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Table of Contents
Acknowledgements .................................................................................... Error! Bookmark not defined. Table of Contents .................................................................................................................................... i List of Figures ........................................................................................................................................ iv Abstract ................................................................................................................................................... v
iv Figure 2.4: Calculated distributions of void fraction (a) and temperature (b) in the channel; (c)
- Chapter 1 Introduction Nomenclature vi
- 1.1 Boiler (Steam Generator)
- 1.1.1 Working of a Steam Generator
- 1.2 Mass Transfer
- 1.3 Multiphase Flow
- 1.4 Phase Diagram
- 1.5 Boiling
- 1.5.1 Nucleate Boiling
- 1.5.2 Transition Boiling
- 1.5.3 Film Boiling
- 1.6 Computational Fluid Dynamics (CFD)
- 1.7 FLUENT
- 1.8 GAMBIT
- 1.9 Mesh (Grid)
- 1.10 Discretization Methods
- 1.10.1 Finite Volume Method (FVM)
- 1.10.2 Finite Element Method (FEM)
- 1.10.3 Finite Difference Method (FDM)
- 1.10.4 Boundary Element Method
- 1.10.5 High-Resolution Schemes..........................................................................................
- 1.11 User-Defined Function (UDF)
- 1.11.1 Importance of UDFs
- 1.11.2 Limitations of UDFs
- Chapter 2 Literature Review
- 2.1 Multidimensional Modeling of Two-Phase Flow and Heat Transfer
- design................................................................................................................................................. 2.2 CFD modeling of subcooled boiling - Concept, validation and application to fuel assembly
- Chapter 3 Methodology
- 3.1 The Mixture Model
- 3.1.1 Continuity Equation for the Mixture
- 3.1.2 Momentum Equation for the Mixture ii
- 3.1.3 Energy Equation for the Mixture
- 3.1.4 Volume Fraction Equation for the Secondary Phases.....................................................
- 3.2 Models relevant for bubbly flows
- 3.3 Computing the source terms.....................................................................................................
- 3.3.1 Source from the liquid to the vapor
- 3.3.2 Source from the vapor to the liquid
- 3.4 Custom heat transfer at the wall
- 3.4.1 General idea
- 3.4.2 Wall heating model and modeling assumptions
- 3.4.3 Further modeling
- 3.4.4 The test cases
- 3.5 Other possibilities
- Chapter 4 Code Implementation
- 4.1 Introduction
- 4.2 Macros and structure of the solver for multiphase problems
- 4.3 Strategies for multiphase problems
- 4.4 Different macros utilized
- 4.4.1 DEFINE_SOURCE Macro
- 4.4.2 Hooking a Source UDF to FLUENT
- 4.4.3 Compiled and Interpreted macros
- 4.5 Personal comments
- Chapter 5 Analysis and Results
- 5.1 Introduction
- 5.2 Test case of the 2D heated tube................................................................................................
- 5.2.1 Assumptions
- 5.2.2 Qualitative results
- 5.2.3 Validation
- 5.3 Test case of the 3D heated column...........................................................................................
- 5.3.1 Assumptions
- 5.3.2 Qualitative results
- 5.3.3 Validation
- Chapter 6 Discussion
- 6.1 Introduction
- 6.2 Findings from the literature
- 6.2.1 The wall evaporation model
- 6.2.2 Variable bubble diameter................................................................................................
- 6.2.3 Selection of test cases
- 6.3 Methodology and decisions......................................................................................................
- 6.4 Implementation issues and solutions
- 6.5 Results and Simulations iii
- 6.5.1 Results for the 2D tube heating
- 6.5.2 Problem of the 3D column..............................................................................................
- 6.6 Limitations of FLUENT
- Chapter 7 Conclusion and Future Recommendation
- 7.1 Conclusions
- 7.2 Future recommendations
- References
- Figure 1.1: A typical phase diagram......................................................................................................... List of Figures
- Figure 1.2: The boiling curve
- Figure 1.3: Mesh (Grid)............................................................................................................................
- Figure 1.4: Cartesian grid
- Figure 1.5: Rectilinear grid
- Figure 1.6: Curvilinear grid
- Figure 1.7: Unstructured grid
- Figure 2.1: Calculated temperature, void fraction and velocity contours in subcooled boiling
- Figure 2.2: Predicted radial velocity and void fraction distributions in subcooled boiling
- subcooled boiling Figure 2.3: Predicted axial distributions of the nucleate boiling heat flux and near-wall void fraction in
- temperature measured vs. calculated averaged void fraction, averaged temperature, axis temperature and wall
- Figure 4.1: Data and grid component
- Figure 4.2: Domain and thread structure hierarchy
- Figure 4.3: The Fluid Panel
- Figure 5.1: Contours of static temperature
- Figure 5.2: Contours of liquid velocity
- Figure 5.3: Contours of vapor velocity
- Figure 5.4: Contours of void fraction
- Figure 5.5: Comparison between actual and calculated temperature
- Figure 5.6: Comparison between actual and calculated liquid velocity
- Figure 5.7: Comparison between actual and calculated vapor velocity
- Figure 5.8: Contours of static temperature
- Figure 5.9: Contours of void fraction
- Figure 5.10: Comparison between actual and calculated temperature
- Figure 5.11: Comparison between actual and calculated void fraction
- Figure B.1: Test case of the 2D heated tube
- Figure B.2: Test case of the 3D heated column
v
Abstract
The purpose of this study is to incorporate user defined functions (UDFs) for modeling of boiling and evaporation. CFD code FLUENT is being effectively used in the industry for fluid flow and heat transfer problems. However, no universal model for mass transfer between two phases is currently available, therefore, user defined functions in FLUENT solver are used to model the boiling phenomenon. This study will lead to the modeling of complete steam generators and boilers. The modeling of boiling phenomenon in such equipment will improve the design and trouble shoot faults in the existing equipment. The investigations on the modeling of boiling heat transfer using the software FLUENT are reported in this thesis. Subroutines, easy to use and implementation via User Define Functions (UDFs) for the CFD package FLUENT, are discussed and tested in this work. Different test cases will be simulated to validate the code; these are classic test cases and also challenging to compute. Investigations are summarized at the end of the thesis on the capabilities of FLUENT to simulate this problem.
vii
ρ Density, Kg/m³
Subscripts b Bubble bub Bubbly zone g Vapor phase h Hydraulic diameter i Interface l Liquid phase nb Nucleate boiling m mth^ phase p pth^ phase sat Saturation sub Sub-cooling w Wall
Acronyms 1D One-Dimensional 2D Two-dimensional 3D Three-dimensional CFD Computational Fluid Dynamics CHF Critical Heat Flux GUI Graphical User Interface UDF User Defined Functions
This project is modeling of boiling phenomenon using FLUENT solver. Now-a-days boilers are commonly used in process as well as power industries. CFD code FLUENT is being effectively used in the industry for fluid flow and heat transfer problem. However, no universal model for mass transfer between two phases is currently available; therefore, UDFs are incorporated for modeling of boiling in a steam generator. Boiling encloses a very large amount of energy available at constant temperature. The bubbles created can remove a very large amount of energy without harming the material and also drive the flow due to the density gradient. Thus the need to understand and control the phenomena has been the challenge of many researchers for past several years. Since Computational Fluid Dynamics (CFD) has been more and more affordable for companies, the demand on modeling has increased; companies are looking for the understanding of their products but also optimization in order to be more competitive and reliable. The aim for this project was to write a set of subroutines in C code which would then be compiled using the CFD package FLUENT; no boiling models are provided in this software, however a couple of tutorials are available to understand how the software can solve this type of problem. This chapter gives a general idea and know-how of the different equipments, solvers, codes, software, phenomena, terms and conditions used in the subsequent chapters.
1.1 Boiler (Steam Generator)
A boiler or steam generator is a device used to create steam by applying heat energy to water. Although the definitions are somewhat flexible, it can be said that older steam generators were commonly termed boilers and worked at low to medium pressure (1~300 psi), but at pressures above that figure it is more usual to speak of a steam generator [1].
Chapter 1
Introduction
1.3 Multiphase Flow In fluid mechanics, multiphase flow is a generalization of the modeling used in two- phase flow to cases where the two phases are not chemically related (e.g. dusty gases or water and air) or where more than two phases are present (e.g. in modeling of propagating steam explosions). Each of the phases is considered to have a separately defined volume fraction (the sum of which is unity), and velocity field [2]. Conservation equations for the flow of each can then be written down straightforwardly. Two-phase flow is a particular example of multiphase flow.
1.3.1 Two-Phase Flow
In fluid mechanics, two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases [3]. In boilers, pressurized water is passed through heated pipes and it changes to steam as it moves through the pipe. The design of boilers requires a detailed understanding of two-phase flow heat-transfer and pressure drop behavior, which is significantly different from the single-phase case. This case is for a single fluid occurring by itself as two different phases, steam and water. The term 'two-phase flow' is also applied to mixtures of different fluids having different phases, such as air and water, or oil and natural gas.
1.4 Phase Diagram A phase diagram, Figure 1.1, is a type of chart used to show conditions at which thermodynamically-distinct phases can occur at equilibrium.
Figure 1.1: A typical phase diagram
1.5 Boiling Boiling, a type of phase transition, is the rapid vaporization of a liquid, which typically occurs when a liquid is heated to its boiling point, the temperature at which the vapor pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding environmental pressure [4]. Thus, a liquid may also boil when the pressure of the surrounding atmosphere is sufficiently reduced, such as the use of a vacuum pump or at high altitudes. Boiling occurs in three characteristic stages, which are nucleate, transition and film boiling, as shown in Figure 1.2. These stages generally take place from low to high surface temperatures, respectively.
1.5.1 Nucleate Boiling
Nucleate boiling is characterized by the growth of bubbles on a heated surface, which rise from discrete points on a surface, whose temperature is only slightly above the liquid‟s saturation temperature. In general, the number of nucleation sites is increased by an increasing surface temperature. An irregular surface of the boiling vessel (i.e. increased surface roughness) can create additional nucleation sites, while an exceptionally smooth surface, such as glass, lends itself to superheating. Under these conditions, a heated liquid may show boiling delay and the temperature may go somewhat above the boiling point and fail to boil [4].
1.5.2 Transition Boiling
Transition boiling may be defined as the unstable boiling, which occurs at surface temperatures between the maximum attainable in nucleate and the minimum attainable in film boiling [4].
1.5.3 Film Boiling
If a surface heating the liquid is significantly hotter than the liquid then film boiling will occur, where a thin layer of vapor, which has low thermal conductivity insulates the surface. This condition of a vapor film insulating the surface from the liquid characterizes film boiling [4].
1.7 FLUENT FLUENT is a general-purpose CFD code based on the finite volume method on a collocated grid. FLUENT technology offers a wide array of physical models that can be applied to a wide array of industries [6]. Dynamic and Moving Mesh: The user simply sets up the initial mesh and prescribes the motion, while FLUENT software automatically changes the mesh to follow the motion prescribed. This is useful for modeling flow conditions in and around moving objects. Turbulence: A large number of turbulence models are used to approximate the effects of turbulence in a wide array of flow regimes. Acoustics: The acoustics model lets users perform "on-the-fly" sound calculations. Reacting Flows: FLUENT technology has the ability to model combustion as well as finite rate chemistry and accurate modeling of surface chemistry. Heat Transfer, Phase Change, and Radiation: FLUENT software contains many options for modeling convection, conduction, and radiation. Multiphase: It is possible to model several different fluids in a single domain with FLUENT. Post-processing: Users can post-process their data in FLUENT software, creating - among other things - contours, pathlines, and vectors to display the data.
1.7.1 Methodology
During preprocessing [5] The geometry (physical bounds) of the problem is defined. The volume occupied by the fluid is divided into discrete cells (the mesh). The mesh may be uniform or non-uniform. The physical modeling is defined - for example, the equations of motions, enthalpy, radiation, species conservation. The fluid properties are defined. Boundary conditions are defined. This involves specifying the fluid behavior and properties at the boundaries of the problem. For transient problems, the initial conditions are also defined.
The simulation is started and the equations are solved iteratively as a steady-state or transient. Finally a postprocessor is used for the analysis and visualization of the resulting solution.
1.8 GAMBIT It is a geometric modeling and grid generation tool often shipped with FLUENT technology. GAMBIT software allows users to create their own geometry or import geometry from most CAD packages. It can automatically mesh surfaces and volumes while allowing the user to control the mesh through the use of sizing functions and boundary layer meshing [7].
1.9 Mesh (Grid) A regular grid (Figure 1.3) is a tessellation of the Euclidean plane by congruent rectangles or a space-filling tessellation of rectilinear parallelepipeds (e.g. bricks). Grids are used in finite element analysis as well as finite volume methods and finite difference methods. Since the derivatives of field variables can be conveniently expressed as finite differences, structured grids mainly appear in finite difference methods. Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods. Each cell in the grid can be addressed by index ( i, j ) in two dimensions or ( i, j, k ) in three dimensions, and each vertex has coordinates ( i. dx , j. dy ) in 2D or ( i. dx , j. dy , k. dz ) in 3D for some real numbers dx, dy, and dz representing the grid spacing [7].
Figure 1.3: Mesh (Grid)
A curvilinear grid or structured grid (Figure 1.6) is a grid with the same combinatorial structure as a regular grid, in which the cells are quadrilaterals or cuboids rather than rectangles or rectangular parallelepipeds.
Figure 1.6: Curvilinear grid An unstructured grid (Figure 1.7) is a tessellation of a part of the Euclidean plane or Euclidean space by simple shapes, such as triangles or tetrahedral, in an irregular pattern. Grids of this type may be used in finite element analysis when the input to be analyzed has an irregular shape.
Figure 1.7: Unstructured grid Unlike structured grids, unstructured grids require a list of the connectivity which specifies the way a given set of vertices make up individual elements.
1.10 Discretization Methods The stability of the chosen discretization is generally established numerically rather than analytically as with simple linear problems. Special care must also be taken to ensure that the discretization handles discontinuous solutions gracefully. The Euler equations and Navier-Stokes equations both admit shocks, and contact surfaces [5]. Some of the discretization methods being used are:
1.10.1 Finite Volume Method (FVM)
This is the "classical" or standard approach used most often in commercial software and research codes. The governing equations are solved on discrete control volumes. FVM recasts the PDE's (Partial Differential Equations) of the N-S equation in the conservative form and then discretize this equation [5]. This guarantees the conservation of fluxes through a particular control volume. (1.1)
where „ Q ‟ is the vector of conserved variables, „ F ‟ is the vector of fluxes, „ V ‟ is the cell volume, and „ A ‟ is the cell surface area in equation (1.1). "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages.
1.10.2 Finite Element Method (FEM)
This method is popular for structural analysis of solids, but is also applicable to fluids. The FEM formulation requires, however, special care to ensure a conservative solution. The FEM formulation has been adapted for use with the Navier-Stokes equations. Although in FEM conservation has to be taken care of, it is much more stable than the FVM approach. Generally stability/robustness of the solution is better in FEM though for some cases it might take more memory than FVM methods [5]. In this method, a weighted residual equation is formed:
are executed as interpreted or compiled functions. must have all values returned to the FLUENT solver specified in SI units. User-defined functions can perform a variety of tasks in FLUENT. They can: return a value. modify an argument. return a value and modify an argument. modify a FLUENT variable (not passed as an argument). write information to (or read information from) a case or data file.
1.11.1 Importance of UDFs
UDFs allow us to customize FLUENT to fit our particular modeling needs. UDFs can be used for a variety of applications, some of which are listed below: Customization of boundary conditions, material property definitions, surface and volume reaction rates, source terms in FLUENT transport equations, source terms in user-defined scalar (UDS) transport equations, diffusivity functions, etc. Adjustment of computed values on a once-per-iteration basis. Initialization of a solution. Asynchronous execution of a UDF (on demand). Post-processing enhancement. Enhancement of existing FLUENT models (e.g., discrete phase model, multiphase mixture model, discrete ordinates radiation model).
1.11.2 Limitations of UDFs
Although the UDF capability in FLUENT can address a wide range of applications, it is not possible to address every application using UDFs. Not all solution variables or FLUENT models can be accessed by UDFs. Specific heat values, for example, cannot be modified; this would require additional solver capabilities [8].
2.1 Multidimensional Modeling of Two-Phase Flow and
Heat Transfer
Michael Z. Podowski, in his research article “Multidimensional modeling of two- phase flow and heat transfer” [9] has given an overview of selected issues concerning the formulation of multidimensional models of two-phase flow and heat transfer. He presented a complete computational multiphase fluid dynamics (CMFD) model of two-phase flow, including local constitutive models applicable to two-phase flows in heated channels. Results are shown of model testing and validation. In the results, as shown in Figure 2.1 ~ Figure 2.3, he demonstrated that the overall model is capable of capturing various local flow and heat transfer phenomena in general, and the onset of temperature excursion (CHF) in low quality forced- convection boiling, in particular. The proposed approach can be used to predict multidimensional velocity field and phase distribution in two-phase flow devices and components used in thermal power plants, nuclear power plants and chemical processing plants.
Figure 2.1: Calculated temperature, void fraction and velocity contours in subcooled boiling
Chapter 2
Literature Review
