Interface Height Research Articles

Effects of surface shapes on properties of turbulent/non-turbulent interface in turbulent boundary layers

The effects of directional riblets surfaces on the turbulent/non-turbulent (T/NT) interface in turbulent boundary layers are experimentally investigated using two-dimensional time-resolved particle image velocimetry (PIV). The velocity field of streamwise—wall-normal plane for the smooth surface, converging and diverging riblets surfaces are measured. The interface is detected using the criterion of local kinetic energy. The statistical properties of interface height and conditional averaged velocity for different surfaces are analyzed. It is shown that, the converging and diverging riblets surfaces have little effect on the fractal dimension of the T/NT interface, but they cause the intermittency profile deviate from error function and the probability distribution of interface height deviate from Gaussian function. To be specific, the distribution of interface height for the converging riblets surface shows a positive skewness while it shows a negative skewness for the diverging riblets surface. Moreover, the conditional averaged streamwise velocity and spanwise vorticity across the interface are analyzed, and it is found that their self-similarities are preserved for different surfaces when normalized with respective friction velocity. The correlation analysis reveals that near-wall streamwise velocity fluctuation and interface height show a negative correlation.

Time-averaged height distribution of the Kardar–Parisi–Zhang interface

We study the complete probability distribution of the time-averaged height at point x = 0 of an evolving 1 + 1 dimensional Kardar–Parisi–Zhang (KPZ) interface . We focus on short times and flat initial condition and employ the optimal fluctuation method to determine the variance and the third cumulant of the distribution, as well as the asymmetric stretched-exponential tails. The tails scale as and , similarly to the previously determined tails of the one-point KPZ height statistics at specified time . The optimal interface histories, dominating these tails, are markedly different. Remarkably, the optimal history, , of the interface height at x = 0 is a non-monotonic function of time: the maximum (or minimum) interface height is achieved at an intermediate time. We also address a more general problem of determining the probability density of observing a given height history of the KPZ interface at point x = 0.

Estimating leaked hydrogen gas flow in confined space through coupling zone model and point source buoyancy plume theory

A semi-analytical model combining zone model and virtual point source buoyancy plume theory is proposed to predict the gas flow and dispersion behaviors of leaked hydrogen in confined space with an opening. The height of interface between the upper and lower layers, outflow velocity and hydrogen molar fraction in outflow at steady stage are quantitively analyzed to study the effects of leakage mass flux and opening geometry. A computational fluid dynamics (CFD) tool, FLACS, is employed to simulate the interested scenarios and validate the reliability of the developed model. The results show that the interface height declines as the leakage mass flux increases, but the outflow velocity and hydrogen molar fraction exhibit inverse tendencies. The interface height is positively proportional to both opening width and height, but the opening height plays a more important role. At steady stage, the simulated interface height fluctuates within 0.1 m uncertainty range, which is identical to the grid size, and it well fits the analytical estimations. The opening width affects the outflow velocity more greatly than that of opening height. The fluctuation of the simulated interface height enhances the inaccuracy of the predicted outflow velocity in the acceptable range. Meanwhile, it is found that with fixed opening geometry the ratio of outflow velocity with higher leakage mass flux to that with lower leakage mass flux remains at 1.28 when the leakage mass flux is doubled. The variations of opening width and height have little and significant effects on outflow hydrogen molar fraction, respectively. Similarly, for given opening geometry the ratio of hydrogen molar fraction with higher leakage mass flux to that with lower leakage mass flux is about 1.58 when the leakage mass flux is doubled.

Mechanism of molasses–water mixing behavior in bioethanol fermenter. Experiments and CFD modeling

Molasses is a first-generation bioethanol feedstock that is a byproduct of sugar production. Molasses is a viscous fluid; consequently, when it serves as a substrate, it needs to be dissolved in water to obtain the appropriate conditions for the yeast. Therefore, the mixing process of molasses and water is an essential factor that significantly affects the efficiency of the fermentation process. This work aims to study the molasses–water mixing behavior in a cylindrical cone-shaped stirred-tank system reviewed by the effect of the molasses–water rheological characteristics. The molasses–water mixing behavior was investigated through a simple visualization method by using a camera and a 650 nm red laser as an observation plane of molasses–water interface height changes. Based on the results of the rheological characterization, it is known that molasses are a non-Newtonian fluid that exhibits shear thinning behavior. A rheological model molasses–water mixture has been developed. The behavior of molasses–water mixture comprises three zone mechanisms. The Eulerian multiphase model is the closest to the experimental results, and the combination of the Eulerian multiphase model and Large Eddy Simulation can be applied to predict the mixing behavior in an industrial scale stirred-tank.

A theoretical and experimental study on the buoyancy-driven smoke flow in a tunnel with vertical shafts

In this study, a series of small-scale experiments was carried out in a model scale tunnel with dimensions of 20 m (Length) × 2 m (Width) × 1 m (Height) to investigate the characteristics of buoyancy-driven smoke flow in a tunnel with vertical shafts. Different shaft settings and four different longitudinal ventilation velocities were tested in the experiments. A theoretical model for the mass flow rate of buoyancy-driven smoke flow in the shaft was developed and validated. The gas temperature along the tunnel ceiling and smoke stratification were subsequently analyzed and discussed. The results showed that more shafts, greater shaft heights and greater shaft cross sectional areas can significantly increase the smoke extraction rate, and the total smoke mass flow rate in the shafts increases with the increasing ventilation velocity. The local pressure loss coefficient at the shaft inlet may not be a fixed value. An average value of 1.0 for this coefficient was recommended for engineering estimation and design of rectangular-shaped natural shafts. The presence of vertical shaft is beneficial to the smoke stratification and could increase the height of the smoke layer interface, especially for the downstream of the shaft.

Interface height fluctuations and surface tension of driven liquids with time-dependent dynamics.

Interfaces in phase-separated driven liquids are one example of how energy input at the single-particle level changes the long-length-scale material properties of nonequilibrium systems. Here, we measure interfacial fluctuations in simulations of two liquids driven by time-dependent forces, one with repulsive interactions and one with attractive interactions. The time-dependent forces lead to currents along the interface, which can modify the scaling of interface height fluctuations with respect to predictions from capillary wave theory (CWT). We therefore characterize the whole spectrum of fluctuations to determine whether CWT applies. In the system with repulsive interactions, we find that the interface fluctuations are well-described by CWT at one amplitude of the driving forces but not at others. In the system with attractive interactions, they obey CWT for all amplitudes of driving, allowing us to extract an effective surface tension. The surface tension increases linearly over two orders of magnitude of the driving forces, more than doubling its equilibrium value. Our results show how the interfaces of nonequilibrium liquids with time-dependent forces are modified by energy input.

Chaos in wavy-stratified fluid-fluid flow.

We perform a nonlinear analysis of a fluid-fluid wavy-stratified flow using a simplified two-fluid model (TFM), i.e., the fixed-flux model (FFM), which is an adaptation of the shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the short-wave physics leading to the Kelvin-Helmholtz instability (KHI). The interface dynamics are chaotic, and analysis beyond the onset of instability is required to understand the nonlinear evolution of waves. The two-equation FFM solver based on a higher-order spatiotemporal finite difference scheme is used in the current simulations. The solution methodology is verified, and the results are compared with the measurements from a laboratory-scale experiment. The finite-time Lyapunov exponent (FTLE) based on simulations is comparable and slightly higher than the autocorrelation function decay rate, consistent with previous findings. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square of the interface height exhibits a square-root dependence. It is demonstrated that this simple 1-D FFM captures the essential chaotic features of the interface dynamics. This study also adds to a growing body of work indicating that a TFM with appropriate short wavelength physics is well-behaved and chaotic beyond the KHI.

Study of interface composition and height column during absorption process

Packed and tray columns are widely used in the study of gas-liquid interaction during mass and heat transfer process. There exist a variety of column configurations and each design is performed according to specific purposes, such as nature of processing feed, number of components, product streams, type of operation, etc. Continuous contact between phases allows mass transfer, which is the case of process like absorption, distillation and extraction were fluid phases can be added at constant rate to the column. Understanding of mass transfer during such process is important for design purposes because proper design will allow correct separation and extraction of components. The concentration of components being transferred changes as it flows through the column. As a result, the concentration driving force changes along the height of the column. In the present paper we aim to model a gas absorption process after performing a mass balance along the column and determining the interface composition (mole fraction) and height of a packed tower.

Effect of initial placement level and wall thickness on maintenance of the marginal bone level in implants with a conical implant-abutment interface: a 5-year retrospective study.

PurposeImplant wall thickness and the height of the implant-abutment interface are known as factors that affect the distribution of stress on the marginal bone around the implant. The goal of this study was to evaluate the long-term effects of supracrestal implant placement and implant wall thickness on maintenance of the marginal bone level.MethodsIn this retrospective study, 101 patients with a single implant were divided into the following 4 groups according to the thickness of the implant wall and the initial implant placement level immediately after surgery: 0.75 mm wall thickness, epicrestal position; 0.95 mm wall thickness, epicrestal position; 0.75 mm wall thickness, supracrestal position; 0.95 mm wall thickness, supracrestal position. The marginal bone level change was assessed 1 day after implant placement, immediately after functional loading, and 1 to 5 years after prosthesis delivery. To compare the marginal bone level change, repeated-measures analysis of variance was used to evaluate the statistical significance of differences within groups and between groups over time. Pearson correlation coefficients were also calculated to analyze the correlation between implant placement level and bone loss.ResultsStatistically significant differences in bone loss among the 4 groups (P<0.01) and within each group over time (P<0.01) were observed. There was no significant difference between the groups with a wall thickness of 0.75 mm and 0.95 mm. In a multiple comparison, the groups with a supracrestal placement level showed greater bone loss than the epicrestal placement groups. In addition, a significant correlation between implant placement level and marginal bone loss was observed.ConclusionsThe degree of bone resorption was significantly higher for implants with a supracrestal placement compared to those with an epicrestal placement.

Hybrid Data Regression Model Based on the Generalized Adaptive Resonance Theory Neural Network

The Generalized Adaptive Resonance Theory (GART) model is a supervised online learning neural network based on an integration of Adaptive Resonance Theory (ART) and the Generalized Regression Neural Network (GRNN). It is capable of online learning, and is suitable for undertaking both classification and regression problems. In this paper, we further enhance GART (EGART) with four improvements to formulate a new EGART model. Three operating strategies for the EGART model to undertake regression problems are suggested. The first operating strategy is a fully online learning EGART model. The second operating strategy involves Ordering Algorithm for determining the presentation sequence of training samples during the initial training of EGART model. This strategy is considered as offline learning because a set of data samples must be available for the Ordering Algorithm to compute the best presentation sequence (hereinafter denoted as Ordered-EGART). The third operating strategy aims to demonstrate online learning capability of EART model (the first operating strategy) can still be resumed after training on the Ordered-EGART. It is most suitable for applications with a set of ready data samples and their sequences are predetermined by Ordering Algorithm prior to training of EGART model in offline mode, and triggers online learning when more new data samples become available (hereinafter denoted as IO-EGART). A series of experiments with five benchmark data sets from various application domains is conducted to assess and compare the effectiveness of the EGART model and three operating strategies with those of other methods published in literature as well as two fire safety engineering problems, i.e., predicting the thermal interface height in a single compartment fire and evacuation times in the event of fire. The results and comparisons with other approaches positively demonstrate the efficacy and applicability of EGART model as a useful data regression model for tackling fire safety engineering problems.

Separated oil-water flows with drag reducing polymers

The effects on velocity and turbulent properties of drag reducing polymers added in the water phase of oil-water flows were studied with Particle Image Velocimetry (PIV). The experiments were performed in separated horizontal oil-water flows in an acrylic pipe with an internal diameter of 14 mm. The test fluids were tap water (1.0 mPas, density = 1000 kg/m3) and a middle distillate oil (Exxsol D140; viscosity = 5.5 mPas, density = 828 kg/m3). Magnafloc 1011 (hydrolysed copolymer of polyacrylamide and sodium acrylate, HPAM; mol. wt. = 10 × 106 g/mol) was used as drag reducing agent in the water phase at 20 ppm concentration. Results showed that the polymer reduced frictional pressure drop at all conditions studied. The addition of polymer decreased the interface height and increased the in-situ average water velocity. The velocity profile in the water phase became more parabolic compared to the flow without polymer while the maximum velocity value increased. In addition, when polymer was added the axial stress tensor decreased close to the interface and the wall but increased in the middle of the flow, while the Reynolds and radial stress tensors reduced throughout the water phase. Two types of polyethylene oxide (PEO) polymers with different molecular weights, 5 × 106 g/mol and 8 × 106 g/mol were also tested. Drag reduction was found to increase with polymer molecular weight but depended also on the mechanical degradation of the polymers at high Reynolds numbers and on their ionic strength.

Review and Validation of the Current Smoke Plume Entrainment Models for Large-Volume Buildings

The design of smoke management systems in large-volume enclosures is of utter importance for life safety, property protection, and business continuity in case of fire. Despite the recent international trend in smoke control design towards the use of advanced fire models, simple plume entrainment correlations are the basis of the discipline and are still a common practice since they are often incorporated in technical documents for the design of smoke control systems. Different plume entrainment correlations have been developed over the years and are cited in different national codes and design guides. These correlations have been widely investigated for fires in small enclosures, but their applicability and accuracy in large enclosures is not clear. The present work studies the suitability and applicability of these approaches to properly predict the fire induced conditions within large volumes. The results obtained from the plume entrainment correlations have been compared with full scale experimental data in an 8.000 m3 enclosure. Based on the results obtained by this analysis performed in a large-volume enclosure, the current methods available of modelling fire and determining the smoke produced by the fire might not be suitable. It was observed that for the steady state, the McCaffrey correlation gave results closest to the experiments, and for the transient evolution of the smoke layer, the Zukoski correlation. On the contrary, the popular Thomas method underpredicted smoke production and entrainment, giving the highest smoke layer interface heights and leading to estimations that are not conservative (with errors between 36.5% and 101%). The authors analyze the reasons for the discrepancies and give some practical recommendations for the design of smoke control in large volume buildings, such as that the use of such models to predict the smoke production of a given fire shall be only a first approximation and not a design tool, especially when using those models that have not shown a good match to the experimental data.

An experimental study on gas/liquid/solid three-phase flow in horizontal coalbed methane production wells

Coal particles caused by well drilling and completion, hydraulic fracturing, and formation pressure decreasing would migrate into the horizontal well carried by fracturing flow-back fluid, formation water and CBM, and then deposit on the low side of pipe leading to the decrease of cross section area of pipe for flow and even blocking of the pipe. The purpose of current research was to obtain the flow pattern while there was stationary solid particle bed on the low side of the pipe and an explicit equation to predict the height of solid particle bed was proposed. In this study, with the coal particle, water, and air as the solid, liquid, and gas phases respectively, gas/liquid/solid three-phase flow experiments in horizontal well were carried out and 4 crucial factors including different water flow rate, gas flow rate, coal particle size, and coal particle mass concentration were considered. Fluid's real apparent velocity was defined and used to analyze the distribution of flow pattern coordinate points. Results show that the flow pattern coordinate points determined by real gas apparent velocity and real water apparent velocity distribute near the flow pattern transition lines of Taitel and Dukler flow pattern map. Besides, coal particle size, water flow rate, and gas flow rate have obvious impact on the height of coal particle bed and the coal particle mass concentration has a negligible effect while the height of interface between gas layer and water layer is only dramatically affected by the gas flow rate. At last, an explicit equation for predicting the cross section area of coal particle bed based on the experimental data was proposed which is crucial to predict the flow pattern and calculate the pressure drop in horizontal well. The predicting cross section area of coal particle bed is in good agreement with the measured cross section area of coal particle bed and the average relative differences are 9.38% and 13.45% for stratified smooth flow and stratified wavy flow respectively. The equation is applicable for a range of coal particle size (8–30 mesh) and water apparent velocity (0.025–0.123 m/s).

Hydrodynamic Limit and Viscosity Solutions for a Two‐Dimensional Growth Process in the Anisotropic KPZ Class

AbstractWe study a two‐dimensional stochastic interface growth model that is believed to belong to the so‐called anisotropic KPZ (AKPZ) universality class [4,5]. It can be seen either as a two‐dimensional interacting particle process with drift that generalizes the one‐dimensional Hammersley process [1,24], or as an irreversible dynamics of lozenge tilings of the plane [5,29]. Our main result is a hydrodynamic limit: the interface height profile converges, after a hyperbolic scaling of space and time, to the solution of a nonlinear first‐order PDE of Hamilton‐Jacobi type with nonconvex Hamiltonian (nonconvexity of the Hamiltonian is a distinguishing feature of the AKPZ class). We prove the result in two situations: (1) for smooth initial profiles and times smaller than the time Tshock when singularities (shocks) appear or (2) for all times, including t &gt; Tshock, if the initial profile is convex. In the latter case, the height profile converges to the viscosity solution of the PDE. As an important ingredient, we introduce a Harris‐type graphical construction for the process. © 2018 Wiley Periodicals, Inc.

Effect of intermediate fluid layer on Kelvin–Helmholtz instability

Two-dimensional K-H (Kelvin–Helmholtz) instability of the three-component immiscible fluids with an intermediate fluid layer is numerically studied using the front-tracking method (FTM). The instability is governed by the Navier–Stokes equations and the conservation of mass equation for incompressible flow. A finite difference method is used to discretize the governing system. This study focuses on the influence of flow configuration, the thickness of intermediate fluid layer and the distribution of intermediate fluid layer on K-H instability. It is shown that the larger the initial horizontal velocity difference is, the faster the internal disturbance increases, and the characteristic form of K-H instability becomes more obvious for different flow configuration. It is also observed that the thickness of the intermediate fluid layer is negatively correlated to the billow height and the numerical growth rate. In addition, when the intermediate fluid layer is thicker than 0.4 times the disturbance wavelength, the billow height and the numerical growth rate for the K-H instability of the upper and lower interfaces change over time synchronously. The higher the initial height of the lower interface is, the greater the growth rate and billow height of the upper interface are. Besides, the upper and lower interfaces are rolled up synchronously over time when the intermediate fluid layer is symmetrically distributed with y = 0.5 in the fluid system.

Capillary Graph-Interfaces “in-the-Large”

This paper continues ongoing investigations into questions initiated by seventeenth-century experiments of Mariotte on mutual attractions and repulsions of floating objects, later reformulated mathematically by Laplace in the context of idealized surface tension theory. The characteristic nonlinearity in the governing equations imposes restrictions on behavior of solutions as graphs in the Laplace model, to the effect that a priori relations connecting height and inclination of a presumed surface interface occur, severely restricting the heights that can be achieved by solution curves. We develop below some relevant consequences of that phenomenon. The initial section provides general (perhaps inadequate) background, characterizes global qualitative behavior of all solutions of the underlying equations, and elucidates the significant distinctions in behavior that occur for solutions over an interval that extends unboundedly in one base direction. The section next following presents a non-existence result ensuing from the limitations imposed on such solutions (this result is elaborated in the Appendix). Next follow individual properties of general solutions. The remainder of the paper addresses the forces arising between partially submerged bodies. Theorem 6 offers an alternative derivation of a discovery due to Aspley, He, and McCuan, which displays a remarkable identification of net horizontal force with a first integral of the basic equations. These relations simplify significantly some earlier literature; additionally, as indicated in Section 5, they open the way to consideration of a much larger class of partially immersed objects than appears in the Laplace formulation. We complete Section 5 with an illustrative example in a particular case, indicative of a general study currently underway.

A modified zone model on vertical cable tray fire in a confined compartment in the nuclear power plant

Room fire with vertical cable tray involves upward flame spread along the cable. Assessing the vertical cable tray fire hazard in confined spaces has been challenging because of the strong coupling between flame spread and heat transfer. Long computing time is required in using sophisticated field model with computational fluid dynamics. Therefore, developing an appropriate zone model in a cable room fire with experimental validation is required for engineering applications. In this study, a vertical cable tray fire in a confined compartment was simulated using a modified zone model along three new areas on having temporal variations of the fire position, upward-spreading cable flame considered as a burning source moving at a constant speed, and validated through full-scale experiments on vertical cable tray fire with two typical cable-line spacing. The modified zone model can predict accurately the upper-layer temperature in the compartment. The accuracy is at least 25% higher than the model with fixed fire position. The measured temperature at different heights started to decrease at different times, which was due to the vertical spreading of the cable flame. For interface height, the relative error and normalized Euclidean distance in the time-varying fire position model can be improved by 50%.

Towards a CFD-based analysis of a full-scale sludge tank to enhance dewatering capacity of the downstream filter press

Abstract A computational fluid dynamics (CFD) model was developed for sludge mixing-settling in a laboratory scale sludge tank based on the Takacs exponential function. A dynamic experimental program was also undertaken at different rotational speeds of mixers and the concentration of sludge to validate the sludge sump model. The deviation between the simulated interface height and the experimental data was 2%. The validated CFD model was then employed to develop a novel operating methodology for operation of a full-scale sludge tank. The proposed model includes two consecutive periods of sludge mixing and settling, resulting in reducing the mixers’ working time. In the current operating mode, the energy consumption of mixers has been reduced by 91.67%. Based on the two-phase, 3-D modeling results of the sludge tank, the post-construction sludge tank is simultaneously able to act as a secondary clarifier, as well as a storage tank. As a key finding of the study, the treatment capacity of the filter press in downstream has accelerated, so that the working hours and energy consumption of the filter press has been improved by 55%.

Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica

We consider the fluctuations in the stochastic growth of a one-dimensional interface of height described by the Kardar–Parisi–Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the interface heights at two-times t1 and , with droplet initial conditions at t = 0. In the large-time limit, this JPDF is expected to become a universal function of the time ratio , and of the (properly scaled) heights h(x,t1) and h(x,t2). Using the replica Bethe ansatz method for the KPZ equation, in De Nardis and Le Doussal (2017 J. Stat. Mech. 053212) we obtained a formula for the JPDF in the (partial) tail regime where h(x,t1) is large and positive, subsequently found to be in excellent agreement with the experimental and numerical data (De Nardis et al 2017 Phys. Rev. Lett. 118 125701). Here we show that our results are in perfect agreement with Johansson’s recent rigorous expression of the full JPDF (Johansson 2018 in preparation (arXiv:1802.00729)), thereby confirming the validity of our methods.

A two-layer model for buoyant displacement flows in a channel with wall slip

We study theoretically buoyant displacement flows of two generalized Newtonian fluids in a two-dimensional (2-D) channel with wall slip. We assume that a pseudo-interface separates two miscible (immiscible) fluids at the limit of negligible molecular diffusion (negligible surface tension). A heavy fluid displaces a light fluid at near-horizontal channel inclinations, implying that a stratified flow assumption is relevant. We develop a classical lubrication approximation model as a semi-analytical framework that includes a number of dimensionless parameters, such as a buoyancy number, the viscosity ratio, the non-Newtonian properties and the upper and lower wall slip coefficients. For specified interface heights and slopes, the reduced model can furnish the flux and velocity functions in displacing and displaced phases. We numerically solve the interface kinematic condition for four different wall slip cases: no slip (Case I), slip at the lower wall (Case II), slip at the upper wall (Case III) and slip at both walls (Case IV). The solutions for these cases deliver the interface propagation in time, for which leading and trailing displacement front heights, shapes and speeds and several key displacement features, such as front characteristic spreading lengths and short time behaviours, can be directly predicted by simplified analyses. The results reveal in detail how the presence of a channel wall slip may significantly affect the overall displacement flow and the interface evolution characteristics, for both Newtonian and non-Newtonian fluids. Regarding the latter, our analysis quantifies in particular the appearance and removal of static residual wall layers of the displaced phase, versus the wall slip cases.