Finite-rate Mass Transfer Research Articles

Maximizing power of irreversible multistage chemical engine with linear mass transfer law using HJB theory

Chemical engine is an abstract model for many devices and processes. Its thermodynamic performance analysis and optimization is meaningful. A model of irreversible multistage isothermal chemical engine (MICE) system with linear mass transfer law [g∝Δμ] and the irreversibilities of internal dissipation effect of working fluid and finite rate mass transfer is built, and its performances is investigated and optimized. For fixed initial key component concentration and fixed initial time, the maximum power output (MPO) of the irreversible MICE is obtained by applying Hamilton-Jacobi-Bellman optimization theory analytically. Numerical examples are provided. The results indicate that difference between chemical potential of key component concentration (KCC) and Carnot chemical potential (See Eq. (12) in this paper for its definition) for MPO is constant, KCC at high-chemical-potential side decreases with increase of time nonlinearly, and irreversibility factor affects MPO of irreversible MICE and the corresponding optimal KCC configuration qualitatively.

Numerical simulations for incompressible turbulence cavitation flows with tangent of hyperbola interface capturing (THINC) scheme

In this work, we developed high-fidelity numerical solvers for turbulent cavitation flows and presented numerical simulations of cavitation and supercavitation behind an axisymmetric projectile and a conical cavitator. The proposed numerical solver is based on the homogeneous equilibrium model where the mass transfer rate between vapor and liquid is dependent on a volume of fraction (VOF) function. As a result, the numerical results of cavitation turbulent flow are heavily affected by the accuracy of the VOF evolution prediction. Thus, the proposed solver employs the Tangent of Hyperbola for INterface Capture method with Quadratic surface representation and Gaussian Quadrature scheme to accurately resolve the interfacial structures of cavitation bubbles. To effectively model the turbulent effects, the solver utilizes two approaches, respectively, i.e., the Smagorinsky model of large eddy simulation and the shear stress transport model of the Reynolds-averaged Navier–Stokes equation. The homogeneous turbulence equation systems are then discretized by the linear second-order schemes in space and time. The phase transition including both evaporation and condensation is described by the finite-rate mass transfer models such as Schnerr–Sauer and Kunz models. Numerical simulations and comparison studies are performed with the proposed solvers. Compared with previous simulation works, the current simulation results of cavity shape patterns and related hydrodynamic characteristics are in better agreement with experimental data and analytical theories, as well as reference solutions. These results validate that the proposed solver can produce high-fidelity predictions for solving the flow structures of cavitation and reentrant jet in the turbulent cavitation simulations.

A numerical approach to address the acoustic stiffness in cavitating flows

A numerical approach based on preconditioning and dual-time stepping (DTS) is proposed to simulate cavitating flows at low Mach numbers. The methodology is based on a fully-compressible homogeneous mixture model and finite rate mass transfer as discussed in Gnanaskandan and Mahesh (2015). The method has shown promising results for capturing the large-scale cavitation in developed cavitation regimes (e.g. Bhatt and Mahesh, 2020; Gnanaskandan and Mahesh, 2016a). Small-scale vapor regions in the incipient cavitation, cavitation inception and wetted conditions are sensitive to free-stream nuclei content (e.g. Hsiao and Chahine, 2005; Bhatt and Mahesh, 2019, 2020). In these regimes, lower values of free-stream nuclei are necessary than what is typically prescribed in homogeneous mixture models that use a fully-compressible formulation. While important for the physical modeling, lower values of free-stream nuclei lead to acoustic stiffness. The goal of the present work is to present a numerical approach to enable such low free-stream nuclei calculations in an accurate manner and in a reasonable amount of time. The key aspects of the numerical approach are: (i) preconditioning applied to the cavitating flow equations in a fully-compressible (density-based) solver, (ii) modifications based on the all-speed Roe-type scheme to the characteristic-based filtering, and (iii) implementation in parallel and on unstructured grids that allow the simulation of complex problems. The numerical formulation of the time-derivative preconditioning matrix, the DTS framework, and modification to the shock-capturing are discussed. A proper conditioning of the preconditioned system of equations is obtained. The methodology is demonstrated for the unsteady flow over a cylinder under wetted and cavitation inception conditions, and LES of flow over a propeller under wetted conditions. Overall, a significant saving in total run-time as compared to the original solver is obtained, without compromising accuracy.

Numerical study of cavitation regimes in flow over a circular cylinder

Cavitating flow over a circular cylinder is investigated over a range of cavitation numbers for both laminar and turbulent regimes. We observe non-cavitating, cyclic and transitional cavitation regimes with reduction in freestream $\sigma$. The cavitation inside the Karman vortices in the cyclic regime, is significantly altered by the onset of "condensation front" propagation in the transitional regime. At the transition, an order of magnitude jump in shedding Strouhal number is observed as the dominant frequency shifts from periodic vortex shedding in the cyclic regime, to irregular-regular vortex shedding in the transitional regime. In addition, a peak in pressure fluctuations, and a maximum in St versus $\sigma$ based on cavity length are observed at the transition. Shedding characteristics in each regime are discussed using dynamic mode decomposition. It is demonstrated that the condensation fronts observed in the transitional regime are supersonic (referred as "condensation shocks"). In the presence of NCG, multiple condensation shocks in a given cycle are required for complete cavity condensation and detachment, as compared to a single condensation shock when only vapor is present. This is explained by the reduction in pressure ratio across the shock in the presence of NCG effectively reducing its strength. In addition, at $\sigma=0.85$ (near transition from the cyclic to the transitional regime), presence of NCG suppresses the low frequency irregular-regular vortex shedding. Vorticity transport at $Re=3900$, in the transitional regime, indicates that the region of attached cavity is nearly two-dimensional with very low vorticity, affecting Karman shedding in the near wake. In addition, the boundary-layer separation point is found to be strongly dependent on the amounts of vapor and gas in the freestream for both laminar and turbulent regimes.

Numerical investigation of partial cavitation regimes over a wedge using large eddy simulation

Partial cavitation over incipient, transitory and periodic regimes is investigated using large eddy simulation (LES) in the (experimental) sharp wedge configuration of Ganesh et al. (2016). The numerical approach is based on a compressible homogeneous mixture model with finite rate mass transfer between the phases. Physical mechanisms of cavity transition observed in the experiments; i.e. re-entrant jet and bubbly shock wave, are both captured in the LES over their respective regimes. Vapor volume fraction data obtained from the LES is quantitatively compared to X-ray densitometry. In the transitory and periodic regimes, void fractions resulting from complex interactions of large regions of vapor in the sheet/cloud show very good comparison with the experiments. In addition, very good agreement with the experiments is obtained for the shedding frequency and the bubbly shock wave propagation speed. In the incipient regime, the qualitative characteristics of the flow (e.g. cavitation inside spanwise vortices in the shear layer) are captured in the simulations. Conditions favoring either the formation of the re-entrant jet or the bubbly shock wave are analyzed by contrasting the LES results between the regimes. In the transitory regime, large pressure recovery from within the cavity to outside, and the resulting high adverse pressure gradient at the cavity closure support the formation of re-entrant jet. In the periodic regime, overall low pressures lead to reduced speed of sound and increased medium compressibility, favoring the propagation of shock waves. In a re-entrant jet cycle, vapor production occurs predominantly in the shear layer, and intermittently within the cavity. In a bubbly shock cycle, vapor production is observed spanning the entire thickness of the cavity. Bubbly shock wave propagation is observed to be initiated by the impingement of the collapse-induced pressure waves from the previously shed cloud. Supersonic Mach numbers are observed in the cavity closure regions, while the regions within the grown cavity are subsonic due to the negligible flow velocities.

The reversed chemical engine cycle with application to desalination processes

In this paper, a novel thermodynamic cycle is proposed, termed the reversed chemical engine cycle. In the cycle, a net input of work is used to transfer mass from a low chemical potential reservoir to a high chemical potential reservoir. The cycle has two mass exchangers, a pump and a turbine. The only irreversibility considered in the model is finite-rate mass transfer. Similar to the reversed Carnot cycle, expressions for the performance ratio (analogous to the coefficient of performance) are obtained under the condition of minimized power requirement for the endoreversible and, in turn, the reversible case. The reversed mass engine cycle is shown to be a special case of the reversed chemical engine. An equipartitioned hybrid forward osmosis reverse osmosis (FO–RO) system is considered as an example of the cycle.

Evaluation of finite rate homogenous mixture model in cavitation bubble collapse

The objective of this study is to evaluate the performance of finite rate homogeneous mixture models in three key aspects: (a) the ability of the model to predict the dynamics of resolved small scale vapor regions, (b) the importance of finite rate mass transfer and (c) the impact of assuming 2D flow as is done in RANS simulations with a statistically homogeneous direction. We consider a bubble collapse problem to evaluate all these effects.

An Investigation of the Vortex in a Submersible Axial Flow Pump Impeller

The paper presents numerical simulation of the vortex in a submersible axial flow pump impeller using OpenFoam code. A mixture assumption and a finite rate mass transfer model were introduced to analyze vortex. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that the cavitation may occur on the lower portion of impeller suction side. And the blade channel vortex will be formed in the impeller. It can induce the pressure pulsation in the impeller and can result in reduced efficiency of the submersible axial flow pump.

Re-Entrant Jet Analysis of Cavitating Turbulent Flow on a Hydrofoil

The paper presents the re-entrant jet analysis of cavitating turbulent flow on a hydrofoil. Analysis was performed by OpenFOAM code. A mixture assumption and a finite rate mass transfer model were introduced. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. The result of numerical simulation clearly explained the mechanism of re-entrant jet and quasi-periodic law of cavitating flow on a hydrofoil.

Numerical investigations of supercavitation around blunt bodies of submarine shape

Cavitation occurs when liquid is subjected to rapid changes of pressure. If the local pressure is lower than the liquid saturation pressure, the liquid changes its phase into vapor. A fast moving solid body underwater will reduce the local pressure around the body. Under certain conditions, the local pressure can be lower than the water saturation pressure, accordingly causing cavitation. If the velocity of the moving body increases further, a supercavitation will occur. In this paper, the cavitation and supercavitation were studied by the SST k–ω turbulence model combined with a finite-rate mass transfer modeling under the mixture assumption. The validations of these models were performed through comparisons between numerical simulations and experiments. After the validations, the supercavitation generated by a high speed moving body, which can be described as a large bubble, was studied. The studies were on several blunt bodies, such as a submarine hull shape, a submarine hull shape with appendages and a full submarine shape with sail and appendages. It was found that the naked submarine hull is difficult to have the supercavitation covering the whole body. The sail and appendages can help supercavitation occurs earlier. Furthermore the effects of the supercavitation on the submarine and generation mechanism of the supercavitation is discussed based on the simulations.

Numerical Simulation of Blade Channel Vortex in a Low Head Francis Turbine

The paper presents numerical simulation of blade channel vortex in a low head Francis turbine using OpenFoam code. A mixture assumption and a finite rate mass transfer model were introduced to analyze blade channel vortex. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that using cavitation model to analyze blade channel vortex is very effective.

Numerical Simulation of Cavitating Turbulent Flow in a Francis Turbine with Draft Tube Natural Air Admission

The paper presents numerical analysis of cavitating turbulent flow in a high head Francis turbine with draft tube natural air admission at part load operation. Analysis was performed by OpenFOAM code. A mixture assumption and a finite rate mass transfer model were introduced. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. The pressure distribution and the flow of air in the draft tube are analyzed in detail. Simulation results show that the pressure fluctuations on the draft tube wall can reduce with natural air admission.

Numerical Investigation of Cavitating Turbulent Flow in a Francis Turbine Runner Fitted with Splitter Blades

The paper presents numerical investigation of cavitating turbulent flow in a high head Francis turbine runner fitted with splitter blades at part load operation. Analysis was performed by OpenFOAM code. A mixture assumption and a finite rate mass transfer model were introduced. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results show that the volume fraction of water vapor and the pressure uneven distribution on the main blade and splitter blade. It will lead to cavitation and fatigue damage.

Numerical Prediction of Cavitation Erosion on a Francis Turbine Runner

The paper presents numerical prediction of cavitation erosion on a Francis turbine runner using CFD code. The SST turbulence model is employed in the Reynolds averaged Navier–Stokes equations in this study. A mixture assumption and a finite rate mass transfer model were introduced. The computing domain is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators(PISO) procedure. Comparison the numerical prediction results with a real runner with cavitation damage, the region of higher volume fraction by simulation with the region of runner cavitation damage is consistent.

Numerical simulation of cavitation around a two-dimensional hydrofoil using VOF method and LES turbulence model

In this paper simulation of cavitating flow over the Clark-Y hydrofoil is reported using the large eddy simulation (LES) turbulence model and volume of fluid (VOF) technique. We applied an incompressible LES modelling approach based on an implicit method for the subgrid terms. To apply the cavitation model, the flow has been considered as a single fluid, two-phase mixture. A transport equation model for the local volume fraction of vapour is solved and a finite rate mass transfer model is used for the vapourization and condensation processes. A compressive volume of fluid (VOF) method is applied to track the interface of liquid and vapour phases. This simulation is performed using a finite volume, two phase solver available in the framework of the OpenFOAM (Open Field Operation and Manipulation) software package. Simulation is performed for the cloud and super-cavitation regimes, i.e., σ=0.8, 0.4, 0.28. We compared the results of two different mass transfer models, namely Kunz and Sauer models. The results of our simulation are compared for cavitation dynamics, starting point of cavitation, cavity’s diameter and force coefficients with the experimental data, where available. For both of steady state and transient conditions, suitable accuracy has been observed for cavitation dynamics and force coefficients.

NUMERICAL INVESTIGATIONS OF CAVITATION AROUND A HIGH SPEED SUBMARINE USING OPENFOAM WITH LES

Under water cavitation occurs when the liquid changes the phase into its vapor due to the local pressure is lower than the water saturation pressure. If a body is moving very fast under water, the local pressure around it at a certain flow regime will be lower than the water saturation pressure. The cavitation around the body will occur. Following the increase of the intensity of the cavitation, a cloud cavitation will occur. Under the cloud cavitation occurrence, the cavitation is unsteady and periodic, which involves formation, detachment and collapse of sheet cavities. In this paper, large Eddy simulation (LES) is employed together with a mixture assumption and a finite rate mass transfer modeling into OpenFOAM to study the cavitation phenomena. The validation comparisons of numerical simulations with experiments of a sphere under water are performed. After the validation, a full submarine model with sail and appendages under water is studied. The submarine is under water around 450 m deep with a moving speed at 60 m/s. It is found that the cavitation changes under the different cavitation numbers (from 1.0 to 0.1). Small cavitation numbers induce a large area cavitation, whereas large ones reduce this phenomenon. A supercavitation, which can be described as a large bubble, is found around the high speed submarine at cavitation number equals to 0.1.

Numerical simulation of cavitating turbulent flow in a high head Francis turbine at part load operation with OpenFOAM

The paper presents numerical analysis of cavitating turbulent flow in a high head Francis turbine at part load operation. Analysis was performed by OpenFOAM code. Thekω−SST turbulence model is employed in the Reynolds averaged Navier–Stokes equations in this study. A mixture assumption and a finite rate mass transfer model was introduced. The computing domain includes the spiral casing, the guide vanes, the runner, and the draft tube, which is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations of the mixture model and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators(PISO) procedure. The tendency of the cavitating flow in the runner and draft tube agrees well with the turbine empirical results.

Capturing Secondary Cavitation – A Step Towards Numerical Assessment of Cavitation Nuisance

Numerical simulations using incompressible Large-Eddy Simulation together with a mixture assumption and a finite-rate mass transfer model demonstrate the presence of several cavitation mechanisms important for cavitation nuisance of hydrodynamic machinery such as marine propellers and power turbines. One of such mechanisms is brought about by re-entrant jets, which can cut sheet cavities and thus lead to shedding and travelling cavities which in turn may cause nuisance as they collapse. However, severe erosion and noise generation also stem from the formation and development of small scale structures called secondary cavitation, formed e.g. in shear layers through vortex roll-up, which are also important for cavitation nuisance risk. The extent of the resolution of the secondary cavitation in the computational setting is discussed. Cavitation on a NACA0015 foil at 6° angle of attack and σ = 1.0 in a three-dimensional domain is studied.

Implicit LES Predictions of the Cavitating Flow on a Propeller

We describe an approach to simulate dynamic cavitation behavior based on large eddy simulation of the governing flow, using an implicit approach for the subgrid terms together with a wall model and a single fluid, two-phase mixture description of the cavitation combined with a finite rate mass transfer model. The pressure-velocity coupling is handled using a PISO algorithm with a modified pressure equation for improved stability when the mass transfer terms are active. The computational model is first applied to a propeller flow in homogeneous inflow in both wetted and cavitating conditions and then tested in an artificial wake condition yielding a dynamic cavitation behavior. Although the predicted cavity extent shows discrepancy with the experimental data, the most important cavitation mechanisms are present in the simulation, including internal jets and leading edge desinence. Based on the ability of the model to predict these mechanisms, we believe that numerical assessment of the risk of cavitation nuisance, such as erosion or noise, is tangible in the near future.

Parametric optimum analysis of an irreversible chemical potential transformer and its performance bounds

SYNOPSIS A general cyclic model of an irreversible chemical potential transformer is put forward, in which finite-rate mass transfer, mass leak and internal irreversibility resulting from friction, eddy currents and other dissipation inside the cyclic working substance are taken into account. The performance of the chemical potential transformer is optimised. The optimal relationship between the coefficient of performance and the rate of energy pumping is derived. The optimal operating region of the chemical potential transformer is determined. Moreover, the bounds of some important parameters, such as the chemical potentials of the cyclic working substance in the three mass-transfer processes and the time spent on those processes, are discussed. The results obtained here can include some important conclusions for an endoreversible chemical potential transformer and an irreversible chemical engine which have been investigated in detail.