Two-phase Computational Fluid Dynamics Research Articles

Empirical correlations and CFD simulations of vertical two-phase gas–liquid (Newtonian and non-Newtonian) slug flow compared against experimental data of void fraction

Gas-Newtonian liquid two-phase flows (TPFs) are presented in several industrial processes (e.g. oil-gas industry). In spite of the common occurrence of these TPFs, the understanding of them is limited compared to single-phase flows. Various studies on TPF focus on developing empirical correlations based on large sets of experimental data for void fraction, which have proven accurate for specific conditions for which they were developed limiting their applicability. On the other hand, few studies focus on gas-non-Newtonian liquids TPFs, which are very common in chemical processes. The main reason is due to the characterization of the viscosity, which determines the hydraulic regime and flow behaviours of the system.The focus of this study is the analysis of the TPF (slug flow) for Newtonian and non-Newtonian liquids in a vertical pipe in terms of void fraction using computational fluid dynamics (CFD) and comparing this directly with experimental measurements and empirical relationships found in literature. A vertical tube of 3.4m with an internal diameter of 0.1905m was used. The two-phase CFD model was implemented in Star CCM+ using the volume of fluid (VOF) model.A relatively good agreement was found between the experimental measurements, the CFD results and the empirical relationships. In terms of void fraction for Newtonian and non-Newtonian liquids, the empirical correlations perform much worse than the CFD simulations, errors of 48 and 25%, respectively, against the experimental data. This shows that CFD can be used to predict void fraction relatively well for comparison against empirical correlations and they can be used for design and scale-up processes.

Numerical investigation of single phase and two phase flow through thin orifices in horizontal pipes

Pressure drop due to single phase flow of water and two phase flow of air-water mixture through thin orifices in horizontal pipes have been numerically investigated. Two-phase computational fluid dynamics (CFD) calculations, using Eulerian–Eulerian model have been employed to calculate the pressure drop through orifices. The operating condition covers the gas and liquid superficial velocity ranges Vsg=0.3–4 m/s and Vsl=0.6–2 m/s, respectively. The local pressure drops have been obtained by means of extrapolation from the computed upstream and downstream linearized pressure profiles to the orifice section. Simulations for the single-phase flow of water have been carried out for local liquid Reynolds number (Re based on orifice diameter) ranging from 3×104 to 2×105 to obtain the discharge coefficient and the two-phase local multiplier, which when multiplied with the pressure drop of water (for same mass flow of water and two phase mixture) will reproduce the pressure drop for two phase flow through the orifice. The effect of orifice geometry on two-phase pressure losses has been considered by selecting eight different orifice plates with two area ratios (σ=0.73 and σ=0.54) and four different thicknesses (s/d = 0.025-0.59). The results obtained from numerical simulations are validated against experimental data from the literature and are found to be in good agreement. Keywords: Orifice, Pressure drop, Two phase flow, Computational fluid dynamics, Area ratio, Discharge coefficient

Single-Phase and Two-Phase Flow Through Thin and Thick Orifices in Horizontal Pipes

Two-phase flow pressure drops through thin and thick orifices have been numerically investigated with air–water flows in horizontal pipes. Two-phase computational fluid dynamics (CFD) calculations, using the Eulerian–Eulerian model have been employed to calculate the pressure drop through orifices. The operating conditions cover the gas and liquid superficial velocity ranges Vsg = 0.3–4 m/s and Vsl = 0.6–2 m/s, respectively. The local pressure drops have been obtained by means of extrapolation from the computed upstream and downstream linearized pressure profiles to the orifice section. Simulations for the single-phase flow of water have been carried out for local liquid Reynolds number (Re based on orifice diameter) ranging from 3 × 104 to 2 × 105 to obtain the discharge coefficient and the two-phase local multiplier, which when multiplied with the pressure drop of water (for same mass flow of water and two phase mixture) will reproduce the pressure drop for two phase flow through the orifice. The effect of orifice geometry on two-phase pressure losses has been considered by selecting two pipes of 60 mm and 40 mm inner diameter and eight different orifice plates (for each pipe) with two area ratios (σ = 0.73 and σ = 0.54) and four different thicknesses (s/d = 0.025–0.59). The results obtained from numerical simulations are validated against experimental data from the literature and are found to be in good agreement.

New insights into retention aids dosage and mixing

Abstract In this work, critical design and operational parameters for retention aids dosage are studied through a combination of computational fluid dynamics (CFD), experimentation and pilot-scale production trials. In the first part of this work, three different retention aids dosage strategies are investigated in conjunction with pilot scale production trials. In all dosage strategies, a maximum in the percentage filler retention was observed at a speed ratio of 1.1, while considerably lower retention levels were observed when the speed ratio was greater than 2.2. However, the different dosage strategies led to markedly different retention of filler material. In the second part of this work, two-phase computational fluid dynamics (CFD) was used to model the three different dosage strategies implemented in the pilot production trials. The location and magnitude of maximum strain in each nozzle was determined and for each dosage case this was found to occur just outside the dosage nozzle at the point of impingement between the dosage and outer flows. In the third part of this work, conditions leading to the onset of retention polymer degradation were determined using an experimental flow loop. The effect of dosage speed and elongational strain created inside the dosage nozzle were studied systematically. These experiments showed that the effect of relative dosage velocity on polymer degradation was minimal. However, large levels of polymer degradation were observed when the elongational strain in the dosage nozzle was increased, i.e. when the exit nozzle diameter was decreased. Together, the three sets of experiments suggest that elongational strain during dosage degrades retention aids polymers and therefore hinders filler retention during production.

Numerical Investigation of Single Phase and Two Phase Flow through Thin Orifices in Horizontal Pipes

Pressure drop due to single phase flow of water and two phase flow of air-water mixture through thin orifices in horizontal pipes have been numerically investigated. Two-phase computational fluid dynamics (CFD) calculations, using Eulerian-Eulerian model have been employed to calculate the pressure drop through orifices. The operating condition covers the gas and liquid superficial velocity ranges V sg =0.3-4 m/s and V sl =0.6-2 m/s, respectively. The local pressure drops have been obtained by means of extrapolation from the computed upstream and downstream linearized pressure profiles to the orifice section. Simulations for the single-phase flow of water have been carried out for local liquid Reynolds number (Re based on orifice diameter) ranging from 3×10 4 to 2×10 5 to obtain the discharge coefficient and the two-phase local multiplier, which when multiplied with the pressure drop of water (for same mass flow of water and two phase mixture) will reproduce the pressure drop for two phase flow through the orifice. The effect of orifice geometry on two-phase pressure losses has been considered by selecting eight different orifice plates with two area ratios (σ=0.73 and σ=0.54) and four different thicknesses (s/d = 0.025-0.59). The results obtained from numerical simulations are validated against experimental data from the literature and are found to be in good agreement.

CFD Simulation of Hydraulics of Dividing Wall Sieve Trays

A 3D two-phase flow computational fluid dynamics (CFD) model containing gas mal-distribution is developed in the Eulerian framework to predict the hydraulics of a dividing wall sieve tray. Variable and position dependent gas superficial velocity is used in the calculation. Using water-air system, simulations of flow patterns and hydraulics of a commercial- scale 1.2m diameter sieve tray are carried out using this model to testify its precision. Then, the same simulations of a dividing wall sieve tray with equal diameter are carried out. The results show that there are two backflow regions on a dividing wall tray, one is in the segmental area, and the other is in the region nearby junction of dividing wall and outlet weir. In the segmental area of trays with equal diameter, the area of backflow region of dividing wall trays is basically equal to that of conventional trays.

3D Modeling and Simulation of a Two-Phase Mixing Jet Flow

Gas-solid mixing jet flows are an essential feature of typical chemical engineering processes. A proper analysis of the mixture flow optimizes process qualities and efficiencies. In this contribution, a numerical study of the solids dispersion in a two-phase jet flow is presented. The mathematical model treats the gas and the solid phases with an Eulerian approach. Radial profiles of the solid-phase mean velocity were computed on five axial levels, subdivided in five cases, in the mixing jet flow using a two-phase 3D computational fluid dynamics model. The computed solids velocities were compared with experimental data on a jet with an internal diameter of 12mm, at different inlet conditions of solid mass load for rates (3 to 7) and velocities (8 to 16m/s). The mean particle diameter used was 50μm and a density of 2500kg/m3.Three different drag models were applied to evaluate the solids dispersion, Wen and Yu [1], Gidaspow [2] and Massarani [3] correlations, the latter being a continuous one. The two-equation (k-e) turbulence model was employed to describe the gas-phase, while the zero-equation (kinematic viscosities analogy) turbulence model describing the solid-phase in a jet flow. The mathematical model predicts a developed flow regions similar to that found experimentally.

CFD Simulation of Annular Centrifugal Extractors

Annular centrifugal extractors (ACE), also called annular centrifugal contactors offer several advantages over the other conventional process equipment such as low hold-up, high process throughput, low residence time, low solvent inventory and high turn down ratio. The equipment provides a very high value of mass transfer coefficient and interfacial area in the annular zone because of the high level of power consumption per unit volume and separation inside the rotor due to the high g of centrifugal field. For the development of rational and reliable design procedures, it is important to understand the flow patterns in the mixer and settler zones. Computational Fluid Dynamics (CFD) has played a major role in the constant evolution and improvements of this device. During the past thirty years, a large number of investigators have undertaken CFD simulations. All these publications have been carefully and critically analyzed and a coherent picture of the present status has been presented in this review paper. Initially, review of the single phase studies in the annular region has been presented, followed by the separator region. In continuation, the two-phase CFD simulations involving liquid-liquid and gas-liquid flow in the annular as well as separator regions have been reviewed. Suggestions have been made for the future work for bridging the existing knowledge gaps. In particular, emphasis has been given to the application of CFD simulations for the design of this equipment.

Applicability of two-phase CFD to nuclear reactor thermalhydraulics and elaboration of Best Practice Guidelines

Two-phase Computational Fluid Dynamics (CFD) is now increasingly applied to some nuclear reactor thermalhydraulic investigations. A Writing Group of the OECD–NEA on the “Extension of CFD to two-phase safety issues” has identified a list of Nuclear Reactor Safety (NRS) issues for which the use of 2-phase CFD can bring a real benefit and proposed a general multi-step methodology. Various modeling options were identified and classified and some first Best Practice Guidelines (BPG) were proposed in the final report of the WG3. The purpose of this paper is to specify the methodology in more detail for the selection of model options, to discuss the conditions and limits of applicability of the various options. Four main modeling approaches are considered, the porous body approach, the RANS approach for open medium, the filtered methods, and the pseudo-DNS (Direct Numerical Simulation).A classification of the modeling approaches is proposed with a nomenclature. The conditions to ensure the consistency between the various choices and steps of the methodology are specified, including the coherence between turbulence and interface filtering, between averaging and formulation of the closure laws. A list of frequent errors is given. A checklist for application of two-phase CFD to reactor thermalhydraulic issues is proposed.

A Numerical Study on Defects in High Temperature Membranes through Solidification

Defects such as air bubbles in membranes have been shown to arise during manufacturing. These defects can lead to premature degradation or failure in applications such as fuel cells. In this numerical study, a non-isothermal two-phase computational fluid dynamics (CFD) model is created to investigate the behavior of air bubbles entrained in polyphosphoric acid doped polybenzimidazole (PPA/PBI) membrane solution during casting as it progresses through membrane solidification. The enthalpy-porosity method is used in the CFD model to simulate the solidification process. It is shown that initially the air bubbles are semi-circular. However, as the PPA/PBI solution solidifies and passes through the mushy zone, the shape of the air bubbles change to semi- elliptical. Hence, it is found that the air bubbles will not diffuse but rather remain in the membrane post solidification.

Performance evaluation of a direct methanol fuel cell: combination of three-dimensional computational fluid dynamic modelling and one-dimensional diffusion layer mathematical modelling

In this study, to define the distribution of CO2 and methanol concentration in the anode channel, three-dimensional (3D) two-phase homogeneous computational fluid dynamics (CFD) modelling for the anode channel and one-dimensional (1D) two-phase mathematical modelling for the porous media have been considered. In the anode channel, two flow configurations, single-serpentine flow field (SSFF), and parallel flow field (PFF) were studied. Here also, the effects of inlet mass flowrate, flow configurations, inlet temperature of aqueous solution, and inlet feed concentration on the CO2 concentration in the anode channel and cell performance have been investigated. To define the interface boundary conditions between the channel and diffuser layers, the CFD modelling of the anode channel was coupled with the mathematical modelling in the porous media. The results show that the corner of the channel rib is the proper site for coalescence of CO2 gas bubbles. The finer distribution of methanol concentration and less number of gas bubbles at the SSFF configuration have been observed. This leads to a better performance of the cell in the SSFF configuration relative to the PFF configuration. With increase of the mass flowrate, the molar concentration of CO2 (gas bubbles) reduces and the cell performance improves. With increase in the temperature of aqueous methanol solution, cell performance will improve. The main reasons should be attributed to the enhanced activity of the catalyst and increase of diffusion coefficient of the methanol solution. The CO2 gas bubbles will emerge more at higher temperatures, but it is clear that the effect of enhanced activity of the catalyst and increase of the diffusion coefficient of the methanol surmounts that of numerous CO2 gas bubbles, thus leading to the improvement of the cell performance.

Sprays in containment: Final results of the SARNET spray benchmark

The influence of containment sprays on atmosphere behaviour, a sub-task of the Work Package WP12-2 CAM (Containment Atmosphere Mixing), has been investigated through benchmark exercises based on TOSQAN (IRSN) and MISTRA (CEA) experiments. These tests are being simulated with lumped-parameter (LP) and Computational Fluid Dynamics (CFD) codes. Both atmosphere depressurization and mixing are being studied in two phases: a ‘thermalhydraulic part’, which deals with depressurization by sprays (TOSQAN 101 and MISTRA MASPn), and a ‘dynamic part’, dealing with light gas stratification break-up by spray (TOSQAN 113 and MISTRA MARC2b). In the thermalhydraulic part of the benchmark, participants have found the appropriate modelling to obtain good global results in terms of experimental pressure and mean gas temperature, for both TOSQAN and MISTRA tests. It can thus be considered that code users have a good knowledge of their spray modelling parameters. On a local level, for the TOSQAN test, single droplet behaviour is found to be well estimated by some calculations, but the global modelling of multiple droplets, i.e. of the spray, specifically for the spray dilution, is questionable in some CFD calculations. It can lead to some discrepancies localized in the spray region and can thus have a high impact on the global results, since most of the heat and mass transfers occur inside this region. In the MISTRA tests, wall condensation mass flow rates and local temperatures were used for code-experiment comparison and show that improvement of the local modelling, including initial conditions determination, is needed. In this dynamic part, a general result, in both tests, is that calculations do not recover the same kinetics of the mixing. Furthermore, concerning global mixing, LP contributions seem not suitable here. For the TOSQAN benchmark, the one-phase CFD calculations recover partially the phenomena involved during the mixing, whereas the two-phase flow CFD contributions generally recover the phenomena. Moreover, one important result is also that none of the contributions finds the exact amount of helium remaining in the dome above the spray nozzle in the TOSQAN 113. Discrepancies are rather high (above 5%vol of helium). Results are thus encouraging, but the level of validation should be improved. The same kind of conclusions can be drawn for the MISTRA MARC2B tests. As a conclusion of this SARNET spray benchmark, the level of validation obtained here is encouraging for the use of spray modelling for risk analysis. However, some more detailed investigations are needed to improve model parameters and decrease the uncertainty for containment applications as well as to increase the predictability of the phenomena within the containment analyses. Further activities are well encouraged on this topic, such as numerical benchmarks on analytical separate-effect experiments.

TWO-PHASE CFD: THE VARIOUS APPROACHES AND THEIR APPLICABILITY TO EACH FLOW REGIME

Two-phase Computational Fluid Dynamics (CFD) or CMFD (Computational Multi-Fluid Dynamics) is being applied to some nuclear reactor thermalhydraulic investigations. The NURESIM and NURISP projects of the European 5th and 6th Framework programs made some pioneering efforts to start some applications to a few selected reactor issues such as the Critical Heat Flux or the Pressurized Thermal shock. The extreme variety of flow configurations in steam-water two-phase flow makes the modeling issue very complex. Myriads of model options are available in the vast domain of CMFD, with various treatments of turbulence and of interfaces; the methods for choosing model options depending on the application have to be clarified. The purpose of this paper is to list and classify model options, to discuss some conditions and limits of applicability of the various options, and to identify the modeling needs for closure of the system of equations. The proposed classification of the modeling approaches is based on the space and time filtering or averaging of basic equations and on the number of phases and fields that are distinguished. The various flow processes that must be modeled by closure relations are identified for each type of approach. The applicability of each of these methods to each flow regime is defined and the present degree of maturity of the models is evaluated. Considering only Eulerian approaches used in an open medium, it is shown that five main approaches are considered: the RANS approach, the pseudo-DNS approach, and three types of space-filtered methods. Some of these methods can be applied only to a reduced number of flow regimes. Attention is drawn on the need to specify the model options, to guaranty the consistency between options, and to ensure completeness of closure terms. © 2011 by Begell House, Inc.

Numerical assessment of dependence of polymer electrolyte membrane fuel cell performance on cathode catalyst layer parameters

In this work, a three-dimensional, non-isothermal and two-phase computational fluid dynamics model of a proton exchange membrane (PEM) fuel cell with straight flow field channel is developed and validated. The model is used to predict the performance of the PEM fuel cell with changing parameters of the cathode catalyst layer which was usually assumed to be composed of spherical agglomerates. The effect of cathode catalyst layer parameters such as catalyst layer thickness, ionomer film thickness, agglomerate size and porosity, on the current density and power output of the PEM fuel cell is investigated. The numerical results reveal that competitive influence of resistances to transport of species, electron and proton within the cathode catalyst layer determines the performance of the PEM fuel cell in terms of area specific power density (W cm −2) and mass specific power density ( kW g Pt − 1 ).

Experimental and CFD Analyses of Bubble Parameters in a Variable-Thickness Fluidized Bed

Bubble characteristics in a variable-thickness fluidized bed containing nine tubes were experimentally investigated by analyzing absolute and differential pressure fluctuations. The latter were obtained from vertically aligned probes traversing the bed interior for three bed thicknesses: thin, square, and full. The important bubble parameters, namely, frequencies, effective diameters, and velocities, were determined by analyzing autocorrelations and cross-correlations obtained from these differential pressure signals for the thin and square beds. Wall effects were assessed by comparing the pressure fluctuations as the bed thickness was increased from thin to square. It was found that bubbles move faster within and above the tube bank than below it. This behavior was also found to be more pronounced in the wall regions of the full bed, which might explain why some commercial fluidized-bed combustors experience unusual metal wastage near their tube supports. Although bubble sizes consistently agreed between thin and square beds, bubble velocity reduction was observed for the thin bed. The experimental thin-bed differential pressure measurements were analyzed using a two-phase computational fluid dynamics (CFD) hydrodynamic model. Excellent agreement was obtained between the experimental results and predictions from our hydrodynamic model for autocorrelations, cross-correlations, power spectral densities, and bubble parameters.

A two-phase Eulerian approach using relative permeability concept for modeling of hydrodynamics in trickle-bed reactors at elevated pressure

Most commercial trickle-bed reactors (TBRs) employed in hydroprocessing and other industrially relevant operations normally operate at elevated pressures. Two-phase pressure drop and liquid holdup are two foremost important hydrodynamic parameters to consider for analysis and design of a TBR, including those operating at higher pressures. Even after several decades of research efforts directed towards the development of TBR technology, know-how about the hydrodynamics of two-phase flow in a TBR especially operating at high-pressure conditions has been inadequate. In this study, an effort has been made to assess the complex hydrodynamics of high-pressure TBR through the development of a Computational Fluid Dynamics (CFD) based model to predict pressure drop and liquid saturation. A two-phase Eulerian CFD model envisaging the flow field as porous region has been utilized for evaluating these hydrodynamic parameters. Different combinations of relative permeability correlations in the closure terms have been exercised to realize the best fit. The comparisons between model predictions and numerous experimental data, collected from different independent sources under a varied set of operating conditions, lead to the favourable implementation of this less computationally intensive, yet first-principle based CFD model to forecast the two-phase hydrodynamics for high-pressure TBRs.

Validation of NEPTUNE_CFD Module with Data of a Plunging Water Jet Entering a Free Surface

This work presents a validation of NEPTUNE_CFD against plunging water jet experiments by Iguchi et al., with sensitivity tests to turbulence modeling. NEPTUNE_CFD is the thermal-hydraulic two-phase computational fluid dynamics tool of NURESIM (European Platform for Nuclear Reactor Simulations) and is designed to simulate two-phase flow in situations encountered in nuclear power plants. Iguchi et al.’s flow configuration shares common physical features with the emergency core cooling injection in a pressurized water reactor uncovered cold leg during a small-break loss-of-coolant accident. This work contributes to the validation of the NEPTUNE_CFD code capability to predict the turbulence below a free surface produced by a plunging jet. In the experiment, the water was injected vertically down a straight circular pipe into a cylindrical vessel containing water. Mean velocity and turbulent fluctuations were measured below the jet at several depths below the free surface. The influence of several models on code predictions was investigated, and both standard and modified turbulence models were tested. A single-phase jet case was also simulated and compared with both measurements and two-phase calculations, to investigate bubble entrainment influence on turbulence prediction. The calculated mean velocity field was always in quite good agreement with the experimental data, while the turbulence intensity was generally good with some underestimation far from the jet axis region.

Experimental determination and numerical simulation of mixing time in a gas–liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas–liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9–17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas–liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas–liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas–liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.

Numerical simulation of the Reynolds number effect on gas-phase turbulence modulation

The enhancement of the gas-phase turbulence intensity at high Reynolds number (Re) has been observed experimentally by Hadinoto et al., in dilute-phase particle-laden flows of non-massive particles ( ⩽ 200 μ m ) . This work attempts to assess the predictive capability of a two-phase flow computational fluid dynamics (CFD) model, which is based on the kinetic theory of granular flow, in capturing the trend in the gas-phase turbulence modulation as a function of Re. In addition, the model predictive capability in simulating gas-particle flow regime of moderate Stokes number ( St T ) and low Re is examined. The use of different drag correlations and turbulence closure models is explored for this purpose. The simulation results suggest that the current state of the two-phase flow CFD model is not yet capable of accurately predicting the Re dependence of the gas-phase turbulence modulation. The two-phase flow CFD model, however, is more than capable in yielding good predictions at both the mean and fluctuating velocity levels for the case where the turbulence enhancement at high Re is not evident.

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.