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To analyze two‐phase flow in micro‐channel heat exchangers used for high flux micro‐electronics cooling and to obtain performance parameters such as thermal resistance, pressure drop, etc. Both uniform and non‐uniform micro‐channel base heat fluxes are considered.

Energy balance equations are developed for two‐phase flow in micro‐channels and are solved using the finite element method (FEM). A unique ten noded element is used for the channel descritization. The formulation also automatically takes care of single‐phase flow in the micro‐channel.

Micro‐channel wall temperature distribution, thermal resistance and the pressure drop for various uniform micro‐channel base heat fluxes are obtained, both for single‐ and two‐phase flows in the micro‐channel. Results are compared against data available in the literature. The wall temperature distribution for a particular case of non‐uniform base heat flux is also obtained.

The analysis is done for a single micro‐channel and the effects of multiple or stacked channels are not considered. The analysis needs to be carried out for higher heat fluxes and the validity of the correlation needs to be ascertained through experimentation. Effects of flow mal‐distribution in multiple channels, etc. need to be considered.

The role of two‐phase flow in micro‐channels for high flux micro‐electronics cooling in reducing the thermal resistance is demonstrated. The formulation is very useful for the thermal design and management of microchannels with both single‐ and two‐phase flows for either uniform or non‐uniform base heat flux.

A simple approach to accurately determine the thermal resistance in micro‐channels with two‐phase flow, for both uniform and non‐uniform base heat fluxes is the originality of the paper.

An easy‐to‐use numerical model for transient two‐phase pipe flow analyses was developed by applying the split‐coefficient matrix method (SCMM) to a homogeneous equilibrium two‐phase flow model. The basic idea of the SCMM is to split the Jacobian coefficient matrix into two sub‐vectors, each associated with eigenvalues of the same sign. Hence, one‐sided finite difference schemes can accordingly be applied to the sub‐vectors. The present model was validated against experiments. It is numerically stable provided that a criterion is met due to the use of a time explicit format. The satisfactory agreement between the numerical and experimental results indicates that the model may be used as a simple, efficient tool for general engineering analyses of transient two‐phase flow. The advantages of applying SCMM to transient two phase flows are briefly addressed, and it is applicable to systems having real eigenvalues.

A mathematical model is developed for the description of the thermohydraulics of the two‐phase flow phenomenon in a vertical pipe. Using an additional momentum equation for the slip velocity, it is shown that the computation of slip and pressure drop from the model equations is possible without the use of any external correlations. The finite element method is used to solve the governing equations. The predictions for a steam‐water two‐phase flow in vertical upflow with constant wall heat flux agree well with experimental results and with widely used correlations.

The purpose of this paper is to compute the pressure drop through sudden expansions and contractions for two‐phase flow of oil/water emulsions.

Two‐phase computational fluid dynamics (CFD) calculations, using Eulerian–Eulerian model, are employed to calculate the velocity profiles and pressure drops across sudden expansions and contractions. The pressure losses are determined by extrapolating the computed pressure profiles upstream and downstream of the expansion/contraction. The oil concentration is varied over a wide range of 0‐97.3 percent by volume. The flow field is assumed to be axisymmetric and solved in two dimensions. The two‐dimensional equations of mass, momentum, volume fraction and turbulent quantities along with the boundary conditions have been integrated over a control volume and the subsequent equations have been discretized over the control volume using a finite volume technique to yield algebraic equations which are solved in an iterative manner for each time step. The realizable per phase k‐ ε turbulent model is considered to update the fluid viscosity with iterations and capture the individual turbulence in both the phases.

The contraction and expansion loss coefficients are obtained from the pressure loss and velocity data for different concentrations of oil–water emulsions. The loss coefficients for the emulsions are found to be independent of the concentration and type of emulsions. The numerical results are validated against experimental data from the literature and are found to be in good agreement.

The present computation could not use the surface tension forces and the energy equation due to huge computing time requirement.

The present computation could compute realistically the two‐phase pressure drop through sudden expansions and contractions by using a two‐phase Eulerian model and hence this model can be effectively used for industrial applications where two‐phase flow comes into picture.

The original contribution of the paper is in the use of the state‐of‐the‐art Eulerian two‐phase flow model to predict the velocity profile and pressure drop through industrial piping systems.

Numerical results are reported for a dilute turbulent liquid‐solid flow in an axisymmetric sudden‐expansion pipe with an expansion ratio 2:1. The two‐phase flow has a mass‐loading ratio low enough for particle collision to be negligible. The numerical predictions for the dilute two‐phase flow are based on a hybrid Eulerian‐Lagrangian model. A nonlinear k‐ε model is used for the fluid flow to account for the turbulence anisotropy and an improved eddy‐interaction model is used for the particulate flow to account for the effects of turbulence anisotropy, turbulence inhomogeneity, particle drift, and particle inertia on particle dispersion. The effects of the coupling sources, the added mass, the lift force and the shear stress on two‐phase flow predictions are separately studied. The numerical predictions obtained with the improved and conventional particle dispersion models are compared with experimental measurements for the mean and fluctuating velocities at the different measured planes.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain represents a one‐ended pipe with holes at its upper wall which lead into an enclosure. The aim of this study is to determine the parameters of such a flow. More specially, an analytical solution is compared with numerical results to assess the mass flow rates through the vents in the pipe. Inertia effects dominate the dynamic behaviour of droplets, which causes a non‐homogeneous flow in the cavity. The unsteady effects are also important, which makes isentropical calculation irrelevant and shows the necessity of the use of CFD tools to predict such flows. No relation can be extracted from the numerical results between the gas and the dispersed mass flow rates across the holes. But a linear variation law for the droplet mass flow versus the position of the holes is pointed out, which is independent of the incoming flow when the evaporating effects are quite low.

The purpose of this paper is to study the transition process from the crystalline particles appearing before the pump inlet to the stable operation of the pump.

Firstly, a modeling test method was put forward for the high-temperature molten salt pump. Then, according to a modeling test scheme, the experiment of the solid–liquid two-phase flow was carried out by using a model pump similar to the prototype pump. Meanwhile, the numerical method to simulate the transition process of a molten salt pump was studied, and the correctness of the numerical model was verified by the experimental results. Finally, the transition process of the molten salt pump was studied by the verified numerical model in detail.

In the simulation of the transition process, it is more accurate to judge the end of the transition process based on the unchanged particle volume fraction (PVF) at the pump outlet than on the periodic fluctuation of the outlet pressure. The outlet pressure is closely related to the PVF in the pump. The variation of the outlet pressure is slightly prior to that of the PVF at the pump outlet and mainly affected by the PVF in the impeller and volute. After 0.63 s, the PVF at each monitoring point changes periodically, and the time-averaged value does not change with time.

This study is of great significance to further improve the design method of molten salt pump and predict the abrasion characteristic of the pump due to interactions with solid particles.

A numerical method is established to simulate the transition process of a molten salt pump, and a method is proposed to verify the numerical model of two-phase flow by modeling test.

This paper investigates the multi‐phase behaviour of droplets injected into a nozzle at two separate wall locations. The physical features of the droplets (rate of mass, density and radius) at each injector location are identical. This system can be described by a two‐phase Eulerian—Eulerian approach that yields classical systems of equations: three for the gaseous phase and three for the dispersed droplet phase. An underlying assumption in the two phase model is that no interaction occurs between droplets. The numerical solution of the model (using the MacCormack scheme) indicates however that the opposite jets do interact to form one jet. This inconsistency is overcome in the current paper by associating the droplets from a given injection location with a separate phase and subsequently solving equations describing a multiphase system (here, three‐phase system). Comparison of numerical predications between the two‐phase and the multiphase model shows significantly different results. In particular the multiphase model shows no jet interaction.

This paper deals with a numerical simulation of the thermal and fluid‐dynamic behaviour of double‐pipe condensers and evaporators. The governing equations of the fluid flow (continuity, momentum and energy) in both the tube (evaporating or condensing flow) and the annulus (single‐phase flow), together with the energy equation in the tube wall, are solved iteratively in a segregated manner using a one‐dimensional, transient formulation, based on an implicit step by step numerical scheme in the zones with fluid flow (tube and annulus), and an implicit central difference numerical scheme in the tube wall, solved by means of the Tri‐Diagonal Matrix Algorithm (TDMA). This formulation requires the use of empirical information for the evaluation of convective heat transfer, shear stress and void fraction. Two criteria to calculate the location of the points of transition between single‐phase and two‐phase flow are tested. An analysis of the different parameters used in the discretization is made. Some illustrative results corresponding to the solution of a condenser and an evaporator using two different working fluids (R–12 and R–134a) are presented.