Local Pressure Drop Research Articles

Eulerian multi-fluid simulations of local liquid distribution in a bed packed with cylindrical particles

Packed bed reactors (PBRs) are extensively used in chemical process industries to perform solid-catalyzed gas–liquid reactions. Their performance is significantly influenced by liquid distribution which is a strong function of particle shape and size. In the present work, we simulated the steady-state local liquid distribution, pressure drop (ΔP/L), and overall liquid holdup (〈εL〉) for the beds packed with spherical and cylindrical particles using a three-dimensional (3D) Eulerian multifluid model and validated the predictions using corresponding high-speed imaging measurements performed in pseudo-2D packed beds. We showed that the Eulerian model with existing closures significantly underpredicts the liquid distribution for the bed randomly packed with cylindrical particles. To address this, we proposed a modification in existing mechanical dispersion force (F→D) model as a function of average particle orientation angle (θ). The modification significantly improved agreement between the predictions and the corresponding measurements. Using the modified model, we showed that the increased magnitude of F→D in the lateral direction leads to higher lateral liquid spreading for cylindrical particles as compared to that for the spherical particles. Importantly, the modified model also predicted the local liquid distribution and ΔP/L for beds packed manually with cylindrical particles oriented at different θ in a satisfactory agreement with the corresponding measurements. On increasing θ, the F→D in lateral direction (i.e., perpendicular to flow) as well as liquid–solid interaction force (F→LS) in axial direction (i.e., parallel to flow) found to increase significantly. As a result, the lateral liquid spreading as well as ΔP/L decrease substantially on increasing θ.

Experimental analysis of the R290 variable geometry ejector with a spindle

The aim of this work was to experimentally analyze the variable geometry gas ejector with a spindle designed for operation with the natural working fluid propane (R290). The performance of the ejector was evaluated based on the mass entrainment ratio and critical temperature, being the most crucial parameters for optimizing the cooling capacity in ejector refrigeration systems, as well as the ejector efficiency using common literature notation. Additionally, local pressure drop measurements allowed for the determination of pressure profiles inside for different spindle positions used for capacity regulation. The experimentally defined ejector efficiency curves demonstrated the ability to control the ejector capacity by means of the spindle, irrespective of the unfavorable operating conditions. By decreasing the effective throat area using spindle, the ejector mass entertainment ratio increased by 35%. Spindle movement allowed for the decrease of the motive nozzle flow rate by up to 65%, while still maintaining the suction of the secondary flow of the ejector. Moreover, the behavior of a slight increase in suction nozzle flow with a decrease in motive nozzle flow has been observed for the initial movement of the spindle followed by a huge drop for further reduction of the effective throat area, confirming the previous conclusions shown in the literature.

Micro segment analysis and machine learning prediction for thermal-hydraulic parameters of propane condensation flow in a PCHE straight channel

In the LNG regasification process, the printed circuit heat exchangers(PCHE) is an ideal choice for vaporizer, with propane as the intermediate working medium in the hot side of PCHE. In this work, numerical simulations of propane condensation flow and heat transfer at different operating parameters was carried out in a semi-circular straight channel of PCHE. The micro-segment analysis method was used to present the local heat transfer coefficient and pressure drop in the channel. The results indicate that the propane condensation process can be divided into three stages: the “constant temperature condensation stage” in the droplet condensation state, the “varying temperature condensation stage” in the film condensation state, and the “subcooled stage” in the liquid phase state. Different operating parameters can affect the start and end position of each stage, as well as the parameter values in the same state. An artificial neural network method was used to predict the local heat transfer coefficient and pressure drop, with the predicting error of less than 5 % and 10 % respectively. This study provides a machine learning method to accurately predict the flow and heat transfer parameters for propane condensation flow in PCHE channel and valuable for future design of LNG vaporizer.

Thermal and hydrodynamic analysis inside a channel partially filled with porous material

AbstractIn this work, the transfer of heat and changes in fluid pressure within a rectangular channel fairly packed with porous material have been studied numerically for various Darcy numbers and dimensionless porous layers. The model was run with the following assumptions: laminar flow, forced convection, isotropic porous material, local thermodynamic equilibrium, constant wall temperature boundary condition, and no thermal dissipation. The study covers a broad range for the dimensionless porous layer, 0 ≤ hr < 1, and the Darcy number, 10−4 < Da < 10−2. The fully developed and developing flow over the channel is investigated in numerical study. It was observed that the inertia effect may be disregarded when Da < 10−4. The local dimensionless bulk temperature distribution, pressure drop, and velocity profiles were all shown to be impacted by the Darcy number and dimensionless porous layers, according to the numerical analysis results. The maximum heat transfer rate was attained when the ratio of the porous layer inside the channel was 0.8, and the pressure gradient was the highest. Partial packing of the channel with a porous material has two advantages: it increases the rate heat transmission rate and results in a much smaller pressure drop than a filled porous medium.

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.

Modeling of cryogenic heated-tube flow boiling experiments of hydrogen and helium with the Generalized Fluid System Simulation Program

Accurate modeling of cryogenic boiling heat transfer is vital for the development of extended-duration space missions. Such missions may require the transfer of cryogenic propellants from in-space storage depots or the cooling of nuclear reactors. Purdue University in collaboration with NASA has assembled a database of cryogenic flow boiling data points from steady-state heated-tube experiments dating back to 1959, which has been used to develop new flow boiling correlations specifically for cryogens. Computational models of several of these experiments have been constructed in the Generalized Fluid System Simulation Program (GFSSP), a network flow code developed at NASA’s Marshall Space Flight Center. The new Purdue-developed universal correlations cover the full boiling curve: onset of nucleate boiling, nucleate boiling, critical heat flux, and film boiling. These correlations have been coded into GFSSP user subroutines. The fluids modeled in this study are liquid hydrogen and liquid helium. Predictions of local wall temperature and pressure drop are presented and compared to the test data.

Deflector device optimization for controlling nitrogen oxide emissions and pressure drop in selective catalytic reduction denitrification system

ABSTRACT Selective catalytic reduction technology effectively controls nitrogen oxide emissions from coal-fired power plants. In denitrification systems, exceeding nitrogen oxide emissions and excessive local pressure drop are common issues. Numerical simulation methods are used in this study to optimize the flow field to enhance denitrification efficiency and reduce pollutant emissions. Specifically, four deflector plate schemes for the variable-section flue duct segment are proposed. In actual retrofitting, the optimization scheme led to a reduction in nitrogen oxide emissions from 97.3 mg/Nm3 to 48.6 mg/Nm3 and an increase in the outlet pressure of the denitrification system from −3000 Pa to −2959 Pa, resulting in a 41 Pa decrease in local pressure drop. This optimization will further reduce pollutant emissions from power plants and the power consumption of induced draft fans.

Cavitation Onset In Counter-Rotating Vortices From Diverging Disks

Cavitation occurs when the local pressure, induced by high local velocities, drops below the vapor pressure, leading to the formation of vapor bubbles. The subsequent collapse of these bubbles can cause noise, erosion, and vibrations. Recent studies show that cavitation is sensitive to water quality, i.e., the nuclei populations, the chemical composition of water, and the presence of particles. Motivated by investigating the effects of water quality on cavitation, experiments are performed in a dedicated experimental facility. This consists in two co-axial disks that are initially at rest and mutually in contact, in a tank filled with water. The fast diverging movement of the top disk with respect to the bottom one produces a jet flow inside the gap between the disks, which leads to the formation of two counter-rotating vortices. The local pressure drop induced by high flow velocities leads to a phase change. To characterize the phenomenon, two optical techniques are applied, i.e., shadowgraphy and particle image velocimetry (PIV). In performing PIV reconstruction, the sum of correlation enhances the spatial resolution of the velocity vector fields. The pressure field in the region where the vortices occur is obtained from velocity data. The water quality effects on cavitation are investigated by adding salt and using water with an abundance of nuclei inside the tank.

Modelling of heat transfer and pressure drop during flow boiling of CO2 in a horizontal tube with periodic open cellular inserts

During flow boiling in horizontal tubes, highly porous inserts can improve the wetting of the tube wall and the convective boiling. The literature focuses on solid sponge structures with irregular cell geometries. Hence, in this work the local heat transfer and pressure drop during flow boiling of CO2 in periodic open cellular structures with cubic and Kelvin cell geometry were investigated. A strong influence of the cell geometry on the heat transfer and pressure drop was found. By combining the Forchheimer term with a two-phase flow method (homogeneous model, drift flux model) a new pressure drop model is proposed. The model has a mean absolute percentage error (MAPE) of 12%. Regarding the heat transfer, high-speed video recordings and an evaluation of the local heat transfer were used to test the tube segments for complete wetting. Thereafter, the convective boiling contribution was extracted from the local data of completely wetted tube segments by subtracting the nucleate boiling contribution. A separate model of the convective boiling is proposed for each cell type. The models have a MAPE of 20%. Finally, the circumferentially averaged heat transfer coefficient was found to follow a superposition of the heat transfer of the liquid and vapor phase.

Numerical Simulation of Hydraulic Fracture Propagation on Multilayered Formation Using Limited Entry Fracturing Technique

Hydraulic fracturing is one of the most effective stimulation methods for unconsolidated sandstone reservoirs. However, the design of hydraulic fracturing must take into account the mechanical and stress properties of different geological formations between layers. In this paper, a three-dimensional coupled fluid-solid model using the finite element method is developed to investigate multiple vertical fractures at different depths along a vertical wellbore under different geological and geomechanical conditions. The finite element model does not require further refinement of any new cracks, requiring much smaller degrees of freedom and higher computational efficiency. In addition, new elements were used to account for local pressure drop due to perforation entry friction along the vertical wellbore. Numerical simulation results indicate that hydraulic fracture connections are observed from adjacent layers. Furthermore, the low stress contrast and high Young’s modulus between the layers increases the likelihood of multiple fracture connections. Higher fluid leakage rates increase the likelihood of fracture branching, but decrease the area of fracture coverage near the wellbore. Increasing fluid viscosity is effective in improving the area of fracture coverage near the wellbore. These findings are useful for the design of hydraulic fracturing in multi-layered formations in unconsolidated sandstone formations.

Bubble breakup dynamics and fluid distribution in a honeycomb microreactor with chemical reaction

The bubble breakup dynamics and fluid distribution in a honeycomb microreactor with chemical reaction were visually investigated. The bubble split and collide behavior in multistage divergent-convergent branching structures were observed and studied. It was demonstrated that the bubble breakup at bifurcations relies dramatically on the collision behavior of the bubble pairs at the downstream convergence. Four bubble flow regimes were observed at the convergence: no collision, collision-slipping, squeezing-slipping, and blockage-slipping. The non-uniformity of the fluid distribution mainly stems from uneven breakup of bubbles at the upstream bifurcation, the lack of bubble breakup, the feedback effects of downstream and the manufacturing errors. Furthermore, the variation of pressure drop in a honeycomb microreactor was explored. The overall pressure drop was found to increase by the local pressure drop, whereas reduced with the increased absorption capacity of liquid phase. Taking these impact factors into account, a modified Lockhart-Martinelli pressure drop model was developed.

Thermal-hydraulic and structural analyses of an additive manufactured panel mock-up for Wendelstein7-X

After the successful short pulse operation phase 1 (OP1) of the stellarator Wendelstein 7-X with maximal plasma energies of 200 MJ, the upcoming long pulse OP2 aims at stepwise higher energies up to 18 GJ. A series of the stainless steel wall protection panels is positioned behind the divertor pumping gaps for average stationary heat loads of 100 kW/m². These panels were produced by electron beam welding of stainless steel parts to build the housing of the cooling channels. This technology was more demanding than foreseen due the complicated 3D weld seams required by the shaping of the panels. An innovative technology which is more adapted to the panel geometry is additive manufacturing. It intends to bring significant advantages by printing the housing as a single piece without welds.The paper introduces the thermal-hydraulic and structural analyses of an additive manufactured panel mock-up performed with ANSYS V2022R2. The purpose of the calculation is to compare the thermal, hydraulic and structural performance of the improved design based on additive manufacturing and the present one. The welding process dictated the design of the cooling channel that induced local recirculation areas, additional local pressure drops, non well cooled areas for weld seams integration. In addition the weld strength assessment required special codes and methods, which cost more time and efforts. Without these constraints, additive manufacturing offers the opportunity of more freedom for the design of the cooling channel to reach better heat transfer performance of the panel.

Heat transfer performance of supercritical CO2 in a vertical U-tube

Supercritical carbon dioxide (sCO2) is taken as an excellent working medium for efficient and compact energy conversion devices. However, heat transfer performance (HTP) of sCO2 in a vertical U-tube is intricate owing to dramatic variation of its temperature-dependent thermophysical properties. In this study, flow and heat transfer performance (FHTP) of sCO2 in a vertical U-tube is studied with an improved shear stress transfer model. Additionally, the impacts of operational parameters (heat flux q, mass flux G and pressure P), flow directions and bending diameters (dbend) of U-tube on FHTP are investigated. In both directions, the differences in local pressure drop caused by buoyancy effect and thermal expansion are analyzed deeply. The results demonstrate that the bend section can disturb flow and vortexes persist in downstream, thus improve the HTP. However, an apparent heat transfer deterioration zone can be observed in the ascending section. Under both directions, the average heat transfer coefficient (havg) raises with the growing G and P and decreasing q and dbend, while the total pressure drop (ΔPtotal) rises with the raising G and q as well as decreasing P. Moreover, the U-tube with down-up direction obtains higher havg and lower ΔPtotal than up-down.

Thermodynamic effects in cavitating flow

Cavitation is a phenomenon characterized by vapor generation and condensation in liquid flows, at approximately constant temperature. Cavitation is usually triggered by a local pressure drop in the vicinity of a cavitation nucleus. As the bubble grows, latent heat is supplied from the surrounding liquid to the interface, creating a thermal boundary layer. This creates a thermal boundary layer. The result is a local drop in the liquid temperature, which leads to a drop in vapor pressure. This delays the further development of the bubble, as a greater pressure drop is required to maintain the process. This phenomenon is known as thermal delay or thermodynamic effect and plays a moderating role in the development of cavitation. Thermodynamic effects can usually be neglected for liquids whose critical temperature is much higher than the operating temperature. However, this is not the case for liquids whose operating temperature is close to the critical temperature, such as in cryogenics.The understanding of the thermodynamic effects of cavitating flow is crucial for applications like turbopumps for liquid hydrogen LH2 and oxygen LOx in space launcher engines. Experimental studies of this phenomenon are rare as most of them were performed in the 1960s and 1970s. Due to the extreme difficulties of experimental investigation, predicting of thermodynamic effects in cavitation often bases on data in liquids other than cryogenics. Most often used surrogate liquids are hot water or certain refrigerants, which are selected by a single fluid property, most commonly by the thermodynamic parameter ∑.

Pressure drop model of gas-liquid phase for Venturi scrubber in fog-annular flow

Venturi scrubber is widely used in wet dust removal. Its pressure drop performance determines the dust removal efficiency. The commonly used models, most of them are empirical ones, are hard to accurately predict the friction loss between the gas core and the liquid film near the wall, the proportion of the atomized droplets to the deposited liquid film, and the gas holdup, where the influence of the throat length on throttling and the local resistance formation mechanism were not discussed. Therefore, in this study, we established a pressure drop model for Venturi based on the theoretical derivation of two-phase flow and revision of local resistance pressure drop. It uses the similar theoretical method of straight pipe for Venturi, where the iterative method was employed to calculate the liquid-phase conversion coefficient which is related to the cross-flow ratio and the gas holdup. Meanwhile, the experiments and CFD simulations were carried out to validate the model and judge whether the local resistance should be considered. The results show that if the vena contracta extends out of the throat, the unconstrained expansion flow can cause the boundary layer separation, and the fluctuation of the two-phase flow in throat can induce Kelvin-Helmholtz instability, resulting in apparent energy loss. Accordingly, the critical throat length criterion was developed, and the pressure drop model was modified with the deviation less than 17.14%. It provides a scientific basis for establishing the universal two-phase theoretical pressure drop model of Venturi scrubber.

Drafting behaviors in fish induced by a local pressure drop around a hydrofoil model

Fish schooling has the improvement in hydrodynamic propulsive efficiency through the interaction of flow field induced by fish bodies and tail beat. Such energy-saving behaviors due to flow interactions also occur with changes in the flow field caused by structures. We examined the differences between a live fish swimming around a streamlined hydrofoil model prepared to represent fish body and swimming alone in a flow tank. We observed that the fish can remain in the same place without tail beating. It called “drafting” behavior. The analysis of fish drafting showed that fish obtained thrust using a local pressure drop caused by the high velocity flow even in the vicinity of the hydrofoil model at an angle of attack α of 10° to 20°without flow separation, and fish balanced forces by using an α of fish body. This tendency was confirmed in the model experiment using a two-axis load cell, and the forces acting on the fish body was the smallest value when the fish model was placed in the same conditions as a live fish experiment. We also confirmed by simulation and found that the α of fish body generated lift force and counteract the suction force. Above results indicate that a fish can balance the anterior–posterior and lateral direction forces by using a local pressure drop around a hydrofoil model as suction force, and using angle of attack on its body, thereby realizing drafting.

Study on cooling of bionic leaf-vein channel liquid-cooled plate for lithium-ion battery pack

order to improve the cooling effect of lithium-ion battery packs, a bionic leaf-vein channel liquid-cooled plate was proposed. The liquid-cooled plate was numerically simulated using ANSYS FLUENT. The results show that at different Reynolds numbers, the pressure drop of the bionic leaf-vein channel is always smaller than that of the serpentine channel, and the local pressure drop of the bionic leaf-vein channel is 88.43% lower than that of the serpentine channel. The pressure drop of the bionic leaf-vein channel increases gradually with the increase of the branching angle, the branching angle increases from 35?to 45?, and the pressure drop increases by 212.27 Pa. The Reynolds number increases from 500 to 7500, and the maximum temperature of the lithium-ion battery pack reduces by 3.74 K, and the maximum temperature difference reduces by 2.25K.

Mechanism of long-range hydrophobic force based on cavitation of metastable liquid film

Hydrophobic force, a key driving force in colloid physicochemical system and biological macromolecular system, exhibits a distinct multi-scale effect. The prevailing scholarly consensus attributes long-range hydrophobic force to bubble bridging, facilitated by unstable liquid film cavitation, while short-range force is thought to arise from the reorganization of water molecules at the solid-liquid interface. However, a comprehensive theoretical study remains elusive. To further elucidate the mechanism of the long-range hydrophobic force based on unstable liquid film cavitation, we carry out systematic research on the long-range hydrophobic force between perfluorooctyl trichlorosilane hydrophobic particles and the surface, by utilizing atomic force microscopy (AFM) and molecular dynamics simulations. According to AFM force tests, the long-range hydrophobic force escalates incrementally with subsequent close contacts before reaching a plateau. On the tenth contact, the penetration curve exhibits a sudden jump to an adhesion distance of 502.01 nm. A distinct step in the retraction curve suggests the rupture of the cavitation bubble capillary bridge. Importantly, the classical capillary force mathematical model provides an effective fit for the penetration curve. Our calculations estimate the volume of the capillary bridge at 0.30 μm³, offering direct theoretical evidence of the unstable liquid film cavitation bubble capillary bridge. Further insights are gained from large-scale tensile molecular dynamics simulations by using GROningen MAchine for Chemical Simulations (GROMACS). The inherent correlation mechanism of the formation, evolution, and mechanical behavior of the cavitation bubble capillary bridge in the separation process of hydrophobic particles are further explored from a molecular perspective. The results demonstrate that the local pressure drop occurring at the moment of “jump-out” separation of the hydrophobic particles attracts nitrogen molecules to diffuse into the liquid film, thereby forming a cavitation bubble capillary bridge. Simultaneously, a jumping behavior is observed in the calculated spring potential curve at the moment of capillary bridge rupture. Finally, the influence of solution gas content on long-range hydrophobic force is investigated. There is a positive correlation between gas molecule content and both the growth rate of cavitation bubble capillary bridge volume and the length of capillary bridge stretch-rupture, further demonstrating the gas concentration dependence of long-range hydrophobic forces. In a word, revealing the long-range hydrophobic force mechanism based on the cavitation of unstable liquid film can enhance our understanding of the interaction between colloid physical chemistry and biological macromolecules. Meanwhile, hydrophobic force is the fundamental driving force of particle-bubble adhesion in mineral flotation system, and the revelation of its action mechanism has important guiding significance for regulating the actual mineral flotation process.

Subcooled flow boiling in ultrahigh-aspect-ratio microchannels for high heat flux cooling

In present work, the numerical simulation and experimental investigations were performed on the subcooled flow boiling behavior in ultrahigh-aspect-ratio microchannel heat sink (AR = 25). As the heat flux is low, the unique discotic bubble expands the condensation area while ensuring an adequate evaporation area in the channel. When the heat flux increases, the violently fluctuating liquid-vapor interface forms a throat shape that effectively reduces the cross-section of vapor flow. Furthermore, the flow pattern of annular flow at the channel bottom and nucleate bubble at the channel top realizes a combined heat transfer mechanism (nucleate boiling and liquid film evaporation occurs simultaneously). Moreover, the phenomenon of “droplet inside the bubble” caused by bubble coalescence also significantly enhances the thermal process. The fluctuation of local pressure drop in UARM acts gently, which effectively inhibits the boiling instability, and its average value can be reduced by 68.9%. The maximum CHF reaches 1258.1 W/cm2 under a mass flux of 410.2 kg/(m2·s) based on the experimental data, indicating a tremendous potential for the efficient heat dissipation.

Numerical analysis of sodium-argon two-phase flow in narrow channels under severe accident conditions in pool type SFR

A two-phase flow model for sodium-argon mixture flow through the reactor vessel head penetrations under the energetic core disruptive accident in a sodium fast reactor (SFR) is presented. The model evaluates the total sodium mass in sodium-argon mixture released to the reactor containment building (RCB) through penetrations. The driving pressure at the penetration entrance is given as input. The two-phase frictional and local pressure drops, inertial and piezo-metric heads are accounted for in the model. Depending on the argon volume fraction, either a homogenous or separated flow approach is adopted to evaluate the mixture flow. Reactor-scale analysis show that the presence of argon in vessel head penetrations can significantly mitigate the total sodium release mass during the slug impact phase. Also, the two-phase frictional pressure drop plays a mitigating role and needs to be included in the model formulation to avoid overestimation of the sodium release mass. Fluid-structure interaction effects such as vessel head bending and hold-down bolt elongation have negligible influence on sodium release mass as long as the deformations are within the elastic limit. The model is conceived to be part of an integrated code system to evaluate the sodium fire and the maximum RCB pressure under severe accident conditions in a pool-type SFR.