Inertial Flow Research Articles

Microgravity two-phase flow research in the context of vapor compression cycle experiments on parabolic flights

Research on two-phase channel flow in microgravity has extensively investigated flow regimes, pressure drop, and heat transfer during evaporation and condensation processes over several decades. This literature has been primarily motivated by the goal of enabling future space applications for two-phase thermal management systems, among them vapor compression refrigeration cycles. However, relative to the number of two-phase channel flow experiments, research on vapor compression cycles in microgravity has been almost non-existent. This paper reviews two-phase flow research and compares key outcomes with those from system-level measurements obtained from recent testing of a vapor compression cycle at varying inclination angles and on parabolic flights. Previous two-phase channel flow experiments have resulted in several microgravity-specific flow regime maps and have also generally found reduced condensation heat transfer coefficients in microgravity as compared to normal gravity. The flow pattern map of Jayawardena et al. (1997) and generally reduced condensation heat transfer are confirmed by the vapor compression cycle experiments. Regarding evaporation heat transfer coefficients and friction factors, there is not a consensus in the literature on the effects of microgravity in two-phase channel flows. Similarly, the system-level experiments do not show repeatable increases or decreases for those parameters. Lastly, the dependence of system-level behavior on orientation with respect to gravity was tested by performing dynamic inclination experiments, where the inclination angle was changed every 2 min by a 90-degree increment. These tests reveal an increased relative dependence of the vapor compression cycle to orientation with decreasing mass fluxes, in line with two-phase channel flow research that has generally shown that increasing the flow inertia acts to mitigate various flow instabilities and dependence on orientation. However, inclination testing with longer locking times per angle showed a constant relative dependence of the vapor compression cycle to orientation changes.

Turbulence via intermolecular potential: A weakly compressible model of gas flow at low Mach number

In our recent works, we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature behave unrealistically in our inertial flow model. The goal of the current work is to demonstrate the technical possibility of modeling compressible, turbulent flow at a low Mach number where both density and temperature behave in a more realistic fashion. Here, we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible, and inertial flow. Similar to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically.

A method to measure non-Newtonian fluids viscosity using inertial viscometer with a computer vision system

The theory of rheology of non-Newtonian fluids is based on the generalized Newtonian hypothesis of viscosity. The viscometers for non-Newtonian fluids should implement fluid flows with the known stress and strain state parameters distributions. Ideally, the distributions should be homogeneous in the flow domain. The idea of the proposed method is based on a combination of a capillary and a rotational viscometers implemented in the torus-shaped capillary viscometer. Analysis of the mathematical model of the inertial non-Newtonian fluid flow in the torus allowed to determine the conditions of homogeneity of the mechanical and thermal parameters in the flow domain and to develop method of viscosity measurement. The measured values are the shear rate on the inner surface of the capillary and the flow rate. The measurements are implemented with the computer vision system that processes data obtained from the high speed CMOS camera that records inertial flow in the transparent capillary illuminated with laser. The computer vision system is based on the application of deep convolutional neural network for laser speckle contrast imaging processing. During the experiments, the proposed viscometer was compared with the Brookfield rotational viscometer. The relative error of the proposed viscometer and method is less than 2%. The inertial viscometer is compact, it allows to study the wide range of shear rates per one test in automatic mode, and it has low fluid capacity of approximately 1.87 ml. That makes it possible to use the viscometer as a point on care testing device in medicine to study the rheology of physiological fluids, in particular blood.

Flow dynamics and mixing past pairs of confined microfluidic cylinders

Placing cylindrical obstacles in a micromixer is a promising means to enhance mass transport. However, there is still a lack of fundamental understanding on the effect of obstacle arrangement on the flow. The present work provides new experimental insights into confined inertia flows past two cylindrical pins, placed either in tandem or staggered arrangement in a Y-type micromixer, and their effect on mixing, through micro Particle Image Velocimetry (μPIV) and Laser Induced Fluorescence (μLIF) measurements. It is found that in such confined microfluidic environments, adding a second pin suppresses vortex-shedding for spacings less than 3.5-pin diameters in a tandem arrangement or 0.25-pin diameters in the staggered configurations. Vortex-shedding is found to enhance mixing in tandem configurations but not in staggered ones. The results highlight the important roles of both pin arrangement and flow instabilities in micromixer performance and can serve as a guide to micromixer design.

A Design for High-Speed Journal Bearings with Reduced Pad Size and Improved Efficiency

Improving efficiency is a general task in the design process of high-speed journal bearings. A specific fixed-pad bearing geometry featuring reduced pad length and additional design measures with the intention of reducing frictional power loss is investigated, experimentally and theoretically, for a journal diameter of 500 mm up to surface speeds of 94 m/s and unit loads of 5.0 MPa. To model fluid flow in the bearing outside the lubricant gap, an extension to Elrod’s cavitation algorithm based on assuming the inertia of fluid flow is proposed. Validation of the extended thermo-elasto-hydrodynamic lubrication (TEHL) model shows good agreement between measurement and prediction in wide operating ranges, however, with systematic tendencies of the remaining deviations. Furthermore, measured local pressure and film thickness distributions indicate a complex formation of cavitation with an influence of axial flow that is not covered by pure Couette-flow in the cavitation region. Measured as well as predicted data prove increased bearing efficiency for high rotor speeds. To provide understanding on the impact of the applied design measures improving efficiency, their combination is separated into the individual ones. Reduced axial and peripheral pad length both contribute almost equally to the reduction in power loss and improve its value by 37% compared to the standard design. Finally, further steps to deeper identify the behavior of the bearing are comprehensively discussed.

Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids.

In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the HiGTree/HiGFlow system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software RheoTool that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation (VVF). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the HiGFlow software. More importantly, we show that our methodology implemented in the HiGTreee/HiGFlow system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids.

Hydrodynamics of aqueous two-phase systems (ATPS) in millichannels

Aqueous Two-Phase Systems (ATPS) have been recently employed for purification, concentration, synthesis, and separation of biomaterials and nanomaterials. Depending on the application, either parallel flow or segmented flow in microchannels is preferred. These ATPS are characterized by interfacial tensions, which are two orders of magnitude lower than typical organic aqueous systems. This results in only parallel flows in microchannels as the capillary numbers are high (Ca ≫ 3). Consequently, the flow observed here is stratified flow or core annular. The internal circulations in segmented flows in microchannels offer enhanced mixing. In the context of nanoparticle synthesis, this results in monodisperse particles. In this work, we show that Ca can be lowered to Ca≪1 by using a millichannel.In this work, we have studied the different flow patterns of ATPS (Polyethylene glycol 6000 -trisodium citrate system). Experiments were carried out in a milli-channel to span different flow patterns. Two cases were investigated i) the feed containing pure PEG and pure Citrate and ii) the feed containing the PEG-rich and citrate-rich solutions, which are at equilibrium. In the former case, there is a range of operating conditions when a single-phase flow is observed, while in the latter, we are always guaranteed a two-phase flow. The pattern formation was analysed and classified into three main categories, i.e., slug flow (interfacial tension dominated), transition flow, and core annular flow (inertia dominated). Flow regime maps based on the Reynolds number, Capillary number, and Weber number of each phase were found to be qualitatively similar to those of the Organic Aqueous System (OAS). Slug lengths and film thickness measured experimentally were validated with predictions of numerical simulation.

Influence of slurry delivery rate and height from cooling slope outlet on solidification and structural behaviors of molded AZ91 magnesium alloy

AZ91 magnesium alloy melt experiences partial solidification while flowing on cooling slope with counter flowing water channel underside. It results in continuous production of semisolid slurry available at cooling slope outlet. Current experimental investigations pertain to the influence of slurry delivery rate and slurry delivery height from cooling slope outlet on solidification and structural behaviors (microstructure along with mechanical properties) of AZ91 magnesium alloy intended for semisolid casting. Slurry delivery rate along with slurry delivery height warrant necessary solidification and shear for grain growth and globularization within metal mold for producing semisolid casting. Moderate slurry delivery rate of 0.025 kg/s along with slurry delivery height of 150 mm results fairly modest solidification that would greatly contribute toward enhanced structural behaviors. As, quite smaller/bigger slurry delivery rate/height generate low shear due to slurry flow inertia or accelerated slurry flow resulting stick-slip flow/motion of alloy slurry on cooling slope. It results poorer structural behaviors amid extremely unwanted casting issues. As, throughout the course escape/retain of metal with gas arise. Since, lesser slurry delivery rate/height allows metal to escape thereby reduces strength and vice-versa. Additionally, lesser slurry delivery rate/height allows gas to escape thereby enhances strength and vice-versa. Therefore, moderate cooling slope casting parameter magnitudes guarantee solution to bewilderment.

Particle clusters within inertial vortical flows in micro-cross-shaped channels

Inertial vortical flows can be used as a tool to capture and manipulate microparticles, vesicles, or cells. Current work follows our previous report [Zhang et al., Int. J. Multiphase Flow 150, 104030 (2022)] to study the flow of diluted particle suspension in micro-cross-shaped channels at 20 < Re < 500 by micro-laser-induced fluorescence and high-speed photography. Effects of inlet aspect ratio (α) and Reynolds numbers (Re) on flow regimes and particle capture were studied. Numerical simulation was adopted to reveal vortex breakdown dynamics associated with particle capture. For each α, as Re increases, segregated flows, steady engulfment flows, vortex shedding flows, and unsteady engulfment flows appear in turns. Experimental results demonstrate a flow-induced, Re and α-dependent particle cluster within steady engulfment and vortex shedding flows, and an increase in α decreases the onset Re of the cluster. With increasing Re, an interesting oscillation of the cluster is established, which triggers the escape of captured particles. Simulation results show that the oscillation frequencies of the cluster and fluid are comparable. Although isolated particles display brief recirculating paths under unsteady engulfment flows, the particle cluster disappears.

Flow rate–pressure drop relations for new configurations of slender compliant tubes arising in microfluidics experiments

We investigate the steady-state fluid–structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a cylindrical fluidic channel surrounded by an annulus of soft material with a rigid outer wall, while the second one is a cylindrical fluidic channel extruded from a soft rectangular slab of material. In each configuration, we derive a mathematical theory for the nonlinear flow rate–pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall’s deformation. Using the flow conduit’s axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement in each configuration from a plane-strain configuration. The predicted displacement field, and the resulting closed-form flow rate–pressure drop relation, are each validated against three-dimensional direct numerical simulations via SimVascular’s two-way-coupled fluid–structure interaction solver, svFSI, showing good agreement. We also show that weak flow inertia can be easily incorporated in the derivation, further improving the agreement between theory and simulations for larger imposed flow rates.

Computational homogenization of unsteady flows with obstacles

AbstractModeling flows in domains containing obstacles becomes challenging when the obstacles are very small compared to the domain. This problem is often known as modeling flow through permeable or porous media. Darcy's law is well known to provide a robust solution to this problem for viscous flows, given that the permeability of the medium can be characterized. Solutions for inertial flows have not been proposed yet. In this article, a principle multiscale virtual power is formulated for the computational homogenization of unsteady incompressible flows in domains containing small obstacles. In this theory, the coarse scale of the domain is separated from the fine scale of the obstacles. The finite element (FE) implementation of this theory is developed in the form of a parallel (FE) algorithm with two‐way coupling between the two scales. The incompressibility constraint is handled with special care by introducing an independent pressure variable at both scales and relying on the Taylor–Hood P2/P1 pair. Simulations are conducted to analyze the accuracy and efficiency of the proposed multiscale approach. The results show that the method is robust and interesting from both the points of view of computational cost and accuracy when the ratio between the domain size and the obstacle size is larger than 100.

Contributions of strong and weak subnetworks to the shear strength of dense granular inertial flow

Discrete element method simulations are employed to quantitatively analyze the contributions of strong and weak subnetworks to the shear strength of dense granular inertial flow. All the individual anisotropy parameters of subnetworks contribute positively, except the weak subnetwork’s normal contact force. The contribution weight of strong subnetwork is significantly greater than that of weak subnetwork, but decreases slightly with shear velocity increasing, which is caused by the attenuation of the transverse support provided by weak subnetwork. The whole network’s equilibrium is dynamically achieved by balancing the difference and compensation in the stability of subnetworks.

Model Predictive Controller-Based Voltage and Frequency Regulation in Renewable Energy Integrated Power System Coordinated with Virtual Inertia and Redox Flow Battery

Model Predictive Controller-Based Voltage and Frequency Regulation in Renewable Energy Integrated Power System Coordinated with Virtual Inertia and Redox Flow Battery

Nonlinear seepage erosion model of water inrush considering particle size distribution of karst collapse column and its engineering applications

Water inrush through karst collapse column is one of the great disasters which threaten coal mine safety production. The particle size distribution of karst collapse column is one of its most basic physical properties, which has a strong correlation with particle migration, and is an important basis for evaluating the water inrush risk of collapse column. The nonlinear flow tests of broken rock under different gradation conditions were carried out by a custom-built apparatus, and the relationship equation between nonlinear flow parameters (permeability and non-Darcy factor) and Talbol power exponent n were constructed. A nonlinear flow model with variable mass of water inrush from karst collapse column was established. The spatio-temporal evolution law of pressure, velocity, porosity and concentration under particle loss and the influence of particle gradation on the water inrush risk of karst collapse column at Fan gezhuang mine were discussed. During the water inrush, the flow state of fluids in karst collapse column gradually transitions from a weak inertial flow to a strong one, eventually becoming a turbulent flow. The flow model based on single flow state cannot reflect the essence of flow regime transition in water inrush. The larger n is, the stronger the water permeability of the karst collapse column, the faster the particles migrate and are lost, the faster the flow channel with high porosity develops, the shorter the time for the water inflow to reach its peak value, and the greater the risk of water inrush.

Effect mechanism of contact sliding state on rheological properties of dense granular inertial flow

The contact sliding state of particles within a granular system can significantly affect the macroscopic rheological behaviors. Here, the whole contact network of a dense granular inertial flow is partitioned into nonsliding and sliding subnetworks. Discrete element method simulations are employed to comprehensively study the microstructure characteristics, anisotropies, and contributions of subnetworks, by virtue of a unified expression of stress-force-fabric relationship. In terms of the microstructure characteristics, the nonsliding subnetwork is segmented by the sliding subnetwork, which reduces the whole system's stability. All the individual anisotropic parameters of subnetworks contribute positively to the whole network's shear strength, except the anisotropy in the sliding subnetwork's normal contact force. The nonsliding subnetwork always makes more contribution to the shear strength; however, its contribution weight decreases with flow rate increasing. Additionally, the difference and complementarity in stability between subnetworks make the whole network maintain a dynamic balance between collapse and reconstruction. • The whole contact network is partitioned into sliding and nonsliding subnetworks. • The contributions of subnetworks are unified by stress-force-fabric relationship. • The nonsliding subnetwork dominates both load-bearing capacity and shear strength. • Anisotropy in the sliding subnetwork's normal contact force contributes negatively. • The difference and complementarity in stability between subnetworks are revealed.

Experimental investigation of maldistribution characteristics of gas‐liquid two-phase flow in a horizontal pipeline

In the flow distribution of oil and gas gathering and transportation system, the flow pattern, inertia force, gravity, and other factors will lead to uneven flow distribution of each outlet pipe, which will seriously affect the economy and safety of the gathering and transportation system. Therefore, it is of great significance to analyze the characteristics of gas–liquid two-phase flow in horizontal pipelines. For this reason, an experimental device for maldistribution control of gas–liquid two-phase flow is developed in this article. In order to solve the problem of flow maldistribution in gas–liquid two-phase flow pipe, the test experiments of maldistribution control under the conditions of three flow patterns (stratified flow, slug flow, and annular flow) are carried out. Through experiments, we revealed the control law of flow pattern to liquid maldistribution and gas maldistribution with or without flute pipes and formed the maldistribution control scheme of gas–liquid two-phase flow in the horizontal pipeline. It is found that it is more beneficial to the control of average liquid maldistribution degree under the condition of slug flow pattern in horizontal manifold without flute pipe, and it is more beneficial to the control of average gas maldistribution degree under the condition of annular flow pattern without flute pipe. Without the function of the flute pipe and in the annular flow pattern, it is beneficial to the control of average maldistribution degree of gas–liquid two-phase flow. The findings of this research can be used as a reference for the field maldistribution control of oil and gas gathering and transportation systems.

Near-Net Shape Manufacture of Ultra-High Strength Maraging Steel Using Flow Forming and Inertia Friction Welding: Experimental and Microstructural Characterization

Abstract Flow forming and inertia friction welding (IFW) have been widely used as manufacturing processes that produce high-value engineering components. Combining these two advanced processes facilitates the fabrication of near-net shape components leading to optimized designs. This study introduces the joining of flow-formed seamless tubes of MLX®19 maraging steel using the IFW process to fabricate a near-net shape component used in landing gears and missile parts. The as-received material was initially provided ≈30% reduction in thickness from the flow forming trials and then welded at four varying weld energies while maintaining constant friction and forge pressures. The mechanical behavior of the weldments was characterized, and the optimized weld parameters were determined. The concomitant microstructural evolution of the optimized weld was also examined to comprehend the underlying deformation mechanisms. The weld strength, axial shortening, and width of dynamic recrystallization (DRX) displayed an increasing trend with an increase in the weld energy. The weld-zone (WZ) and thermomechanical affected zone (TMAZ) showed the presence of martensite, whereas in the HAZ presence of intermetallic precipitates and reverted austenite was confirmed along with tempered martensite. Based on microstructural evidence, it was concluded that the peak temperature attained in the WZ was above Ac3, whereas in the TMAZ it was in-between Ac1 and Ac3. The evolution of crystallographic texture implied that WZ was subjected to pure shear deformation during the welding whereas the TMAZ experienced a combined shear and compressive deformation.

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ( $Re$ ), Bingham ( $Bi$ ) and slip ( $b$ ) numbers, as well as the groove periodicity length ( $\ell$ ) and the slip area fraction ( $\varphi$ ). By increasing $Bi$ , the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.

Granular effects in sea ice rheology in the marginal ice zone.

Sea ice in the marginal ice zone (MIZ) consists of relatively small floes with a wide size span. In response to oceanic and atmospheric forcing, it behaves as an approximately two-dimensional, highly polydisperse granular material. The established viscous-plastic rheologies used in continuum sea ice models are not suitable for the MIZ; the collisional rheology, in which sea ice is treated as a granular gas, captures only one aspect of the granular behaviour, typical for a narrow range of conditions when dynamics is dominated by binary floe collisions. This paper reviews rheology models and concepts from research on granular materials relevant for MIZ dynamics (average stress as a result of ‘microscopic’ interactions of grains; and collisional rheologies). Idealized discrete-element simulations are used to illustrate granular effects and strong influence of the floe size distribution on strain–stress relationships in sheared sea ice, demonstrating the need for an MIZ rheology model capturing the whole range of ‘regimes’, from quasi-static/dense flow in the inner MIZ to the inertial flow in the outer MIZ.This article is part of the theme issue ‘Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks’.

Shear-induced motion of a bead on regular substrates at small particle Reynolds numbers

We study experimentally the impact of substrate topology on shear-flow-induced motion of a single bead at low particle Reynolds numbers. The substrates are regular quadratic and triangular arrangements of fixed spherical particles. Their topology is varied by using different spacings between the spheres. Here, we show that it has a strong impact not only on the critical Shields number for incipient bead motion but also on its motion above threshold. We focus on Shields numbers where the bead velocity is smaller than the settling velocity. For the different substrates, the data on the average bead velocity collapse on a master curve, showing the impact of the critical Shields number on the bead motion. To describe the bead motion, we develop a model for creeping flows based on expressions by Goldman, Cox and Brenner for the flow-induced forces and torques on a moving bead near a plane. Our model considers rolling and sliding motion. The bead detaches from the substrate on the downhill side at larger substrate spacing or higher Shields numbers, and flies through the interstices of the substrate until hitting the neighbouring substrate spheres. While sliding has only a minor effect on the average bead velocity, detachment has a strong impact. At large substrate spacings, it leads to a bistability, usually associated with inertial flows, even for adhesionless particles under creeping-flow conditions. The model shows good agreement with the experimental results.