Vapor Cavitation Research Articles

A Volume of Fluid Method for Air Ingestion in Squeeze Film Dampers

The present work introduces a numerical model for squeeze film dampers (SFDs) operating simultaneously with vapor cavitation and air ingestion. The pressure is given by the Reynolds equation. The vapor cavitation model used in this work is based on Rayleigh-Plesset equation and was previously presented. Air ingestion occurring in open-end SFDs is dealt with by using a volume of fluid computational fluid dynamics (CFD) method not previously employed in lubrication problems. The original volume of fluid (VOF) method proposed by Hirt and Nichols was adapted to capture and track the free boundary between air and liquid in a thin-film lubricant. Numerical results are compared with experimental data of Adiletta and Pietra showing the simultaneous influence of vapor cavitation and air ingestion in an open-end SFD. These two phenomena have typical pressure values and appear at different locations and with a different extent. The vapor threshold is located on the low-pressure zone and is the lowest pressure value in the SFD, usually close to absolute zero. The air ingestion is characterized by a zone of almost constant pressure, usually close to atmospheric pressure (or, more generally, equal to the outer, exit pressure) and located between the minimum and the maximum pressures in the SFD. The numerical model proposed in this article deals simultaneously with these two effects. A simplified version of the air ingestion model for standard SFD applications is also introduced.

The definition of non-dimensional integration temperature difference and its effect on organic Rankine cycle

The integration temperature difference ΔTi considers the heat transfer routes, linking the heat transfer process with the thermodynamic behavior of heat exchangers. The first and second non-dimensional integration temperature differences are defined as ΔTi,h∗=ΔTi/Th,i and ΔTi,s∗=ΔTi/(Th,i-T0) respectively, where Th,i is the heat source temperature and T0 is the environment temperature. This paper is the first to experimentally verify the significance of the non-dimensional integration temperature differences on organic Rankine cycle (ORC) systems. The first non-dimensional temperature difference is shown to have linear relationship with the revised entropy generation numbers (Ns). With increases of the second non-dimensional integration temperature difference, the expander powers, system thermal and exergy efficiencies had parabola distributions. They simultaneously reached maximum at ΔTi,s∗=0.282, under which the vapor cavitation in the expander disappears and the exergy losses of heat exchangers are acceptable to elevate the expander efficiency. Beyond the optimal point, the ORC performance is worsened either due to the vapor cavitation in the expander, or due to the poor thermal matches in the evaporator and condenser. The second non-dimensional integration temperature difference comprehensively reflects the effects of heat source temperatures, heating powers and organic fluid flow rates and pressures, etc. It balances exergy destructions of various components to optimize the system. Thus, it can be an important parameter index to maximize the power or electricity output for a specific heat source. The usefulness of the integration temperature difference and the future work are discussed in the end of this paper.

Flow characteristics of control valve for different strokes

The article deals with the determination of flow characteristics and loss coefficients of control valve when the water flows in the interval of operating parameters, including the evaluation of vapour and air cavitation regime. The characteristics of the control valve are measured on the experimental equipment and subsequently loss coefficients are determined. Data from experimental measurements are used for creating of mathematical model with vapour and air cavitation and verification results. This validation will enable the application of methods of numerical modelling for valves of atypical dimensions e.g. for use in nuclear power industry. The correct knowledge of the valve characteristics and fundamental coefficients (e.g. flow coefficient, cavitation coefficient and loss coefficient) is necessarily required primarily for designers of pipe networks.

Mathematical and experimental modelling of flow of air-saturated water through a convergent-divergent nozzle

In hydraulic elements an under-pressure is generated during fluid flow around sharp edges or changing the flow cross-section (e.g. for valves, switchgear, nozzles). In these locations air suction by leakages or release of air from the liquid during cavitation may occur. When flow modelling using classical mathematical model of cavitation at higher flow rates there is disagreement in the measured and calculated hydraulic variables before and behind hydraulic element. Therefore, it is necessary to use a mathematical model of cavitation applied to the three-phase flow (water, vapour, air). Nowadays it is necessary to look for mathematical approaches, which are suitable for quick engineering use in sufficiently precision numerical calculations. The article is devoted to theoretical investigation of multiphase mathematical model of cavitation and its verification using a laboratory experiment. At first case the k-e RNG turbulent mathematical model with cavitation was chosen in accordance [9] and was applied on water flow with cavitation (water and vapour) in a convergent-divergent nozzle. In other cases a solution of water flow with cavitation and air saturation was investigated. Subsequently, the results of mathematical modelling and experimental investigation focused on monitoring of air content and its impact on the value of hydraulic parameters and the size of the cavitation area were verified.

Cavitation Phenomena and Performance Implications in Archimedes Flow Turbines

Cavitation produces undesirable effects within turbines, such as noise, decreases in efficiency, and structural degradation of the device. Two microhydro turbines incorporating Archimedean spiral blade geometries were investigated numerically for cavitation effects using computational fluid dynamics (CFD). Separate blade geometries, one with a uniform blade pitch angle and the other with a 1.5 power pitch, were modeled using the Schnerr–Sauer cavitation model. The method used to determine where cavitation occurs along the blade and within the flow involved varying inlet flow rates and the rotation rate of the blade. Cavitation analysis was conducted locally as well as globally, using both cavitation number and Thoma number. The cavitation number was used to correlate the single-phase to the multiphase results for rotation rates of 250 and 500 rpm, allowing for the single-phase simulations to be used to determine where the onset of cavitation occurs. It was determined that cavitation occurred at the exit of the blade at a flow coefficient of approximately 0.33 for the 1.5 pitch blade geometry, while the uniform blade geometry had a value of 1.35. When the rotation rate was reduced to 250 rpm, cavitation occurred at a flow coefficient of 0.72. From the simulations at both rotation rates, it was determined that both geometry and rotation rate have a significant effect on the onset of cavitation and water vapor inception within the flow field. As the rotation rate of the turbine decreases, the onset of cavitation will be prolonged to larger flow coefficients. As the flow coefficient increased beyond the value at which the onset of cavitation occurs, the intensity of cavitation increases and efficiency drops of up to 20% were experienced by the turbines. Based on the net positive suction head required in the system and the available head in the system, the cavitation results were validated. It was determined that the inception cavitation number, Cai, where the onset of cavitation occurs is approximately −1.51.

Diffuse interface modeling of a radial vapor bubble collapse

A diffuse interface model is exploited to study in details the dynamics of a cavitation vapor bubble, by including phase change, transition to supercritical conditions, shock wave propagation and thermal conduction. The numerical experiments show that the actual dynamic is a sequence of collapses and rebounds demonstrating the importance of nonequilibrium phase changes. In particular the transition to supercritical conditions avoids the full condensation and leads to shockwave emission after the collapse and to successive bubble rebound.

Application of cone-beam micro-CT on high-speed Diesel flows and quantitative cavitation measurements

X-ray computed tomography (CT) is well-known and widely used in the medical sector for diagnosis of various illnesses. The technique is based on the absorption (i.e. attenuation) of the ionising electromagnetic radiation by the object. The amount of energy to be absorbed depends on the density and its thickness; the transmitted radiation through the object is then compared to the incident radiation that leads to a reconstruction of attenuation coefficients versus spatial position in the object. Thus, the resulting three-dimensional slices of the object are used (a) to identify internal geometric features of objects, and (b) to distinguish between media of different densities, i.e. liquid and air/vapour. In this study, the geometry extraction capability has been applied on time-averaged cavitation pocket shapes, as well as, the capability of density differentiation measurements on Diesel fuel flows. Results appear promising and pose a challenge in providing quantitative measurements of cavitation vapour fraction inside an injection hole.

Analysis of the Stability of Elliptical Journal Bearings under Vapor Cavitation Erosion

The phenomenon of lubricant cavitation in hydrodynamic bearings and its effect on the stability has been rigorously studied and reported in the literatures. In certain cases, cavitation has significant effect on the dynamic and stability characteristics of the rotor-bearing system. With a proper control of the cavitation condition and groove location, stability can be achieved over a wide range of operating speed, in the case of elliptical journal bearings. On the other hand, the stability is not affected by the presence of vapor cavitation, in the case of multi-lobe journal bearings with the oil supplied at atmospheric pressure. For the unstable, submerged, circular bearings, vapor cavitation phenomena results in a distinctive vibration response observable on the vibration plots. The stability of the elliptical journal bearings under the influence of vapor cavitation erosion was analyzed. It is found that vapor cavitation erosion on elliptical bearings results in instability of the whirling shaft. Collapse of the vapor cavitation bubbles causes erosion wear that falls within the pressure zone of the elliptical bearing, thus causing the instability.

Development and Validation of a Three-Dimensional Computational Fluid Dynamics Analysis for Journal Bearings Considering Cavitation and Conjugate Heat Transfer

Computational fluid dynamics (CFD) analysis, which solves the full three-dimensional (3D) Navier–Stokes equations, has been recognized as having promise in providing a more detailed and accurate analysis for oil-film journal bearings than the traditional Reynolds analysis, although there are still challenging issues requiring further investigation, such as the modeling of cavitation and the modeling of conjugate heat transfer effects in the CFD analysis of bearings. In this paper, a 3D CFD method for the analysis of journal bearings considering the above two effects has been developed; it employs three different cavitation models, including the Half-Sommerfeld model, a vaporous cavitation model, and a gaseous cavitation model. The method has been used to analyze a two-groove journal bearing and the results are validated with experimental measurements and the traditional Reynolds solutions. It is found that the CFD method which considers the conjugate heat transfer and employs the gaseous cavitation model gives better predictions of both bearing load and temperature than either the traditional Reynolds solution or CFD with other cavitation models. The CFD results also show strong recirculation of the fresh oil in the grooves, which has been neglected in the traditional Reynolds solution. The above results show conclusively that the present 3D CFD method considering the conjugate heat transfer and employing the gaseous cavitation model provides an efficient tool for more detailed and accurate analysis for bearing performance.

Experience using pressure-based CFD methods for Euler–Euler simulations of cavitating flows

The paper is devoted to different approaches of a pressure–velocity coupling method to account for density variations in cavitating two-phase flow simulations. Results obtained from two strategies are investigated in detail. A simpler engineering approach associated the variations of the local density solely with the changes of the vapor-volume fraction computed by a cavitation model and assumes incompressible vapor and water phases. A more elaborate method additionally accounts for the compressibility of the two individual fluid phases. Numerical issues of significance for engineering applications are discussed in the paper, such as the occurrence of ill-conditioned matrices or cavitation-model dependencies. The single-phase verification and validation study refers to prominent aerodynamic benchmarks, i.e. a convergent-divergent nozzle flow and the flow over a bump in a channel. Cavitating flow validations are concerned with a stationary flow over a hydrofoil. An unsteady cavitating flow over a NACA0015 hydrofoil is computed to demonstrate merits of the implemented compressible fluid method to simulate sheet and vapor cavitation including the collapse of a vapor cloud followed by a shock wave formation and propagation. Results demonstrate that the predicted cavitation pattern of the two approaches are very similar and the compressible flow model is only required when attention is directed to the evolution of pressure waves of the collapsing cavities, e.g. in erosion studies.

EFFECTS OF NONCONDENSABLE GAS ON CAVITATING NOZZLES

This paper focuses on the analysis of low-pressure regions inside fuel injector nozzles, where fuel vapor formation (strictly referred to as cavitation, or vaporous cavitation) and expansion of noncondensable gas (also referred to as pseudo cavitation, or gaseous cavitation) can simultaneously occur. Recently, X-ray radiography experiments of a 500 µm diameter cavitating nozzle showed that the presence of dissolved gas in the fuel can cause significant changes in the apparent distribution of projected void fraction. In this article, the effect of dissolved gas on cavitation measurements is investigated in further detail through experimentation and numerical simulations. Test conditions have been selected to have highly cavitating conditions. Tests with a standard gasoline calibration fluid and equivalent degassed fluid are compared and discussed. Numerical simulations have been conducted under the same conditions as the radiography experiments. The primary goal of the study is a quantification of the separate contributions of gas expansion as opposed to actual cavitation to the measurement of total void fraction. The multiphase flow is represented using a mixture model. Phase change is modeled via the homogeneous relaxation model. Particular attention is paid to quantifying the effective amount of noncondensable gas included in the mixture, in order to predict the response of regular and degassed fuels. The presence of dissolved gas in the multiphase flow is taken into account using a compressible fluid model with three distinct components (liquid, vapor, and gas). Issues surrounding estimation of the effective amount of noncondensable gas are discussed. Numerical simulation results match well with the experiments and indicate that when a sufficient quantity of gas is dissolved in the fuel, a void is evident in the central region of the channel that can be attributed to local expansion of noncondensed gas. Conversely, degassed fuel shows only intense cavitation at the nozzle wall, with very little contribution from noncondensed gas.

Modeling gaseous and vaporous cavitation in liquid flows within the context of the thermodynamics of irreversible processes

This paper deals with the modeling of gaseous and vaporous cavitation in homogeneous and isothermal flows of compressible Newtonian liquids. The constitutive equations are derived within the framework of the thermodynamics of irreversible processes. The rate mass transfer related to the cavitation phenomena are consistently described as irreversible processes, being each of these mechanisms associated with a specific rate of energy dissipation. By means of a simple numerical simulation, which describes an expansion motion of water at room temperature confined in a piston–cylinder system, the influence of each type of cavitation on the mechanical response of the fluid is investigated, when they act isolatedly and simultaneously. The obtained results show that quite distinct physical behaviors are observed. The vaporous cavitation significantly inhibits the mass transfer process associated with the gaseous cavitation, but the reciprocal is not true.

Experimental Investigation of Vibration Characteristics for Vapor Cavitation in Plain Journal Bearing

The phenomenon of lubricant cavitation in hydrodynamic bearings and its detrimental effects have been documented in many literatures. Collapse of vapor cavitation bubbles may cause erosion wear that limits the life of the bearings. The ability to detect the occurrence of vapor cavitation using a well established condition monitoring technique is essential for the equipment operator. An experiment was conducted to investigate the vibration characteristics of vapor cavitation in steadily loaded plain journal bearings. Vibration data were collected from the bearings operating under the influence of vapor cavitation. It is shown that, vapor cavitation exhibits distinct characteristics on the vibration plots. Low amplitude, forward and reverse 0.063X frequency components, and a series of harmonics with frequencies lower than 0.5X, are observed on the full spectrum. A unique waveform with the positive peak amplitude fluctuating above and below the zero axis line is also observed.

Prototype and Laboratory Low-Level Outlet Air Demand Comparison for Small-to-Medium-Sized Embankment Dams

AbstractLow-level outlet works through dams are typically used to provide irrigation, reservoir sediment flushing, reservoir draw down, and/or minimum downstream flows to meet biological needs. To reduce the likelihood of negative pressure development downstream of the control gate, which may lead to cavitation noise, vibration, and damage, air vents are typically installed downstream of the gate. Undersized air vents may allow vapor pressure and cavitation to occur; oversized air vents have a negative economic impact. Air demand design criteria have been developed for vertical control gates (common to larger dams). The guidance for sizing air vents for an inclined slide gate, which are common for small-to-medium-sized embankment dam geometries, however, is limited. This study compares laboratory-scale and prototype-scale air-demand data. The influences of conduit slope, hydraulic jump presence, and air delivery system geometry on air demand were found to influence air demand. A method for estimating the ...

Modeling Vaporous Cavitation in Transient Pipe Flow Using the Zielke’s Friction Model

This study provides a theoretical and numerical modeling of transient vaporous cavitation in a horizontal pipeline, anchored to the upstream reservoir. The model approach is, essentially, based on that of the column separation model (CSM). The basic system of partial differential equations to solve is a hyperbolic type and adapts perfectly to the method of characteristics. This code, allows us, taking into account the unsteady part of the friction term, to determine at any point of the pipe, and at each instant, the average piezometric head, the average discharge and the change in volume of the vapour cavity. This study illustrates the effect of the presence of air pockets, resulting in cavitation, on the amplitude of the pressure wave. The calculation results are in good agreement with those reported in the literature

Geometry as a Catalyst: How Vapor Cavities Nucleate from Defects

The onset of cavitation is strongly enhanced by the presence of rough surfaces or impurities in the liquid. Despite decades of research, the way the geometry of these defects promote the nucleation of bubbles and its effect on the kinetics of the process remains largely unclear. We present here a comprehensive explanation of the catalytic action that roughness elements exert on the nucleation process for both pure vapor cavities and gas ones. This approach highlights that nucleation may follow nontrivial paths connected with a sharp decrease of the free energy barriers as compared to flat surfaces. Furthermore, we demonstrate the existence of intermediate metastable states that break the nucleation process in multiple steps; these states correspond to what is commonly known as cavitation nuclei. A single dimensionless parameter, the nucleation number, is found to control this rich phenomenology. The devised theory allows one to quantify the effect of the geometry and hydrophobicity of surface asperities on nucleation. Within the same framework, it is possible to treat both vapor cavitation, which is relevant, e.g., for organic liquids, and gas-promoted cavitation, which is commonly encountered in water. The theory is shown to be valid from the nano- to the macroscale.

Analysis of Transient Vaporous Cavitation in Pipes by a Distributed 2D Model

AbstractThe features of an axial-symmetric two-dimensional (2D) model in a transient cavitating pipe flow are investigated. A distributed vaporous cavitation model is proposed, based on the mass and momentum balance equations for a liquid-vapor mixture. A conservation form of the continuity equation allows a simple numerical solution. Both one-dimensional (1D) and 2D models are considered to quantify the effect of friction in the simulation of experimental data. The axial-symmetric 2D model allows the evaluation of the velocity profile and a more accurate estimate of the wall shear stress. The comparison between the results of numerical runs and experimental data of pressure head oscillations in transient cavitating pipe flows shows that the errors on maximum head oscillations of 2D model are generally greatly reduced with respect to those of the 1D model. As expected, the quasi-steady 1D model does not adequately represent the experimental data, with exception of the first maximum oscillations, whereas t...

High-resolution large eddy simulations of cavitating gasoline–ethanol blends

Cavitation plays an important role in the formation of sprays in fuel injection systems. With the increasing use of gasoline–ethanol blends, there is a need to understand how changes in fluid properties due to the use of these fuels can alter cavitation behavior. Gasoline–ethanol blends are azeotropic mixtures whose properties are difficult to model. We have tabulated the thermodynamic properties of gasoline–ethanol blends using a method developed for flash-boiling simulations. The properties of neat gasoline and ethanol were obtained from National Institute of Standards and Technology REFPROP data, and blends from 0% to 85% ethanol by mass have been tabulated. We have undertaken high-resolution three-dimensional numerical simulations of cavitating flow in a 500-µm-diameter submerged nozzle using the in-house HRMFoam homogeneous relaxation model constructed from the OpenFOAM toolkit. The simulations are conducted at 1 MPa inlet pressure and atmospheric outlet pressure, corresponding to a cavitation number range of 1.066–1.084 and a Reynolds number range of 15,000–40,000. For the pure gasoline case, the numerical simulations are compared with synchrotron X-ray radiography measurements. Despite significant variation in the fluid properties, the distribution of cavitation vapor in the nozzle is relatively unaffected by the gasoline–ethanol ratio. The vapor remains attached to the nozzle wall, resulting in an unstable annular two-phase jet in the outlet. Including turbulence at the conditions studied does not significantly change mixing behavior, because the thermal nonequilibrium at the vapor–liquid interfaces acts to low-pass filter the turbulent fluctuations in both the nozzle boundary layer and jet mixing layer.

Compressible Fluid Model for Hydrodynamic Lubrication Cavitation

In this paper, it is shown how vaporous cavitation in lubricant films can be modeled in a physically justified manner through the constitutive (compressibility) relation of the fluid. The method treats the flow as a homogeneous mixture employing a “void fraction” variable to quantify the intensity of cavitation. It has been already proposed to study cavitation in fluid mechanics. It is shown how the widely used Jakobsson–Floberg–Olsson (JFO) / Elrod–Adams (EA) mass flow conservation model can be compared with this new model. Moreover, the new model can incorporate the variation of the viscosity in the cavitation region and allows the pressure to fall below a cavitation pressure. Numerical computations show that discrepancy with JFO/EA is mostly associated with light loading condition, starved situation or viscosity effects.

Hydraulic Transients Induced by Pigging Operation in Pipeline with a Long Slope

Pigging in pipelines basically performs operations for five reasons including cleaning the pipe interior, batching or separating dissimilar products, displacement, measurement, and internal inspection. A model has been proposed for the dynamic simulation of the pigging process after water pressure testing in a long slope pipeline. In this study, an attempt has been made to analyze two serious accidents during pigging operation in 2010 by the model which is developed by the method of characteristic (MOC) by Wylie et al. (1993) and the two-phase homogeneous equilibrium vaporous cavitation model deveoped by Shu (2003) for vaporous cavitation. Moreover, simulation results of the third operation show good agreement with field data from the previous field trial. After investigation, it was showed that the impulse pressures produced during collapse of a vapor cavity result in severe damage of tubes.