Stirling Engine Heat Exchangers Research Articles

Two‐Dimensional Solidification Simulation of PCM Molten Salt as a Thermal Energy Storage for Stirling Engine

ABSTRACTThermal energy storage technologies have been widely used to mitigate intermittency from renewable energy sources such as solar energy. Phase change material (PCM) is a material that can be used as a heat storage medium and is available in a wide range of operating temperatures. Molten salt is one of the PCMs that has the advantage of a very high operating temperature. The PCM solidification simulation based on HitecXL molten salt using COMSOL Multiphysics software was carried out with variations in heat absorption of 1–5 kW/m2, assuming constant heat absorption. The results showed that the PCM solidification process started from the surface of the Stirling engine heat exchanger pipe. The part of the PCM that is solidified falls due to gravity, causing a phenomenon similar to a droplet. The flow that occurred was natural, driven by the buoyancy force resulting from density changes due to temperature gradients in the solidification process. The time required for the PCM to completely solidify was closely related to the amount of heat absorption; the greater the heat absorption from the pipe, the faster the PCM is fully solidified.

Simulation on solidification process of molten salt-based phase change material as thermal energy storage medium for application in Stirling engine

Abstract Thermal energy storage technologies have been widely used to mitigate intermittency from renewable energy such as solar energy. Phase change material (PCM) is a certain material that can be used as a heat storage medium and is available in a wide range of operating temperatures. Molten salt is one of the PCMs that has the advantage of a very high operating temperature. The PCM solidification simulation based on HitecXL molten salt using COMSOL Multiphysics software will be carried out with variations in heat absorption of 1 - 5 kW/m2, assuming constant heat absorption. The results show that the PCM solidification process starts from the surface of the Stirling engine heat exchanger pipe. The part of the PCM that has been solidified will fall following the direction of gravity and cause a phenomenon such as a droplet. The flow that occurs is a natural flow caused by the buoyancy force due to changes in density due to temperature gradients in the solidification process. The time required for the PCM to completely solidify is closely related to the amount of heat absorption. The greater the heat absorption from the pipe, the faster the PCM to fully solidified.

Evaluation of the operating conditions of the Stirling engine heat exchangers

The development of modern energy is inextricably linked with the further improvement of heat engines, which are still the only primary sources of mechanical energy on an industrial scale. Given the existing environmental problems, Stirling engines can be a good alternative to internal combustion engines and turbines. Of the many problems of creating such a sufficiently powerful and economical engine, it is customary to consider three main ones: 1) efficient transfer of large heat fluxes in the heater, regenerator and refrigerator; 2) creation of reliable and durable seals to hold the working fluid in the cylinder; 3) ensuring minimal friction in bearings and seals. And yet, of the three listed problems, the first should be given more attention, first of all, due to the unique conditions associated with the continuously changing thermo and mechanical loads. The instability of the loads is further complicated by the sharply different heat transfer coefficient on the external and internal heat transfer surfaces. That is, there are factors that contradict the requirements for the size of the heat transfer surface, the friction resistance of the working medium and the dead volume of the engine as a whole. In this regard, it is of interest to search for possible ways to reduce the effect of negative factors of non-stationary heat transfer in the calculation of heat exchangers. The current lack of suitable theoretical methods of calculation forces the use of semi-empirical methods. The aim of the paper is to assess the significance of the unique, characteristic of Stirling engines, the negative phenomenon of the delay in the flow of the working fluid in heat exchangers. For this purpose, a real kinematic diagram of the movement of the engine pistons with a rhombic drive by R. Meyer, created using the design program, is used. The analogue is the 4–235 type real engine of the Philips Company. In the calculations, a step-by-step procedure for calculating the time-varying parameters of the working fluid is used. The need for such a solution is due to the fact that in the rhombic drive of R. Meyer, the pistons movement and the change in the displaced volumes complexly depend on the angle of rotation of the engine shaft. In addition, the exact value of the real change in volume is possible only when the terms of the analytic equation of volume change under consideration are decomposed into a Fourier series.

Numerical correlation for the pressure drop in Stirling engine heat exchangers

New correlation equations, to be valid for the pressure drop and heat exchange calculation under the developing transitional reciprocating flow encountered in Stirling heat exchangers are numerically derived. Reynolds-Averaged Navier–Stokes (RANS) equations based turbulence models are used to analyse laminar to turbulent reciprocating flow, focussing on the onset of turbulence and transitional reciprocating flow regime. The relative performance of four turbulence models in more accurately capturing the characteristics of the flow of interest is assessed in relation to overcoming the problems identified in previous numerical studies. The simulation results are compared with published and well-known experimental data for reciprocating pipe flows, indicating that the effects of the turbulence anisotropy need to be taken into account in order to accurately predict the laminar to turbulent transition. The anisotropic Reynolds stress turbulence model is selected as a best choice among the tested turbulence models for analysis of this transitory phenomenon based on the comparative qualitative and quantitative results. This model is used to evaluate the heat transfer and pressure drop and propose new correlations considering the working and dimensional characteristics of Stirling heat exchangers: 100 ≤ Reω ≤ 600, A0 ≤ 600, βcri > 761 and 40 ≤ L/D ≤ 120. These correlation equations reduce the unsteady 2D behaviour in reciprocating pipe flow into a manageable form that can be incorporated into Stirling engine performance codes. It is believed that the validated numerical model can be used with confidence for studying the transitional reciprocating flow and the obtained correlations, can be applied as a cost effective solution for the development of Stirling engine heat exchangers.

Oscillating flow in a stirling engine heat exchanger

Three heat exchangers exist in modern Stirling engines: a heater, a cooler, and a regenerator. Here a study that deals principally with tubular heaters and coolers is carried out. The calculation procedure for the oscillating flow heat transfer is presented. Literature sources are studied to find the most suitable correlations by comparing them to each other and to the classical turbulent flow correlations encountered in the literature. The enhancement of heat transfer by means of a few circumferential slots inside the tubes and the pressure losses of oscillatory flow are discussed. Non-circular cross-section conduits with rectangular and triangular cross-sections are investigated and compared to the smooth circular tubes. The increment of the performance of an idealised Stirling engine with slotted heat exchanger tubes is compared to the case with smooth ones. The ratio of the gain in the shaft power and pumping losses is 2.22. The Carnot efficiency increment is 2.7%.

Porous materials for thermal management under extreme conditions

A brief analysis is presented of how heat transfer takes place in porous materials of various types. The emphasis is on materials able to withstand extremes of temperature, gas pressure, irradiation, etc. i.e. metals and ceramics, rather than polymers. A primary aim is commonly to maximize either the thermal resistance (i.e. provide insulation) or the rate of thermal equilibration between the material and a fluid passing through it (i.e. to facilitate heat exchange). The main structural characteristics concern porosity (void content), anisotropy, pore connectivity and scale. The effect of scale is complex, since the permeability decreases as the structure is refined, but the interfacial area for fluid-solid heat exchange is, thereby, raised. The durability of the pore structure may also be an issue, with a possible disadvantage of finer scale structures being poor microstructural stability under service conditions. Finally, good mechanical properties may be required, since the development of thermal gradients, high fluid fluxes, etc. can generate substantial levels of stress. There are, thus, some complex interplays between service conditions, pore architecture/scale, fluid permeation characteristics, convective heat flow, thermal conduction and radiative heat transfer. Such interplays are illustrated with reference to three examples: (i) a thermal barrier coating in a gas turbine engine; (ii) a Space Shuttle tile; and (iii) a Stirling engine heat exchanger. Highly porous, permeable materials are often made by bonding fibres together into a network structure and much of the analysis presented here is oriented towards such materials.

Feasibility Study on SOFC-Stirling Engine Combined System.

Cycle simulations have been made on solid oxides fuel cell-Stirling engine combined system (SOFC-SE C.S.) fueled with methane to investigate the feasibility of the combined system. The model system consists of an SOFC with internal reforming, a combustor burning residual fuel exhausted from the SOFC, a conventional Stirling engine and an air-preheater recovering the exhausted heat from the engine. In this system, the SOFC serves simply as the topper of the engine. The cycle calculations focus on the influences of temperature effectiveness of the preheater, the number of transfer unit of the Stirling engine heat exchanger and the air excess ratio on the system efficiency and the operation condition. The system analysis shows that the system efficiency attains up to 55% at reasonable preheater temperature effectiveness of 0.8 and the air excess ratio of 3.0, while the operation is restricted to a narrow range of the number of transfer unit due to the allowable preheater temperature and the required SOFC inlet temperature. The cell temperature is not sufficiently high at the air excess ratio of 3.0 and the lower air excess ratio improves the system efficiency. At the air excess ratio of 2.0, the combined system shows 10% gain in efficiency compared to the pure SOFC system.

Optimal Allocation of Heat Exchanger Inventory Associated with Fixed Power Output or Fixed Heat Transfer Rate Input

The purpose of this study is to determine the optimal distribution of the heat transfer surface area or conductance among the Stirling engine heat exchangers when the minimum of the total heat transfer surface area of the heat exchangers is sought. The optimization procedure must fulfill one of the following constraints: (1) fixed power output of the engine, (2) fixed heat transfer rate available at the source, or (3) fixed power output and heat transfer rate at the source. Internal and external irreversibilities of the Stirling engine are considered. An analytic approach, when heat transfer occurs at small temperature differences at the heat reservoirs, provides several restrictions with regard to variables of the model. A sensitivity analysis of the minimum of the total heat transfer surface area of the heat exchangers with respect to these variables and parameters is presented. The results show optimal temperatures of the working fluid and optimum allocation of heat exchanger inventory.

A fuzzy knowledge base to support routine engineering design

Much of engineering design can be characterised as putting together variants of existing mechanisms to meet novel requirements. This paper describes an approach to engineering design in which fuzzy sets are used to represent the range of variants on existing mechanisms. Membership functions are chosen to reproduce the distinctions and classifications used by experienced designers. Methods are introduced to calculate the fuzzy performance range achievable by each component type, and a metric is suggested for the ranking of design candidates against design requirements. The underlying approach to design evaluation derives from that developed by Antonsson, Wood and Otto. If the components model the design domain accurately, this architecture will always find a successful design, where one exists. However, finding this design may involve exhaustive search of the design space, and the time required for such an exhaustive search is typically far greater than is available for the task. The architecture is therefore augmented by the introduction of design agents, embodying heuristic rules to direct the search intelligently, so that a satisfactory design is found within a reasonable length of time. As an example, the method is applied to preliminary design of a Stirling engine heat exchanger.

Numerical simulation of fully developed flow and heat transfer characteristics in a curved tube with pulsating pressure gradient

Characteristics of fluid flow and convective heat transfer of a pulsating flow in a curved tube have been investigated numerically. The tube wall is assumed to be maintained at a uniform temperature peripherally in a fully developed pulsating flow region. The temperature and flow distributions over a cross-section of a curved tube with the associated velocity field need to be studied in detail. This problem is of particular interest in the design of Stirling engine heat exchangers and in understanding the blood flow in the aorta. The time-dependent, elliptic governing equations are solved, employing finite volume technique. The periodic steady state results are obtained for various governing dimensionless parameters, such as Womersley number, pulsation amplitude ration, curvature ratio and Reynolds number. The numerical results indicate that the phase difference between the pressure gradient and averaged axial velocity increases gradually up to π/2 as Womersley number increases. However, this phase difference is almost independent of the amplitude ratio of pulsation. It is also found that the secondary flow patterns are strongly affected by the curvature ratio and Reynolds number. These, in turn, give a strong influence on the convective heat transfer from the pipe wall to the pulsating flow. The results obtained lead to a better understanding of the underlying physical process and also provide input that may be used to design the relevant system. The numerical approach is discussed in detail, and the aspects that must be included for an accurate simulation are discussed.

Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re max = 1,920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are here compared with experimental results of previous investigators. Predictions of the flow regime on present oscillating flow conditions are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k- ϵ turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k- ϵ model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.

Flow Losses in Stirling Engine Heat Exchangers

Closed-form expressions are sought which will allow the rapid and accurate calculation of pressure variation, flow velocities, and flow friction losses in crank-driven Stirling cycle machines. The compression and expansion spaces of the Stirling machine are assumed to be isothermal and their volumes are assumed to vary sinusoidally. It is further assumed that the cyclic pressure variation of the working fluid and the flow velocities within the passages of the machine can be represented by sinusoids. Closed-form expressions are deduced for the amplitude and phase of these variations. Using the expressions so deduced, formulae are derived for frictional losses in the three heat exchangers, taking into account the variation in mass flow rate over the cycle and the difference in amplitude of mass flow between the two ends of the regenerator. By comparing these expressions with calculations based on the assumption of an average flow rate over the cycle, it is shown that the latter method leads to flow losses being underestimated by more than 50 percent. It is recommended that the formulae deduced here be used for first-stage design work.