平面叶栅跨音流场气动特性的数值研究

通过对模型方程的分析，给出了一种新的隐格式构造思想。将它运用到关通量分裂格式中，可得到无近似因子分解、无矩阵运算的高效二阶精度隐式矢通量分裂差分格式，并用来直接求解时间平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组。数值计算标明：该方法具有精度高、稳定性好、计算量少、收敛快等优点，在平面叶栅跨音流场的计算中，较好地捕获了激波，与实验比较，结果令人满意。     

高精度迎风紧致差分格式与热流计算研究的注记

利用高精度差分格式求解了可压缩 N-S方程球头热流问题。分析了不同差分格式在对球头粘性绕流热流计算中存在的问题 ,并分析了相应的网格雷诺数。在利用高精度迎风紧致 [1 ] 格式求解粘性绕流热流问题时 ,采用 Steger-Warming[2 ]的通量分裂技术将守恒型方程中的流通向量分裂成两部分 ,在此基础上据风向构造逼近于无粘项的高精度迎风格式。对方程中的粘性部分采用中心差分格式。数值结果表明 :高精度差分格式能在较大的网格雷诺数下较好地计算球头驻点热流     

一种求解Euler方程的新型高阶精度数值方法

提出了一种求解Euler方程的新型高阶精度数值方法.该数值方法基于一种新的矢通量分裂格式,将矢通量项分裂成压力通量项和对流通量项.与传统矢通量分裂格式相比,新的矢通量分裂格式能够更好地捕捉特征场内的中间特征波,从而增强格式的分辨率.同时,为了提高这种矢通量分裂格式的空间精度,我们在近似求解压力通量项黎曼问题时对界面处的独立物理变量进行高阶插值.在时间步上,采用显式最优的三阶龙格-库塔方法进行推进.数值试验表明,与传统数值方法相比,本文提出的新方法同时具有高精度和高分辨率的优点.     

数值求解Navier—Stokes方程的迎风紧致差分格式

从迎风紧致逼近^[1]出发,提出数值求解可压Navier-Stokes方程的一种高精度的数值方法。利用Steger-Warming的通量分裂技术^[2]将守恒型方程中的流通向量分裂成两部分,在此基础上据风向构造逼近于无粘项的三阶迎风紧致有限差分格式。对方程中的粘性部分采用通常的二阶差分逼近。所建立的差分格式被用来数值求解了三维粘性绕流问题。     

N-S方程在非结构网格下的求解

在Ｒｏｅ的矢通量差分分裂的基础上，吸收了ＮＮＤ格式的优点，提出了一种非结构网格下求解Ｅｕｌｅｒ方程和Ｎ－Ｓ方程的高分辨率高精度迎风格式．这种格式具有捕捉强激波和滑移线的良好性能．在时间方向上采用了显式和隐式两种解法．文中还给出了自适应技术．最后，成功地完成了ＧＡＭＭ超音速前台阶绕流、二维平板无粘激波反射、三维Ｈｏｂｓｏｎ叶栅流动、ＶＫＩ叶栅流动、Ｃ３Ｘ叶栅流动的数值模拟，得到了满意的结果     

一种激波稳定的对流-压力通量分裂格式

针对欧拉方程三种流行的对流-压力通量分裂方法(Liou-Steffen,Zha-Bilgen和Toro-Vázquez)进行特征分析,进而提出一种新的对流-压力通量分裂格式。采用Zha-Bilgen分裂方法将欧拉方程的通量分裂成对流项和压力项两部分,使用TV格式来计算这两部分的数值通量。利用压力比构造激波探测函数,并且在强激波附近的亚声速区域增加TV格式的剪切粘性来克服数值模拟中的激波不稳定性。数值算例的计算结果表明,新的对流-压力通量分裂格式不仅保留了原始TV格式精确分辨接触间断的优点,而且具有更好的鲁棒性,在数值模拟多维强激波问题时不会出现不稳定现象。因此,该格式是一种精确并且具有强鲁棒性的数值方法,可以广泛地应用于可压缩流体的数值计算中。     

二维双曲型守恒律的一种五阶松弛格式

松弛格式是Jin和Xin提出的无振荡有限差分方法,其主要思想是将守恒律转化为松弛方程组进行求解.本文用逐维五阶WENO重构和显隐式Runge-Kutta方法对松弛方程组的空间和时间进行离散,得到了一种求解二维双曲型守恒律五阶松弛格式.所得格式保持了松弛格式简单的优点,不用求解Riemann问题和计算通量函数的雅可比矩阵.通过二维Burgers方程和二维浅水方程的数值算例验证了格式的有效性.     

一种新的隐格式构造及在跨音流动中的应用

本文提出了一种任意曲线坐标系下的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组的隐式矢通量分裂格式的构造方法．该方法避开了近似因子分解、无矩阵运算，具有精度高、稳定性好、计算量少等优点．在扩压器进气道跨音流场的计算中，准确地捕获了激波，与实验比较，结果令人满意．     

非结构混合网格化学非平衡粘性绕流数值模拟

在非结构混合网格上对化学非平衡粘性绕流进行了数值模拟。控制方程为考虑了化学非平衡效应的二维Navier-Stokes方程,化学动力学模型为7组元、7反应模型。控制方程中的对流项采用VanLeer逆风分裂格式处理,并应用MUSCL方法及Minmod限制器扩展到二阶精度,粘性项用中心差分格式处理。时间推进采用显式5步龙格-库塔方法。为了适应高超声速流场计算,对VanLeer通量分裂方法进行了改进,并引入了化学反应时间步长。对RAMC-II模型的飞行试验流场进行了数值模拟,计算结果与试验测量数据符合较好,并与参考文献中的数值模拟结果吻合。     

用三维半人工瞬变法计算圆管内圆柱绕流

本文提出一种计算三维定常流动的半人工瞬变法,本方法的特点是直接利用流体力学的原始基本方程组进行数值计算。运动方程中的一个分量方程被用于计算压力,另外两个分量方程被加入人工瞬变项而成为人工瞬变方程,这两个人工瞬变方程被用于计算速度的两个分量,第三个速度分量则通过连续性方程进行计算得到。根据半人工瞬变方程组的特点和流动区域的特性,本方法采用半交错不等距非正交曲线贴体混合网格系进行数值计算,并利用质点导数差分格式使计算更简便。本文以圆管中不可压缩流体对圆柱的三维定常绕流问题为算例,具体画出计算用的半交错不等距非正交曲线贴体混合网格系,介绍三维半人工瞬变法的计算方法和步骤,并通过数值计算得到了此算例的计算结果。     

THE SOLUTION FOR TRANSIENT TWO-PHASE FLOW BY SPLIT FLUX VECTOR METHOD

In this paper the transient two-phase flow equations and their eigenvalues are first intreduced. The flux vector is then split into subvectors which just contain a specially signed eigenvalue. Using one-sided spatial difJerence operators finite difference equations and their solutions are obtained. Finally comparison with experiment shows the predicted results produce good agreement with experimental data.     

Analysis of frictionless two-phase flow in tubes under centrifugal acceleration and minimum heating for choked flow

To determine the void fraction in a tube of a rotating heat exchanger, an analytical investigation was undertaken to model frictionless two-phase flow boiling. Steady, one-dimensional separated two-phase conservation equations in differential form, were first applied to a stationary system. The equations were integrated between the inlet and exit of the flow channel to yield three coupled algebraic equations. The algebraic equations were then modified to represent rotating systems. To obtain closure, the velocity ratio, mass quality and void fraction are defined as a function of pressure.

A numerical technique was used to solve the equations. Sample results are presented in a graph of mass quality versus void fraction. The graph demonstrates that a minimum heat input must be exceeded to change from a single-phase flow to saturated two-phase flow boiling. Also, the void fraction was found to increase for increasing heat input, decreasing mass flow rate, increasing inlet mass quality and decreasing pressure difference between the inlet and exit.     

Modeling transient churn-annular flows in a long vertical tube

This work investigates the transient behavior of high gas fraction gas-liquid flows in vertical pipes (annular and churn flows). Hyperbolic balance equations for mass, momentum and entropy are written for the gas and liquid, which is split between a continuous film and droplets entrained in the gas core. Closure relationships to calculate the wall and interfacial friction and the rates of droplet entrainment and deposition were obtained from the literature. A finite-difference solution algorithm based on a coefficient matrix splitting method was implemented to deal with sharp variations in the spatial and temporal domains, such as pressure and phase holdup waves. The model results were compared with steady-state experimental data from eight different sources, totaling more than 1500 data points for pressure gradient, liquid film flow rate and void/core fraction. The absolute average deviation between the model and the data was 17% for the pressure gradient and 5.8% for the void fraction. A comparison of the model results with fully transient air-water data generated in a 49-mm ID, 42-m long vertical pipe is also presented. The experimental results consist of two outlet pressure-induced and two inlet mass flow rate-induced transient tests. Two main transient parameters are compared, namely the local void fraction and the pressure difference between selected points along the test section and the outlet (taken as a reference). The comparisons between the experiments and the numerical model indicate that the model was capable of describing the transient annular to churn flow transition with absolute average deviations of 14.5% and 7.9% for the pressure difference and void fraction, respectively.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

Finite element solution of multi-dimensional two-phase flow through porous media with arbitrary heating conditions

Mechanistic models for flow regime transitions and drag forces proposed in an earlier work are employed to predict two-phase flow characteristics in multi-dimensional porous layers. The numerical scheme calls for elimination of velocities in favor of pressure and void fraction. The momentum equations for vapor and liquid then can be reduced to a system of two partial differential equations (PDEs) which must be solved simultaneously for pressure and void fraction.

Solutions are obtained both in two-dimensional cartesian and in axi-symmetric coordinate systems. The porous layers in both cases are composed of regions with different permeabilities. The finite element method is employed by casting the PDEs in their equivalent variational forms. Two classes of boundary conditions (specified pressure and specified fluid fluxes) can be incorporated in the solution. Volumetric heating can be included as a source term. The numerical procedure is thus suitable for a wide variety of geometry and heating conditions. Numerical solutions are also compared with available experimental data.     

Void fraction measurement of bubble and slug flow in a small channel using the multivision technique

Using the multivision technique, a new void fraction measurement method was developed for bubble and slug flow in a small channel. The multivision system was developed to obtain images of the two-phase flow in two perpendicular directions. The obtained images were processed—using image segmentation, image subtraction, Canny edge detection, binarization, and hole filling—to extract the phase boundaries and information about the bubble or slug parameters. With the extracted information, a new void fraction measurement model was developed and used to determine the void fraction of the two-phase flow. The proposed method was validated experimentally in horizontal and vertical channels with different inner diameters of 2.1, 2.9, and 4.0 mm. The proposed method of measuring the void fraction has better performance than the methods that use images acquired in only one direction, with a maximum absolute difference between the measured and reference values of less than 6%.     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.     

An application of the wavelet analysis technique for the objective discrimination of two-phase flow patterns

This paper presents an application of the wavelet analysis technique for two-phase flow pattern identification by using the void fraction signals obtained from a multi-channel Impedance Void Meter (IVM) in a vertical-upward air–water flow. A new method for the objective discrimination of the two-phase flow pattern has been developed to provide information regarding the local energy of void fraction signals at a given scale on the joint time–frequency diagram. The void signals are processed with Continuous Wavelet Transform (CWT) to get the local wavelet energy coefficients map on the time–frequency diagram. The effective local wavelet energy and the effective scale are then calculated. Then the criteria for flow pattern identification are, finally, obtained. A series of void fraction measurements were conducted over a wide range of air–water vertical-upward flow condition to provide an extensive database to cover several types of flow patterns. The results show that the proposed method has a high precision for characterizing different flow regimes in two-phase flow, and is considerably more promising for the online recognition of two-phase flow patterns due to the short time of data processing.     

The prediction of two-phase mixture level and hydrodynamically-controlled dryout under low flow conditions

A theory is given for the thermal-hydraulic phenomena during uncovery of a flow channel. This is relevant to a reactor core under typical small break or operational transient conditions. A distinct equivalent collapsed liquid level and a two-phase-mixture level are defined in the model. The former represents the liquid inventory in the channel, while the latter characterizes the heat transfer regimes. The definition of these levels are coupled through the mass and energy conservation equations, and the constitutive relations for void fraction and net vapor generation location.Analytical solutions are obtained for the transient variation of both the collapsed liquid and the two-phase mixture levels.The analyses have been compared with existing single-tube data with uniform heat flux, and rod bundle experiments with an axial power profile and inlet feedwater flow. The results demonstrate the potential of the present model for application to reactor conditions.     

On the Construction of an Experimentally Based Set of Equations to Describe Cocurrent and Countercurrent, Two-Phase Flow of Immiscible Fluids Through Porous Media

Generalized flow equations developed for two-phase flow through porous media contain a second term that enables proper account to be taken of capillary coupling between the two flowing phases. In this study, a partition concept, together with a novel capillary pressure equation for countercurrent flow, have been introduced into Kalaydjian’s generalized flow equations to construct modified flow equations which enable a better understanding of the role of capillary coupling in horizontal, two-phase flow. With the help of these equations it is demonstrated that the reduced flux observed in countercurrent flow, as compared to cocurrent flow, can be explained by the reduction in the driving force per unit volume which comes about because of capillary coupling. Also, it is shown experimentally that, because fluids flow through a void space reduced in magnitude due to the presence of immobile irreducible and residual saturations, the capillary coupling parameter should be defined in terms of a reduced porosity, rather than in terms of porosity. Moreover, it is shown statistically that the countercurrent relative permeability curve is proportional to the cocurrent relative permeability curve, the constant of proportionality being the capillary coupling parameter. Finally it is suggested that one can eliminate the need to determine experimentally countercurrent relative permeability curves by making use of an equation constructed for predicting the magnitude of the capillary coupling parameter.