Diameter-based Reynolds Number Research Articles

Characterization of a canonical helicopter hub wake

The current study investigates the long-age wake behind rotating helicopter hub models composed of geometrically simple, canonical bluff body shapes. The models consisted of a 4-arm rotor mounted on a shaft above a 2-arm (scissor) rotor with all the rotor arms having a rectangular cross section. The relative phase between the 2- and 4-arm rotors was either $0\deg$ (in-phase) or $45\deg$ (out-of-phase). The rotors were oriented at zero angle-of-attack and rotated at 30 Hz. Their wakes were measured with particle-image-velocimetry within a water tunnel at a hub diameter based Reynolds number of $820,000$ and an advance ratio of $0.2$. Mean profiles, fluctuating profiles and spectral analysis using time-series analysis as well as dynamic mode decomposition were used to characterize the wake and identify coherent structures associated with specific frequency content. The canonical geometry produced coherent structures that were consistent with previous results using more complex geometries. It was shown that the dominant structures (2 and 4 times per hub revolution) decay slowly and were not sensitive to the relative phase between the rotors. Conversely, the next strongest structure (6 times per hub revolution) was sensitive to the relative phase with almost no coherence observed for the in-phase model. This is strong evidence that the 6 per revolution content is a nonlinear interaction between the 2 and 4 revolution structures. This study demonstrates that the far wake region is dominated by the main rotor arms wake, the scissor rotor wake and interactions between these two features.

Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of $1\times 10^{6}$. The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97 % of the total acoustic energy at these angles and more than 65 % (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin–Helmholtz mode in the near-nozzle region.

Numerical investigations of the effect of rotating and non-rotating shaft on aerodynamic performance of small scale urban vertical axis wind turbines

The shaft is a very important part of small scale vertical axis wind turbines (VAWTs) being used in urban environments. The shedding vortices will be formed as wind passes around the shaft, the shedding vortices released by the shaft have a negative effect on the aerodynamic performance of the blades passing the wake of the wind shaft, and this will lead to lower power output of the wind turbine. The objective of this study is to explore the differences of the effect of the rotating and non-rotating shafts of VAWTs on the aerodynamic performance of small scale urban VAWTs. In addition, the effect of surface roughness on the performance of the rotating and non-rotating shaft wind turbines is also investigated. The dynamic analysis of the VAWT is carried out by the method of Computational Fluid Dynamics. The aerodynamic loads in the study are obtained by solving the two-dimensional (2D) unsteady Navier-Stokes equations with the Transition SST turbulence model. The results are validated with experimental results. The results show that when the ratio of the shaft diameter to the wind turbine diameter (α) is 3.9%, the power coefficient (Cp) of the rotating shaft wind turbine is 2.2% higher than that of the non-rotating shaft wind turbine. Increasing the shaft diameter-based Reynolds number (Res) will increase the Cp of rotating and non-rotating shaft wind turbines, when Res is 2.6 × 104 and the Cp of the non-rotating shaft wind turbine is 5.7% higher than that of the rotating shaft wind turbine. The Cp of the non-rotating and rotating shaft wind turbines is reduced by 6.9% and 6.3%, respectively, by increasing the turbulence intensity from 4% to 16%. The optimal power output occurs under the condition of the non-rotating shaft wind turbine, and the relative surface roughness (ks/ds) is 0.005, where it is observed that Cp increased by 2.1% in comparison to that of the smooth shaft wind turbine.

Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation

Three isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number of 105 are computed by large-eddy simulation using four different meshes in order to investigate the grid sensitivity of the jet flow field and noise. The jets correspond to two initially fully laminar jets and one initially strongly disturbed jet considered in previous numerical studies. At the exit of a pipe nozzle of radius r0, they exhibit laminar boundary-layer mean-velocity profiles of thickness [Formula: see text] and [Formula: see text], respectively. For the third jet, a peak turbulence intensity close to 9% is also imposed by forcing the boundary layer in the nozzle. The grids contain up to one billion points, and, compared to the grids used in previous simulations, they are finer in the axial direction downstream of the nozzle and in the radial direction on the jet axis and in the outer region of the mixing layers. The main flow field and noise characteristics given by the simulations, including the mixing-layer thickness, the centerline mean velocity, the turbulence intensities on the nozzle lip line and the jet axis, spectra of velocity and far-field pressure obtained from the jet near field by solving the isentropic linearized Euler equations, are presented. With respect to those from previous studies, the results are very similar for the initially laminar jet with thick boundary layers, but they differ significantly for the initially laminar jet with thin boundary layers and for the initially disturbed jet. For the latter two jets, using a finer grid leads to a faster flow development, to higher turbulence intensities in the shear layers and at the end of the potential core, to stronger large-scale structures, and to the generation of more low-frequency noise. Moreover, very small mesh spacings appear to be necessary all along the jet mixing layers, and in particular during their early stages of growth, to properly capture the formation and dynamics of the flow coherent structures and thus obtain results in good agreement with measurements available for high-Reynolds-number jets.

Summary of frictional drag coefficient relationships for spheres: Evolving solution strategies applied to an old problem

In 1851 Stokes reported his analytical solution for the kinetic force (form drag plus frictional drag) exerted by an unbounded fluid on a steadily falling sphere under very slow or creeping flow conditions. This so called Stokes’ law was improved in the early 20th Century by several authors, who included diverse approximations to the inertia term neglected by Stokes in the Navier-Stokes equation describing Newtonian fluid motion around the sphere. Lapple and Shepherd (1940) followed this fundamental theoretical work with a landmark plot relating the experimental frictional drag coefficient f (directly proportional to the magnitude of the kinetic force) to the sphere diameter-based Reynolds number (Re) for 0.1≤Re≤3.0E+06. Researchers quickly realized that Stokes’ law (valid for Re<0.1) was insufficient to explain the data over the entire span of Re, giving rise to new solution methodologies to predict f(Re). This communication gives a chronological listing of well-known f(Re) relationships, providing insights on the rationale and strategies used in their development. The modern chemical engineer can therefore readily assess the evolution of this problem and realize the remaining research gaps in the field of fluid flow around submerged spheres.

Airside heat transfer and pressure loss characteristics of bare and finned tube heat exchangers used for aero engine cooling considering variable air properties

Numerical studies have been conducted to investigate the airside thermal-hydraulic characteristics of bare tube bank and plain finned tube heat exchangers intended for use in aero-engine cooling. The exchangers use small diameter tubes (3.0mm) with compact tube layout and operate at high temperatures with large temperature changes over the exchanger depth. Calculations are performed for frontal air velocities between 5 and 20m/s, yielding tube diameter based Reynolds numbers from 4898 to 19,592. Calculations are implemented using the Realizable k-ɛ turbulence model with consideration of the air physical property variations caused by the air temperature changes. The results show that ignorance of the air property variability leads to overestimations of both heat transfer and pressure loss, with a smaller air velocity yielding a more serious overestimation. The numerical fin efficiency agrees with the Schmidt fin efficiency within 7.0%. The plain finned tube heat exchanger is superior to the bare tube bank heat exchanger if the exchanger performance is evaluated using the heat transfer rate to pressure drop ratio.

On Numerical Investigation of Non-dimensional Constant Representing the Occurrence of Secondary Peaks in the Nusselt Distribution Curves

The Study of heat transfer augmentation in micro scale and electronic packaging systems are some of the paramount areas of the impending universe. In such systems the cooling of the heat sinks are generally achieved through the impingement of air jet. Assuming the air jet to be continues & incompressible fluid, the heat dissipation rate over the target surface seems to either uniform or well characterized in radial direction. In order to study the characteristic of heat dissipation rate, a graph of Nusselt number versus radial distance over the target surface is plotted. This is done at various injection and geometric parameters. The resulting trend of Nusselt profile manifests a gradual decrement in its magnitude with increase in the radial distance from the stagnation point. This is the property of characterized Nusselt distribution profile. In order to study the Nusselt distribution profile in more accurate sense, the present research takes an effort in numerically simulating the present geometry. A 2-D axis-symmetric geometric model is being proposed which consists of air (fluid) and aluminum (solid) as two vital computational domains. The computational simulations are being carried out using an appropriate turbulence model, in order to correctly predict the most accurate flow regime. This also enables the recording of necessary heat interactions. As far as the transition and intermediacy in the flow structure which occurs at target surface is concerned, prediction of accurate flow profile using commercial turbulence model becomes difficult. In order to predict these vital phenomenon, SST turbulence model along with Gamma – Theta transitional model is solved simultaneously in a commercial CFX solver. At lower nozzle - target spacing and higher impinging velocity, Nusselt distribution curve was observed to posses some unpredicted and localized secondary rise. The occurrence of such secondary peaks increases the magnitude of area average heat transfer rate. As per the survey, very less light is observed in the research areas of determining the exact cause and the intervening range for the occurrence of such peaks. Looking into this issue the current research focuses over the determination of the critical constant and its magnitude within which these peaks exists. The non dimensional constant representing the critical magnitude is defined as a ratio of diameter based Reynolds number with nozzle - target spacing (Z/d). While the corresponding critical magnitude was approximately investigated to be 6000. Not only that the present work takes an initiative in mapping the velocity contours at different values of this non dimensional constant. This enables a physical understanding of the flow profile at different impinging condition. A very contiguous observation of such contours demonstrates the occurrence of a transition region in the flow regime to be responsible for the origin of such peaks

An Experimental Investigation of the Performance Impact of Swirl on a Turbine Exhaust Diffuser/Collector for a Series of Diffuser Strut Geometries

A comprehensive experimental investigation was initiated to evaluate the aerodynamic performance of a gas turbine exhaust diffuser/collector for various strut geometries over a range of inlet angle. The test was conducted on a 1/12th scale rig developed for rapid and accurate evaluation of multiple test configurations. The facility was designed to run continuously at an inlet Mach number of 0.40 and an inlet hydraulic diameter-based Reynolds number of 3.4 × 105. Multihole pneumatic pressure probes and surface oil flow visualization were deployed to ascertain the effects of inlet flow angle and strut geometry. Initial baseline diffuser-only tests with struts omitted showed a weakly increasing trend in pressure recovery with increasing swirl, peaking at 14 deg before rapidly dropping. Tests on profiled struts showed a similar trend with reduced recovery across the range of swirl and increased recovery drop beyond the peak. Subsequent tests for a full diffuser/collector configuration with profiled struts revealed a rising trend at lower swirl when compared to diffuser-only results, albeit with a reduction in recovery. When tested without struts, the addition of the collector to the diffuser not only reduced the pressure recovery at all angles but also resulted in a shift of the overall characteristic to a peak recovery at a lower value of swirl. The increased operation range associated with the implementation of struts in the full configuration is attributed to the deswirling effects of the profiled struts. In this case, the decreased swirl reduces the flow asymmetry responsible for the reduction in pressure recovery attributed to the formation of a localized reverse-flow vortex near the bottom of the collector. This research indicates that strut setting angle and, to a lesser extent, strut shape can be optimized to provide peak engine performance over a wide range of operation.

Simulations of Initially Highly Disturbed Jets with Experiment-Like Exit Boundary Layers

Two isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number of have been computed by compressible large-eddy simulation using high-order finite differences on a grid of 3.1 billion points. At the exit of a straight pipe nozzle in which a trip forcing is applied, the jet flow velocity parameters, including the momentum thickness and the shape factor of the boundary layer, the momentum-thickness-based Reynolds number, and the peak turbulence intensity, roughly match those found in experiments using two nozzles referred to as the ASME and the conical nozzles. The boundary layer is in a highly disturbed laminar state in the first case and in a turbulent state in the second. The exit flow conditions, the shear-layer and jet flowfields, and the far-field noise provided by the large-eddy simulation are described. The jet with the ASME-like initial conditions develops a little more rapidly, with slightly higher turbulence levels than the other. Overall, however, the results obtained for the two jets are very similar, and they are in good agreement with measurements available for Mach 0.9 jets. In particular, this similarity holds for the far-field spectra. Because the ASME nozzle has been reported to yield higher noise levels than the conical nozzle, this suggests that the nozzle-exit conditions in the large-eddy simulation do not adequately reflect those in the experiments and/or that the link between the noise differences and the jet initial conditions using the two nozzles is not as simple as was first thought, and that other parameters, associated for instance with the nozzle geometry such as the presence of pressure gradients, may also play an important role.

锯齿射流与圆射流流场和远场噪声特性的对比研究

Large eddy simulation (LES) is performed to study high subsonic round and chevron jets with a diameterbased Reynolds number Re=10⁵.2 different chevron jet flows are considered, which are with 6 lobes and 4 lobes respectively.The simulation results are checked by comparing mean axial velocity profiles and overall sound pressure levels (OASPLs) of the round jet with the existent experimental and LES results, and they are in good agreement with each other. Then the properties of chevron jets are compared with those of round jets. The chevron jets show higher radial expansion rate in the nearnozzle region and shorter potential core lengths. The OASPLs of the chevron jets decrease as high as 4 dB at the shallow angles compared with the round jets and without apparent noise increment at the sideline. 3 azimuthal modes,m=0,1,2of the farfield pressure fluctuations from both the round and chevron jets are investigated. All cases show similar OASPL distribution profiles vs. the polar angles for each azimuthal mode. But, apparent noise increment is found at high polar angles in the zeroth and first azimuthal modes for the chevron jet with 4 lobes when compared with the round jet. By performing proper orthogonal decomposition (POD), the most energetic coherent structures at specified coupled azimuthal wavenumbers are extracted. The wavepacket features associated with coherent structures of round and chevron jets are analyzed in detail to explain changes of noise properties in the far fields.

Tip-vortex instability and turbulent mixing in wind-turbine wakes

Kinetic-energy transport and turbulence production within the shear layer of a horizontal-axis wind-turbine wake are investigated with respect to their influence on the tip-vortex pairwise instability, the so-called leapfrogging instability. The study quantifies the effect of near-wake instability and tip-vortex breakdown on the process of mean-flow kinetic-energy transport within the far wake of the wind turbine, in turn affecting the wake re-energising process. Experiments are conducted in an open-jet wind tunnel with a wind-turbine model of 60 cm diameter at a diameter-based Reynolds number range$\mathit{Re}_{D}=150\,000{-}230\,000$. The velocity fields in meridian planes encompassing a large portion of the wake past the rotor are measured both in the unconditioned and the phase-locked mode by means of stereoscopic particle image velocimetry. The detailed topology and development of the tip-vortex interactions are discussed prior to a statistical analysis based on the triple decomposition of the turbulent flow fields. The study emphasises the role of the pairing instability as a precursor to the onset of three-dimensional vortex distortion and breakdown, leading to increased turbulent mixing and kinetic-energy transport across the shear layer. Quadrant analysis further elucidates the role of sweep and ejection events within the two identified mixing regimes. Prior to the onset of the instability, vortices shed from the blade appear to inhibit turbulent mixing of the expanding wake. The second region is dominated by the leapfrogging instability, with a sudden increase of the net entrainment of kinetic energy. Downstream of the latter, random turbulent motion characterises the flow, with a significant increase of turbulent kinetic-energy production. In this scenario, the leapfrogging mechanism is recognised as the triggering event that accelerates the onset of efficient turbulent mixing followed by the beginning of the wake re-energising process.

Boiling Heat Transfer From an Array of Round Jets With Hybrid Surface Enhancements

The effect of a variety of surface enhancements on the heat transfer achieved with an array of impinging jets is experimentally investigated using the dielectric fluid HFE-7100 at different volumetric flow rates. The performance of a 5 × 5 array of jets, each 0.75 mm in diameter, is compared to that of a single 3.75 mm diameter jet with the same total open orifice area, in single-and two-phase operation. Four different target copper surfaces are evaluated: a baseline smooth flat surface, a flat surface coated with a microporous layer, a surface with macroscale area enhancement (extended square pin–fins), and a hybrid surface on which the pin–fins are coated with the microporous layer; area-averaged heat transfer and pressure drop measurements are reported. The array of jets enhances the single-phase heat transfer coefficients by 1.13–1.29 times and extends the critical heat flux (CHF) on all surfaces compared to the single jet at the same volumetric flow rates. Additionally, the array greatly enhances the heat flux dissipation capability of the hybrid coated pin–fin surface, extending CHF by 1.89–2.33 times compared to the single jet on this surface, with a minimal increase in pressure drop. The jet array coupled with the hybrid enhancement dissipates a maximum heat flux of 205.8 W/cm2 (heat input of 1.33 kW) at a flow rate of 1800 ml/min (corresponding to a jet diameter-based Reynolds number of 7800) with a pressure drop incurred of only 10.9 kPa. Compared to the single jet impinging on the smooth flat surface, the array of jets on the coated pin–fin enhanced surface increased CHF by a factor of over four at all flow rates.

回転円柱による矩形流路の熱伝達促進

Heat transfer measurement has been done for a low speed water channel with an insertion of rotation circular cylinder in order to find an effective way to achieve high heat transfer enhancement by dynamic flow control method. In the present study, a ratio of the gap between the cylinder and heat transfer wall to the cylinder diameter was kept to be 0.6. The diameter based Reynolds number was set for 200 and 400. It was found that the cylinder rotation achieves remarkable heat transfer enhancement. Counter clockwise rotation, the direction of which accelerates the gap flow, intensifies the unsteady vortex in the shear layer above the low speed area downstream the circular cylinder and this enhances the wall heat transfer over the extensive downstream region. Heat transfer enhancement becomes large as the rotation speed becomes higher within the present experimental condition. Clockwise rotation suppresses the vortex formation, although high speed rotation induces the fast flow approaching near the wall and achieves large heat transfer enhancement there.

Low-dimensional dynamics of a turbulent axisymmetric wake

AbstractThe coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$. Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$. In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

The Experimental Studies of Improving the Aerodynamic Performance of a Turbine Exhaust System

Analysis and testing were conducted to optimize an axial diffuser–collector gas turbine exhaust. Two subsonic wind tunnel facilities were designed and built to support this program. A 1/12th scale test rig enabled rapid and efficient evaluation of multiple geometries. This test facility was designed to run continuously at an inlet Mach number of 0.41 and an inlet hydraulic diameter-based Reynolds number of 3.4 × 105. A 1/4th geometric scale test rig was designed and built to validate the data in the 1/12th scale rig. This blow-down rig facilitated testing at a nominally equivalent inlet Mach number, while the Reynolds number was matched to realistic engine conditions via back pressure. Multihole pneumatic pressure probes, particle image velocimetry (PIV), and surface oil flow visualization were deployed in conjunction with computational tools to explore physics-based alterations to the exhaust geometry. The design modifications resulted in a substantial increase in the overall pressure recovery coefficient of +0.07 (experimental result) above the baseline geometry. The optimized performance, first measured at 1/12th scale and obtained using computational fluid dynamics (CFD) was validated at the full scale Reynolds number.

Laminar and turbulent nozzle-jet flows and their acoustic near-field

We investigate numerically the effects of nozzle-exit flow conditions on the jet-flow development and the near-field sound at a diameter-based Reynolds number of ReD = 18 100 and Mach number Ma = 0.9. Our computational setup features the inclusion of a cylindrical nozzle which allows to establish a physical nozzle-exit flow and therefore well-defined initial jet-flow conditions. Within the nozzle, the flow is modeled by a potential flow core and a laminar, transitional, or developing turbulent boundary layer. The goal is to document and to compare the effects of the different jet inflows on the jet flow development and the sound radiation. For laminar and transitional boundary layers, transition to turbulence in the jet shear layer is governed by the development of Kelvin-Helmholtz instabilities. With the turbulent nozzle boundary layer, the jet flow development is characterized by a rapid changeover to a turbulent free shear layer within about one nozzle diameter. Sound pressure levels are strongly enhanced for laminar and transitional exit conditions compared to the turbulent case. However, a frequency and frequency-wavenumber analysis of the near-field pressure indicates that the dominant sound radiation characteristics remain largely unaffected. By applying a recently developed scaling procedure, we obtain a close match of the scaled near-field sound spectra for all nozzle-exit turbulence levels and also a reasonable agreement with experimental far-field data.

Closed-Loop Active Flow Control of a Three-Dimensional Turret Wake

An experimental study has been performed to investigate the wake of a three-dimensional turret with aspect ratio of 1.17 at a diameter-based Reynolds number of . Stereoscopic particle image velocimetry was used to evaluate the spatial structure of the wake, and dynamic surface-pressure measurements were used to study the time-dependent behavior. The uncontrolled wake was seen to be strongly three-dimensional with two main structures on opposing sides of the center plane. Cross correlations from the surface pressure indicated that opposite sides of the wake had nearly zero correlation in time. With the application of active flow control, both the spatial structure and time-dependent behavior of the wake were significantly altered. The downwash velocity along the center plane was seen to increase significantly, causing the wake to spread more rapidly near the support plate, and the spectra from the pressure sensors contained multiple peaks at different frequencies throughout the wake that were not seen in the baseline case. Closed-loop control achieved similar control authority as steady open-loop forcing, but with a 45% reduction in the mean jet-momentum coefficient.

Simulation of Subsonic Turbulent Nozzle Jet Flow and Its Near-Field Sound

A direct numerical simulation framework is developed and validated for investigating a jet-flow configuration in which a short cylindrical nozzle and the acoustic near field are included in the simulation domain. The nozzle flow is modeled by a potential flow core and a developing turbulent wall boundary layer, which is numerically resolved. The setup allows to create well-controlled physical nozzle-exit flow conditions and to examine their impact on near-nozzle flow dynamics, jet-flow development, and the near-field sound. Turbulence at the nozzle inflow is generated by the synthetic-eddy method using flat-plate boundary-layer direct numerical simulation data and imposed softly in a sponge layer. The jet Mach number in the present investigation is , the diameter-based jet Reynolds number is , and the maximum axial rms fluctuations attain 13% at the nozzle exit. The accuracy of the numerical results is checked by varying grid resolution and computational domain size. The rapid flow development in the changeover region from wall turbulence to the turbulent free shear layer within about one nozzle diameter is documented in detail. Near-field sound pressure levels compare favorably with experimental reference data obtained at the much higher Reynolds number of 780,000. This agreement is essentially attributed to a compensation of the effects of Reynolds number and turbulence level on the noise for which an empirical scaling is derived from published data. A brief comparison is also made to the jet sound field arising from a laminar nozzle-exit boundary layer.

Investigation of flow features around shallow round cavities subject to subsonic grazing flow

The focus of this work is the study of the asymmetric mean flow which can appear inside shallow cavities of circular planform, and for which limited experimental data is available. To this end, the behaviour of cylindrical cavities in grazing flow is investigated numerically, for varying ratios of diameter to depth. Large-eddy simulations (LESs) of cylindrical cavities of diameter D = 10 cm and depths H ranging from 1 to 10 cm, grazed by a flow at a Mach number 0.25, are reported. The diameter-based Reynolds number of these cavity flows is 600 000. The incoming boundary layer, of thickness δ/D = 0.17, is numerically tripped, in order to reach a highly disturbed state upstream of the cavity. Numerical flow results are compared to experimental findings obtained for similar configurations, and mean flow dependence on the ratio H/D is shown to be correctly reproduced. For cavities of depth greater than 0.7 times their diameter, a symmetric mean flow is obtained, as expected. For shallower cavities, of depth between 0.4 and 0.7 times the diameter, an asymmetric mean flow regime is observed, as previously described in a few experimental papers. Over a small range of depths, from 0.2 to 0.4 times the diameter, very low frequency flow unsteadiness or switching is found. Based on the LES results, a detailed description of these different flow patterns, in terms of both steady and unsteady aspects, is proposed. This description both confirms and adds to the relatively small amount of experimental data available for shallow cylindrical cavity flows.

The effect of flow pulsation on drag and heat transfer in an array of heated square cylinders

Laminar 2-D pulsating flow through homogeneous linear arrays of heated square tubes is simulated for pulsation frequencies of 0–80 Hz for tube diameter-based Reynolds numbers from 50 to 200. The objective is to examine the effects of flow pulsation on drag and heat transfer in heat exchanger tube bundles. Cycle-averaged and maximum drag coefficients, as well as the instantaneous and cycle-averaged Nusselt numbers are reported for each of the ten rows of tubes in the simulated array. The results show that flow pulsations can enhance heat transfer in tube bundles, and the level of enhancement increases with pulsation frequency and mean flow Reynolds number. A wake interference effect has been observed which significantly amplifies the drag on the leading rows and reduces and instantaneously reverses the sign of the drag force on the tubes located in the wake region. Cycle-average drag coefficients decreased with increasing Reynolds number and porosity, and were only a weak function of pulsation frequency. Peak drag coefficients were found to decrease with increasing Reynolds number and porosity, but increase with frequency approximately linearly. Empirical correlations are presented for a tube bundle with 64% porosity that relate maximum and cycle-average drag coefficients as well as Nusselt numbers to the Reynolds number and frequency.