Advanced Thermodynamics and Heat Transfer - Research Paper Example

Running head: Thermo-fluid Assignment Advanced Thermodynamics and Heat Transfer College: Table of Contents 4 0 Introduction 5 Aim 5 2.1 Processing 8 2.2 Post processing 9 2.3 Application in food industry 10 2.4 Biomedical Applications 10 3. Navier-Stokes Equations: 11 3.1 Incompressible Flow 12 3.2 Compressible Flow 12 4. Reynolds-Average Navier –Stokes (RANS) 13 5. Turbulent Flow and Turbulence Modeling 16 6. Turbulent Flow and Turbulence Model 18 7. Computational Fluid Dynamic (CFD) Techniques 19 7.1 Finite Volume Method (FVM) 19 8. Advantages and limitations of Using CFD 20 8.1 Advantages 20 8.2 CFD Limitations 21 9. Simulation 21 9.1. Introduction to ANSYS Fluid Dynamic 22 10. The Experiment 23 10.1 Geometry Modeling 23 10.2. Meshing 24 10.3. Creating of Boundary Conditions: 25 10.4 Problem Solving 26 11. Results 27 11.1 Temperature 27 11.2 Pressure 29 11.3 Velocity 29 11.4 Turbulence Kinetic Energy 30 11.5 Comparison of Temperatures for each Angle at specific Distances 31 32 33 12. Discussion 33 Conclusion 34 Bibliography 35 Abstract The general objective of the study is to demonstrate the understanding of Thermal analysis and Computational Fluid Dynamics Methods, as well as the role played by these techniques in the development of fluids as well as heat transfer systems, the associated benefits of their use and limitations and problems faced when using these methods. After the invention of computers, the CFD methods were developed and the flow problems were solved through several numerical methods. The major objective of simulation method is to understand the flow behavior for a particular set of inlet and outlet conditions of systems. The principles of fluid motion are usually applied in the applied fields of engineering and computer science and this concept is symbolized by the navier Stockes equations. In this case, the complex equations are applied whereby the latest development in technology has been considered as they come. This is clearly evident that it is a big challenge in finding analytical solutions. To resolve these challenges, Computational fluid dynamics (CFD) has been used more often whereby a broad array of flows problems has been solved. Furthermore CFD has been applied onto linear partial equations in the flow process through simultaneous simulation. Complicated problems fluid problems can be solved through CFD in cases such as turbulent flow. There will be a major focus on the Navier Stokes equation and turbulence modeling. In this case ANSYS CFX solver was used in case study 1 to model K-s models under the systems’ steady state conditions. The systems were based on cold and hot pipes that included air-mixing process. 1.0 Introduction Computational fluid dynamics is known to be a fluid mechanics branch which involves the use of computational techniques in solving problems of fluid dynamics. This science field majorly focuses on solving governing fluid equations usually referred to as navier- Stokes equations of which its analytical solutions don’t exist. Currently, CFD has been applied in solving most fluid problems. More so, computational analysis is seen to be part of design process of every space, air or water based equipment. Furthermore this CFD provides the most accurate understandable and reliable solutions to problems related to submarine space shuttle or even blood flow in human body system. The idea behind fluid motion modeling is given by the equations that include Navier-Stokes and continuity equations. The law of motion in this case can as well be applied to liquids, gases and solids. But there is need to consider distortions. The solid particle direction response is seen to be followed by fluid particles in response to forces. The major CFD stimulation stages include the following Approximation of Geometry Formation of numerical grid inside the geometrical model Model selection as well as selection of key model parameters Calculation of variable values Defining the appropriate converged solutions Post processing Verification and validation of solutions Aim The general objective of the study is to demonstrate the understanding of Thermal analysis and Computational Fluid Dynamics Methods, as well as the role played by these techniques in the development of fluids as well as heat transfer systems, the associated benefits of their use and limitations and problems faced when using these methods. Objectives The above aims were achieved through the following processes Establishment of the of the computational fluid dynamics (CFD) application base. The method was then used to highlight the usage and purpose of these techniques in different heat transfer analysis modeling and thermo fluid system design Detailed discussion of the fluid motion Navier –Stoke partial differential equations as well as the way the equations are averaged in time Average NS equations linearization through finite volumes and finite differences Discussion in details the turbulent models applied in closing the resultant system of Reynolds-Averaged Navier Stokes(RANS).In this case, the techniques used to solve such equations in a given computational domain was be considered. Consideration of the designing and modeling of thermo fluids systems in relation to these methods through case study application Discussion of the advantages of thermal analysis and CFD methods application in relation to thermal fluid systems’ design and efficiency Discussion in details he thermal and CFD methods with reference to their limitations as well as drawbacks 2.0 The role of computational fluid dynamics and computational heat transfer methods in modeling and designing of thermo-fluid systems In early 20th century, there was a need of studying airflow in detail after aircraft invention. The development of basic fluid flow solution techniques was in early 1930s.The solutions were only based on analytical solutions that included numbers that comprised of simplifying assumptions that had basic accuracy and application of the systems developed. However, after the invention of computers, the CFD methods were developed and the flow problems were solved through several numerical methods. The major objective of simulation method is to understand the flow behavior for a particular set of inlet and outlet conditions of systems. The boundary conditions were the terms referred to these conditions. The major boundary conditions for both fluid flow and combustion chambers in the pipes include temperature, velocity, pressure and inlets and outflow. It is critical to calculate the main values of the flow for various points in the thermo-fluid systems. The points have been connected through a numerical mesh or grid. There is transformation of differential equations system into algebraic equation systems and this takes process. This equation demonstrates the flow interdependency at these particular points and in solving these problems by the systems the digital computers play a big role. Complicated problems are solved continuously by the CFD techniques in the process of modeling and designing of thermo-fluid systems. In the due course, the speed of the computer is continuously increased as well as the development of fast and valid numerical processes. There is reduction of cost as well as increase in speed through these CFD techniques (Sorensen et al., 2001) Since the late 1960s, a significant growth has emerged in the application and development of CFD to all fluid dynamics aspects (Parviz and John 1997).Consequently, CFD has emerged to be an integral part of the analysis environment and the engineering design for many companies. This is due to the capacity of predicting the performance of new process or design before they are ever implemented or manufactured (Schaldach et al., 2000).Process engineers, researchers and equipment designers are increasingly applying the CFD in the analyzing of the performance and flow of the process equipment like baking ovens (Mills 1999), heat exchanger (Kumar 1995), spay dryers (Kieviet et al., 1997) and other equipment. In development and design, the programs of CFD are currently considered to be standard numerical tools which have the capacity of predicting not only fluid flow behavior but as well the transfer of heat, mechanical movement (like rudders, fans or an impeller turning),mass( like in dissolution or perspiration),phase change(like boiling, melting or freezing), deformation or stress or related solid structures( like mast bending in the wind) and chemical reaction (like combustion or rusting).In addition the application of CFD has been utilized in dealing with problems in architecture and environment. However, the CFD was applied in the food processing area in the recent past(Scott,1994).There has been stimulation of the development of new technologies and food processing practices since the increasing growth of the consumer demand for convenient as well as high quality meals over the past several years. The application of CFD in the food industry could help in better understanding of the most complex physical mechanisms that are related to thermal, rheological and physical food material properties (Quarini 1995). CFD is seen to have grown from a mathematical curiosity to critical tool in about all branches of fluid dynamics. Deep analysis of local effects and mechanics in many equipment is made possible. The CFD results provide an improved performance improved product consistency reliable scaled up confident and improved productivity(Bakker et al.,2001).The designs used CFD in analyzing new systems before making a decision on which and how many validation tests are required to be performed. 2.1 Processing Processing entails using a computer in solving fluid flow mathematical equations. After the completion of meshing, the model input values are required to be specified then the software will be able to solve the equations of state for every cell until the attainment of an acceptable convergence. This process is too intensive and normally it needs the computer to solve thousands of the equations. In every situation, there is integration of the equations and there is application of boundary conditions on it. This is referred to as equation discretization and is used to each individual mesh of cell. There is a repeat of the process in an iterative way until the appropriate accuracy is attained.Such step could be time wasting process despite it is the core of the software package of CFD. Figure1. Commercial air blast chiller meshing structure with a ham inside (Hu and Sun 2001) 2.2 Post processing Post processing tools of powerful CFD software could generate visualization that ranges from simple 2-D graphs to 3-D representations. Graphs generated by post processor could have a section of the mesh that is together with velocity field vector plots or scalar variable contour plots like pressure. Colors are used in such graphs to differentiate between various value sizes. Figure 2 shows velocity vectors in the chiller of figure 1 Figure 2.Flow field in the chiller shown in figure 1 that is predicted by CFD code (Hu and Sun 2000) 2.3 Application in food industry As a research tool for understanding of basic physical nature of fluid dynamics and enhancing the design process, CFD can be of beneficial to the food processing industry in several areas that include sterilization, drying, mixing refrigeration as well as other applications. 2.4 Biomedical Applications The biomedical fields use CFD techniques for blood flow modeling in the heart as well as airflow in an inhaler (Sayma 2009) Figure 3: airflow modeling in an inhaler (Sayma, 2009) 3. Navier-Stokes Equations: The Navier-Stokes Equations are known to describe the fluid behaviors in mathematical way. Useful information could be provided by these Navier-Stokes Equations solutions on distribution of temperature, velocity, turbulence, density as well as other prime parameters related to fluid flow. The idea behind fluid motion modeling is given by these equations that include Navier-Stokes and continuity equations. The law of motion in this case can as well be applied to liquids, gases and solids. But there is need to consider distortions. The solid particle direction response is seen to be followed by fluid particles in response to forces. Forces applied to particles will result to acceleration. Such effects are in line with the second law of motion which states that the momentum rate of a given body is relative to the unbalanced forces that are acting upon it. The forces position is to the force direction of pressure, viscous action gravitational and electromagnetic forces and rotational forces are forces included in this case (Sayma 2009) 3.1 Incompressible Flow In cases where the temperature is constant, the below equations can be used. In this case, there is no inclusion of the body forces (Sayma 2009) Variation of temperature can be determined after solving of the energy equation for incompressible flows with existing variation in temperature. 3.2 Compressible Flow For the flow that is compressible, the equations below are termed to be key and can be used (Sayma 2009) The continuity equation: Navier-stoke equation: Energy equation In the equation above can be determined as below, In the equation above, the variables u, v and w are the velocity components used in the direction x, y and z direction. On the other hand represents temperature, cp represents specific heat at a constant pressure, p represents pressure, µ represents viscosity, and Þ represents density. Continuity equation indicates the conserved flow of the system .The sum of masses that flows in and out per time are equal to the change in mass based on the density change per unit time. All fluid types can apply the equation of continuity like non-Newtonian and Newtonian fluids, compressible and incompressible fluids (Sayma 2009) 4. Reynolds-Average Navier –Stokes (RANS) The equations of Reynolds-Average Navier –Stokes (RANS) are known to be the most complex form of N-S equations which includes the turbulence effects into consideration. Therefore, these equations are applied in solving turbulent flows. In such equations, the fluctuating parameter of flow (pressure, temperature, velocity etc) is considered to be time averaged as well as is included in the equations. The models of turbulence that are based on RANS equations are referred to as statistical turbulence models because of the statistical averaging procedure used in obtaining the equations. The aim of turbulence models is to solve a new set of transport through the introduction of a time averaged equation. For instance(x, y, z, t) is taken to be the function of time and spatial motion. The u value does fluctuate about the mean value of u when a fixed location turbulent flow field is taken and it is defined by time –averaging operation. The time averaged value Ū is not dependent to time in case the period p of time –averaging operation is more the period of the slowest fluctuation seen on the variable U that is actual variable. This time –averaging procedure end results is the actual flow decomposition into a mean value plus the correction that is time dependent labeled u. The same rule of decomposition is applicable to the flow field remaining variables. Equations (1.9) and 1.10) could be substituted into the governing equations later the time-averaged operation (1.9) could be applicable to every resulting equations terms. Such do follow specific algebraic rules Therefore it is not that complicated to show that in the end that there is a reduction in the governing equation to the following: 5. Turbulent Flow and Turbulence Modeling The ratio that exists between the viscous and inertia force is denoted by states Osborne Reynolds (the Reynolds number).Below shows how Reynolds’s number is calculated. The following is the Reynolds-Average Navier –Stokes (RANS) equation derivation for a two dimensional steady state incompressible flow The pipe’s diameter is denoted by U and D as well as the average velocity. The flow is considered to be turbulence in cases where Re is at least 2400.The instantaneous and average velocity in the turbulence flow are indicated in the figure 4 Figure 4: instantaneous and average velocity in turbulent flows (Sayma 2009) Below includes the calculations for time average velocity for the given time t These equations could be applied to other flow variables like the below equation which could be applied to other flow variables. Different numerical modeling and engineering applications could apply this averaging process. Coarser grids and large time steps are needed for average quantities. Such could simplify further the CFD computations (Sayma 2009) Below are Reynolds’s average Navier Stokes equations for a 2 dimensional steady incompressible flow. The corresponding Reynolds-average equations is as shown below 6. Turbulent Flow and Turbulence Model There are several models proposed to be used for RANS solutions. Commonly, these models are referred to as turbulence models. The development of each model is always for a given set of conditions and a relevant area of interest. Some common models available are listed as follows: Eddy viscosity assumption One equation model Zero equation models Two equation models Large eddy simulation Reynolds stress model Two equation model This model is one of the commonly applied models in CFD. It a two equation model type and it two transported variables are employed (omega and K) and this represents the turbulent flow. K represents the kinetic energy whereby it represents the energy in turbulence. The computation of turbulent eddy viscosity is from: The phenomenon of Turbulence transport is a name related to processes that involves transfer of momentum, heat and mass. Several fluid flows exhibited in the engineering field are turbulent and hence need different treatment. Various mathematical methods do exist that result to turbulence flows solutions. All these methods need solutions related to conservation differential equations of momentum, mass, chemical species or energy. The approach of engineering to the fluid flow solution properties depends on the techniques of differential equations by algebraic equations system that may be solved numerically. 7. Computational Fluid Dynamic (CFD) Techniques Various CFD techniques do exist and include the finite element technique and finite volume technique. The most commonly used technique is as follows (Bakkar 2006) Finite difference technique Velocity based technique Boundary element technique Spectral techniques Lattice Boltzmann/Lattice gas 7.1 Finite Volume Method (FVM) This method was first applied by Evans and Harlow (1957).The variables of mass, energy and momentum applied in this method made it interesting. This method helps in problem solving like as turbulence flow source term dominated flows like combustion and higher speed flow. In case there is use of simple numeric .This methods will result to false diffusion that is considered to be an advantage for this method(Bakker 2006).The following equations are used in this method and they have been generated through Gauss Theory and original shape integration of Navier-Stokes equation over control volume(Zou 2005) Momentum and mass of control volume P is calculated through the application of the following equations The pressure force if determined through the following equation 8. Advantages and limitations of Using CFD 8.1 Advantages CFD is seen to have grown from a mathematical curiosity to critical tool in about all branches of fluid dynamics. Deep analysis of local effects and mechanics in equipment is made possible. The CFD results provide an improved performance improved product consistency reliable scaled up confident and improved productivity(Bakker et al.,2001).The designs used CFD in analyzing new systems before making a decision on which and how many validation tests are required to be performed. The CFD advantages can be classified as (Wanot, 1996) There is a detailed understanding of flow distribution, heat and mass transfer, weight losses, separation of particulates etc. As a result all these will provide plant manager a deeper as well as detailed understanding on what is taking place in a given process or system Geometric changes evaluation is made possible with much less cost and time that it would be in laboratory settings It could answer many questions of what if in a very short time Scale up problems can be reduced so easily due to the models are based on fundamental physics as well as are considered to be scale independent. It is mostly relevant in simulating conditions whereby taking detailed measurements is not possible. For instance, dangerous environment or high temperatures in an oven The modeling and design process of thermo-fluid systems could be speeded up by the computer based CFD techniques. The CFD techniques could be applied in developing high performance and reliable designs. 8.2 CFD Limitations The process of Real world Physical models determines the CFD solutions. For example, turbulence, multi phase chemistry and compressibility. Accurate results are only based on physical based models Numerous models with initial boundary conditions provide accuracy to CFD solutions 9. Simulation The major objective of simulation method was to understand the flow behavior for the given set of inlet and outlet conditions of system. The boundary conditions were the terms referred to these conditions. The major boundary conditions for both fluid flow and combustion chambers in the pipes include temperature, velocity, pressure and inlets and outflow. It was critical to calculate the main values of the flow for various points in the thermo-fluid systems. The points were connected through a numerical mesh or grid. 9.1. Introduction to ANSYS Fluid Dynamic Modeling of any physical phenomenon particularly fluid flow can be through ANSYS fluid dynamics. This is a complete product that is suited to its requirements. This software is able to provide unparalleled fluid flow analysis skills. Tools required in optimization and designing of new fluid equipment is provided by the software. Furthermore the software is able to provide trouble shooting for the installation available. There is also computational fluid dynamics software as well as specialized products which are included in the ANSYS fluid dynamics. This ANSYS CFX is the most commonly used analysis tool and it is usually available in ANSYS CFD bundle. It is possible to calculate in depth the flow fields using this application by computational fluid dynamics (CFD).Accessing of the provided ANSYS CFX can be through CFD. Problems of fluid flow can be solved easily by these products of fluid simulation. This product was used to simulate the case study provided. In this case, for basic mixing pipe ANSYS CFX can be used for the flow. 10. The Experiment The experiment involved steps which were taken to solve the problem and they have been described as below: 10.1 Geometry Modeling ANSYS Workbench was employed to design the shape geometry) of the pipe as well as finding the design dimension. The geometry had two pipes of which the dimensions are as below: Joining angle of 2 pipes: 28o Large pipe Length: 500mm Large pipe diameter: 100mm Small pipe length: 50mm Small pipe Diameter: 20mm Point of mixing: 100mm Figure 5 shows mixing pipe Geometry Figure 6.Final Design 10.2. Meshing Meshing is a very crucial step to engineers because the results are highly accurate and the process entails a long simulation time even in cases where a small unit of mesh is requested. For bigger mesh on the other hand, the process takes a short time but the accuracy is lower than that of the small unit. The results were saved as CFX after simulation. Fluid dynamics simulation needs meshes that are of high quality. Figure 7 below shows the shape after the process of meshing Figure 7.Meshed Geometry 10.3. Creating of Boundary Conditions: After the completion of meshing, the model input values were required to be specified then the software was able to solve the equations of state for every cell until the attainment of an acceptable convergence. This process is too intensive and normally it needs the computer to solve thousands of the equations. In every situation, there is integration of the equations and there is application of boundary conditions on it. ANSYS CFX software was used to generate the parameters of the boundary conditions. The conditions of the boundary were set after the mesh was created through CFX12 PRE. The cold and hot air were defined in the geometry. The hot air temperature had to be shifted to 150 degrees while cold air temperature was shifted to 25 degrees. The outflow temperature was indicated after solving the system. The generated geometry after shifting the conditions of the boundary was presented in the figure below Figure 8 Setting up the Boundary Conditions 10.4 Problem Solving After coming up with the final geometry as well as setting up the required boundary conditions, the solution to the problem was run in ANSYS CFX solver. The steady state calculations determined the ANSYS CFX12 solver basing on the k-s model. This model is one of the commonly applied models in CFD. It a two equation model type and it two transported variables are employed (omega and K) and this represents the turbulent flow. K represents the kinetic energy whereby it represents the energy in turbulence. The results were then posted with the use of ANSYS CFX12 postprocessor. Contours for pressure velocity and temperature were used to get the results. The simulation results in form of images are indicated as below: 11. Results 11.1 Temperature The figure 9, 10 and 11 below indicate the division of the tube into 3 parts basing on the temperature behavior. The thermal stratifications have been indicated and different colors were applied in the figure to express contours of temperature distribution across the mixing pipe. According to the figure, the lowest temperature region is shown by dark blue color (2.831e+002) while the highest temperature region is indicated by the red color (3.731e+002).The beginning region; the temperature is at a steady state of 150 degrees centigrade. At the convergence region of hot air (150oC) with cold air (25oC), the temperature is seen to be unstable due to the difference speed and temperature of the air entering the tubes. At the post –convergence of hot air with cold air region, it is seen that there is an attempt of mixing of air in order to attain equilibrium again. This observed behavior is similar to all the three pipes with angles of 0,-15 and +15 Figure 9.Behaviour of Temperature at an angle of zero Figure10. Behavior of Temperature at an angle of -15 Figure11. Behavior of Temperature at an angle of +15 11.2 Pressure Basing on the figure 12, it is seen that pressure was constant up to convergence zone. At this point the difference in temperature and speed resulted to a substantial pressure difference. This pressure difference is observed to have decreased gradually again at the moment the air moved away from the air mixing area. The pressure is seen to be stable at the hot air opening and there were pressure variations observed at the cold air opening with values ranging from 1.000e +000 Pa to 3.550e+001Pa .On the other hand, the maximum pressure value reached inside the pipe was 7.000e+001 Pa. Figure 12.Behaviour of Pressure 11.3 Velocity Basing on the velocity contours (capture vector at 0 angle) as presented in figure 13 below, there was constant speed between the area at the beginning of the tube and at the intermixing of cold and warm air area. Since there was a difference in air speed, the distribution in velocity was exhibited at the region where both air flows mixed. The speed started to converge at the post mixing region as well as there was an attempt by the air to regain constant speed. The velocity was constant at cold air opening with value 2.732e+001m/s. The maximum velocity attained inside the pipe was 1.366e+001 Figure13. Behavior of Velocity at an angle of 0 11.4 Turbulence Kinetic Energy Turbulence Kinetic Energy is considered to be a critical characteristic of fluid turbulence flow that needs to be evaluated critically. The kinetic per unit mass as shown in figure 14 below is a value linked with eddies in the turbulent flow. The TKE has values that vary at the cold air spot. Inside the mixing pipe on the other hand, the TKE is seen not to be constant with values ranging from 0.000 to 5.000. The kinetic energy per unit mass which is minimum value is seen to be approximately 0.000, and it is located to the interior region. The maximum value for kinetic energy per unit mass is seen to be approximately 5.000. Various mathematical methods do exist that result to turbulence flows solutions. All these methods need solutions related to conservation differential equations of momentum, mass, chemical species or energy. The approach of engineering to the fluid flow solution properties depends on the techniques of differential equations by algebraic equations system that may be solved numerically Figure 14.Turbulence Kinetic Energy 11.5 Comparison of Temperatures for each Angle at specific Distances The temperature behavior for each angle at specific distances that include 200mm, 400mm and 600mm was compared. The temperature behavior tends to be similar but it is seen to differ at the joining angle between the main pipe with hot air and the small pipe with cold air. This is observed at 200m and possibly it’s where the cold air converges with hot air. This observation is similar to all the temperature behaviors with the three angles that include 0,+15 and -15 as shown in the figures 15,16 and 17 below. Figure 15. Temperature behavior plotted against different distances at angle +15 Figure16. Temperature behavior plotted against different distances at angle 0 Figure17. Temperature behavior plotted against different distances at angle -15 12. Discussion The general objective of the study was to demonstrate the understanding of Thermal analysis and Computational Fluid Dynamics Methods, as well as the role played by these techniques in the development of fluids as well as heat transfer systems, the associated benefits of their use and limitations and problems faced when using these methods. Basing on solving problems of pipe flow as well as having detailed analysis and interpretation of the results, it can be concluded that the objective of the study was met. It can be noted that the output values could be calculated from the input values whereby these input values require appropriate selection to enable the output results to be closer to the actual values. In this case, the simulation software used is very useful in calculating the final output values as well as in designing of prototypes. There was a major focus on the Navier Stokes equation and turbulence modeling. In this case ANSYS CFX solver was used in the case study 1 to model K-s models under the systems’ steady state conditions. The systems were based on cold and hot pipes that included air-mixing process. The steady state calculations determined the ANSYS CFX12 solver basing on the k-s model. The results were then posted with the use of ANSYS CFX12 postprocessor. Contours for pressure velocity and temperature were used to get the results. One of the objectives of the experiment was to establish the computational fluid dynamics (CFD) application base. The method was then used to highlight the usage and purpose of these techniques in different heat transfer analysis modeling and thermo fluid system design. Conclusion In conclusion, Computational fluid dynamics is known to be a fluid mechanics branch which involves the use of computational techniques in solving problems of fluid dynamics. This science field majorly focuses on solving governing fluid equations usually referred to as navier- Stokes equations of which its analytical solutions don’t exist. In the experiment, it was evident that, CFD can be applied in solving most fluid problems. More so, computational analysis is seen to be part of design process of every space, air or water based equipment. 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