Liquid Volume Fraction Research Articles

Large-Eddy Simulation of Turbulent Dispersion Effects in Direct Injection Diesel and Gasoline Sprays

<div class="section abstract"><div class="htmlview paragraph">In most large-eddy simulation (LES) applications to two-phase engine flows, the liquid-air interactions need to be accounted for as source terms in the respective governing equations. Accurate calculation of these source terms requires the relative velocity “seen” by liquid droplets as they move across the flow, which generally needs to be estimated using a turbulent dispersion model. Turbulent dispersion modeling in LES is very scarce in the literature. In most studies on engine spray flows, sub-grid scale (SGS) models for the turbulent dispersion still follow the same stochastic approach originally proposed for Reynolds-averaged Navier-Stokes (RANS). In this study, an SGS dispersion model is formulated in which the instantaneous gas velocity is decomposed into a deterministic part and a stochastic part. The deterministic part is reconstructed using the approximate deconvolution method (ADM), in which the large-scale flow can be readily calculated. The stochastic part, which represents the impact of the SGS flow field, is assumed to be locally homogeneous and isotropic and, therefore, governed by a Langevin-type equation. The model is applied to the spray G and spray H conditions defined by the engine combustion network (ECN) group. Simulation results are compared with the available experimental data for spray characteristics such as penetration rates, mixture fraction profile, and droplet velocity and Sauter mean diameter (SMD) distributions. Simulations with no dispersion and the commonly used RANS-type stochastic model are also performed for comparison purposes. Results show that the turbulent dispersion has a considerable impact on quantitative spray characteristics such as projected liquid volume (PLV) fraction, droplet SMD and velocity, and fuel vapor mixture fractions. On the other hand, the macroscopic spray characteristics such as liquid- and vapor-phase penetrations are not significantly affected by the dispersion modeling. The proposed SGS model also improves the prediction of spray and ignition characteristics at the spray conditions studied in this work.</div></div>

Numerical simulation of 4-turns nitrogen pulsating heat pipe

In the present study, an investigation of temperature and pressure behavior in a two-dimensional closed-loop pulsating heat pipe (PHP) in vertical bottom heating mode has been carried out numerically. Nitrogen was used as working fluid in this 4-turns PHP. Structured meshing configuration has been used and Volume of Fluid (VOF) method has been employed for the two-phase flow simulation. Constant heat flux and constant temperature boundary conditions have been applied for the evaporator and the condenser sections, respectively. The initial condition was set as 0.5 liquid volume fraction and 77 K in every cell. Under the combined function of gravity and surface tension, pure liquid and vapor phase were produced, and the random liquid slugs and vapor bubbles distribution was formed. The temperature oscillation of every channel in evaporator and condenser sections was obtained and analysed.

Characterization of unsteady cavitating flow regimes around a hydrofoil, based on an extended Schnerr–Sauer model coupled with a nucleation model

The present work is aimed at the numerical spatio-temporal characterization of the unsteady cavitating flow structures on a hydrofoil by means of Proper Orthogonal Decomposition (POD) and Fast Fourier Transform (FFT) techniques. Three different cavitation regimes have been investigated: bubble cavitation, cloud cavitation and supercavitation. The homogeneous mixture approach has been used, in combination with an extended Schnerr–Sauer cavitation model. The accuracy of the numerical predictions has been improved by means of the implementation of a Density Correction Model of the turbulent viscosity, and a simplified Population Balance Modeling (PBM) which solved the spatial distribution and the temporal evolution of the nuclei. In particular, the PBM has led to a reduction of the intensity of the evaporation inside the vapor cavities and a consequent condensation enhancement at the cavity closure and in the wake downstream. This phenomenon mainly impacted on the vapor cavity dynamics during supercavition by facilitating the formation of the re-entrant jet and the vapor cavity detachment. Also, during supercavitation the nuclei density nb exhibited maximum variations of about 35.6% with respect to the inlet nuclei density. As the cavitation number increased, both the intensity and the extension of oscillations significantly reduced, and in bubble cavitation regime nb fluctuated at amplitudes of about 10% of the inlet nuclei density.The characterization of the cavitation regimes revealed that the bubble cavitation regime had a more stable and periodic dynamics highlighted by a higher hydrodynamic efficiency and a reduced root mean square of the lift force. The cloud cavitation and the supercavitation exhibited a more violent bubble detachment which caused stronger oscillations of the vapor cavity as well as the pressure upstream. This was retrieved in an increase of the average drag coefficient of about the 38% due to the presence of vapor cloud transported downstream, which promoted the surge of the flow. The vorticity analysis underlined that the formation of the re-entrant jet and the bubble detachment were promoted by the baroclinic vorticity, while the dilatation vorticity drove the dynamics of the detached clouds, governed by the phase change phenomena. The FFT analysis of the dynamics of the vapor cavity and the pressure upstream led to the detection of the most representative frequencies and Strouhal numbers of each cavitation regimes, in particular (fs=16.6Hz,St=0.355) for bubble cavitation, (fs=10.74Hz,St=0.358) for cloud cavitation, and (fs=8.79Hz,St=0.300) during supercavitation.The POD analysis allowed for the detection of the most relevant cavitating structures, in relation to the vapor cavity fluctuations and their frequency content. Furthermore, the FFT analysis of the temporal eigenfunctions demonstrated that the first POD mode of the liquid volume fraction described the overall unsteady behavior previously detected. Instead, high order POD modes revealed frequency values well above the overall ones of the main flow previously detected.

Spray dynamics of HVO and EN590 diesel fuels

This investigation aims at quantifying the spray dynamics of diesel-like injection at the steady stage. A 1D model based on momentum flux conservation and combined with Gaussian radial profiles is derived to predict the axial and radial velocity, fuel concentration, liquid volume fraction and density distribution within the steady spray field. To validate the model over a range of conditions, global quantities such as spray tip penetration, spray cone angle, spray tip velocity, and spray volume was measured by diffused back-illumination imaging. The spray characteristics of hydrotreated vegetable oil (HVO) and European standard diesel fuel (EN590) under different ambient air conditions (36 kg/m3 and 115 kg/m3) are compared to further predict the local velocity, fuel concentration, liquid volume fraction and density distribution. The present results indicate that an accurate model of diesel-like spray evolution can be obtained for different fuel types and ambient air densities.

Planar liquid volume fraction and SMD distribution of Jatropha vegetable oil spray: effect of ethanol blending and GLR

This research paper presents the planar distribution of Sauter Mean Diameter (SMD) and liquid volume fraction in airblast sprays of Jatropha vegetable oil. The effect of ethanol blending at different gas to liquid mass ratios (GLRs) is presented. The planar SMD distributions are obtained using Structured Laser Illumination and Planar Imaging-Laser Sheet Drop sizing (SLIPI-LSD) and Particle/droplet Imaging Analysis (PDIA) techniques. The straight vegetable oil (SVO) spray showed poor atomization at GLR 1, which rose with increasing GLR. The blending of ethanol significantly improved the atomization of SVO even at GLR 1 condition. The liquid volume fraction distribution increased with higher GLR and with the increase in the percentage of ethanol in the blend. The impact of the increase in ethanol on drop size is small at GLR of 5. The E30 blend showed uniformly distributed liquid in the spray plane with uniform SMD distribution in the range of 50 \(\upmu \)m at GLR 5.

Pore scale simulation of evaporation in a porous wick of a loop heat pipe flat evaporator using Lattice Boltzmann method

The evaporation heat transfer of a loop heat pipe (LHP) flat evaporator with porous wick is numerically simulated at pore scale using an advanced phase-change Lattice Boltzmann Method (LBM). The effects of heat flux and surface wettability (contact angle) on the patterns and dynamics of liquid-vapor interface, liquid volume fraction, temperature distribution at wick-fin and wick-groove interfaces, as well as effective heat transfer coefficient of the evaporator are investigated. It is found that liquid-vapor interface will appear five kinds of patterns or dynamics sequentially with the increase of heat flux, i.e., (a) entirely saturated wick, (b) partially saturated wick with periodical nucleation and vanishing of bubbles, (c) partially saturated wick with periodical growth and shrink of bubbles, (d) partially saturated wick with stable liquid-vapor interface, and (e) fully dry-out at wick-fin interface. Generally, the higher the heat flux and the larger the contact angle, the smaller the steady-state liquid volume fraction in the wick. However, at a certain range of heat flux, the liquid volume fraction oscillates periodically corresponding to periodical oscillations of liquid-vapor interface, and its amplitude and period increases with increasing heat flux and contact angle. Due to the random pore size distribution of porous wick, the temperature distributions are not symmetric between the left and the right outlets. This discrepancy is especially significant for partially saturated wicks, revealing the remarkable impacts of local pore structure on evaporation characteristics. With the increase of heat flux, the effective heat transfer coefficient at first increases owing to the inception and development of bubble nucleation within the wick, and then decreases due to the occurrence and enlargement of dry out. The larger the contact angle, the smaller the heat flux to trigger the bubble nucleation, and therefore the earlier to achieve the maximum effective heat transfer coefficient. Nevertheless, contact angles studied in this paper have no obvious effect on the maximum value of effective heat transfer coefficient.

Decompaction of wet granular materials under freeze-thaw cycling.

The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction ω in the considered range of 0.03<ω<0.32. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents ω≳0.15, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.

Modeling of the spherical explosion attenuation process using aqueous foam

The two-phase model of dry aqueous foam dynamic behavior under the strong shock wave influence is presented under assumption that the foam structure under shock loading is destroyed into a suspension of monodispersed microdrops with the formation of a gas-droplet mixture. The system of equations for the model of aqueous foam includes the laws of conservation of mass, momentum and energy for each phase in accordance with the single-pressure, two-speed, two-temperature approximations in a three-dimensional formulation, taking into account the Schiller–Naumann interfacial drag force and the Ranz–Marshall interfacial contact heat transfer. The thermodynamic properties of air and water forming a gas-droplet mixture are described by the Peng–Robinson and Mie–Grueneisen equations of state. The presence of non-uniform process in height of aqueous foam syneresis, which is due to gravitational forces, is taken into account by setting the distribution of the liquid volume fraction in the foam. An additional consideration of the syneresis process during calculating the intensity of interphase drag forces according to the Schiller–Naumann model was controlled by introducing the parameter depending on the spatial distribution of the initial liquid volume fraction of the foam. The spherical explosion is modeled in the form of the shock wave pulse whose energy coincided with the charge energy of the HE used in the experiments. The problem numerical solution is implemented using the OpenFOAM free software package based on the two-step PIMPLE computational algorithm. The numerical solution of the problem, obtained on the basis of the proposed gas-droplet mixture model, is in satisfactory agreement with the experimental data on a spherical explosion in aqueous foam. The analysis of the spherical shock wave dynamics while its propagation through aqueous foam is given. The causes of the significant decrease in the amplitude and velocity shock waves propagation in the medium under study are investigated.

Modelling phase change in a novel turbo expander for application to heat pumps and refrigeration cycles

A novel turbo expander based on the Tesla turbine is proposed to be applied to a heat pump or refrigeration cycle to improve the overall cycle efficiency. Initial numerical modelling of this turbo expander at representative conditions was carried out using the homogeneous relaxation model (HRM) to assess the influence of phase change on performance. The presence of a dense cloud of liquid droplets within the rotor was predicted to produce a significant back pressure on the turbine nozzle postponing the phase change. This was expected to occur in the vicinity at the outlet of the nozzle, but high volume fractions of liquid was predicted to penetrate deeper inside the rotor, especially at higher RPM. The resulting lower velocities of the liquid flow at the inlet of the rotor was predicted to significantly degrades the performance of the turbine. It is thus important for a successful implementation of this concept to remove as much liquid droplets as possible before the flow enters the rotor in order to minimise the back pressure.

Shock waves dynamics and evolution of vortex formation during the interaction of spherical air pulse with aqueous foam layer

The numerical study of the powerful air spherical shock-wave pulse interaction with the protective aqueous foam barrier with the initial liquid volume fraction of 0.2 is carried out. The foam layer thickness is selected to satisfy the condition of the non-reflection of compression wave from the foam external boundary at the considered time intervals. In studying the wave flows dynamics, we used the assumption of the foam structure destruction into the microdrops suspension behind the strong shock wave front. The two-phase medium is described on the basis of the gas-droplet mixture model, which includes the laws of conservation of mass, momentum and energy for each phase in accordance with the single-pressure, two-speed, two-temperature approximations in a two-dimensional axisymmetric formulation. The Schiller–Naumann model is used for taking into account the interfacial drag forces. The contact heat transfer influence at the interface between the phases is taken into account by the Ranz–Marshall model. To describe the properties of air and water, the Peng–Robinson and perfect fluid equations of state are used. The numerical implementation of the model is carried out using the OpenFOAM open-source software with the two-step PIMPLE algorithm. The numerical study results are presented as spatial distributions of pressure fields, velocities and streamlines. The significant attenuation of the spherical shock wave intensity during its interaction with the aqueous foam layer has been established. The causes and dynamics of the toroidal vortices series formation in the gas region behind the shock front are investigated. The results reliability is confirmed by comparison with the solutions of the similar problem, found by another numerical method.

Experimental study and dynamic characteristics analysis of partially liquid-filled annulus tubes.

As a useful technology, the horizontal drilling for underground coalmine has been applied in many fields such as gas drainage, water control, exploration and accurate drilling borehole engineering. In this paper, the annulus tubes are used to simulate the fluid transportation process between drilling rod and casing tube when drilling horizontally. The main goal of this research is to analyze the effects of eccentricity, fluid velocity, outer tube length and volume fraction on dynamic characteristics of partially liquid-filled annulus tube in a drillstring system. According to the Euler-Bernoulli beam model, the partially liquid-filled inner tube model and outer tube model are established respectively when considering the effect of transport fluid inside the annulus tubes. Based on the vibration characteristics of the tube, the added mass coefficient is proposed to calculate the natural frequencies of the outer tubes. And natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. According to the compared results of experiments and simulations, the natural characteristics of outer tube depend on the tube design parameter (outer tube length) and the volume fraction of liquid filled in the outer tube. Furthermore, experiments have verified that the natural frequencies of the outer tubes can be directly calculated from the length of outer tubes. Therefore, it is feasible to propose the method of attaching liquid mass to tube mass to obtain the natural frequencies of outer tubes. According to the results, it can be concluded that: (i) The natural frequencies of tube decrease as the length of the tube increases; (ii) The increase of volume fraction of liquid in the tube can significantly reduce the natural frequencies of tube; (iii) The fluid velocity and eccentricity have less effects on the natural frequencies of tube; (ⅳ) The added mass coefficient of outer tubes can be calculated and it is not a fixed value, it varies with the volume fraction of fluid in annulus tubes. In this work, the inner and outer tube models are established respectively for fluid transportation process between a horizontal drilling rod and casing tube. The effects of four factors on the natural frequencies are compared, and the concept of added mass coefficient is proposed to obtain reasonable tube natural frequencies.

CFD investigation of iodine mass transfer in venturi scrubbing solution of Filtered Containment Venting System

Removal of elemental iodine from gases using Filtered Containment Venting System (FCVS) was studied. Iodine was scrubbed from gases by passing it through venturi placed in scrubbing solution. This task was performed using ANSYS 14.0 FLUENT. Scrubbing solution was aqueous solution of sodium hydroxide and sodium thiosulphate in water. Two phase Euler-Euler multiphase model was used while transfer of iodine from gaseous phase to liquid phase was modelled using species transport model. No specific model was available in any CFD software package to model mass transfer of iodine in scrubbing solution. Therefore, a user defined function (UDF) for iodine mass transfer based on mathematical model proposed by Majid et al. was developed and implemented through FLUENT. Droplet diameter effect on mass transfer of iodine was studied. Large decrease in gas phase iodine, large mass transfer rate and sharp increase in liquid phase iodine was observed on decreasing droplet diameter. About 98% removal efficiency was observed in case of 1 micron droplet diameter while it decreased as the droplet diameter was increased. Thus, validating the mass transfer model for removal of iodine as removal efficiency lies within range reported in previously published experimental results. Increase in liquid volume fraction along venturi length was also noted due to mass transfer of iodine. Liquid droplets of smaller diameter achieved peak velocity close to gas phase. This peak velocity shifted more towards the diverging section as droplet diameter was increased.

Experimental investigation of the oil based Aphron drilling fluid for determining the most stable fluid formulation

Colloidal gas Aphrons, as a type of low weighted drilling fluid, have been recently used and their positive effect on formation damage has been proven. The stability of Aphron fluids is an important issue that can affect fluid loss. The purpose of this study is to provide the most stable oil-based Aphron drilling fluids. In this study, the continuous phase of the created fluids are made using oil based fluids and bubbles covered with Dodecyl benzene sulfonate and dispersed in the continuous phase which was viscositfied with the vegetable oil based polyurethane polymer. The stability of Aphron fluid is analyzed taking the drained liquid volume, Aphron half-life, and gas void fraction into account. It is observed that the oil based Aphron fluid including 13.4 kg/m3 concentration of the surfactant and 15 kg/m3 polymer was the most stable fluid, in which the sizes of bubbles have minimum variation with time.

Numerical Modeling of Heat and Specie Transfer in a Diffusion Dominated Continuum Model of Binary-Alloy Castings

A numerical modeling of diffusion-controlled heat and specie transfer using a source base method to determine evolution of liquid/solid fraction from energy equation both for constant densities in the phases and variable densities as a function of temperature and concentration was developed to predict macro-solute redistribution in binary alloy system. From the results, it is observed that there was a solute depleted zone near the chill surface and that, the source base method can be effectively implemented without the need for setting a large arbitrary value in determining the derivative of liquid fraction-temperature function . The cooling curve and the liquid volume fraction versus temperature profile shows a smooth transition from fully liquid to mushy zone and then to fully solid state, hence, adequate handling of the jump discontinuity was ensured. The liquid fraction-temperature relation outlined in this work is suitable for tracking the liquid/solid interface.

Estimating slug liquid holdup in high viscosity oil-gas two-phase flow

Slug flow is one of the most critical and often encountered flow patterns in the oil and gas industry. It is characterised by intermittency which results in large fluctuations in liquid holdup and pressure gradient. A proper understanding of its parameters (such as slug holdup) is essential in the design of transport facilities (e.g. pipelines) and process equipment (slug catchers, separators etc.). In this paper, experimental investigation of slug liquid holdup (defined as the liquid volume fraction in the slug body of a slug unit) is performed. Mineral oil with viscosity, μ=−0.0043T3+0.0389T2−1.4174T+18.141 and air were used as test fluids. A 0.0254 m and 0.0762 m pipe internal diameters facilities with pipe lengths of 5.5 and 17 m respectively were used in the study. Electrical Capacitance Tomography was used for slug holdup measurements. Results obtained in the study shows that slug liquid holdup varied directly as the viscosity and inversely as the gas input fraction. Existing slug holdup correlations and models in literature did not sufficiently predict present experimental results. A new empirical predictive correlation for estimating slug liquid holdup was derived from present experimental databank and from data obtained in literature. The databank's liquid viscosity ranges from 0.189 to 8.0 Pa s. Statistical analysis of the new correlation vis-à-vis existing ones showed that the present correlation gave the best performance with an average percent error, E1; absolute average percent error, E2 and standard deviation, E3 of 0.001, 0.05 and 0.07 respectively, when tested on the high viscosity liquid–gas databank.

Clearance Effects on Rotordynamic Performance of a Long Smooth Seal With Two-Phase, Mainly-Air Mixtures

This paper experimentally studies the effects of changing radial clearance Cr on the performance of a long (length-to-diameter ratio L/D = 0.65) smooth seal under mainly-air (wet-gas) conditions. The test fluid is a mixture of air and silicone oil. Tests are conducted with Cr = 0.188, 0.163, and 0.140 mm, inlet pressure Pi = 62.1 bars, exit pressure Pe = 31 bars, inlet liquid volume fraction LVF = 0%, 2%, 5%, and 8%, and shaft speed ω = 10, 15, and 20 krpm. The seal's complex dynamic stiffness coefficients Hij are measured. The real parts of Hij cannot be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, frequency-dependent direct KΩ and cross-coupled kΩ stiffness coefficients are used. The imaginary parts of direct Hij produce frequency-independent direct damping C. Test results show that, for all pure- and mainly-air conditions, decreasing Cr decreases (as expected) the leakage mass flow rate m˙. Under mainly-air conditions, decreasing Cr decreases KΩ. This outcome is contrary to the test results at pure-air conditions, where KΩ increases as Cr decreases. Since an unstable centrifugal compressor rotor may precess at approximately 0.5ω, the effective damping Ceff at about 0.5ω is used as an indicator of the impact a seal would have on its associated compressor. For pure-air conditions, when Ω ≈ 0.5ω, decreasing Cr increases Ceff and makes the seal more stabilizing. This trend continues after the oil is added. A bulk-flow model developed by San Andrés (2011, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) produces predictions to compare with test results. m˙ predictions correlate with measurements. Under pure-air conditions, the model correctly predicts the effects of changing Cr on KΩ and the Ceff value near 0.5ω. After the oil is added, as Cr decreases, predicted KΩ increases while measured KΩ decreases. Also, for mainly-air cases and Ω ≈ 0.5ω, decreasing Cr does not discernibly change predicted Ceff but increases the measured value.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration (SSV). To improve the annular seal behavior and increase the rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique, and the multifrequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of noncontact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth (LABY) seal, and a fully partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance, and axial length. The accuracy and the availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVFs) of 0%, 2%, 5%, and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15,000 rpm, and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and 14 subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that the inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal (PDS) and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.

Leakage and Rotordynamic Force Coefficients of A Three-Wave (Air in Oil) Wet Annular Seal: Measurements and Predictions

In subsea environments, multiphase pumps and compressors add pressure to the process fluid, thus enabling long distance tie back systems that eliminate topside oil and gas separation stations. One challenge to construct a reliable multiphase pump or a reliable wet gas compressor is that the first must handle, without process upset, a mixture whose gas volume fraction (GVF) changes suddenly; while the other must remain stable while working with a liquid volume fraction (LVF) changing over long periods of time. The mixture GVF/LVF affects the static and dynamic forced performance of secondary flow components, namely seals, and which could lead to an increase in both rotor lateral or axial vibrations, thus compromising system reliability and availability. The current research is a planned endeavor toward developing seal configurations amenable to maintain rotor dynamic characteristics during changes in the contents of flow components. This paper extends prior work with uniform clearance annular seals and presents the static and dynamic forced performance of a three-wave surface annular seal designed to deliver a significant centering stiffness. The test element has length L = 43.4 mm, diameter D = 127 mm, and mean radial clearance cm=0.191 mm. At a shaft speed of 3.5 krpm (23 m/s surface speed), an air in ISO VG 10 oil mixture with an inlet GVF, 0 to 0.9, feeds the seal at 2.5 bara pressure and 37 °C temperature. The mixture mass flow rate decreases continuously with an increase in inlet GVF; shaft speed has little effect on it. Dynamic load tests serve to identify the seal dynamic force coefficients. The liquid seal (GVF = 0) shows frequency independent force coefficients. However, operation with a mixture produces stiffnesses that vary greatly with excitation frequency, in particular the direct one that hardens. The direct damping coefficients are not functions of frequency albeit dropping rapidly in magnitude as the GVF increases. The work also compares the performance of the wavy seal against those of two other seals: one with clearance equal to the mean clearance of the wavy seal, and the other with a large clearance emulating a fully worn wavy seal. The small clearance seal leaks 20% less than the wavy seal, whereas the leakage of the worn seal is twofold that of the wavy seal. For the three seals, the leakage normalized with respect to a pure liquid condition collapses into a single curve. The wavy seal produces the greatest direct stiffness and damping coefficients, whereas the worn seal produces the smallest force coefficients. Derived from a homogeneous mixture bulk flow model, predicted force coefficients for the three-wave seal match well with the test data for operation with a pure oil and an inlet GVF 0.2. For operation with GVF &gt; 0.2, the discrepancy between the prediction and experimental data grows rapidly. The extensive test campaign reveals a wavy-surface seal offers a centering stiffness ability, a much desired feature in vertical submersible pumps that suffer from persistent static and dynamic stability issues.

Packed Bed Performance Analytics Based on Gamma Scans

Refinery and chemical plant operations depend heavily on distillation and separation towers. Tower gamma scanning is well established in the process industries as a qualitative tool to help troubleshoot towers. Advancements in data analysis have led to a quantitative approach in expressing gamma scan data in numerical terms easily understood by process and operations engineers.For packed towers, a grid-scan of 3 or 4 equal-distant scans crossing through the beds of packing would typically be used to investigate the quality of liquid distribution. The conventional approach to “analyzing” a gamma scan has been to visualize how well the scan data from the individual scans matched each other or how well they “overlaid” with each other. This is a totally subjective analysis lacking consistency, open to varying interpretation and does not translate well from tower-to-tower. Therefore, the resulting conclusions from this approach can be very ambiguous regarding the magnitude of any detected liquid mal-distribution.An alternative analytical approach, termed PackView™, has been developed whereby a relative density scale is calculated from data that the grid-scan provides. The density scale begins at the density of the dry or non-operating packing. The density scale displays the calculated density of liquid retained in the bed of packing based on the scan data results.Another calculation by which to put the liquid distribution into perspective and to get a measure on the useful capacity of the packing is to calculate the liquid holdup fraction or liquid volume fraction. If the measured liquid retention density is divided by the process liquid density at bed conditions (the liquid density at the actual operating temperature and pressure), liquid holdup or liquid volume fraction can be established. A comparison of the liquid holdup fraction to the packing operating capacity curves provides an objective appraisal of current operating capacity.It is always easier to understand and discuss technical issues when quantitative information can be used to compare operational parameters with engineering design. This advanced analysis provides a new method of extracting quantitative information from gamma scan data to diagnose and characterize the operation of distillation and separation towers. It is our goal that using the advanced analytics presented will improve the value of gamma scan data and facilitate improvements in the operation of mass transfer equipment.

A study on capillary actions of power-law fluids in porous fibrous materials via W-M function

The study of fluid diffusion is an important aspect of heat and mass transfer of the porous fibrous materials. This work established a fractal model for the diffusion of power-law fluids in porous fibrous materials by considering the pore size distribution and the tortuosity of the capillary. Adopting the Darcy’s law and the Hagen–Poiseuille’s law, the diffusion coefficient of power-law fluids is derived as a function of the tortuosity fractal dimension, the pore size fractal dimension and the flow behavior index, in which the phase transition and the adsorption effect of fiber as well as the influence of gas diffusion and temperature change are taken into consideration. And the Weierstrass–Mandelbrot (W-M) function is applied to manifest the detailed fractal characters of the pores. Focusing on an analytical expression of the diffusion of power-law fluids in porous fibrous materials, the changes of liquid volume fraction, gas concentration and temperature distribution subjected to the specification initial and boundary conditions are simulated numerically. The test of this approach on the height of fluids when the bottom of cotton fabrics is immersed in the water display the clear diffusion of fluid in fiber. Our preliminary results indicate the important roles that the porosity and flow behavior index play in the fluids transfer in the porous fibrous materials: the fluids with lower power law index rise higher heights and diffuse more rapidly, meanwhile, the height increases with the porosity.