High Reynolds Number Research Articles

Analysis of flow heat transfer characteristics of helium-xenon gas mixtures during natural circulation

Helium-xenon(He-Xe) gas mixture is a commonly used cooling medium in fourth-generation advanced reactor systems. The thermal conductivity of a passive waste heat system is related to the safety and reliability of the reactor system. Therefore, it is crucial to explore the passive characteristics of the helium-xenon gas mixture. The passive waste heat removal characteristics of a helium-xenon gas mixture are influenced by the flow and heat transfer characteristics of the mixture. However, existing research on the flow and heat transfer characteristics of helium-xenon gas mixture mainly focuses on single tube bundles and plate bundles with fixed flow rates and high Reynolds numbers. However, existing research on the flow and heat transfer characteristics of the He-Xe mixtures mainly focuses on single tube bundles and plate bundles with fixed flow rates and high Reynolds numbers, and most empirical formulas apply to Reynolds numbers greater than 10000. However, the natural circulation flow rate under the influence of gravity varies with the variation of heating power, and in most operating conditions, the Reynolds number is less than 10000. Due to the lack of research on the convective heat transfer characteristics of the He-Xe mixtures at low Re, this paper investigates the flow and heat transfer characteristics of the He-Xe under natural circulation conditions. A three-dimensional model of the natural circulation circuit was established using numerical calculation methods. Comparing the numerical simulation results of natural air circulation with empirical formulas, it was found that the error was less than 20 %. This proves that the SST k-ω turbulence model can be used to study the flow and heat transfer characteristics of He-Xe gas mixtures in natural circulation. On this basis, natural cycle numerical simulations of He-Xe mixtures with different mixing ratios were carried out at a heat flux of 5000 W/m2, as well as natural cycle numerical simulations of 40 g/mol He-Xe gas mixture at different heating powers, to study the effects of heating power and He-Xe mixing ratio on the natural cycle heat transfer characteristics of the He-Xe gas mixture. The existing He-Xe gas mixture flow heat transfer equation was modified, and the error of the modified Nu empirical equation was less than 12 %, which can be used for the development of the passive waste heat export system program for subsequent He-Xe gas-cooled fast reactors.

Utilizing indicator functions with computational data to confirm nature of overlap in normal turbulent stresses: Logarithmic or quarter-power

Indicator functions of the streamwise normal-stress profiles (NSP), based on careful differentiation of some of the best direct numerical simulations (DNS) data from channel and pipe flows, over the range 550<Reτ<16 000, are examined to establish the existence and range in wall distances of either a logarithmic-trend segment or a 1/4-power region. For nine out of 15 cases of DNS data we examined where Reτ<2000, the NSP did not contain either of the proposed trends. As Reτ exceeds around 2000 a 1/4-power, reflecting the “bounded-dissipation” predictions of Chen and Sreenivasan [“Law of bounded dissipation and its consequences in turbulent wall flows,” J. Fluid Mech. 933, A20 (2022); “Reynolds number asymptotics of wall-turbulence fluctuations,” J. Fluid Mech. 976, A21 (2023)] and data analysis of Monkewitz [“Reynolds number scaling and inner-outer overlap of stream-wise Reynoldss stress in wall turbulence,” arXiv:2307.00612 (2023)], develops near y+=1000 and expands with Reynolds numbers extending to 1000<y+<10 000 for Reτ around 15 000. This range of 1/4-power NSP corresponds to a range of outer-scaled Y between around 0.3 and 0.7. The computational database examined did not include the zero-pressure-gradient boundary layer experiments at higher Reynolds numbers where the logarithmic trend in the NSP has been previously reported around y+ of 1000 by Marusic et al. [“Attached eddy model of wall turbulence,” Annu. Rev. Fluid Mech. 51, 49–74 (2019); “The logarithmic variance of streamwise velocity and conundrum in wall turbulence,” J. Fluid Mech. 933, A8 (2022)] according to a “wall-scaled eddy model.”

An algebraic global linelet preconditioner for incompressible flow solvers

Given the wide range of scales present in fluid dynamics, highly anisotropic meshes are often employed to resolve boundary layer flow at high Reynolds numbers. However, such meshes result in distorted elements, which can deteriorate the convergence of the preconditioned conjugate gradient solver (PCG) used to solve the discrete pressure equations. To address this issue, the Linelet Preconditioner is commonly used to accelerate the convergence rate of the PCG by building line segments (linelets) along the direction of the strongest couplings and applying a specific operation to each linelet. Under the current state of the art, linelets are constrained to operate independently within each domain partition. In these scenarios, PCG convergence was observed to deteriorate when the number of domain partitions is increased. This work proposes a communication step to be integrated into the preconditioning step, enabling different linelets to exchange information. The proposed method is observed to improve the convergence rate of linear systems with high stiffness due to highly stretched elements. Also, an algorithm is developed to generate the preconditioning matrix by purely algebraic considerations, in contrast to the usual approach of building linelets based on geometrical considerations. Furthermore, since the current approach is agnostic to the domain partition, it does not impose any constraint on the domain decomposition. Hence, the proposed method is a robust preconditioner with a numerical performance almost independent of the quality of the domain decomposition, providing a way for a more balanced load distribution.

A three-dimensional meshless fluid–shell interaction framework based on smoothed particle hydrodynamics coupled with semi-meshless thin shell

Meshless methods are suitable for fluid–structure interaction simulations due to its Lagrangian feature and capability of handling large deformations. A three-dimensional meshless framework for the fluid–structure interaction simulation with shell structures is proposed in this study. The weakly compressible smoothed particle hydrodynamics is deployed in the fluid domain, where the boundary integral terms are incorporated to handle the one-layer shell boundary. On the other hand, a semi-meshless finite volume modeling method based on the Reissner–Mindlin shell is deployed in the one-layer shell domain. A one-way coupling method is employed for the interactive forcing between the fluid and shell particles near the interface, where the boundary integral method is employed to approximate the gradient and Laplacian operators in the fluid governing equations. Regarding the no-slip boundary, the original boundary integral method always leads to the artificial slipping phenomenon between the fluid and shell interface. To this end, a velocity penalty term with a relaxation factor is proposed to enforce the no-slip boundary condition, which substantially improves the accuracy of the original boundary integral method. In order to reduce computational costs, a multi-resolution strategy for the meshless framework is employed. A set of challenging cases with low and high Reynolds numbers are simulated by the present framework, and good accuracy is observed with the velocity penalty term in these cases. Overall, the new framework shows a satisfactory performance.

On the influence of porous coating on vibration response and noise reduction of cylinders at high Reynolds numbers

On the influence of porous coating on vibration response and noise reduction of cylinders at high Reynolds numbers

Aerodynamic force characteristics and flow field mechanism of multiple square cylinders in a tandem arrangement

Wind tunnel tests and large eddy simulations were employed to obtain the aerodynamic coefficients and flow fields of two and three tandem square cylinders across various spacing ratios. The spacing ratio L/D, defined as the ratio of the center-to-center spacing between adjacent square cylinders to their width, ranges from 1.2 to 8. By analyzing these results, the aerodynamic force characteristics and their generation mechanism of the three tandem square cylinders at a high Reynolds number (Re = 3.2 × 104) were revealed. By comparing the results of the two and three tandem square cylinders, the effect of adding a third square cylinder behind the two tandem square cylinders on its aerodynamic characteristics was clarified. The results show that unlike the two tandem square cylinders, the three tandem square cylinders exhibit two critical spacing ratios, (L/D)cr1 = 2.5–3 and (L/D)cr2 = 3.5–4, respectively. Based on these two critical spacing ratios, the flow around the three tandem square cylinders is identified as single blunt body, reattachment, and co-shedding regimes. In the single blunt body and reattachment regimes, the addition of a third square cylinder behind significantly alters the flow around the two tandem square cylinders, leading to reduced mean drag coefficients, fluctuating lift coefficients, and Strouhal numbers, along with an increased critical spacing ratio. In the co-shedding regime, this addition has little effect on the flow.

Numerical and experimental investigations of flow features over a wedge exposed to supersonic flow at high Reynolds numbers

Numerical and experimental investigations of flow features over a wedge exposed to supersonic flow at high Reynolds numbers

A numerical study of the wall-modeled large-eddy simulations of attached and separated flows with a semi-coupled synthetic turbulence generator

The predictive accuracy of the fluctuations inside turbulent boundary layers directly relies on the upstream turbulence synthesizer in wall-modeled large-eddy simulations (WMLESs). The conventional fully coupled synthetic turbulence generator (STG) strongly depends on the grid topology and simultaneous advancement of the unsteady Reynolds-averaged region. In this study, the two-stage semi-coupled STG, which is tolerant to the grid topology and is cost-effective due to the compatibility with precursor methods, was investigated. First, the semi-coupled STG efficiently generated artificial turbulence based on the existing benchmark data in the calculations of the fully developed channel flow. The adaptation length of the STG was less than ten boundary layer thicknesses by means of the Reynolds stresses and wall shear stresses, while the downstream turbulence was sufficiently “mature” for the predictions of more complex flows. The semi-coupled method with different wall-modeling strategies was validated for the mildly separated flow over a flat strut. The steady two-dimensional (2D) precursor data at the inlet were effectively utilized by the STG to generate turbulence and the monitored pressure fluctuations agreed well with the experimental data. Finally, the calculations of the flow around a wing–body junction showed that the algebraic wall-modeled large-eddy simulation demonstrated good accuracy in predicting the horseshoe vortex at the symmetry plane, and coherent structures rapidly developed from the artificial turbulence generated by the STG. To conclude, the WMLES with the semi-coupled STG can effectively predict the unsteady fluctuations in the attached and separated boundary layers. The compatibility of the semi-coupled STG with precursor methods and the relatively low computational cost of the WMLES can broaden the application areas of the STG method in complex flows at high Reynolds numbers.

High-fidelity simulations of boundary layer transition on an underwater axisymmetric body with stability theory

During the cruise status of an underwater high-speed vehicle, the flow around the vehicle's head typically transitions from a laminar to a turbulent state, triggering flow noise that can interfere with the normal operation of sonar. In order to accurately investigate this flow noise through numerical simulation, a high-fidelity turbulent flow field solution is essential. Common traditional turbulence numerical simulation methods, such as unsteady Reynolds-averaged simulation and large eddy simulation (LES), struggle to capture high-frequency turbulent fluctuations accurately due to their inability to directly resolve small-scale eddy structures, which results in compromising the simulation accuracy of high-frequency flow noise. To address this issue, this paper employs direct numerical simulation (DNS) to achieve high-fidelity resolution of the turbulent flow field, thereby enabling a more accurate assessment of flow noise distribution on the vehicle's surface. Meanwhile, considering significant computational resources required to solve the entire flow field in an underwater high Reynolds number environment, this study also incorporates the fixed transition modeling method and stability theory to confine the DNS computational domain to the vicinity of the transitional zone to improve simulation efficiency. Comparative analysis of flow noise monitoring results in the laminar, transitional, and turbulent zones revealed that the flow noise source in the laminar zone exhibits the lowest amplitude across all frequencies, while the flow noise source in the transitional zone features the highest amplitude, approximately 10 dB higher than that in the turbulent zone. Moreover, significant amplitudes in high-frequency components (above 30 kHz) are detected in both the transition and turbulent zones. Additionally, this study employs LES with the Smagorinsky model to simulate the flow field within the same computational domain as DNS, demonstrating the limitations of the Smagorinsky model-based LES in capturing high-frequency flow noise.

Implementation and validation of a generalized wall stress function

The generalized wall function by Shih et al. [Report No. M-1999-209398 (1999)], which accounts for non-equilibrium effects by the presence of favorable and adverse pressure gradients in turbulent flows, is addressed with the aim of performing high Reynolds number large-eddy simulations of the wall-bounded flow. The model uses a corrected law of the wall with a pressure gradient contribution to approximate the wall stress and applies to the entire viscous layer, buffer layer, and inertial region. A fully developed channel flow is first tested to validate the solver and model implementation, and then the wall function is assessed for the flow over a periodic hill. Wall-resolved simulations are in good agreement with reference results. A priori investigation with own experimental results corroborates the mathematical form of the model and suggests using different coefficients. The wall-modeled simulations show that the implemented wall model is able to improve the wall shear stress predictions compared to a standard equilibrium wall model. It corrects the underestimation of wall shear stresses by equilibrium models in the favorable pressure gradient region and the overestimation of wall shear stresses in the adverse pressure gradient region. The positions of the separation and reattachment points are also in good agreement with reference results. Furthermore, the prediction of the wall shear stress maximum in the favorable pressure gradient zone at the windward side of the hill is quite robust against coarsening the wall-normal grid spacing.

Simulation of Flow and Pressure Loss in the Example of the Elbow

One of the most basic issues in fluid mechanics is the description of flow in closed flows; more precisely, the calculation of pressure drops and the description of the flow form. Therefore, in this paper, the numerical simulation of the flow through the elbow was presented. This case was used to comprehensively describe the most important phenomena that should be taken into account during closed flows. The elbow was chosen as one of the most frequently used fittings in practice. The simulation was made with ANSYS Fluent, with the use of the turbulent model k-ω, SIMPLE simulation method, and at Reynolds number . The minor and major pressure loss were presented and discussed in the paper. The minor loss coefficient at the high Reynolds number was equal to around 0.2, which is close to the value of 0.22 used in engineering calculations. The influence of the Reynolds number on the shift of the stream separation point in the elbow was described. The secondary flow in the elbow was observed and the vortex structure was discussed and shown with the use of the Q-criterion (Q iso surface for level 0.005). This analysis allowed us to better visualize and describe the complex flow structure observed in the investigated case.

Navier-Stokes-ω model with slip and friction boundary conditions at high Reynolds numbers

Navier-Stokes-ω model with slip and friction boundary conditions at high Reynolds numbers

Numerical investigation of thermal-hydraulic performance enhancement in helical coil heat exchangers with twisted tube geometries

This numerical study examines the thermal-hydraulic performance of helical coil heat exchangers (HCHEs) using twisted tubes versus conventional circular tubes. The effects of Reynolds number (Re = 10,000 to 100,000), pitch length (11, 7.2, 5.5, 3.6 mm), and twisted tube orientation (co-current, counter-current) on heat transfer efficiency and pressure drop were investigated. The results show that higher Reynolds numbers can reduce the Resistance factor by approximately 25 % and improve heat transfer by approximately 35 %. An optimal pitch length of 5.5 mm was found to balance enhanced heat transfer and manageable pumping costs. Twisted tubes demonstrate significant performance advantages at lower Re, with 20–33 % higher Performance Evaluation Criterion (PEC) values compared to circular tubes. However, the benefit diminishes at higher Re, with less than 10 % PEC increase. Implementing counter-current twisted tube configurations leads to approximately 13 % higher Nusselt number and 11 % higher Resistance factor, resulting in a 10 % overall PEC improvement. These findings highlight the superior thermal-hydraulic performance of twisted tubes in HCHE applications, especially at lower Reynolds numbers. Future work could explore different fluids, advanced optimization, energy analysis, cost assessment, and additional geometric parameters to further enhance twisted tube heat exchanger design and performance.

Flow Topology Optimization at High Reynolds Numbers Based on Modified Turbulence Models

Flow topology optimization (TopOpt) based on Darcy’s source term is widely used in the field of TopOpt. It has a high degree of freedom, making it suitable for conceptual aerodynamic design. Two problems of TopOpt are addressed in this paper to apply the TopOpt method to high-Reynolds-number turbulent flow that is often encountered in aerodynamic design. First, a strategy for setting Darcy’s source term is proposed based on the relationship between the magnitude of the source term and some characteristic variables of the flow (length scale, freestream velocity, and fluid viscosity). Second, we construct two modified turbulence models, a modified Launder–Sharma k − ϵ (LSKE) model and a modified shear stress transport (SST) model, that consider the influence of Darcy’s source term on turbulence and the wall-distance field. The TopOpt of a low-drag profile in turbulent flow is studied using the modified LSKE model. It is demonstrated by comparing velocity profiles that the model can reflect the influence of solids on turbulence at Reynolds numbers as high as one million. The TopOpt of a rotor-like geometry, which is of great importance in aerodynamic design, is conducted using the modified SST model. In all the cases considered, the drag, the total pressure loss, and the energy dissipation are significantly reduced by TopOpt, indicating the proposed model’s ability to handle the TopOpt of turbulent flow.

Reynolds number effects in shock-wave/turbulent boundary-layer interactions

We investigate Reynolds number effects in strong shock-wave/turbulent boundary-layer interactions (STBLI) by leveraging a new database of wall-resolved and long-integrated large-eddy simulations. The database encompasses STBLI with massive boundary-layer separation at Mach $2.0$ , impinging-shock angle $40^{\circ }$ and friction Reynolds numbers ${\textit {Re}}_\tau$ $355$ , $1226$ and $5118$ . Our analysis shows that the shape of the reverse-flow bubble is notably different at low and high Reynolds number, while the mean-flow separation length, separation-shock angle and incipient plateau pressure are rather insensitive to Reynolds number variations. Velocity statistics reveal a shift in the peak location of the streamwise Reynolds stress from the separation-shock foot to the core of the detached shear layer at high Reynolds number, which we attribute to increased pressure transport in the separation-shock excursion domain. Additionally, in the high Reynolds case, the separation shock originates deep within the turbulent boundary, resulting in intensified wall-pressure fluctuations and spanwise variations associated with the passage of coherent velocity structures. Temporal spectra of various signals show energetic low-frequency content in all cases, along with a distinct peak in the bubble-volume spectra at a separation-length-based Strouhal number $St_{L_{sep}}\approx 0.1$ . The separation shock is also found to lag behind bubble-volume variations, consistent with the acoustic propagation time from reattachment to separation and a downstream mechanism driving the shock motion. Finally, dynamic mode decomposition of three-dimensional fields suggests a Reynolds-independent statistical link among separation-shock excursions, velocity streaks and large-scale vortices at low frequencies.

Nanofluid heat transfer enhancement in microchannels: Investigating phases interactions using multiphase Eulerian model

This study employs a robust multiphase Eulerian model to mimic heat transfer enhancement using nanofluids in a circular microchannel. Unlike the Eulerian models reported in the literature, the current model incorporates phase interactions, and its accuracy is significantly improved by integrating collision viscosity, kinetic viscosity, and frictional viscosity. Comparative analysis against other models like mixture and discrete phase models demonstrates superior performance of the current model, particularly for solid particle volume fractions exceeding 1 %. The model evaluates water-based nanofluids (Ag NPs, MgO, ZnO, Al2O3, ZrO2, SiO2) in circular microchannels. Ag NPs/water excels at low volume fractions and high Reynolds numbers, while MgO/water performs better at higher volume fractions. Moreover, the analysis of the Euler number indicates a decreasing trend with increasing Reynolds number across all nanofluids. However, no notable variation in the Euler number is observed when maintaining constant volume fraction and Reynolds number. Ultimately, the model is applied to obtain bulk fluid properties, such as viscosity and thermal conductivity, after suspending the nanoparticles. Subsequently, these properties were incorporated into the single-phase model. Utilizing these derived bulk properties was found to substantially enhance the accuracy of the single-phase model, demonstrating its reliability by yielding results within 13.52 % of experimental data.

URANOS-2.0: Improved performance, enhanced portability, and model extension towards exascale computing of high-speed engineering flows

We present URANOS-2.0, the second major release of our massively parallel, GPU-accelerated solver for compressible wall flow applications. This latest version represents a significant leap forward in our initial tool, which was launched in 2023 (De Vanna et al. [1]), and has been specifically optimized to take full advantage of the opportunities offered by the cutting-edge pre-exascale architectures available within the EuroHPC JU. In particular, URANOS-2.0 emphasizes portability and compatibility improvements with the two top-ranked supercomputing architectures in Europe: LUMI and Leonardo. These systems utilize different GPU architectures, AMD and NVIDIA, respectively, which necessitates extensive efforts to ensure seamless usability across their distinct structures. In pursuit of this objective, the current release adheres to the OpenACC standard. This choice not only facilitates efficient utilization of the full potential inherent in these extensive GPU-based architectures but also upholds the principles of vendor neutrality, a distinctive characteristic of URANOS solvers in the CFD solvers' panorama. However, the URANOS-2.0 version goes beyond the goals of improving usability and portability; it introduces performance enhancements and restructures the most demanding computational kernels. This translates into a 2× speedup over the same architecture. In addition to its enhanced single-GPU performance, the present solver release demonstrates very good scalability in multi-GPU environments. URANOS-2.0, in fact, achieves strong scaling efficiencies of over 80% across 64 compute nodes (256 GPUs) for both LUMI and Leonardo. Furthermore, its weak scaling efficiencies reach approximately 95% and 90% on LUMI and Leonardo, respectively, when up to 256 nodes (1024 GPUs) are considered. These significant performance advancements position URANOS-2.0 as a state-of-the-art supercomputing platform tailored for compressible wall turbulence applications, establishing the solver as an integrated tool for various aerospace and energy engineering applications, which can span from direct numerical simulations, wall-resolved large eddy simulations, up to most recent wall-modeled large eddy simulations. Program summaryProgram title: Unsteady Robust All-around Navier-StOkes Solver (URANOS)CPC Library link to program files:https://doi.org/10.17632/pw5hshn9k6.2Developer's repository link:https://github.com/uranos-gpu/uranos-gpu, https://github.com/uranos-gpu/uranos-gpu/tree/v2.0Licensing provisions: BSD License 2.0Programming language: Modern Fortran, OpenACC, MPINature of problem: Solving the compressible Navier-Stokes equations in a three-dimensional Cartesian framework.Solution method: Convective terms are treated with high-resolution shock-capturing schemes. The system dynamics is advanced in time with a three-stage Runge-Kutta method. Parallelization adopts MPI+OpenACC.

A defect correction weak Galerkin finite element method for the Kelvin–Voigt viscoelastic fluid flow model

In this paper, we present a defect correction weak Galerkin finite element method for solving the Kelvin–Voigt viscoelastic fluid flow model, which can guarantee that the discrete velocity is globally divergence-free. The second-order Crank–Nicolson difference scheme is considered for temporal discretization. In particular, combined with the defect correction method, the numerical oscillation effect is reduced at high Reynolds number. Our algorithm not only gives the stability and convergence of the numerical solutions of velocity and pressure but also is uniformly valid at the retardation time κ→0. Several numerical experiments are performed to verify the method has good behaviors.

Numerical study of the drag force, interfacial area and mass transfer in bubbles in a vertical pipe

A systematic numerical study of drag force and mass transfer in gravity-driven bubbles in a vertical pipe is performed at Re∼O(100−1000). This research employs a parallel multi-marker unstructured conservative level set method for interface capturing, avoiding the numerical coalescence in bubble swarms. The finite volume method discretizes transport equations on 3D collocated unstructured meshes. Unstructured flux limiter schemes solve the convective term of transport equations, preserving the numerical stability at high Reynolds numbers and high-density ratios. Thermodynamic equilibrium is assumed at the interface for the concentration of chemical species. The hydrodynamics and mass transfer of bubbles are validated against classical correlations from the literature. Finally, direct simulations are executed to develop new correlations for the drag force, normalized bubble surface and Sherwood number for bubbles in a vertical pipe.

Enhancing thermal performance of heat exchanger by using different 4-lobed swirl tube arrangements

This study numerically and experimentally investigated the thermal performance of a 4-lobed swirl tube. A double-pipe heat exchanger was built using 3D-printed steel tubes with PD ratios ranging from 4, 6 to 8. In addition, a 3D-printed circular pipe was also manufactured to investigate the influence of the 3D-printing method. In the experimental results, the PD4 decaying swirl tube had the highest performance for all PD ratios. The effects of different pitch-to-diameter (PD) ratios and tube arrangements on the swirl pipe were also investigated during simulations. The results reveal that the tube with a smaller PD ratio and crossover arrangement has a larger thermal enhancement and pressure drop. However, in comparison, the decaying arrangement has a relatively higher overall performance since it has a lower pressure drop. The PD6 decaying tube arrangement is the highest, especially at higher Reynolds numbers. Moreover, by showing the streamline within the swirl tube, small-scale vortices are found within the swirl tube, especially in the crossover arrangement. These vortices are formed due to the swirl motion and can enhance mixing and the heat transfer rate. Based on these simulation results, a regular-spaced swirl tube arrangement is proposed and its thermal performance is evaluated. In the experimental results, the PD4 decaying swirl tube gave the highest overall performance from 1.12 to 1.09 across all configurations. In the numerical results, the regularly-spaced swirl tube can further improve the overall performance with moderate pressure drop. Type 2 PD4 has the highest performance value at 1.06.