Turbulent Two-phase Flow Research Articles

Void drift in narrow rectangular channels for highly advective bubbly flows: A macroscopic drift-flux model derived from two-fluid local simulations

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications. This work is an application based on Bois (2021) theoretical derivations to connect the spatially-averaged drift-flux model (DFM) to the local Reynolds-averaged two-fluid model (TFM). It presents new opportunities to calibrate closure laws or propose new models based on finer-scale descriptions. Highly convective steady bubbly flows with wall-peaking void fraction profiles are considered. Dispersed bubbles are weakly deformable. A new model dedicated to void fraction dispersion in flat rectangular channels is developed for application into the DFM. The model is calibrated based on reference local Euler-Euler two-fluid simulations of pressurised water and steam mono-dispersed bubbles, in adiabatic conditions. 64 conditions are considered to cover regularly the 3D parameter space in void fraction, Reynolds and Eötvös numbers. The new formulation proposed shows a very good fit with the post-processed predictions of local CFD simulations along with a substantial reduction in grid requirement. The model contains sub-filter correlations between vapour concentration and mixture or relative velocities. This model derived from local simulations is validated a posteriori in an industrial component scale code where the full space-filtered DFM is implemented and resolved. This work proves the benefits and feasibility of one-by-one model development and calibration based on two-fluid simulations.

Simulation study of heat transfer behaviour of turbulent two-phase flow in a 3D cubic shell and tube heat exchanger using water and different nanofluids

This research utilizes a two-phase flow model to replicate the thermal exchange in a counter flow shell and tube heat exchanger, comparing the efficacy of different nanofluids against pure water. The shell space is represented as a closed cubic area filled with diverse fluids, while the tube functions as the thermal exchange component. It investigates parameters like nanofluid variations, nanoparticle dimensions, and volume ratios to enhance the efficiency of temperature exchange between the shell and tube fluids. The Reynolds-averaged Navier-Stokes (RANS) technique is employed to analyze turbulence within the heat exchanger, utilizing ANSYS@FLUENT (Version 2022 R1) for simulations, which were considered reliable when convergence criteria reached 10−5. The outcomes are assessed based on velocity, thermal conductivity, Nusselt number, temperature dispersion, and turbulent kinetic energy. Notably, the results underscore that integrating nanoparticles into the fluid amplifies its thermal conductivity, with higher concentrations yielding more significant enhancements. Nanofluids, particularly those comprising SiO2-H2O with small nanoparticles and high volume fractions, exhibit notable improvements in heat transfer compared to pure water. TiO2-H2O follows in second place, trailed by CuO-H2O and Al2O3-H2O. The application of the RANS method effectively elucidates turbulence patterns and their impact on heat transfer dynamics between the shell and tube. An increase in Reynolds number has shown an adverse effect on heat transfer. Overall, this study furnishes valuable insights for optimizing heat transfer performance in such systems.

A four-way coupled numerical investigation of draft tube baffled crystallizer

In the present paper, the liquid–solid two-phase turbulent flow in a Draft Tube Baffled crystallizer has been simulated using Computational Fluid Dynamics. In this respect, multiphase Eulerian model along with population balance equations were applied. To implement four-way coupling, aggregation and breakage were considered. The RNG k-ε and RSM turbulence models were employed to conduct numerical simulation of two phase turbulent flow. Results demonstrated that applying RNG k-ε and RSM turbulence models, a significant difference in axial velocity profiles along the x-axis is observed, while those along the z-axis exhibit less difference. Moreover, a significant difference in volume fraction between the two models was observed which mostly concerns the region within the draft tube and the distance between the baffle and crystallizer wall. Furthermore, changing the propeller speed from 165 to 495 rpm, the speed of 330 rpm showed to be optimal in terms of particles residence time. The results also showed that a rise in impeller speed is one of the major contributors to mass exchange enhancement between the liquid and the solid phases. Accordingly, as the impeller speed rises, the rate of mass exchange increases from 9.92 kg/h for 165 rpm to 29.07 kg/h for 495 rpm.

On the Water Jet Quality at Part-Load Operation of Pelton turbines

Abstract Pelton turbines with multiple nozzles are characterised by their excellent performance over a wide operating range of mass flow rates. Thus, Pelton turbine manifolds must also be designed to deliver good flow quality to the nozzles at part-load operating conditions to accomplish the expectations. A reduced number of nozzles are opened at low mass flow rate operating conditions, where the choice of the open nozzles depends on the water jet quality generated at the individual nozzles. We investigate the flow phenomena occurring in the manifold with the operation of a reduced nozzle number employing numerical simulations to analyse beneficial nozzle opening selections. The turbulent two-phase flow is predicted by the Volume-Of-Fluid (VOF) approach and the k–ω SST turbulence closure model. Different nozzle operating scenarios are simulated, and the implications on the water jet quality, i.e. deviation and shape deformation, are reported. The results show that the free water jet quality criteria can change drastically at individual nozzle operating conditions because of the velocity changes at the branch line junctions.

Scale-Resolving Simulation of Shock-Induced Aerobreakup of Water Droplet

Two different scale-resolving simulation (SRS) approaches to turbulence modeling and simulation are used to predict the breakup of a spherical water droplet in air, due to the impact of a traveling plane shock wave. The compressible flow governing equations are solved by means of a finite volume-based numerical method, with the volume-of-fluid technique being employed to track the air–water interface on the dynamically adaptive mesh. The three-dimensional analysis is performed in the shear stripping regime, examining the drift, deformation, and breakup of the droplet for a benchmark flow configuration. The comparison of the present SRS results against reference experimental and numerical data, in terms of both droplet morphology and breakup dynamics, provides evidence that the adopted computational methods have significant practical potential, being able to locally reproduce unsteady small-scale flow structures. These computational models offer viable alternatives to higher-fidelity, more costly methods for engineering simulations of complex two-phase turbulent compressible flows.

A robust phase-field method for two-phase flows on unstructured grids

A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to local grid size. In addition to this, we present a novel formulation for two-phase flows on collocated grids that is provably energy stable, which is a critical feature for robust simulations of two-phase turbulent flows. The proposed method is first evaluated on canonical test cases, including scenarios like drop advection and drop in a shear flow. The accuracy of the proposed method in the presence of grid transitions, which is important for simulations in complex geometries using unstructured grids, is also evaluated. We assess the robustness of our method by performing simulations of a drop in homogeneous isotropic turbulence at infinite Reynolds number with varying density ratios. Furthermore, as a step toward verification and validation, simulations of test cases in complex geometries and conditions, such as, a damped surface wave, infinitesimal interface distortion on a liquid jet, and the atomization of a liquid jet from the engine combustion network's Spray A nozzle are presented. These simulations illustrate the accuracy, robustness, and applicability of the proposed method in various kinds of complex two-phase flow applications of engineering interest.

Mathematical modeling of droplet collisions in sprays under microgravity conditions

Two-phase flows under microgravity conditions play a crucial role in Space technology and science. Studying the behavior of dispersed droplets suspended in a gas flow and their influence on the characteristics of the carrier flow is the main task of computational modeling of turbulent two-phase flows. To understand the features and predict the behavior of such flows, along with experimental studies, it is necessary to develop mathematical models, which adequately describe all the basic physical and chemical processes in a gas-droplet environment at different scales.In this paper we obtain solutions for the problem of two droplets collision, using solutions for cumulative jets, and propose droplet collision outcome criterion. This research will focus on the process of two interacting droplets coalescence into one and coalescence with subsequent separation into two or more droplets. A semi-analytical method has been developed for application of the solution of the cumulative jet problem to the problem of droplet collision. A differential equation has been obtained that describes the following possible outcomes of droplet collision: coalescence and coalescence with subsequent separation. A criterion for determining the outcome of on-head droplet collision has been obtained. In accordance with the developed criterion, the number and size of formed droplets are obtained. The effect of collision on moving droplet evaporation in a heated atmosphere was regarded.

Large Eddy Simulation of a Turbulent Polydisperse Spray Flow: A Comparative Study of Subgrid Scale Models and Droplet Injection Models

Abstract This study performs an investigation of the effects of the subgrid-scale (SGS) and droplet injection models in the large eddy simulation (LES) of turbulent two-phase spray flows. Three LES SGS models (Smagorinsky, wall-adapting local eddy viscosity (WALE), and dynamic Smagorinsky) and two droplet injection models (cone nozzle injection and conditional droplet injection) are validated to the experimental measurements. For both gaseous and liquid phases, all SGS models provide comparable results, indicating that the current two-phase flow field does not exhibit a pronounced sensitivity to the LES SGS model. As for different droplet injection models and spray dispersion angles, minimal differences are observed in the prediction of the gaseous mean and root-mean-square (RMS) velocity profiles. However, for the result of liquid phase, CDIM (conditional droplet injection model) predictions of the droplet mean diameter and velocity are in better agreement with experiments, and less sensitive to spray dispersion angle settings. While the CNIM (cone nozzle injection model) prediction of droplet diameter is less accurate when increasing the dispersion angle. The study suggests that turbulent two-phase spray flows are more influenced by the spray boundary conditions rather than the LES SGS models.

Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow

The prediction of sediment transport, related to different environmental and engineering problems, requires accurate mathematical models. Most available mathematical models for the concentrations of suspended sediments are based on the classical advection diffusion equation, which remains not efficient enough to describe the complete behavior related to sediment–water two-phase flows and the feedback between the turbulent unsteady flow and suspended sediments. The aim of this paper is to reinvestigate the kinetic model for turbulent two-phase flows, which accounts for both sediment–turbulence interactions and sediment–sediment collisions. The present study provides a detailed and rigorous derivation of the kinetic model equations, clarifications about the mathematical approach and more details about the main assumptions. An explicit link between the kinetic model and the classical advection diffusion equation is provided. Concentration profiles for suspended sediments in open channel flows show that the kinetic model is able to describe the near-bed behavior for coarse sediments.

Numerical modelling and experimental validation of dripping, jetting and whipping modes of gas dynamic virtual nozzle

PurposeThis study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).Design/methodology/approachThe physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.FindingsThe half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.Practical implicationsThe model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.Originality/valueTo the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.

Turbulence topology evolution in weakly turbulent two-phase flows

In turbulent two-phase flows, not only the isotropy of velocity fluctuations can be altered by the presence of liquid blobs, ligaments, or pockets, the structure of the turbulent flow field and associated flow topology may also be significantly modified. In this respect, the small-scale wrinkling and curvature of the liquid–gas interface, which is associated with sharp and large density variations, impact turbulence in the gas phase. In the present study, the joint probability density function of the second and third invariants of the velocity gradient tensor (VGT)—and especially its traceless counterpart—is considered so as to scrutinize how the turbulent flow topology in the gas may be altered. These quantities are analyzed on the basis of direct numerical simulation databases of two-phase flows evolution in homogeneous isotropic turbulence. Statistics of the invariants of the VGT are gathered at various distances to the interface so that the gas phase is divided into three sub-regions according to the values of the level-set G, i.e., the signed distance to the liquid/gas interface. The analysis of the VGT invariants shows that turbulent small-scale structures and associated flow topology are modified in the vicinity of the liquid–gas interface. Lagrangian evolution equations of the VGT and its invariants are thus studied to get a refined view of the corresponding changes. To the best of the authors' knowledge, this is first time that these budgets are scrutinized in such conditions. Special emphasis is placed on conditional mean rates of change of the VGT invariants in the plane of the second and third invariants. In the corresponding set of coordinates, the obtained trajectories are found to be mainly driven by (i) mutual interactions between invariants and (ii) pressure Hessian contributions, thus confirming the importance of the latter for the dynamics and structure of turbulent two-phase flows.

Crankcase Explosions in Marine Diesel Engines: A Computational Study of Unvented and Vented Explosions of Lubricating Oil Mist

Accidental crankcase explosions in marine diesel engines are presumably caused by the inflammation of lubricating oil in air followed by flame propagation and pressure buildup. This manuscript deals with the numerical simulation of internal unvented and vented crankcase explosions of lubricating oil mist using the 3D CFD approach for two-phase turbulent reactive flow with finite-rate turbulent/molecular mixing and chemistry. The lubricating oil mist was treated as either monodispersed with a droplet size of 60 μm or polydispersed with a trimodal droplet size distribution (10 μm (10 wt%), 250 μm (10 wt%), and 500 μm (80 wt%)). The mist was partly pre-evaporated with pre-evaporation degrees of 60%, 70%, and 80%. As an example, a typical low-speed two-stroke six-cylinder marine diesel engine was considered. Four possible accidental ignition sites were considered in different linked segments of the crankcase, namely the leakage of hot blow-by gases through the faulty stuffing box, a hot spot on the crankpin bearing, electrostatic discharge in the open space at the A-frame, and a hot spot on the main bearing. Calculations show that the most important parameter affecting the dynamics of crankcase explosion is the pre-evaporation degree of the oil mist, whereas the oil droplet size distribution plays a minor role. The most severe unvented explosion was caused by the hot spot ignition of the oil mist on the main bearing and flame breaking through the windows connecting the crankcase segments. The predicted maximum rate of pressure rise in the crankcase attained 0.6–0.7 bar/s, whereas the apparent turbulent burning velocity attained 7–8 m/s. The rate of heat release attained a value of 13 MW. Explosion venting caused the rate of pressure rise to decrease and become negative. However, vent opening does not lead to an immediate pressure drop in the crankcase: the pressure keeps growing for a certain time and attains a maximum value that can be a factor of 2 higher than the vent opening pressure.

An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data – applied to technical flows

The article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept.With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×107 and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (108×104) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10−2%). This qualifies the method for an efficient subsequent data processing.

Numerical Analysis of Transient Vortex Formation at the Outlet of a Tank Containing Gas-Liquid Phases

One of the basic phenomena when a liquid leaves a tank is the formation of vortices. This phenomenon can have a significant impact on the liquid mass remaining in the tank and the ingress of air and bubbles into the system. As a result, the performance of the system can be disturbed. The purpose of this study is to numerically investigate the effect of gas pressure on vortex formation and critical height. It also verifies the relationships presented for turbulent viscosity. In addition, the near-wall behavior of the analytical relationships proposed for the tangential velocity is revised based on the boundary layer theory. Some common effective factors such as angular velocity, discharge time, and liquid height are also investigated. The volume of fluid (VOF) model and the Transitional SST k-ω turbulence model were used to solve the two-phase turbulent flow. The results show that increasing the gas pressure from 1 to 5 bar and its direct impact on the liquid surface significantly accelerates the formation of the vortex and the critical height. This phenomenon causes the air core to reach the inlet of the outlet pipe approximately 7 seconds earlier after the start of the liquid discharge. As a result, much more liquid mass remains in the tank. The increase in the angular velocity of the reference frame from 0.1 to 1 rad/s also causes the critical height to be reached much earlier and the remaining liquid mass to increase by 32 kg. In addition, the amount and variations of turbulent viscosity differ significantly from the semi-empirical constants, limiting their use to certain flows.

РАСЧЁТ КОМБИНИРОВАННОЙ КОНСТРУКЦИИ ЖИДКОСТНОКОЛЬЦЕВОГО ВАКУУМНОГО НАСОСА

Liquid ring vacuum pumps are widely used in many areas of the agro-industrial complex, in particular for milking processes, storage of plant materials, their drying and extraction, as well as pneumatic transport. It has been revealed that one of the main disadvantages of liquid ring vacuum pumps - low efficiency (25-50%) is often caused by hydraulic losses during rotation of the liquid ring on a stationary body, as well as inaccurate physical prerequisites in the equations describing the movement of the liquid ring - a two-phase turbulent flow in the working pump cavity. As a consequence, the pump engineering calculation method leads to overestimated performance characteristics at the design stage. In this regard, a combined design of a liquid ring vacuum pump with a rotating casing has been proposed, in which rotation can be transmitted from the impeller blades to the casing blades (in the case of low and medium speed pump size), through involute engagement, or from the casing blades to the impeller blades (in in case of high and especially high speed of action). The basis for calculating the liquid ring is the continuity equation, the stability condition of the liquid ring and the threshold for the occurrence of cavitation phenomena, as well as a coefficient characterizing the drop in speed for turbulent motion in a bladeless space in areas (suction, maximum, compression, discharge). In this case, the mechanism of movement of the liquid ring in the working cavity of the pump is represented by physical processes in the form of the interaction of two power flows: the hydraulic flow of the working fluid and the thermodynamic flow of the gaseous medium. When calculating the main operating parameter of the pump - the actual speed of action - the evaporation of liquid droplets due to changes in the temperature of the liquid ring was taken into account. The forces acting on the rotating wheel and the rotating body of the combined design of a liquid ring vacuum pump are determined analytically.

Effect of probe size on phase-detection probe measurements of air-water flow properties in hydraulic jumps

This experimental study investigated the air-water flow properties and bubble characteristics in hydraulic jumps with Froude numbers Fr1 = 2.4 and 6.3, using four dual-tip phase detection probes with sensor sizes from 0.25 mm to 0.64 mm. The hydraulic jumps were characterized by a fully breaking roller with substantial air entrainment and turbulent two-phase flow patterns. The measurements encompassed distributions of void fraction, bubble count rate, interfacial velocity and bubble clustering properties and the data sets were consistent with previous studies. The comparison of the different probes showed a small impact of the tested sensor sizes on the air-water flow properties, in terms of the trends, magnitude and maximum values. Some differences were observed in terms of the bubble count rate, with the larger probes detecting a lesser number of bubbles. The trend was further confirmed through a comparison with the data set of Chanson and Brattberg (2000) [10] with a smaller probe sensor size (Ø1 = 0.025 mm), in which the maxima of bubble count rates were almost twice that of the present dataset for identical flow conditions. The present results confirm that the traditional signal processing techniques can be used for relatively small probe sizes, although different approaches might be needed for larger probes which cannot detect sub-millimetric bubbles. Overall, the findings should facilitate the development of sturdier phase-detection needle probes and help breaching the gap between laboratory and prototype.

CO2 capture using steam ejector condenser under electro hydrodynamic actuator with non-condensable gas and cyclone separator: A numerical study

The concept for condensation of steam and CO2 separation in a negative CO2 emission gas power plant involves the utilization of a steam ejector condenser (SEC) for direct-contact condensation of vapor with inert gas (CO2) on a spray of subcooled liquid, integrated with a separator to produce pure CO2. Due to the increasing diffusion resistance and reduced convective heat transfer between the steam and subcooled water phases in the presence of non-condensable gas (CO2), the study utilized an electrohydrodynamic (EHD) actuator to enhance heat transfer rate in the SEC. To optimize CO2 purification, the effect of single, dual and quadruple inlets on separation efficiency was analysed. In the SEC, the Eulerian-Eulerian multiphase model is employed, treating water as the continuous phase and the compressible gas mixture (steam and CO2) as the dispersed phase. The standard k-ε model is chosen to depict the turbulence in the ejector. The separator is transient, turbulent, and three-dimensional, using the control volume method. The RSM turbulent model and mixture model are utilized to simulate the turbulent two-phase flow in the gas–liquid separator. The findings indicated that when the mass flux of steam and voltage are increased, the condensation heat transfer coefficient also increases. For a mass flux of steam of 51 (kgm2.s), the condensation heat transfer coefficients were measured to be 0.98, 1.029, 1.08, and 1.134 (MWm2.K) at electrode voltages of 0, 20, 25, and 30 kV, respectively. In addition, a single-inlet cyclone attains a separation efficiency of 95.1 %, while incorporating two inlets improves the performance to 97.9 %. However, the most remarkable outcome is witnessed in cyclones with four inlets, where an impressive separation efficiency of 99.9 % is achieved.

Downward two-phase (Gas - Solid) turbulent flow through a vertical sudden expansion duct with a backward-facing step

Downward two-phase (Gas - Solid) turbulent flow through a vertical sudden expansion duct with a backward-facing step

Measurement of a gas–liquid two-phase turbulent flow in a horizontal channel under a sudden decrease in the local void fraction

Measurement of a gas–liquid two-phase turbulent flow in a horizontal channel under a sudden decrease in the local void fraction

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in the rectangular channel. The model is based on the Eulerian approach applied to 3D Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. The uniqueness of the method lies in the direct calculation of normal and transverse components of the Reynolds stresses for both gas and particles. Two cases were examined: a conventional channel flow and grid-generated turbulence flow. The obtained numerical results have been verified and validated by the experimental data, received from the turbulent particle dispersion test. The computed values of the particles’ turbulent dispersion and the maximum value of the particulate concentration distribution show good agreement with the experimental results. The examples are ranged from coal and other bulk material pneumatic transport, vertical fluidized beds, coal gasifiers, and chemical reactors.