Homogeneous Flow Assumption Research Articles

Dynamics of a single cavitation bubble near a cylindrical blind hole

Cavitation bubble dynamics, such as microjets and moving shock waves, are strongly influenced by their surroundings. We investigated the complex bubble behavior during the growth and collapse stages near a blind hole. The simultaneous study, which is a combination of experiment and numerical methods, was performed. The single bubble was induced by a laser focus beam near a blind hole in the cuvette and measured by a high-speed camera with an image processing method. Numerical predictions were conducted for a detailed further investigation of the pressure and velocity fields near and inside the bubble. A fully compressible two-phase Navier-Stokes solver based on the homogeneous flow assumption was used. Both experimental and numerical results showed good agreement with each other. Strong deformation of the bottom bubble surface evolution was observed at low standoffs above the hole entrance. An extremely high-velocity microjet with a mushroom cap-shaped bubble was predicted under high standoffs below the hole entrance. Secondary cavitation in the blind hole was observed experimentally, and we discussed the low-pressure region caused by the interaction among the shock wave, bubble, and blind hole. Consequently, the tendencies of maximum microjet velocity and time-dependent surface pressure in the collapse phase are suggested.

Uncertainty and bias on velocities determined from an arc-scanning lidar

Accurate determination of wind speed offshore is important for the progression of offshore wind energy. Arc-scanning lidars offer precise measurements of both wind speed and direction. They can be placed on a fixed footing, such as a transition piece of a fixed-bottom wind turbine, or on the coast. However, the procedure to derive the wind vector relies on the assumption of homogeneous flow, i.e., that the wind vector is constant along the scanning arc. In this study, we derive a theoretical expression for the wind speed bias due to inhomogeneity in the mean flow. We show that inhomogeneity in the flow will mostly affect the wind component tangential to the arc. The dominating term in the bias equation is equal to the range gate distance times the gradient of the wind speed away from the lidar in the direction along the arc, i.e. crudely, how fast the wind component away from the lidar changes with the scan angle. Atmospheric simulations using the Weather Research and Forecast (WRF) model of flow near mountainous coasts (Madeira Island), where the wind gradients are supposed to be largest, are used to estimate the gradient and, thereby, the bias in a real case. Errors in special situations exceed 50%.

Comparison and analysis of the performance of a spiral groove mechanical seal subjected to phase change with different sealing media

The goal of this research is to investigate the impact of four kinds of easily vaporized sealing media(liquid hydrogen, liquid oxygen, liquid nitrogen and water) on phase change and sealing characteristics of a spiral groove mechanical seal(SGMS). Based on homogeneous flow assumption, a dynamic continuous boiling model is developed taking into account phase change of fluid film. With fluid pressure and fluid enthalpy as primitive variables, the properties of single-phase fluid and mixture fluid can be obtained by REFPROP software. The influence of the sealing medium on phase state stability criterion, steady-state and dynamic performances, and geometric structure parameter optimization is investigated. The findings reveal that dynamic viscosity is the key physical parameter of the sealing medium, affecting the seal stability and the phenomenon of phase change of an SGMS. The sealing medium with a high dynamic viscosity may obviously block the phenomenon of vaporization, which is advantageous in delaying the process of phase change and shortening the temperature range of quasi-vapor phase state in which an SGMS is unstable. The trends of steady-state and dynamic performances of an SGMS undergoing phase transition are identical for any type of easily vaporized fluid indicated in this work as a sealing medium. Taking into account both steady-state and dynamic performances, and independent of the type of sealing medium used, the best range of groove-to-dam ratio of an SGMS undergoing phase change is 0.5 < γ < 1.5.

The five main influencing factors for lidar errors in complex terrain

Abstract. Lidars have become a valuable technology to assess the wind resource at hub height of modern wind turbines. However, because of the assumption of homogeneous flow in their wind vector reconstruction algorithms, common wind profile Doppler lidars suffer from errors at complex terrain sites. This study analyses the impact of the five main influencing factors for lidar measurement errors in complex terrain, i.e. orographic complexity, measurement height, surface roughness and forest, atmospheric stability, and half-cone opening angle, in a non-dimensional, model-based parameter study. In a novel approach, the lidar error ε is split up into a part εc, caused by flow curvature at the measurement points of the lidar, and a part εs, caused by the local speed-up effects between the measurement points. This approach allows for a systematic and complete interpretation of the influence of the half-cone opening angle φ of the lidar on the total lidar error ε. It also provides information about the uncertainty in simple lidar error estimations that are based on inflow and outflow angles at the measurement points. The model-based parameter study is limited to two-dimensional Gaussian hills with hill height H and hill half-width L. H/L and z/L, with z being the measurement height, are identified as the main scaling factors for the lidar error. Three flow models of different complexity are used to estimate the lidar errors. The outcome of the study provides various findings that enable an assessment of the applicability of these flow models. The study clearly shows that orographic complexity, roughness and forest characteristics, and atmospheric stability have a significant influence on lidar error estimation. Based on the error separation approach it furthermore allows for an in-depth analysis of the influence of reduced half-cone opening angles, explaining contradiction in the previously available literature. The choice and parameterization of flow models and the design of methods for lidar error estimation are found to be essential to achieve accurate results. The use of a Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) model in conjunction with an appropriate forest model is highly recommended for lidar error estimations in complex terrain since forest (and roughness) tends to reduce the lidar error. If atmospheric stability variation at a measurement site plays a vital role, it should also be considered in the modelling. When planning a measurement campaign, an accurate estimation of the predicted lidar error should be carried out in advance to choose a reasonable measurement location. This will decrease measurement uncertainties and maximize the value of the measurement data.

Numerical investigation of turbulent cavitating flow in an axial flow pump using a new transport-based model

With the aim to enhance the capability of predicting cavitating flows for conventional cavitation models, a developed alternative numerical model was proposed based on an alternative truncated Rayleigh-Plesset equation and the homogeneous flow assumption. Particularly, the effect of vortex on mass transfer was accounted in the formulation of the proposed model. Turbulent cavitating flows under various flow rates in an axial flow pump with a specific speed ns = 692 were computed and compared by the proposed and the Schnerr-Sauer models, for which the experimental results were also presented for guidance. The results show that the cavitation performance predicted by the proposed model agrees better with the experiments than that by the Schnerr-Sauer model. The effect of vortex on mass transfer results in different patterns of the tip leakage vortex (TLV) cavitation near the tip leakage. Further, the solution of the proposed model reveals the corner vortex cavitation, shear layer cavitation and TLV cavita-tion could be integrated into a cloud vapor at critical cavitation number, and the cloud cavity sheds and collapses periodically near trailing edge of blade.

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Summary Espresso is a beverage brewed using hot, high-pressure water forced through a bed of roasted coffee. Despite being one of the most widely consumed coffee formats, it is also the most susceptible to variation. We report a novel model, complimented by experiment, that is able to isolate the contributions of several brewing variables, thereby disentangling some of the sources of variation in espresso extraction. Under the key assumption of homogeneous flow through the coffee bed, a monotonic decrease in extraction yield with increasingly coarse grind settings is predicted. However, experimental measurements show a peak in the extraction yield versus grind setting relationship, with lower extraction yields at both very coarse and fine settings. This result strongly suggests that inhomogeneous flow is operative at fine grind settings, resulting in poor reproducibility and wasted raw material. With instruction from our model, we outline a procedure to eliminate these shortcomings.

Removal of Saline Water due to Road Salt Applications from Columns of Two Types of Sand by Rainwater Infiltration: Laboratory Experiments and Model Simulations

Mass transport and residence time of saline water from road salt applications in soil columns composed of Toyoura sand and weathered granite sand were investigated by simulations and in laboratory experiments. Both are sands found in Japan, especially the weathered granite sand. The Toyoura sand has a fairly uniform particle size of 0.1 to 0.4 mm diameter, and a saturated hydraulic conductivity Ks = 0.0296 cm/s, while the weathered granite sand used consisted of 13% fine materials (silt and clay) and 87% coarse materials (sand and gravel) with a saturated hydraulic conductivity Ks = 0.00393 cm/s. A model was developed to simulate rinsing of brine from a soil column. Assuming a steady, homogeneous flow induced by rainwater infiltration into the soil column, the model was found to match the experimental results for Toyoura sand very well. The normalized salt concentration in the effluent from the 40 cm tall soil column remained constant until about t = 500 s; the concentration then decreased with time quickly and, finally, approached zero. For the weathered granite sand, however, the salt concentrations in the effluent simulated by the model with assumption of homogeneous flow are inconsistent with the experimental data collected. A substantial delay occurs in mass transport of salt from the column, which is different from the Toyoura sand. The delay is attributed to shifts in “active” and “inactive pores” created in the soil due to fine particles such as silt and clay. The proportion of “active pores” and “inactive pores” is not constant but variable with time due to physical and/or electrochemical processes such as pore-size distributions and salt depletion in the soil. A modified model presented, using a time-variable active pore parameter k(t), can reproduce the experimental results for salt mass left in the soil better.

A mechanistic model to predict pressure drop and holdup pertinent to horizontal gas-liquid-liquid intermittent flow

In this work a mechanistic model is proposed to predict pressure drop and phase holdup for viscous oil-water-gas flows within horizontal duct. The model is suitable for three phase intermittent (slug) flows where oil and water phases are fully mixed. However, validation is also made for slug flow with core-annular oil and water flow. This approach makes use of a correlation for total slug unit length developed by Babakhani Dehkordi (2017) as an input in the model so that the continuity equation is explicitly solved, reducing complexity of the present models in the literature survey. Furthermore, oil and water are assumed to have a homogeneous behavior to simplify three-phase flow equations. The model predictions are compared with experimental data of viscous oil-water-gas slug flows. Results revealed that inclusion of slug unit data together with assumption of homogeneous flow for oil and water in mechanistic model improved prediction of pressure drop over the range of investigated flow conditions.

Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

Assessment of improved Schnerr-Sauer model in cavitation simulation around a hydrofoil

To enhance the capability of Schnerr-Sauer model in simulating cavitating flows, in this study, we developed an improved Schnerr-Sauer model based on the Rayleigh-Plesset equation and homogeneous flow assumption. The model considers the effects of turbulent fluctuation and noncondensable gas. The unsteady cavitating flow over a two-dimensional Clark-Y hydrofoil was numerically investigated combined with the SST k-ω turbulence model, in which the turbulence eddy viscosity is corrected. We obtain the time-averaged lift and drag coefficients, the cavity shape evolution at cloud cavitation, and its x-velocity profiles from these calculations. Compared with available experimental data in the literature, the time-averaged lift and drag coefficients predicted from the improved Schnerr-Sauer model agree better with the experimental results than with those of the original. In addition, the modified model can accurately predict the characteristics of the time-averaged lift and drag coefficients during different cavitation conditions. Moreover, the improved model can better simulate the inception, growth, shedding, and collapse of cloud cavitation than the original model. The overall results prove the reliability and accuracy of the improved Schnerr-Sauer model in cavitating flow simulations over a hydrofoil.

Modelling emergency isolation of carbon dioxide pipelines

The development and experimental validation of a mathematical model for simulating the dynamic response of in-line Emergency Shutdown Valves (ESDVs) for high pressure Carbon Dioxide (CO2) transportation pipelines is presented. Based on the homogeneous flow assumption, the model accounts for the pertinent valve characteristics, including the activation and closure times, as well as its proximity to the rupture location. The validation of the model is based on the comparison of its predictions against measurements taken following the controlled Full Bore Rupture (FBR) of a 113-m long, 148mm i.d. pipeline containing CO2 at 15.1MPa and 300K, incorporating a ball valve along its length. The data recorded and simulated include the transient fluid temperatures and pressures immediately upstream and downstream of the closing valve following FBR. In all cases, very good agreement between the model predictions and recorded data is reported. Importantly, the minimum fluid temperature downstream of the closing valve is found to fall below the CO2 triple point indicating solid CO2 formation.

Nonuniform Flow Distribution Analysis of Air-Cooled Heat Exchanger

The header and the multiple microchannel tubes connected to the header compose a complicated fluid network with several circuits, and the refrigerant flow into the header and is distributed to the microchannels in parallel by the refrigerant pressure driving in the inlet. So all changed details of geometry, operating conditions and thermophysical properties of the fluids lead to nonuniform refrigerant flow distribution in the microchannels. In the present work, one 6-pass 40-tube microchannel condenser as the research objective was equipped in a window type air conditioner prototype with the cooling capacity 5200W for Middle East T3 climate. A mathematical model based on fluid network theory was developed to predict flow distribution and phase separation in 9 flat tubes and their connecting headers on the second pass of the microchannel condenser. In the assumption of homogeneous flow, the mesh current analysis was employed to solve the mass flow of the loopi+1 by that of the loopi upon two phase pressure drop. The simulated mass flow rate distribution in 9 tubes is parabolic and approaches to uniform distribution when inlet quality comes to the median 0.45 from both directions.

Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics

Abstract. Wind-profiling lidars are now regularly used in boundary-layer meteorology and in applications such as wind energy and air quality. Lidar wind profilers exploit the Doppler shift of laser light backscattered from particulates carried by the wind to measure a line-of-sight (LOS) velocity. The Doppler beam swinging (DBS) technique, used by many commercial systems, considers measurements of this LOS velocity in multiple radial directions in order to estimate horizontal and vertical winds. The method relies on the assumption of homogeneous flow across the region sampled by the beams. Using such a system in inhomogeneous flow, such as wind turbine wakes or complex terrain, will result in errors. To quantify the errors expected from such violation of the assumption of horizontal homogeneity, we simulate inhomogeneous flow in the atmospheric boundary layer, notably stably stratified flow past a wind turbine, with a mean wind speed of 6.5 m s−1 at the turbine hub-height of 80 m. This slightly stable case results in 15° of wind direction change across the turbine rotor disk. The resulting flow field is sampled in the same fashion that a lidar samples the atmosphere with the DBS approach, including the lidar range weighting function, enabling quantification of the error in the DBS observations. The observations from the instruments located upwind have small errors, which are ameliorated with time averaging. However, the downwind observations, particularly within the first two rotor diameters downwind from the wind turbine, suffer from errors due to the heterogeneity of the wind turbine wake. Errors in the stream-wise component of the flow approach 30% of the hub-height inflow wind speed close to the rotor disk. Errors in the cross-stream and vertical velocity components are also significant: cross-stream component errors are on the order of 15% of the hub-height inflow wind speed (1.0 m s−1) and errors in the vertical velocity measurement exceed the actual vertical velocity. By three rotor diameters downwind, DBS-based assessments of wake wind speed deficits based on the stream-wise velocity can be relied on even within the near wake within 1.0 m s−1 (or 15% of the hub-height inflow wind speed), and the cross-stream velocity error is reduced to 8% while vertical velocity estimates are compromised. Measurements of inhomogeneous flow such as wind turbine wakes are susceptible to these errors, and interpretations of field observations should account for this uncertainty.

Numerical simulation and analysis of the internal flow in a Francis turbine with air admission

In case of hydro turbines operated at part-load condition, vortex ropes usually occur in the draft tube, and consequently generate violent pressure fluctuation. This unsteady flow phenomenon is believed harmful to hydropower stations. This paper mainly treats the internal flow simulation in the draft tube of a Francis turbine. In order to alleviate the pressure fluctuation induced by the vortex rope, air admission from the main shaft center is applied, and the water-air two phase flow in the entire flow passage of a model turbine is simulated based on a homogeneous flow assumption and SST k-ω turbulence model. It is noted that the numerical simulation reasonably predicts the pressure fluctuations in the draft tube, which agrees fairly well with experimental data. The analysis based on the vorticity transport equation shows that the vortex dilation plays a major role in the vortex evolution with air admission in the turbine draft tube, and there is large value of vortex dilation along the vortex rope. The results show that the aeration with suitable air volume fraction can depress the vortical flow, and alleviate the pressure fluctuation in the draft tube.

Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres

Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple 'blob' argument, leading to the scaling γ̇0 ∝ σ3/2, where γ̇0 is the critical transition shear rate and σ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity - dominant effects for the brush and glycocalyx, respectively - which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.

Two-phase air–water flow in micro-channels: An investigation of the viscosity models for pressure drop prediction

Adiabatic two-phase air–water flow is experimentally studied in this work. Two channels, made of fused silica, with different diameters of 0.53 and 0.15 mm are used as test sections. The void fraction data for both tubes are obtained by image analysis. For the larger channel, the void fraction is found to be a linear relationship with the volumetric quality. In the case of the smaller one, however, the non-linear void fraction is obtained. The measured frictional pressure drop data are compared with the predictions regarding the homogeneous flow assumption. Several well-known two-phase viscosity models are subsequently evaluated for applicability to micro-channels.

Two-phase flow model of refrigerants flowing through helically coiled capillary tubes

This paper presents a numerical study of the flow characteristics of refrigerants flowing through adiabatic helically coiled capillary tubes. The theoretical model is based on conservation of mass, energy and momentum of the fluids in the capillary tube. The two-phase flow model developed was based on the homogeneous flow assumption. The viscosity model was also based on recommendations from the literature. The developed model can be considered as an effective tool for designing and optimizing capillary tubes working with newer alternative refrigerants. The model is validated by comparison with the experimental data of Kim et al. (2002) for R-22, R-407C and R-410A, and Zhou and Zhang (2006) for R-22. The results obtained from the present model show reasonable agreement with the experimental data. The proposed model can be used to design helical capillary tubes working with various refrigerants.

A multiscale mass transfer model for gas–solid riser flows: Part II—Sub-grid simulation of ozone decomposition

This article is to test the EMMS-based multiscale mass transfer model through computational fluid dynamics (CFD) simulation of ozone decomposition in a circulating fluidized bed (CFB) reactor. Three modeling approaches, namely types A, B and C, are classified according to their drag coefficient closure and mass transfer equations. Simulation results show that the routine approach (type C) with assumption of homogeneous flow and concentration overestimates the ozone conversion rate, introduction of structure-dependent drag force will improve the model prediction (type B), while the best fit to experimental data is obtained by the multiscale mass transfer approach (type A), which takes into account the sub-grid heterogeneity of both flow and concentration. In general, multiscale behavior of mass transfer is more distinct especially for the dense riser flow. The fair agreement between our new model with literature data suggests a fresh paradigm for the CFB related reaction simulation.

Two-phase pressure drop in a horizontal thin annulus: Effects of channel vibration and wall gas injection

Two-phase pressure drop in a narrow horizontal annular test section was experimentally investigated, using air and water as the working fluids. The annular test section had inner and outer diameters of 7.93 mm and 9.53 mm, respectively. In one group of tests (constant quality tests) air and water were mixed before entering the test section. In another group (variable quality tests), gas was injected into the test section via the porous inner test section wall. The liquid Reynolds number varied in the Re L = 50–9000 range, and the test section exit qualities covered the 0–25% range. The measured total pressure drops were compared with the predictions of a one-dimensional model with several two-phase frictional pressure drop correlations. The pressure variations caused by flow acceleration were calculated based on the homogeneous flow assumption. The correlation of Beattie and Whalley [D.R.H. Beattie, P.B. Whalley, A simplified two-phase frictional pressure drop prediction method, Int. J. Multiphase Flow 18 (1982) 83–87] agreed reasonably well with results of both groups of tests. The effect of lateral mechanical vibrations, imposed at the center of the test section, on two-phase pressure drop was also studied, with vibration amplitudes in the 0.034–0.2 mm range, and frequencies in the range 5–400 Hz. These effects were generally small.

Numerical modeling of two-phase refrigerant flow through adiabatic capillary tubes

Literature shows that the homogeneous flow assumption has been commonly used in most of the adiabatic capillary tube modeling studies due to its simplicity. The slip effect between the two phases was often not considered in this small diameter capillary tube. This paper attempts to exploit the possibility of applying the equilibrium two-phase drift flux model to simulate the flow of refrigerant in the capillary tube expansion devices. Attempts have been made to compare predictions with experimental results. The details flow characteristics of R134a in a capillary tube, such as distribution of pressure, void fraction, dryness fraction, phase’s velocities and their drift velocity relative to the center of the mass of the mixture are presented.