Strojniški vestnik - Journal of Mechanical Engineering 51(2005)7-8, 411-417 UDK-UDC 536.2 Izvirni znanstveni članek - Original scientific paper (1.01) Numerical analysis of heat transfer and fluid flow in rotary regenerative air pre-heaters Sandira Alagič , Nikola Stošič , Ahmed Kovačevič , Indira Buljubašič 1Faculty of Mechanical Engineering, University of Tuzla, Univerzitetska 4, Tuzla, BiH, sandira.alagic@untz.ba 2 School of Engineering and Mathematical Sciences, City University London, Northampton Square, EC1V 0HB, UK Abstract The Ljungström rotary air pre-heater is a regenerative heat exchanger used for preheating the combustion air, mainly in steam boiler plant. The hot gas and cold air ducts are arranged to allow both the flue gas and the inlet air to flow simultaneously through the machine. The hot flue gas heats the rotor material and as the rotor rotates, the hot rotor section moves into the flow of the cold air and preheats it. Existing simulations of regenerative air pre-heaters are mainly based on empirical approximations where some of the effects of the process are neglected. Although this usually gives reasonably acceptable results, it was thought that CCM analysis of such devices, which stands for Computational Continuum Mechanics, would result in a better understanding of the process features, such as the fluid-solid interaction. A grid interface was developed to transfer the geometry of such a Ljungström air pre-heater to a finite volume numerical mesh which is later used for the calculation of unsteady fluid-solid interactions. Results were obtained by use of the commercial CCM solver ”Comet” of Star CD. In this paper the results are presented in the form of diagrams of the velocity and temperature fields as functions of time and space. The results of both the one- and three-dimensional calculations and field measurements are compared and good agreement was achieved. The result of this study is the development of an effective procedure for computer calculation of processes in a Ljungström air pre-heater to optimise its parameters, which can be used either for research and development or in everyday engineering practice. Introduction Much effort has been spent to maximise the efficiency of each stage of the transformation of the chemical energy of fuel to electrical power. In a steam boiler, the most significant loss is associated with the energy of the outgoing flue gas. This can be reduced by the use of an air pre-heater which transfers energy from the outgoing exhaust gases, to the incoming air, prior to combustion. The Ljungström air pre-heater, as shown in Figure 1, is a regenerative heat exchanger often used for this function in industrial power plant. In it, the hot gas and cold air are arranged to flow in opposite directions through parallel ducts, each of which, passes through a section of a rotor. The combustion products heat the rotor as it revolves through that section. Further rotation of the rotor brings it into contact with the incoming air, where it is cooled by it. The air is thereby preheated before passing to the boiler furnace, where it is used for combustion of the fuel. The rotor is divided into a number of sections, which are separated by seals, in order to prevent mixing of the flue gases and combustion air. These sections consist of small passages formed by profiled sheets, as shown in Figure 2, and the performance of the air pre-heater depends on the size and shape of these small cells. A number of studies have already been published, which describe methods of estimating the performance of regenerative pre-heaters. However, all of them are based on dimensionless or one-dimensional models in which some significant effects are either neglected or estimated empirically. A three dimensional approach was therefore regarded as a useful tool to analyse heat and fluid flow within the cell elements more precisely and how varying their size and shape would affect the interaction between the rotor and the fluid. 411 Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 411-417 Nomenclature A - area of contact between the solid body c - specific heat and gas, area C - turbulence model constants e - internal energy f - body force h - heat transfer coefficient, enthalpy i - unit vector I - unit tensor k - conductivity, kinetic energy of turbulence m - mass p - pressure P - production of kinetic energy of turbulence q - source term s - control volume surface t - time u - displacement in solid v - fluid velocity V - volume x - spatial coordinate z - axial coordinate a - temperature dilatation coefficient r - diffusion coefficient e - dissipation of kinetic energy of turbulence - variable X - Lame coefficient ^ - viscosity r| - Lame coefficient p - density a - Prandtl number Indices eff - effective g - gas in - inflow out - outflow s - solid T - turbulent The use of Computational Fluid Dynamics, CFD, to analyse the flow in a variety of thermal equipment has been widely reported, but there is no record in the open literature of its use and use of CCM for calculations of flows in Ljungström air pre-heaters. One possible reason for this is the complexity of the geometry and flow within these devices. Figure 1 Fluid flows in rotary regenerator A further complication of the analysis is that the flow processes involved are unsteady and their nature can only be properly understood by consideration of the interaction between the fluid flow and solid structure. More recently, the use of continuum mechanics and a substantial increase in computer speed and capacity have made it possible to develop specialized computer codes for simultaneous application of finite volume numerical methods to both fluid flow and its surrounding solid structure in the form of commercial CCM codes. In order to apply these advanced numerical methods to the calculation of rotary regenerator devices, the authors have developed a general and flexible grid generation procedure. An interface program written in FORTRAN enables an arbitrary geometry of a pre-heater to be automatically mapped with the discrete volumes and then used for calculation in a standard CCM code. By this means, a study was carried out on an existing pre-heater in “Tuzla” power station, using the commercial CCM solver “Comet”. The results are displayed in the form of the temperature distribution within the pre-heater solid elements and fluid flow of both the hot combustion products and cold air as a function of both time and spatial position Figure 2 Filling of a rotary regenerator 412 AlagičS. -StošičN. - KovačevičA. - Buljubašič I. Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 411-417 One-dimensional energy balance of the pre-heater A one-dimensional model is developed and described in this paper, which assumes that each control volume consists of solid and fluid parts connected via a common area surface. The solid and fluid components of the cell exchange heat through certain regions of the known surface area. As a result of the rotation of the device, the temperature within it changes continuously both in space and time. In such a case, a one-dimensional numerical model of heat transfer between the hot combustion products and solid material on one side, and the cold air and solid body on another, can be applied to estimate the pre-heater performance reasonably well. [1] The control volumes are positioned next to each other and a constant speed of rotation is assumed for all of them. The mathematical model utilized here consists of two energy balance equations, one for the solid body, (1) and one for the fluid phase, (2). The interface between these two equations is the convective heat transfer between the fluid and the solid. mscs s + k sAi ^2s = hA(Tg-Ts) Pit P ^ ' heat source d2T (1) dT mgcp g+m gcpfTin-ToutHgAi 2 g=hA Tg-Ts) (2) convection conduction in gas heat source 3t ri2T mscs —s + ksAz z = hA (T - Ts) gp dt p dz mc— + mc— = hA(Tg -Ts) (3) (4) Since each flow passage is narrow and surrounded by thin material, the fluid temperature change in the direction perpendicular to the main flow can be regarded as small and neglected. Also, since it is assumed that heat is not exchanged with the surroundings in the radial direction, conduction in the solid body only occurs along the axial coordinate z. Heat transfer by conduction in the fluid is neglected because of the low fluid thermal conductivity. By means of these simplifications, the equations are reduced to those of unsteady 1-D flow, as shown in equations (3) and (4). These can be solved by a finite difference method. Depending on the spatial position of the calculating domain, i.e. the angle of rotation, the fluid medium in these equations is either air or combustion products. The inlet temperatures and mass flow rates are assumed to be constant during the each half-period of the process and their assumed values are those obtained from industrial plant measurements. The spatial domain is discretised by assuming constant steps in the axial direction. The time step is assumed to be constant. The resulting system of algebraic equations is then solved numerically by iterative procedure contained in the computer program written by the authors. The results obtained are in the form of instantaneous temperatures of the flue gas or air and solid, and the mass flows of the flue gas and air at every point along the axial coordinate z. Three-dimensional analysis of the pre-heater Both, the fluid flow and structural behaviour of the solid parts in a regenerative pre-heater are fully described by the mass averaged equations of continuity, momentum and energy conservation which are accompanied by equations of the turbulence model and state, as given, for example, in [4]. The solution of these equations is then made possible by inclusion of constitutive relations in the form of Stoke’s and Fourier’s law for the fluid momentum and energy equations respectively and Hooke’s law for the momentum equations of the thermo-elastic solid body. The generic 3-D transport equation is then given as: Numerical analysis of heat transfer and fluid flow in rotary regenerative air pre-heaters 413 Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 411-417 — \p(/)dV + \p(/)v ¦ ds = fr^grad ¦ ds + fq^ • ds + q V ¦ dV dt V S (5) S SV The terms in the equation which describe the pre-heater case are given in Table 1. The resulting system of partial differential equations is then discretised by means of a finite volume method in a general Cartesian coordinate system. This method maintains the conservation of the governing equations, while at the same time enables a coupled system of equations for both, solid and fluid parts to be solved simultaneously. Connection between the solid and fluid parts is explicitly determined if the temperature on the solid body surface is a boundary condition for the fluid flow and vice versa. The numerical grid, as explained in the next section, is attached to the CCM solver to obtain the distribution of the fluid temperature and velocity throughout the fluid domain and the temperature of the solid elements. This mathematical scheme is accompanied by the boundary conditions for both the solid and fluid parts. Whether the fluid part contains hot gas or cold air it is entirely surrounded by the walls. Cyclic boundary conditions are applied to all sides of the domain except to the top and bottom parts. These are represented either as inlet or outlet. The initial values for all physical variables are given at the centre of each numerical cell within the domain and preset to the values of the air inlet flow. Table 1 Terms in the generic transport equation (5) Equation