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For various rock engineering, injection of fluids into rock fractures through boreholes is quite common. It is of great significance to investigate the characteristics of radial flow (RF) in rock fractures for these activities. In this study, macroscopic and mesoscopic characteristics of RF in rough rock fractures were investigated and compared with those of unidirectional flow (UF) by theoretical analysis, tests and simulations. An equation for nonlinear RF was derived for rock fractures according to conservation law of mass and Izbash’s law. Four scanned rough rock fracture models were established and used to experimentally investigate the macroscopic flow characteristics in both UF and RF. Numerical simulations were performed to clarify the mesoscopic differences in fluid pressure distributions and the flowlines of RF and UF in rock fractures. The parameters of hydraulic aperture and equivalent width for RF were obtained and correlated to those for UF. A method to calculate fracture roughness coefficient of fractures for RF related to the flow direction was proposed. The characteristic parameters, i.e., critical Reynolds numbers for the flow transition from linear to nonlinear flow, effective hydraulic apertures and non-Darcy coefficients, were obtained for the UF and RF based on the test results. It was indicated that the fracture roughness plays a critical role in the macroscopic and mesoscopic characteristics of both RF and UF. According to the test results, the macroscopic characteristic parameters for RF are related to those for UF, and the nonlinearity of RF was stronger than that of UF at a specified flow rate, which was consistent with the mesoscopic characteristics observed in the simulation that the distribution of water pressure, flow velocity and the streamlines in RF were more non-uniform than that in UF. The study results were useful to describe the RF characteristic in rock fractures with the characteristic parameters for UF, which have been investigated extensively in literature.HighlightsA nonlinear flow equation for radial flow in rock fractures was derived to describe the relationship between the hydraulic head and flow rate.The differences and relations between radial and unidirectional flow were studied from macroscopic and mesoscopic aspects.The parameters of hydraulic aperture and equivalent width for radial flow were obtained and correlated to those for unidirectional flow.The effect of fracture roughness on radial and unidirectional flow was related to the flow direction and was incorporated in the Forchheimer equation.

In rock grouting, idealized 2D-radial laminar flow of yield stress fluids (YSF) is a fundamental flow configuration that is used for cement grout spread estimation. A limited amount of works have presented analytical and numerical solutions on the radial velocity profiles between parallel disks. However, to the best of our knowledge, there has been no experimental work that has presented measured velocity profiles for this geometry. In this paper, we present velocity profiles of Carbopol (a simple YSF), measured by pulsed ultrasound velocimetry within a radial flow model. We describe the design of the physical model and then present the measured velocity profiles while highlighting the plug-flow region and slip effects observed for three different apertures and volumetric flow rates. Although the measured velocity profiles exhibited wall slip, there was a reasonably good agreement with the analytical solution. We then discuss the major implications of our work on radial flow.

The radial flow field structure, which has the advantages of low pressure drop, good water removal and good mass transfer, is an emerging structure for proton exchange membrane fuel cell (PEMFC) flow fields. However, optimization work on the design the structure is scarce for a complex structure that is difficult to manufacture. A comprehensive three-dimensional, non-isothermal and single-phase mathematical model is developed to describe the flow and heat, mass and charge transfer processes in a PEMFC. The transport phenomena and cell performance of radial flow fields with different gradient channels and parallel flow fields are studied and compared using the commercial computational fluid dynamics (CFD) software Fluent ® . The distribution of oxygen concentration, pressure drop and temperature with different radial lengths is obtained. The effects of gradient channels, gas supply modes and radial lengths on cell performance are investigated. The results show that radial flow fields could offer more uniform oxygen distributions and lower pressure drops compared with parallel flow fields. Larger gradient channel sizes contribute to larger transfer volumes and higher gas molar concentrations in the catalyst layers and lower pressures in channels. The counter-flow supply mode is superior to the co-flow supply mode because it can enable a higher oxygen velocity and hence a higher current density.

The low-pressure and low-density conditions encountered at high altitudes significantly reduce the operating Reynolds number of micro radial-flow turbines, frequently bringing it below the self-similarity critical threshold of 3.5 × 104. This departure undermines the applicability of conventional similarity-based design approaches. In this study, micro radial-flow turbines with rotor diameters below 50 mm are investigated through a combined approach integrating high-fidelity numerical simulations with experimental validation, aiming to elucidate the mechanisms by which low Reynolds numbers influence aerodynamic and thermodynamic performance. The results demonstrate that decreasing Reynolds number leads to boundary-layer thickening on blade surfaces, enhanced flow separation on the suction side, and increased secondary-flow losses within the blade passages. These effects jointly produce a pronounced and non-linear deterioration of turbine efficiency. Geometric scaling analysis further indicates that efficiency losses intensify with decreasing turbine size, and become particularly severe at low rotational speeds and high expansion ratios. Detailed flow-field analyses reveal a direct link between the degradation of blade loading distribution and the amplification of transverse pressure gradients under low-Reynolds-number conditions, providing physical insight into the observed performance decline.

Membrane chromatography (MC) is an emerging bioseparation technology combining the principles of membrane filtration and chromatography. In this process, one type of molecule is adsorbed in the stationary phase, whereas the other type of molecule is passed through the membrane pores without affecting the adsorbed molecule. In subsequent the step, the adsorbed molecule is recovered by an elution buffer with a unique ionic strength and pH. Functionalized microfiltration membranes are usually used in radial flow, axial flow, and lateral flow membrane modules in MC systems. In the MC process, the transport of a solute to a stationary phase is mainly achieved through convection and minimum pore diffusion. Therefore, mass transfer resistance and pressure drop become insignificant. Other characteristics of MC systems are a minimum clogging tendency in the stationary phase, the capability of operating with a high mobile phase flow rate, and the disposable (short term) application of stationary phase. The development and application of MC systems for the fractionation of individual proteins from whey for investigation and industrial-scale production are promising. A significant income from individual whey proteins together with the marketing of dairy foods may provide a new commercial outlook in dairy industry. In this review, information about the development of a MC system and its applications for the fractionation of individual protein from whey are presented in comprehensive manner.

In this paper, the flow channel of the radial proton exchange membrane fuel cell (PEMFC) is optimized by the topological optimization method. Using the SNOPT algorithm, a two-dimensional stable constant temperature model is freely constructed in the cyclic sector design domain. Topology optimization aims to maximize the efficiency of PEMFC and minimize the energy dissipation of reaction gas. We analyze radial topology flow channels’ mass transfer capacity and cell performance with different maximum volume constraints. The results show that under high current density, the performance of the optimized channel is significantly better than that of the traditional channel. Increasing the maximum volume constraint is beneficial for improving the mass transfer of PEMFC. At 0.6 V, the cell performance of Scheme 4 is 14.9% higher than the serpentine flow channel and 9.5% higher than the parallel flow channel. In addition, in the optimal selection, 3D simulation modeling is carried out for more accurate verification.

The general radial flow (GRF) could successfully analyze the groundwater flow in a fractured medium which has generally a more complex mechanism due to the scale-dependent heterogeneity and dynamic processes for both individual fracture and fracture networks. A new optimization scheme, referred to as the automatic shifting method (ASM), was established in order to eradicate the subjectivity and some definite difficulties in classical graphical curve matching (GCM) for the determination flow parameters of GRF from in-situ pumping test data. The logic behind the ASM is similar to GCM but it simplifies and enhances the estimation process by optimizing newly introduced parameters (the horizontal and vertical shifts) together with the flow dimension parameter via Water Cycle Algorithm (WCA). The proposed ASM was tested with several hypothetical pumping test scenarios as well as a number of real field data. In addition, the capability of WCA was thoroughly compared with other competitive derivative-free, nature inspired population-based optimization algorithms by implementing a multi decision criteria analysis. The proposed ASM with WCA could achieve the outstanding estimation performance for the implemented analyses. In conclusion, ASM has a great potential to be modified for interpreting test data obtained from different groundwater models.

Forced vibrations of turbine blades induced by airflow excitation can severely threaten the service life of radial flow turbines in aircraft environmental control systems (ECSs). However, existing studies on airflow excitation in ECS radial flow turbines using novel tubular nozzles are limited. To address this research gap, the ultra-high-frequency airflow excitation characteristics and resonance behavior in an ECS radial flow turbines were studied using numerical simulations and experiments. The effects of radial clearance between the nozzle and the impeller, as well as the nozzle layout, on airflow excitation were investigated. The results indicate that, with the current tubular nozzle design, no shock waves were generated at the nozzle outlet. The rotor–stator interaction was the primary source of excitation in ECS radial flow turbines employing tubular nozzles, inducing significant first-order airflow excitation and leading to turbine fatigue failure. Increasing the radial clearance between the impeller and the nozzle can effectively reduce airflow excitation; however, this effect was nonlinear. With increasing radial clearance, the reduction in airflow excitation became less effective. Meanwhile, the airflow excitation was significantly influenced by the nozzle layout. The single-row nozzle layout exhibited pronounced first-order airflow excitation characteristics and the high-amplitude regions were distributed throughout the entire impeller flow passage. For the double-row staggered nozzle layout, the first-order airflow excitation was greatly diminished, reaching only 50% of the maximum amplitude observed in the single-row layout and the high-amplitude regions were confined to the impeller leading-edge area. This investigation is beneficial for the design of ECS radial flow turbines with novel tubular nozzles.

A novel integrated detection system that introduces a paper-chip-based molecular detection strategy into a polydimethylsiloxane (PDMS) microchip and temperature control system was developed for on-site colorimetric detection of DNA. For the paper chip-based detection strategy, a padlock probe DNA (PLP)-mediated rolling circle amplification (RCA) reaction for signal amplification and a radial flow assay according to the Au-probe labeling strategy for visualization were optimized and applied for DNA detection. In the PDMS chip, the reactions for ligation of target-dependent PLP, RCA, and labeling were performed one-step under isothermal temperature in a single chamber, and one drop of the final reaction solution was loaded onto the paper chip to form a radial colorimetric signal. To create an optimal analysis environment, not only the optimization of molecular reactions for DNA detection but also the chamber shape of the PDMS chip and temperature control system were successfully verified. Our results indicate that a detection limit of 14.7 nM of DNA was achieved, and non-specific DNAs with a single-base mismatch at the target DNA were selectively discriminated. This integrated detection system can be applied not only for single nucleotide polymorphism identification, but also for pathogen gene detection. The adoption of inexpensive paper and PDMS chips allows the fabrication of cost-effective detection systems. Moreover, it is very suitable for operation in various resource-limited locations by adopting a highly portable and user-friendly detection method that minimizes the use of large and expensive equipment.

There is currently a lack of regulation of the caffeine found in cola and energy drinks by the FDA, which fails to protect the consumers of these products. Due to this lack of regulation, cola and energy drinks can have noticeable differences in their caffeine content when compared to the average amount per serving labelled on the product. In this study, we demonstrate the ability to analyse caffeine rapidly in under 20 s, and with HPLC pressures under 3500 psi (241 bar). To facilitate a high-throughput routine HPLC analysis of the caffeine content found in energy and cola drinks, two HPLC column technologies are studied, a conventional run HPLC column, and a newly commercialised Radial Flow Splitting end fitted HPLC column. The Radial Flow Splitting fitted column demonstrated the following benefits: a 37% reduction in pressure, an increased signal intensity sensitivity of 35%, a reduced analysis time by 20%, and improved metrics in assay precision based on triplicate injections associated with retention time, peak area, and peak height precision %RSD values. Both rapid HPLC methods offer greater opportunity for expanded beverage testing, which can ultimately help protect the consumer. The quantified energy drinks that were tested had a higher caffeine content, on average, than the labelled caffeine content, with an approximately ±16 mg difference per serving size for the energy drinks. In the case of the cola drinks, which did not include caffeine levels on the food label, we compared the levels to the USDA guidance and found up to double the recommended amount of caffeine in one serving for the samples studied. This highlights the need to have stricter regulations for caffeinated beverages to protect consumers and provide transparency regarding the caffeine content.