This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
Biomass is in trend now-a-days as an alternate energy source because of reduced CO2 emissions, abundance and cost effectivity. Gasification of biomass is the first activity done in order to obtain bio-syn-gas, which is processed downstream to produce motor fuels, but the products from biomass gasifier contain tar. The work presented here is concerned to tar and its removal by means of cracking to improve carbon conversion efficiency. Volatiles obtained from biomass gasification require further processing to justify biomass usage as an alternate; it is then, when tar comes to picture. Processes downstream to gasification use catalysts like Fischer- Tropsch process, in such processes tar poisons the catalysts, i.e., the carbon blocks the active sites in the catalysts. Also tar in raw gas causes corrosion and blockage in pipes. So, tar removal is of prime interest and it done by means of two processes thermal cracking and catalytic cracking.
The work presented here is analysis of tar cracking using CFD, i.e., to analyze the hydrodynamics along with chemical kinetics in a packed bed reactor. The analysis is done in 2D as well as 3D. The 2D model is simple model with consideration of a single homogeneous phase of gas and catalysts. The reactor has dimensions of 12" X 2" with a mass flow rate of 0.0003 kg/s (5 mg min-1). The analysis of 2D model was done to get a proper hydrodynamic and reaction profile occurring inside the reactor. On validation of the trends in the 2D model the input conditions were applied on the 3D model. In the 3D model two separate phases' gas and solid were considered so as to obtain correct trends of hydrodynamics and reaction profile. A simple first order reaction was taken into consideration but it was an overall reaction. The activation energy and rate exponent was used in accordance with literature (Rath et al, 2001). The reactor is 6" long and 2" diameter and the catalysts used in the study are spherical dolomite particles of 0.5inch diameter and are stacked in structured manner.
The vital factor in the study was tar characterization. As we know that tar is a complex mixture of PAH's (Polycyclic Aromatic Hydrocarbons) and consists of numerous compounds. In this study model compound toluene C6H5-CH3 was used in feed either than actual tar. Moreover, in the exit stream products with maximum concentration were accounted for as Fluent Solver requires detailed chemical kinetics along with balanced chemical reactions for apt results. The feed was fed 7000C (923.15 K). The reaction is an endothermic reaction. Products obtained are CO2, CO, H2, H2O and CH4.
Analysis in 3D was done at steady state to understand the effect of rate exponent (n) on the reaction kinetics as well as on hydrodynamics. Finally, contour plots for pressure, temperature distribution, and mass fraction of components engaged in the reaction and velocity vectors were plotted.
Work cited here is a nascent one, flaws may be embedded in the system but the study was focused to analyze the affect of reaction on hydrodynamics in packed bed reactor. Simplicity in - design and parameters fed to Fluent solver, was done to make the work feasible in all possible manners and minimize errors in the output.
It is tried that the work cited below may thus act and serve as the road for CFD to enter into analysis of intense chemical phenomena.
Table of Contents
2.1 Kinetics review
Kinetics for catalytic cracking of tar was analyzed by Faundez et al, 2001. The model proposed was based on gas-oil cracking and was validated by using three types of tars used by Weekman .V et al, 1970 . The catalyst used is calcined limestone (11m2/g). The reactions were carried out in a stainless steel cylindrical catalytic fixed bed reactor of 30mm diameter with 1.5cm catalyst bed-height with tar feed rate as 5.04 mg/min. The work was concentrated on: 1) The proposal of a mechanism and a model for the kinetics of catalytic pyrolysis of tars main products, i.e. gases, lighter tars and solid carbon or char; 2) the validation of the proposed model by the experimental catalytic pyrolysis of different tars; and, 3) The determination of the kinetic and catalytic deactivation parameters of the model. It may be noted that flow rate used in this project is inferred from this literature.
P. Morf et al, 2001 studied the change of mass and composition of biomass tar due to secondary reactions in an experimental set-up consisting of wood pyrolyser, a catalytic tubular reactor for heterogeneous reactions of tar and finally gas analyzer for product measurement and characterization. Spruce woods chips of 10-40 mm dia were sent to pyrolyser at a rate of 1.6 kg h-1. The wood pyrolysis gas obtained at a mean temperature of 350oC was sent to the reactor containing tar approx. 300g nm-3. The residence time in the reactor was 0.2 s after a steady state was attained. The reactor was operated in a temperature range of 500-1000oC. The author classified tar according to Milne T. A. et al, 1998  and fed external oxidizer. The reactions occurring in the reactor was analyzed and found the product gas to contain mostly of CO2, CH4, CO, H2O & H2. The results reflected that CO is the major product. The overall product distribution remains stable within the temperature range of 450-600 oC. Then the product concentration increased linearly with temperature especially for CH4 and CO.
Rath et al, 2001 conducted an experimental study to investigate the vapor phase cracking of tar obtained from pyrolysis of spruce wood (0.5-1.0 mm) using a thermogravimetric analyzer (TGA) and in coupling of the TGA with a consecutive tubular reactor. The products from the reactor were analyzed using GC-MS analyzer. In all cases the TGA was heated from 105 oC to 1050 oC at a rate of 5 K min-1 and the reactor consisted of three different heating zones namely 600 oC, 700 oC, 900 oC in order to achieve different residence times for the volatiles. The motto this study was to analyze three different types of tars that were produced from gasification of spruce wood under different thermal conditions and the way these tars catalytically cracked. The tubular reactor was fed with 3.62 mg/min of wood volatiles. There were in total nine (9) experimental runs with variations in residence time. The kinetic model proposed by him was used in the CFD analysis done in this project. The table 2.1.1 below shows his findings.
3.02e+21(g mg-1 s-1)
Table 2.1.1: Kinetic parameters for cracking of three different tars.
Source: Rath et al, 2001
Taralas et al, 2003 investigated the cracking of tar obtained from pyrolysis of exhausted olive husks (kernels) using calcined dolomite as catalyst. The pyrolysis was carried out in a screw reactor at 975 K at a bio-fuel feed rate of 0.101 kg/h. the volatiles produced were introduced into the catalytic reactor (20mm dia and 400mm long) using N2 as carrier gas with flow rate of 0.5-0.1 L/h. The catalyst particles were less than 1mm in dia. The basic motto of this study was to study feasibility of the dolomite as a catalyst and determining the difference it makes in product concentration obtained from thermal cracking as well as catalytic cracking. The results obtained from his study shows considerable increase in product concentration at lower temperatures, i.e, and 1175K for thermal cracking versus 1075K for catalytic cracking. It was also observed that thermal cracking required a considerable residence time about 20seconds more as compared to catalytic cracking to obtain the same exit gas concentration from the catalytic reactor.
Kumar et al, 2009 did a study of existing processes for biomass gasification and its subsequent processing for effective commercial application. In relation to gasification products clean-up and effective carbon conversion they analyzed tar cracking using addition reactor such as fixed bed reactors consecutive to the gasifier for different sets of catalysts such as dolomite, olivine, Ni and hot sand. After 20 hours of test they concluded that dolomites and olivine proved as a better catalyst then Ni and hot sand w.r.t to various operating parameters such as temperature, flow rate, bed height, residence time and carbon conversion. Although olivine and dolomite faired equally but olivine was beaten when it came to bed capacity (tar processing capability for same amount of catalyst loading) and dolomite fails when it comes to attrition.
Tasaka et al, 2006 analyzed steam reforming of tar produced from cellulose gasification using Co/MgO as catalyst. The reactor was 22mm in dia and 300mm long. The catalyst particles were 0.5-0.3mm in dia. The tests were conducted for 120 min at a feed rate of 15gm/min at a temperature of 623 K and three sets of catalyst loading namely 12% Co/MgO, 24% Co/MgO and 36% Co/MgO. They finally concluded that at 36% Co/MgO the concentration of CO and H2 remained for whole 2hrs.
Lopamudra Devi, 2005 in her analysis for catalyst selection for tar cracking studies three catalysts Ni, dolomite and untreated olivine. Although dolomite and Ni-based steam reforming catalysts have been proven to be active in terms of tar reduction, dolomite is relatively soft and very easily eroded, whereas Ni-based catalysts are easily deactivated. Olivine has advantages over dolomite in terms of its attrition resistance. The experiments were conducted at the facility of ECN, (Petten, Netherlands). A slip stream of the biomass gasification gas from the lab-scale atmospheric bubbling fluidized bed gasifier was passed through a secondary fixed the stainless steel secondary reactor has a 3 cm internal diameter and is 50 cm long. The experiments were performed in a temperature range of 800-900oC and temperature across the catalyst was taken to be constant during each experiment. The catalysts were mixed with sand (0.17 mass fraction of catalyst) and the mixture was placed on top of a bed of coarse sand. The reactor was fed with 1kg/h with a residence time of 20s for each catalyst (200-300Î¼m). Experiments were also carried out using sand only as the catalyst. The figure 2.2.1 below shows the results obtained from her experiments for 900oC. It can be clearly seen that dolomite is an excellent catalyst for tar cracking.
Figure 2.2.1: Conversion of tars with different additives TR = 9000C; Gas flow: 1.2 l min-1; Ï„'=0.26 s; Ï„ = 0.066kg h m-3
Source: Lopamudra Devi; University of Eindhoven, Netherlands; 2005.
Zhang et al; 2004 investigated tar catalytic destruction in a tar conversion system consisting of a guard bed and catalytic reactor. Three Ni-based catalysts (ICI46-1, Z409 and RZ409) were proven to be effective in eliminating heavy tars (499% destruction efï¬ciency). Hydrogen yield was also improved by 6-11 vol% (dry basis). The experimental results also demonstrated that increasing temperature boosted hydrogen yield and reduced light hydrocarbons (CH4 and C2H4) formation, which suggested that tar decomposition was controlled by chemical kinetics.
Dou et al; 2003 compared five catalysts on tar removal from fuel gases in a fixed-bed reactor. The Y-zeolite and NiMo catalysts were found to be the most effective; such that 100% tar removal can be achieved at 550 oC. It was also observed that process variables like temperature and space velocity had very significant effect on tar removal. The visual observation demonstrated that only very small amount of coke appeared at the surface of catalyst even with 168 h operation.
Although the dolomite can effectively remove tar in some cases, there are still many problems during biomass gasification. Zhang Xiodong; 2003 reviewed the shortcomings of dolomite as the following: The conversion rate of tar catalyzed by dolomite was difficult to reach or exceed 90-95%; Although dolomite could reduce the tar in syngas and change the distribution of tar compositions, it was difficult to convert the heavy tars by dolomite; The dolomite would be inactive since the particle was easily broken during gasification; The melting point of dolomite was low and the catalyst would be inactive resulting from the melting of dolomite.
In the table below are the results of experiment conducted to analyze and compare the catalytic cracking of gasifier tars using different catalysts. The study was conducted using a 20cm long reactor and 5cm in diameter. 1.03 kg of catalysts of each type was used in this study. Temperature stated is the averaged value along the length of the reactor.
D:\sandeepan project\pics\comparision of catalysyts.PNG
Figure 2.2.: Catalytic cracking of gasifier tars using different catalysts.
Catalyst selection has always been major concern in process industry. It is been found that for the same process we actually have lot of options in selecting the catalyst. In the case of tar cracking dolomite, olivine, Ni-based catalysts, Co/Mo based catalysts and Si-based catalysts are available, but literature shows that dolomite is most apt catalysts for high surface area and active sites concentration per unit surface area, easily available and cheap. Also, it can catalyze tar at lesser temperatures than olivine which is the next best catalyst. The only drawback of dolomite is that it has high attrition rate. This can be controlled to a certain extent by using calcined dolomite. Calcinations of dolomite also increase its surface adsorptivity.
model compound review
In a lab scale experiment by Nikola Sundac; 2003 related to biomass gasification and tar cracking. He analyzed dolomite and olivine catalysts but it was only preparation phase. Now instead of using real tar the author considered using model compounds like Naphthalene and Xylene. The author presented the following arguments to support the use of model compounds: 1) These compounds show similar cracking activity as real tar. 2) Ease of formulation of a kinetic model, 3) Simplicity to design, and 4) These compound constitute 4.5% in real tar composition .
Milne T.A. et al; 1998 investigated biomass gasification and their conversion using three model compounds Naphthalene, toluene and cyclo-hexane. The author justified the use of these compounds by comparing the reaction kinetics they show when compared real tar cracking. Although there was not an exact match in output obtained from cracking of real tar versus models compounds but they faired equivalently. On the basis of this research toluene was considered as model compound in the study done in this project.
Coll et al; 2001 also studied the model compounds like benzene; toluene, naphthalene, anthracene, and pyrene. All of these were cracked using two commercial nickel catalysts: UCG90-C and ICI46-1 at 700-800 oC. The order of these model tars reactivity was: benzene > toluene > anthracene > pyrene > naphthalene. Toluene conversion rate ranged from 40% to 80% with the ICI46-1 catalyst, and 20% to 60% for the UCI G90-C catalyst.
Simell et al; 1998 compared a commercially available metal based catalyst (NiMo/Î³-Al2O3) with non-metallic mineral catalysts during the catalytic pyrolysis of toluene. The non-metallic mineral catalysts included Norwegian dolomitic magnesium oxide [MgO], Swedish low surface quicklime [CaO], and calcined dolomite [CaMg(O)2]. Among these catalysts, the catalytic effect followed the sequence: CaO > CaMg(O)2 > MgO > NiMo/Î³-Al2O3.
Gil et al; 1999 also investigated the impact of temperature on the composition of tar samples obtained from steam cracking of wood at 700-900oC. He listed the compositions and concentration of tar at 700, 800 and 900oC, respectively, as shown in Table 2. It can be seen that phenol, cresols and toluene were predominant at 700 1C, while naphthalene and indene were the major components at 900 oC.
Table 2.3.1: Effect of temperature on distribution of major organic tar compounds (g/kg dry wood)
Source: Gill J et al; Biomass Bio-energy; 1999.
cfd in packed bed modelling
3.1 CFD (Computational Fluid Dynamics)
CFD is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the millions of calculations required to simulate the interaction of fluids and gases with the complex surfaces used in engineering. However, even with simplified equations and high speed supercomputers, only approximate solutions can be achieved in many cases. More accurate codes that can accurately and quickly simulate even complex scenarios such as supersonic or turbulent flows are an ongoing area of research.
3.1.1 Applications of CFD
CFD useful in a wide variety of industrial and non-industrial applications. Currently, it is been seen an advanced engineering tool to provide data, which suits to solving a lot of real time situations seen in this physical world. Applications of CFD are numerous and wide spread, some which are as follows:
In chemical industry, CFD is very useful in analyzing the flow conditions in a CSTR, Fluidized bed reactor, Fixed bed reactor, Heat Exchangers, combustion systems and material and polymer handling equipments.
Designing of aerodynamically stable ground vehicles, spacecrafts, jets and passenger crafts, missiles CFD is considered as very effectives and successful.
CFD has found its application bio-medical engineering to analyze the flow in arteries and veins.
In structures it is found that CFD is good tool to analyze the affects of wind and water on tall structures.
In steel industry, due to opacity of steel CFD has been very successful in determining the flow conditions of liquid molten steel in the furnace vessels.
CFD is has provided with reliable results when analyzing turbo-machinery equipments like diffusers, compressors and turbines.
3.1.2. Discretization Methods in CFD
There are three discretization methods in CFD:
1. Finite difference method (FDM)
2. Finite volume method (FVM)
3. Finite element method (FEM)
220.127.116.11. Finite difference method (FDM): A finite difference method (FDM) discretization is based upon the differential form of the PDE to be solved. Each derivative is replaced with an approximate difference formula (that can generally be derived from a Taylor series expansion). The computational domain is usually divided into hexahedral cells (the grid), and the solution will be obtained at each nodal point. The FDM is easiest to understand when the physical grid is Cartesian, but through the use of curvilinear transforms the method can be extended to domains that are not easily represented by brick-shaped elements. The discretization results in a system of equation of the variable at nodal points, and once a solution is found, then we have a discrete representation of the solution.
18.104.22.168. Finite volume method (FVM): A finite volume method (FVM) discretization is based upon an integral form of the PDE to be solved (e.g. conservation of mass, momentum, or energy). The PDE is written in a form which can be solved for a given finite volume (or cell). The computational domain is discretized into finite volumes and then for every volume the 12 governing equations are solved. The resulting system of equations usually involves fluxes of the conserved variable, and thus the calculation of fluxes is very important in FVM. The basic advantage of this method over FDM is it does not require the use of structured grids, and the effort to convert the given mesh in to structured numerical grid internally is completely avoided. As with FDM, the resulting approximate solution is a discrete, but the variables are typically placed at cell centers rather than at nodal points. This is not always true, as there are also face-centered finite volume methods. In any case, the values of field variables at non-storage locations (e.g. vertices) are obtained using interpolation.
22.214.171.124. Finite element method (FEM): A finite element method (FEM) discretization is based upon a piecewise representation of the solution in terms of specified basis functions. The computational domain is divided up into smaller domains (finite elements) and the solution in each element is constructed from the basis functions. The actual equations that are solved are typically obtained by restating the conservation equation in weak form: the field variables are written in terms of the basis functions, the equation is multiplied by appropriate test functions, and then integrated over an element. Since the FEM solution is in terms of specific basis functions, a great deal more is known about the solution than for either FDM or FVM. This can be a double-edged sword, as the choice of basis functions is very important and boundary conditions may be more difficult to formulate. Again, a system of equations is obtained (usually for nodal values) that must be solved to obtain a solution.
Comparison of the three methods is difficult, primarily due to the many variations of all three methods. FVM and FDM provide discrete solutions, while FEM provides a continuous (up to a point) solution. FVM and FDM are generally considered easier to program than FEM, but opinions vary on this point. FVM are generally expected to provide better conservation properties, but opinions vary on this point also.
3.1.3. How does a CFD code work?
CFD codes are structured around the numerical algorithms that can be tackle fluid problems. In order to provide easy access to their solving power all commercial CFD packages include sophisticated user interfaces input problem parameters and to examine the results. Hence all codes contain three main elements:
This is the first step in building and analyzing a flow model. Preprocessor consist of input of a flow problem by means of an operator -friendly interface and subsequent transformation of this input into form of suitable for the use by the solver. The user activities at the Pre-processing stage involve:
Definition of the geometry of the region: The computational domain.
Grid generation the subdivision of the domain into a number of smaller, non-overlapping sub domains (or control volumes or elements Selection of physical or chemical phenomena that need to be modeled).
Definition of fluid properties
Specification of appropriate boundary conditions at cells, which coincide with or touch the boundary. The solution of a flow problem (velocity, pressure, temperature etc.) is defined at nodes inside each cell. The accuracy of CFD solutions is governed by number of cells in the grid. In general, the larger numbers of cells better the solution accuracy. Both the accuracy of the solution & its cost in terms of necessary computer hardware & calculation time are dependent on the fineness of the grid. Efforts are underway to develop CFD codes with a (self) adaptive meshing capability. Ultimately such programs will automatically refine the grid in areas of rapid variation.
GAMBIT (CFD PREPROCESSOR): GAMBIT is a state-of-the-art preprocessor for engineering analysis. With advanced geometry and meshing tools in a powerful, flexible, tightly-integrated, and easy-to use interface, GAMBIT can dramatically reduce preprocessing times for many applications. Complex models can be built directly within GAMBIT's solid geometry modeler, or imported from any major CAD/CAE system. Using a virtual geometry overlay and advanced cleanup tools, imported geometries are quickly converted into suitable flow domains. A comprehensive set of highly-automated and size function driven meshing tools ensures that the best mesh can be generated, whether structured, multiblock, unstructured, or hybrid.
The CFD solver does the flow calculations and produces the results. FLUENT, FloWizard, FIDAP, CFX and POLYFLOW are some of the types of solvers. FLUENT is used in most industries. FloWizard is the first general-purpose rapid flow modeling tool for design and process engineers built by Fluent. POLYFLOW (and FIDAP) are also used in a wide range of fields, with emphasis on the materials processing industries. FLUENT and CFX two solvers were developed independently by ANSYS and have a number of things in common, but they also have some significant differences. Both are control-volume based for high accuracy and rely heavily on a pressure-based solution technique for broad applicability. They differ mainly in the way they integrate the fluid flow equations and in their equation solution strategies. The CFX solver uses finite elements (cell vertex numeric's), similar to those used in mechanical analysis, to discretize the domain. In contrast, the FLUENT solver uses finite volumes (cell centered numerics). CFX software focuses on one approach to solve the governing equations of motion (coupled algebraic multigrid), while the FLUENT product offers several solution approaches (density-, segregated- and coupled-pressure-based methods)
The FLUENT CFD code has extensive interactivity, so we can make changes to the analysis at any time during the process. This saves time and enables to refine designs more efficiently. Graphical user interface (GUI) is intuitive, which helps to shorten the learning curve and make the modeling process faster. In addition, FLUENT's adaptive and dynamic mesh capability is unique and works with a wide range of physical models. This capability makes it possible and simple to model complex moving objects in relation to flow. This solver provides the broadest range of rigorous physical models that have been validated against industrial scale applications, so we can accurately simulate real-world conditions, including multiphase flows, reacting flows, rotating equipment, moving and deforming objects, turbulence, radiation, acoustics and dynamic meshing. The FLUENT solver has repeatedly proven to be fast and reliable for a wide range of CFD applications. The speed to solution is faster because suite of software enables us to stay within one interface from geometry building through the solution process, to post-processing and final output.
The numerical solution of Navier-Stokes equations in CFD codes usually implies a discretization method: it means that derivatives in partial differential equations are approximated by algebraic expressions which can be alternatively obtained by means of the finite-difference or the finite-element method. Otherwise, in a way that is completely different from the previous one, the discretization equations can be derived from the integral form of the conservation equations: this approach, known as the finite volume method, is implemented in FLUENT (FLUENT v6.3 User's guide, 2006), because of its adaptability to a wide variety of grid structures. The result is a set of algebraic equations through which mass, momentum, and energy transport are predicted at discrete points in the domain. In the freeboard model that is being described, the segregated solver has been chosen so the governing equations are solved sequentially. Because the governing equations are non-linear and coupled, several iterations of the solution loop must be performed before a converged solution is obtained and each of the iteration is carried out as follows:
Fluid properties are updated in relation to the current solution; if the calculation is at the first iteration, the fluid properties are updated consistent with the initialized solution.
The three momentum equations are solved consecutively using the current value for pressure so as to update the velocity field.
Since the velocities obtained in the previous step may not satisfy the continuity equation, one more equation for the pressure correction is derived from the continuity equation and the linearized momentum equations: once solved, it gives the correct pressure so that continuity is satisfied. The pressure-velocity coupling is made by the SIMPLE algorithm, as in FLUENT default options.
Other equations for scalar quantities such as turbulence, chemical species and radiation are solved using the previously updated value of the other variables; when inter-phase coupling is to be considered, the source terms in the appropriate continuous phase equations have to be updated with a discrete phase trajectory calculation.
Finally, the convergence of the equations set is checked and all the procedure is repeated until convergence criteria are met.
The conservation equations are linearized according to the implicit scheme with respect to the dependent variable: the result is a system of linear equations (with one equation for each cell in the domain) that can be solved simultaneously. Briefly, the segregated implicit method calculates every single variable field considering all the cells at the same time. The code stores discrete values of each scalar quantity at the cell centre; the face values must be interpolated from the cell centre values. For all the scalar quantities, the interpolation is carried out by the second order upwind scheme with the purpose of achieving high order accuracy. The only exception is represented by pressure interpolation, for which the standard method has been chosen.
Figure .1.1: Algorithm of numerical approach used by simulation softwares'
Source: Amit Kumar; CFD Modeling of Gas-Liquid-Solid Fluidized Bed; NIT Rourkela; 2009
This is the final step in CFD analysis, and it involves the organization and interpretation of the predicted flow data and the production of CFD images and animations. Fluent's software includes full post processing capabilities. FLUENT exports CFD's data to third-party post-processors and visualization tools such as Ensight, Fieldview and TechPlot as well as to VRML formats. In addition, FLUENT CFD solutions are easily coupled with structural codes such as ABAQUS, MSC and ANSYS, as well as to other engineering process simulation tools. Thus FLUENT is general-purpose computational fluid dynamics (CFD) software ideally suited for incompressible and mildly compressible flows. Utilizing a pressure-based segregated finite-volume method solver, FLUENT contains physical models for a wide range of applications including turbulent flows, heat transfer, reacting flows, chemical mixing, combustion, and multiphase flows. FLUENT provides physical models on unstructured meshes, bringing you the benefits of easier problem setup and greater accuracy using solution-adaptation of the mesh. FLUENT is a computational fluid dynamics (CFD) software package to simulate fluid flow problems. It uses the finite-volume method to solve the governing equations for a fluid. It provides the capability to use different physical models such as incompressible or compressible, inviscid or viscous, laminar or turbulent, etc. Geometry and grid generation is done using GAMBIT which is the preprocessor bundled with FLUENT. Owing to increased popularity of engineering work stations, many of which has outstanding graphics capabilities, the leading CFD are now equipped with versatile data visualization tools. These include
Domain geometry & Grid display.
Line & shaded contour plots.
2D & 3D surface plots.
View manipulation (translation, rotation, scaling etc.)
3.1.4. Advantages of CFD:
Over the past few decades, CFD has been used to improve process design by allowing engineers to simulate the performance of alternative configurations, eliminating guesswork that would normally be used to establish equipment geometry and process conditions. The use of CFD enables engineers to obtain solutions for problems with complex geometry and boundary conditions. A CFD analysis yields values for pressure, fluid velocity, temperature, and species or phase concentration on a computational grid throughout the solution domain.
Advantages of CFD can be summarized as:
It provides the flexibility to change design parameters without the expense of hardware changes. It therefore costs less than laboratory or field experiments, allowing engineers to try more alternative designs than would be feasible otherwise.
It has a faster turnaround time than experiments.
It guides the engineer to the root of problems, and is therefore well suited for trouble-shooting.
It provides comprehensive information about a flow field, especially in regions where measurements are either difficult or impossible to obtain.
CFD solutions are reliable can very much depict the real flow conditions. The numerical methods embedded in FLUENT solver is improving day-by-day. The results too obtained are consistent with experimental results.
CFD allows an engineer to analyze and examine data at numerous locations in the model. In the experimental models data can be extracted at specific locations only.
CFD can simulate a lot of real time flow and heat transfer processes, e.g., hypersonic flow and processes occurring at high temperatures and pressures etc. CFD can be used for simulation of almost all theoretical processes.
3.1.5 Limitations of cfd:
In spite of large advantages of CFD, it has some limitations which are as follows (Bakker, 2002):
Physical models - CFD solutions rely upon physical models of real world processes (e.g. turbulence, compressibility, chemistry, multiphase flow, etc.).The CFD solutions can only be as accurate as the physical models are.
Numerical errors - Solving equations on a computer invariably introduces numerical errors. Round-off error is due to finite word size available on the computer. Round-off errors can be always found in CFD solutions but they may be very small in most cases. Second most common error found in CFD solution is truncation error, due to approximations in numerical models.
Boundary conditions - The cfd solution will only be as good as the initial/boundary conditions provided to the numerical model.
CFD SIMULATION OF packed bed reactor for tar cracking
4.1 computational flow model
All of CFD is based on the fundamental governing equations of fluid dynamics, i.e, the continuity, momentum and energy conservation equations. These are mathematical statements of three fundamental physical principles upon which whole of fluid dynamics is based. They are:
Mass is conserved.
Newton's second law.
Energy is conserved.
A solid body is rather easy to say and define but on the other hand fluid is a squishy substance that is hard to grab hold of. If a sold body is in translational motion, the velocity of each part of the body was assumed to be same but if a fluid was in motion, the velocity may be different at each location in the fluid. It's a question how a moving fluid can be visualized so as to apply in it the fundamental physical principles. For a continuum fluid, one of the four models described below is to be constructed so as to apply it in fundamental physical principles (Anderson. J; 1995):
Model of finite control volume fixed in space.
Model of finite control volume moving with fluid flow.
Model of infinitesimally small fluid elements fixed in space.
Model of infinitesimally small fluid element moving with fluid flow.
Figure .1: Basic governing forms used in CFD from fundamental physical principles.The governing equations can be obtained in various different forms. For most application theory the particular form of the equations makes little difference but however, for a given algorithm in CFD, the use of equations in one form may lead to success, whereas the use of alternate forms may lead to different numerical results as in incorrect or unstable results. Therefore, in the world of CFD, the various forms of equations are of vital role n application. The governing equations which come from finite control volume are in integral form where as those originates from model of an infinitesimally small fluid element are in differential form. Fig shows the generation of basic governing form used in CFD from fundamental physical principles.Capture.PNG
Source: Anderson. J; 1995.
4.1.1 Governing Equations
In the present work model of finite volume fixed in space is considered which is differential and conservation form. In the 2D model a single homogenous phase of catalyst and reacting fluid (gas) mixture was assumed while in the 3D model two phases were assumed solid catalyst particles and reacting fluid (gas phase). In the both the case motion of each phase was governed by respective mass and momentum conservation equations.
Equation 4.: Continuity Equation
Ï is the density of gas.
Îµ is volume fraction of solids.
denotes superficial velocity of the gas.
Equation 4.: Momentum equation
If we assume that the system is at steady state with no appreciable body forces, insignificant viscous dissipation and taking the axial velocity diffusion to be negligible then the momentum equation reduces to the Ergun equation:
Equation 4. : Ergun Equation
P is the pressure.
Î¼ is the effective viscosity.
Equation 4. : Energy Equation
Cp, Cp, s are specific heat capacity of fluid and solids respectively.
k, ks are thermal conductivity of fluid and solids respectively.
q, qs are heat for fluid and solid phases respectively.
4.1.2 Turbulence Modeling
It is a very unfortunate fact that no single turbulence model is universally accepted as being superior for all classes of problems. The choice of turbulent model will depend on considerations such as the physics encompassed in the flow, the established practice for a specific class of problem, the level of accuracy required, the available computational resources, and the amount of time available for simulation. In present simulation (Îº-Îµ) model has been taken for turbulence modeling.
The standard (Îº-Îµ) model is a semi-empirical model based on model transport equations for the turbulent kinetic energy (Îº) and its dissipation rate (Îµ). The model transport equation for turbulent kinetic energy is derived from the exact equation, while the model transport equation for dissipation rate is extracted from Fluent v6.3 User's Guide, 2006. The equations are as follows:
Equation 4.: Model transport equation for turbulence.
Equation 4.: Model transport equation for turbulent energy dissipation.
Source: Anderson.J; 1995
In the equations above (equation 4.5 & 4.6), GÎº represents the generation of turbulent kinetic energy due to mean velocity gradients, Gb is the generation of turbulent kinetic energy due to buoyancy, YM represents the contribution of fluctuation dilatation in compressible turbulence to the overall dissipation rate, C1Îµ , C2Îµ and C3Îµ are constants. ÏƒÎº and ÏƒÎµ are the turbulent Prandtl numbers for turbulent kinetic energy and dissipation rate respectively. SÎº and SÎµ are user defined source terms with CÂµ being constant.
The turbulent viscosity (Âµt), is calculated using Îº and Îµ as follows:
Equation 4.: Turbulent viscosity
Source: Anderson.J; 1995
Where, CÂµ is constant.
To obtain an approximate numerical solution, we have to use a discretization method which approximates the differential equations by a system of algebraic equations, which can then be further solved. The approximations are applied to small domains of space of time so that the numerical solutions provide results at discrete locations in space in time. It concerns to the process of transferring models and equations into the discrete counterparts. This process is usually carried out as a first steps toward making them suitable for numerical evaluation and implementation on digital computers. For a given, differential equation there are many possible ways to derive the discretized equations such as finite difference, finite element and finite volume to achieve a stable numerical result as explained by fig 4.2.
Figure 4.2: Discretization Techniques
Source: Anderson.J, 1995.
Finite volume methods ensure integral conservation of mass and momentum over any group of control volumes. The effectivity of the numerical solution depends on the type and quality of the discretization method used. Each type of method yields quite similar results if the grid used is very fine; however, some problems require some specific set of discretization method (Ferziger, 2002). In the present work discretization based on finite volume method is used.
Fluent uses Finite Volume Analysis (FVM) of discretization to convert governing equation to algebraic equation to solve them numerically in an effective manner. FVM recasts the PDE's (Partial Differential Equations) of the Navier's - Stoke Equation in the conservative form and discretized this equation. The solution domain is divided into finite number of contiguous control volumes (CV), where conservation equations are applied. At the centroid of each CV, there lies a computational node at which the values of the variables are calculated. Interpolation is used to express the variable values at the CV surface in terms of nodal (CV centre) values. Surface and volume integrals are approximated using suitable quadrature formulae. The integration approach yields a method that is inherently conservative (i.e., quantities such as density remain physically meaningful). This is demonstrated by the following equation written in integral form for any arbitrary control volume, V as:
Equation 4.: Integral form of a differential equation for any elemental control volume 'dV'
Q is the vector of conserved variables.
F is the vector of fluxes.
V is the cell volume.
A is the cell surface area.
The FVM approach is the simplest to understand and easy to program, also it can accommodate any kind of grid and as such, it can be used for complex grid analysis too. The grid defines only the control volume boundaries and need not to be related to coordinate systems. There are three levels by which a system can be solved by FV Analysis, i.e. approximation, interpolation and differentiation. So it is the disadvantage of the FVA that systems higher than second (2nd) order cannot be very effectively solved by FV method for 3D systems.
4.1.4 Computation of Energy Flows
In packed bed reactors the energy in the gas feed stream is evenly distributed in the mean flow of the gas and liquid (if any produced) and very tiny solid particles (attrition of solid particles). Also, a part of the input energy is dissipated in the turbulence created in the bed and some is lost due to friction between the gas and solid phases and the walls of the reactor. Apart, from these energy dissipation factors energy is lost to surroundings, collision among gas and solid particles and solid fluctuations. Although model in this study is a single phase system with solid particles as obstacles in fluid flow these modes of energy dissipation cannot be quantified. Hence, these terms are neglected in the energy calculation. In general, the difference in energy between the input and output stream should account for the energy loss due to dissipation in the bed. Thus, energy lost in this system by a very simple rule, i.e.
Figure 4.9: Energy calculation
Source: Anderson.J, 1995.
E1 is entering the packed bed reactor.
Eout is energy in the exit stream from packed bed.
ET is energy gained by the solid particles.
Ee is energy dissipated by gas phase dissipation.
Eblg is energy dissipated due to interaction between gas and solid catalyst particles.