Three Dimensional Numerical Simulation of Parallel Plate Stack Heat Exchanger in Beta-type Stirling Engine

• Main Authors: Shu-WeiChang, 張書維
• Other Authors: Chang-Da Wen
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/92097027817994095145

碩士 === 國立成功大學 === 機械工程學系 === 102 === Three Dimensional Numerical Simulation of Parallel Plate Stack Heat Exchanger in Beta-type Stirling Engine Author : Shu-Wei Chang Advisor : Chang-Da Wen National Cheng Kung University Department of Mechanical Engineering SUMMARY This study considers three dimensional parallel plate stack in beta-type Stirling engine to observe the effect of dimensionless width and kinetic Reynolds number on time-space average friction coefficient and Nusselt number of the heat exchanger. Correlations among these parameters are eventually built and will be helpful to design better Stirling engine heat exchanger. Key words: Beta-type Stirling Engine, Parallel Plate Stack Heat Exchanger, Oscillatory flow, Three Dimensional Numerical Simulation. INTRODUCTION In recent years, the study of low temperature difference and focus type solar Stirling engine are booming. The heat exchanger performance becomes more important to the engine overall efficiency. In previous numerical investigations of Stirling engine heat exchanger, two dimension numerical simulation and straight pipe are often chosen for discussion. In this research three dimensional wall boundary condition is taken into consideration and the numerical simulation is conducted. This research is mainly analyzed the effect of the dimensionless width and kinetic Reynolds number of the parallel plate stack in beta type Stirling engine. The friction coefficient and Nusselt number of the heated plate are investigated. The “annular effect” (i.e. the maximum axial velocity in a fast oscillatory flow) can be clearly observed near the wall either in velocity or temperature field in three dimensional model. The change of dimensionless width do not affect the annular effect, but when kinetic Reynolds number arises, the annular effect becomes more apparent and important near the wall. At last, correlations are established to express time-space average friction coefficient and Nusselt number with dimensionless width and kinetic Reynolds number. The importance of dimensionless width and kinetic Reynolds number on time-space average friction coefficient and Nusselt number are observed and analyzed. METHOD The main purpose of this research is to carry out the simulation in parallel plate stack in beta type Stirling engine and conduct the analysis for the fluid flow and the heat transfer. The oscillatory flow in the Stirling engine is driven by the sinusoidal displacer under three dimensional wall boundary condition. The commercial software Ansys is first used to establish the physical model and mesh. The whole model is then numerically simulated by Fluent. Because of the large change near the plate entrance and the exit, the method of discretization should use higher order to discrete continuity, momentum, energy equation. QUICK (Quadratic Upwind Interpolation for Convective Kinematics) scheme is employed to discrete the convection term, and the second-order central difference method is adopted for the diffusion term. SIMPLE (Semi-Implicit Method for pressure-Linled Equation) scheme is chosen as the simulation method for iteration. The tested kinetic Reynolds number ranges from 100 to 1000. The dimensionless width is examined from 4 to 40. Then the corresponding friction coefficient and Nusselt number at different kinetic Reynolds number and dimensionless width are found. RESULTS AND DISCUSSION From the results, the “annular effect” is also discovered in three dimensional simulation, not only in velocity field but also in temperature field. The maximum time-space average Nusselt number occurs near the wall. The “annular effect” is more visible with higher kinetic Reynolds number, but independent of the dimensionless width. The comparison of results between two dimensional model and the symmetry plane in three dimensional model is obtained. Also the results of overall plate in three dimension are compared and studied. From Figure 1, a correlation is obtained to calculate time-space average friction coefficient of the parallel plate stack in beta type Stirling engine with kinetic Reynolds number and dimensionless width. Time-space Nusselt number is divided into two distributions. One is with dimensionless width below 10 which is shown in Figure 2 and the other is above 10 which is shown in Figure 3. Figure 1 The correlation to express time-space average friction coefficient with dimensionless width and kinetic Reynolds number. Figure 2 The correlation to express time-space average Nusselt number with dimensionless width below 10 and kinetic Reynolds number. Figure 3 The correlation to express time-space average Nusselt number with dimensionless width above 10 and kinetic Reynolds number. CONCLUSION The purpose of this research is to analyze the flow and heat transfer characteristics of three dimensional parallel plate stack heat exchanger in beta type Stirling engine by numerical simulation. By changing dimensionless width and kinetic Reynolds number, the influence of the three dimensional walls on flow and heat transfer are investigated. Then Nusselt number and friction coefficient of the whole plate are further discussed. Findings from this study are as follows. 1. The “annular effect” exists not only in velocity field but also in temperature field for the reciprocating flow in three dimensional stack plate. 2. Friction coefficient of the symmetry plane exists a constant difference with two dimensional results. Nusselt number of the symmetry plane is consistent with two dimensional results at long dimensionless width. However, while kinetic Reynolds number increases, the dimensionless width needs to be longer. 3. Time-space average friction coefficient of the whole plate is independent of dimensionless width. It becomes lower with higher kinetic Reynolds number. A maximum time-space average Nusselt number of the whole plate is found at dimensionless width 10 regardless of the change of kinetic Reynolds number. 4. At last, correlations are established to express time-space average Nusselt number and friction coefficient with dimensionless width and kinetic Reynolds number. It will be helpful to design better heat exchanger in Stirling engine.