Wide Reynolds Number Range Research Articles

Numerical Simulation of Turbulent Fluid Flow in Rough Rock Fracture: 3D Case

We investigate both laminar and turbulent flow regimes in a 3D rock fracture via numerical CFD simulations. We construct our realistic fracture model from 3D scan data of a fractured rock sample and implement changes in both shear displacement and contact ratio, examining their effect on fracture permeability and friction factor. While previous studies were investigating either fully viscous Darcy or inertial Forchheimer laminar flow regimes, we chose to cover the wide Reynolds number range of 0.1–106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^6$$\\end{document}. We introduce CFD simulation of a turbulent flow for realistic 3D fractures, implementing the RANS approach to turbulence modeling. We focus on 3D fracture geometries and implement changes in both shear displacement and contact ratio, systematically examining their effect on fracture permeability and friction factor in a manner similar to the fundamental studies of the flow in rough-walled pipes. Growing Re leads to first stationary–non-stationary and then laminar–turbulent transitions. The presence of contact spots severely disrupts the flow pattern and adversely affects the overall permeability of the fracture. Regardless of shear displacement, ‘no contact’ 3D models can be reasonably approximated by the 2D profiles. Depending on the fracture geometry, Forchheimer β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} fitting for both laminar and turbulent regimes can be performed either by a single or by two parameter values.

Reynolds number dependence of turbulent kinetic energy and energy balance of 3-component turbulence intensity in a pipe flow

Measurement data sets are presented for the turbulence intensity profile of three velocity components ( $u$ , $v$ and $w$ ) and turbulent kinetic energy (TKE, $k$ ) over a wide range of Reynolds numbers from $Re_\tau =990$ to 20 750 in a pipe flow. The turbulence intensity profiles of the $u$ - and $w$ -component show logarithmic behaviour, and that of the $v$ -component shows a constant region at high Reynolds numbers, $Re_\tau >10\,000$ . Furthermore, a logarithmic region is also observed in the TKE profile at $y/R=0.055\unicode{x2013}0.25$ . The Reynolds number dependences of peak values of $u$ -, $w$ -component and TKE fit to both a logarithmic law (Marusic et al., Phys. Rev. Fluids, vol. 2, 2017, 100502) and an asymptotic law (Chen and Sreenivasan, J. Fluid Mech., vol. 908, 2020, R3), within the uncertainty of measurement. The Reynolds number dependence of the bulk TKE $k^+_{bulk}$ , which is the total amount of TKE in the cross-sectional area of the pipe also fits to both laws. When the asymptotic law is applied to the $k^+_{bulk}$ , it asymptotically increases to the finite value $k^+_{bulk}=11$ as the Reynolds number increases. The contribution ratio $\langle u'^2\rangle /k$ reaches a plateau, and the value tends to be constant within $100< y^+<1000$ at $Re_\tau >10\ 000$ . Therefore, the local balance of each velocity component also indicates asymptotic behaviour. The contribution ratios are balanced in this region at high Reynolds numbers as $\langle u'^2\rangle /k\simeq 1.25$ , $\langle w'^2\rangle /k\simeq 0.5$ and $\langle v'^2\rangle /k \simeq 0.25$ .

Direct numerical simulation of turbulent flow in pipes with realistic large roughness at the wall

We carry out direct numerical simulation (DNS) of turbulent flow in rough pipes. Two types of irregular roughness are investigated, namely a grit-blasted and a graphite surface. A wide range of Reynolds numbers is tested, from the laminar up to the fully rough regime, attempting to replicate Nikuradse's pioneering study. Despite the large relative roughness, outer-layer similarity is achieved at high Reynolds number as hypothesised by Townsend, with deviations from the smooth wall case of 4 % for the grit-blasted surface and 13 % for the graphite surface. This makes it possible to define a roughness function and the equivalent sand-grain roughness. The results are compared with those obtained in plane channels, with small differences pointing to the residual influence of the duct cross-sectional shape in the presence of relatively large roughness. The computed friction factors behave similar to those Nikuradse's chart, with differences in terms of the friction factor in the laminar region and of the critical Reynolds number, which are partly absorbed by using the hydraulic radius as reference length scale. The distributions of the velocity fluctuations intensities point to a isotropisation of turbulence in the near-wall region resulting from the roughness, with influence of the roughness geometry. Comparison of the computed equivalent sand-grain roughness height suggest that existing correlations suffer from poor predictive power, at least for surfaces with large relative roughness.

Feature identification in complex fluid flows by convolutional neural networks

Recent advancements have established machine learning’s utility in predicting nonlinear fluid dynamics, with predictive accuracy being a central motivation for employing neural networks. However, the pattern recognition central to the networks function is equally valuable for enhancing our dynamical insight into the complex fluid dynamics. In this paper, a single-layer convolutional neural network (CNN) was trained to recognize three qualitatively different subsonic buffet flows (periodic, quasi-periodic and chaotic) over a high-incidence airfoil, and a near-perfect accuracy was obtained with only a small training dataset. The convolutional kernels and corresponding feature maps, developed by the model with no temporal information provided, identified large-scale coherent structures in agreement with those known to be associated with buffet flows. Sensitivity to hyperparameters including network architecture and convolutional kernel size was also explored. The coherent structures identified by these models enhance our dynamical understanding of subsonic buffet over high-incidence airfoils over a wide range of Reynolds numbers.

Experimental characterization of pressure and friction factor in an interior subchannel of a 61-pin wire-wrapped rod bundle with a porous blockage

Comprehending and counteracting accident conditions presented by impedances of flow in diminutive subchannels of a Liquid Metal Fast Reactor (LMFR) hexagonal rod bundle are imperative toward their development and safety. Scarce experimental research currently exists in the literature to characterize the pressure and friction factor for partial blockages in LMFR assemblies. Experimental pressure measurements were conducted in a 61-pin prototypical LMFR fuel assembly using specialized instrumented wire-wrapped rods with a three-dimensional printed porous blockage installed. The pressure drop was measured for one helical pitch at four distinct interior subchannel locations: two in the blocked subchannel and two unblocked adjacent locations (near-center and near-wall of the assembly). A wide range of Reynolds numbers between 140 and 24 000 were studied to evaluate the blocked subchannel friction factor and to determine the flow regime boundaries for laminar-to-transition and transition-to-turbulent flows. Power spectral density analysis of the pressure fluctuations for three distinct locations (one upstream and two downstream of the porous blockage) revealed the mechanisms of coherent structure formations and transport, and dominant location-dependent Strouhal numbers. One-dimensional continuous wavelet transforms of the pressure fluctuations demarcated temporal instances of flow events with their frequency content. Temporal cross correlation quantified the temporal delay between the blocked subchannel pressure fluctuations in the blockage vicinity. The presented research provides first-of-its-kind datasets and fluid physics based-analyses for the interior LMFR subchannel in the presence of a porous blockage and provides a benchmark for the validation of computational flow models and predictive correlations for the safety enhancement of LMFR rod bundles.

Numerical Simulation of a thin liquid film over a heated rotating disc and cone

A computational fluid dynamics (CFD) model, based on the volume of fluid (VOF) approach, is used to simulate heat transfer from a rotating disc and cone to a thin water film flowing over it. Simulations are carried out on a 2D-axisymmetric Eulerian mesh for a wide range of Reynolds and Rossby numbers. The temperature of the disc is kept below the saturation temperature for all cases. The prediction shows film thickness exhibits a radial decay at the entry and three distinct zones are identified: inertia, Coriolis, and centrifugal. The magnitude and the location of the peak of the film are a function of the combined effect of the Reynolds number and the Rossby number. Specifically, a reduction of Rossby number from 103 to 0.5 at fixed Reynolds number of 105, reduced the average film thickness by nine times. A further 21 % reduction in film thickness was achieved by increasing the Reynolds number from 105 to 107 at Rossby of 0.5. However, the thinner film thickness under these conditions did not result in improved heat transfer (Tout at Re = 107 is 9 % lower than Re = 105 for TS = 353 K). The higher Reynolds number is detrimental to the heat transfer due to the greater mass flow rate and velocity in the radial direction impacting the heat transfer rate. Further improvement in heat transfer is achieved by greater centrifugal force via reduced cone angle. Overall, optimal heat transfer was reached with a lower (or smaller) cone angle of 60° at a lower Reynolds number of 105 and a lower Rossby number of 0.5.

Experimentally investigating the pressure drop of liquid-liquid Taylor flows over varying viscosity ratios

Micro-capillary liquid-liquid Taylor flows have emerged as a promising new platform for achieving higher heat and mass transfer compared to single-phase flows. In any application benefiting from such flows, pressure drop is a fundamental characteristic in evaluating the required input power in order to achieve an optimum configuration. Despite several attempts to develop an all-encompassing model to estimate pressure drop in immiscible liquid-liquid flows, existing models are still limited to narrow ranges of Reynolds, Capillary and Weber numbers and are insufficiently accurate over a wide range of viscosity ratios. To push the limits, the present study proposes a new expression for interfacial pressure drop based on experimental investigations over a wide range of Capillary (3×10−4≤CaC≤7.6×10−2), Reynolds (0.1≤ReC≤49) and Weber (7×10−4≤We≤1.5) numbers while continuous to dispersed viscosity ratio (μC/μD) spanned from 0.058 to23.2. To obtain these ranges, five distinct liquid-liquid fluid combinations were examined within a capillary of diameter 800 µm. A novel experimental setup is employed in this study to ensure high accuracy and repeatability of the measurements. The strengths and weaknesses of existing models are identified and a more fundamental understanding of predicting pressure drop in Taylor flow regimes is developed. The new model uses standard Hagen–Poiseuille flow theory in combination with an empirical optimized term for predicting the effect of differential Laplace pressure between leading/trailing caps of dispersed phase droplets. This correlation fits the experimental data within ±20% and can provide a prediction certainty for estimating pressure drop in applications that deal with such flows.

Investigations on fluid flow and mixing in fractal tree like biomimetic microchannel based on Murray's law

In this novel study, nature inspired biomimetic based micromixers with asymmetric bifurcation are designed and analysed, incorporating daughter vessel ratios (rdv) of 0.6, 0.7, 0.8, and 0.9 based on Murray's law. By leveraging the concept of Murray's law, four micromixers were developed to address the challenges of mixing at the microscale. Achieving efficient mixing is crucial for microfluidic devices in bioengineering and chemical applications. In this work, we examined asymmetric and symmetric bifurcated micromixers across a wide range of Reynolds numbers, from 0.01 to 300. The results demonstrate that almost all the Reynolds number are better handled by the asymmetric bifurcated micromixer having rdv=0.8. The unbalanced collision of the two fluid streams in this configuration promotes enhanced mixing performance. In contrast, the symmetric micromixer, which lacks such imbalances, shows comparable mixing performance across different Reynolds numbers, except for a Reynolds number of 10. In some cases of asymmetric bifurcated micromixers, inadequate mixing occurred due to the dominance of the larger daughter vessel, impeding the participation of the smaller one in the mixing process. The research reveals that asymmetric bifurcated micromixers with rdv=0.8 are exhibit slightly higher mixing efficiency than symmetric bifurcated micromixers with rdv=1.0.

Design and Mixing Analysis of a Passive Micromixer Based on Curly Baffles.

A novel passive micromixer based on curly baffles is proposed and optimized through the signal-to-noise analysis of various design parameters. The mixing performance of the proposed design was evaluated across a wide Reynolds number range, from 0.1 to 80. Through the analysis, the most influential parameter was identified, and its value was found to be constant regardless of the mixing mechanism. The optimized design, refined using the signal-to-noise analysis, demonstrated a significant enhancement of mixing performance, particularly in the low Reynolds number range (Re< 10). The design set obtained at the diffusion dominance range shows the highest degree of mixing (DOM) in the low Reynolds number range of Re< 10, while the design set optimized for the convection dominance range exhibited the least pressure drop across the entire Reynolds number spectrum (Re< 80). The present design approach proved to be a practical tool for identifying the most influential design parameter and achieving excellent mixing and pressure drop characteristics. The enhancement is mainly due to the curvature of the most influential design parameter.

Performance enhancement of fin and tube heat exchanger employing curved delta winglet vortex generator with circular punched holes

The generation of vortices has recently gained attention as a potential passive technique for improving air-side heat transfer in a fin and tube heat exchanger. This study proposes novel configurations of a curved delta winglet vortex generator (CDWVG) with and without circular holes to improve heat transfer in FTHEs. The present study utilizes a three-dimensional numerical analysis to investigate the thermal-hydraulic performance analysis of fin and tube heat exchanger (FTHE) with curved delta winglet vortex generators (CDWVG) with or without circular holes, operating across a wide Reynolds number range (i.e., from 400 to 2000). In addition to being arranged in vertical and horizontal configurations, the CDWVGs are oriented in the same way as the flow direction. Therefore, the pressure distribution, temperature distribution, and flow structure distribution of an FTHE with a four-in-line circular tube configuration are analyzed and compared between FTHE without vortex generator (VG) and five different configurations of CDWVG (i.e., CDWVG without hole, CDWVG with 1 hole, CDWVG with 2 holes, CDWVG with 3 holes and CDWVG with 6 holes). The pressure drop (ΔP), London area goodness factor (LAGF) (j/f), Nusselt number (Nu), and Colburn factor (j) are also used to evaluate the thermo-hydraulic performance of FTHE. The FHTE performance with CDWVGs can be affected by the number of punched holes, which is evaluated using a dimensionless number including Performance Evaluation Criteria (PEC), Colburn factor, etc. The thermo-hydraulic efficiency of the FTHE is improved significantly by using CDWVGs with circular punched holes. Nusselt number decreases across all the VG configurations (i.e., CDWVG without hole, CDWVG with 1 hole, CDWVG with 2 holes, CDWVG with 3 holes, and CDWVG with 6 holes) due to the lower flow resistance. Compared to other CDWVG configurations, the 6-hole configuration of CDWVG is the most effective. The Nusselt number of CDWVG with 6 holes increases by 77.25% and 42.51% at Reynolds numbers of 400 and 2000, with respect to fin and tube heat exchangers without vortex generator, respectively. On the other hand, friction is decreased by 5.11%. Therefore, when considering the London area goodness factor, CDWVG with six holes is found to be superior to other CDWVG configurations.

Hybrid Computation of the Aerodynamic Noise Radiated by the Wake of a Subsonic Cylinder

The noise radiated by the flow around a cylinder in the subcritical regime at ReD=1×104 and at a subsonic Mach number of M=0.5 is here studied. The aerodynamic sound radiated by a cylinder has been studied with a wide range of Reynolds numbers, but there are no studies about how the Mach number affects the acoustic field in the subsonic regime. The flow field is resolved by means of large-eddy simulations of the compressible Navier–Stokes equations. For the study of the noise propagation, formulation 1C of the Ffowcs Williams–Hawkings analogy is used. The fluid flow results show good agreement when comparing the surface pressure coefficient, the recirculation length, the vortex shedding frequency and the force coefficients against other studies performed under similar conditions. The dynamic mode decomposition of the pressure fluctuations is used to relate them with the far-field noise. It is shown that, in contrast to what happens for low Mach numbers, quadrupoles have a significant impact mainly in the observers located in the streamwise direction. This effect leads to a global monopole directivity pattern as the shear fluctuations compensate for the lower value of the aeolian tone away from the cross-stream direction.

New formulations for the mean wall-normal velocity and Reynolds shear stress in a turbulent boundary layer under zero pressure gradient

In this study, a novel analytical solution is derived rigorously for the mean wall-normal velocity in a turbulent boundary layer (TBL) under zero pressure gradient (ZPG), without relying on any a priori assumptions regarding the mean streamwise velocity. By neglecting the higher-order terms in the exact solution, an approximate formulation for the mean wall-normal velocity is obtained. The accuracy of this approximation is then validated through a comparison with data from direct numerical simulations (DNS). Drawing upon the distinct behaviours of force balance in the inner and outer regions of the ZPG TBL, simplified approximate mean momentum equations are derived by decomposing the Reynolds shear stress into inner and outer parts. The inner and outer Reynolds shear stresses are then obtained through integration of the corresponding approximate mean momentum equations. The outer Reynolds shear stress is revealed to exhibit a strong connection to the mean wall-normal velocity. Specifically, it is observed that $R_{uv-{out}}/u^2_\tau \approx 1 - UV/(U_e V_e)$ , where $u_\tau$ represents the friction velocity, and $U_e$ and $V_e$ denote the mean streamwise and wall-normal velocities at the boundary layer edge, respectively. Finally, an approximate formulation for the Reynolds shear stress across the entire TBL is developed by synthesizing the inner and outer parts. Extensive validation against both DNS and experimental data, spanning a wide range of Reynolds numbers, demonstrates the excellent agreement achieved.

A non-Darcy flow CFD–DEM method for simulating ground collapse induced by leakage through underground pipeline defect

Ground collapse due to soil erosion near pipeline defects involves soil loss and orifice outflow, which may lead to non-Darcy flow, but it is often ignored in numerical simulations. In this study, a computational-fluid-dynamics and discrete-element-method (CFD–DEM) coupling method is developed considering the non-Darcy flow. In contrast to the Darcy Equation, which tends to overestimate fluid velocity and drag force at high Reynolds numbers, the newly developed CFD-DEM method has been validated and found to be applicable across a wide range of Reynolds numbers. Utilizing the capabilities of this method, the investigation of ground collapse mechanism is conducted. Results show that the trajectories of lost particles approximately form a straight line from their initial positions towards the defect, with higher velocities for particles closer to the defect. It is likely the main reason that the evolution of particle loss closely resembles a progressive contraction of an ellipse, while the evolution of the loosening zone resembles an upward movement and expansion of an ellipse. The soil settlement is uneven both in the horizontal and vertical direction. As the particle loss increases, the shape of the surface settlement curve transitions from a normal distribution to a logarithmic function.

FEATURES OF THE FLOW STRUCTURE IN A RECTANGULAR TRENCH

The study of features of the flow structure in rectangular trenches in a wide range of Reynolds numbers was carried out by means of direct numerical simulation of the flow in the channel and on а plate. Both isothermal and non-isothermal formulations of the problem were considered. Water and air were used as the investigated fluids. The flow structure inside and around the trench in the rectangular channel in the range of Reynolds numbers based on the trench length Re&lt;=9000 was studied in a three-dimensional setting. In the Reynolds numbers range Re&gt;=10000, unsteady flow around a plate with a trench was considered in two-dimensional formulation of the problem. Depending on the Reynolds number, the flow structure in the trench, the influence of geometric parameters on the vortices scales in the trench, their localization and intensity were analyzed. The scale of inhomogeneity of the trench flow in the transverse direction was obtained. The features of non-stationary behavior and interaction of vortex formations with each other and with the external flow at higher Reynolds numbers are considered, development of instability of the vortex structure in the trench and its influence on characteristics of the external flow are shown: from regular oscillations at certain frequency to gradual chaosization of the flow around the trench as the Reynolds number increases, when fractional and multiple frequencies appear. A comparison was made with the vortex structure obtained by other researchers for similar geometric parameters of the trench. The contributions of frictional drag and shape drag to the overall hydraulic drag of the trench, as well as the streamlined surface downstream the trench, are considered. Intensity of heat exchange processes inside the trench, localization of the maximum values of heat fluxes, dependence of heat transfer on the oncoming flow speed were evaluated.

A data-driven Reynolds-number-dependent model for turbulent mean flow prediction in circular jets

This paper proposes a data-driven turbulence model for predicting the mean flow in turbulent circular jets over a wide range of Reynolds numbers (Re). The main formulation is adapted from the well-known k–ε model (where k is the turbulent kinetic energy, and ε is the dissipation rate) with a set Re-dependent variation of the model constants. The k–ε model with Tam–Thies correction is applied with model constants optimized using data assimilation based on the ensemble Kalman filter to minimize the deviation between the model prediction and experimental data. The model constants of converging jets at Re = 10 700, 20 100, and 95 500 are fitted using logarithmic curves with respect to Re to obtain a universal formulation for predicting the jet mean flow under various flow conditions. The model using the fitted model constants, named the k–ε–Re model, can accurately predict the mean flow in both converging and orifice jets at various Re. While the k–ε–Re model is directly applied to the pipe jets, much better prediction can be obtained at high Reynolds numbers (Re ≥ 21 000 presently) compared with the default k–ε model. However, certain discrepancy with experimental data is observed at 5 ≤ x/D ≤ 15 at Re = 6000 and 16 000. Further improvement can be achieved by assimilating the fitting coefficients based on the pipe jet data. The k–ε–Re model is adequately generalizable and can predict the mean flow in different circular jets at a moderate or high Re (≥ 21 000), while further improvement can be obtained by the data assimilation and recalibration based on the specific nozzle type at a small Re.

Artificial neural networks and guided gene expression programming to predict wall pressure spectra beneath turbulent boundary layers

This study evaluates the efficacy of two machine learning (ML) techniques, namely, artificial neural networks (ANNs) and gene expression programing (GEP), that use data-driven modeling to predict wall pressure spectra (WPS) underneath turbulent boundary layers. Different datasets of WPS from experiments and high-fidelity numerical simulations covering a wide range of pressure gradients and Reynolds numbers are considered. For both ML methods, an optimal hyperparameter environment is identified that yields accurate predictions. Despite a higher memory consumption, ANN models are faster to train and are much more accurate than the GEP models, yielding an order of magnitude lower logarithmic Mean Squared Error (lMSE) than GEP. Novel training schemes are devised to address the shortcomings of GEP. These include (a) ANN-assisted GEP to reduce the noise in the training data, (b) exploiting the low- and high-frequency trends to guide the GEP search, and (c) a stepped training strategy where the chromosomes are first trained on the canonical datasets, followed by the datasets with complex features. When compared to the baseline scheme, these training strategies accelerated convergence and resulted in models with superior accuracy (≈30% reduction in the median lMSE) and higher reliability (≈75% reduction in the spread of lMSE in the interquartile range). The final GEP models captured the complex trends of WPS across varying flow conditions and pressure gradients, surpassing the accuracy of Goody's model.

Wall-resolved versus wall-modeled LES of the flow field and surface forced convective heat transfer for a low-rise building

Large eddy simulation (LES) is widely used to investigate the aerodynamics and convective heat transfer (CHT) at the surfaces of sharp-edged bluff bodies for a wide range of Reynolds (Re) numbers. Due to the heavy computational costs associated with implicit filtering in LES at high Reynolds number flows (Re ≥ 105), wall-modeled (WM) rather than wall-resolved (WR) LES is often adopted. However, the performance of LES-WM for such applications has not yet been systematically investigated. Therefore, this study evaluates the performance of LES-WM and LES-WR for the flow and thermal field at the facades of a low-rise building immersed in an atmospheric boundary layer. Four grids are constructed for LES-WM, each employing different resolution at the building surfaces reaching maximum non-dimensional wall distance y+ = 43, 57, 70, and 95. In addition, the performance of two wall functions, namely the Werner and Wengle and the enhanced wall function is investigated. The results show that the use of LES-WM can result in significant deviations in the predicted near-facade flow pattern and the surface convective heat transfer coefficient (CHTC). Grid resolution significantly impacts the CHTC results and deviations go up to 88% (at the base of the windward facade). Considerable deviations among the employed wall functions are apparent only on the finest grid. In this case, the implementation of the enhanced wall function indicates better performance compared to the non-blended law of the wall (combined with the Werner and Wengle) for CHTC in the regions of the leeward facade where the flow remains attached to the wall. The deviation of the enhanced wall function for surface-averaged CHTC is found to be 10.8% against the wall-resolved LES results, while for the non-blended law of the wall this is 19.2%.

Turbulent drag reduction by spanwise wall forcing. Part 1. Large-eddy simulations

Turbulent drag reduction (DR) through streamwise travelling waves of the spanwise wall oscillation is investigated over a wide range of Reynolds numbers. Here, in Part 1, wall-resolved large-eddy simulations in a channel flow are conducted to examine how the frequency and wavenumber of the travelling wave influence the DR at friction Reynolds numbers $Re_\tau = 951$ and $4000$ . The actuation parameter space is restricted to the inner-scaled actuation (ISA) pathway, where DR is achieved through direct attenuation of the near-wall scales. The level of turbulence attenuation, hence DR, is found to change with the near-wall Stokes layer protrusion height $\ell _{0.01}$ . A range of frequencies is identified where the Stokes layer attenuates turbulence, lifting up the cycle of turbulence generation and thickening the viscous sublayer; in this range, the DR increases as $\ell _{0.01}$ increases up to $30$ viscous units. Outside this range, the strong Stokes shear strain enhances near-wall turbulence generation leading to a drop in DR with increasing $\ell _{0.01}$ . We further find that, within our parameter and Reynolds number space, the ISA pathway has a power cost that always exceeds any DR savings. This motivates the study of the outer-scaled actuation pathway in Part 2, where DR is achieved through actuating the outer-scaled motions.

TEORETICAL-EXPERIMENTAL COMPARISON OF THE MODELS OF ADDITIVELY MANUFACTURED SWIRL INJECTORS BASED ON THE HYDRAULIC TESTING RESULTS

Annotation. Recent success in development of the technology stipulated the appearance of advanced additive manufacturing aimed to shift conventional subtractive manufacturing from its position in the engineering field. Thus, for LPRE manufacturing there is an obvious advantage of additive manufacturing in terms of ability to produce single-piece parts with complex geometry must be seriously considered. In the modern world there is a constant competition between complex engineering decisions and cost efficiency of the production on the market of liquid propellant rocket engines. On the one hand, mixing head is one of the most demanding parts of LPRE in terms of designing. On the other hand, the earliest stage of its development starts with the choice of a type of mixing elements to ensure combustion stability, efficiency, and overall production cost [1]. Typically this step requires advanced knowledge in the real characteristics of produced injectors, or extensive experimental study should be carried out otherwise. In this work a problem of determining the characteristics of additively manufactured swirl injectors is considered. Laser Powder Bed Fusion [10] was chosen as a production method using Haynes 230 as a main material. A range of the swirl injectors with varied geometrical parameters was manufactured. Hydraulic testing was carried out in a wide range of Reynolds numbers for determining flow characteristics. Typically, discharge coefficient and spray angle are the desired values to know. Sauter mean diameter and film thickness were not studied due to lack of equipment. Considering a problem of prediction of the main characteristics of the produced injectors, a review on known equations for calculation of the main parameters was performed. Comparative analysis between calculated and experimental data was carried out. Results show that there is severe discrepancy between calculated values of characteristics of injectors and experimentally obtained data for additively manufactured swirl injectors. Even though the conducted study gives a base to form consistent conclusions of the behavior of the obtained characteristics, additional investigation is required.

Computational Framework Development for Heat Transfer Studies in Liquid Metal-Cooled Small-Scale Heat Sinks With Non-Circular Cross Sections

Abstract The present work provides a reliable computational framework to investigate the laminar and turbulent forced convection of sodium and sodium–potassium (Na, NaK) in small-scale heat sinks with hydraulic diameters between 1 mm and 5 mm. Na and NaK flow and heat transfer are studied numerically for a wide range of Reynolds numbers from 600 to 9000 in three sharp-cornered miniature heat sinks with rectangular, pentagonal, and hexagonal cross sections. For a fixed surface area to volume ratio, it is observed that the rectangular minichannel heat sink provides the highest convective heat transfer rates. The rectangular miniature heat sink is shown to provide 280% higher convective heat transfer rates in comparison with the pentagonal heat sink. Moreover, the obtained convective heat transfer coefficients for NaK are almost 20% higher than the ones for Na in the investigated pentagonal heat sink. For the same flow Peclet number in the rectangular and hexagonal heat sinks, both Na and NaK provide nearly identical average Nusselt numbers. However, NaK shows greater local and average Nusselt numbers compared to Na at the same Reynolds number.