基於流體體積法之兩相流(包含熱質傳)數值方法及其應用

Abstract

本研究最主要的目標是發展一套可用於非結構性網格中的含相變化的兩相流數值方法。基於流體體積法(VOF)，本文提出兩套相關的計算方法。第一種方法稱為通量混合介面捕捉法(FBICS)，其是透過直接求解流體體積分率的傳輸方程式來捕捉介面的運動。在計算的過程中，為了同時維持介面的鮮明度及體積分率的界限性，本研究是使用通量混合的方式來處理網格控制面上所需要的對流通量，然而本方法的缺點在於其所獲得的介面通常佔據了多個網格的寬度。另外一套方法則稱為守衡內插介面追蹤法(CISIT)，本方法是先以內差的方式重建介面後，再以先預測後修正的方式處理介面的移動。此方法計算後所得的流體體積分率分布，除了介面所在的網格外，其餘皆是0或1的均勻分布，而且介面只有佔據一個網格的寬度。不同於PLIC法，由於CISIT法的方法相當簡單，因此可輕易地在幾何外觀較為複雜的非結構性網格中使用，而且不需任何複雜的處理便可推展至三維的問題之中。在PLIC法中，其介面重建的方式並非簡單容易處理的，而且在計算面上體積通量時必須考慮許多類型的介面形狀(二維流場中有16種情形而三維則有64種)來進行，因此也造成其介面推移的計算上相當複雜。經由許多問題的測試，可知本研究的兩套數值方法於自由表面流中模擬後所得的結果與理論解或實驗數據都相當吻合並且可在非結構性的網格中所使用。 接著為了能夠模擬含相變化的兩相流問題，本研究特別將相變化所產生的質熱傳效應導入守衡內插介面追蹤法之中。經由介面處質量及能量的跳躍邊界條件可獲得通過介面的質傳量並將此質傳量以源項的方式導入連續方程式之中。然後，對於溫度場而言本研究是將介面視為一組能量內邊界的方式來處理，並且最後將以全隱性的求解方式來計算能量方程式。此外，基於假設介面處溫度及熱傳量連續性的條件來取代跳躍邊界，本方法亦可推展至模擬無相變化的雙流體熱傳問題。將本方法應用於鄰近臨界壓力的水平平板薄膜沸騰問題中，其結果顯示在不同的壁過熱溫度下將有不同的沸騰模式出現。根據不同的壁面過熱度，沸騰的模式主要可分為五種：單氣泡模式( )、單/多氣泡模式( )、單噴流模式( )、雙氣泡模式( )及雙噴流模式( )。在單氣泡模式中，模擬所得的時均化Nusselt數與半經驗式之結果相當一致。再者，透過模擬水平圓管的薄膜沸騰問題可以證明本文所提出的含相變化之兩相流數值方法可使用於複雜幾何外觀的沸騰流動中。 本文最後將含相變化的守衡內插介面追蹤法修改為可用於計算三維兩相流的流場之中。不同於二維的流場，在網格中本研究是使用多個不共面的三角形介面來進行三維介面的重建。本方法首先透過許多不含相變化的雙流體問題來驗證其在三維流場中對於介面追蹤及預測的能力。另外，也將本方法應用至三維水平平板的薄膜沸騰流動之中。結果顯示利用本方法模擬所獲得的時均化Nusselt數與Klimenko所提出的半經驗公式之結果相當吻合，尤其是在壁過熱度為10℃的情況下。最後，無相變化的熱傳模型也用於模擬油槽內的熔解錫液滴及水中的高溫辛烷噴流之問題中。

This paper is aimed at developing a numerical method for two-phase flows with phase change on unstructured grids. In this article, two schemes are presented based on VOF (volume-of-fluid) method. The first scheme is to capture the interface by solving the advection equation of the volume fraction directly, termed as FBICS. In order to maintain the sharpness and boundedness of the interface, the convective flux through each cell face is determined by means of flux blending. The weakness of this method is that the interface region will occupy several grid spaces. In the other scheme (termed as CISIT), the interface is reconstructed first using interpolation practice, following by a predicted-correction procedure to handle the movement of the interface. Except for the interface cells, the VOF distribution is uniform, either in 1 or 0, and the interface occupies only one cell in its width. Unlike the PLIC method, the CISIT can be easily extended to unstructured grids with arbitrary geometry and 3-D problems without causing any further complication because its formulation is very simple. In PLIC, the reconstruction of the interface is not straightforward and the procedure to advance the interface is complicated because a large number of interface configurations (16 configurations for 2-D flows and 64 for 3-D flows) must be considered for determining of the flux across cell faces. Tests on a number of cases reveal that results via these two schemes in this study, which can be used on the unstructured grids, give good agreement with exact solutions or experimental data of free surface flows. In order to simulate the two-phase flow with phase change, the CISIT method is extended to include heat and mass transfer due to phase change. The mass transfer across the phase boundary is determined by taking into account the mass and energy jump conditions at the interface and added as a source term in the continuity equation. Then, the interface is treated as an internal boundary condition in the temperature flied. Finally, the energy equation is solved in an implicit way. Besides, this method is also extended to simulate the heat transfer of two-fluid flows without phase change based on the assumption of the continuity conditions of the temperature and heat flux instead of jump conditions at the interface. Application to film boiling flow on a horizontal plate at a state near the critical pressure shows that the boiling mode will be different at different superheat temperatures. According to different superheat tempera- tures, the boiling flows can be divided into five modes: single-bubble mode ( ), single/multiple bubble mode ( ), single-jet mode ( ), double-bubble mode ( ), and double-jet mode ( ). In the single-bubble mode, good agreement with semi-empirical correlations was obtained in terms of averaged Nusselt number. Furthermore, simulation of film boiling flow on a cylinder demonstrates that this method is applicable to boiling flow with complex geometry. Finally, the CISIT method with phase change is modified to calculate three-dimensional two-phase flows. Unlike two-dimensional flow, the interface is reconstructed with several non-coplanar triangular interfaces within the grid. First, this method was tested through computations of a number of two-fluid flows without phase change to validate the capability of tracking the interface in three- dimensional flows. In addition, this method was also applied to simulated film boiling flow on a horizontal plate. It can be shown that the space and time averaged Nusselt numbers obtained from the current simulations have good agreement with the semi-empirical correlations of Klimenko, especially for .Finally, the heat transfer model without phase change was used to simulate the molten tin droplet in oil and the octane inlet in water.