High Reynolds Number Research Articles

Ambient-gas forced convection dictated evaporation kinetics of generic sessile droplets

We probe the temporal evolution of internal thermo-hydrodynamic features of evaporating sessile droplets under external forced convection. A transient numerical model based on Arbitrary Lagrangian-Eulerian (ALE) framework is adopted. The governing equations corresponding to the transport phenomena (mass, momentum and energy) are solved in a fully coupled manner in both the droplet (liquid) and ambient (gaseous) domains while accurately tracing the droplet interface evolution. The role of initial wetting state, external convection velocity and convective heating/cooling effects due to the air-flow are explored in details, and good agreements are noted with previous reports from literature. Results show that although the evaporation rate is augmented significantly in forced convection conditions, the same does not increase in proportion at higher Reynolds numbers. This is primarily due to the enhanced cooling effects that reduce saturated vapor concentration at droplet surface, and thereby supress the diffusion mechanism. Also, depending upon the contact angle, the evaporative cooling effects are compensated partially or completely due to convective heating. This altered thermal profile substantially influences internal hydrodynamic features (Marangoni flow and heat advection) during the transient and stable regimes of droplet evaporation. At higher degrees of convective heating, the droplet interface temperature becomes higher than its base temperature. This condition results in a completely opposite internal Marangoni vortex at stable state compared to that induced due to evaporative cooling effects. We also provide a regime map to show the role of the gas-phase Stefan number on the droplet-phase hydrodynamic regimes.

Efficient finite element strategy using enhanced high-order and second-derivative-free variants of Newton's method

In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular p-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Innovative design and experimental research on the world's first pilot plant for continuous supercritical hydrothermal synthesis nano copper

Supercritical hydrothermal synthesis (SCHS) is a promising nanomaterial preparation technology. We have successfully constructed the world's first continuous supercritical hydrothermal synthesis of nano copper pilot plant, with a yield of 100 kg/d and a grain size of nano copper products between 48–90 nm. In this work, the progressiveness of the supercritical hydrothermal synthesis pilot plant is systematically introduced, including rapid and uniform mixing, high Reynolds number, precise control of reaction time, avoidance of blockage and corrosion, and automation and safety control of the pilot plant. In addition, the synthesis mechanism and experimental results of supercritical hydrothermal synthesis of nano copper are further introduced. Finally, we analyze the economy of the pilot plant. The experimental research on the continuous hydrothermal synthesis of nano copper on a pilot scale may provide some guidance for future commercialization.

A Josephson–Anderson relation for drag in classical channel flows with streamwise periodicity: Effects of wall roughness

The detailed Josephson–Anderson relation equates the instantaneous work by pressure drop over any streamwise segment of a general channel and the wall-normal flux of spanwise vorticity spatially integrated over that section. This relation was first derived by Huggins for quantum superfluids, but it holds also for internal flows of classical fluids and for external flows around solid bodies, corresponding there to relations of Burgers, Lighthill, Kambe, Howe, and others. All of these prior results employ a background potential Euler flow with the same inflow/outflow as the physical flow, just as in Kelvin's minimum energy theorem, so that the reference potential incorporates information about flow geometry. We here generalize the detailed Josephson–Anderson relation to streamwise periodic channels appropriate for numerical simulation of classical fluid turbulence. We show that the original Neumann b.c. used by Huggins for the background potential creates an unphysical vortex sheet in a periodic channel, so that we substitute instead Dirichlet b.c. We show that the minimum energy theorem still holds and our new Josephson–Anderson relation again equates work by pressure drop instantaneously to integrated flux of spanwise vorticity. The result holds for both Newtonian and non-Newtonian fluids and for general curvilinear walls. We illustrate our new formula with numerical results in a periodic channel flow with a single smooth bump, which reveals how vortex separation from the roughness element creates drag at each time instant. Drag and dissipation are thus related to vorticity structure and dynamics locally in space and time, with important applications to drag-reduction and to explanation of anomalous dissipation at high Reynolds numbers.

Nitsche method for Navier–Stokes equations with slip boundary conditions: convergence analysis and VMS-LES stabilization

In this paper, we analyze Nitsche’s method for the stationary Navier–Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e., Navier) boundary conditions in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using the Banach Nečas–Babuška and Banach fixed point theorems under standard small data assumptions. We also provide optimal convergence rates for the approximation error. Furthermore, we propose a quasi-static VMS-LES formulation with Nitsche for the Navier–Stokes equations with slip boundary conditions to address the simulation of incompressible fluids at high Reynolds numbers. We validate our theory through several numerical tests in well-established benchmark problems.

Effective battery pack cooling by controlling flow patterns with vertical and spiral fins

Battery Thermal Management System (BTMS) is essential for dissipating heat and controlling temperature distribution within the battery pack of an electric vehicle to maintain its optimal operating temperature. This research focuses on the influence of cooling fins in achieving balanced temperature distribution inside the battery pack. Vertical and spiral fins are attached around 21,700 cylindrical cells for this investigation. ANSYS FLUENTsoftwareis employed to conduct the numerical simulations, where a finite volume approach is used to solve the mass conservation, Navier–Stokes, and energy transport equations. The study also uses a set of polynomial functions to calculate the heat generation inside the cells. It assesses the effects of the Reynolds number, fin loop number, and outlet section of BTMS at numerous discharge rates. The findings indicate that the spiral fins significantly impact the thermal performance, reducing Tmax by 21.31 % due to the enhanced flow circulations within the BTMS. A high Reynolds number also positively affects Tmax by reducing the temperature uniformity caused by the shorter time for air-cooling contact with the cell surfaces. More specifically, at a Reynolds number ≥9433, a Z-type BTMS with the spiral fins can maintain the temperature uniformity at a temperature difference of 5 °C. Among the six different BTMSs analysed, a U-type BTMS is reported to have the best performance, reducing Tmax and ΔTmax by 4.11 % and 38.1 %, respectively. The pressure drop in this case is also reduced by 8.46 %, thus lowering the overall power consumption.

A modified linear drag induced deceleration using a transformation of Newton’s second equation of motion

The drag force exerted on a body moving in a fluid is empirically known to follow a linear drag law at low Reynolds numbers and a quadratic drag law at very high Reynolds numbers. The major challenge with the empirical description of the drag lies in the uncertainty of the description of the drag coefficient as a function of velocity. If the function is precisely known, it may be possible to find a general formula for the drag, which would, in principle, be applicable for all Reynolds numbers. The general law can consequently be tested using the linear and quadratic drag laws within their validity regimes to confirm its reliability and validity. The current absence of such a general law implies that the prediction of the dynamics of a body moving under drag forces in the intermediate regime of the Reynolds number can only be approximate and inaccurate since it is not guided by any valid law. In this study, we derive a general relation for the drag force, which may be applicable in all the Reynolds number regimes. We achieve this through a simple transformation of Newton’s second equation for uniformly decelerated motion. It turns out that our general relation is a modification of the linear drag law. The effect of the introduced correction term in the dynamics of a projectile is evidently promising, as can be seen in the more realistic results generated.

Drag force on an accelerating flat plate at low Reynolds numbers

The accelerating flat plate is a useful model for studying the drag-based flapping flight (where drag is used to provide the weight-supporting force or thrust). Previous studies have mainly focused on the high Reynolds number (Re) regime pertaining to the flight of relatively large insects and birds. In this study, we numerically investigate the unsteady drag and flows of a uniformly accelerating flat plate at low Re that is typical of miniature insect flight (Re = 10–40). The following is shown. Unlike high-Re cases where the acceleration effect on drag is insensitive to Re, at low Re, the effect exhibits a strong dependence on Re: As Re decreases below 100, the acceleration effect increases rapidly, becoming 33%–56% greater than that of high-Re cases in the Re range of 10–40, before gradually decreasing. A simple model that consists of the quasi-steady, added-mass, and history force terms is proposed for drag at low Re. The scalings of the quasi-steady and added-mass force terms are well known; we find that the history force term scales approximately with the square root of the acceleration and velocity. The above result that relatively large drag is produced by the accelerating wing at Re = 10–40 is especially interesting and might explain why miniature insects fly in this Re range.

Effects of Turbulence on Upper-Tropospheric Ice Supersaturation

Abstract Effects of turbulence on ice supersaturation at cirrus heights (>8 km) remain unexplored. Small-scale mixing processes become important for high Reynolds number flows, which may develop below the buoyancy length scale (10–100 m). The current study couples a stochastic turbulent mixing model with reduced dimensionality to an entraining parcel model to investigate, in large-ensemble simulations, how supersaturation evolves due to homogeneous turbulence in the stably stratified, cloud-free upper troposphere. The rising parcel is forced by a mesoscale updraft. The perturbation of an initially homogeneous vertical distribution of supersaturation is studied after a 36-m ascent in a baseline case and several sensitivity scenarios. Turbulent mixing and associated temperature fluctuations alone lead to changes in ensemble-mean distributions with standard deviations in the range 0.001–0.006, while mean values are hardly affected. Large case-to-case variability in the supersaturation field is predicted with fluctuation amplitudes of up to 0.03, although such large values are rare. A vertical gradient of supersaturation (≈10−3 m−1) is generated for high turbulence intensities due to the development of a dry-adiabatic lapse rate. Entrainment of slightly warmer (less than 0.1 K) environmental air into the parcel decreases the mean supersaturation by less than 0.01. Supersaturation fluctuations are substantially larger after entrainment events with an additional small offset in absolute humidity (by ±3.5%) between the parcel and environmental air. The predicted perturbations of ice supersaturation are significant enough to motivate studies of turbulence–ice nucleation interactions during cirrus formation that abandon the assumption of instantaneous mixing inherent to traditional parcel models. Significance Statement The purpose of our study is to investigate the effects of microscale turbulence on ice supersaturation in the upper troposphere. The associated variability in temperature and moisture fields is not resolved in cloud models and cannot easily be represented in terms of large-scale flow variables. We specify the conditions in which turbulent mixing and entrainment cause substantial variations in distributions of supersaturation. These include high turbulence intensity, strong atmospheric stability, and large moisture gradients. Our results suggest that turbulence may affect the strongly supersaturation-dependent ice formation processes in high-altitude clouds, pointing to the need to investigate cirrus formation in the presence of turbulence.

Numerical investigation on the tracer followability of nitrogen droplets over the airfoil in cryogenic wind tunnel

Cryogenic wind tunnels (CWT) achieve high Reynolds number aerodynamic performance measurements by cooling the medium with liquid nitrogen. Utilization of naturally-occurring liquid nitrogen droplets as tracer particles for non-intrusive measurement applications in CWT shows great potential in the previous work. However, the droplet motion characteristics over the airfoil remain to be investigated, and the followability evaluation approach is lacking. Accordingly, an Euler-Lagrange model for transonic particle flow over the NACA0012–64 airfoil was established. The effect of flow characteristics on the particle motion was explored. The results reveal that the flow separation and shock wave phenomenon over the airfoil causing velocity deviation between airflow and droplet. The shock wave is the main deviation driver, and flow separation causing trace blind zones. Droplets larger than 10 μm fail to effectively follow the variation of airflow. The blind zone enlarges with angle of attack (AoA), particularly when AoA exceeding 10 degrees. Moreover, Stokes number is found to be inadequate for characterizing the followability of tracer particles in turbulent flow. Consequently, an evaluation method based on the Basset-Boussinesq-Oseen equation was developed. This research provides theoretical and technical support for advancing the use of nitrogen droplets as tracer particles in CWT.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids: extension of a global geometric approach for thin boundary layers and strong flow incidence

This paper presents further improvements to the immersed boundary method introduced in [1]. The proposed developments take place during the pre- and post-processing stages of the simulation workflow and aim to further increase the accuracy of the approach for steady-state simulations of high Reynolds number turbulent flows around aerodynamic geometries facing strong incidence. To this end, the location of the forcing points is further optimized prior to simulation, with an adaptive and local modeling height that accounts for the evolution of the turbulent boundary layer thickness, especially at the leading edge. In addition, the direct extrapolation of the pressure solution at the wall is replaced by first- and second-order reconstructions using the normal pressure gradients interpolated at a new set of image points. This second approach is used only in post-processing, after the simulation, and prevents the degradation of the wall pressure in the presence of strong curvatures or thin boundary layers. These developments have been validated by simulating subsonic turbulent flows around the NACA0012 profile, 2D multi-element airfoil (2DMEA), and HL-CRM half-plane at significant angles of attack. Smooth and accurate skin pressure and friction coefficients are observed, in excellent agreement with body fitted wall-resolved solutions, even for coarser Cartesian meshes. Better drag and lift coefficients calculated by direct near-field integrations are obtained, along with accurate predictions of the near-wall flow physics throughout the turbulent boundary layer.

Analysis on heat transfer enhancement mechanism in a cross-wavy primary surface heat exchanger based on advection thermal resistance method

This paper numerically investigates the flow and heat transfer characteristics in the primary surface heat exchanger (PSHE) with cross-wavy (CW) structures. The comprehensive performance affected by hydraulic diameters is evaluated. Moreover, the airflow shuttling behavior at the mixing area of CW-type PSHE is discussed, showing rapid heat transfer enhancement. The advection thermal resistance method and local thermal resistance analysis is proposed, while the impacts of longitudinal pitch and flowrates are considered. Results show that the case with a large hydraulic diameter displays much better comprehensive performance at lower flowrates. When raising the hydraulic diameter from 1.58 mm to 15.8 mm, the heat transfer rate per unit pumping power grows by 36.1 %. However, the priority of large channel is gradually disappeared after increasing the flowrates. Meanwhile, the larger longitudinal pitch of the CW channel may result in pronounced improvement on the heat transfer performance due to the presence of airflow shutting behavior at the mixing area as well as the secondary flow near the channel boundary layers. When no airflow shuttling exists, very high advection thermal resistance region can be observed due to the formation of boundary layers. It can be recognized that the case with airflow shuttling behavior can display similar heat transfer improvement compared to that with increasingly high Reynolds numbers, yet the pressure loss is rarely increased.

Development and deployment of data-driven turbulence model for three-dimensional complex configurations

Abstract In recent years, the synergy between artificial intelligence and turbulence big data has given rise to a new data-driven paradigm in turbulence research. Data-driven turbulence modeling has emerged as one of the forefront directions in fluid mechanics. Most existing studies focus on feature construction, selection, and the development of modeling frameworks, often overlooking the practical deployment and application of trained models. This paper examines the entire process from model construction to real-world deployment, using data-driven turbulence modeling for high Reynolds number flows over complex three-dimensional configurations as a case study. Key stages include data generation, input-output feature construction, model training, model compilation and optimization, deployment, and validation. We successfully implemented the entire workflow in a heterogeneous supercomputing environment and, through mixed programming techniques, integrated the resulting turbulence model into the Platform for Hybrid Engineering Simulation of Flows (PHengLEI) open-source software framework. This allowed for mixed-precision simulations, with the main equations solved in double precision and the turbulence model in half precision. The new computational framework was validated through large-scale parallel numerical simulations on grids with tens of millions of elements for three-dimensional complex configurations. The results highlight the efficiency of our model deployment, with overall computational efficiency improving by 13.35% and the turbulence model’s solution speed increasing by approximately 3.9 times. The accuracy of the computations was also confirmed, with the average relative error in the lift and drag coefficients calculated by the data-driven turbulence model within 3%. Across various computing nodes, the relative error in the computed aerodynamic coefficients remained within 1%, demonstrating the framework’s scalability. Notably, our contributions have been incorporated as a case study in the latest PHengLEI open-source project5 5 https://forge.osredm.com/PHengLEI/PHengLEI-TestCases/tree/master/Y02_ThreeD_M6_Unstruct_Branch_Ascend. .

Large/small eddy simulations: A high-fidelity method for studying high-Reynolds number turbulent flows

Direct numerical simulations (DNS) are one of the main ab initio tools to study turbulent flows. However, due to their considerable computational cost, DNS are primarily restricted to canonical flows at moderate Reynolds numbers, in which turbulence is isolated from the realistic, large-scale flow dynamics. In contrast, lower fidelity techniques, such as large eddy simulations (LES), are employed for modeling real-life systems. Such approaches rely on closure models that make multiple assumptions, including turbulent equilibrium, small-scale universality, etc., which require prior knowledge of the flow and can be violated. We propose a method, which couples a lower-fidelity, unresolved, time-dependent calculation of an entire system (LES) with an embedded small eddy simulation (SES) that provides a high-fidelity, fully resolved solution in a sub-region of interest of the LES. Such coupling is achieved by continuous replacement of the large SES scales with a low-pass filtered LES velocity field. The method is formulated in physical space, with no assumptions of equilibrium, small-scale structure, and boundary conditions. A priori tests of both steady and unsteady homogeneous, isotropic turbulences are used to demonstrate the method's accuracy in recovering turbulence properties, including spectra, probability density functions of the intermittent quantities, and sub-grid dissipation. Finally, SES is compared with two alternative approaches: one embedding a high-resolution region through static mesh refinement and a generalization of the traditional volumetric spectral forcing. Unlike these methods, SES is shown to achieve DNS-level accuracy at a fraction of the cost of the full DNS, thus opening the possibility to study high-Re flows.

Parametric analysis of reverse electrodialysis process for improved power generation: Influence of spacer thickness, feed solution flow rate, membrane, and concentration

Reverse electrodialysis (RED) technology produces electrical energy from a salinity gradient by transporting ions through ion-exchange membranes (IEM). Although research into this technology has recently seen considerable growth, there is still interest in improving its efficiency. As a result, a mathematical model to study the RED process was developed using Aspen Custom Modeler software, focusing on three membranes (Fumasep (FAD/FKD), Fujifilm Type 10, and Selemion (AMV/CMV)). A parametric analysis was conducted, considering spacer thickness, salinity gradient, and feed-solution flow rates. Evaluation of internal resistance, gross power density, and net power density was also performed. Results showed that using a thicker spacer (270 μm) in the high compartment and a thinner spacer (150 μm) with a high Reynolds number in the low compartment led to higher net power densities of 2.17 W·mcp−2 and 6.74 W·mcp−2 for Fumasep (FAD/FKD) membrane with (brackish/seawater) and (brackish/brine), respectively. Among the membranes tested, Fumasep (FAD/FKD) and Fujifilm Type 10 had similar results, with the former slightly exceeding the latter. However, the Selemion membrane (AMV/CMV) performed poorly in all tests.

Aerodynamic noise generated in three-dimensional lock-in and galloping behavior of square cylinder in high Reynolds number turbulent flows

Aerodynamic noise generated in three-dimensional lock-in and galloping behavior of square cylinder in high Reynolds number turbulent flows

High-fidelity fluid-structure interaction applied to static aeroelasticity in transonic flows

Transonic flows at high Reynolds numbers can lead to high dynamic pressures and, consequently, to aerostructural deflections of aircraft structures. This study aims to develop and validate a high-fidelity static aeroelastic analysis environment that is efficient and that can be used in an industrial setting. The aerodynamics is represented by numerical solutions of the Reynolds-averaged Navier-Stokes equations with appropriate turbulence closures. The load transfer process uses finite element shape functions in order to distribute the aerodynamic loads into the structural discretization. The structural analysis employs a modal basis approach, and a wingtip deflection convergence study is performed to find an adequate modal basis size. Radial basis functions are used for the fluid mesh displacement, and the influence of the support radius is evaluated to determine the optimal values relative to the wing mean aerodynamic chord. The capability is tested using the static aeroelastic benchmarks of the High Reynolds Aerostructural Dynamics Project (HIRENASD) and NASA's Common Research Model (CRM). The static aeroelastic results demonstrate robustness and consistency for the aerodynamic coefficients, pressure distributions, and structural deflection predictions at different normalized dynamic pressure values and grid refinement levels.

Modulation of re-circulation zone behind a square obstruction by single inclined turbulent wall jet with varying angle of attack

The modulation of the re-circulation region is one of the primary interests of this numerical study. This study investigates the modulation of the re-circulation zone behind a square obstruction by a single inclined turbulent wall jet with varying angles of attack. The flow field is visualized using the post-processing system of the simulation software and the results have been analyzed. The experiments are carried out for different angles of attack of the wall jet and a range of high Reynolds numbers. The results show that the re-circulation zone is significantly affected by the angle of attack of the wall jet. The maximum length of the re-circulation zone decreased with increasing angle of attack. The wall jet angles of attack (AOA) also affect the strength and position of the vortex structures in the re-circulation zone. The results of this study provide insights into the use of inclined wall jets for controlling the flow field behind obstructions in engineering applications such as flow control and mixing enhancement. The numerical simulation is based on a two-phase volume of fluid (VOF) model with open channel boundary conditions. The standard k–ω SST turbulence model is applied to solve the Reynolds averaged equation.

The effect of Reynolds number on the separated flow over a low-aspect-ratio wing

At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10{\,}000$ . In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings ( $Re \approx 10^2$ ) and turbulent flows at higher Reynolds numbers ( $Re \approx 10^4$ ). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2500$ . Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2500$ , an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.