graphs clearly shown that the flow does
                                             not take place at the wall and the centre of the pipe.
0.74   231.65    465.75    118659.89
                                             Conclusion and Recommendations
0.76   156.44    314.53    80133.95          With the (TVMS) that was developed, we concluded with the
                                             following:
0.78    79.22    159.28    40580.66                  1.   Temperature always has effect on fluid flow
                                                         patterns.
0.80    -0.00     -0.00      NaN
                                                     2.   The radius of the pipe also determine the flow
                                                         rate and the higher the radius the higher the flow
                                                         pattern.
                                                     3.   The neighborhood of the centre of the pipe
                                                         always has the higher discharge rate.
                                                     4.   The centre of the pipe must always be protected
                                                         in other to avoid spillage of the fluid.
                                                     5.   The flow of fluid is in parabolic shape in which
                                                         the flow does not take place in centre and edges.
                                                         Also recommended the following:
                                                         1. The learners can use (TVMS) as a guide to
                                                              determined the flow patterns of any fluid.
                                                         2. The flow pattern of different fluid can be
                                                              compare easily.




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                                                                                                          ISSN 1947-5500
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             3.   (TVMS) can assist designers of pipe                       option in computer science, he is currently undergo
                  especially when the determination of head                 his PhD. In computer science. His area of study
                  loss is need to quantify the economy wise.                include Data Mining and visualization graphics.

                                                                            Dr. O.A Taiwo is an Associate professor of
                                                                            Mathematics and Ph.D Supervisor to the first author.
Further Study                                                               He has published many articles both in the National
The research work should be carried out further by compare                  and International Journals and his area of study
the flow patterns with emphasis on head loss by compare                     include numerical computing.
smooth pipe and rough pipe of different material.

Acknowledgment
I wish to acknowledg the following people with, thanks
professor J.S Sadiku of Department of Computer Science,
Faculty of Communication and Information Sciences,
university of Ilorin, Ilorin, Nigeria and also DR. R.G Jimoh of
the same Department and faculty. I also appreciate Mr. A.O
Ameen and Rasheed Tomori of university of Ilorin, Nigeria.
Finally I thank the management and staff of kwara state
polytechnic Ilorin, for their support at all time.

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              Author’s Profile
              Olagunju Mukaila, was born on the 19th of
              September, 1966 in offa, kwara state Nigeria.
              He obtained his first degree in mathematics
        and computer science (combined honor) from federal
        University of Technology Minna, Nigeria. He
        obtained his secondary degree in mathematics with




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