Dean Number Research Articles

Dynamics of Barred Coast at Different Temporal Scales (by the Example of Vistula Spit in the Baltic Sea)

According to fundamental concepts, the morphodynamic system of an accumulative sandy coast with underwater bars exhibits cyclic behavior across various time scales. This raises the question: which factor is more significant for the dynamics of a given coast—individual storms or seasonal changes in wave activity? While observations and studies addressing this issue have primarily been conducted on oceanic coasts, there is a lack of comparable data for fetch-limited areas. Monitoring of the bottom topography along the west coast of Vistula Spit (Baltic Sea) revealed a cyclic behavior in morphology, transitioning from a straightened external bar to its connection with the shore. Analysis of field measurement results indicated that seasonal variations in wave intensity do not significantly impact coastal relief. Furthermore, it was found that the complete cycle of underwater bar evolution lasts approximately two years, during which the coast profile maintains a stable shape at the stage of the straightened external bar. The identification of the primary factor influencing coastal evolution can be characterized by the Dean number (Ω), which combines wave parameters (wave height and period) with sediment fall velocity. Utilizing ERA5 wave reanalysis data, we compared the variability of Ω values on both annual and monthly scales. The analysis revealed that for the section of the coast under consideration, there is no clearly dominant evolutionary factor; rather, the coast is influenced approximately equally by individual storm events and seasonal fluctuations in wave energy. Modeling storm-induced bed profile deformations using the CROSS-PB model demonstrated that the position of the external underwater bar remains nearly constant even during intense and prolonged storms. It is concluded that under specific conditions—determined by a combination of sediment size, coastal slope, and wave regime characteristics—the coast can remain stable, exhibiting minimal response to relatively strong storms and seasonal variations in wave energy. Such coasts are characterized by an absence of a dominant evolutionary factor as indicated by fluctuations in the Dean parameter, allowing their morphodynamic cycles to span several seasons. This type of morphodynamics in coastal accumulative relief appears to be typical for conditions found in fetch-limited areas, such as regional and semi-closed seas.

Ethanol Production Using Zymomonas mobilis and In Situ Extraction in a Capillary Microreactor

The bacterium Zymomonas mobilis is investigated as a model organism for the cultivation and separation of ethanol as a product by in situ extraction in continuous flow microreactors. The considered microreactor is the Coiled Flow Inverter (CFI), which consists of a capillary coiled onto a support structure. Like other microreactors, the CFI benefits from a high surface-to-volume ratio, which enhances mass and heat transfer. Compared to many other microreactors, the CFI offers the advantage of operating without internal structures, which are often used to ensure good mixing. The simplicity of the design makes the CFI particularly suitable for biochemical applications as cells do not get stuck or damaged by internal structures. Despite this simplicity, good mixing is achieved through flow vortices caused by Taylor and Dean vortices. The reaction system consists of two phases, in which the aqueous phase carries the bacterium and an oleyl alcohol phase is used to extract the ethanol produced. Key parameters for evaluation are bacteria growth and the amount of ethanol produced by the microorganism. The results show the suitability of the CFI for microbial production of valuable compounds. A maximum ethanol concentration of 1.26 g L−1 was achieved for the experiment in the CFI. Overall, the cultivation in the CFI led to faster growth of Z. mobilis, resulting in 25% higher ethanol production than in conducted batch experiments.

Numerical Study of Heat Transfer Enhancement Using Nano-Encapsulated Phase Change (NPC) Slurries in Wavy Microchannels

Researchers have attempted to improve heat transfer in mini/microchannel heat sinks by dispersing nano-encapsulated phase change (NPC) materials in base coolants. While NPC slurries have demonstrated improved heat transfer performance, their applications are limited by decreasing enhancement at increased flow rates. To address this challenge, the present study numerically investigates the effects of wavy channels on the performance of NPC slurries. Simulation results reveal that a wavy channel induces Dean vortices that intensify the mixing of the working fluid and enlarge the melting fractions of the NPC material, thus offering a significantly higher heat transfer efficiency than a straight channel. Moreover, heat transfer enhancement by NPC slurries varies with the imposed heat flux and flow rate. Interestingly, the maximum heat transfer enhancement obtained with the wavy channel not only exceeds the straight one, but also occurs at a higher heat flux and faster flow rate. This finding demonstrates the advantage of wavy channels in management of intensive heat fluxes with NPC slurries. The study also investigates wavy channels with varying amplitude and wavelength. Increasing the wave aspect ratio from 0.2 to 0.588 strengthens Dean vortices and consequently increases the Nusselt number, optimal heat flux, and overall thermal performance factor.

Experimental and theoretical study on liquid film thickness of upward annular flow in helically coiled tubes

The liquid film thickness is crucial for studying the thermal hydraulic mechanism of the annular flow region in helically coiled tubes (HCTs). This paper introduces a refined experimental study on the liquid film thickness of annular flow in HCTs, utilizing a newly developed liquid film sensor. The experimental results indicate that the smaller coil diameters and pitches result in thinner average liquid film thicknesses. The average liquid film thickness decreases with increasing superficial gas velocity and decreasing superficial liquid velocity. However, the liquid film thickness at different circumferential positions on the cross-section of the tube exhibits varying sensitivities to superficial gas and liquid velocities. The experimental data reveal that the existing typical correlation formula for the average liquid film thickness of annular flow in straight tubes does not apply to HCTs. Consequently, a new prediction model is proposed for the average liquid film thickness of the annular flow region in HCTs, based on the modified Froude number, modified Dean number, Ekman number, and Reynolds number. This model comprehensively incorporates the structural characteristics of HCTs and fluid properties, and its validity is verified through the utilization of available and current data in the literature.

Spiral microchannels with concave cross-section for enhanced cancer cell inertial separation.

Inertial microfluidic technologies have proven effective for particle focusing and separation in many microchannels, typically the channels with the rectangular and trapezoidal shapes. To advance particle focusing in complex channels, we propose a spiral channel combining rectangular and concave cross-sections for high-resolution particle and cell focusing and separation. Numerical simulations were conducted to illustrate the effects of channel geometry on secondary flow distribution and particle focusing positions. The simulation shows the concave cross-section generates two asymmetrical Dean vortices skewing towards the inner and outer channel walls, resulting to stronger flow velocity magnitudes near the walls than the channel center. Consequently, larger particles focus near the inner wall, while smaller particles are trapped closer to the outer wall under the influence of the stronger velocity magnitude near the walls. A microfluidic chip with the proposed channelgeometry, along with a traditional rectangular channel, was fabricated by 3D printing and PDMS casting. Fluorescent microbeads were used to investigate inertial focusing and separation behaviors in the microfluidicchips. Experimental results show that the concave channel facilitates particle focusing or trapping much closer to the walls than the traditional rectangular channel, achieving better separation resolution. Finally, the proposed channel was applied to separate lung cancer A549 cells from human blood, achieving a cancer cell recovery rate of ~ 84.78% (enrichment ratio over 820-fold) and a blood cell rejection rate of ~ 99.88%. This innovative channel design in inertial microfluidics offers new insights for enhanced particle focusing and holds significant promise for cell manipulation with improved separation resolution.

Numerical simulation study of liquid–liquid mixing of high-viscosity fluids under laminar flow in a reverse flow multi-stage Tesla valve

In this study, computational fluid dynamics was employed to conduct a numerical simulation of the mixing performance and flow characteristics of two highly viscous liquids under laminar flow conditions within a reversed Tesla valve. Scalar transport techniques are employed to analyze the efficiency of liquid–liquid mixing in high-viscosity fluids. The focus of this study is to investigate the optimal mixing behavior between different parameters. Results indicate that an increase in Reynolds number leads to intensified Dean vortices, thereby promoting liquid–liquid mixing efficiency. Additionally, the mixing coefficient shows a negative correlation with Schmidt number (Sc), with a diminishing impact on the mixing coefficient when Sc ≥ 104. This is attributed to the dominance of fluid flow in controlling mixing within the channel at higher Schmidt numbers. Furthermore, this study compares the influence of valve angles (α) and stage numbers (n) on the mixing coefficient under identical Reynolds and Schmidt number conditions. As the number of Tesla valve stages increases, fluid acceleration within the pipeline is enhanced. Moreover, larger valve angles result in increased lengths of the curved section, leading to higher mixing efficiency. Therefore, to enhance mixing efficiency, it is recommended to increase the valve angle and the number of stages in the Tesla valve.

Study on secondary motions in supersonic boundary layers of a bent pipe

The present study employed direct numerical simulation to investigate the supersonic flow of Mach 3 in a bent pipe with a curvature of 0.0825, elucidating the dynamic mechanism of secondary motions within the turbulent boundary layer. The findings indicate that the compressible flow, affected by the wall curvature, is differentiated into several motion patterns as the bending angle increases: a portion of the outer fluid close to the wall, driven by the circumferential pressure gradient, moves inward through the lateral wall, causing an increase in the mass rate toward the lateral boundary layer and promoting the circumferential transport of energy and vorticity; other outer fluids at the start of the bent section, due to the centrifugal force, approach the wall to form a thinner boundary layer downstream; meanwhile, the fluid near the inner wall experiences the expansion, followed by the flow separation and reattachment at a bending angle of 14.6° and 22.0°, respectively, which induce a shear layer that develops from the inner end point toward the mainstream center, gradually reshaping the high-speed flow area within the pipe cross section into a U-shape, and enhancing the vorticity and temperature field of the inner region. Additionally, this study reveals a remarkable phenomenon that the separated flow in a localized inner region forms a rotating field, inducing vortices distinct from the mainstream Dean vortices in the low-speed flow region enclosed by the shear layer.

Experimental and numerical study on the performance index of mixing for low aspect ratio serpentine microchannels

In this work, the effect of a range of Dean numbers (De) varying from 0.01–70 on low aspect ratio (AR = 0.05–0.2) serpentine microfluidic devices was studied experimentally and numerically. It was observed that the AR, the number of circular bumps, and the angular positions of bumps transverse to the flow have a significant influence on the pressure drop and flow features (i.e., the position and shape of flow separation zones). Mixing was exclusively driven by diffusive mechanisms at low De values and at high De values, it was primarily induced by Dean vortices. The lowest mixing index (MI) was observed for De = 1 in all channel types, highlighting the transition region between the diffusion and Dean vortices-dominant mixing regimes. The MI was generally increased by increasing the AR of the channels. However, at high De, Dean vortices became strong enough to induce rapid mixing that was largely independent of the AR and bump placement. A dimensional performance index (PI) was defined as a function of the MI and the pressure drop per unit length. Distinct flow patterns arising from various positioning of bumps resulted in significant variations in the MI and PI values, with different dependencies on De. This underscored the importance of bump positioning based on the operational De range to optimize the mixing performance. Despite minor deviations between the designed and fabricated channels, the use of 3D-printed molds proved effective even at scales close to the resolution of the printer, resulting in mixing patterns consistent with the designed channels. These findings provide valuable insights into optimizing serpentine microchannels for efficient mixing while considering the trade-offs between enhanced mixing and increased pressure drop.

A Multivariable Numerical Investigation of Wavy-Based Microchannel Heat Sink Geometry Towards Optimal Thermal Performance

Abstract This research provides a comprehensive multivariable comparative investigation of the effect of various microchannel configurations on their thermal performance. Three-dimensional fluid flow and heat transfer simulations are performed with different arrangements of the channel's width tapering and cross-sectional aspect ratio with an emphasis on the synergistic proven effects of geometrical parameters in innovatory combinations. Results confirm that wavy channels are significantly superior to straight channels in terms of thermal performance due to the creation of secondary flow (Dean Vortices), which improves the processes of advective mixing and, therefore, overall heat transfer characteristics with minimal pumping power penalty. Width-tapering of wavy channels also shows better thermal resistance than untapered wavy channels producing almost 10 percent thermal resistance improvement. The study indicates a significant dependency of thermal performance on the cross-sectional aspect ratio of the channel which suggests that there are ideal tapering and aspect ratio conditions. An innovative wavy-tapered microchannel heat sink has been introduced, featuring an optimal parametric configuration and directionally alternating coolant flow. This design results in additional thermal resistance improvement by 15% and significantly improves substrate temperature distribution uniformity. Overall, the results demonstrate the superior potential of the configuration for high-end electronics cooling tasks. These results provide interpretive insight into microchannel heat sink design and optimization.

CFD—ANN study on axial dispersion in helical and serpentine millimetric coils

CFD simulations are reported to compare hydrodynamic/axial dispersion in a classical helical-shaped and planar serpentine-shaped tubular reactor at a millimetric scale (1-5 mm) for the first time. A two-step simulation approach is validated against experimental data on residence time distribution in serpentine coils. The method is then used for parametric analysis to explore the impact of geometric parameters on the coiling factor and axial dispersion coefficient. Dean vortices in the coiling region are visualized. The findings from the parametric analysis are utilized to develop empirical correlations and Artificial Neural Network (ANN) models for estimating coiling factors and axial dispersion coefficients in both serpentine and helical coils. The absolute average relative error (AERR) in predicting the coiling factor is 3.5% for helical coils and 4.6% for serpentine coils. The AERR of the ANN model for predicting the axial dispersion coefficient is 14% for helical coils and 10% for serpentine coils. The study reveals that both axial dispersion coefficient and pressure drop are higher in serpentine coils compared to helical coils. Axial dispersion is found to be relatively unaffected by pitch (helical) or bend diameter (serpentine) and tube diameter but shows significant reduction with a decrease in pitch circle diameter (helical) or gap between bends (serpentine). The developed correlations and ANN models can aid in the precise sizing of tubular reactors designed as helical or serpentine coils. This is exemplified through a case study involving the synthesis of an ionic liquid, where the helical configuration demonstrated a performance advantage of approximately 6% over the serpentine configuration.

Determining of the thermo-hydraulic characteristics and exergy analysis of a triple helical tube with inner twisted tube

An innovative technique to enhance heat transfer as a passive method was investigated. The combination of the twisted tube and helical coil to increase the swirl intensity is presented. The current investigation showed experimentally and numerically the exergy and thermal performance analysis of a new design of a triple tube design called a triple helical tube with inner twisted tube, THTITT. The new design is a modified design of a double helical tube with inner twisted tube, DHTITT which is created by twisting the inner tube. Besides the benefits of adding the third fluid to DHTITT that achieve extra contact surface area per unit length between the intermediate tube and the new passage in the outer tube. In which expected to enhance the temperature gradient between the three fluids and consequently, the thermal characteristics augment occurred. The twisted tube increased the intensity of the swirl flow and more intense disturbance of the fluid in the tube occurred. A 3d CFD model was established to get more insight at a level of detail not always available in the experiment. The effects of twisted pitch ratio, ξ hydraulic diameter, ω, helical coil torsion, α, helical coil inclination angle, φ, as well as Dean number, NDn, h were explored. Four groups of test specimens include various ξ of 5.32, 7.97, and ∞, various ω of 3.8, 6.8, and 9.9 mm, various α of 0.068, 0.095, and 0.121, and various φ of 0°, 45°, and 90° were established, manufactured and examined in this investigation. The investigation covered Reynolds number, NRe,h, for a range of 2450:29300 corresponding to Dean number, NDn, h, for a range of 570:4800. The results showed a higher Nusselt number, NNu, h, of THTITT compared to DHTITT by 61.8 %%, while the increase in fh is approximately negligible. Also, by decreasing ξ from ∞ to 5.32 increases NNu, h by 33.4 %, with an increase in friction factor, fh by 57.6 %. Furthermore, with a decreasing ω from 9.9 mm to 3.8 mm, a significant increase in NNu, h occurs by 20.6 %, at the expense of increasing fh by 36.4 %. In addition, with decreasing α from 0.121 to 0.068, a significant increase in NNu, h occurs by 27.6 %, at the expense of increasing fh by 17.1 %. Finally, the THTITT decreases the heat loss (exergy destruction) between the hot and cold fluids. New correlations to predict NNu,h, and fh are presented.

Mean streaming in reciprocating flow in a double bifurcation

This paper reports the mean streaming flow generated in a double bifurcation during reciprocating flow calculated using direct numerical simulations. Motivated by the medical ventilation technique of high-frequency ventilation (HFV), we investigate the potential for mean streaming to be maintained in this geometry as the frequency of reciprocation is increased while concurrently reducing the amplitude (and thereby reducing the volume per cycle). We identify four distinct regimes of flow. The first and second occur at low to moderate frequencies and generate significant streaming flows due to the interaction between Dean vortices that are generated during both the in- and out-flows. The third and fourth occur at high frequencies and produce reduced streaming, due to the reduction in formation length of the Dean vortices. Notably, the fourth regime at the highest frequencies investigated appears to show a switch in the direction of the streaming flow at the wall. Considering the motivating application of HFV, we show that currently employed frequencies are low, and much higher frequencies (and subsequently lower volumes per cycle) could potentially be employed.

Thermal characteristics of nanofluid ice slurry flowing through a spiral tube: A computational study

Nanofluid ice slurry (NICS) has recently attracted significant attention in the field of thermal engineering as an alternative refrigerant, offering a cost-effective, stable, and environmentally friendly cold storage solution. To maximize its potential, a thorough understanding of its heat transfer characteristics is crucial. Unfortunately, this information is not available for spiral tubes which are commonly used in thermal systems due to their superior heat transfer performance. This may hinder further development and implementation of this technology. Hence, the present investigation aims to analyze the flow characteristics and heat transfer mechanisms of a graphene oxide hybrid NICS within a spiral tube employing a computational fluid dynamics (CFD) methodology. More specifically, an interphase heat and mass transfer model, derived from the Euler–Euler model, is formulated to accurately represent the phase transition phenomena occurring within the nanofluid. The results indicate that the spiral tube structure enhances ice crystal accumulation inside the tube, leading to lower outlet temperatures and improved heat transfer without causing ice blockage. The NICS shows a 3% higher pressure drop compared to pure water ice slurry. Increased nanoparticle concentrations enhance thermal conductivity, benefiting heat transfer, but also raise viscosity, resulting in greater internal friction. A Nusselt correlation based on Prandtl and Dean numbers is formulated to aid future studies and the design of NICS systems. When the Reynolds number increases from 3600 to 6600, the Nusselt number rises by approximately 21% for pure water ice slurry and 22% for nanofluid ice slurry.

Investigation on the Flow and Heat Transfer Characteristics in a Multi-Pass Channel Using Magnetic Resonance Velocimetry and Transient Thermochromic Liquid Crystal

Abstract The three-dimensional flow field in multi-pass channels with and without ribs was measured by magnetic resonance velocimetry (MRV), while heat transfer performance on the endwall of channels in the same geometry was investigated using transient thermochromic liquid crystal (TLC) technique. The evolution of comprehensive three-dimensional flow field and their correlation with local heat transfer enhancement on end wall of multi-pass channels with and without ribs were revealed as a whole picture. Results show that the flow characteristics in the right-angle bend as well as the second pass are dramatically different for the smooth and ribbed channels, resulting in totally different features of heat transfer distribution on the end wall in those two channels. For the smooth channel, strong dean vortices form around the bend region near the outer wall where heat transfer is enhanced substantially. For the ribbed channel, no dean vortex but complex three-dimensional flow presents around bends. Heat transfer downstream of ribs close to the reattachment regions is strengthened noticeably. Comparison between velocity and heat transfer results suggest that one of the principle mechanisms driving heat transfer enhancement is both endwall directed velocity for smooth and ribbed channels, even though they are induced by different flow structures.

Full-cycle study on developing a novel structured micromixer and evaluating the nanoparticle products as mRNA delivery carriers

Achieving precise control of nanoparticle size while maintaining consistency and high uniformity is of paramount importance for improving the efficacy of nanoparticle-based therapies and minimizing potential side effects. Although microfluidic technologies are widely used for reliable nanoparticle synthesis, they face challenges in meeting critical homogeneity requirements, mainly due to imperfect mixing efficiency. Furthermore, channel clogging during continuous operation presents a significant obstacle in terms of quality control, as it progressively impedes the mixing behavior necessary for consistent nanoparticle production for therapeutic delivery and complicates the scaling-up process. This study entailed the development of a 3D-printed novel micromixer embedded with hemispherical baffle microstructures, a dual vortex mixer (DVM), which integrates Dean vortices to generate two symmetrical counter-rotating intensified secondary flows. The DVM with a relatively large mixer volume showed rapid mixing characteristics even at a flow rate of several mL min−1 and produced highly uniform lipids, liposomes, and polymer nanoparticles in a size range (50–130 nm) and polydispersity index (PDI) values below 0.15. For the evaluation of products, SARS-CoV-2 Spike mRNA-loaded lipid nanoparticles were examined to verify protein expression in vitro and in vivo using firefly luciferase (FLuc) mRNA. This showed that the performance of the system is comparable to that of a commercial toroidal mixer. Moreover, the vigorous in-situ dispersion of nanoparticles by harnessing the power of vortex physically minimizes the occurrence of aggregation, ensuring consistent production performance without internal clogging of a half-day operation and facilitating quality control of the nanoparticles at desired scales.

Continuous flow production of bioactive ceria quantum dots: New paradigms to the effect of process parameters on surface oxygen vacancy tuning

Precisely monitored nucleation-growth kinetics for governing the size, surface chemistry, and sought-after attributes of quantum dots (QDs) for large-scale manufacturing remains a formidable challenge. This study evinces the importance of ultrafast mixing and high heating rates for rapid nucleation, particularly in synthesizing monodispersed QDs with enriched surface defects. Recently, cerium oxide (CeO2) nanostructures have gained prominence in antioxidant therapy owing to the co-existence of Ce3+ and Ce4+. However, current batch processes lack scalability, reproducibility, and control over the reaction kinetics, key for fine-tuning the surface defect-driven properties of CeO2 nanostructures. Addressing this knowledge gap, we demonstrate a unique, sustainable, continuous flow platform that allows simultaneous engineering of surface oxygen vacancies (VO●) and regulates the size of L arginine functionalized CeO2 QDs (VO●-rich l-arg-CeO2 QDs). Introduction of the helical coil reactor regulated by dean vortices yields monodispersed QDs with enhanced Ce3+/Ce4+ratio and VO● at the surface. Through various experimental methodologies, we showed how adjusting temperature, flowrate, and pH enables achieving the desirable size (3 nm), thereby bestowing an optimal surface Ce3+ and VO● fractions, pivotal for size-dictated photo-response, physiochemical properties, and biofunctionality of the QDs. The abundant surface VO● (72 %) entails narrowing of the band gap (∼ 2.5 eV), resulting in unprecedented photothermal response (ΔT = 19.7 ± 0.6 °C) and photoluminescence, features not typically found in defect-free conventional CeO2 nanostructures. With a strategic combination of process parameters, the defect-rich material system displayed excellent biocompatibility (95.6 %), and antioxidant efficacy on human keratinocyte (HaCaT) cells, and long-term stability (ζ = -29±1.5 mV) in suspensions, even after 120 days. This economical, high throughput continuous flow platform for fabricating biofunctionalized VO●-rich l-arg-CeO2 QDs outperforms conventional batch processes, opening numerous possibilities for lab-to-clinic translation in the fight against oxidative stress-related disorders.

Experimental and numerical study of improving flow and heat transfer in a serpentine cooling channel with topology-optimized TPMS porous structures

Serpentine cooling channels have been employed in various industrial applications to control the heat loads in the system by increasing heat transfer while lowering the total pressure loss. As additive manufacturing (AM) enables the fabrication of complex structures, more sophisticated cooling models have been proposed to improve the thermal performance of the serpentine channel. This work designs a high-performance serpentine cooling channel based on topology optimization and triply periodic minimal surface (TPMS). The transient liquid crystal thermography (TLC) is used to reveal the endwall heat transfer characteristics of the optimized serpentine channel infilled with the Diamond TPMS topology within the Reynolds number of 10,000–40,000. The overall and local flow structures are revealed by numerical simulation, and the results are compared with the baseline serpentine channel. The experimental results show that at the Reynolds number of 10,000, the topology-optimized model with the Diamond structure shows a higher wetted-area averaged Nusselt number in the second pass by 70.7 % while reducing the total pressure loss by 19.2 %, compared to the smooth channel. Within the studied Reynolds numbers, the heat transfer enhancement in the second pass is 2.30–2.39 times relative to a smooth channel. The numerical results show that the topology-optimized model significantly improves the thermal performance by up to 82.7 % compared to the baseline because the flow recirculation and the regions of low heat transfer are eliminated. The optimized channel also mitigates the negative effect of the Dean's vortices while keeping high turbulence and improving flow and heat transfer uniformity.

Investigation on large fluctuation transient process of high head Pelton turbine

Abstract With the development of hydropower in southern western China, the Pelton turbine is the only choice in this ultra-high head condition which is nearly 1000 m. However, the complex coupling structure of the internal and external flow of the Pelton turbine, the change of flow pattern during the transition process, and the fluid-solid interaction of the bucket greatly increases the difficulty of accurate numerical simulation. Therefore, there are relatively few studies and applications on the transition process of the Pelton turbine. In this paper, the theoretical analysis, numerical calculation on the internal complex flow and the external characteristics of the turbine during the large fluctuation transition process are carried out in three aspects. First, the internal flow mechanism under optimized conditions is investigated, such as Dean vortex pairs, secondary flow, etc. And then analyze the influence of the flow state distribution on the jet flow. Secondly, study the instability and flow characteristics in the large fluctuation transition process of the opening and closing process of the nozzle, and predict the mechanism of the jet flow and the impact on the bucket during the dynamic process. Finally, study change of the hydraulic characteristics under the dynamic process which provides a theoretical guarantee for the safe operation of the Pelton turbine.

Maximizing liquid-cooled heat sink efficiency with advanced topology-optimized fin designs

Direct-to-chip liquid cooling offers significant advantages in managing higher power densities compared to traditional air-cooling methods. This approach utilizes nearly half the power required by server fans and air conditioners, enhances cooling efficiency in data centers. The effectiveness of this cooling strategy is intricately linked to the layout of the cold plate fins. In this research, a density-based topology optimization method is implemented in generating free-forming and non-intuitive fin structures. A pseudo-optimization model, which approximates the 3D heat sink as two 2D thermally coupled problem is selected and optimized with ‘pressure drop’ and ‘average junction temperature’ as objective function and constraint, respectively. Several fin layouts with inlet flow velocities and temperature constraints are generated. Three-dimensional numerical simulations reveal that the average junction temperature with the topology-optimized fin pattern is ∼2°C higher, and the pressure drop is significantly lower compared to size-optimized straight channel. Building on this, an inverted topology-optimized design is introduced along the channel length, inspired by the wavy nature of sectional fins. The average junction temperature with the inverted TO design is 3 to 4°C lower compared to the straight design, with a similar pumping power of 0.023 W. The TO fin layout capitalizes on frequent re-initialization of boundary layers, secondary flow-induced mixing, and the formation of Dean vortices along the channel length. Further refinement leads to the derivation of drop-oblique-trapezoidal and oval-shaped (DOTO) fins. These fins reduce average junction and wall temperatures by ∼23% compared to the inverted TO design, owing to the persistent effects of fluid dynamic phenomena along the channel length. Comparison with benchmarked designs indicates that DOTO fins reduce the average junction temperature by 3 to 6°C compared to size-optimized offset strip fins and step fins, with a similar pumping power of 0.083 W. The study indicates that optimizing DOTO fins dimensions can further enhance heat sink performance.

Modal stability analysis of toroidal pipe flow approaching zero curvature

The present study investigates the modal stability of the steady incompressible flow inside a toroidal pipe for values of the curvature $\delta$ (ratio between pipe and torus radii) approaching zero, i.e. the limit of a straight pipe. The global neutral stability curve for $10^{-7} \leq \delta \leq ~10^{-2}$ is traced using a continuation algorithm. Two different families of unstable eigenmodes are identified. For curvatures below $1.5 \times 10^{-6}$ , the critical Reynolds number ${{Re}}_{cr}$ is proportional to $\delta ^{-1/2}$ . Hence, the critical Dean number is constant, ${{De}}_{cr} = 2\,{{Re}}_{cr}\,\sqrt {\delta } \approx 113$ . This behaviour confirms that the Hagen–Poiseuille flow is stable to infinitesimal perturbations for any Reynolds number and suggests that a continuous transition from the curved to the straight pipe takes place as far as it regards the stability properties. For low values of the curvature, an approximate self-similar solution for the steady base flow can be obtained at a fixed Dean number. Exploiting the proposed semi-analytic scaling in the stability analysis provides satisfactory results.