Development of evaporation models for CFD

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Abstract, The objective of this thesis was to develop a method to reliably model the complete process of drying of. materials with fluid dynamics software CFD The main applications for this are evaporation from. porous bodies in industry processes The modeling included the separate behaviors of the drying periods. and was a time dependant process A number of assumptions were made which allowed the. formulation of a model to be implemented using user defined functions in Fluent The main limitations. included in these assumptions were treatment of a porous rigid body and stationary liquid water Two. different approaches were tried trying to model the constant and the falling rate periods respectively . In the end the model for the falling rate period was useable for both types of behavior and proved to. give reliable results corresponding closely to experimental data There are possibilities for modifying the. final model for application in a wider range of situations . Keywords CFD evaporation UDF drying water modeling. Thanks to , Prof Bengt Andersson for continuous assistance involvement and support during the project . Ph D student Andreas Lundstr m for support help with the UDFs and the chance to test the model against an. advanced case , Everyone else at Chemical Engineering Department Chalmers for the welcoming and helpful atmosphere . The Coffee Machine for being there when I need you . 2, Table of Contents,ABSTRACT 2,TABLE OF CONTENTS 3. 1 INTRODUCTION 5,2 PROBLEM DESCRIPTION 7,3 THEORY 8.
3 1 TERMINOLOGY 8, 3 1 1 Equilibrium Moisture 8, 3 1 2 Bound Unbound Moisture 9. 3 1 3 Types of Materials 9, 3 2 PERIODS OF DRYING 9. 3 3 KINETICS 11, 3 3 1 Surface evaporation 11, 3 3 2 Body evaporation 13. 3 4 CFD THEORY 15, 3 4 1 Fundamental Equations 15. 3 4 2 Turbulence Models 15,4 METHOD 17, 4 1 TEST CASE 17.
4 1 1 Geometry 17, 4 1 2 General Boundary Conditions 18. 4 1 3 Setup 18, 4 2 SOFTWARE USED 18,5 CONSTANT RATE MODEL 19. 5 0 1 Applications 19, 5 1 MODEL DEVELOPMENT 19, 5 1 1 Assumptions 19. 5 1 2 Expressions 19, 5 1 3 Limitations Problems 20. 5 2 MODELING 21, 5 2 1 Validation Results 22, 5 3 APPLICATION FRUIT DRYER 24.
5 3 1 Presentation 24, 5 3 2 Modelling 24, 5 3 3 Results 25. 3, 6 FALLING RATE MODEL 26, 6 0 1 Applications 26. 6 1 MODEL DEVELOPMENT 26, 6 1 1 Assumptions 26, 6 1 2 Expressions 27. 6 1 3 Limitations Problems 28, 6 1 4 Geometry and Boundary Conditions 28. 6 2 MODELING 28, 6 2 1 Case Results 29, 6 3 APPLICATION DRYING OF CATALYST 32.
6 3 1 Presentation 32, 6 3 2 Modeling 33, 6 3 3 Results 35. 6 DISCUSSION CONCLUSIONS 37,REFERENCES 38,APPENDIX 39. A 1 RELATIONS 39, A 2 UDF FILES 40, A 2 1 Presentation of UDF Constant Rate 40. A 2 2 Presentation of UDF Falling Rate 41, A 3 PRETTY PICTURES 42. A 3 1 Test Case Constant Rate 42, A 3 2 Dryer Plate Case 43.
A 3 3 Dryer Baffled Case 44, A 3 4 Falling Rate Test Case Startup 45. A 3 6 Catalyst 100s 46, A 3 6 Catalyst 350s 47, A 3 7 Catalyst 425s 48. 4, 1 Introduction, Traditionally calculations on industrial equipment in chemical engineering are performed with. simplified models of the specific process It has been difficult to examine in detail the conditions in. specific parts of the equipment and engineers have had to rely on their skills and intuition coupled with. experiments to analyze and design plant processes The methods developed have been largely. successful in the creation of equipment and production trains and remain today absolutely necessary for. the design of any industrial equipment , The exponential increase in computational power the last few decades has lifted a number of new. methods to the surface Old and tested methods can be combined to create dynamic simulations of. whole process plants for example Another new method is the use of CFD computational fluid. dynamics to directly simulate flows and processes CFD approximates a domain with a finite number of. cell elements and allows an engineer to visualize the problem in detail by directly solving the equations. for flow and transport in these cells Due to the increased availability of cheap computational power . CFD is moving from its previous place as a tool for research into the area of complex problems and. equipment design in the industry Development of CFD software has resulted in several products . among them FLUENT and CFX 4 , While the software enables an engineer to solve flows and reactions for a design it is required of him or.
her to provide the correct models and data CFD has largely been used to model different types of gas. flows for the design of airplanes and cars Therefore the largest part of its development has been in the. areas of laminar and turbulent flows and the development of methods to accurately simulate and. model these flows As a design tool for chemical equipment it has not seen as much development and is. still adapting For the design of any chemical process with CFD reliable models are needed to model the. chemical reactions and interactions , The possibilities when using CFD to design industrial equipment are many and the utility of including. CFD in the development process gives rise to more specific design opportunities as well as provides new. methods of validation A simulation may include chemical reactions and transfer of heat and mass along. with the flow simulation This lets the designer check for things such as optimal injection points flow. patterns for maximum heat transfer and validation of previous simplifications and assumptions in the. models used , One of the areas where CFD will prove useful is in the simulation of evaporation of water or drying As. one of the most common separation processes it is present in the food industry textile industry paper. industry and many others The process is well known and the study of drying has provided a large. number of models and designs for comparison of results However the implementation of CFD in. evaporation problems is still rather limited 8 Development of standard methods to solve the problems. of evaporation is therefore needed this will be the focus of this thesis . 5, The types of problems that arise when dealing with evaporation are in many cases quite complex It is. often possible to simplify the problems a great deal if one is interested in the overall process such as. the effectiveness of a dryer However if the goal is to study the drying of an isolated body and see the. differences and effects on the drying process in different areas of the problem will be increasingly. complex It will most likely require a number of simplifying assumptions especially since all detail cannot. be resolved due to the differing length scales of the process . The evaporation process is interesting in many different situations and the type of information needed. may require different approaches to it Depending on the limiting step in the process different ways to. model it may be appropriate In some cases the evaporation from a surface is the interesting step in a. process such as the estimation of the efficiency of different dryer geometries In others the level of. water in different regions of a porous body will be important such as when checking that the material in. the dryer is dried evenly in all regions This is important for clay burning and fruit drying processes . among others 10 11 , By using numerical simulation it will be possible to further optimize previous designs of equipment and. provide more effective equipment to the industry As an example of how this can be done this thesis will. detail different types of processes and how one might simulate them with CFD The lessons learned. from this will hopefully provide ideas for the development of similar methods for other applications . 6, 2 Problem Description, When treating drying with numerical simulation a number of different issues arise As will be described.
in the theory section below the process of drying consist of several stages interaction between different. phases and a large spectrum of time scales , The time scale problem is probably the most complex one to solve A drying process can stretch over. several hours for drying of dense and wet materials However the reactions take place very quickly the. two mechanisms of evaporation and condensation are extremely fast and most of the time only the. difference between them can be observed and is often termed the drying rate When performing. numerical simulation this becomes a problem since not only space but time is discretized and the time. step chosen needs to be sufficiently small so that everything is resolved correctly A too large time step. will result in calculation error and in this case a large overestimation of the reaction rate with a. divergent solution as result Since choosing a very small time step will result in vastly increased. computational times the modeling of a whole drying process will be an extremely arduous process if at. all possible , The phase interaction between liquid water and water vapor between water contained within the. material and water on the surface would require a lot of factors to be taken into account if they need to. be resolved in detail There are CFD models for multiphase flows that keep track on liquid gas surfaces. and are able to model the interaction between them they are however not suited for this type of. situation and are not suited to describe liquid contained within a solid object It could be possible but. could again require too much computational effort to be of any real use for real applications . The third problem of stages of drying arises when treating the whole drying process In reality drying of. an object is divided into several periods with very different behavior which means that a model or. method must be able to describe all of these behaviors and can as a result not be too simplified It could. be possible to divide the method into several models one for each period but this would not be the. preferred solution , 7, 3 Theory, If studied in detail evaporation is a complex process with a large number of factors A simple case is. evaporation from a water body in motionless air It can be convenient to regard some processes to be. similar to this case and the study of it can be of help when developing models for more complex cases . For industrial purposes the processes involved are often much more complex such as the drying of food. products This situation can have internal and external diffusion a gradually changing shape of the body. and constants that change with temperature and water content To produce a model for cases like this . it is important to describe in detail how the process takes place . 3 1 Terminology, For the treatment of evaporation problems a number of useful variables can be defined These terms. will be used throughout the report and will be presented thoroughly here 1 3 2 . When dealing with the drying of bodies it is common to define the terms moisture content and. humidity Moisture content X is the mass fraction of water Mw to solid Ms in a solid body or object . It is used to track the level of moisture in the area of interest and has a fixed point of reference Related. to X is W the moisture fraction It is the fraction of moisture mass to total mass of the object W is. useful because it only ranges between 0 and 1 whereas X can range to infinity For a gas we can define. the humidity Y This is the fraction of water vapor mass Mv to mass of the dry vapor free gas Mg . 3 1 3 2 3 3 3 4 , Further it is convenient to define expressions for the level of moisture in air relative to its maximum.
possible value Water vapor has a maximum partial pressure in air of a given temperature and pressure . for which the gas is said to be saturated with moisture This pressure is defined as PO We can define a. relative humidity which is the ratio of the current water vapor pressure Pv to its maximum value . This is a useful measure of the evaporation potential of the air . 3 5 ,3 1 1 Equilibrium Moisture, When a wetted object is in equilibrium with the surrounding air at constant T P and humidity the. moisture left in the object is said to be the equilibrium moisture content When using the dry basis. moisture content X one might define the equilibrium moisture as X The difference between the. current moisture content and X is called the free moisture Xf This is the amount of moisture that can be. released before the system reaches its equilibrium and is an important term since it can be seen as a. driving force for the evaporation 1 , 3 6 3 7 1 , According to Keey 1 the dependence on the equilibrium moisture content with temperature can be. correlated by the above expression is said to vary between 0 005 and 0 01 1 K . 8, 3 1 2 Bound Unbound Moisture, When contained inside a porous material a liquid can be said to be unbound or bound The unbound. liquid behaves like free water and is not adsorbed in any way to the material The bound moisture is. characterized by an adsorption heat and a lower enthalpy state The adsorbed water will require. additional heat to be able to be evaporated This heat of wetting may be approximated according to. Smith and van Ness 3 by assuming that the vapor phase behaves as an ideal gas and that the volume of. The main applications for this are evaporation from porous bodies in industry processes The modeling included the separate behaviors of the drying periods and was a time dependant process A number of assumptions were made which allowed the formulation of a model to be implemented using user defined functions in Fluent The main limitations

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