Cho Lik Chan

Analysis of Heat Storage and Delivery of a Thermocline Tank Having Solid Filler Material

Thermal storage has been considered as an important measure to extend the operation of a concentrated solar power plant by providing more electricity and meeting the peak demand of power in the time period from dusk to late night everyday, or even providing power on cloudy days. Discussed in this paper is thermal energy storage in a thermocline tank having a solid filler material. To provide more knowledge for designing and operating of such a thermocline storage system, this paper firstly presents the application of method of characteristics for numerically predicting the heat charging and discharging process in a packed bed thermocline storage tank. Nondimensional analysis of governing equations and numerical solution schemes using the method of characteristics were presented. The numerical method proved to be very efficient, accurate; required minimal computations; and proved versatile in simulating various operational conditions for which analytical methods cannot always provide solutions. Available analytical solutions under simple boundary and initial conditions were used to validate the numerical modeling and computation. A validation of the modeling by comparing the simulation results to experimental test data from literature also confirmed the effectiveness of the model and the related numerical solution method. Finally, design procedures using the numerical modeling tool were discussed and other issues related to operation of a thermocline storage system were also studied.

A Boundary Element Method Analysis of the Thermal Aspects of Metal Cutting Processes

In this paper, the b oundary e lement m ethod (BEM) approach is used to analyze the thermal aspects of steady state metal cutting processes. Particular attention is paid to modeling of the boundary conditions at the tool-chip and the chip-workpiece interfaces. Since the velocities in each of the regions are different, the heat transfer within the tool, the chip, and the workpiece are first calculated separately. A complete model for heat transfer during steady state turning is then obtained by matching the boundary conditions across the primary and the secondary shear zones. An exact expression for matching is developed to avoid any iterations. The temperature fields within the workpiece, the chip, and the tool for various processing conditions are obtained and presented. The numerical results obtained by the BEM are also compared to Jaeger solutions and existing FEM results reported in the literature. The BEM is found to be efficient and robust for this class of steady state conduction-convection problems.

An algorithm for handling corners in the boundary element method: Application to conduction-convection equations

Accurate and efficient determination of temperatures and fluxes along with their design sensitivities in conduction-convection problems involving geometric or generalized corners is the primary objective of this paper. A boundary element method (BEM) approach is used for this purpose, and the design sensitivities are obtained through direct differentiation of the governing integral equations. Conforming elements are used, and corners are treated through constraint equations. Several numerical results are presented, and a few of them are compared with existing analytical results to establish the validity of this approach.

Experimental investigation of thermal storage processes in a thermocline tank

This paper presents an experimental study of the energy charge and discharge processes in a packed bed thermocline thermal storage tank for application in concentrated solar power plants. A mathematical analysis was provided for better understanding and planning of the experimental tests. The mathematical analysis indicated that the energy storage effectiveness is related to fluid and solid material properties, tank dimensions, packing schemes of the solid filler material, and the durations of the charge and discharge times. Dimensional analysis of the governing equations was applied to consolidate many parameters into a few dimensionless parameters, allowing scaling from a laboratory system to an actual industrial application. Experiences on the system design, packing of solid filler material, system operation, and data analysis in a laboratory-scale system have been obtained in this work. These data are used to validate a recently published numerical solution method. The study will benefit the application of thermocline thermal storage systems in the large scale concentrated solar thermal power plants in industry.

Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer

Smith & Davis ( J. Fluid Mech ., vol. 132, 1983, pp. 119–144) considered the stability of thermocapillary convection in a horizontal fluid layer with an upper free surface generated by a horizontal temperature gradient. They showed that for a return-flow velocity profile, the convection will become unstable in the hydrothermal mode with waves propagating upstream obliquely. Their findings provided a theoretical explanation for the defects often found in crystals grown by the floating-zone technique and in thin-film coating processes. Their predictions were verified experimentally by Riley & Neitzel ( J. Fluid Mech ., vol. 359, 1998, pp. 143–164) in an experiment with 0.75 mm thick layer of silicone oil. Their results with 1 and 1.25 mm thick layers show that as the thickness of the layer is increased, the angle of propagation, the frequency of oscillation and the phase speed of the hydrothermal wave instability decrease, while the wavelength stays nearly constant. We have extended the linear stability analysis of the problem with the effect of gravity included. It is found that when the Grashof number Gr is increased from zero, the angle of propagation first increases slightly, reaches a maximum and then decreases steadily to zero at Gr = 18. The phase speed, the frequency of oscillation and the wavelength of the instability waves all decrease with increasing Grashof number. For Gr larger than 18, there is the onset of the instability into travelling transverse waves. We have also carried out energy analysis at the time of the instability onset. It is found that the major contribution to the energy of the disturbances is from the surface-tension effect. As the gravitational effect is increased, there is a reduction in the kinetic energy supply to sustain the motion of the disturbances. We also found that it requires more kinetic energy to sustain the hydrothermal mode of instability than that required for the travelling transverse mode of instability. As a result, with increasing Grashof number, the kinetic energy available for the disturbances decreases, causing the angle of propagation to gradually decrease until finally reaching zero at Gr = 18.

Transient Heat Delivery and Storage Process in a Thermocline Heat Storage System

Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The current study aimed to effectively model the heat transfer of a working fluid interacting with filler material. An effective numerical method and efficient computation schemes were developed and verified. A thermocline storage system was modeled under specific conditions and results of great significance to heat storage design and operation were obtained.Copyright

Boundary element method analysis for the transient conduction - convection in 2-D with spatially variable convective velocity

Abstract A boundary element method (BEM) formulation for the solution of transient conduction–convection problems with spatially variable convective velocities is developed in this paper. A time-dependent fundamental solution for a moving heat source with constant velocity is utilized for this purpose. Such a formulation is expected to be accurate and stable at high Peclet numbers. Numerical examples are included to establish the validity of the approach. It is observed that the BEM scheme avoids considerable false diffusion, and the numerical results for sample problems compare very well to analytical results.

A Boundary Element Method Formulation for Design Sensitivities in Steady-State Conduction-Convection Problems

A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes.

Heat Transfer in Thermocline Storage System With Filler Materials: Analytical Model

Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The heat transfer between the heat transfer fluid and filler materials are governed by two conservation of energy equations, often referred as Schumann [1] equations. We solve these two coupled partial differential equations using Laplace transformation. The initial temperature distribution can be constant, linear or exponential. This flexibility allows us to apply the model to simulate unlimited charging and discharging cycles, similar to a day-to-day operation. The analytical model is used to investigate charging and discharging processes, and energy storage capacity. In an earlier paper [2], the authors presented numerical solution of the Schumann equations using method of characteristics. Comparison between analytical and numerical results shows that they are in very good agreement.Copyright

Effect of gravity modulation on the stability of a horizontal double-diffusive layer

The instability characteristics of a horizontal stably stratified fluid layer being heated from below, including its subsequent nonlinear evolution under steady and modulated gravity, have been investigated by experiments and two-dimensional numerical simulations. The critical condition at instability onset is also checked using linear stability analysis. The fluid is contained in a horizontal test tank with an initial stable solute gradient and a constant-temperature gradient imposed by heating from below. Because of the non-diffusive boundaries, the vertical solute gradient slowly decreases and, eventually, the layer becomes unstable. From the time of the onset of instability, the critical solute Rayleigh number is determined. For the experiments with modulated gravity, the tank is fixed onto a platform that oscillates vertically at 1 Hz with an amplitude of 10cm. The experiment is designed such that no internal wave mode of instability can be excited. The experimental results show that gravity modulation destabilizes the system slightly by increasing the solute Rayleigh number at onset by 8.4 % and causes the oscillation frequency at onset to increase by 32.6 %. Linear stability analysis and two-dimensional numerical simulations for the steady gravity case yield results that are in good agreement with the experiment. For the gravity modulation case, linear stability results do not show any effect of gravity modulation at the frequency of 1 Hz. Numerical simulation results do show increases in both the onset solute Rayleigh number and the oscillation frequency; however, their values are smaller than those obtained in the experiment. The characteristics of the internal wave mode of instability are explored by numerical simulations of a stably stratified solute fluid layer under gravity modulation. The interference effects between the internal wave mode and double-diffusive mode of instabilities are studied by imposing an adverse temperature gradient on the stratified layer.