Flow Regime Transition Research Articles

Thermal and flow dynamics of an inclined air heat exchanger equipped with spring turbulators in the transition flow regime

AbstractThe research involves an experimental investigation into the performance of a flow assisting air heat exchanger under varying angular orientation and uniform external heat fluxes without and with spring turbulators. The investigation was performed for Reynolds numbers ranging from 511 to 9676 and inclination angle 15° and 30°. Three heat fluxes (2, 3, and 4 kW/m2) were applied to the test section to investigate the effect of external surface heating on the range of transition flow regime and thermohydraulic performance. Transition from laminar to turbulent flow for plain channel at different heat fluxes and inclinations occurs within specific Reynolds number ranges: 2436–4446 for 15° inclination at 4 kW/m2, 2574–4289 at 3 kW/m2, and 2850–4152 at 2 kW/m2; for 30° inclination, the ranges are 2518–4151, 2712–4361, and 2992–4346 at the respective heat fluxes. When it comes to the effect of inclination on Nusselt number, the transition occurs sooner at lower angles, but is delayed as the angle increases. Additionally, the Nusselt number decreases as the angle of inclination increases. When comparing the Nusselt numbers of plain tubes to those with spring turbulators, the latter shows a significantly greater enhancement. In laminar flow, a maximum 100% deviation exists between highest and lowest friction factors, decreasing to 75% with increasing Reynolds number; all insert configurations exhibit highest friction factor at 15° due to stronger buoyancy forces.

Airflow characteristics of the stepped dropshaft in the deep tunnel storage system

ABSTRACT The deep tunnel storage system, mainly consisting of underground tunnels and dropshafts, is effective for dealing with urban waterlogging. A stepped dropshaft is suitable for the system to safely transport water to underground tunnels and efficiently release air carried by water. In this study, the air inflow discharge, air vent discharge, and air discharge into the underground tunnel are investigated experimentally. As the dimensionless water flow discharge increases to 0.56, the water flow successively forms the nappe flow, transition flow, and skimming flow regimes, the relative air inflow discharge decreases from 0.97 to 0.32, the relative air vent discharge decreases from 0.85 to 0.22, and the relative air discharge into the underground tunnel fluctuates below 0.20. The exhaust capacity (the ratio of the air vent discharge to the air inflow discharge) reaches a maximum of 0.87 at the threshold between the nappe flow and the transition flow. Influences of flow discharge, step height, step rotation angle, outlet diameter of the central exhaust pipe, and underground tunnel blockage on airflow characteristics are revealed. The prediction formulas for air inflow discharge, air vent discharge, and exhaust capacity are obtained with accuracies over 80%, providing a guide to the practical design and operation of stepped dropshafts.

Numerical and Experimental Simulation of Supersonic Gas Outflow into a Low-Density Medium

This study is aimed at developing methods for the experimental and numerical simulation of the outflow of underexpanded gas jets into a rarefied medium. The numerical method is based on using Navier–Stokes equations in the continuum flow regime and the direct simulation Monte Carlo method in the transitional flow regime. The experimental method includes the modeling of jet flows in the LEMPUS-2 gas-dynamic setup with electron beam diagnostics for the jet density measurements. The results of the experimental modeling for the nozzles of various diameters confirm that a key parameter determining the jet structure is the Reynolds number based on the characteristic length ReL. The results of the numerical simulations agree well with the experimental data both for the maximum values of the ReL considered (approximately 30) when a barrel jet structure with Mach disks is formed and for the minimum values (approximately 4) when no Mach disks are formed. In the entire range of parameters, significant thermal nonequilibrium is observed at all jet segments where the measurements are performed.

Spatiotemporal structure of flow field by a dielectric-barrier-discharge plasma actuator using phase-resolved particle image velocimetry

A typical dielectric-barrier-discharge plasma actuator (DBD-PA) operating in continuous mode generates a self-similar starting vortex followed by a quasi-steady wall jet. In the burst mode, it generates periodic vortices, leading to a spatially wider mean flow field. The characteristics of periodic vortices can be controlled by adjusting the duty cycle α and burst frequency fb of the actuation signal. In the present study, the flow field generated by the actuator in burst mode is studied for 50%≥α≤90%, and 10 Hz ≥fb≤90 Hz. The Reynolds number of mean flow based on the maximum induced velocity and jet half-width ranges from 171 to 524. High-speed laser-sheet visualization and time-resolved particle image velocimetry are used for flow field measurements. The flow field generated during burst mode operation shows the strong influence of the burst frequency. Periodic vortices with comparable size and convection speed of starting vortex are generated at low fb. Dipoles and small-scale vortices are formed at moderate fb similar to the behavior of a transitional wall jet. Kelvin–Helmholtz instability is observed at higher burst frequency. An ornamental vortex consisting of several small periodic vortices is formed at high values of fb during the starting period. Based on the temporal evolution of momentum, the flow field generated by the DBD-PA can be classified into (i) starting flow regime, (ii) transitional flow regime, and (iii) periodic flow regime. The self-similarity of the mean flow field generated by the DBD-PA is verified by comparing the mean velocity profile at multiple downstream locations with the self-similar solutions of laminar and turbulent wall jets. The entrainment coefficient of the mean flow field is similar to that of an axisymmetric turbulent wall jet. The bi-orthogonal analysis shows that both coherent mode energy content and the entropy are minimum (about 5% only) for the continuous mode actuation. For the burst mode actuation, both the coherent mode energy content and the entropy are higher in magnitude compared to that of continuous mode and decrease with increasing burst frequency. The vortices in the periodic flow regime are locked in with fb. The distance between subsequent vortices, λx and flow frequency, f follow a power-law relationship, λx=cf−n, where c is a constant and n can be approximated as 2/3.

Experimental investigation on transitional flow of supercritical hydrocarbon fuel within straight channels of Printed Circuit Heat Exchangers for hypersonic thermal management systems

The onboard supercritical CO2 closed Brayton cycle (SCBC) has established an effective thermal management pathway for hypersonic vehicles operating at high Mach numbers. A Printed Circuit Heat Exchanger (PCHE) is employed within the cycle system to facilitate heat transfer between fuel and carbon dioxide, with its thermo-hydraulic characteristics significantly impacting both power generation and propulsion performance. Given the insufficient research on the flow and heat transfer of hydrocarbon fuels in PCHEs, this study aims to experimentally address the gaps in understanding transition flow for supercritical hydrocarbon fuels, particularly within semi-circular microchannels. We conducted experiments on the flow transitions using a specially designed test piece with a diameter of 1 mm, replicating the PCHE channel characteristics. The experimental Reynolds number range from 300 to 8300 spans laminar, transition, and turbulent flow regimes. Friction factors for n-decane are obtained under adiabatic and heated conditions. The results validate the nomenclature of the quasi-turbulent region and reveal that the critical Reynolds numbers for the transitional, quasi-turbulent and hydraulic smooth turbulent regions under adiabatic conditions are 2200, 2440 and 2980, respectively. A reduction in friction drag attributed to boundary layer viscosity is observed to alter the friction factor under heating conditions, while heating influences both the onset and termination of the transition region, but does not affect its width. Classical correlations are compared with the experimental results, and new empirical correlations for both adiabatic and non-adiabatic conditions are developed, showing superior predictive accuracy compared to existing models. This provides a reliable tool for the engineering design of heat exchangers in the onboard thermal manage systems.

Numerical simulations for the flow-induced vibrations of tandem dual flexible circular cylinders

The three-dimensional large-eddy-simulation coupled with a mode superposition method was applied to numerically simulate the flow-induced vibrations (FIVs) of tandem dual flexible cylinders at Re = 1000 with three different spacing ratios (Sx/D = 2.5, 3.5, and 5, Sx is center-to-center spacing for tandem cylinders, and D is the diameter of the cylinder), corresponding to the reattachment flow, transition flow, and co-shedding flow regimes in stationary tandem cylinders, respectively. The effects of Sx/D on structural vibrations, flow fields, distributions of the surface pressures, and energy properties were investigated to reveal the mechanism for the FIV. Increasing Sx/D weakens the influence of the upstream cylinder on maximum response amplitudes and lock-in region for downstream cylinder. The wake patterns for tandem flexible cylinders are more complex compared to stationary or vibrated rigid tandem cylinders. The shielding effect reduces surface pressure on the downstream cylinder significantly when its vibrations are smaller, leading to a decrease in mean power as well. Furthermore, different mechanisms contribute to amplified FIV in downstream cylinders depending on Sx/D: when Sx/D = 2.5, the upstream vortices collide with the downstream cylinder's front surface and merge with the vortices generated by the downstream cylinder, increasing negative pressure on both front and rear surfaces of the downstream cylinders and promoting FIV; however when Sx/D =3.5 and 5, a binary vortex street forms behind the downstream cylinder without obvious negative pressures on its front surface, the dominant causes of FIV are primarily attributed to interactions among upstream and downstream vortices.

Study and Analysis of Flow Regime Transitions in Straight Channels Using the Lattice Boltzmann Method for Shallow Water

Study and Analysis of Flow Regime Transitions in Straight Channels Using the Lattice Boltzmann Method for Shallow Water

Experimental investigations of flow boiling heat transfer performance in finned micro-channels

The flow boiling heat transfer and pressure drop in rectangular-finned micro-channels (i.e. micro-channel with rectangular fins) were experimentally investigated at five different fin-heights. At three different mass fluxes and a range of heat fluxes, heat transfer coefficients and pressure drops in the micro-channels were measured. The flow patterns during the flow boiling process were visualized to estimate the flow regime transitions in the micro-channels. The experimental results showed that the micro-channel with 500 μm height fins (i.e. tip clearance = 100 μm) performs the highest heat transfer and shows the highest resistance to flow boiling instability among the studied cases. Compared to the smooth micro-channel, the averaged heat transfer coefficient in the micro-channel with 500 μm height fins has been improved by up to 133.9 % at the same wall temperature. Compared to the micro-channel with 600 μm height fins (i.e. tip clearance = 0 μm), the averaged heat transfer coefficient in the micro-channel with 500 μm height fins has been improved by up to 45.8 %. At the initial point of flow instability, the micro-channel with 500 μm height fins has the highest pressure drop fluctuation frequency, the highest surface wetting frequency, and the lowest pressure drop variation coefficient among the studied cases. However, the micro-channel with 600 μm height fins has the lowest pressure drop fluctuation frequency and highest pressure drop variation coefficient, hence experiencing the longest dry-out process among the studied cases.

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Influence of the gas phase on a large-scale bubble column fluid dynamics: Gas holdup, flow regime transitions, and bubble size distributions

We present the results of an experimental study of a large-diameter bubble column operating in batch mode with air or CO2 as the gas phase and water as the liquid phase. The bubble column has an inner diameter of 0.24 m and is 5.3 m in height. The superficial gas velocity varied between 0.0037 m/s and 0.0233 m/s. The experimental investigation consists of gas holdup measurements and image analysis. Flow regime transitions were detected by gas holdup measurements, and image analysis was used to investigate the bubble size distributions. The results suggest that the homogeneous flow regime is stabilized when CO2 is used as the gas phase. The gas holdup is higher for the CO2-water system at fixed superficial gas velocity, especially in the heterogeneous flow regime. In the homogeneous flow regime, the mean bubble diameter and the fraction of large bubbles are lower for the CO2-water system, explaining the higher gas holdup.

Experimental and Numerical Investigation of Slip Effect on Nanofiber Filter Performance at Low Pressures.

Nanofiber filters are widely used in air filtration applications due to their superior performance over microfiber filters. Velocity slip around nanofibers has been identified as a key factor contributing to their high figure of merit, yet its impact on filter performance, especially particle collection efficiency, remains unclear due to the difficulty in isolating the slip effect as the sole variable. This study combines experimental and simulation methods to investigate the slip effect by adjusting the air molecule mean free path, rather than varying fiber size as done in previous studies. Filter media with mean fiber sizes ranging from 16.2 to 0.084µm are utilized. An image-based regression method is developed to address the challenge of determining the solidity of thin nanofiber layers. The results show that the slip effect is enhanced as the testing pressure decreases, reducing pressure drop by less than 15% for microfiber filters and over 50% for nanofiber filters ≈100nm. The enhanced slip effect at low pressures (i.e., relatively low pressure compared to the ambient environment) significantly improves filtration efficiency, especially for particles larger than 100nm. It also proposes semi-empirical equations for predicting filter performance in slip and transition flow regimes.

Influence of back pressure adjustment of porous media on cavity flow noise control

Control of self-sustained oscillation and noise reduction poses a significant challenge. The present study employs Implicit Large Eddy Simulation at a Mach number of 0.85 to investigate the influence of a porous cavity floor on flow dynamics. By substituting the solid floor with porous media, the fundamental pressure–velocity relationship within the medium is established according to Darcy's law. Findings reveal marked suppression of wall pulsations, accompanied by a 10 dB decrease in sound pressure levels. The porous medium induces blowing and suction effects, effectively modulating large-scale re-circulation and mitigating shear layer instability, thereby approximating free mixing layer characteristics and suppressing cavity flow oscillations. At an optimized porosity for maximum noise reduction, altering back pressure at the cavity floor induces a transition in the local flow regime from suction-dominated to blowing-dominated state. Excessive reduction of back pressure promotes suction; conversely, increased pressure intensifies blowing, further attenuating feedback mechanisms and enhancing noise reduction. To explore noise reduction mechanisms, mode decomposition analyses demonstrate the efficacy of porous media in disrupting large-scale coherence structures within shear layer and redistributing energy from dominant modes to a broader frequency spectrum that engages smaller flow structures. This energy reallocation mechanism contributes to the mitigation of cavity flow noise and deepens insights into the role of porous media in flow modulation and noise control.

From Darcy to turbulent flow: Investigating flow characteristics and regime transitions in porous media

This research addresses the flow characteristics within a porous medium composed of a monolayer of closely packed spheres, spanning from viscous-dominated to turbulent flow regimes. In the first part of this paper, the turbulent flow characteristics at a 30 MPa pressure drop within the domain are presented. The results are averaged across different cross sections between the inlet and outlet. In the second part of the study, simulations are conducted with pressure drops, ranging from nearly 0 to 100 MPa. The analysis finds distinct flow patterns within the domain and provides estimations for the permeability and the inertial term coefficient. Moreover, the transition from Darcy to non-Darcy and turbulent flow is achieved through the use of different criteria. The specified geometry is suitable for validating and calibrating simplified discrete element method models coupled with computational fluid dynamics. The main goal of this research is to produce a reliable benchmark to figure out the challenge of limited experimental data concerning fluid flow characteristics in densely packed granules specially subjected to high pressure conditions. To do this, representative specimens are designed, accurate simulations are conducted, and precise assessments of the results are carried out.

Dynamic Thermomechanical Modeling of Rock‐Ice Avalanches: Understanding Flow Transitions, Water Dynamics, and Uncertainties

AbstractThe rapid melting of glaciers and thawing of permafrost in mountainous regions have heightened the danger of rock‐ice avalanches. These avalanches pose a severe threat due to their potential to transform into water‐saturated debris flows. The catastrophic event in Chamoli, India, on 7 February 2021, illustrates the devastating consequences of such processes. Developing a model capable of predicting the dynamics and extent of these events is imperative for natural hazard science and disaster mitigation. In response, we propose a depth‐averaged rock‐ice avalanche model encompassing four distinct materials: rock, ice, snow, and water. The model integrates crucial physical processes, including frictional heating, phase changes, ground material entrainment, and air‐blast hazards. Through a system of mass and momentum balance equations extended with grain flow and internal energy equations, the model captures heat exchanges and resulting phase changes as the fragmented material flows. Focusing on identifying the primary water source in the flow and testing the model on the 2021 Chamoli event, we quantify water's influence on flow dynamics and regime transitions. However, uncertainties persist in heat transfer physics and quantifying the hydro‐meteorological state of the flow path. Our thermo‐mechanical model enables the simulation of complex avalanches and identifies key flow transitions: powder cloud formation and potential debris flow transformation. The study underscores the pivotal role of water in avalanche dynamics and the challenge of accurately quantifying water content within the flow, necessitating comprehensive ground assessments for effective disaster management.

Magneto-Stokes flow in a shallow free-surface annulus

In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.

Distribution of transitional flow deposits in sedimentary environments of mixed sand-mud turbidite system

Predicting facies distribution in turbidite systems is essential for resource exploration and identifying geohazards from an economic standpoint. Models that describe facies distribution depend heavily on understanding the mechanisms of particle transport and deposition. These processes are closely tied to the volume, concentration, and composition of sediment gravity flows, which display a range of behaviours between turbulent and laminar flow extremes. Recently, there has been a rise in studies on transitional flow deposits, although they remain much less understood than fully turbulent or laminar flows.For the first time, the distribution of Structured sandstone–mudstone associated with transitional flow deposits has been quantitatively presented for various sedimentary environments within the turbidite system. The distribution of Structured sandstone–mudstone was analysed for six areas of the Ropianka Fm (Skole Nappe, Polish Outer Carpathians) across twelve sedimentary environments, including channels, channel-levees, channel-mouths, and sub-environments of the depositional lobe. An increased amount of Structured sandstone–mudstone was observed in proximal settings away from the transport axis and in the distal parts of the turbidite system. It was found that flow transformation can occur in both proximal and distal zones of the turbidite system. Structured sandstone–mudstone in proximal zones is more often deposited from diluted mud-laden flows of small volume, where fine-grained cohesive material likely underwent vertical segregation. In contrast, Structured sandstone–mudstone formed basinward tend to be initially formed by larger flows. In proximal part of depositional lobe setting, the flow transformation due to longitudinal or longitudinal and vertical segregation of fine-grained cohesive material occurs slowly. At this point the velocity of sediment gravity flow is too high and the concentration of cohesive particles is too low for common development of cohesive bonds. Flow transformation accelerates in lobe fringe and lobe distal fringe/interlobe, due to flow deceleration, changes in sand-to-mud ratio, and the time required for development of cohesive bonds and the transition to a transitional flow regime, leading to increased deposition of Structured sandstone–mudstone distally.

Coupled Wall Boiling and Population Balance Model for High Void Fraction Flows Under Sub-Cooled Nucleate Boiling Regime: Model Development and Validation

Abstract The subcooled flow boiling of water in a vertical annulus channel is studied numerically at low-pressure conditions. The two-fluid model is developed with flow-regime dependent interfacial transfers for mass, momentum, and energy using the algebraic interfacial area density (AIAD) framework. A discrete population balance model is used to mechanistically determine the vapor bubble diameter in the flow channel by considering the bubble aggregation and breakup effects. Energy balance at the heated wall for the subcooled nucleate boiling is handled using a suitable wall boiling model. A coupling is achieved between the discrete population balance and the wall boiling model for the nucleation and the growth rate of the vapor bubbles along the heated wall. The developed model simulates the reference experimental cases of flow boiling in a vertical channel for various flow and thermal conditions. At low wall heat flux, the wall boiling generates vapor bubbles near the heated wall and within the bubbly flow regime. With an increase in the wall heat flux, the aggregation and evaporation cause the formation of larger bubbles, which progress toward the flow channel core region, a phase that is representative of the transitional flow regime. The model's capability to predict such flow regime transition is validated with the experimental results. The bubble aggregation is found to be dominant compared to the breakup, and thus, proper choice of the aggregation factor is important for the accurate prediction of vapor parameters for the subcooled flow boiling at low-pressure conditions.

Experimental investigation into thermal characteristics of subcooled flow boiling in horizontal concentric annuli for cooling ultra-fast electric vehicle charging cables

In an effort to reduce the charging time of electric vehicles (EVs), the thermal management of the charging system has emerged as one of the most urgent issues. The charging rate has been restricted to avoid thermal failure especially in charging cable. Recently, a direct contact cooling technique that utilizes subcooled flow boiling for charging cables has been proposed and has shown promising thermal management performance. However, there has been a lack of clear explanation regarding its thermal characteristics due to its intrinsically complicated flow features. This study investigates the thermal characteristics of subcooled flow boiling in a horizontally aligned concentric annular tube intended to simulate the direct contact cooling technique employed for charging cables. For the experimental investigation, the wall temperature measurements and high-speed flow visualization images acquired from the transparent test module annulus, with inner and outer diameters of 6.35 mm and 22.0 mm, were utilized. Three key axial thermal characteristics of subcooled flow boiling in annulus have been analyzed, and they are flow regime transition, variation of heat transfer mechanisms, and occurrence of critical heat flux (CHF). The transition of flow regimes and the variation of dominant heat transfer mechanisms in the axial direction are mutually influencing due to the coupled effects between the hydrodynamic and thermal characteristics of simultaneously developing flows. The flow regime changes from partially developed boiling (PDB) to fully developed boiling (FDB) as the intensities of nucleate boiling and bubble recondensation vary in the axial direction, while the dominant heat transfer mechanism shifts from single-phase convection to nucleate boiling, corresponding to the flow regime transition from PDB to FDB. The departure from nucleate boiling (DNB) type CHF is observed, manifested by the wavy interface propagating from the far downstream to the upstream region, and the intensities of nucleate boiling and bubble recondensation are also identified as the dominant parameters in determining the occurrence of CHF. Charging time estimation reveals that the proposed method can achieve an 80 % charge for 100-kWh EV batteries in 98 s, while maintaining the cable wire temperature below the safety limit of 80 °C. This strongly supports its potential as a promising thermal management technique for future ultra-fast charging systems.

Study on the hydraulic conveyance characteristics of suspended coarse particles within pipelines

The Flow Regime Transition Device transforms the gelled crude oil mass into gelled crude oil particles for hydraulic conveying. The gelled crude oil particles may reaggregate into gelled crude oil mass at the later stage of hydraulic conveying. Therefore, understanding the patterns of hydraulic suspension conveying gelled crude oil particles is vital for safely gathering and efficiently conveying crude oil. This paper employs the CFD-DEM coupling technique to conduct a numerical study on the hydraulic conveying characteristics of gelled crude oil particles. The accuracy of the model and the solution method is verified by comparing them with the experimental data of particle concentration distribution, and single particle rise behavior, and particle transport flow of gelled crude oil. The size range of gelled crude oil particles spans from 0.0001 m to 0.003 m. We operate the transportation within a velocity range of 0.5 to 4 m/s and a concentration range of 0.022 to 0.0537. Simulation results indicate two flow regimes in the hydraulic conveying of gelled crude oil particles: an upper-moving bed flow and a heterogeneous suspension flow. With increased conveying velocity, the upper moving bed flow gradually transitions to a heterogeneous suspension flow. Beneath the upper moving bed flow, some scattered particles exist, likely resulting from the action of turbulent diffusion. Changes in conveying concentration and particle size have a minor impact on the velocity distribution of particles and fluid but a more significant effect on the particle distribution across the pipe cross-section. Also, when conveying particles of different sizes, most smaller particles travel along the pipe wall.

POD Analysis of the Wake of Two Tandem Square Cylinders

This study aims to investigate the wake of two tandem square cylinders based on the Proper Orthogonal Decomposition (POD) analyses of the PIV and hotwire data. The cylinder centre-to-centre spacing ratio L/w examined is from 1.2 to 4.2, covering the four flow regimes, i.e., extended body, reattachment, transition and co-shedding. The Reynolds number examined was 1.3 × 104. A novel Proper Orthogonal Decomposition (POD) technique (hereafter referred to as PODHW) is developed to analyse data from single point hotwire measurements, offering a new perspective compared to the conventional POD analysis (PODPIV) based on Particle Image Velocimetry (PIV) data. A key finding is the identification of two distinct states, reattachment and co-shedding, within the transition flow regime at L/w = 2.8, which PODPIV fails to capture due to the limited duration of the PIV data obtained. This study confirms, for the first time, the existence of these states as proposed by Zhou et al. (2024), highlighting the advantage of using PODHW for capturing intermittent flow phenomena. Furthermore, the analysis reveals how the predominant coherent structures contribute to the total fluctuating velocity energy in each individual regime. Other aspects of the flow are also discussed, including the Strouhal numbers, the contribution to the total fluctuating energy of the flow from the first four POD modes, and a comparison between different regimes.