Heat, Fluids, and Aerodynamics - Case Study Example

Optimum Thickness of Insulation Insulation thickness Good thermal insulation in the buiding results in the efficient use heating energy in the buiding. When deciding on thermal insulation, considerations are made on estimation of long term economic viability and technical solutions. This is based on physical parameters of thermal comfort in the room and the economic calculations. Optimum insulation thickness is based on climate condition, heat loads and the location of the building. This include internal heat loads, average day and night temperatures based on 24 hr/365 day period at a given location and providing protection against solar radiation in summer and heat loss in winter. For the room to be thermally insulated, the external walls should attain the overall heat transfer coefficient less than 0.4 W/m2K. Considering the thermal insulation material like glass wool, the building should conform to a certain standards regarding the costs of energy and the use. Economic thickness of thermal insulation Insulation reduces the heat loss on cold and hot surface and thus saving the energy considerably. Therefore considerations are made on the suitable choice, its maintenance over the insulation lifetime and application to the surface. A balance has to be made between the capital cost of thermal material used in the building and the potential reduction in fuel costs resulting in the lowest total cost of the two cash flows. This is obtained through economic approach. If the thickness of the insulation is increased, the heat loss is reduced and therefore reduces the operation costs. On the other hand, the cost of insulation increases with thickness. For example, if we consider the insulation applied on the hot surface, as the thickness of the insulation increases, the amount of heat loss from the surface reduces. In other words, as the cost of energy lost reduces, the cost of labour and material continue increasing. The two opposing factors which should thus be considered when determining the combined cost are decrease the cost of energy due to loss and reduce the expenditure for labour and the material towards the insulation. Optimum thickness is the thickness of the insulation is the thickness for which the combined cost of insulation (labour and material) and the cost of energy lost through insulation is a minimum as shown below. (Thirumaleshwar, 2006). The cost is usually recovered through fuel cost savings in the two or three years of use, but longer periods are needed for major structural items like double glazing and cavity fill, which will provide additional benefits like better thermal storage capacity, less external noise transmission and draughts and add value to the property (Chadderton, 2013). The cost of heat loss per square metre through the structure is: The fuel usage cost for a range of thermal transmittances U can be obtained for a given structure, which is usually a decreasing curve for increase in the insulation thickness as the additional layer reduces thermal transmittances. For known cost £/m3 of the insulation material, the cost of thickness per square meter of surface area can be found by: (Chadderton, 2013) The data obtained from these equations can be used to draw a graph. A total cost curve is obtained by adding the two curves and the lowest point on the curve gives the optimum insulation thickness. A flat lower part means that any number of commercially available thicknesses is economical (Chadderton, 2013). Case study A new single roomed building is to be built at MMU for contractors to use as a rest room during the period of new building work. The building is to measure 10.0m x 10.0m x 2.5m and it is vital that for the comfort of the contractors the room is maintained throughout the day at a temperature of between 18-23°C. Each wall is to be constructed from 2 layers of common brick, an internal particle board and a layer of insulation. The building is to be heated using standard space heaters that will run on natural gas. The gas currently costs 5p/kWh and is burnt at an efficiency of 70%. During heating calculations it is assumed that the same thickness of insulation is applied to floor, wall and roof and that mineral wool at a current price of £50/m3 is utilised. The building has been designed to have a lifetime of 2 years before it will be demolished at the end of the building period. R = Thickness (m) 0.025 0.050 0.075 0.100 0.125 0.150 U W/m2K Insulation cost (£) Energy cost (£) Total cost (£) 0.625 1.25 1.875 2.5 3.125 3.75 Assumptions regarding building insulation: The heat loss calculations are based on U values for walls, floor and roof. The load factor is 0.608 The temperature of the outside is 40C. The annual heating is 365 days. The amount of materials which will go to waste is negligible. Technical insulation is segmented into three temperature intervals when used in technical installations. When making heat loss calculations, an average temperature in each interval rather than a maximum temperature is used Model Inputs The figure below shows a simple design flow chart which illustrates some of the inputs, processes and outputs. Geometry This refers to the things that affect the flow of air in the room, which include: the floor, in and out of the wall, equipment, roof, windows and the door. Computational fluid dynamics (CFD) Computational fluid mechanics deals with the study of fluid mechanics using computational method. It is used to predict heat transfer, fluid flow, chemical reaction, mass transfer and related occurrences using mathematical equations in a computer. CFD packages are built on differential equations for compressible flow of fluid based on conservation of physical system. These include: Conservation of mass (Law of continuity) Conservation of momentum (Newton’s second law) Conservation of energy (1st law of thermodynamics) The three variables that can be obtained from the above equations are absolute temperature, T, thermodynamic pressure, p, and the velocity, V. The absolute pressure and thermodynamics pressure are independent thermodynamics variables. Other thermodynamic variables contained in the conservation equations are: the enthalpy h, density ρ, and the transport properties conduction k and viscosity h. To fully specify a given problem, different conditions for T, p and V has to be known at every boundary point. I Conservation of momentum – Navier–Stroke equations Navier –Strokes equations shows the proportion between the force applied and the acceleration of a particle, and it is normally called Newton’s second law of motion. The equations are expressed as follows: Where µ = Viscosity because of linear deformation (kg/m.s) λ =Viscosity due to volumetric deformation (kg/m.s) SM = Body force in x, y and z directions II Conservation of energy (1st law of thermodynamics) The energy takes the form of Where Φ = deformation heating k = conduction of continuum (W/mK) h = enthalpy (kJ/kg) P = Pressure (Pascal) Solving methods Complex fluid flow problem are solved using differential equations through numerical method. It contain a set of numbers that can be used to construct the distribution of the dependent variables, which is unlike analytical solution that describes the continuous values within the domain resulting in the infinite number of dependent variables. The governing partial differential equations are replaced with algebraic equations, which can be solved by replacing continuous information in the differential equation with dependent variables (discrete values) at a given number of points in the spatial domain. The descritisation can be do using finite element, spectral and finite difference methods. Finite volume method which falls under finite difference has commonly been used in most well established CFD codes like ANSYS CFX, STAR _CD and ANSYS FLUENT. The numerical algorithm has of the following: Integrating fluids flow governing equations over a finite volume in the domain. Converting the integral equations into algebraic equations. Solving the algebraic equations using iterative method. ANSYS CFX ANSYS CFX uses a sophisticated solver for the Navier-Stokes equations with pre- and post-processing capabilities. Computational domain Computational domain is a portion of the facility that is input into the model which provides spatial information about the fluid motion. It is a large number of small control volumes in a space domain. A room is divided into many cells as shown below, and the model calculates the temperature, densities and species for each cell. Keeping into account the conservation of energy, chemical process, energy, momentum and mass flow for the control volumes in the domain is recorded. This can be done as time dependent or a steady state computation. The model has ability to perform complicated geometric simulation using complex boundary conditions like thermal loads equipments and ventilation. The Navier-Stokes equations involve dividing the spatial domain into finite control volumes using a mesh, before integrating the governing equation over each control volume, so that quantities such as momentum, mass or energy is conserved in each control volume. Governing equations ANSYS CFX uses the unsteady Navier-Stokes equations set of equations together with fluid equation of state. Velocity components, temperature, pressure and other quantities of the fluid are solved using scalar transport equations. Solution strategy The Navier-Stokes equations are solved by discretizing the spatial domain using a mesh into finite control volumes. The equations are then integrated over each control volume, such that energy, momentum, mass, etc. is conserved, before solving the equations using a coupled solver. The time step behaves like acceleration parameter in guiding the approximate solutions in a physically based manner to a steady-state solution, which reduces the number of iterations needed to calculate the solution for each time step or for convergence to a steady state in analysis. Pre-processing The main work here includes interactive process geometry and mesh, for input in the next step. The main step involve defining the geometry of the required space, creating region with fluid flow, surface boundary names and solid regions, and therefore setting the properties of mesh and definition of physics model and create input needed by the solver. The mesh is load into physics pre-processor. Software modules of ANSYS CFX Solving CFD problems are solved as follows: Integrating the partial differential equations over the control volume over the spatial domain. This is the same application of conservation laws such as mass and momentum to each control volume. The integral equation is converted to algebraic equation system from approximation sets are generated for the terms in the integral equations. The algebraic equations are solved in iterative way, since the solution converge. An error is reported in the process. The accuracy of the solution depends on the shape and size of the control volume. Boundary conditions, Relevant boundary conditions are set by setting the type of conditions existing at the faces of relevant control volumes, and they are classified into two major classes, which include thermal and fluid boundaries. The names imply that the boundary types specify the environmental conditions like heat transfer but the boundary types also include the boundary between the computational domain and the infinity. Boundary conditions define the inputs of the simulation model and therefore provide a connection between the simulation model and its surroundings. Boundary condition can be steady state which persist throughout the simulation or transient which varies with time. This will result in a better prediction of temperature, chemical concentration and density. Boundary condition include heat flux which defines the interchange of energy by the model with the surrounding environment, surface temperature defined for all zones including windows, and zone boundary conditions like supply diffusers. Volume mesh Volume mesh is the mathematical description of a geometry or space that is being solved in simulation. Simulation is done by solving fluid flow equations using computational techniques in a grid that has been generated in a domain. Types of volume mesh models in star CCM Tetrahedral meshing model The tetrahedral meshes present simple and efficient solution for complex mesh problems. It is fast and use small size of memory for a specific number of cells. Polyhedral meshing model It provides a balanced solution for a mesh generation problems. They are efficient and easy to build and require no surface preparation as compared to tetrahedral mesh. They also has almost five times fewer cells than tetrahedral mesh for a given surface. Trimmer meshing model It provides efficient and robust method for creating a high quality mesh for complex and simple mesh generation problems. The model is influenced depends on the quality of the starting surface and theerfore more likely to produce a better quality mesh is many situations. The trimmer and polyhedral cell type meshes produce the more accurate solution than tetrahedral mesh in terms of general accuracy for a specific number of cells. Expected results Post-processing tools This process is used to analyze, present and visualize the simulation results. It includes point values or complex animated features. Furthermore, some of the manipulation of commercial and closed-source CFX codes can be used in the user FORTRAN Interface, which has a set of user –defined subroutines. The subroutines enable the user to access Memory Management Systems of the code, and therefore allowing a fine control over the simulation. Computer simulation using Star CCM+ Before starting simulation in star CCM+, the geometry of the space in which the flow is to be simulated must be done. This is done by using drawing and design software such as Auto CAD, Solid Works, etc. it is then saved in file types that can be imported by star CCM+ e.g. .dbs –pro-STAR surface database mesh file, .pat –PATRAIN shell file, etc. Pro’s/Con’s of using CFD as opposed to other methods for this project. One of the advantages of CFD modelling technique is that it is a very non-intrusive, compelling and virtual with powerful visualization capabilities that can be used effectively in presentations. Engineers can therefore perform a wide range of system configurations on the computer without the expense, time and difficulty required to make real changes on site. It can be applied in aircraft and automobile design, weather science among others. CFD model will not only predict performance before modifying and installing systems, but it also provide exact details and information of the design parameters. Before modification and installation of actual systems, CFD can predict designed changes which are important in enhancing performance. CFD model is less costly since physical modification is not necessary, and also in terms of time. Since the methods and the numerical schemes through which CFD is based have been improving rapidly, so its results have been reliable tool in design and analysis. CFD data can be used in the validation of different design parameters the number of exhausts, diffusers and location, and temperature of supplied air. Limitations One of the limitations of CFD is the computing power used to perform precise simulations. Since it limits the size of the computational domain, it may require the use of models like turbulence to resolve it, resulting in the loss of the results and uncertainties. Also, in CFD codes, the multiphase flows have not been fully developed. Although the absence of topological information for the interfaces is not an limitation in two-phase flow, there are circumstances when the two phases are greatly separated and therefore require knowledge on position and geometry of the interfaces. In this case, interface tracking and reconstruction is needed for resolving physics in the system. References Chadderton D. V., 2013. Building Services Engineering, 6th Ed., Routledge, p 68-69 Thirumaleshwar M., 2006. Fundamentals of heat and mass transfer, New Delhi : Pearson, p110. Zhai, J., Hermansen, K., and Al-Saasi, S., (2012) “The Development of Simplified Rack Boundary Conditions for Numerical Data Center Models,” RP-1487, ASHRAE, Atlanta GA. Schmidt, R. , Cruz, E., and Iyengar, M., (2005) “Challenges of data center thermal management,” IBM J Res & Dev 49:4/5 pp 709-723. Karki, K., Radmehr, A., and Patankar, S., (2003) “Use of Computational Fluid Dynamics for Calculating Flow Rates Through Perforated Tiles in Raised-Floor Data Centers,” Int J HVAC R, 9:2, pp. 153-166. Bukowski, R..W. and Transue, R. “Modeling the Performance of Fire Protection Systems in Modern Data Centers,” Rolf Jensen and Associates, Suppression and Detection Symposium 2012. Bukowksi, R.W., et al. Performance of Home Smoke Alarms Analysis of the Response of Several Available Technologies in Residential Fire Settings. NIST Technical Note 1455- 1. National Institute of Standards and Technology, Gaithersburg, MD, 2008. Read More