numerical analysis of pressure loss and heat transfer
TRANSCRIPT
NUMERICAL ANALYSIS OF PRESSURE LOSS AND HEAT TRANSFER
IN A NATURAL-DRAFT STACK
MISS SUTIDA PHITAKWINAI
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE MASTER OF SCIENCE IN MECHANICAL ENGINEERING
SIRINDHORN INTERNATIONAL THAI-GERMAN GRADUATE SCHOOL OF ENGINEERING
(TGGS)
GRADUATE COLLEGE
KING MONGKUT’S UNIVERSITY OF TECHNOLOGY NORTH BANGKOK
ACADEMIC YEAR 2007
COPYRIGHT OF KING MONGKUT’S UNIVERSITY OF TECHNOLOGY NORTH BANGKOK
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Name : Miss Sutida Phitakwinai Thesis Title : Numerical Analysis of Pressure Loss and Heat Transfer in a Natural-Draft Stack Major Field : Mechanical Engineering King Mongkut’s University of Technology North Bangkok Thesis Advisor : Assistant Professor Dr. Pumyos Vallikul Academic Year : 2007
Abstract Natural-draught stacks are the most widely used in a steam-generating boiler,
industrial furnace and the gases. Designing and constructing stacks to provide the correct amount of natural draft involves a number design factor, many of which require trial-and-error reiterative method. In this thesis, the fluid flow will be analyzed in terms of available draft resulting from stack effect and pressure loss that are determined at four different mass flow rates. In order to achieve a better knowledge of the stack process, the numerical techniques have been used as a useful tool. Pressure losses and exit temperature for the four cases agree well with the results obtained in the empirical-solution within 1%. Thus, the CFD help the industry reduced commissioning times and costs for design and construct.
(Total 78 pages) Keywords : Natural-draft, Stack , FLUENT
______________________________________________________________Advisor
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ช่ือ : นางสาวสุธิดา พิทักษวินยั ช่ือวิทยานพินธ : การวิเคราะหความดนัตกครอมและการถายเทความรอนใน
ปลอง ควันแบบ Natural-draft ดวยระเบียบวิธีการเชงิตัวเลข สาขาวิชา : วิศวกรรมเครื่องกล มหาวิทยาลัยเทคโนโลยีพระจอมเกลาพระนครเหนือ อาจารยที่ปรึกษาวิทยานิพนธหลัก : ผูชวยศาสตราจารย ดร.ปูมยศ วัลลิกุล ปการศึกษา : 2550
บทคัดยอ Natural-Draft Stack นั้นใชกันอยางกวางขวางทั้งในระบบเครื่องผลิตไอน้ํา หรือในโรงงาน
อุตสาหกรรมที่เกี่ยวกับการเผาไหมและแกส ในสวนของการออกแบบและกอสรางปลองควันนั้น ตองทําการคํานวณคาที่เกี่ยวของโดยใชวิธีการลองผิด-ลองถูก (Trial and Error)ในวิทยานิพนธเลมนี้ การไหลของของไหลจะถูกวิเคราะหในรูปแบบของ Available Draft ซ่ึงเปนผลของ Stack
Effect และความดันตกครอม โดยแบงการพิจารณาเปนอัตราการไหล 4 กรณี ดังนั้นวิธีการคํานวณเชิงตัวเลขไดถูกนําใชเปนเครื่องมือในการวิเคราะหที่เหมาะสมที่สุดที่จะทําใหเขาใจถึงกระบวนการตางๆที่เกิดขึ้นภายในปลองควันไดอยางถองแท ความดันตกครอมและอุณหภูมิ ณ ทางออกสําหรับผลจากการใชโปรแกรมทาง CFD ในการวิเคราะหของทั้ง 4 กรณีนี้เมื่อนํามาเทียบกับทฤษฎีมีความสอดคลองกันซึ่งมีความแตกตางเพียง 1 เปอรเซ็นตเทานั้นเอง ดังนั้น CFD ชวยทางโรงงานอุตสาหกรรมในดานการลดระยะเวลาและคาใชจายสําหรับการออกแบบและการสราง
(วิทยานิพนธมีจํานวนทั้งส้ิน 78 หนา)
คําสําคัญ : ปลองควันไฟ,โปรแกรมคอมพิวเตอร (FLUENT)
_____________________________________________อาจารยที่ปรึกษาวิทยานิพนธหลัก
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to Assistant Professor Dr.Pumyos Vallikul of King Mongkut’s University of Technology North Bangkok for his helpful guidance, suggestion and encouragement throughout this study. I am grateful to Patkol Public Co., Ltd., who took care of me along 4 months of our visit internship their guidance and suggestion and provides the data for this thesis. I am indebted to Mechanical Engineering Department, Faculty of Engineering of King Mongkut’s University of Technology North Bangkok for license of FLUENT 6.3 software. I would like to thank to my teachers, my family, my friends and the staff of the Sirindhon Thai-German Graduate School, King Mongkut’s University of Technology North Bangkok for their helpful suggestion and valuable assistance throughout the entire research.
Sutida Phitakwinai
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TABLE OF CONTENTS Page
Abstract (in English) ii Abstract (in Thai) iii Acknowledgements iv List of Tables vi List of Figures vii Chapter 1 Introduction 1 1.1 Introduction 1 1.2 Objectives 1 1.3 Scope of the study 2 1.4 Methodology 3
1.5 Utilization of the study 3 1.6 Literature Review 3 Chapter 2 Theory: Stack effect 8 2.1 Mathematical modeling 8 2.2 Stack effect in a natural-draft stacks 10
2.3 Stack effect in the household fireplace 12 Chapter 3 Analyses of flow through system component 17 3.1 Flow resistance 17 3.2 Dynamic viscosity model 17 3.3 Numerical simulation 20 Chapter 4 Problem definition and results 29
4.1 Problem Definition 29 4.2 Methodology 32
4.3 Calculation Results 32 4.4 Numerical Simulation 38
Chapter 5 Conclusion 45 References 47 Appendix A Laminar and Turbulent Velocity Profiles 49 Appendix B Discharge Coefficient 54 Appendix C Flow across Tube Bundles 60 Appendix D Static Mixer 71 Biography 78
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LIST OF TABLES Table Page
2-1 Stack effect of chimney 14 4-1 Gas composition & Mixture volume fraction 32 4-2 Available Draft 33 4-3 Major losses: the C1, C2, C3 and C4 cases 34 4-4 Minor losses: the C1, C2, C3 and C4 cases 35 4-5 Total pressure losses 36 4-6 Data for internal convection heat transfer analyses 37 4-7 Data for external convection heat transfer analyses 38 4-8 Exit temperature 38 4-9 Total pressure losses of stack 41 4-10 Exit temperatures of stack 41 C-1 Constants c0 and n of Eq.C-7 63 C-2 Correlation factor c1 for Eq.C-9 64 C-3 Constant c2 and exponent m of Eq.C-10 64 C-4 Geometry and Boundary conditions of tube bundles 66 D-1 Mixer geometrical and fluid properties of static mixer 73 D-2 Mean Velocity magnitudes (m/s) 75
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LIST OF FIGURES Figure Page 1-1 Schematic of a natural-draft stack 2 1-2 Configuration of the boiler 4 1-3 Schematic arrangement of burners and heat recovery sections in the case-study boiler 5 1-4 Schematic of the experimental system 6 1-5 Schematic of the boiler being studied (unit : mm ; MP-monitor port) 7 2-1 Stack effect in a natural-draft stacks 11 2-2 Geometry of the chimney (unit : m) 13 2-3 Pressure loss within chimney 15 2-4 Contour of static pressure in chimney 15 2-5 Contours of velocity magnitude in chimney 16 2-6 Contours of temperature in chimney 16 3-1 The fit of the viscosity model Eq.3-1 to the available viscosity data 18 3-2 Circular Tube Geometry 20 3-3 Grid of the Circular Tube 20 3-4 Friction factor for fully developed flow through a Circular Tube 21 3-5 Nusselt number for fully developed flow through a Circular Tube 21 3-6 Flow across the circular Tube (unit : m) 22 3-7 Nusselt number for flow across a circular pipe 22 3-8 Geometry of 90º mitered bend without guide vanes and with guide vanes 23 3-9 Grid of 90º mitered bend without guide vanes and with guide vanes 23 3-10 Loss coefficient for a 90º mitered bend without vanes 24 3-11 Loss coefficient for a 90º mitered bend with vanes 24 3-12 Geometry of (a) Sudden contraction and (b) Sudden expansion (unit : m) 25 3-13 Grid of (a) Sudden contraction and (b) Sudden expansion 25 3-14 Loss coefficients for a sudden contraction and a sudden expansion 26 3-15 Geometry of 90º Smooth Bend 26 3-16 Loss coefficient for a 90º smooth bend 27
3-17 Geometry of a Gradual conical expansion (unit : m) 27 3-18 Grid of a Gradual conical expansion without internal vanes(a) and
with internal vanes (b) 27 3-19 Loss coefficients for gradual expansion without vanes and with vanes 28 4-1 Schematic diagram of the stack system 29 4-2 Detail stack dimensions 31 4-3 Locations of major losses 33 4-4 Description of Minor Loss 35 4-5 Distributed temperature locations 37 4-6 Grid Generation of stack (36743 nodes and 171038 tetrahedral elements) 40 4-7 Static pressure (the case C1) 42 4-8 Velocity magnitude (the case C1) 43 4-9 Static temperature (the case C1) 44 A-1 The pipe geometry 50 A-2 The relation of pressure and distance 51 A-3 Laminar velocity profiles 51 A-4 Turbulent velocity profiles 51
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LIST OF FIGURES (CONTINUED) Figure Page
A-5 Laminar and Turbulent Velocity Profiles 52 B-1 Orifice pressure tap location 55 B-2 The orifice pipe geometry 57 B-3 Velocity Vectors at β= 0.4 57 B-4 Velocity Vectors at β= 0.6 58 B-5 Pressure contours at β= 0.4 58 B-6 Pressure contours at β= 0.6 58 B-7 Orifice discharge-coefficient Chart 59 C-1 The in-line arrangement 61 C-2 The staggered arrangement 61 C-3 Geometry of the in-line arrangement 65 C-4 Geometry of the staggered arrangement 66 C-5 Temperature contours of XL = 1.5 67 C-6 Pressure contours of XL = 1.5 67 C-7 Velocity vectors of XL = 1.5 68 C-8 Turbulence intensity contours of XL = 1.5 68 C-9 Friction factor for in-line tube arrangement 69 C-10 Friction factor for staggered tube arrangement 69 C-11 Nusselt Number for in-line tube arrangement 70
D-1 A six-element static mixer 73 D-2 Velocity Streamline at Re = 0.15 74 D-3 Contours of the axial velocity at Re = 0.15 74 D-4 The influence of Reynolds number and aspect ratio on the Z factor 75 D-5 Pressure drop within a six element Kenics Mixer for Re = 0.15 76 D-6 Pressure drop within a six element Kenics Mixer for Re = 0.15, 1, 10 and 100 76
CHAPTER 1 INTRODUCTION
1.1 Introduction
Natural-draught stacks are still widely used in steam-generating boilers, industrial furnaces and household fireplace (in colder countries). Designing and constructing the stacks to provide correct amount of natural draft involves a number design factor, many of which require trial-and-error and reiterative methods. In order to achieve a better knowledge of the stack process, in this thesis, computational fluid dynamics simulation (CFD) has been used as a useful tool to analyze the flow resistance and heat transfer process along an artificial small scale household stack and a large scale industrial stack.
At present days, forced draft stacks are used in most industries; they are usually designed and come together at the first place with the new plant or processes. The stacks are desired to exhaust just enough amounts of waste gases from an individual furnace or process. However, in some situations, there are processes where additional waste gases are generated without any force drafted devices designed to exhaust such gases. It is therefore needed to design/modify the stack in order to support the additional loads those excess the exiting positive forced draft stack, exploiting the natural-draft concept.
The driving potential of the flow through the natural-draught stack is called the stack effect. This is caused by difference in densities between higher density of the cold environment gas and the lower density of the hot gas within the stack. The calculation procedure to solve for the pressure difference created by the stack effect is based on the fluid statics. The solution obtained is the function of the pressure difference and the height of the stack. When there is flow through the stack and system connected to it, the pressure difference obtained from the stack effect balances with the pressure drop along the system caused by the flow resistances.
In this thesis, the flow situation through an artificial household fireplace and the stack connected to it is simulated. The stack effect is simulated numerically and compared with the analytical solution (see chapter 2). In chapter 3, a real industrial type stack is analyzed into components. Flow resistance and heat transfer process of each component are analyzed. The CFD- and the empirical-solutions are calculated and compared. It is shown from the numerical simulation that each classical formula represents the stack effect and flow resistance losses very well. However, in some situations the minor loss coefficients depend on both kinetic and viscous dissipation losses, e.g. flow through the gradually expansion fitting. In such case, the minor loss coefficient can be found vary from different from one report to other report. The CFD-simulation is then being an important mean to simulate and predict the kind of situations. 1.2 Objectives
1.2.1 To study buoyancy driven flow in a natural draft stack using computational fluid dynamics simulation.
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1.2.2 To analyze flow resistances and heat transfer processes on components of the stack system.
1.3 Scope of the study
1.3.1 Two types of stacks are studied, they are a stack of small scale fictitious stack using in household fire place and an industrial type stack of 135-m-height.
1.3.2 The simulation software FLUENT is used in this thesis. 1.3.3 The components of the stack system considered are 90º mitered bend with
vanes and without vanes, a sudden contraction, a sudden expansion, 90º bend and a typical conical diffuser.
1.3.4 Minor loss coefficients of the components will be determined via the CFD-simulation and compared with the empirical values.
1.3.5 The empirical friction factor correlation and the internal and external flows Nusselt number correlations for the fully developed flow are verified via the CFD-simulation results.
1.3.6 For the industrial stack, effect of pressure losses and heat transfer are studies based on four different mass flow rates: 568808, 606067, 537268, and 545262 kg/hr. The inlet gas temperature for the corresponding mass flow rates are 200, 218, 186 and 194 oC.
1.3.7 Schematic diagram and dimension of the industrial stack is shown in Figure 1-1
FIGURE 1-1 Schematic of a natural-draft stack (unit : m)
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1.4 Methodology 1.4.1 Study of Stack effect
Buoyancy driven flow in a natural draft stack (stack effect) is studied using computational fluid dynamics simulation and compare with the analytical solution. The analytical solution is based on static fluid analysis.
The comparative study is done on a fictitious household fireplace. The height of the stack will be used as an independent variable and pressure developed to drive the flow is the dependent variable.
1.4.2 Analyses of the industrial stack The CFD and the analytical stack effect calculation techniques are applied to an
industrial stack analyses. Minor losses Pressure losses due to the fluid flow through the smooth pipe (internal flow) and
flow across the cylindrical (external), a 90º mitered bend with vanes and without vanes, a sudden contraction, a sudden expansion, 90º bend, a typical conical diffuser are determined both via CFD technique and empirical formula. The comparative study is advanced in order to verify the obtained solutions.
Fully developed flow resistances and heat transfer process The comparative studies between the CFD technique and the empirical
correlations for resistances and heat transfer processes in fully developed flows are also applied. Pressure losses along the piping system where the flow is assumed to be fully developed are calculated via the CFD-simulation technique. The pressure losses with the flow geometry are used determined friction factor and the corresponding Reynolds number. The friction factor-Reynolds number obtained will be compared with the standard empirical friction factor correlation.
Local heat transfer along the stack piping system is calculated by CFD-technique. The resulting heat transfer together with flow properties are used to calculate Nusselt-Reynolds-Prandtl number correlation. The obtained correlations are compared with the standard empirical correlations, to verify the simulation results.
1.4.3 Application of the CFD-Simulation Calculation results of the total pressure losses and heat transfer from the
industrial stack are determined at different given mass flow rate and inlet temperature as given in 1.3.6. The results will be used as operating data for the stack at a gas separation plant in Rayong. 1.5 Utilization of the Study
1.5.1 Gain insight into the influence of stack draft on pressure losses and heat transfer behavior.
1.5.2 Help the industry to design and construct of the stack. 1.5.3 Reduced commissioning times and costs.
1.6 Literature surveys
Computational fluid dynamics (CFD) have been applied successfully to simulate combustion process within the fuel, within furnace or boiler and along the natural draft stack. For the analyses of for through the stacks, the effects of interested are pollution formation, stack effect, heat and mass transfer along the flow as function of stack height.
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For the pollution formation proposed, CFD has been used to study the effect of chimney height on boiler flue gases reaction and pollution formations [1], the study, however, used the commercial software FLUENT as a simulation tool. The results show that the pollutant emissions and thermal behavior are sensitive to draught produced by the chimney and there is and optimum chimney height, that corresponds to minimum are pollution emission.
In other situation when high temperature combustion is involved, NOx are formed. M.A. Habib , M. Elshafei and M. Dajani [2] studied the NO distribution in the combustion chamber and the exhaust gas at various operating conditions of fuel to air ratio with varying either the fuel or air mass flow rate, inlet air temperature and combustion primary air swirl angle. The results have shown that the furnace average temperature and NO concentration decrease as the excess air factor k increases for a given air mass flow rate. Fix value of mass flow rate of fuel, that increasing k in a maximum value of thermal NO concentration at the exit of the boiler. As the combustion air temperature increases, furnace temperature increases and the thermal NO concentration increases sharply. NO concentrations at exit of the boiler have a minimum value at around swirl angle of 45º.
FIGURE 1-2 Configuration of the boiler [2] Swirl effects that have been used to reduce pollution formation are sometimes
generated by tangential fired boiler. The flow field in such situation is very complicated. Luis I. Diez , Cristobal Cortes and Javier Pallares [3] simulated the fluid and particle flow through the tangentially-fired boiler by analyses with 3D nurmerical to predicted gas temperature, species concentration and NOx emissions reduction when overfire air operation is adopted.
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FIGURE 1-3 Schematic arrangement of burners and heat recovery sections in the case-study boiler [3]
Heat and mass transfers are also of important effects in natural draft stack. They
appear in the cooling tower operation. N. Williamson, S. Armfield and M. Behnia [4] simulated the heat and mass transfer inside a natural draft wet cooling tower by determine the extent of the non-uniformities across its. The model was a two-dimensional axisymmetric two-phase. The effect of tower inlet height on radial non-uniformity is small but the model is very sensitive to changes in water flow rate. At small fill depths the water temperatures entering the rain zone tend to be higher, which in turn slightly increases the heat transfer rate.
Simulation of gas phase reaction system also can be found in heat utilization combustion system. J.J. Ji *, Y.H. Luo and L.Y. Hu [5] simulated the natural gas within the traveling grate boiler by analyzed with large eddy simulation. Under the condition of two typical air distribution modes, dynamic pressure signals at various flow rates. Determined influence factors on the unsteady combustion and the occurrence in boiler.
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FIGURE 1-4 Schematic of the experimental system [5]
When solid combustion is involved, the problem does not govern by the Navier-
Stokes equations hence some numerical model has to be developed for this purposed. Most commercial CFD software such as FLUENT can not be used in this situation. F.Chejne, J.P.Hernandez, W.F.Florez and A.F.J.Hill [6] simulated the combustion of piled coal particles, which using a time-dependent mathematical model and a numerical algorithm, to predicted the profiles of unburned solid fraction along the bed height, the gas combustion, heat of reaction, gas temperature and the coal (solid phase) temperature. When the combustion process starts, the radius of the unburned core and the height of the bed will change rapidly being this behavior typical of all violent combustion. The temperature increases, it reaches a point where the reaction rates are extremely high.
Other large scale solid combustion simulation was advanced by Fang Qing-yan, Zhou Huai-chun, Wang Hua-jian, Yao Bin, and Zeng Han-cai [7]. They studied the flexibility of a 300 MW Arch Firing (AF) coal-fired boiler when burning low quality coals. They used a water-cooled suction pyrometer to measure gas temperature, species concentration and char sampling along the furnace elevation. The results indicate that the flexibility of boiler under a moderate boiler load is better than a high boiler load.
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FIGURE 1-5 Schematic of the boiler being studied (unit : mm ; MP-monitor port) [7]
One of the most important effects applied in natural draft stack system is the stack effect. Numerical simulation to verify the effect has not been found. This is because the effect include as part within the Navier-Stokes equations. In this thesis, CFD will be used to simulate the stack effect and the results are compared with the classical solution one. In addition the CFD will also be used as a tool to verify the loss coefficients, which most of them are usually available in engineering hand books, other than use to simulate the whole system. With this approach of using the CFD, it avoids the time to analyses the system. The CFD will be used only once to calculate the loss coefficients and/or heat transfer coefficients. Those obtained coefficients will in turned be used in the analyses of the system in the classical engineering calculations.
CHAPTER 2 THEORY: STACK EFFECT
2.1 Mathematical modeling
For the prediction of the non-reacting thermal turbulent flow field, equations of mass, momentum and energy conservation along with the standard k-ε turbulence model [8] are employed.
2.1.1 Conservation of Mass (Continuity Equation):
( ) 0=∂∂
ii
ux
ρ Eq.2-1
2.1.2 Momentum Equation:
( ) ( ) ⎟⎠⎞
⎜⎝⎛ ′′−
∂∂
+⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛
∂∂
−∂
∂+
∂∂
∂∂
+∂∂
−=∂∂
+∂∂
jijj
iij
i
j
j
i
jiji
ji uu
xxu
xu
xu
xxPuu
xu
tρδµρρ
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Eq.2-2
These Reynolds stresses, ′′− ji uuρ , must be modeled in order to close Eq.2-2 for variable-density flows.
2.1.3 Energy equation:
( ) ( ) ( )( ) (( vTTkpEEvE ))t effeff
vv ⋅+∇∇=+ρ∇+ρ⋅∇+ρ∂∂ Eq.2-3
where keffis the effective conductivity (k + kt , where kt is the turbulent thermal conductivity, defined according to the turbulence model being used). The two terms on the right-hand side of Eq.2-3 represent energy transfer due to conduction, and viscous dissipation, respectively.
2.1.4 Buoyancy-driven flow Since the flow is Buoyancy-driven, the density in the buoyancy term in the
momentum equation is set to be g)TT(g)( ooo −βρ−≈ρ−ρ Eq.2-4
where ρo is the density of the flow, To is operating temperature, and β is the thermal expansion coefficient. Eq.2-4 is obtained by using the Boussinesq approximation to eliminate ρ from the buoyancy term. The density appears elsewhere are set to be a constant ρo. By doing this we can get faster convergence than by setting up the problem with fluid density as a function of temperature.
2.1.5 Boussinesq Approach and Reynolds Stress Transport Models The Reynolds-averaged approach to turbulence modeling requires that the
Reynolds stresses in Eq.2-2 be appropriately modeled. A common method employs the Boussinesq hypothesis [9] to relate the Reynolds stresses to the mean velocity gradients:
ijk
kt
i
j
j
itji x
uk
xu
xu
uu δµρµρ ⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
+−⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂+
∂∂
=′′−32 Eq.2-5
The Boussinesq hypothesis is used in the k-ε models. The advantage of this approach is the relatively low computational cost associated with the computation of
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the turbulent viscosity, µt. In the case of the k-ε models, a additional transport equations (for the turbulence kinetic energy, k, and either the turbulence dissipation rate,ε) is solved, and µt is computed as a function of k and ε. The disadvantage of the Boussinesq hypothesis as presented is that it assumes µt is an isotropic scalar quantity, which is not strictly true.
2.1.6 k-ε Turbulence Model : The turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from
the following transport equations [9,10]
( ) ( ) Mbkjk
t
ji
i
YGGxk
xku
xk
t−ρε−++
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
⎟⎟⎠
⎞⎜⎜⎝
⎛σµ
+µ∂∂
=ρ∂∂
+ρ∂∂ Eq.2-6
and
( ) ( )k
CGCGk
Cxx
uxt bk
j
t
ji
i
2
231 )( ερεεσµ
µρερε εεεε
−+⎟⎠⎞
⎜⎝⎛+
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
⎟⎟⎠
⎞⎜⎜⎝
⎛+
∂∂
=∂∂
+∂∂
Eq.2-7 In these equations, Gk represents the generation of turbulence kinetic energy due
to the mean velocity gradients. Gb is the generation of turbulence kinetic energy due to buoyancy. YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C1ε, C2ε, and C3ε are constants. σk and σε are the turbulent Prandtl numbers for k and ε, respectively.
2.1.7 Modeling the Turbulent Viscosity The turbulent (or eddy) viscosity, µt, is computed by combining k and ε as
follows:
ερµ µ
2kCt = Eq.2-8
where Cµ is a constant. 2.1.8 Model Constants
The model constants C1ε , C2ε ,Cµ , σk and σε have the following default value
C1ε = 1.44, C2ε = 1.92, Cµ = 0.09, σk = 1.0, σε = 1:3
2.1.9 Modeling of turbulent production in k-ε models The term Gk, representing the production of turbulence kinetic energy, is
modeled identically for the standard, RNG, and realizable k-ε models. From the exact equation for the transport of k, this term may be defined as
i
jjik x
uuuG
∂
∂′′= ρ Eq.2-9
To evaluate Gk in a manner consistent with the Boussinesq hypothesis,
Gk=µtS2 Eq.2-10
where S is the modulus of the mean rate-of-strain tensor, defined as
ijij SSS 2≡ Eq.2-11
2.1.10 Effects of Buoyancy on Turbulence in the k-ε Models When a non-zero gravity field and temperature gradient are present
simultaneously, the k-ε models in the software FLUENT account for the generation of
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k due to buoyancy ( Gb in Eq.2-5), and the corresponding contribution to the production of ε in Eq.2-6.
The generation of turbulence due to buoyancy is given by
it
tib x
TgG∂∂
=Prµ
β Eq.2-12
where Prt is the turbulent Prandtl number for energy and gi is the component of the gravitational vector in the ith direction. For the standard and realizable k-ε models, the default value of Prt is 0.85. In the case of the RNG k-ε model, Prt =1/α, but with α0 = 1/Pr = k/µCp. The coefficient of thermal expansion, β, is defined as
PT⎟⎠⎞
⎜⎝⎛∂∂
−=ρ
ρβ 1 Eq.2-13
For ideal gases, Eq.2-11 reduces to
it
tib x
gG∂∂
−=ρ
ρµPr
Eq.2-14
In the software FLUENT 6.3, the effects of buoyancy on the generation of k are always included when you have both a non-zero gravity field and a non-zero temperature (or density) gradient.
While the buoyancy effects on the generation of k are relatively well understood, the effect on ε is less clear. In the software FLUENT, by default, the buoyancy effects on ε are neglected simply by setting Gb to zero in the transport equation for ε in Eq.2-6.
2.2 Stack effect in a natural-draft stacks
The stacks are a system for venting hot flue gases or smoke from a steam-generating boiler, industrial furnace and the gases to the outside atmosphere. It is almost vertical to ensure that the hot gases flow smoothly, drawing air into the combustion through the stack effect. The space inside a stack is called “a flue”.
When coal, oil, natural gas, wood or any other fuel is combusted in a stack, the hot combustion product gases that are formed are called flue gases. Those gases are generally exhausted to the ambient outside air through stacks.
The combustion flue gases inside the stacks are much hotter than the ambient outside air and therefore less dense than the ambient air. That causes the bottom of the vertical column of hot flue gas to have a lower pressure than the pressure at the bottom of a corresponding column of outside air. That higher pressure outside the stacks is the driving force that moves the required combustion air into the combustion zone and also moves the flue gas up and out of the stacks. That movement or flow of combustion air and flue gas is called “natural draught/draft”, “natural ventilation”, or “stack effect”. The taller the stack, the more draught or draft is created. Figure 2-1 the gauges represent absolute air pressure and the airflow is indicated with light grey arrows. The gauge dials move clockwise with increasing pressure [11].
11
FIGURE 2-1 Stack effect in a natural-draft stacks
2.2.1 Stack effect equation The stack effect [12] which varies with height and the mean temperature of the
column of hot gas can be calculated from Eq.2-15. The effect is the static draft produced by a stack, at sea level, with no gas flow. Eq.2-15 provides an approximation of the pressure difference, ∆P, (between the bottom and the top of the flue gas stack that is created by the draft:
⎟⎟⎠
⎞⎜⎜⎝
⎛−=∆
TiTRgHP
Patmg
atm 11 Eq.2-15
where: ∆P = available pressure difference, in PaRg = Gas constant
Patm = atmospheric pressure, in PaH = height of the flue gas stack, in m
Tatm = absolute outside air temperature, in KTg
= absolute average temperature of the flue gas inside the stack,
in K 2.2.2 The stack gas constant
Since the stack gas is a mixture then the gas constant, , is based on averaged molar weight of the gaseous species constituted the mixture. The value of is
gR
gR
MRRg = Eq.2-16
12
where R is the universal gas constant (= 8.314×103 J/kmol⋅K) and M is the average molecular weight of the stack gas in kg/kmol. Given the mole fractions, , of the stack gas, the average molecular weight [13] can be calculated from
iY
∑=i
ii WYM Eq.2-17
2.3 Stack effect in the household fireplace
2.3.1 Modelling of a household fireplace stack A fictitious household fireplace (see Figure 2-2) is studied in this section. The
stack is a square duct of 0.21×0.21 m2. We assume that the wall of the stack is lining with 1-cm-thick insulator of conductivity 0.054 W/m⋅K. The stack effect given in Eq.2-15 is used to calculate natural draft pressure as a function of the stack’s height. The pressure at the stack exit is 101.3 kPa, the hot gas temperature at the exit is assumed to be a free jet of 218oC and that the outside wall temperature along the stack is constant. Given that the ambient temperature is at 35oC. Geometry of the fire place and the stack are given in Figure 2-2. Stack gas compositions uses in this case are similar to those in the industrial stack to be mentioned in chapter 4. It will be shown that, for a case study number C2 = 599792 kg/hr, the molecular weight and gas constant are 1.33M = kg/kmol and R = 251.23 J/kg⋅K respectively. The stack effect can then be calculated as a function of the stack height as
⎟⎠⎞
⎜⎝⎛ −
×=∆
4911
3081
23.251)103.101)(8.9( 3Hpstack
The values of driving pressure caused by the stack effect at different heights are listed in Table 2-2. The values are compared with the results obtained by CFD-simulation obtained as following.
Simulated the chimney model in turbulent flow by The stack effect ∆Pstack and dimension of chimney and assume friction factor [14] to find velocity which follow by
Lv
PDfav2
21 ρ
∆= Eq.2-18
In the CFD-simulation, the pressure loss is the solution to the boundary condition problem. Below are boundary conditions to the above of governing equations. Table 2-1 shows the boundary condition to the above problem. Pressure drops are made between the pressure at the plane inside the fireplace at the stack surface and the exit pressure.
13
Outlet
H
Inlet
FIGURE 2-2 Geometry of the chimn
2.3.2 Boundary conditions of chimney Fluid Material Air Fluid Properties:
Density 0.824 Viscosity 2.64 × 10-5
Inlet Velocity Varies velocityTemperature 218
Outlet Pressure (Pgauge) 0 Wall Temperature Constant Temp
Height of the stack Varies height o
3, 3.5 and 4
ey (unit : m)
kg/m3
N.s/m2
ºC
Pa
erature =35ºC
f the chimney at 1, 1.5, 2, 2.5,
14
2.3.3 Numerical method The numerical model has been built within Fluent, a general purpose CFD code.
The mesh geometry was produced using GAMBIT. The mesh of the chimney height 1, 1.5, 2, 2.5, 3, 3.5 and 4 m have total of 320, 480, 640, 800, 960, 1120 and 1280 hexahedral elements respectively. The code has been used to solve the steady Reynolds Averaged Navier-Stokes Equations closed with the standard k-ε turbulence model with buoyancy terms included in both k and ε transport equation. The semi-implicit method for pressure linked equations (SIMPLE) was employed with second order upwind discretisation employed for the advective terms. A segregated implicit solver was used. The solution is regarded as converged when the maximum value of normalized residuals of any equation is less than 5 × 10-5. TABLE 2-1 Stack effect of chimney
Pressure losses (Pa) Height (m) mass flow rate (kg/s) V (m/s) Theory CFD-simulation
1 0.1236 3.403 4.772 4.198 1.5 0.1515 4.168 7.158 7.913 2 0.1748 4.813 9.544 9.211
2.5 0.1955 5.381 11.930 11.523 3 0.2142 5.895 14.316 12.891
3.5 0.2314 6.367 16.702 16.560 4 0.2473 6.807 19.088 19.155
Table 2-1 shows the driving pressure caused by the stack effect (the theory) and
the pressure loss calculated by the CFD-simulation. The pressure losses from the CFD-simulation are greater than those created by the stack effect. The pressure is the average value across a plane is used. Pressure at local points across any plane calculated from the CFD-simulation is not uniform. It has been found form the solution that at the below cross-section local pressure are partly negative pressure and partly are positive pressure. The overall trend is however acceptable. The plot of table 2-2 is shown in Figure 2-2. Solutions to the CFD-simulation problem are also shown in term of pressure, velocity and temperature contour (see Figure 2-3 to 2-5 respectively)
15
0
5
10
15
20
25
1 1.5 2 2.5 3 3.5 4
Height
Pre
ssur
e lo
sses
Empirical solutionFLUENT
FIGURE 2-3 Pressure Losses within chimney
FIGURE 2-4 Contour of static pressure in chimney
16
FIGURE 2-5 Contours of velocity magnitude in chimney
FIGURE 2-6 Contours of temperature in chimney
CHAPTER 3 ANALYSES OF FLOW THROUGH SYSTEM COMPONENT
In this chapter, a real industrial type stack is analyzed into components. Flow
resistance and heat transfer process of each component are discussed. The CFD-simulation and the empirical-solutions are calculated and compared.
3.1 Flow resistance
When flow occurs, a portion of the stack effect is used to establish gas velocity and the remainder is used to overcome the resistance of the connected system. The flow resistances cause pressure drops (losses) along the piping system. There are two types of pressure losses; the major and the minor losses; those values will be determined below. It is of important to first to look into the flow property, the viscosity used in the analysis.
3.2 Dynamic viscosity model
It is well known that viscosity is very sensitive to temperature. In our study, conditions designed in the stack analysis are given at different temperature. We use mathematical model to predict the viscosity of the stag gas at different temperature. The effect of temperature on viscosity of gas can be closely approximated using an empirical formulae, the Sutherland equation [15], can be expressed as
STCT 2/3
+=µ Eq.3-1
The parameters C and S are constants and depend on the gas being considered. In this calculation we assume that the stack gas has the viscosity equal to that of air at the same temperature. Then the values for C and S are obtained from least square fit of the model Eq.3-1 to the already available air viscosity data. Figure 3-1 shows the fitting result, the dots are data available and the solid line is the model. The model allows us to calculate the viscosity at a particular temperature.
It is found from the curve fitting, Figure 3-1, that the value of C and S are 1.22×10-6 and 11 respectively. The constants depend on of system of unit. The unit of viscosity is N⋅s/m2 and the temperature is in absolute temperature, K.
18
FIGURE 3-1 The fit of the viscosity model Eq.3-1 to the available viscosity data
3.2.1 Energy equation
We consider the energy equation for steady flow between two locations as is given in Eq.3-2 [16,17]
Lhzg
vg
Pzg
vg
P+++=++ 2
222
1
211
22 ρρ Eq.3-2
where hL is the head loss between section 1 and 2 with the assumption of a constant horizontal (z1=z2). It has not the elevation difference between pressure taps because both pressure at a common elevation. For a constant-density fluid, this reduces Eq.3-2 to the form
gvv
gPPhL 2
22
2121 −
+−
=ρ
Eq.3-3
3.2.2 Major loss The major loss occurs at the sections where the pipe is straight with constant
cross-sectional area. In addition, the flow along the section of the piping system is fully developed or the velocity profile is unique. In practice, it is found convenient to express the pressure loss for all types of fully developed internal flows as [18]
2V
DLfP
2avg
major,loss
ρ=∆ Eq.3-4
f is the Dracy friction factor. L and D are length and diameter of the pipe respectively. ρ is the density of the mixture.
avgV is the average velocity.
19
The friction factor can be evaluated using empirical formula, usually expressed implicitly. An approximate explicit relation used in this work is given by S.E. Haaland in 1983 [18,19];
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ ε+−=
11.1
7.3D/
Re9.6log8.1
f1 Eq.3-5
ε is the roughness of the pipe. Re is the Reynolds number.
µ
ρ=
DVRe avg Eq.3-6
µ is the dynamic viscosity 3.2.3 Minor losses
The fluid in a typical piping system passes through various fittings, valves, bends, elbows, tees, inlets, exits, enlargements, and contractions in addition to the pipes. These components interrupt the smooth flow of the fluid and cause additional losses because of the flow separation and mixing they induce. In a typical system with long pipes, theses losses are minor compared to the total head loss in the pipes (the major losses) and are called minor losses[18]. The minor losses are calculated from
Lormin,loss ghP ρ=∆ Eq.3-7 hL is the minor head losses in meter (m).
The minor head losses are based on the kinetic energy of the flow, depending
mainly on the shape of the components, and can be evaluated as
g2VKh
2
LL = Eq.3-8
KL is the loss coefficient It will be shown in the calculation result of the next section that for this problem,
the minor losses contribute most of the pressure loss to the piping system. 3.2.4 Nusselt number and convection heat transfer coefficient
The convective heat transfer coefficients are calculated from the correlation for Nusselt numbers within pipe of fully developed flow [15] are given by and external to the tube, are defined by:
3/15/4 PrRe023.0 DiuN = Eq.3-9 For external flow across the stack, the Nusselt number correlation
( )[ ]5/48/5
4/13/2
3/12/1
000,282Re1
Pr/4.01
PrRe62.03.0⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛+
++= DD
ouN Eq.3-10
The convective heat transfer coefficient for any part of the piping system are calculated from
DkuNh = Eq.3-11
20
3.3 Numerical simulation 3.3.1 Flow Inside a Circular Tube
For fully developed of internal flows, the friction factor and Nusselt number correlations are given in Eq.3-5 and 3-9. In this section the values are determined directly from CFD-simulation. For a circular pipe (Figure 3-2), a fully developed flow can be simulated and the velocity as well as pressure field for all grid points (Figure 3-3) can be determined. The pressure drop along a length is calculated by using the velocity and pressure solutions and substitute into the equation defining friction factor as shown in Eq.3-4
Another dimensionless parameter used in analyzing fluid flow and constitutes the friction factor correlation is Reynolds number which is defined by
µρ
=VDRe Eq.3-10
FIGURE 3-2 Circular Tube Geometry
8 m Wall
Inlet Outlet R=0.1 m
Axis
FIGURE 3-3 Grid of the Circular Tube For any fully develop flow situations the Re can be found from the simulation
parameters. Pairs of the friction factor and Reynolds number determining from the numerical experiment are plot against the empirical formula friction factor Eq.3-4. CFD-simulation also gives local temperature distribution along the flow. This temperature distribution allows one to calculate heat transfer dissipated to the wall.
When local heat flux is known, the convective heat transfer coefficient, h, can then be determined. The convective heat transfer coefficient is related to the Nusselt number through Eq.3-11. The Nusselt and Reynolds numbers obtained from CFD-simulation is plot against the ones obtained from the correlation Eq.3-9 and shows in Figure 3-5.
21
0.001
0.01
0.1
1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08
Re
Fric
tion
Fact
orLaminarf=64/ReSmooth pipeColebrook
FIGURE 3-4 Friction factor for fully developed flow through a Circular Tube
10
100
1000
10000
1.00E+03 1.00E+04 1.00E+05 1.00E+06
Re
Nu
Correlation Eq.3-9
Fluent
FIGURE 3-5 Nusselt number for fully developed flow through a Circular Tube
3.3.2 Flow Across a Circular pipe
External flows are unconfined, free to expand no matter how thick the viscous layers grow [13]. Although boundary layer theory and computational fluid dynamics (CFD) are helpful in understanding external flows, complex body geometries usually require experimental data on the forces and moments caused by the flows.
Another common external flow involves fluid motion normal to the axis of a circular cylinder. As shown in Figure 3-4, the free steam fluid is brought to rest at the forward stagnation point, with an accompanying rise in pressure.
22
(a)
(b)
FIGURE 3-6 Flow across the circular Tube (unit : m)
External flow (see Figure 3-6) correlation for Nusselt number, Eq.3-10, is plot against the Reynolds number and compared with the values obtained by CFD-simulation. The result is shown in Figure 3-7. The dot line is empirical formula while the line is the numerical results from CFD-simulation. The results agree very well.
10
100
1000
1.00E+03 1.00E+04 1.00E+05 1.00E+06Re
Nu
Correlation Eq.3-10
Fluent
FIGURE 3-7 Nusselt number for flow across a circular pipe
23
3.3.3 90º mitered bend with vanes and without vanes
(a)
(b)
FIGURE 3-8 Geometry of 90º mitered bend without guide vanes and with guide vanes
(a) (b)
FIGURE 3-9 Grid of 90º mitered bend without guide vanes and with guide vanes
The pressure loss through the 90º mitered bend reduces considerably when the guide vanes are introduced that help direct the flow with less unwanted swirl and disturbances. The empirical values for the losses for each case are 1.1 and 0.2 respectively. The plots of discrete values of minor loss coefficients, calculated from CFD-simulation, against the velocity square are plotted in the Figure 3-10 and 3-11. The plots are then fitted with straight line equations, resulting in the value of slope for each case. It is shown in the Figure 3-9 (a) and (b) shown that the values of the coefficients are 1.13 and 0.21 respectively which agree well with the empirical formula
24
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5
v^2/(2g)
(Pin
-Pou
t)/(D
ensi
ty*g
)
without vanes
× 10
-5
FIGURE 3-10 Loss coefficient for a 90º mitered bend without vanes
0
0.5
1
1.5
2
2.5
3
3.5
0 5
(Pin
-Pou
t)/(D
ensi
ty*g
)
× 10 -5
Slope = 1.1387
× 10
-5
FIGURE 3-11 Los
3.3.4 Sudden contraction Sudden contractions in
provided that there is little or the vena contracta formed wit[19], as shown in Figure 3-12
As a fluid flows fromenlargement (see Figure 3-12(which generates an energy lo
Slope = 0.212
0 100 150 200
v^2/(2g)
vanes
× 10 -5
s coefficient for a 90º mitered bend with vanes
and Sudden expansion a duct or pipe may also be dealt with in this way, no loss between the upstream large-section conduit and hin the smaller conduit just downstream of the junction (a). a smaller pipe into a larger pipe through a sudden b)), its velocity abruptly decreases, causing turbulence, ss [20]. The amount of turbulence, and therefore the
25
amount of energy loss, is dependent on the ratio of the sizes of the two pipes. The minor loss is calculated from the Eq.3-8.
There are approximation equations for the sudden expansion and sudden contraction fitting. The equations for the loss coefficient of sudden expansion and sudden contraction [17] are
2
2
2
1 ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
out
inSE D
DK Eq.3-12
and
⎟⎟⎠
⎞⎜⎜⎝
⎛−= 2
2
15.0in
outSC D
DK Eq.3-13
It can be seen from the empirical formula that the values of both coefficients merge at high value of d/D (Figure 3-12).
(a)
(b)
FIGURE 3-12 Geometry of (a) Sudden contraction and (b) Sudden expansion
(unit : m)
(a)
Dout Din
Wall
100 m
Inlet
Axis
Outlet
Dout Din Inlet Outlet
(b)
FIGURE 3-13 Grid of (a) Sudden contraction and (b) Sudden expansion
The energy losses for both are graphed in Figure 3-14. It also occurs because of the change in pipe diameter. Figure 3-13, we see that the energy loss from a sudden contraction is somewhat smaller. In general, accelerating a fluid causes less turbulence than decelerating it for a given ratio of diameter change.
26
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1d/D
KEmpirical of SuddencontractionEmpirical of Suddenexpansionsudden contraction
sudden expansion
FIGURE 3-14 Loss coefficients for a sudden contraction and a sudden expansion
3.3.5 90º Smooth Bend Outlet
Inlet
FIGURE 3-15 Geometry of 90º Smooth Bend
A bend or curve in a pipe, as in Figure 3-15, always induces a loss larger than the simple straight-pipe Moody friction loss, due to flow separation on the curved walls and a swirling secondary flow arising from the centripetal acceleration [20]. The smooth-wall loss coefficients K in Figure 3-16, are for total loss, including Moody friction effects. The separation and secondary flow losses decrease with R/D, while the Moody losses increase because the bend length increases.
27
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0 0.5 1 1.5 2
R/D
K
FIGURE 3-16 Loss coefficient for a 90º smooth bend
3.3.6 Gradual conical expansion
FIGURE 3-17 Geometry of a Gradual conical expansion (unit : m)
Outlet Inlet
(a)
Outlet Inlet
(b)
FIGURE 3-18 Geometry of Gradual expansion without internal vanes (a) and with internal vanes (b)
28
If the transition from a smaller to a larger pipe can be made less abrupt than the square-edged sudden expansion, the energy loss is reduced. This is normally done by placing a conical section between the two pipes as shown in Figure 3-17. The sloping walls of the cone tend to guide the fluid during the deceleration and expansion of the flow steam. Therefore, the size of the zone of separation and the amount of turbulence are reduced as the cone angle is reduced. The energy loss for a gradual enlargement is calculated from Eq.3-8. Plot the minor loss against the velocity square of the gradual expansion without internal vanes and with internal vanes. Figure 3-19 that the plots are then fitted with straight line equation, the resulting in the value of slope are the loss coefficients (K) are 0.3838 and 0.3787 respectively.
0
50
100
150
200
250
300
350
0 200 400 600 800
v^2/2g
Hea
d Lo
ss
without vaneswith vanes
Slope=0.3838
Slope=0.3787
FIGURE 3-19 Loss coefficients for gradual expansion without vanes and with vanes
CHAPTER 4 PR0BLEM DEFINITON AND RESULTS
4.1 Problem Definition
In this project a new 135-m-high stack system is to be constructed to replace the old 40-m-high stack. The new stack is to connect to the old system on the top of the old stack foundation; the connecting point is 11.95 m from the ground (Figure 4-1).
Given the height of the stack, the first requirement in this project is to verify that the mass flow rates induced by “the stack effect” meet the amounts of mass flow rates for four operating conditions (see Table 4-1). The second requirement is that the temperature drop of the stack gas for all cases should be less than 5oC. In this section, geometrical descriptions, gaseous inlet conditions, and parameters to calculate convective heat transfer are given.
FIGURE 4-1 Schematic diagram of the stack system (unit : m)
30
4.1.1 Geometrical Descriptions Geometrical description of the stack and system connected to it is shown below
in Figure 4-2. Note that the dimensions given in the Figure 4-2 are for the internal diameters for each section.
4.1.2 Inlet conditions Four inlet cases for the stack gas conditions are studied, the atmospheric
conditions are however similar for all cases. The inlet gases are different in temperature, gaseous mixing fractions and total mass flow rates and the atmospheric condition are given in the Table 4-1.
4.1.3 Atmospheric conditions The atmospheric pressure and temperature at the stack exit are set to be 101 kPa
and 35 oC respectively; at the ground level the temperature is set to be 40oC. The cross wind velocity is assumed to be varied linearly with the height above the ground. In this report we assume that the velocity at the ground level is 5 m/s and at the top of the stack are 20 m/s.
4.1.4 Requirements 4.1.4.1 Mass flow rates of the stack gas at different inlet conditions are
required. It is the constraint that the mass flow rates, caused by the stack effect, must be greater than the constraint values at different gaseous inlet conditions. The constraint values for mass flow rates and the corresponding inlet conditions for the stack gas are listed at the last part of Table 4-1.
4.1.4.2 For the heat transfer analyses, the exit temperature of the flow is required. This temperature drop is due to the heat losses from the flow between the inlet to the exit of the piping and stack system. It is assumed that convection is of the only mode of heat transfer involving the losses. Note that the entire system is insulated to prevent the heat losses.
31
Left top = front view Left = top view Top = side view
FIGURE 4-2 Detail stack dimensions
32
TABLE 4-1 Gas composition & Mixture volume fraction
Gas CO2 N2 CH4 C2H6 C3H8 C4 C5+ H2S H2O O2 Ar Molecular
Weight 44.01 28.01 16.04 30.07 44.10 0.0 0.0 34.06 18.02 32.00 39.95
Volume Fraction :
C1=568808 kg/hr
25.38 56.12 0.02 0.01 0.00 0.0 0.0 0.01 9.56 8.22 0.67
Volume Fraction :
C2=606067 kg/hr
36.90 46.30 0.04 0.01 0.00 0.0 0.0 0.01 10.93 5.24 0.56
Volume Fraction :
C3=537268 kg/hr
16.38 61.86 0.01 0.00 0.00 0.0 0.0 0.00 9.61 1.68 0.22
Volume Fraction :
C4=545262 kg/hr
11.17 15.72 0.00 0.00 0.00 0.0 0.0 0.00 9.61 11.38 0.77
4.2 Methodology
Theoretical background and methodology used to analyze the flow and heat transfer processes in the problem will be presented in this chapter. In the analysis of the flow processes, phenomena driving and dissipating the energy of the flow are discussed. Stack effect resulting in natural draft to the stack system, adds energy to the flow whereas friction in the form of the major loss dissipates the energy. Another form of the energy loss is minor loss. Minor losses vary with kinetic energy of the flow, occurring at fittings within the piping and the stack system. The last form of energy loss is in the form of the heat transfer process, resulting in the temperature drop along the flow. The stack effect, flow resistance (major and minor losses) and heat transfer process are discussed in detail in following sections. 4.3 Calculation Results
4.3.1 Stack effect calculation The atmospheric pressure and temperature are assumed to be 101 kPa and 35oC
respectively. The stack gas temperature is averaged over the inlet and the exit temperatures, 218 and 214oC. The inlet stack temperature is the temperature of the exhaust from the process entering the stack system and is fixed at 218oC. On the other hand, the exit temperature given is the constraint that the acid gaseous component within the stack will not condense before leaving the stack system and assumed to be lesser that 5 oC. With the constraint number in mind, we set the exit temperature to be 214oC and use this number to calculate the available pressure. It will be shown later in the heat transfer analyses that this figure is an acceptable value. The height of the stack is fixed at 135 m above the sea level. Then by using Eq.2-15, the values of draft generated by the stack effect at the design temperatures of 200, 218, 186 and 194 oC are calculated and summarized in Table 4-2.
33
Table 4-2 shows the data for the assumed atmospheric temperature and pressure used; the volume fraction of the mixture and molecular weight for each gas; the given inlets gas temperature and the assumed exit gases temperature. The last line shows the calculation results of the desire available drafts for the stack for all cases: C1 = 568808 kg/hr, C2 = 606067 kg/hr, C3 = 537268 kg/hr and C4 = 545262 kg/hr respectively. TABLE 4-2 Available Draft
Results C1 C2 C3 C4 Mass flow rate (kg/hr) 568808 606067 537268 545262 Int. gas temperature (oC) 200 218 186 194 Avg. gas temperature (oC) 198 216 184 192 Avg. Molecular Weight 31.52 33.1 30.2 30.4 Gas constant (J/kgK) 263.78 251.3 275.2 273.5 Available Draft (Pa) 545.05 641.25 515.9 537.6
4.3.2 Calculation of Major losses
There are six major losses in the piping system. The lengths to each section are 15, 17, 22, 27, 18 and 40-m while the internal diameters to each section are 3, 4, 5.4, 7.6, 9 and 4-m consecutively. Figure 4-3 shows schematic drawing of the piping system; the marks locate the sections of piping system producing major losses.
Within the calculation procedure, the averaged velocity, mass flow rate through the piping system was gradually increased from an appropriate initial value to the velocity at which the total pressure losses match with the available draft is reached. The resulting velocity, therefore, gives mass flow rate corresponds to the available draft calculated in section 4.3.1.
FIGURE 4-3 Locations of major losses
34
Fluid properties are evaluated at the average temperatures between the inlet and the exit temperatures. The inlet temperatures to the four cases C1, C2, C3 and C4 are 200oC, 218oC, 186 oC and 194 oC respectively. For these values, we assume the exit temperatures to by 4oC for all cases. We find later that those assumed values for the exit temperature of all cases are the reasonable ones.
With the assumed exit temperatures for all cases, the average temperature over the entire piping system can be calculated and is used as the temperature to determine the fluid properties, e.g. density and viscosity. The averaged temperature for all cases from the case C1, C2, C3 and C4 are 198, 216, 184 and 192 oC respectively. TABLE 4-3 Major losses: the C1, C2, C3 and C4 cases
Analysis of major losses: Vavg(m/s) Ploss (Pa) Sec.
No. D
(m) L(m) C1 C2 C3 C4 C1 C2 C3 C4
1 3.00 15.00 27.4 28.8 26.2 26.8 27.5 30.9 24.9 25.9 2 4.00 17.00 15.4 16.2 14.7 15.1 6.9 7.8 6.3 6.5 3 5.40 22.00 8.4 8.9 8.0 8.2 1.9 2.1 1.7 1.7 4 7.60 27.00 4.2 4.4 4.0 4.1 0.4 0.4 0.3 0.3 5 9.00 18.00 3.0 3.2 2.9 2.9 0.1 0.1 0.1 0.1 6 4.00 40.00 15.4 16.2 14.7 15.1 16.4 18.4 14.8 15.4
Table 4-3 shows the dimensions for each sections of the pipe generating the
major losses. The conservation of mass and energy equations give velocities and pressure losses at each section. It can be noticed that the highest value for major losses is at the piping section where the velocity is maximum. Whereas minimum pressure loss is at the section of largest diameter where the loss is negligible small compared with the losses at other sections.
4.3.3 Calculation of minor losses As shown in the Figure 4-6 below, there are ten minor losses in the system. The
first four fittings are sudden contraction (number 1-4). The fitting number 5 is sudden expansion. To keep the expansion loss to its minimum value; it is designed with expansion angle of 8o. Bending at the fitting number 6 and 8 are 90o bends with long radii. Fitting number 9 is a sudden contraction and fitting number 10 is assumed to be a 90o bend with guide vanes. The guide vanes are used in order to ease the flow.
As shown in Table 4-4, it can be seen that the largest minor loss occur at gradually expansion, fitting number 7. The pressure loss across the gradually expansion is greater than 200 Pa. for most cases except C3. The effect of the expansion loss can also be seen at the sudden expansion at fitting number 5 where the pressure losses give figure around 100 Pa. The losses due to the expansion of the fluid dominate other minor losses along the flow. Comparing to the flow past contractions, the minor loss due to the expansion is always much greater, indicating that it is difficult to efficiently decelerate a fluid.
Note that the losses may be quite different if the expansion is gradual. For very small angles, the diffuser is excessively long and most of the head loss is due to the wall shear stress as in fully developed flow. For moderate or large angles, the flow
35
separates from the walls and the losses are due mainly to a dissipation of the kinetic energy of the jet leaving the smaller diameter pipe.
In fact, for moderate or large values of expansion angle,θ, the conical diffuser is perhaps unexpectedly, less efficient than a sharp-edged expansion which has K = 1. There is an optimum angle for which the loss coefficient to be minimum.
FIGURE 4-4 Description of Minor Loss
TABLE 4-4 Minor losses: the C1, C2, C3 and C4 cases
Analysis of minor losses vav(m/s) Ploss(Pa)
No. Description K C1 C2 C3 C4 C1 C2 C3 C4
1 gradual contraction 0.02 27.4 28.8 26.2 26.8 6.1 6.8 5.5 5.7
2 gradual contraction 0.02 15.4 16.2 14.7 15.1 1.9 2.1 1.7 1.8
3 gradual contraction 0.02 8.4 8.9 8.0 8.2 0.5 0.6 0.5 0.5
4 gradual contraction 0.02 4.2 4.4 4.0 4.1 0.1 0.1 0.1 0.1
5 sudden expansion 1.00 15.4 16.2 14.7 15.1 96.9 108.7 87.5 91.1
6 90o Long Radius 0.20 15.4 16.2 14.7 15.1 19.3 21.7 17.5 18.2
7 gradual expansion 0.40 36.4 38.4 34.8 35.8 217.1 243.7 196.1 204.2
8 90o Long Radius 0.20 36.4 38.4 34.8 35.8 108.5 121.8 98.0 102.1
9 sudden contraction 0.10 12.6 13.3 12.1 12.4 54.2 60.9 49.0 51.0
10 90o Bend wanes 0.20 12.6 13.3 12.1 12.4 13.1 14.7 11.8 12.3
36
At the long radius elbow, fitting number 8, the values of the pressure loss are also of great values around 100 Pa. The high value of the loss is due to the turning effect at the elbow where the flow separates. The effect is more pronounce when the velocity of the flow is high. This can be seen by comparing the losses through two different size long radius elbow, the fitting number 6 and number 8. Although the loss coefficients for the two elbows are equal, the values of the pressure losses are significantly apart. The different varies to the order of square of the flow velocity (see Eq.3-8). TABLE 4-5 Total pressure losses
Flow analysis of the piping system Cases Mass flow (kg/h) Major losses(Pa) Minor losses(Pa) Total loss
C1 568808 53.2 517.7 570.9 C2 606067 59.7 581.1 640.8 C3 537268 48.1 467.7 515.8 C4 545262 49.9 487 536.9
As shown in Table 4-5, the minor losses are much greater than the major losses.
This indicate that the kinetic energy dissipation due to separation of the flow at the fittings along the piping system dominate the pressure losses. The total pressure losses of the two cases are set to be equal to the draft produced by the stack effect.
The resulting mass flow rates for the all cases are larger than the desired mass flow rates which are given in the last line of Table 4-1. It can then be concluded that the available draft created by the stack effect for both cases are enough to pull the flow at the design flow rates through the stack and the system connected to it.
4.3.4 Calculation of stack gas temperature distribution Exit stack gas temperature distribution for all cases: C1, C2, C3 and C4 are to
be determined. Figure 4-5 shows the sections of the piping system to be analyzed for heat transfer, given the inlet temperature for all cases at 200 oC, 218 oC, 184 oC and 196 oC respectively. At the external environment, the air is at the temperature of 30
oC. Velocity of the cross wind is assumed to vary with the stack height the value for each elevated level starting from the horizontal pipe passing across each section to the end of the stack are 5, 6, 10, 12, 15, and 20 m/s from the horizontal section to the top vertical section. These are overestimated wind speeds for an ordinary calm day. Since the maximum allowable temperature drop is limit to 5 degree Celsius, the assumed over estimated cross wind speeds play as a safety factor for heat transfer analyses.
37
FIGURE 4-5 Distributed temperature locations
This calculation divided the piping and stack into six sections where heat is
being lost from each section. Temperatures at the end of each section and at the stack exit are calculated using Eq.2-4, given the inlet temperature. All sections are assumed to be straight and the flow is in the fully developed flow. Figure 4-5 shows the location along the stack where those temperatures are to be determined for both two cases.
External and internal fluid properties are assumed constants and equal to the properties of air at the same conditions. Those values necessary for the analyses are kinematics viscosity, dynamic viscosity, Prandlt numbers, conduction coefficients and heat capacity at constant pressure. The material properties needed for evaluating conduction through the piping and insulators are the pipe and thickness insulator thickness and conductivities for both materials. These values are assumed to be constant for our heat transfer analyses. The values of the properties used in our analyses are shown in Table 4-6 and 4-7. TABLE 4-6 Data for internal convection heat transfer analyses
Data for internal convection heat transfer
Case µint (Pa⋅s)
kint
(W/m⋅K) PrintCpint
(J/kg⋅K) C1 2.59E-05 3.76E-02 0.698 1023 C2 2.64E-05 3.88E-02 0.696 1026 C3 2.55E-05 3.67E-02 0.699 1021 C4 2.57E-05 3.72E-02 0.698 1021
38
TABLE 4-7 Data for external convection heat transfer analyses
Data for external convection heat transfer ηext m2/s 1.61E-05 equal for all cases kext W/m⋅Κ 0.0259 Prext - 0.7282 ksteel W/m⋅Κ 15 kins W/m⋅Κ 0.054
C1 C2 C3 C4
The mass flow rates used to calculate heat losses for each case the value shown
in Table 4-6 and 4-7 which are the design values. It is found in Table 4-8 that the temperature differences are less than four degree Celsius for all cases which are less than the 5-degree maximum limits. TABLE 4-8 Exit temperature
Heat transfer analysis results Cases Tinlet T1 T2 T3 T4 T5 Texit
C1 200 199.1 198.0 197.3 196.9 196.6 196.5 C2 218 217.3 216.3 215.7 215.3 215.1 215.0 C3 186 184.9 183.7 182.9 182.4 182.1 181.9 C4 194 192.9 191.7 190.9 190.3 190.0 189.9
4.4 Numerical Simulation
In order to verify the calculation results obtained in the previous sections. We apply computational fluid dynamics (CFD) to simulate the entire flow field for both fluid and heat transfer processes. It is also of important to compare the minor loss coefficients given by the empirical formula with those obtained from the numerical formulation.
4.4.1 Numerical method Three-dimensional simulations of the turbulent fully develop flows of fluid in
the stack were carried out using the commercial CFD software FLUENT 6.3. The mesh geometry was produced using GAMBIT. The mesh used for all subsequent computations in this analysis contains 36743 nodes and 171038 tetrahedral elements. The code has been used to solve the steady Reynolds Averaged Navier-Stokes Equations closed with the standard k-ε turbulence model with buoyancy terms included in both k and ε transport equation. The semi-implicit method for pressure linked equations (SIMPLE) was employed with second order upwind discretisation employed for the advective terms. A segregated implicit solver was used. The solution is regarded as converged when the maximum value of normalized residuals of any equation is less than 5 × 10-5.
39
4.4.2 Boundary conditions
Fluid Material Air Fluid Properties: Density
C1 C2 C3 C4
0.815 kg/m3 at T = 200 ºC 0.824 kg/m3 at T = 218 ºC 0.805 kg/m3 at T = 186 ºC 0.796 kg/m3 at T = 194 ºC
Viscosity C1 C2 C3 C4
2.59 x 10-5 N.s/m2
2.64 x 10-5 N.s/m2
2.55 x 10-5 N.s/m2
2.57 x 10-5 N.s/m2
CPC1 C2 C3 C4
1023 J/kg.K 1026 J/kg.K 1021 J/kg.K 1021 J/kg.K
Thermal Conductivity C1 C2 C3 C4
3.76 x 10-2 W/m.K 3.88 x 10-2 W/m.K 3.67 x 10-2 W/m.K 3.72 x 10-2 W/m.K
Inlet
Mass flow rate C1 C2 C3 C4
568808 kg/hr = 158.00 kg/s at T = 200 ºC 606067 kg/hr = 168.35 kg/s at T = 218 ºC 537268 kg/hr = 149.24 kg/s at T = 186 ºC 545262 kg/hr = 151.46 kg/s at T = 194 ºC
Outlet Pressure (Pgauge) 0 Wall Temperature 35 ºC
Thermal Conductivity 0.054 W/m.K Surround temperature 35 ºC
40
4.4.3 Grid Generation
FIGURE 4-6 Grid Generation of stack (36743 nodes and 171038 tetrahedral elements)
41
TABLE 4-9 Total pressure losses of stack
Pressure loss (N/m2) No. Description C1 C2 C3 C4 1 gradual contraction 30.47586 34.08849 28.00372 51.56643 2 gradual contraction 9.8414 11.01037 9.04358 16.45117 3 gradual contraction 2.96833 3.31983 2.73129 5.306894 4 gradual contraction 0.20205 0.22155 0.18445 0.807671 5 sudden expansion 30.57043 30.6265 30.52179 11.62673 6 90o Long Radius 3.03965 3.32364 2.84314 1.256489 7 gradual expansion 224.488 225.0526 224.0996 104.0643 8 90o Long Radius 147.1904 195.872 113.7157 9.924027 9 sudden contraction 74.17158 83.11383 68.01786 100.9851 10 90o Bend w/vanes 44.44629 56.02881 45.71716 16.60808
Total 536.9181 608.5691 496.8746 517.0866 The static pressure and velocity obtained from the CFD simulation are shown in
Figure 4-7 and 4-8. The pressure and velocities at the different points are used to calculate the head losses along the stack system. The summation of the losses (total losses) is shown in Table 4-9 of all cases: C1, C2, C3 and C4. Theses values are comparable to those values of stack effect shown in Table 4-2 or the total losses shown in Table 4-5. TABLE 4-10 Exit temperatures of stack
Temperature (ºC) No. Description C1 C2 C3 C4 1 Inlet 200 218 186 194 2 T1 199.8008 217.8025 185.8071 193.8098 3 T2 199.2718 217.278 185.2955 193.3053 4 T3 198.9273 216.9361 184.9625 192.9768 5 T4 198.7363 216.7465 184.7781 192.7949 6 T5 198.6332 216.6442 184.6783 192.6966 7 Outlet 198.1942 216.207 184.2557 192.28
The temperature distribution within the stack system is shown in Figure 4-9.
The temperature at each particular point, as shown in the Figure 4-5, is listed in Table 4-10. The temperature drops, for all cases, are within allowable values (less than 5ºC). Theses temperature obtained from the CFD simulation are agree well with the empirical solutions shown in section 4.3.4.
42
4.5 Pictorial results
FIGURE 4-7 Static pressure (the case C1)
43
FIGURE 4-8 Velocity magnitude (the case C1)
44
FIGURE 4-9 Static temperature (the case C1)
CHAPTER 5 CONCLUSION AND RECOMMENDATION
At present days, Natural-draft stacks are used in most industries; they are usually
designed and come together at the first place with the new plant or processes. Designing and constructing the stacks to provide correct amount of natural draft involve a number design factor, many of which require trial-and-error and reiterative methods. In order to achieve the better knowledge of the stack process, computational fluid dynamics simulation (CFD) has been used as a useful tool to analyze. We studied the literature surveys, which are guidelines to apply this thesis.
This thesis studies the buoyancy driven to flow in a natural draft stack using computational fluid dynamics simulation and analyzes flow resistances and heat transfer processes on components of the stack system.
Simulated the fluid flow through a square duct of 0.21×0.21 m2 household fireplace for validate the commercial CFD software FLUENT 6.3. The stack effect obtained from CFD-simulation compared with the analytical solution. Pressure losses from CFD-simulation are closed to ones created by the stack effect. The results shown that the effect of the height will be used as an independent variable and pressure developed to drive the flow is the dependent variable.
The analysis of flow through components of stack system is analyzed by using CFD-simulation. Simulated the fluid flow through the smooth pipe (internal flow) and flow across the cylindrical (external), a 90º mitered bend with vanes and without vanes, a sudden contraction, a sudden expansion, 90º bend, a gradually conical expansion are determined pressure losses and local heat transfer. Pressure losses and heat transfer together with properties of fluid are used to calculate Friction factor and Nusselt number correlation. Compare the results from CFD-simulation and the empirical-solutions. The results shown that loss coefficients of components obtained from CFD-simulation are agreed well with the empirical solution over the range of interest. The error value is under-tolerances and can be accepted. It may be cause from the parameters input.
For the analyses of four mass flow rates flow through the industrial stack of 135-m-height. Four different mass flow rates: C1=568808 kg/hr, C2=606067kg/hr, C3=537268 kg/hr and C4=545262 kg/hr. The inlet gas temperature for the corresponding mass flow rates are 200, 218, 186 and 194 oC respectively. Simulated the flow to determine pressure losses and exit temperature for four cases within the stack and piping components system. The results shown that pressure losses and exit temperature for four cases are obtained form CFD-simulation are agree well with the results obtained in the empirical solution within less than one percent. The draft created by the stack effect for all cases C1, C2, C3, and C4 are enough to drive the flow through the stack system. Therefore, the effects of pressure losses and heat transfer on the temperature drop of the stack gas are acceptable for all cases.
The comparative study is done on a household fireplace, the piping system and stack in an industrial type stack of 135-m-heigh. The CFD-simulation is then being an important mean to simulate and predict the kind of situations. Therefore, the computational fluid dynamics simulation (CFD) has been used as a useful tool to
46
analyze the flow resistance and heat transfer process along an artificial small scale household stack and a large scale industrial stack because the results from this program approach to the theory.
REFERENCES 1. Moghiman M. Measurements and Modeling of Flue Height Influence on Air
Pollution Emissions and Thermal Efficiency of Natural-Draught Gas Fired Boilers. Masters Thesis, Faculty of Mechanical Engineering, Ferdowsi University of Mashhad, 2002.
2. Habib A., Elshafei M. and Dajani M. “Influence of Combustion Parameters on Nox Production in an Industrial Boiler.” Journal of Computer & Fluids. 37 (2008) : 12-23.
3. Diez L.I., Cortes C. and Pallares J. “Numerical Investigation of NOx Emissions from a Tangentially-fired Utility Boiler under Conventional and Overfire Air Operation.” Journal of Fuel. 87 (2008) : 1259-1269.
4. Williamson N., Armfield S. and Behnia M. “Numerical Simulation of the Flow in a Natural Draft Wet Cooling Tower-The Effect of Redial Thermofluid Fields.” Journal of Thermal Engineering. 28 (2008) : 178–189.
5. Ji J.J, Luo Y.H. and Hu L.Y. “Study on the Mechanism of Unsteady Combustion Related to Volatile in a Coal Fired Traveling Grate Boiler.” Journal of Applied Thermal Engineering. 28 (2008) : 145-156.
6. Chejne F., Hernandez J.P., et al. “Modelling and Simulation of Time-Dependent Coal Combustion Processes in Stack.” Journal of Fuel. 79 (2000) : 987–997.
7. Fang Qing-yan, Zhou Huai-chun, et al. Flexibility of a 300 MW Arch Firing Boiler Burning Low Quality. Masters Thesis, Faculty of Mining and Techology, Huazhong University of Science and Technology, 2007.
8. FLUENT 6.3 Documentation. Labanon : Fluent,Inc., 2006. 9. Hinze J.O. Turbulence. New York : McGraw-Hill Publishing Co., 1975. 10. Hoffmann K.A. and Chiang S.T. Computational Fluid Dynamics. 4th ed.
Wichita-Kansas : A publication of Engineering Education System., 2000. 11. Beychokb B. and Milton J. Stack Effect. England : WoodHead Publishing
Limited, 2005. 12. ASME : STS-1-2006, Steel Stack. 13. Ozisik M.N. Heat Transfer : A Basic Approach. United States of America :
McGraw-Hill Publishing Co., 1985. 14. Munson B.R., Young D.F. and Okiishi T.H. Fundamentals of Fluid Mechanics
5th ed. United States of America : John Wiley & Sons (Asia) Pte.Ltd., 2006. 15. Holman J.P. Heat Transfer. Singapore : McGraw-Hill Book Co., 1989. 16. Bennett C.O. and Myers J.E. Momentum, Heat and Mass Transfer. 3rd ed.
Singapore : McGraw-Hill Book Co., 1983. 17. Miller R.W. Flow Measurement Engineering Handbook. United States of
America : McGraw-Hill company, 1986. 18. White F.M. Fluid Mechanics. 6th ed. United States of America : McGraw-Hill
Publishing Co., 2008. 19. Potter M.C. and Wiggert D.C. Mechanics of Fluid. United States of America :
Prentice-Hall international Inc., 1997.
48
20. Douglas J.F., Gasiorek J.M. and Saffield J.A. Fluid Mechanics. England : Prentice-Hall, 2001.
APPENDIX A
Laminar and Turbulent Velocity Profiles
50
A.1 Laminar Flow The fully developed laminar flow profile is parabolic for pipe Reynolds numbers
below 2000 and unaffected by wall roughness. The average pipeline velocity is one-half the centerline velocity, and the relationship between point and maximum velocities is given by
12
max⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛−=
Rrvv Eq.A-1
where lPRv
µ4
2
max∆
= Eq.A-2
Thus, we begin by developing the equation for the velocity profile in fully developed laminar flow. If the flow is not fully developed, a theoretical analysis becomes much more complex.
A.2 Turbulent Flow
The turbulent profile is not fixed geometry, but rather changes with wall roughness and Reynolds number. Turbulent velocity profile in a smooth pipe can be written as
v
yuuu *
* = Eq.A-3
where y = R-r is the distance measured from the wall u is the time-average x component of velocity u* = (τw/ρ)1/2 is termed the friction velocity
FIGURE A
8
-1 The pipe geometry
51
A.3 Boundary condition Solver
Axisymmetric
Fluid Materials Water Material Properties :
Density Viscosity
998.2 kg/m3
1.003 × 10-3 kg/m-s
Inlet The fluid flow is fully developed flow and varies velocities
Wall standard wall
Outlet P(gauge) = 0
A.4 The results
Turbulent
Laminar
FIGURE A-2 The relation of pressure and distance
The graph shown the pressure will be drop along a pipe and the pressure drop
along pipe of turbulent more than laminar. A.4.1 Velocity Profiles: developing and fully developed
FIGURE A-3 Laminar velocity profiles
FIGURE A-4 Turbulent velocity profiles
52
Figure A-3 and A-4 shown the laminar velocity profiles and the turbulent is be fully developed faster than the laminar.
FIGURE A-5 Laminar and Turbulent Velocity Profiles
The velocity profile for laminar flow in a pipe is quite different from the velocity
profile for turbulent flow.
A.5 Fully-developed laminar inlet profiles /*************************************************************\ /* UDFs for fully-developed laminar inlet profiles *\ /*************************************************************\ #include "udf.h" DEFINE_PROFILE (inlet_x_velocity, thread, index) { real x[ND_ND]; /* this will hold the position vector */ real y; face_t f; begin_f_loop(f, thread) { F_CENTROID(x,f,thread); y = x[1]; F_PROFILE(f, thread, index) = 10. - y*y/(.05*.05)*10.; } end_f_loop(f, thread) }
53
A.6 Fully-developed turbulent inlet profiles /*************************************************************\ /* UDFs for fully-developed turbulent inlet profiles *\ /*************************************************************\ #include "udf.h" #define YMIN 0.0 /* constants */ #define YMAX 2600 #define UMEAN 38.48 #define B 1./10. #define DELOVRH 0.5 #define VISC 2.64-05 /* profile for x-velocity */ DEFINE_PROFILE(x_velocity, t, i) { real y, del, h, x[ND_ND], ufree; /* variable declarations */ face_t f; h = YMAX - YMIN; del = DELOVRH*h; ufree = UMEAN*(B+1.); begin_f_loop(f, t) { F_CENTROID(x,f,t); y = x[1]; if (y <= del) F_PROFILE(f,t,i) = ufree*pow(y/del,B); else F_PROFILE(f,t,i) = ufree*pow((h-y)/del,B); } end_f_loop(f, t) }
APPENDIX B
Discharge Coefficient
55
Discharge Coefficient B.1 Theory
FIGURE B-1 Orifice pressure tap location
Bernoulli’s energy equation between locations 1 and 2 gives
2
22
2
21
21
1
1
22gz
gvPgz
gvP
++=++ρρ
Eq.B-1
In practice has not the elevation difference between pressure taps because both pressure at a common elevation. For a constant-density fluid, this reduces Eq.B-1 to the form
gvvPP
2
21
2221 −
=−ρ
Eq.B-2
Eq.B-2 is reduced to the flow-rate units by applying the mass flow continuity equation between planes 1 and 2. This mass balance simply states that the mass of fluid entering plane 1 equals the mass leaving at plane 2 and stays within the confines of the steam tube;
222111 vAvAm ρρ ==& Eq.B-3
and for a constant-density fluid 2211 vAvAQ == Eq.B-4
Substituting Eq.B-4 into Eq.B-2
( )[ ]g
vAAPP2/1 2
22
1221 −=
−ρ
Eq.B-5
Planes 1 and 2 are circular, with measured pipe and bore diameters at flowing temperature of D1 and D2, Eq.B-5 can be rewritten as
( )[ ]
gvDDPP
2/1 2
22
1221 −=
−ρ
Eq.B-6
56
For a given primary element, the discharge coefficient is derived from laboratory data by rationing the true and theoretical flow rates. The true flow rate is determined by weighing or volumetric collection of the fluid over measured time interval, and the theoretical flow is calculated with
ρP
DD
DQtheo
∆
−×= −
412
225
)/(110512407.3 Eq.B-7
where β = D2/D1 Eq.B-7 can be rewritten as
ρβ
PDQtheo
∆
−×= −
4
225
110512407.3 Eq.B-8
The discharge coefficient is then defined as
rateflowltheoreticarate flow ture
=C Eq.B-9
The discharge coefficient corrects the theoretical equation for the influence of velocity profile (Reynolds number), the assumption of no energy loss between taps, and pressure –tap location. The discharge coefficient equation, for D< 2.3 in is calculated with
C∞ = 0.5959+0.0312β2.1–0.184β8+0.039[β4/(1-β4)]–0.0337β3/D+91.71β2.5/Re0.75 Eq.B-10
The discharge coefficient equation, for D>2.3 in is calculated with
C∞ = 0.5959+0.0312β2.1–0.184β8+0.09[β4/D(1-β4)]–0.0337β3/D+1.71β2.5/Re0.75
Eq.B-11 The discharge coefficient equation, for D and D/2 taps is calculated with
C∞ = 0.5959+0.0312β2.1–0.184β8+0.039[β4/(1-β4)]–0.0158β3+91.71β2.5/Re0.75 Eq.B-12
The discharge coefficient at infinite Reynolds number (C∞) is calculated with
C∞ = 0.5959+0.0312β2.1–0.184β8+0.039[β4/(1-β4)]–0.0158β3 Eq.B-13
57
B.2 Boundary Conditions
(a)
(b)
FIGURE B-2 The orifice pipe geometry
Fluid Materials
Water
Material Properties : Density
Viscosity
998.2 kg/m3
1.003 × 10-3 kg/m-s
Inlet turbulent fully developed flow and varies velocities
Wall standard wall
Outlet P(gauge) = 0
β = D2/D1 : vary β at 0.4, 0.5, 0.6
B.3 The results and discuss
Determine Discharge coefficient by vary β to find differential pressure and Substituting it into Eq.B-8.
FIGURE B-3 Velocity Vectors at β= 0.4
58
FIGURE B-4 Velocity Vectors at β= 0.6
Figure B-3 and B-4 shown β = 0.6 have a velocity more than β = 0.4. Thus the β
increase, the velocity will increase because the area is smaller.
FIGURE B-5 Pressure contours at β= 0.4
FIGURE B-6 Pressure contours at β= 0.6
The pressure first increases and then decrease to a minimum at the vena
contracta. Figure B-5 and B-6 shown β = 0.4 have a pressure drop more than β = 0.6. Thus the β increase, the pressure will decrease because the area is larger.
59
Plot Orifice discharge-coefficient with Reynolds number
FIGURE B-7 Orifice discharge-coefficient Chart
After simulated bring the result to computed the Discharge Coefficient for turbulent flow in smooth pipe. And then plotted the result compare to the exact solution, the result from Fluent program closed to the exact solution. The error value is under-tolerances and can be accepted. The vena contracta β = 0.6 have discharge coefficient more than β = 0.5 and β = 0.4. Thus the β increase, the discharge coefficient will increase because the area is larger. And the Reynolds number increase, the discharge coefficient will decrease.
APPENDIX C
Flow across Tube Bundles
61
Flow across Tube Bundles C.1 Theory
FIGURE C-1 The in-line arrangement
FIGURE C-2 The staggered arrangement
Heat transfer and pressure drop characteristics of tube bundles have numerous
applications in the design of heat exchangers and industrial heat transfer equipment. For example, a common type of heat transfer consists of a tube bundle with one fluid passing through the tubes and the other passing across the tubes. Frequently used tube bundle arrangements include the inline and the staggered arrangements, illustrated in Fig.1a and b respectively. The tube bundle geometry is characterized by transverse pitch ST and the longitudinal pitch SL between the tube centers; the diagonal pitch SD between the centers of the tubes in the diagonal row sometimes is used for the staggered arrangement. To define the Reynolds number for flow through the tube bank, the flow velocity is based on the minimum free-flow area available for flow, whether the minimum area occurs between the tubes in a transverse row or in diagonal row. Then the Reynolds number for flow across a tube bank is defined as
µmaxRe
DG= Eq.C-1
where Gmax = ρumax = maximum mass flow velocity Eq.C-2
is the mass flow rate per unit area where the flow velocity is maximum, and D is the outside diameter of the tube, ρ is the density, and umax the maximum velocity based on
62
the minimum free-flow area available for fluid flow. If u∞ is the flow velocity measured at a point inside the heat exchanger before the fluid enters the tube bank, then the maximum flow velocity umax for the in-line arrangement shown in Figure C-1 is determined from
1//
max −=
−= ∞∞ DS
DSuDS
SuuT
T
T
T Eq.C-3
For the staggered arrangement shown in Figure C-2, then the maximum flow
velocity umax is determined from
( ) 1//
21
2max −′=
−′= ∞∞ DS
DSuDS
SuuL
T
L
T Eq.C-4
The maximum mass flow rate Gmax, defined by Eq.B-2, also can be calculated
from
minmax A
MG = Eq.C-5
where M = total mass flow rate through the bundle in kilograms per second Amin = total maximum free-flow area
The flow patterns through a tube bundle are so complicated that it is virtually
impossible to predict heat transfer and pressure drop for flow across tube banks. Experimental investigations indicate that for tube bundles having more than
about N = 10 to 20 rows of tubes in the direction of flow, and the tube length large compared to the tube diameter, the entrance, exit, and edge effects are negligible. For such cases, the Nusselt number for flow across the bundle depends on the following parameters:
Re Pr DSL
DST
And the geometric arrangement of the tubes, namely, whether the tubes are
aligned or staggered. We now present the heat transfer and pressure drop correlations for flow across
the tube bundles. C.1.1 Heat Transfer Correlations
Grimson correlated heat transfer data for air reported by several investigators for both inline and staggered tube arrangements, for tube bundles having 10 or more transverse rows in the direction of flow with an expression in the from
n
om DG
ckDh
⎟⎟⎠
⎞⎜⎜⎝
⎛=
µmax Eq.C-6
for air in the range 2000 < Re < 40000.
This expression has been generalized to fluids other than air by including the
Prandtl number effect in the form
63
3/10 PrRe13.1 nm c
kDh= Eq.C-7
for 2000 < Re < 40000, Pr > 0.7, and N ≥ 10. Here Re defined as
µmaxRe
DG= Eq.C-8
The values of constant c0 and the exponent n are listed in Table C-1. All
physical properties in Eq.C-7 are evaluated at the mean film temperature. TABLE C-1 Constants c0 and n of Eq.C-7
DST
1.25 1.50 2.0 3.0 Arrangement DSL
oc n oc n oc n oc n 0.6 - - - - - - 0.213 0.6360.9 - - - - 0.446 0.571 0.401 0.5811.0 - - 0.497 0.588 - - - - 1.125 - - - - 0.478 0.565 0.518 0.5601.250 0.518 0.556 0.505 0.554 0.519 0.556 0.522 0.5621.50 0.451 0.568 0.460 0.562 0.452 0.568 0.488 0.5682.0 0.404 0.572 0.416 0.568 0.482 0.556 0.449 0.570
Staggered
3.0 0.310 0.592 0.356 0.580 0.440 0.562 0.421 0.5741.25 0.348 0.592 0.275 0.608 0.100 0.704 0.0633 0.7521.50 0.367 0.586 0.250 0.620 0.101 0.702 0.0678 0.7442.0 0.418 0.570 0.299 0.602 0.229 0.632 0.198 0.648
In-line
3.0 0.290 0.601 0.357 0.584 0.374 0.581 0.286 0.608Source : Grimison
Kays, London, and Lo examined experimentally the effects of the row number on the heat transfer coefficient for a variety of tube arrangements. For tube bundles having less than N = 10 transverse rows in the direction of flow, there was some reduction in the heat transfer coefficient. Based on the results of their experiments, the heat transfer coefficient hN for N < 10 could be determined by utilizing the following relation:
101 ≥= NN hch for 1 ≤ N ≤ 10 Eq.C-9
Table C-2 lists the values of the correlation factor c1 for both in-line and staggered tube arrangements, with N varying from 1 to 9. The results depend only slightly on the Reynolds number.
64
TABLE C-2 Correlation factor c1 for Eq.C-9 N 1 2 3 4 5 6 7 8 9 In-line 0.64 0.80 0.87 0.90 0.92 0.94 0.96 0.98 0.99 staggered 0.68 0.75 0.83 0.89 0.92 0.95 0.97 0.98 0.99 Source : Kays, London, and Lo [15]
More recently, Zukauskas reviewed the work of various investigators and
proposed the following correlation for the heat transfer coefficient for flow across tube bundles:
n
w
mm ckDh
⎟⎟⎠
⎞⎜⎜⎝
⎛=
PrPrPrRe 36.0
2 Eq.C-10
where Prw is the Prandtl number evaluated at the wall temperature, and for gases for liquids
which is valid for 0.7 < Pr < 500 and N ≥ 20. For liquids, the physical properties are evaluated at the bulk mean temperature, since the viscosity correction term is included through the Prandtl number ratio. For gases, the properties are evaluated at the film temperature and viscosity correlation term (Pr/Prw)n is omitted.
⎪⎩
⎪⎨⎧
=
410
n
The coefficient c2 and the exponent m were determined by correlating the experimental data for air, water, and oil reported by numerous investigators. Table C-3 lists the recommended values of c2 and m of Eq.C-10. TABLE C-3 Constant c2 and exponent m of Eq.C-10
Geometry Re c2 m Remarks 10 to 102 0.8 0.40 102 to 103 Large and moderate longitudinal pitch, can be
regarded as a single tube 103 to 2×105 0.27 0.63
In-line
2×105 to 106 0.21 0.84 10 to 102
0.9
0.40
102 to 103 About 20 percent higher than that for single tube 103 to 2×105 2.0
35.0 ⎟⎟⎠
⎞⎜⎜⎝
⎛
L
T
SS
0.60 2<
L
T
SS
103 to 2×105 0.40 0.60 2>
L
T
SS
Staggered
2×105 to 106 0.022 0.84
Source : Zukauskas [16].
65
Before calculating the heat transfer, we must recognize that the air temperature increases as the air flows through the tube bank. Therefore, this must be taken into account when using
( )∞−= TThAq w Eq.C-11
As a good approximation, we can use an arithmetic average value of T∞ and write for the energy balance
)(2 1,2,
21∞∞
+∞+∞ −=⎟⎠⎞
⎜⎝⎛ +
−= TTCmTTThAq pw & Eq.C-12
C.1.2 Pressure Drop Correlations
ZNG
fPρ2
2max=∆ Eq.C-13
where f = friction factor
G = ρumax = maximum mass flow rate velocity, kg/(m2⋅s) N = number of tube rows in direction of flow Z = correlation factor for effect of tube bundle configuration
( Z = 1 for a square or equilateral triangle tube arrangements) C.2 Geometry and Boundary conditions of tube bundles
The model shown below simulates a heat exchanger tube bundle in cross flow. This simple geometry is chosen because it offers the opportunity for comparison of the CFD results with experimental correlations.
FIGURE C-3 Geometry of the in-line arrangement
66
FIGURE C-4 Geometry of the staggered arrangement
Fluid Materials
Water
Material Properties : Density
Viscosity Cp k
998.2 kg/m3
1.003 × 10-3 kg/m-s 4182 J/kg-K 0.6 W/m-K
Inlet The bulk temperature of the cross-flow water (T∞) = 300 K
Wall The temperature of the tube wall (Twall) = 400 K
Outlet P(gauge) = 0
Transverse pitch (ST) 1.25, 1.5 cm
Longitudinal pitch (SL) 1.25, 1.5 cm
Diameter 1 cm
XTXLXD
ST/D SL/D SD/D
67
C.3 The results and discuss The results of the CFD simulation of the tube bundle exposed Re = 300 and
Re = 60000 water fluid flow are show below. C.3.1 In-line tube and Staggered arrangements
In-line arrangement
Staggered arrangement
Re = 300
In-line arrangement
Staggered arrangement
Re = 600000
FIGURE C-5 Temperature contours of XL = 1.5 Figure C-5 shows the water temperature increases as fluid flows through the
tube bank, because the heat transfer from wall of tube bank into water. Laminar flow can transfer heat to the fluid better than Turbulent flow.
In-line arrangement
Staggered arrangement
Re = 300
In-line arrangement
Staggered arrangement
Re = 600000
FIGURE C-6 Pressure contours of XL = 1.5
68
Figure C-6 shows the pressure contours of the water passing through the tube banks. The region of maximum pressure is the core tubes of the bundle.
In-line arrangement
Staggered arrangement
Re = 300
In-line arrangement
Staggered arrangement
Re = 600000
FIGURE C-7 Velocity vectors of XL = 1.5
Figure C-7 shown the center areas between tube banks have the maximum velocity because the water flow passes the small area.
In-line arrangement
Staggered arrangement
FIGURE C-8 Turbulence intensity contours of XL = 1.5
Figure C-8 shows the turbulence intensity contours that are indicated the
coefficient of mixing in tube banks. The red colure in figure is the maximum coefficient of mixing and the blue is the minimum coefficient of mixing.
69
0.01
0.1
100 1000 10000 100000 1000000 10000000
Reynolds Number
Fric
tion
Fact
or
XL=1.25XL=1.5
FIGURE C-9 Friction factor for in-line tube arrangement
1
10
100
1000
1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07Reynolds Number
Fric
tion
Fact
or
XL=1.25XL=1.5
FIGURE C-10 Friction factor for staggered tube arrangement
Figure C-9 and C-10 show the friction factor f for in-line arrangement with
square tube and staggered arrangement with equilateral triangular tube. In theses figures xT = ST/D, xL = SL/D, and xD = S’L/D denote, respectively, the dimensionless transverse pitch, longitudinal pitch, and diagonal pitch. Reynolds numbers are increasing, friction factor will be decrease because pressure drop are increased.
70
1
10
100
1000
10000
100000
100 1000 10000 100000 1000000 10000000
Reynolds Number
Nus
selt
Num
ber
exactXL=1.25XL=1.5
FIGURE C-11 Nusselt Number for in-line tube arrangement
Figure C-11 show the Nusselt Number for in-line arrangement and staggered
arrangement. In theses figures, we can see that when Reynolds number increase, the heat transfer also increase. XL =1.25 transfer heat better than XL = 1.5 because XL=1.25 has a small area to transfer heat from the wall of tube bank into the fluid.
APPENDIX D
Static Mixer
72
STATIC MIXER
Mixing is a common unit operation in a large number of processes, and it is used in many different applications where a defined degree of homogeneity of a fluid is desired. Common mixing devices are dynamic mixers for agitated tanks in batch operations and static mixers for inline mixing in continuous operations.
Static mixers have been utilized over a wide range of applications such as continuous mixing, blending, heat transfer processes, chemical reactions, etc. A static mixer consists of a contacting device with a series of internal stationary mixing elements of specific and patented geometry, inserted in a pipe. Some of the advantages of static mixers over dynamic mixers are that they have no moving parts, low maintenance, low space requirements, no moving parts and a short residence time. D.1 Theory
D.1.1 Governing Equations. For steady incompressible flow, the mass conservation equation can be written
as
0=∂∂
i
i
xu
Eq.D-1
and the momentum conservation equation can be written as
( )
iij
ij
ij
ji Fgxx
pxuu
++∂
∂=
∂∂
+∂
∂ρ
τρ Eq.D-2
In the absence of a gravitational body force and any external body force, the two last terms on the right side of Eq.D-2 are zero. The stress tensor, τij, in Eq.D-2 is given by
ijk
k
i
j
j
iij x
uxu
xu
δµµτ∂∂
−⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂+
∂∂
=32 Eq.D-3
Considering the conservation of mass for incompressible flow, ∂uk/∂xk=0, gives
⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂+
∂∂
=i
j
j
iij x
uxu
µτ Eq.D-4
D.1.2 Pressure drop and Z factor The pressure drop over the static mixer was computed for the repeating unit of
two mixer elements, and converted to a pressure per meter. The pressure drop for empty tube, ∆Pet , under laminar flow conditions is calculated as
232Dvl
P xet
µ∆=∆ Eq.D-5
When considering the pressure drop for the static mixer, ∆Psm , a common approach is to define a dimensionless number comparing the pressure drop over a static mixer with that over an empty pipe of the same length as the static mixer. The dimensionless number, referred to as the Z factor, is essentially the increase in energy input required when the static mixer is installed in the pipe. The Z factor is
et
sm
PP
ZZ∆∆
== (Re)& Eq.D-6
At Re ≤ 10, the correlation of Wilkinson and Cliff given by
73
32Re19.7 +=Z Eq.D-7
At Re ≥ 100, the correlation of Grace given by
( )Re21.05.124.3 +=Z Eq.D-8 D.2 Geometry and fluid properties
Mixer geometrical Diameter (D) 5.08 cm Segment (element) length (L) 7.62 cm Plate thickness 0.3175 cm Entrance length 10.16 cm Exit length 10.16 cm Overall length 66.04 cm Fluid properties Density (ρ) 1.20 g/cm3
Viscosity(µ) 500 cP
FIGURE D-1 A six-element static mixer
Static mixer consists of left- twisting and right-twisting helical elements placed
at right angles to each other (Figure D-1). Each element twists through an angle of 180°. The complete mixer consists of a series of elements of alternating clockwise and counterclockwise twist arranged axially within a pipe so that the leading edge of an element is at right angles to the trailing edge of the previous element. D.3 Boundary conditions
Inlet
Re = 0.15 vx = 0.0012 m/s , vy = vz = 0 Re = 1 vx = 0.0082 m/s , vy = vz = 0 Re = 10 vx = 0.082 m/s , vy = vz = 0 Re = 100 vx = 0.82 m/s , vy = vz = 0 Outlet Pressure outlet 0 Pa Blade No-slip
Wall No-slip
74
D.4 Results and discussion D.4.1 Velocity flied
FIGURE D-2 Velocity Streamline at Re = 0.15
Plane 1
Plane 2
Plane 3
Plane 4
Plane 5
Plane 6
FIGURE D-3 Contours of the axial velocity at Re = 0.15
Figure D-3 shows contours of the axial velocity at various intersections in a tube
equipped with six 180 degree elements. Red denotes high velocities and blue denotes low velocities. These elements divert the flow of material radically towards the pipe walls and back to the element, regardless of the velocity.
TABLE D-1 Mean Velocity magnitudes (m/s)
75
Average velocity magnitude (m/s) Re
First Second Third Fourth Fifth Sixth
0.15 0.001395 0.001399 0.001393 0.001399 0.00139 0.001274
1 0.009529 0.009552 0.009516 0.009553 0.009492 0.008708
10 0.095411 0.095703 0.095299 0.095559 0.09511 0.087808
100 1.038486 1.043984 1.035072 1.036251 1.039134 0.926304
D.4.2 Z factor The Z factor was found to be constant for static mixer at low flow rates, but as
the Reynolds number increased and the inertial forces became significant the Z factor increased. The increase in Z factor occurs at the flow rates above a Reynolds number of 10 for static mixer, see Figure D-4.
5
6
7
8
9
10
11
0.1 1 10 100
Re
Z fa
ctor
FluentWilkinson and Cliff
FIGURE D-4 The influence of Reynolds number and aspect ratio on the Z factor
The computed values of the Z factor for the static mixer fit the correlation of
Wilkinson and Cliff well. D.4.3 Pressure drop
A liner least-squares regression on the simulation results at Re = 0.15 provides a correlation of the form:
Z = 7.50 or 29.239Dvl
P xsm
µ∆=∆ Eq.D-9
76
0
5
10
15
20
25
30
0 1 2 3 4 5 6
Positions
Pres
sure
dro
p (P
a)
FluentWilkinson and CliffEq.(D-9)
FIGURE D-5 Pressure drop within a six element Kenics Mixer for Re = 0.15
In Figure D-5, the simulation data for Re = 0.15 is plotted along with Eq.D-5
and D-9. The pressure profile within the Kenics mixer for Re = 0.15 is shown in Figure D-5. The pressure drop is approximately linear over the mixer elements, with a pressure drop of 21.1117 Pa over six elements, excluding the open tube entrance and exit regions. These results are compared to pressure drop correlations available in the literature, which correlate the experimentally determined pressure drop in the mixer with an open tube pressure drop corresponding to similar conditions.
Pressure drop data was also obtained from the simulations corresponding to higher Reynolds numbers (Re = 1, 10, 100). A plot of the total pressure drop over the six mixer elements with Re is shown in Figure D-6.
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0.1 1 10 100Re
Pres
sure
Dro
p (P
a)
FluentWilkinson and CliffEq.4-9Eq.4-6
FIGURE D-6 Pressure drop within a six element Kenics Mixer for Re = 0.15, 1, 10
and 100
77
Figure D-6 shows the Reynolds number increase, the pressure drop will increase. The correlation of Wilkinson and Cliff Eq.D-7, D-6 and D-9 provides a good fit of the simulation data from the Fluent program.
78
BIOGRAPHY Name : Miss Sutida Phitakwinai Thesis Title : Numerical Analysis of Pressure Loss and Heat Transfer in a Natural-
Draft Stack Major Field : Mechanical Engineering Biography
Miss Sutida Phitakwinai studied in bachelor level in Food engineering, faculty of Agricultural Engineering and Technology at Rajamangala Institute of Technology. And, she got bachelor degree in 2003 with GPA 3.45. Now she got the scholarship from Rajamangkala Institute of Technology to study the master degree in Computer-aided Mechanical Engineering at TGGS, KMUTNB. She has internship in Patkol Public Co., Ltd. for one semester. She receives many guidance, suggestion and provides the data which usefully to this thesis.