近幾年來低溫差和聚焦型太陽能史特靈引擎的研究正蓬勃發展著，其中熱交換器的性能對於引擎整體效率顯得更為重要。在以往的研究當中，常使用對稱型溫度邊界做為研究探討的對象，在近期的幾篇文獻當中，開始探討非對稱型溫度邊界，以更貼近現實中實際情況，更準確的分析堆疊式平板中往復流之熱傳效果。
在目前的研究當中，較常使用二維模擬的方式，來獲得所需之結果，例如平板間之紐賽數(Nusselt Number)、摩擦係數(Friction Coefficient)等等，然而忽略三維邊界所造成的影響，是否符合實際的情況，仍值得探討，因此我們利用Ansys所提供模組化的模型建立、網格建立，快速建立欲分析之模型及網格，並且利用Fluent所提供多核心運算，減少進行三維模擬運算所需耗費的時間，以往使用自行撰寫程式碼的方式，並無法將模擬運算最佳化，達到最快速的運算。
本研究希望加入三維邊界的模擬，以分析三維模擬環境下之堆疊式平板往復流之摩擦係數與熱傳效果，並且進行對稱面以及整體加熱平板模擬結果與二維模擬的差異，探討三維牆邊界之重要性，是否可以忽略，最後以模擬結果建立摩擦係數和紐賽數之關係式，以利設計最佳之史特靈引擎熱交換器。
從研究結果中我們可以得知，在對稱面的部分，摩擦係數在低無因次寬度時有著稍微較大的變化，而隨著無因次寬度的提高，摩擦係數仍呈一定值，而紐賽數在對稱面各有一最大與最小值，且無因次寬度於25之後則逐漸與二維模擬結果吻合；從整體平板來看，無因次寬度不影響摩擦係數的改變，僅有動力雷諾數會影響摩擦係數，且動力雷諾數越高，與二維模擬結果的差距越大，即使在對稱面紐賽數有與二維相同之結果，與其他位置仍相差甚多，因此三維邊界在堆疊式平板中佔有一定重要性，而在無因次寬度為10時，各動力雷諾數皆有一最高之時間空間平均紐賽數，因此在此模型中，無因次寬度10為最適當之選擇。
從此研究結果了解到，「環效應(annular effect，往復流中最大軸向速度以及最大溫度梯度)」不僅存在於往復管流中，也存在於三維堆疊式平板往復流中，且其影響力不容小覷。
最後，利用這些模擬資料點，建立時間空間平均摩擦係數、紐賽數之關係式，以動力雷諾數、無因次寬度表示，從關係中我們也可得知參數對於摩擦係數、紐賽數的影響力，以利設計者設計最佳之史特靈引擎熱交換器。

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.

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