Regime Map Research Articles

Identification of flow patterns in an opaque condenser tube by distributed fiber Bragg gratings

Two-phase loops with phase change heat transfer are pivotal for cooling electronics under high heat flux and for thermal control in spacecraft. Numerous studies aim to clarify the mechanisms behind these loops to enhance cooling capacity and stability, which are closely tied to flow patterns. However, conventional flow pattern identification methods, requiring transparent tubes for direct observation, are impractical for simultaneous heat transfer measurement, especially during condensation. This paper introduces a novel approach for identifying flow patterns within an opaque, vertical condensation tube using embedded distributed fiber Bragg gratings (DFBGs) for R134a. The method involves a “fingerprint” derived from temperature profile derivatives and additional criteria based on temperature variation characteristics. These include the relative deviation from saturation temperature, the relative spatial temperature gradients, and the relative amplitude of temperature fluctuations. Validation against high-speed camera images confirms the method’s efficacy. It enables the determination of flow pattern lengths, the endpoint of condensation, and the construction of a flow regime map. Additionally, it allows for the measurement of vapor velocity in slug flow, facilitating the calculation of slip ratio and void fraction, which correlates reasonably with the Zuber-Findlay model, with systematic positive deviations up to 30%. This method also paves the way for simultaneous measurement of in-tube condensation heat transfer characteristics for various flow patterns.

Gas liquid flow pattern prediction in horizontal and slightly inclined pipes: From mechanistic modelling to machine learning

This paper investigates the prediction of two-phase gas-liquid flow regimes in both horizontal and slightly inclined pipes. For this purpose, the mechanistic model of Taitel et al. (1976) and the machine learning approach have been adopted. First, the mechanistic model was implemented, tested and optimised by introducing factors in the transition equations to determine the configuration that gives the highest prediction accuracy for a specific two-phase system for which experimental data points are available. Second, several machine learning models are trained, tested and additionally validated. This is done by splitting the experimental data set corresponding to the pipe inclination range (−10∘ to 10∘) into training, test and validation sets. The best classifier achieved an accuracy of 95.5% after the test step and up to 98.9% after the validation step. Finally, the Taitel et al. model with the optimal configuration and the best machine learning classifier (XGB classifier) are used to generate the two-dimensional flow regime map.

Neural network based two-phase flow classification in a vertical narrow rectangular channel

Flow Regimes in a vertical narrow rectangular channel of cross-section 20×1cm2 are investigated up-to wispy annular flow using a dense test matrix and double sensor conductivity probe at section mid point. The data from the probe is used to calculate void fraction, velocity of interfaces, and chord length of various flow structures. A five unit self organizing neural network is used to identify various flow regimes by using single point geometrical data of flow structures. Six separate flow regimes are found to exist. A new flow regime is identified and is called rolling-wispy flow. A discussion on boiling crisis is given regarding this flow regime. The resultant flow regime map is compared with various existing maps.

Mapping irrigation regimes in Chinese paddy lands through multi-source data assimilation

Water-saving irrigation (WI) is a crucial agricultural management with the benefits to save irrigation water, reduce energy consumption, and suppress methane emissions from paddy lands. Classifying WI practices from traditional flooding irrigation (FI) is a key component in detecting the rice irrigation status, which is significant to estimate the total agriculture-associated greenhouse gas emissions. In this study, we developed an automatic method to map irrigation regimes across Chinese paddy lands. First, we used seven variables related with irrigation facility or vegetation cover as proxy to generate representative WI and FI samples. Besides, we composited 123 features of optical bands and synthetic aperture radar from MODIS and Sentinel-1 data. Then, we trained a random forest model for each province with these samples. Finally, we applied the trained model to generate maps of WI/FI practices at 500 m resolution. Comparisons of the resultant maps with census data indicated highly accurate estimations of the WI area at a city- or province-level, with a R2 higher than 0.92. The overall accuracy of the classification was approximately 0.73, as validated through ground truth samples. Additionally, we also conducted a data quality analysis and confirmed the classification results were reliable in main rice production area of China. With the push towards carbon neutrality goals and the increasing demand for clean management practices, we developed and demonstrated an advanced method to produce near real-time maps of irrigation regimes and provide crucial data support for agricultural emissions reduction and irrigation management decisions.

Modulating outcomes of oil drops bursting at a water–air interface

Recent studies have shown that capillary waves generated by the bursting of an oil drop at the water–air interface produces a daughter droplet inside the bath, while a part of it floats above it. Successive bursting events produce next generations of daughter droplets, gradually diminishing in size until the entire volume of oil rests atop the water–air interface. In this work, we demonstrate two different ways to modulate this process by modifying the constitution of the drop. First, we introduce hydrophilic clay particles inside the parent oil drop and show that it arrests the cascade of daughter droplet generation preventing it from floating over the water–air interface. Second, we show that bursting behavior can be modified by a compound water–oil–air interface made of a film of oil with finite thickness and design a regime map, which displays each of these outcomes. We underpin both of these demonstrations by theoretical arguments providing criteria to predict outcomes resulting therein. Finally, all our scenarios have a direct relation to control of oil–water separation and stability of emulsified solutions in a wide variety of applications, which include drug delivery, enhanced oil recovery, oil spills, and food processing, where a dispersed oil phase tries to separate from a continuous phase.

Ambient-gas forced convection dictated evaporation kinetics of generic sessile droplets

We probe the temporal evolution of internal thermo-hydrodynamic features of evaporating sessile droplets under external forced convection. A transient numerical model based on Arbitrary Lagrangian-Eulerian (ALE) framework is adopted. The governing equations corresponding to the transport phenomena (mass, momentum and energy) are solved in a fully coupled manner in both the droplet (liquid) and ambient (gaseous) domains while accurately tracing the droplet interface evolution. The role of initial wetting state, external convection velocity and convective heating/cooling effects due to the air-flow are explored in details, and good agreements are noted with previous reports from literature. Results show that although the evaporation rate is augmented significantly in forced convection conditions, the same does not increase in proportion at higher Reynolds numbers. This is primarily due to the enhanced cooling effects that reduce saturated vapor concentration at droplet surface, and thereby supress the diffusion mechanism. Also, depending upon the contact angle, the evaporative cooling effects are compensated partially or completely due to convective heating. This altered thermal profile substantially influences internal hydrodynamic features (Marangoni flow and heat advection) during the transient and stable regimes of droplet evaporation. At higher degrees of convective heating, the droplet interface temperature becomes higher than its base temperature. This condition results in a completely opposite internal Marangoni vortex at stable state compared to that induced due to evaporative cooling effects. We also provide a regime map to show the role of the gas-phase Stefan number on the droplet-phase hydrodynamic regimes.

Thermo-hydrodynamic characterization and mapping of the two-phase flow in a capillary tube

The study presents an experimental investigation on the behavior of condensate film and liquid–vapor meniscus in the unit cell of a pulsating heat pipe (PHP) at different operating boundary conditions, and their respective roles in determining PHP’s performance. The orientation and the temperatures of evaporator and condenser sections are taken as the variable operating boundary conditions whereas the amplitude of oscillations influences the performance of the PHP. The entire thermo-hydrodynamic phenomenon is captured using high-speed imaging. By tracking the interface of liquid film and vapor, different regimes for film flow in the condenser section are observed and characterized. Also, the oscillation amplitude has been quantified at different operating boundary conditions. Despite a quite small tube diameter, gravity plays a key role in determining the liquid and vapor phase distributions in the tube. The variation of oscillation amplitude is intimately linked with the nuances of film flow regimes and inter-regime transitions. The optimum inclination angle, and evaporator and condenser temperatures are found to exist for the PHP unit cell which maximize the oscillation amplitude. The dependence of optimum inclination angle on condenser temperature has also been understood along with. Further, the associated film flow regime in condenser which facilitates these optima has also been recognized. All variable operating boundary conditions are observed to have a peculiarly mixed influence on the flow regimes and thus oscillation amplitude. The study would help to achieve a better elementary understanding of the role of condensate film flow in determining PHP’s performance and develop a flow regime map particularly for PHPs.

Influence of nanoparticle concentration on the flow regimes of crude oil – Nanosuspension in a microchannel

This paper presents the results of an investigation into the effect of silica nanoparticles on two-phase flow regimes in a Y-shaped microchannel. The following fluids were subjected to investigation: oil, water, and a water-based suspension containing SiO2 nanoparticles at a weight concentration of 1 ≤ φ ≤ 10 %. A systematic investigation of the flow regimes revealed the following: slug, parallel, and droplet regimes. The ranges of existence of the obtained flow regimes were determined and flow regime maps were constructed as a function of fluid flow rates and dimensionless numbers. The results of the study demonstrated that the slug length and frequency of slug formation are influenced by varying silica concentrations. Furthermore, the correlation between slug length and nanoparticle concentration remains consistent as the suspension flow rate increases. The dependence of the ratio of oil layer width to channel width for suspensions with varying nanoparticle concentrations was quantified. A mathematical simulation of two-phase flow of immiscible fluids was conducted. The results of the numerical simulation demonstrated the existence of the flow regimes that had been previously identified through experimentation. The aforementioned methodology may therefore be employed for the investigation of the two-phase immiscible flow of oil and nanosuspension.

Insights into the fluid dynamics of bioaerosol formation in a model respiratory tract

Bioaerosols produced within the respiratory system play an important role in respiratory disease transmission. These include infectious diseases such as common cold, influenza, tuberculosis, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) among several others. It is, therefore, of immense interest to understand how bioaerosols are produced within the respiratory system. This has not been extensively investigated. The present study computationally investigates how bioaerosols are produced in a model respiratory tract due to hydrodynamic interactions between breathed air and a thin mucus layer, which lines the inner surface of the tract. It is observed that Kelvin–Helmholtz instability is established in the thin mucus layer due to associated fluid dynamics. This induces interfacial surface waves which fragment forming bioaerosols under certain conditions. A regime map is created—based on pertinent dimensionless parameters—to enable identification of such conditions. Analysis indicates that bioaerosols may be produced even under normal breathing conditions, contrary to expectations, depending on mucus rheology and thickness of the mucus layer. This is possible during medical conditions as well as during some treatment protocols. However, such bioaerosols are observed to be larger (∼O(100)μm) and are produced in less numbers (∼100), as compared to those produced under coughing conditions. Treatment protocols and therapeutic strategies may be suitably devised based on these findings.

Splashing impact of a falling liquid drop

The splashing phenomenon associated with the impact of a liquid drop on a liquid pool is investigated in this study using the volume of fluid method. The different outcomes of this phenomena largely depend on the height (/depth) of a liquid pool and the impinging drop velocity. The impingement angle, drop shape, fluid properties, and other non-isothermal effects also play a role, but we have eliminated those dependencies by considering no variation in these parameters. The different phenomena that are observed when a drop impacts a liquid pool are controlled by (i) crater depth and wave-swell (rim of the crater) expansion, (ii) wave-swell retraction followed by crater side retraction, and (iii) crater base retraction. During splashing, a deep crater is produced in the receiving liquid after the drop impact. At its rim, a crown-like cylindrical liquid film is ejected out of the crater. Small droplets are normally shed from this rim. It is seen that the depth of the pool has dramatic effects on the dynamics of the crown formed during splashing. When observed even more comprehensively, the physical attributes of the crown, such as crown height and crown radius, are found to strongly relate to the velocity of the falling drop. Finally, we try to demarcate the regions of splashing with and without the formation of secondary droplets on the regime map of Weber number–dimensionless pool depth.

Experimental characterization of dynamics of bed‐scale liquid spreading in a trickle bed

AbstractWe report measurements performed to understand the effects of gas (QG) and liquid (QL) flow rates, surface tension (σGL), liquid viscosity (μL), and particle diameter (dp) on dynamics of local liquid spreading, pressure drop, and overall liquid holdup in a pseudo‐2D trickle bed. We show that an increase in the gas‐phase inertia leads to a decrease in the lateral liquid spreading, whereas an increase in the liquid‐phase inertia leads to an increase in the lateral liquid spreading. We also show that an increase in dp causes a reduction in the lateral liquid spreading. Using dimensionless numbers (AB and We), we propose a regime map showing contributions of different forces to the local liquid spreading. We show that the interplay between the inertia and capillary forces governs the liquid distribution near the inlet, whereas the relative contribution of gravitational force increases toward the outlet. Finally, we propose a relation between AB and We for “bed‐scale” liquid spreading.

Universal Correlation for Droplet Fragmentation in a Microfluidic T-Junction.

Despite extensive research on droplet dynamics at microfluidic T-junction, for different droplet lengths and Capillary numbers, there remains limited understanding of their dynamics at different viscosity ratio. In this study, we adopt a modeling framework in a three-dimensional (3D) configuration to numerically investigate the droplet dynamics as it passes through a symmetric T-junction with varying Capillary numbers, droplet lengths, and viscosity ratios. We present a 3D regime map for the first time to demarcate the droplet breakup and no breakup regimes. Herein, we propose a simple surface equation accounting for the critical Capillary number for breakup, in terms of viscosity ratio and dimensionless droplet length. The proposed universal relationship aligns well with experimental and computational findings from the existing literature. Furthermore, we reveal a new droplet breakup characteristic at high viscosity ratio and high Capillary number where the droplet spreads almost twice its initial value before splitting. Overall, this research provides comprehensive understanding of droplet dynamics at the T-junction and has significant implications for several related applications, including the large-scale synthesis of microdroplets using microchannel networks.

Flow regime transition maps and pressure loss prediction of gas, oil and water three-phase flow in the vertical riser downstream 90° bend using data driven approach

The simultaneous flow of gas, oil & water is frequently encountered in pipelines during upstream petroleum operations. The multiphase flow results in different types of flow patterns based on the flow rates of fluids, physical properties and geometry of the flow domain. The flow behavior is characterized based on the governing flow patterns. Hence, the information about the flow patterns, regime maps and resulting pressure loss are important for multiphase flow system design and optimization. The current work is focused on construction of gas, oil and water, three-phase flow regime maps and developing pressure loss prediction correlations for the flow through vertical riser downstream 90° bend. The pipe internal diameter (ID) is 6 inch and the bending radius to pipe diameter ratio is 1. The observed gas-liquid flow patterns are slug, churn, and semi-annular churn flow at the given range of superficial velocities of fluids. The flow pattern data has been used to construct flow regime maps to analyze the variation in flow patterns with flow rates of fluids and compared with the available works in the literature. In addition, the change in pressure loss with respect to flow patterns has been analyzed. Previous models are used for the prediction of pressure loss. However, according to the assessment, the models underpredicted the pressure loss. Based on three-phase pressure loss data, multiple linear regression analysis has been carried out to propose new correlations for pressure loss prediction. Comparison of the calculated and experimental data showed good agreement between the results. The knowledge of flow regime variation and pressure loss correlations can help flow assurance engineers in designing and optimization of multiphase flow systems.

Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.

Modeling the evaporation and drying of two-component slurry droplets

In this paper, we present a mathematical model and numerical simulation for the evaporation and drying of a liquid droplet containing suspended solids, relevant to processes such as spray drying and spray pyrolysis in the food and pharmaceutical industries. The model comprises three stages: first is the evaporation of the liquid droplet consisting of solid particles, followed by the second stage starting with the formation of a porous crust around a wet-core region and, finally, the third stage with sensible heating of the dry particle. Using a finite difference method with a moving grid, we account for the moving interface between the crust and wet core. Our model incorporates spatial temperature variations and is validated against experimental data on colloidal silica droplet drying, showing good agreement. We examine model assumptions and analyze the impact of drying conditions on drying rate and final particle morphology. Along with the temperature and velocity of the drying gas, we also find that the shape of suspended solid particles inside the droplet and assuming continuum flow of vapor through the crust influence drying quality. Finally, we develop a regime map to predict whether the final particle will be solid or hollow based on operating conditions.

Liquid metal droplets impacting superhydrophobic surface in a viscous (non-oxidizing) environment

The hypothesis of the present research is the existence of distinct spatial-temporal characteristics of non-oxidized liquid metal (LM) droplets impacting a solid surface. To provide a quantitative claim to this hypothesis, we created a test matrix based on the well-known impingement regime map bounded by two dimensionless quantities—Weber number (We) and Ohnesorge number (Oh). The range of these quantities is from 10−2 to 102 (We) and 10−3 to 101 (Oh), leading to Reynolds number (Re) (≡We1/2/Oh) to vary from 10−2 to 104. The class of LMs opted for are post-transition metals—eutectic gallium alloys—due to their several desired practical features, such as low melting point, non-toxicity, and low vapor pressure. The research is conducted using numerical experiments performed using C++ OpenFOAM libraries. To ensure the reliability of the code, we tested our work with numerous impingement behaviors of fluids available in the literature. A plethora of droplet behaviors are reported, such as deposition, rebound, bubble entrapment, and splash. Several features of droplet impingement were critically examined, such as temporal spreading factor, maximum spreading factor, and contact time of droplets on the surfaces. Moreover, the conventional scaling laws regarding the impingement behavior of droplets were tested, with new ones proposed where deemed necessary. Furthermore, a distinct route for the entrapment of droplet is observed, caused by the bulging of LM droplet during the recoiling stage. Emphasis is made to form delineations for these impingement characteristics using dimensionless groups (i.e., We, Oh, and Re).

Experimental study of the collision behavior between moving and sessile droplets on curved surfaces

In this study, we used pure water droplets to investigate the collision interactions of two droplets on curved surfaces. We captured the collision dynamics at different droplet impact velocities with the use of a high-speed camera. We observed three main modes during droplet collisions: deformation, coalescence, and rebound. We also plotted a collision regime map for different surfaces using the Weber number We and presented the critical We value for coalescence and rebound. With the increases of curvature radius, the critical We variates around 6.7 to 12.3 and presenting the tendency of increases first and then decreases. Furthermore, we quantitatively analyzed the transformation laws of droplet rebound height and compression value. Our main findings describe how the surface curvature radius influences droplet interactions, thus affecting the contact time, compression value and droplet deformation factor. The outcomes of droplet collisions on curved surfaces contribute to the development of technologies related to droplet manipulation and their applications in chemical and industrial processes.

Investigation of Laminar Forced and Mixed Convection in Horizontal Mini Tubes with Uniform Wall Heat Flux Boundary Condition

In this study, a numerical model is established to study the forced and mixed convection heat transfer in the laminar region for horizontal mini tube with different diameters (1.2 mm to 3.0 mm) under the uniform wall heat flux boundary condition. The Reynolds number is set from 100 to 2,000 and the uniform wall heat flux boundary condition is set at 10 and 20 kW/m2. The model is verified with well-established correlation to guarantee good accuracy. The existence of mixed convection is examined by (1) the ratio between the heat transfer coefficients at the top and the bottom of the tube, and (2) the temperature contour plot. Based on the simulation results, the existence of buoyancy superimposed on the main flow is strongly related to the tube diameter, the dimensionless location, the Reynolds number, and the heat flux applied. Under the same heating condition, for small diameter tube with insufficient length, buoyancy effect can never establish. The existing flow regime maps for macro tube were used to predict the forced and mixed convection regimes from the simulated mini tube results and discrepancy was found. A new flow regime map is hence developed for mini tubes, and it classified the simulation results with good accuracy.

Wake transitions of flow past two tandem semi-circular cylinders near a moving wall

Wake transitions of flow past two tandem semi-circular cylinders near a moving wall were numerically investigated using the lattice Boltzmann method at the Reynolds number of 150 with various gap ratios (G/D, where G and D are the spacing between the cylinder and wall and the cylinder diameter, respectively) and spacing ratios (L/D, where L is the distance between the cylinder centers). The analysis aims to clarify the effects of L/D and G/D on wake structures, hydrodynamic forces, Strouhal number, and spectral energy of the flow exerted on both cylinders. This study reveals five distinct flow regimes in the L/D-G/D space, such as overshoot, continuous reattachment, pair-wise, quasi-coshedding, and coshedding. These regimes are identified using plots of vorticity contour, time history of drag and lift coefficients (CD and CL), power spectral density, and proper orthogonal decomposition of the vorticity fluctuation into deterministic spatial structures. Furthermore, the flow regime maps and diagrams of time-averaged pressure coefficients on the surface of the cylinders are given to analyze the influence of the moving wall. A significant change in CD and CL is observed for both cylinders, depending on the L/D and G/D ratios. The time-averaged drag coefficient of the downstream cylinder is remarkably lower than that of the upstream cylinder. A significant increase in the time-averaged lift coefficient of the upstream cylinder is observed when the G/D is small due to near-moving wall effects. The root-mean-squared value of the lift and drag coefficients of the downstream cylinder is lower than that of the upstream cylinder as a result of the proximity effect. Meanwhile, the Strouhal number for both cylinders remains mostly the same.

Solutal Marangoni augmented levitation time of an aqueous surfactant drop over an immiscible oil pool

Droplets are found to exhibit a finite residence time over the volatile liquid pool due to the confined evaporation mediated sustained thin film draining. The levitated drops are quite critical in biomedical applications such as for the biophysical micro reactors. It is hypothesized that the presence of surfactants can induce solutal Marangoni and can further enhance the levitation time. Moreover, the surfactant drops can closely mimic the bio drop assay. Droplets of surfactant solutions are allowed to impact over a series of volatile hydrocarbon oils to understand the effect of surfactant concentration, impact height and the properties of the oil pool using high speed imaging technique. Flow visualization is employed in the pendant droplet mode to understand the Marangoni induced internal circulation. The droplets of surfactant solutions are found to exhibit enhanced residence time compared to the case of non-surfactant drops. The levitation time is a function of the surfactant concentration and the volatility of the oil pool. A mathematical model is developed incorporating the effect of solutal Marangoni to test the hypothesis and is found to predict the levitation time with reasonable accuracy. A universal floating–sinking regime map was developed incorporating the influence of governing parameters.