Velocity Direction Research Articles

Joint inversion of formation radial shear-velocity profiles by dipole acoustic logging while drilling

Formation properties near a borehole are frequently altered by mechanical damage from drilling, leading to variations of formation elastic velocities in the radial direction. Inversions of radial shear profiles are necessary for a real-time evaluation of the drilling conditions. In this study, we investigate acoustic wave propagation in a logging-while-drilling (LWD) model excited by a dipole transducer in cylindrically layered media. It is revealed that the dispersion characteristics of the dipole waves of the LWD are sensitive to the radial formation velocity variation. Accordingly, we develop a joint inversion method that evaluates radial shear-velocity profiles using the dipole modes of the first and second orders. The propagation of these two modes is strongly influenced by formation alterations, but the inversion results obtained using a single dipole mode indicate ambiguity caused by the nonuniqueness problem. Through our joint inversion, the additional second-order dipole wave can effectively help address the nonuniqueness issue in dipole acoustic logging, although its dispersion features differ in fast and slow formations. It is validated that the joint inversion has considerably improved convergence and accuracy in evaluating the thickness and shear velocity of the altered zone, compared with the estimation by a single acoustic mode. Furthermore, we develop numerical results based on synthetic logging data to demonstrate the feasibility of this inversion in a continuously varying profile, regardless of whether the formation surrounding the borehole is fast or slow. Even when strong drilling noises of low frequencies are added to the receiver signal arrays, the means of joint inversion can remain stable, and the shear-velocity profiles can be evaluated with good precision.

Influence of vibration on transient flow characteristics of gas-liquid two-phase flow in inclined pipes

As an advanced method of transportation globally, pipelines play a significant role in the energy sector of many nations. Given the rapid development of offshore oil and gas engineering, it is critical for researchers to focus on the dynamics of pipelines and the flow characteristics of internal fluids under oceanic conditions. In this paper, a gas-liquid two-phase flow numerical model was developed to simulate transient flow characteristics in an inclined pipe at different vibration conditions based on CFD dynamic mesh technology. The CFD model was verified against experimental data, showing that the numerical simulation predicts average pressure drop within 10 % of experimental data. Parametric studies were conducted based on the CFD analysis, including vibration direction (horizontal, vertical, and inclined), vibration amplitude (0.5D∼1.5D) and flow velocities (jsg=0.5∼1.0m/s, jsl=0.1∼1.0m/s). Meanwhile, the downhill and uphill sections of the pipeline were considered. The results indicated that inclined vibration had the most substantial impact on flow, followed by horizontal vibration and vertical vibration. The changes of average liquid holdup were closely related to flow pattern under vibration conditions. These vibration conditions significantly effected pressure fluctuations and secondary flow. The impact of vibration on transient flow heightened with increased vibration amplitude. In addition, transient flow behaviors showed periodicity, and the evolution period was consistent with the vibration period. These findings are helpful to understand the transient flow behaviors in inclined pipe under vibration conditions.

Effects of hydraulic conditions on biofilm detached in drinking water distribution system

It is well documented that after the water has been treated in the treatment plant, the quality of drinking water is degraded during transport to consumers inside the drinking water distribution system (DWDS). One of the critical reasons for altering drinking water quality is the biofilm detached from the pipe wall to the bulk water. In this paper, the effects of hydraulic conditions such as flow velocity and flow direction, on the biofilm were investigated. The results show that, compared with other flow conditions, the biofilm is the thickest (267.4 μm) and the adhesion force is the lowest under the fluctuant flow velocity. The fluctuant flow velocity increased the relative abundance of Sphingobium and Blastomonas, decreased the relative abundance of Dechloromonas and Sediminibacterium. The Sphingobium with strong environmental adaptability and metabolic capacity could accelerate the growth of biofilm under fluctuant flow velocity conditions. The abundance of functional genes that could reflect microbial metabolic capacity in the biofilm under fluctuant flow velocity conditions is significantly higher than that under other hydraulic conditions. The total number of bacteria in the biofilm under reverse flow conditions was 31.48 %–32.01 % and 47.97 %–71.38 % lower than that under low and high flow conditions, respectively, indicating that the shear force generated by the reverse flow had resulted in biofilm detachment. This study improved our understanding of the influence of different hydraulic conditions on biofilms in the DWDS and helped us understand how to operate the DWDS without causing additional biofilm detachment.

Numerical study of transient flow characteristics of gas-liquid two-phase flow in inclined upward tube under periodic vibration

The transient flow characteristics of gas-liquid two-phase flow in inclined upward tubes exhibit a high degree of complexity. The tube vibration caused by multiple uncertain factors, such as seawater impacts or subsea earthquakes, poses more significant challenges for flow safety assurance. Thus, it becomes increasingly crucial to explore the transient flow characteristics of gas-liquid two-phase flow in inclined upward tubes under various vibration conditions. In this paper, the transient flow characteristics of gas-liquid two-phase flow in an inclined upward tube under different vibration conditions are numerically studied based on CFD dynamic mesh technique. In the current study, the studied parameters include vibration direction (heaving, transverse and coupling), vibration amplitudes (0.5D, 1.0D and 1.5D), and inlet velocity (jsg=0.5∼1.0m/s; jsl=0.1∼1.0m/s). The transient flow structure, cross-sectional void fraction and pressure drop are analyzed. The findings indicate that the transient flow structure of the slug flow demonstrates periodic variation characteristics under transverse and coupling vibrations, and the cross-sectional void fraction increase. For transition flow, the cross-sectional void fraction increases under transverse and coupling vibrations, while displays an increase initially and subsequently a decrease significant with an increase in the heaving vibration amplitude. Additionally, all considered vibration conditions intensify the pressure drop of the transition flow and decrease the cross-sectional void fraction of the turbulent flow.

Plane-Parallel Laminar Flow of Viscous Fluid in the Transition Zone of the Inlet Section

A study was conducted to analyze how hydrodynamic parameters change in the entrance region of plane-parallel flow under stationary flow conditions, with an initial arbitrary distribution of velocities in the entrance section. This study was based on boundary layer equations, and a boundary problem was formed under the conditions of plane-parallel flow. The boundary conditions were chosen to reflect the pattern of arbitrary velocity distribution in the entrance section. A general solution of the approximating Navier-Stokes equations is provided, which depends on the initial conditions and the Reynolds number. The boundary conditions are established based on the nature of the motion, and the boundary value problem is described. A method for integrating the boundary value problem has been developed, and regularities for the change in velocities along the length of the inlet section have been obtained for both constant and parabolic velocity distributions in the entrance sections. Analytical solutions have been derived to obtain patterns of velocity and pressure changes in any given flow direction. Through computer analysis, velocity change patterns in various sections along the inlet transition area have been constructed, allowing for the determination of fluid velocity at any point on the section and an estimation of the length of the transition area. These proposed solutions provide a framework for accurately constructing individual units of hydromechanical equipment.

Material point method‐based simulation of dynamic process of soil landslides considering pore fluid pressure

AbstractIn this study, the dynamic process of soil landslides is investigated using the material point method (MPM). A basal friction algorithm is developed based on the MPM, and the pore water pressure is considered for calculating the basal friction. A large‐scale debris flow experiment is performed to validate the effectiveness of the MPM in simulating the dynamic process of soil landslides. The calculated depths of the debris flow using the MPM are consistent with the experimental results. The effects of the basal friction angle and internal friction angle on the debris flow depths are discussed. Moreover, a landslide case is simulated using the MPM, and the calculation results are consistent with the measured results. The horizontal velocity, vertical velocity, velocity direction, and kinetic energy of the landslide are analyzed. Finally, a case involving a different slope near a landslide is evaluated using the MPM. The distributions of velocity in different directions and changes in the average velocity, kinetic energy, and sliding distance are analyzed. By setting a retaining wall, the accumulation height of a landslide accumulated at the retaining wall and the normal force on the retaining wall can be estimated.

Spin-velocity locking in a helical chain of atomic p± orbitals.

Observations of a high spin selectivity in various helical structures, which is called the chirality-induced spin selectivity, suggest a common mechanism originating from the helical geometry. In this paper, we consider a helical chain of atomic p± orbitals having the tangential angular momentum l = ±1. We show in this model that the coupling of l and the spin gives rise to spin-velocity locking, i.e., directions of spin and group velocity are parallel or antiparallel depending on the chirality of the helix, and consequently, an almost perfect spin selectivity in a specific energy region in a wide range of the curvature and the torsion of the helix. We find that the present spin-velocity locking originates from the helical symmetry in which the Hamiltonian is invariant with respect to a combined operation of the rotation around the helix axis and the translation along the helix axis. Therefore, we expect that spin-velocity locking occurs in a wide variety of helical structures.

Effect of high pressure on severe slugging and multiphase flow pattern transition in a long pipeline-riser system

Severe slugging poses an enormous threat to the safe operation of high-pressure long petroleum pipelines. However, most published studies are conducted in short pipelines under atmospheric pressure. In this work, the gas–liquid two-phase flow experiment is conducted in the pipeline-riser system of 380 m long and 75 mm inner diameter under the separator pressure from atmospheric pressure to high pressure (10 MPa), and flow pattern maps are established. Under high-pressure conditions, liquid fallback and second blowout of severe slugging disappear. In the flow pattern maps, flow pattern types reduce, and severe slugging region shrinks. The boundary between stable flow and severe slugging appears on the left side of the flow pattern map and moves in the direction of higher superficial gas velocity. Increasing separator pressure leads to the increase in the severe slugging period. A correlation equation applicable to predicting the severe slugging period for different pressures (0, 1 and 5 MPa) is proposed, and the average error is less than ± 7.9%. Due to the inhibition of high pressure, the amplitude of the riser differential pressure decreases at most working points and increases only at a few working points where flow pattern transition occurs.

The influences of flow conditions on heat transfer of supercritical cracked-kerosene

The main component of propulsion system for hypersonic vehicle, such as scramjet, always sustains extremely high thermal loads, and actively regenerative cooling must be considered using its own hydrocarbon fuel as coolant. Due to the limited amount of coolant and the complex physical and chemical problems involved in heat transfer process, the difficulty of cooling channel design increases. In order to explore the ways to improve cooling efficiency, the influences of inlet velocity and flow direction on heat transfer of supercritical cracked-kerosene were investigated via a solid-fluid conjugated simulation method. The results indicate that increasing the coolant velocity can enhance cooling effect with a constant mass flow rate, and the wall temperature at peak heat flux decreased obviously. However, as the wall thickness increases, the enhanced cooling effect is gradually cancelled out. Flow direction has significant influence on heat transfer process. Compared with forward flow, the reverse flow shows considerable uniform wall temperature and low fuel temperature effect. These conclusions can be used as an important reference for cooling channel design under supercritical conditions.

Generalized Hasimoto-type surfaces of null growth in Minkowski 3-space

In this article, the idea of the generalized Hasimoto-type surfaces are put forward based on the interaction between vortex filaments. Meanwhie, the surface of null growth is proposed by evolving a null curve as dictated direction and growth velocity in Minkowski 3-space. The conditions and geometric forms of the generalized Hasimoto-type surfaces of null growth are investigated. Last but not least, several typical examples are presented to characterize such surface growth and the corresponding perturbations explicitly.

Lithospheric deformation in Mongolia revealed by anisotropic Rayleigh wave tomography: Implications for the mechanism of intracontinental orogeny

The Mongolian Plateau is situated in the eastern part of the Central Asian Orogenic Belt that was formed during the Paleozoic era. In the Cenozoic era, the plateau has been reactivated, leading to significant topographic uplift, volcanism, and seismic activity. Several destructive earthquakes, ranging from magnitudes 6 to 8, have occurred in the 20th century. But the mechanism of these neotectonics remains unclear. To better understand these processes, we determined S wave velocity and azimuthal anisotropy in the crust and upper mantle under Mongolia using Rayleigh wave dispersion curves. Our findings indicate that the lithosphere is dominated by NW-SE fast velocity directions (FVDs). However, we observed different patterns in two specific regions. The lithospheric anisotropy under the Hangay Dome is weak, suggesting that it is accompanied by significant mantle upwelling under the dome. On the other hand, the FVDs in the Gobi Desert exhibit a circular pattern that wraps around the Ordos Block, which may have been caused by past and present deformation imposed on the stable block. These results offer new insights into the lithospheric deformation and dynamics of the Mongolian Plateau.

3D motion analysis of kick start motion−Effects of upper limb movements on the body when leaving the platform−

AbstractThe purpose of this study was to clarify the effect of the presence or absence of upper limb movement on the propulsion direction body velocity (TPV) leaving the platform at kick start. The first trial (Standard trial) is a normal kick start, and the second trial (Lower trial) is the same as a normal kick start. The force from the upper limb movement at the time was set so that the start table was not applied, and the start movement calculated the 3D coordinates of the marker attached to the body by 3D movement analysis. As a result, in the movement speed at the time of leaving the platform, the standard trial had a significantly higher value in the propulsion direction and a significantly lower value in the vertical movement speed than the lower trial. In addition, since the standard trial had a significantly lower value in the jumping angle when leaving the platform, the role of the upper limb movement in kick start is to promote by making the jumping angle closer to the horizontal when leaving the platform. It was suggested that it may affect the directional velocity.

Left atrium substrate and wave speed mapping using Omnipolar technology in patients undergoing paroxysmal atrial fibrillation catheter ablation

Abstract Funding Acknowledgements Type of funding sources: None. Background The new Ensite X Cardiac Mapping (Abbott) system, with the introduction of Omnipolar technology (OT), provides three-dimensional information on voltage, direction of activation and conduction velocity of endocardial potentials, regardless of catheter orientation. OT thus enables the creation of more defined voltage maps and a wave speed map, a color map encoded by the numerical value of conduction velocity. Purpose We aimed to evaluate the feasibility and reliability of left atrium (LA) substrate and wave speed mapsperformed with OT in patients undergoing pulmonary vein isolation of paroxysmal atrial fibrillation (AF). Methods We included 39 patients undergoing catheter ablation for paroxysmal AF with the new Ensite X Cardiac Mapping System at five Italian Institution. In all patients the left atrium (LA) was mapped with the Advisor HD Grid catheter (Abbott). A sinus rhythm high-density voltage map and wave speed map were obtained and analyzed to compare low-voltage areas and to identify high conduction velocity areas. Results Thirty-nine pts were included in this analysis (61±10 years, 64% male, 68% with paroxysmal AF, CHA2DS2-VASc = 1.6±1.1, left atrial diameter = 46±9 mm, left ventricle ejection fraction 63±4%). The voltage maps were obtained by acquiring and, after point validation, analyzing significantly more points in the OT analysis than in the bipolar analysis (11455±8833 vs 8186±5826 and 2611±1728 vs 1753±1324, respectively; p < 0.001). Low-voltage area (< 0.05 mV) was significantly less extensive using OT (low-voltage OT area 8.9 cm2 [5.8; 24.2] vs low-voltage bipolar area 10.8 [6.4; 31.4]; p < 0.05), Fig 1. Considering wave speed maps, the pulmonary veins showed significantly higher values than the atrial values (LSPV: 2.89 ms/s ± 1.99; LIPV 2.86 ms/s ± 1.78; RSPV 3.31 ms/s ± 2.07; RIPV 2.86 ms/s ± 1.96; LA 1.67 ms/s ± 0.80; p< 0.001) while, in the atrium, the area of greatest speed was located on the roof (2.35 ms/s ± 1.53; p 0.02) almost drawing a bundle from the RSPV to the LA appendage that could coincide with the anatomical Bachmann’s bundle location, Fig 2. Conclusion OT makes it possible to obtain voltage maps by analyzing a larger number of points and providing a better substrate definition. Wave speed mapping is a promising new map type, allowing characterization and identification of high velocity areas. Further studies are needed to assess the impact of this new technology on procedural workflow and clinical outcome.

Azimuthal seismic reflection characteristics with quality factor Q in viscoelastic horizontal transverse isotropic media

Abstract In seismic exploration, a precise description of the seismic reflection property is critical for reservoir prediction and fluid identification. In the study of seismic wave transmission effects, taking into account both the viscoelastic and anisotropic properties of a medium is compatible with the features of the earth. Moreover, it is advantageous to the characterization of complicated reservoirs. According to the elastic medium foundation and the imaginary component with quality factor Q, seismic reflection properties of viscoelastic media are described in the complex domain. The complex wave number is expressed by phase velocity and Q. The attenuation angle is introduced when the complex wave number is represented by a propagation vector and an attenuation vector. The exact velocity and polarization direction of a viscoelastic medium are expressed using a complex stiffness matrix incorporating Q matrix elements. The quasi-Zoeppritz equation for viscoelastic horizontal transverse isotropic (VHTI) media is derived by using boundary conditions based on the wave function of viscoelastic media. The numerical simulation of reflectivity reveals that the reflection coefficient in a viscoelastic medium is clearly different from that of an elastic medium. Moreover, the difference in reflection coefficient in various orientations has distinct characteristics.

Separation of iron from converter dust by superconducting HGMS: A simulation analysis and experimental study

Converter dust (LT dust) is an important solid waste from steelmaking, in which iron oxides are the preferred raw material for preparing high value-added α-Fe2O3. Since LT dust contains many impurities, the iron oxides in the LT dust must be enriched and purified before the preparation of α-Fe2O3. Particle trapping behaviors of the matrices as well as the magnetic flocculation of LT dust particles in superconducting high gradient magnetic separation (S-HGMS) were investigated with numerical simulations and experiments. The geometric shape, aspect ratio a:b, and angle α between the axis and the magnetic field direction of the matrices affected the maximum magnetic field intensity (Hmax) and effective capture area (Seca). Diamond matrices had better particle-capture capacity than elliptic and circular matrices because the diamond matrices produced a tip effect and increased the magnetic field force. When the cross section of the matrices was parallel to the direction of the particle velocity, magnetic/weakly magnetic particles were more easily captured by the upper and lower ends of the matrices compared with that of two sides because the particle velocity at the upper and lower ends of the matrices was smaller than that of two sides, making the magnetic force greater than the drag force. Fe2MgO4 and Fe2O3 particles were more prone to magnetic flocculation than other particles because of their higher magnetic susceptibility. The dispersant changed the pH of the solution and the charges on the surface of LT dust particles, and the particles were effectively dispersed because of the action of electrostatic forces. When the magnetic induction was 1.8 T, the dispersant dosage was 20 mg/L, the pulp concentration was 1.5%, and the total Fe content increased by 8.72%, corresponding to an Fe recovery of 91.65%. Finally, a method was developed for extracting iron oxides from LT dust using S-HGMS, to prepare high value-added α-Fe2O3.

Sediment settling process revealed by a bottom-tethered sediment trap at the east tip of the Shandong Peninsula

This paper investigates sediment settling process during summer seasons based on in-situ observation and sediment analysis at the east tip of the Shandong Peninsula, which is a pathway for sediments from the Bohai Sea and the North Yellow Sea to enter the South Yellow Sea in China. Bottom-tethered sediment traps, together with platforms equipped with current profilers/meters and temperature/salinity and turbidity sensors, were deployed for approximately 10 days in August 2017 over an elongated deposit off the coast of the Shandong Peninsula. A computed tomography (CT) scan and grain size and 210Pb analyses of trap sediment were carried out to determine the settling process of suspensions at the study site. Twenty-three couplets were found in the CT images of the trap, the time series of which was established using intervalometer disks. Quantitative characterization of rhythmites using a hounsfield unit indicates that the period of couplets is approximately quarter-diurnal, and the settling process could be divided into three stages during Aug. 21st – 27th. Current, wave, wind, and SSC data illustrate that the diversion of the bottom current leads to the formation of couplets, and the thickness of the couplet is controlled by the vertical current velocity and wind direction. Northerly winds enhance the difference in settlement between flood and ebb tides, whereas southerly winds smoothen the difference. The gale event inhibited the settlement of the suspended matter, and the source of the suspensions was converted from local to remote after the event, as evidenced by 210Pb data. No evident erosion can be detected in the sediment traps. The results are of significance to better understand the sedimentary dynamics near the Shandong clinoform and inspire the practical efficiency of bottom-tethered sediment traps in the settling process in coastal areas.

Estimation of Flexural Strength of Plain Concrete from Ultrasonic Pulse Velocity

The aim of this study is to propose mathematical expressions for estimation of the flexural strength of plain concrete members from ultrasonic pulse velocity (UPV) measurements. More than two hundredpieces of precast concrete kerb units were subjected to a scheduled test program. The tests were divided into two categories; non-destructive ultrasonic and bending or rupture tests. For each precast unit, direct and indirect (surface) ultrasonic pulses were subjected to the concrete media to measure their travel velocities. The results of the tests were mointered in two graphs so that two mathematical relationships can be drawn. Direct pulse velocity versus the flexural strength was given in the first relationship while the second equation describes the flexural strength as a function of indirect (surface) pulse velocity. The application of these equations may be extended to cover the assessment of flexural strength of constructed concrete kerb units or in-situ concreting kerbstone and any other precast concrete units. Finally, a relation between direct and indirect pulse velocities of the a given concrete was predicted and suggested to be employed in case when one of the velocities is notavailable can be measured for other ultrasonic pulse test applications

Impact of atmospheric forcing uncertainties on Arctic and Antarctic sea ice simulations in CMIP6 OMIP models

Abstract. Atmospheric reanalyses are valuable datasets for driving ocean–sea ice general circulation models and for proposing multidecadal reconstructions of the ocean–sea ice system in polar regions. However, these reanalyses exhibit biases in these regions. It was previously found that the representation of Arctic and Antarctic sea ice in models participating in the Ocean Model Intercomparison Project Phase 2 (OMIP2, using the updated Japanese 55-year atmospheric reanalysis, JRA55-do) was significantly more realistic than in OMIP1 (forced by the atmospheric state from the Coordinated Ocean-ice Reference Experiments version 2, CORE-II). To understand why, we study the sea ice concentration budget and its relations to surface heat and momentum fluxes as well as the connections between the simulated ice drift and the ice concentration, the ice thickness and the wind stress in a subset of three models (CMCC-CM2-SR5, MRI-ESM2-0 and NorESM2-LM). These three models are representative of the ensemble and are the only ones to provide the surface fluxes and the tendencies of ice concentrations attributed to dynamic and thermodynamic processes required for the ice concentration budget analysis. The sea ice simulations of two other models (EC-Earth3 and MIROC6) forced by both CORE-II and JRA55-do reanalysis are also included in the analysis. It is found that negative summer biases in high-ice-concentration regions and positive biases in the Canadian Arctic Archipelago (CAA) and central Weddell Sea (CWS) regions are reduced from OMIP1 to OMIP2 due to surface heat flux changes. Net shortwave radiation fluxes provide key improvements in the Arctic interior, CAA and CWS regions. There is also an influence of improved surface wind stress in OMIP2 giving better winter Antarctic ice concentration and the Arctic ice drift magnitude simulations near the ice edge. The ice velocity direction simulations in the Beaufort Gyre and the Pacific and Atlantic sectors of the Southern Ocean in OMIP2 are also improved owing to surface wind stress changes. This study provides clues on how improved atmospheric reanalysis products influence sea ice simulations. Our findings suggest that attention should be paid to the radiation fluxes and winds in atmospheric reanalyses in polar regions.

Impact of microplastics on organic fouling of hollow fiber membranes

Given the potential hazards of microplastics (MPs), it is desirable to efficiently remove them during wastewater treatment processes. To this end, ultrafiltration (UF) membranes can significantly increase the removal of MPs, however the fouling of such membrane modules can also be impacted by the presence of MPs. Magnetic Resonance Imaging (MRI) was used here to non-invasively quantify the effect of polyethylene (PE) MPs accumulation in a 3D UF hollow fiber (HF) membrane module containing 400 fibers, via direct non-invasive velocity imaging of the flow distribution between individual fibers during module operation. The co-effect of MPs and alginate (a common organic model foulant mimicking extracellular polymeric substances (EPS)) on fouling of the HF module was then explored. Flow was initially equally distributed with fouling causing flow in particular fibers to be significantly reduced. Fouling with MPs resulted in minimal flow distribution disruption and was easily remediated hydraulically, in contrast alginate fouling required chemical cleaning in order to fully restore homogeneous flow distribution between the fibers. The presence of both MPs and alginate resulted in a more heterogeneous disruption of the fibre flow distribution due to fouling and resulted in much more effective hydraulic cleaning of the module.

Transient mixed convection in a cylindrical cavity with a rotating finned cylinder

This article presents a numerical study of horizontal ring mixed convection with a heated inner cylinder equipped with two fins. Thermal buoyancy forces are maintained by considering the inner and outer cylinders at different uniform temperatures. The flow is generated by the rotation of the inner cylinder with a constant angular velocity (ω) in the counter-clockwise direction while the outer cylinder is held fixed. A finite volume scheme is adopted using the SIMPLE algorithm to solve the transport equations for continuity, momentum and energy. Simulations are made for various combinations of rotating Reynolds (Re = 0 to 1500) and Grashof numbers (Gr = 10 to 106). First, we focused on the criteria and parameters controlling the fully developed periodic regime. Thereafter, the heat transfer rates analyzed through the averaged Nusselt number (instant and over a period) highlights a complex phenomenon. For moderate Grashof numbers (Gr ≤ 103) the overall Nusselt number is not affected by Gr further, Re = 750 constitute a limit for the improvement of the heat transfer beyond which it decreases strongly. For larger Gr (>103), the reverse phenomenon occurs, i.e., the overall mean Nusselt number grows with Gr as Re < 750, then decreases for higher values.