Wide Reynolds Number Range Research Articles

Experimental Results for a Low-Reynolds-Number Airfoil in a Low-Turbulence Wind Tunnel

The Pennsylvania State University (PSU) 94-097 airfoil was originally designed in the mid-1990s for use on winglets of high-performance sailplanes. This design problem is difficult because this application requires the airfoil to operate over a wide range of Reynolds numbers, from to . At that time, over two decades ago, to validate the tools as well as the design itself, high-quality measurements of section characteristics and pressure distributions were made in the PSU low-speed low-turbulence wind tunnel with Reynolds numbers from to . In addition to free-transition measurements, potential drag reductions using artificial turbulators were explored. More recently, this model was retested in the same facility at Reynolds numbers down to . In addition, because this airfoil has been successfully employed on model aircraft and unmanned aerial vehicles, its performance using a simulated simple flap/aileron was measured and found to provide the necessary lift coefficient range to support the flight envelope without significant increases in drag. In this regard, it is comparable to similar flapped-equipped airfoils. Finally, as with the results from the original tests, with the exception of the maximum lift coefficient, theoretical predictions using well-known codes are found to be in good agreement with the wind-tunnel measurements.

An integral method to determine mean skin friction in turbulent boundary layers

This study is concerned with accurately determining the mean skin friction in a zero-pressure-gradient turbulent boundary layer. By assuming a linear relation for the weighted total shear stress in the near-wall region, an integral method to evaluate the skin friction is proposed. The method requires the wall-normal profiles of the mean streamwise velocity and Reynolds shear stress within the range of y/δ≤0.4 at only one streamwise location, where δ is the boundary layer thickness. A number of direct numerical simulation and experimental data available in the literature are employed to validate the accuracy of the method over a wide range of Reynolds numbers. The skin friction coefficient obtained using the proposed method is found to be within ±4% in agreement with the published values in both the smooth- and rough-wall turbulent boundary layers. A comparison of the present approach with several existing methods is presented, showing that the proposed skin friction relation is robust and accurate.

Lagrangian transport in the time-periodic two-dimensional lid-driven square cavity

The Lagrangian transport in the laminar incompressible flow in a two-dimensional square cavity driven by a harmonic tangential oscillation of the lid is investigated numerically for a wide range of Reynolds and Strouhal numbers. The topology of fluid trajectories is analyzed by stroboscopic projections revealing the co-existence of chaotic trajectories and regular Kolmogorov–Arnold–Moser (KAM) tori. The pathline structure strongly depends on the Reynolds number and the oscillation frequency of the lid. Typically, most pathlines are chaotic when the oscillation frequency is small, with few KAM tori being strongly stretched along instantaneous streamlines of the flow. As the frequency is increased, the fluid motion becomes more regular and the size of the KAM tori grows until, at high frequencies, they resemble streamlines of a mean flow.

Outer scaling of the mean momentum equation for turbulent boundary layers under adverse pressure gradient

A new scaling of the mean momentum equation is developed for the outer region of turbulent boundary layers (TBLs) under adverse pressure gradient (APG). The maximum Reynolds shear stress location, denoted as $y_{m}$ , is employed to determine the proper scales for the outer region of an APG TBL. An outer length scale is proposed as $\delta _e - y_{m}$ , where $\delta _e$ is the boundary layer thickness. An outer velocity scale for the mean streamwise velocity deficit is proposed as $U_e - U_{m}$ , where $U_e$ and $U_m$ are the mean streamwise velocities at the boundary layer edge and $y_{m}$ , respectively. An outer velocity scale for the mean wall-normal velocity deficit is proposed as $V_e - V_{m}$ , where $V_e$ and $V_{m}$ are the wall-normal velocities at $\delta _e$ and $y_{m}$ , respectively. The maximum Reynolds shear stress is found to scale as $(\delta _e - y_{m}) U_e \,{\rm d}U_e/{{\rm d}x}$ . The new outer scaling collapses well the experimental and numerical data on APG TBLs over a wide range of Reynolds numbers and strengths of pressure gradient. Approximations of the new scaling are developed for TBLs under strong APG and at high Reynolds numbers. The relationships between the new scales and previously proposed scales are discussed.

Numerical simulations of high Prandtl number liquid jets impinging on a flat plate

In this work, 3D simulations of oil jets impinging on a flat, heated wall are presented. The numerical setup uses the Volume of Fluid (VoF) method to model the two-phase flow. A careful grid definition across the liquid film, along with the use of the Conjugate Heat Transfer (CHT) approach allowed local heat transfer to be solved with fine resolution at the wall. Variations of liquid flow rate, liquid temperature and surface temperature allow to cover a wide range of local Reynolds and Prandtl numbers (226<Re<2850, 77<Pr<161). Resulting surface-averaged heat transfer compares very well with experimental measurements conducted in a previous study. In-depth analysis of the flow has identified expected features from the literature. In particular, the impact of jet axial velocity profiles on the heat transfer distribution in the stagnation zone was clearly stated. The increase in heat transfer when warming the liquid film was also reproduced and explained by a decrease in oil viscosity and an increase in film velocity. All those effects were taken into account in correlations for stagnation and local values of Nusselt number. A grid sensitivity study was also conducted, showing that if the grid solving the thermal boundary layer in the stagnation zone can be coarsened without impacting local and surface-averaged predictions of heat transfer, a minimum resolution (2 to 3 cells) within the thermal boundary layer is however required for an accurate prediction of heat transfer.

Flow Control around the UAS-S45 Pitching Airfoil Using a Dynamically Morphing Leading Edge (DMLE): A Numerical Study

This paper investigates the effect of the Dynamically Morphing Leading Edge (DMLE) on the flow structure and the behavior of dynamic stall vortices around a pitching UAS-S45 airfoil with the objective of controlling the dynamic stall. An unsteady parametrization framework was developed to model the time-varying motion of the leading edge. This scheme was then integrated within the Ansys-Fluent numerical solver by developing a User-Defined-Function (UDF), with the aim to dynamically deflect the airfoil boundaries, and to control the dynamic mesh used to morph and to further adapt it. The dynamic and sliding mesh techniques were used to simulate the unsteady flow around the sinusoidally pitching UAS-S45 airfoil. While the γ-Reθ turbulence model adequately captured the flow structures of dynamic airfoils associated with leading-edge vortex formations for a wide range of Reynolds numbers, two broader studies are here considered. Firstly, (i) an oscillating airfoil with the DMLE is investigated; the pitching-oscillation motion of an airfoil and its parameters are defined, such as the droop nose amplitude (AD) and the pitch angle at which the leading-edge morphing starts (MST). The effects of the AD and the MST on the aerodynamic performance was studied, and three different amplitude cases are considered. Secondly, (ii) the DMLE of an airfoil motion at stall angles of attack was investigated. In this case, the airfoil was set at stall angles of attack rather than oscillating it. This study will provide the transient lift and drag at different deflection frequencies of 0.5 Hz, 1 Hz, 2 Hz, 5 Hz, and 10 Hz. The results showed that the lift coefficient for the airfoil increased by 20.15%, while a 16.58% delay in the dynamic stall angle was obtained for an oscillating airfoil with DMLE with AD = 0.01 and MST = 14.75°, as compared to the reference airfoil. Similarly, the lift coefficients for two other cases, where AD = 0.05 and AD = 0.0075, increased by 10.67% and 11.46%, respectively, compared to the reference airfoil. Furthermore, it was shown that the downward deflection of the leading edge increased the stall angle of attack and the nose-down pitching moment. Finally, it was concluded that the new radius of curvature of the DMLE airfoil minimized the streamwise adverse pressure gradient and prevented significant flow separation by delaying the Dynamic Stall Vortex (DSV) occurrence.

Hollow fiber nanoporous membrane contactors for evaporative heat exchange and desalination

The paper reports the performance of nanoporous polypropylene membrane contactors in water evaporative transfer processes, depending on membrane packing density, flow, and temperature conditions. The membrane evaporator's heat and mass transfer efficiency were evaluated in a wide range of partial pressure gradients and gas phase Reynolds numbers. A protocol for simple evaluation of evaporative heat flux to the heat exchange flux is introduced to reveal the efficiency of mass-to-heat transfer. It has been shown the evaporation efficiency significantly depends on gas flow conditions, increasing at Re ∼ 30 and exceeding 4.6 kg × m-2×h−1 (3.0 kW × m-2×h−1) at the temperature of inlet water of 60 °C. It is achieved by inducing convective flows in the gas phase, which enable the rise of effective heat transfer coefficient for membrane evaporator ∼250 W × m-2×K−1. The attained efficiency is confirmed to originate from heat extraction from the gaseous phase and the evaporation of water from the external surface of fibers. While exhibiting maximal heat flux the regime requires liquid phase penetration through the pores, leading to degradation of the membrane performance in desalination applications. To avoid penetration of ions thin (∼300 nm) graphene oxide coating was deposited onto the internal surface of the nanoporous evaporator, enabling to avoid liquid penetration through the pores and salts crystallization at the external surface, while exhibiting slightly lower performance of the membrane.

Flow Control around NACA0015 Airfoil Using a Dielectric Barrier Discharge Plasma Actuator over a Wide Range of the Reynolds Number

In this study, an experimental investigation of separation control using a dielectric barrier discharge plasma actuator was performed on an NACA0015 airfoil over a wide range of Reynolds numbers, angles of attack, and nondimensional burst frequencies. The range of the Reynolds number was based on a chord length ranging from 2.52 × 105 to 1.008 × 106. A plasma actuator was installed at the leading edge and driven by AC voltage. Burst mode (duty-cycle) actuation was applied, with the nondimensional burst frequency ranging between 0.1–30. The control authority was evaluated using the time-averaged distribution of the pressure coefficient Cp and the calculated value of the lift coefficient Cl. The baseline flow fields were classified into three types: (1) leading-edge separation; (2) trailing-edge separation; and (3) the hysteresis between (1) and (2). The results of the actuated cases show that the control trends clearly depend on the differences in the separation conditions. In leading-edge separation, actuation with a burst frequency of approximately F+= 0.5 creates a wide negative pressure region on the suction-side surface, leading to an increase in the lift coefficient. In trailing-edge separation, several actuations alter the position of turbulent separation.

An alternative full multigrid SIMPLEC approach for the incompressible Navier–Stokes equations

An alternative approach to solve the steady-state incompressible Navier–Stokes equations using the multigrid (MG) method is presented. The mathematical model is discretized using the finite volume method with second-order approximation schemes in a uniform collocated (nonstaggered) grid. MG is employed through a full approximation scheme-full MG algorithm based on V-cycles. Pressure-velocity coupling is ensured by means of a developed modified SIMPLEC algorithm which uses independent V-cycles for relaxing the pressure-correction and momentum equations. The coarser grids are used only internally in these cycles. All other original SIMPLEC steps can be performed only on the finest grid of the current full MG level. The model problem of the lid-driven flow in the unitary square cavity is used for the tests of the numerical model. Computational performance is measured through error and residual decays and execution times. Good performances were obtained for a wide range of Reynolds numbers, with speedups of orders as high as Linear relationships between execution times and grid sizes were observed for low and high Re values ( and 7,500). For intermediate Re values ( and 1,000), the linear trend was observed from more refined grids (512 onwards).

Investigation of the hydrothermal phenomena in a wavy microchannel with secondary flow passages through mid-wall inflection points

Advancement in manufacturing processeshas fuelled research in microchannel heat sinks to meet the demands of modern microelectronics. The heat sink design in the present study considers longitudinally wavy microchannels incorporating secondary flow passages. The secondary flow has been investigated for abrupt flow bifurcation (at 60° angle) and smooth flow bifurcation (at 30° angle). Further, these geometries were tested with different inlet–outlet configurations. The main objective of the paper is to study how a secondary flow would affect the flow profile and thermal performance of a wavy microchannel heat sink. The flow profile, pressure drop, temperature profiles, and average Nusselt number for a wide range of flow rates have been obtained and compared with those for the conventional design, and associated trends have been explored. Furthermore, the overall performance of the heat sink designs has been quantified by plotting the thermal enhancement factor (TEF) against a wide range of Reynolds numbers. The heat sink with flow bifurcation of 30° attains the highest value of Nuselt number below the flow rate of 1.8 × 10-6 m3/s, whereas above this flow rate, the Nusselt number value of the conventional wavy heat sink dominates the proposed heat sink designs. The study corresponds to the demands of modern microchips such as the 13th Gen Intel® Core™ processor and serves as a guideline for manufacturing heat sinks with wavy microchannels incorporating secondary flow passages.

Effects of hydrophobic slips in non-uniform electrokinetic transport of charged viscous fluid in nozzle-diffuser

The mixing efficiency and electro-osmotic flow enhancement over a hydrophobic structured microchannel with nozzle-diffuser under an external electric field is studied. The interfacial surface zeta potential is varied to generate a strong convection effect between two injecting fluids from the reservoirs for a wide range of Reynolds numbers. The Poisson–Nernst–Plank model is incorporated to deal with thick and thin diffuse layers formed by a non-Newtonian electrolyte solution for the numerical simulation of the mobility of ions. To avoid the high-pressure drop complications in the computation, we have scaled the mixing efficiency with the average pressure drop. The analytical validation of the velocity and potential for thin and thick electric double layer with the existing experimental results corroborated and bridged the performance of the present model to achieve faster mixing by reducing pressure gradient. It is demonstrated that hydrodynamic slip increases the flow velocity producing larger mobility; however, the heterogeneous zeta potential generates a backflow that prevents the driving fluids leading to higher mixing efficiency, discussed in the first phase of the work. It is found that the mixing performance of Newtonian fluid is maximum for a nozzle-diffuser-shaped microchannel when all other physical parameters are constant. In the next phase, the mixing performance of shear thickening, shear thinning, and Newtonian fluid has been discussed for various physio-chemical parameters, i.e., slip length, Debye parameter, channel conical angle/slope, and heterogeneous zeta potential strength. The mixing efficiency and the pressure gradient decrease with the increase in the Debye parameter and the slip length. It is observed that the mixing efficiency can further be enhanced by increasing the heterogeneity of zeta potential strength and channel conical angle. This study can be used as a benchmark model for fabrication of chaotic mixers in hydrophobic slips with wall-mounted heterogeneous zeta potential and can be suitable for handling the power-law fluids.

Emitting Electrodes Effect on the Enhancement of Heat Transfer by a Two Stage Electrohydrodynamic Gas Pump

In this study, emitting electrodes effect on the enhancement of heat transfer by a two stage electrohydrodynamic (EHD) gas pump is numerically analyzed. This study is implemented for a two stage EHD gas pump with 24 emitting electrodes configuration and the results are compared with 8 and 56 emitting electrodes configurations. The EHD gas pump is evaluated for a wide range of operating voltages starting from 20 kV up to 28 kV and wide range of Reynolds numbers (Re). The Reynolds numbers considered in this study varies in a range between 100 and 2000. At Re = 100, a maximum increase of 42% in the average Nusselt number is achieved with an applied voltage of 28 kV. The overall effectiveness of the EHD gas pump in heat transfer enhancement is evaluated by the thermal hydraulic performance parameter, (Nu/Nu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> )/(f/f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ), which is always greater than unity. EHD technique has a great potential.

Investigating the Flow Characteristics of Superhydrophobic U-Shaped Microchannels

Hydrophobicity has been widely reported for its superior behavior in drag reduction, self-cleaning, and anti-corrosion in many areas. Especially in engineering design, the research of the unique property of the slip flow with complex flow patterns is essential for practical applications. In this paper, the flow characteristics of a superhydrophobic U-shaped microchannel are systematically investigated, as the curved part is a fundamental component in microfluids. A slip model is established based on theoretical and experimental solutions. Various types of U-shaped microchannels, radii of curvature, and contact angles are studied with a wide range of Reynolds numbers from 0 to 300. We propose a velocity distribution to examine the non-uniformity of slip velocity on the cross-section. This imbalance is improved with an increase in the apparent contact angle and flow rate, and a decrease in the radius of curvature. The secondary flow and vortices generated by the centrifugal force are enhanced, and their positions are changed due to the slippery boundary. The results show a considerable drag reduction from 10% to 40% with different contact angles. The variation of curvature does not have a decisive impact on the final performance when the surface wettability maintains a steady state. Our research elucidates the physical principle of the slip model in curved channels, showing extensive applications of hydrophobicity in the design of complex microchips and the optimization strategy of heat transfer systems.

FEATURES OF THE BOUNDARY LAYER ORGANIZATION IN TESLA DISC TURBINES

To ensure maximum efficiency of bladeless Tesla turbines, it is important to maintain a laminar flow regime within the boundary layer that forms on the disc surfaces. Depending on the flow regime, the state of the disc surfaces, and the geometry of the interdisk gaps, the nature of the boundary layer varies. It is crucial for the flow regime to remain laminar, and the distance between the discs should not exceed twice the thickness of the boundary layer. Experimental investigations of the characteristics of the boundary layer during the flow around turbine blades were proposed to determine the parameters necessary for achieving maximum efficiency. These experiments were conducted in an aerodynamic test rig that provided a uniform velocity field with minimal turbulence (0.7 %) within a speed range up to 0.33 Mach. The primary focus of these studies was to determine the location of the transition zone within the boundary layer, which allows for the examination of conditions for stable maintenance and characteristics of laminar flow. The transition zone was determined based on changes in the tangential friction stress in the experiments. The obtained results facilitated the establishment of the necessary dimensions for the inter-disk gaps and the optimum values of the similarity criterion Re from the perspective of flow regime. For a smooth surface, laminar flow within the boundary layer is maintained up to a relative coordinate of 0.17 x= from the start of the surface, across a wide range of Reynolds numbers. For a rough surface, the extent of the zone with a laminar boundary layer is approximately the same as that for a smooth surface at Re=3.6∙105. However, at Re=7.4∙105 the laminar flow terminates slightly earlier, at 0.13 x= , with a very short transitional zone between laminar and turbulent flow characteristics. The thickness of the laminar boundary layer on a smooth surface is 0.5…0.7 mm, while for a rough surface, it is slightly greater at 0.7…0.8 mm. Therefore, to ensure high efficiency of Tesla disc turbines, the distance between the discs should be maintained at 1…1.5 mm, considering the requirements for laminar flow.

Experimental assessment of wing lower surface buffet effects induced by the installation of a UHBR nacelle

The installation of large bypass ratio engines on classical under wing configurations may lead to shock/boundary layer interaction on the wing lower surface, limiting the flight envelope in a similar way to classical buffet occurring on the wing suction side at high incidences in transonic flight. In this study, buffet effects on the lower surface of the wing induced by the installation of a Ultra-High-Bypass-Ratio through flow nacelle are assessed by means of wind tunnel testing. Unsteady pressure sensitive paint measurements were used to assess the pressure field on the wing with high temporal and spatial resolution. Strong unsteady shock motion associated with shock induced separation was found on the wing lower surface for various combinations of Mach number, Reynolds number and angle of attack. The wing lower surface buffet effects are found to increase with reducing angle of attack and are present over a wide range of Reynolds numbers. Preliminary spectral analysis suggests an upper limit for the buffet frequency at a Strouhal number of about 0.4.

Direct immersogeometric fluid flow and heat transfer analysis of objects represented by point clouds

Immersogeometric analysis (IMGA) is a geometrically flexible method that enables one to perform multiphysics analysis directly using complex computer-aided design (CAD) models. While the IMGA approach is well-studied and has a remarkable advantage over traditional CFD, IMGA still requires a well-defined B-rep model to represent the geometry. Obtaining such a model can sometimes be equally as challenging as creating a body-fitted mesh. To address this issue, we develop a novel IMGA approach for the simulation of incompressible and compressible flows around complex geometries represented by point clouds in this work. The point cloud representation of geometries is a direct method for digitally acquiring geometric information using LiDAR scanners, optical scanners, or other passive methods such as multi-view stereo images. The point cloud object’s geometry is represented using a set of unstructured points in the Euclidean space with (possible) orientation information in the form of surface normals. Due to the absence of topological information in the point cloud model, there are no guarantees for the geometric representation to be watertight or 2-manifold or to have consistent normals. To perform IMGA directly using point cloud geometries, we first develop a method for estimating the inside–outside information and the surface normals directly from the point cloud. We also propose a method to compute the Jacobian determinant for the surface integration (over the point cloud) necessary for the weak enforcement of Dirichlet boundary conditions. We validate these geometric estimation methods by comparing the geometric quantities computed from the point cloud with those obtained from analytical geometry and tessellated CAD models. In this work, we also develop thermal IMGA to simulate heat transfer in the presence of flow over complex geometries. The proposed framework is tested for a wide range of Reynolds and Mach numbers on benchmark problems of geometries represented by point clouds, showing the robustness and accuracy of the method. Finally, we demonstrate the applicability of our approach by performing IMGA on large industrial-scale construction machinery represented using a point cloud of more than 12 million points.

Heat Transfer and Friction in a Rectangular Channel With Varying Numbers of Walls Roughened With 90-Deg Transverse or 45-Deg V-Shaped Ribs

Abstract An experimental investigation was performed to measure the regionally averaged heat transfer distributions and friction factors for fully developed turbulent flow in a rectangular channel with a width-to-height aspect ratio (AR = 3). Data for transverse 90-deg and 45-deg V-shaped, carbon steel ribs placed on one, two, or four sides of the channel were reported for a Reynolds number range (Re = 5,000–60,000). The pitch-to-rib height ratio (P/e) was set at 10 while the rib height-to-channel hydraulic diameter (e/Dh) is 0.041. This corresponds to a roughness Reynolds number range (e+=25−500). For both rib configurations, results show the highest thermal performance was achieved in the channels with four-ribbed wall followed by the two and one-ribbed wall channels, respectively. Using the law of the wall similarity, friction roughness functions (R) and heat transfer roughness functions (G) were developed based on four-sided friction and heat transfer data. Moreover, friction and heat transfer data of similar rib designs were obtained from literature and correlated to the corresponding friction and heat transfer roughness functions. Covering a wide range of roughness Reynolds numbers, more robust heat transfer and friction correlations were developed which can be used by designers to accurately predict both heat transfer and friction in ribbed channels with different numbers of ribbed walls. Using these correlations, one can predict the measured friction and heat transfer data of this study with maximum errors of 9% and 7%, respectively.

Numerical and experimental investigation on a planar passive micromixer embedded with omega-shaped obstacles for rapid fluid mixing

An efficient fluid mixing performance is achieved by a Tesla/hexagon-shaped passive micromixer in a wide range of Reynolds numbers with short mixing length (4.2 mm/1.15 mm from the origin). The passive micromixers are composed of Tesla/hexagonal chambers and Ω-shaped obstacles or combined with straight-shaped obstacles that induce the generation of vortex, contraction and expansion process, the changes of the flow direction, and even the split and recombination of streams. The mixing process of two fluids (water and ferrofluid) is numerically investigated using computational fluid dynamics. For the Tesla-shaped micromixer embedded with Ω-shaped obstacles, a sufficient mixing is obtained as the obstacles are in contact with the internal walls of Tesla chambers. In the hexagon-shaped micromixer, the combination of straight- and omega-shaped obstacles greatly enhance the performance of micromixer in particular at moderate flow rate (1<Re<10). Moreover, reasonable increasing the curvature radius of the omega-shaped obstacles can further improve its mixing performance. The designed passive micromixers were also fabricated, tested and compared with the numerical results through the soft-lithography processes, and the good agreement between the experimental and numerical results identifies our predictions. The good performance of the designed micromixers provides a new direction in designing micromixer with high-throughput and short mixing length.

Fluid flow and heat transfer in a rectangular ribbed channel with a hierarchical design for turbine blade internal cooling

• New design concept to develop high-performance internal cooling of turbine blades. • Greatly reduced pressure loss is achieved with negligible heat transfer reduction. • The underlying physics of pressure drop and heat transfer performance is clarified. • Various designs are examined to verify the feasibility of the new design concept. For internal cooling of a turbine blade, various advanced rib turbulators can markedly contribute to the heat transfer enhancement while suffering a great increase in pressure loss. In those designs, ribs with the same configuration are periodically and evenly mounted on the channel wall. In this context, this work proposes a hierarchical design concept to optimize the rib arrangement with the desired reduction in pressure loss. In terms of the rib height, this new design concept is implemented to construct three new rib configurations. Based on an established turbulence model, three-dimensional (3D) numerical simulations are entirely adopted to verify the feasibility of the new configuration in a wide Reynolds number range. The numerical results demonstrate that the optimal configuration with a linearly decreasing rib height can greatly reduce the pressure loss with a slight heat transfer deterioration. The negligible reduction in the heat transfer performance results from the enhanced fluid impingement on the reattachment region because of the lowering effect of the mainstream, although small ribs weaken the fluid impingement. The marked pressure drop reduction comes from the combination of the lowering effect and small ribs which constrains the separation vortex behind ribs. Furthermore, the comparison of the overall thermal performance is carried out considering a wide range of the Reynolds number, pitch ratios, and aspect ratios. The optimal configuration can greatly enhance the overall thermal performance up to 138.3% for the factor ( Nu / Nu 0 )/( f / f 0 ) and up to 32.5% for the factor ( Nu / Nu 0 )/( f / f 0 ) 1/3 . Eliminating the entrance effect of developing flow, the increment in the overall thermal performance is considerably reduced but still keeps at a high level. Finally, it is significantly highlighted that as a simple but effective improvement, the hierarchical design concept presents great potential in developing high-performance internal cooling of turbine blades.

On the vortex shedding around a circular cylinder modulated by ambient density stratification

Alternating vortex shedding could be developed when the flow past a circular cylinder. Previous laboratory studies indicate that the vortex shedding frequency, which is expressed as dimensionless Strouhal number St, depends on the Reynolds number. Numerical simulations are used to analyze the flow characteristics around cylinder in recent years, however, they cannot reproduce laboratory measurements properly and the Strouhal numbers are overestimated. This discrepancy is attributed to the fault of numerical method and more advanced turbulence models are expected to improve the results. In this study it is postulated that the overestimated Strouhal number could be attributed to the ambient density stratification, which is neglected in previous numerical simulations. Numerical methods and laboratory measurements are used to confirm this assumption. The numerical results show that the Strouhal number decreases with increasing ambient density gradient for a wide range of Reynolds numbers. An electric thermometer with two sensors is used to measure the typical density gradients for various scenarios. The experimental measurements show that the strength of measured ambient density stratification is in the range anticipated from numerical simulation, which further confirms the influence of ambient density stratification on the vortex shedding frequency.