Review and a Theoretical Approach on Pressure Drop Correlations of Flow through Open-Cell Metal Foam

Due to their high porosity, high stiffness, light weight, large surface area-to-volume ratio, and excellent thermal properties, open-cell metal foams have been applied in a wide range of sectors and industries, including the energy, transportation, aviation, biomedical, and defense industries. Understanding the flow characteristics and pressure drop of the fluid flow in open-cell metal foams is critical for applying such materials in these scenarios. However, the state-of-the-art pressure drop correlations for open-cell foams show large deviations from experimental data. In this paper, the fundamental governing equations of fluid flow through open-cell metal foams and the determination of different foam geometry structures are first presented. A variety of published models for predicting the pressure drop through open-cell metal foams are then summarized and validated against experimental data. Finally, two empirical correlations of permeability are developed and recommended based on the model of Calmidi. Moreover, Calmidi’s model is proposed to calculate the Forchheimer coefficient. These three equations together allow calculating the pressure drop through open-cell metal foam as a function of porosity and pore diameter (or strut diameter) in a wide range of porosities ε = 85.7–97.8% and pore densities of 10–100 PPI. The findings of this study greatly advance our understanding of the flow characteristics through open-cell metal foam and provide important guidance for the design of open-cell metal foam materials for different engineering applications.     

Time-Resolved PIV Measurements and Turbulence Characteristics of Flow Inside an Open-Cell Metal Foam

Open-cell metal foams are porous medium for thermo-fluidic systems. However, their complex geometry makes it difficult to perform time-resolved (TR) measurements inside them. In this study, a TR particle image velocimetry (PIV) method is introduced for use inside open-cell metal foam structures. Stereolithography 3D printing methods and conventional post-processing methods cannot be applied to metal foam structures; therefore, PolyJet 3D printing and post-processing methods were employed to fabricate a transparent metal foam replica. The key to obtaining acceptable transparency in this method is the complete removal of the support material from the printing surfaces. The flow characteristics inside a 10-pore-per-inch (PPI) metal foam were analyzed in which porosity is 0.92 while laminar flow condition is applied to inlet. The flow inside the foam replica is randomly divided and combined by the interconnected pore network. Robust crosswise motion occurs inside foam with approximately 23% bulk speed. Strong influence on transverse motion by metal foam is evident. In addition, span-wise vorticity evolution is similar to the integral time length scale of the stream-wise center plane. The span-wise vorticity fluctuation through the foam arrangement is presented. It is believed that this turbulent characteristic is caused by the interaction of jets that have different flow directions inside the metal foam structure. The finite-time Lyapunov exponent method is employed to visualize the vortex ridges. Fluctuating attracting and repelling material lines are expected to enhance the heat and mass transfer. The results presented in this study could be useful for understanding the flow characteristics inside metal foams.     

Influence of Foam Morphology on Flow and Heat Transport in a Random Packed Bed with Metallic Foam Pellets—An Investigation Using CFD

Open-cell metallic foams used as catalyst supports exhibit excellent transport properties. In this work, a unique application of metallic foam, as pelletized catalyst in a packed bed reactor, is examined. By using a wall-segment Computational Fluid Dynamics (CFD) setup, parametric analyses are carried out to investigate the influence of foam morphologies (cell size ϕ=0.45–3 mm and porosity ε=0.55–0.95) and intrinsic conductivity on flow and heat transport characteristics in a slender packed bed (N=D/dp=6.78) made of cylindrical metallic foam pellets. The transport processes have been modeled using an extended version of conventional particle-resolved CFD, i.e., flow and energy in inter-particle spaces are fully resolved, whereas the porous-media model is used for the effective transport processes inside highly-porous foam pellets. Simulation inputs include the processing parameters relevant to Steam Methane Reforming (SMR), analyzed for low (Rep~100) and high (Rep~5000) flow regimes. The effect of foam morphologies on packed beds has shown that the desired requirements contradict each other, i.e., an increase in cell size and porosity favors the reduction in pressure drop, but, it reduces the heat transfer efficiency. A design study is also conducted to find the optimum foam morphology of a cylindrical foam pellet at a higher Rep~5000, which yields ϕ = 0.45, ε = 0.8. Suitable correlations to predict the friction factor and the overall heat transfer coefficient in a foam-packed bed have been presented, which consider the effect of different foam morphologies over a range of particle Reynolds number, 100≤Rep≤5000.     

Microchannel Liquid-Cooled Heat Exchanger Based on a Nonuniform Lattice: Study on Structure Calculation,Formation Process,and Boiling Heat Transfer Performance

A microchannel radiator is advantageous due to its high efficiency and large boiling heat transfer coefficient of two-phase flow. Based on the research of uniform lattice structures, this study proposed a microchannel heat exchanger with a nonuniform lattice structure. The calculation, optimal formation, and boiling heat transfer performance of the nonuniform lattice structure based on selective laser melting (SLM) were investigated, and heat exchange samples were successfully prepared using SLM. The porosity and pore morphology of the samples were analysed, and the contrast experiments of boiling heat transfer were conducted with deionised water. The results revealed that the heat flow density of the lattice structure was a minimum of 244% higher than that of the traditional liquid-cooled plate. The critical heat flux density of the lattice structure is 110 W∙cm⁻², and the critical heat flux density of the traditional flat plate is 45 W∙cm⁻². In addition, the effects of cell structures indicated that for frame cells, the heat transfer effect of nonuniform frames was inferior to that of uniform frames; for face-centred cubic (FCC) cells, the nonuniform and uniform frames exhibited the same trend. However, the heat flow density of FCC cells was 25% higher than that of frame structures.     

Influence of Orientation and Radiative Heat Transfer on Aluminum Foams in Buoyancy-Induced Convection

Two differently-produced open-cell aluminum foams were compared to a commercially available finned heat sink. Further, an aluminum plate and block were tested as a reference. All heat sinks have the same base plate dimensions of four by six inches. The first foam was made by investment casting of a polyurethane preform and has a porosity of 0.946 and a pore density of 10 pores per linear inch. The second foam is manufactured by casting over a solvable core and has a porosity of 0.85 and a pore density of 2.5 pores per linear inch. The effects of orientation and radiative heat transfer are experimentally investigated. The heat sinks are tested in a vertical and horizontal orientation. The effect of radiative heat transfer is investigated by comparing a painted/anodized heat sink with an untreated one. The heat flux through the heat sink for a certain temperature difference between the environment and the heat sink’s base plate is used as the performance indicator. For temperature differences larger than 30 ^°C, the finned heat sink outperforms the in-house-made aluminum foam heat sink on average by 17%. Furthermore, the in-house-made aluminum foam dissipates on average 12% less heat than the other aluminum foam for a temperature difference larger than 40 ^°C. By painting/anodizing the heat sinks, the heat transfer rate increased on average by 10% to 50%. Finally, the thermal performance of the horizontal in-house-made aluminum foam heat sink is up to 18% larger than the one of the vertical aluminum foam heat sink.     

Mass/Heat Transfer Analogy Method in the Research on Convective Fluid Flow through a System of Long Square Mini-Channels

The paper presents the results of experimental investigations of mass transfer processes with the use of the limiting current technique. This experimental work analyzed the not fully developed entrance laminar region. The tested case refers to the convective fluid flow through a system of nine long, square mini-channels that are 2 mm wide and 100 mm long. The method used in the measurements allows one to determine mass transfer coefficients during the electrolyte flow by utilizing electrochemical processes. The received mass transfer coefficients were applied to the analogous heat transfer case. The Chilton–Colburn analogy between mass and heat transfer was applied. The obtained results, in the form of the dependence of Nusselt number within the function of Reynolds and Prandtl numbers, can be a useful formula in the design and analysis of heat transfer processes in mini heat exchangers.     

Modeling of Melt Flow and Heat Transfer in Stationary Gas Tungsten Arc Welding with Vertical and Tilted Torches

A 3D numerical simulation was conducted to study the transient development of temperature distribution in stationary gas tungsten arc welding with filler wire. Heat transfer to the filler wire and the workpiece was investigated with vertical (90°) and titled (70°) torches. Heat flux, current flux, and gas drag force were calculated from the steady-state simulation of the arc. The temperature in the filler wire was determined at three different time intervals: 0.12 s, 0.24 s, and 0.36 s. The filler wire was assumed not to deform during this short time, and was therefore simulated as solid. The temperature in the workpiece was calculated at the same intervals using heat flux, current flux, gas drag force, Marangoni convection, and buoyancy. It should be noted that heat transfer to the filler wire was faster with the titled torch compared to the vertical torch. Heat flux to the workpiece was asymmetrical with both the vertical and tilted torches when the filler wire was fully inserted into the arc. It was found that the overall trends of temperature contours for both the arc and the workpiece were in good agreement. It was also observed that more heat was transferred to the filler wire with the 70° torch compared with the 90° torch. The melted volume of the filler wire (volume above 1750 °K) was 12 mm³ with the 70° torch, compared to 9.2 mm³ with the 90° torch.     

Effect of Thermal Buoyancy on Fluid Flow and Residence-Time Distribution in a Single-Strand Tundish

Natural convection of molten steel flow in a tundish occurs due to the temperature variation of the inlet stream and heat losses through top surface and refractory walls. A computational fluid dynamics (CFD) model was applied to study the effect of thermal buoyancy on fluid flow and residence-time distribution in a single-strand tundish. The CFD model was first validated with the experimental data from a non-isothermal water model and then applied to both scale-down model and prototype. The effects of flow control devices, including weir, dam and turbulence inhibitor, were compared and analyzed. Parameter studies of different heat losses through the top surface were performed. The results show that thermal buoyancy has a significant impact on the flow pattern and temperature distributions of molten steel in the tundish. The increase of heat loss through the top surface shortens the mean residence time of molten steel in the tundish, leading to an increase in dead volume fraction and a decrease in plug flow volume fraction.     

Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range T_λ < T ≤ T_m (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, T_λ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at T_m ≈ T_λ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds T_m, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.     

芪参益气滴丸干预PCI术后急性前壁心肌梗死患者冠脉血流和左室功能的研究

目的：研究芪参益气滴丸对经皮冠脉介入治疗术（PCI）后急性前壁心肌梗死（AMI）患者冠脉血流和左室功能的影响。方法选取符合要求的前壁 AMI患者83例,采用随机对照双盲的方法分为对照组和治疗组,对照组给予常规西药及 PCI治疗,治疗组在对照组用药及 PCI 治疗的基础上加用芪参益气滴丸。比较术后两组患者在冠脉血流和左室功能方面的差异。结果两组共失访3例,失访率3.61%。术后两组间冠脉 TIMI3级血流差异无统计学意义（P〉0.05）;治疗9个月后治疗组在 TIMI3级血流、冠脉内再狭窄情况及侧支循环评分方面均优于对照组,差异有统计学意义（P〈0.05）;超声心动图显示,PCI术后9个月,治疗组在左室射血分数（LVEF）、心搏出量（CO）、心脏指数（CI）和左室收缩末期容积（LVESV）方面明显优于对照组,差异有统计学意义（P〈0.05）,尤其在 LVEF方面,呈稳步提高趋势。结论芪参益气滴丸对改善 PCI术后前壁 AMI患者冠脉血流和左室功能方面有积极影响。     

Effect of Blood Pump Flow and Arteriovenous Fistula Blood Flow on the Blood Pressure and Cardiac Function in Patients Undergoing Maintenance Hemodialysis

The effect of blood pump flow rate on the cardiac functions of hemodialysis patients with arteriovenous fistula (AVF) is largely unknown. This study aimed to investigate if blood pump flow rate (Qb) and AVF access flow rate (Qa) can affect the cardiac function of Chinese hemodialysis patients. A total of 72 patients undergoing AVF hemodialysis were included from March 2010 to June 2014 and dichotomized into the high‐ and low‐flow groups using the medians of Qb (220 mL/min) and Qa (1000 mL/min) as the cutoffs. The cardiac function parameters were measured by ultrasound dilution technique within the first (t + 30) and the last (t ? 30) 30 min of dialysis. At t + 30, Qb‐high group had significantly higher systolic blood pressure (SBP) and mean arterial pressure (MAP) than Qb‐low group. At t ? 30, Qb‐high group had higher SBP, diastolic blood pressure (DBP), and MAP than Qb‐low group. Qa‐high group had higher SBP, MAP, cardiac output (CO), cardiac index (CI), central blood volume (CBV), and lower peripheral resistance than Qa‐low group. Multiple linear regression showed that at t ? 30, Qb was positively correlated with SBP and MAP. Qa was positively correlated with CO, CI, CBV, and PR but negatively correlated with heart rate. Although Qb > 220 mL/min and Qa >1000 mL/min would elevate some parameters, the means of SBP, DBP, MAP remain within the normal range, indicating that appropriate increase in blood pump flow rate has little effect on the cardiac function of hemodialysis patients.     

Experimental and Numerical Investigation of Effect of Static and Fatigue Loading on Behavior of Different Double Strap Adhesive Joint Configurations in Fiber Metal Laminates

Double strap lap adhesive joints between metal (AA 6061-T6) and composite (carbon/epoxy) laminates were fabricated and characterized based on strength. Hand layup methods were used to fabricate double strap match lap joints and double strap mismatch lap joints. These joints were compared for their strength under static and fatigue loadings. Fracture toughness (GIIC) was measured experimentally using tensile testing and validated with numerical simulations using the cohesive zone model (CZM) in ABAQUS/Standard. Fatigue life under tension–tension fluctuating sinusoidal loading was determined experimentally. Failure loads for both joints were in close relation, whereas the fatigue life of the double strap mismatch lap joint was longer than that of the double strap match lap joint. A cohesive dominating failure pattern was identified in tensile testing. During fatigue testing, it was observed that inhomogeneity (air bubble) in adhesive plays a negative role while the long time duration between two consecutive cycle spans has a positive effect on the life of joints.     

Dependence of Heat Transport in Solids on Length-Scale,Pressure, and Temperature: Implications for Mechanisms and Thermodynamics

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D_∞(T)[1 − exp(−bL)]. When L is several mm, D_∞(T) = FT^−G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D_∞^−0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(c_P)/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.     

Effect of Heat Treatments under High Isostatic Pressure on the Transport Critical Current Density at 4.2 K and 20 K in Doped and Undoped MgB2 Wires

Annealing undoped MgB₂ wires under high isostatic pressure (HIP) increases transport critical current density (J_tc) by 10% at 4.2 K in range magnetic fields from 4 T to 12 T and significantly increases J_tc by 25% in range magnetic fields from 2 T to 4 T and does not increase J_tc above 4 T at 20 K. Further research shows that a large amount of 10% SiC admixture and thermal treatment under a high isostatic pressure of 1 GPa significantly increases the J_tc by 40% at 4.2 K in magnetic fields above 6 T and reduces J_tc by one order at 20 K in MgB₂ wires. Additionally, our research showed that heat treatment under high isostatic pressure is more evident in wires with smaller diameters, as it greatly increases the density of MgB₂ material and the number of connections between grains compared to MgB₂ wires with larger diameters, but only during the Mg solid-state reaction. In addition, our study indicates that smaller wire diameters and high isostatic pressure do not lead to a higher density of MgB₂ material and more connections between grains during the liquid-state Mg reaction.     

The Effect on Sound Generation of Varying Both Gas Flow Rate and the Viscosity of Sputum-like Gel in a Simple Tubular Model

Gas flows of 2, 3, and 4 L/min were directed through a sputum-like gel with viscosities of 100, 150, and 200 P and placed in a tube similar in diameter to a human segmental bronchus (4 mm), which was immersed in a bath of water. The sound produced by gas flow through the gel was recorded with a hydrophone. Sound data were subjected to time-expanded waveforms and fast Fourier transform (FFT) analysis. This study demonstrated that the number of crackles generated was directly related to the flow rate and inversely related to gel viscosity. The initial deflection width (IDW), two-cycle duration (2 CD), and peak-to-peak amplitude of crackles were significantly affected by the gas flow rate but not the viscosity of the gel. A lower gas flow rate generated crackles with longer IDW and 2 CD, but higher gas flow rates generated crackles with higher amplitude. Peak sound intensity measured from FFT increased as flow rate increased but decreased as the viscosity of the gel increased. At low gas flows, no gel-induced crackle sound was generated within the data capture window when the most viscous gel was examined. A digital video image of gas flow through the gel was captured, and this confirmed the absence of bubbles or slug formation at low flows through 200 P gel during the 3 seconds of data acquisition. This study describes some characteristics of crackles generated from different combinations of gas flow and gel viscosity and suggests that ``coarse crackles' result from the explosion of gas bubbles in pulmonary secretions. Health care practitioners should consider the combined effect of rate of inspiratory gas flow and sputum viscosity during auscultation of patients' lungs. Accepted for publication 7 October 1999     

Effect of Short- and Long-Term Treatment with Omeprazole on Cell Cycle Distribution in the Gastric Mucosa: Results of a Flow Cytometric Study

Omeprazole may exert an effect on gastric mucosal proliferation by inhibiting gastric acid secretion and increasing serum gastrin levels. It may also influence the kinetics of endocrine cells and the oxyntic mucosa. The aim of the present study was to evaluate the cell cycle in different gastric compartments following short- (1 month) and long-term (6 months) administration of two different dosages of omeprazole by means of a flow cytometric method. We also determined serum gastrin levels at the same time. No differences in cell cycle distribution of the antrum, body, and fundus were found in the two different dosage groups after 1 month of therapy, considering the synthetic phase (S-phase) of the cell cycle. A statistically significant increase in S-phase was reported after long-term therapy in the mucosa of the fundus and body of the stomach in both groups. Gastrin levels showed no clear correlation with cell cycle distribution variables. We postulate a proliferative adaptation of the oxyntic mucosa to long-term drug administration not mediated by gastrin influence.     

Effect of Poloxamer 188 on Collateral Blood Flow, Myocardial Infarct Size, and Left Ventricular Function in a Canine Model of Prolonged (3-Hour) Coronary Occlusion and Reperfusion

Poloxamer 188 is a surfactant with hemorheological, antithrombotic, and neutrophil-inhibitory properties. This agent has been demonstrated to reduce infarct size and to improve left ventricular function in animal models of myocardial infarction and reperfusion, and recently in a randomized trial of patients receiving thrombolytic therapy for acute myocardial infarction. In addition to reducing reperfusion injury, poloxamer 188 might be beneficial by increasing collateral blood flow. The purpose of this study was to determine the effect of poloxamer 188 on collateral blood flow, myocardial infarct size, and left ventricular function in a canine model of prolonged (3 hours) coronary occlusion and reperfusion. Closed-chest dogs (n = 21) underwent a 3-hour coronary occlusion and 3 hours of reperfusion. At 1 hour of occlusion, dogs received poloxamer 188, 75 mg/kg IV bolus, followed by 150 mg/kg/h IV for the final 2 hours of coronary occlusion and throughout reperfusion, or a saline placebo. Regional myocardial blood flow was measured using colored microspheres. Myocardial infarct size and area at risk were determined by postmortem histochemical staining. Compared with controls, poloxamer 188–treated dogs showed no significant increase in collateral blood flow during the final 2 hours of a 3-hour coronary artery occlusion. In addition, poloxamer 188 treatment had no beneficial effect on infarct size or left ventricular function in this model. Increased collateral blood flow is unlikely to be a beneficial mechanism of poloxamer 188 in myocardial infarction. These data also question the benefit of this agent to reduce reperfusion injury in the setting of more prolonged (3-hour) coronary occlusion.