Fluids, Volume 7, Issue 12 (December 2022) – 28 articles

The effect of the excitation frequency of synthetic jet actuators on the mean jet velocity issuing from an array of circular orifices is investigated experimentally, focusing on the acoustic excitation characteristics of the actuator’s cavity. Two cavity configurations are considered. In the first configuration, synthetic jets are generated by exciting a single, large cavity having an array of sixteen orifices via sixteen piezoelectric elements. In the second configuration, the cavity volume of the first configuration is divided into eight isolated compartments, each with two orifices and two piezoelectric elements. Several distinct resonant peaks were observed in the frequency response of the synthetic jet actuator built with a single large-aspect-ratio cavity, whereas the case of compartmentalised cavities exhibited a single resonant peak. Acoustic simulations of the large-aspect-ratio-cavity volume showed that the multiple peaks in its frequency response correspond to the acoustic standing-wave mode shapes of the cavity. Due to its large aspect ratio, several acoustic mode shapes coexist in the excitation frequency range aside from the Helmholtz resonance frequency. When the actuator’s cavity volume is compartmentalised, only the Helmholtz resonance frequency is observed within the excitation frequency range. Full article

The development of portable electronic devices has increased; this development needs to be accompanied by the development of reliable power sources. In this study, two different vortex combustor sets were used in conjunction with a thermoelectric generator to determine their energy output. This study focuses on the development of a meso-scale vortex combustor to obtain the electric energy for a micro power generator; different materials and different vortex designs are analyzed. Numerical and experimental methods have been used to analyze the development of the vortex combustor. A horizontal vortex combustor made from stainless steel had higher wall temperature and voltage output measurements. To analyze the energy output for the micro power generator, a single TEG and double TEG are analyzed; according to the results, a double TEG with a water-cooled system has the highest electric power compared with the other results. Full article

This paper discusses accuracy improvements to Reynolds-Averaged Navier–Stokes (RANS) modeling of supersonic flow by assessing a wide range of factors for physics capture. Numerical simulations reveal complex flow behavior resulting from shock and expansion waves and so, a supersonic jet emanating from rectangular nozzle is considered. PIV based experimental data for the jet is available from literature and is used for validation purposes. Effect of various boundary conditions and turbulence modeling approaches is assessed qualitatively and quantitatively. Of particular interest are the inlet conditions considering the turbulence intensity and the effect of upstream air supply duct, the effect of nozzle wall surface roughness on nozzle internal flow and downstream, wall y+ sensitivity for boundary layer resolution and laminar to turbulent transition modeling. In addition to mesh sensitivity, domain dependency is conducted to evaluate the appropriate domain size to capture the kinetic energy dissipation downstream of the nozzle. To further improve the flow characteristics, accounting for the anisotropy of Reynolds stresses is also one of the focuses. Therefore, non-linear eddy viscosity-based two-equation model and Reynolds stress transport model are also investigated. Additionally, the results of baseline linear (Boussinesq) RANS are compared. Corresponding comparisons with high-fidelity LES are presented. Jet self-similar behavior resulting from all simulation fidelities is assessed and it appears that turbulent flow in LES becomes self-similar, but not in RANS. Finally, various factors such as the nozzle geometry and numerical modeling choices influencing the anisotropy in jet turbulence are discussed. Full article

The purpose of this work is to propose an advanced lubricant model of ILs used as additives to conventional oil. All-atoms molecular dynamics simulations are used to investigate the structure and tribology of oxidatively stable pure imidazolium-based ionic liquids (ILs), branched alkane low friction oil, and a mixture of ILs and oil confined between iron surfaces. Equilibrium and shear simulations are performed at a temperature of 450 K and undergo different applied loads and shear velocities to mimic engine operations. Density profiles reveal the formation of layered structures at the interface. The intensity and number of the density peaks vary according to the composition of the system and the applied pressure. Velocity profiles reveal the presence of no-slip conditions in the pure ILs system and very high slip for the oil. The presence of a stable IL layer at the surface of the mixed lubricant fully reduces the slip of oil. Overall, the mixture displays lower friction in comparison to pure ILs. The formed corrosion protective anion layer on the metal surface makes the mixture a potential candidate for a new generation of high-performance lubricants. Full article

For potential use in wastewater management and health control, this study investigates the disinfection effectiveness of bulk ultrafine bubbles (UFBs) with different bubble number densities and solution pH. Initially, neutral UFB solutions with different bubble concentrations were mixed with E. coli suspension for 120 min, but these solutions did not achieve sterilization. The bubble number density did not affect the disinfection ability of the neutral solution. Next, the pH of the UFB solutions was fixed at 5, 7, and 9. When mixed with E. coli suspension, the acidic UFB solutions reduced the colony counts by 12% after 30 min of cultivation and by 66% after 60 min of cultivation. The colony counts increased slightly in neutral and significantly in alkaline UFB solutions. The acidic UFB solutions had lower zeta potentials and smaller number densities after cultivation, implying that the number density reduced through bubble coalescence rather than increased by bubble collapse. Additionally, the UFBs exhibited insignificant fluorescence intensity, suggesting that the colony counts increased by generated ∙OH radicals. This study revealed that the effect of UFB on E. coli significantly depends on the solution pH. Further, an acidified solvent achieves a bactericidal effect, whereas a neutral or alkaline solvent enhances the growth effect. This result is important when using actual wastewater. Full article

Vibro-acoustic processes are an interacting set of pulsations of the working fluid and vibrations of mechanical structural elements. The simulation of vibro-acoustic processes in a long pipe with an elastic round cylinder is considered. The mathematical model is developed in a coupled formulation, when not only pressure pulsations cause pipe vibrations, but also vibrations of the mechanical subsystem affect sound wave propagation in the working fluid. The influence of vortex formation processes in the channel on the system dynamics is taken into account. The fluid flow is found using delayed detached eddy simulation. The flow regimes around a single round cylinder corresponding to various Reynolds numbers are investigated to validate the computational algorithm. The distributions of the flow quantities and vibro-acoustic behavior of the system are discussed. Full article

Polyatomic gases may be characterized by internal molecular degrees of freedom. As a consequence, at a macroscopic level, dynamic pressure appears, which may be related to the bulk viscosity of the gas. Inspired by the models of a single polyatomic gas with six fields, developed within rational extended thermodynamics (RET) and the kinetic theory of gases, this paper presents a six-field theory for the mixture of polyatomic gases. First, the macroscopic mixture model is developed within the framework of RET. Second, the mixture of gases with six fields is analyzed in the context of the kinetic theory of gases, and corresponding moment equations are derived. Finally, complete closure of the RET model, i.e., computation of the phenomenological coefficients, is achieved by means of a combined macroscopic/kinetic closure procedure. Full article

In this paper, we study the two-dimensional linear stability of a regularized Casson fluid (i.e., a fluid whose constitutive equation is a regularization of the Casson obtained through the introduction of a smoothing parameter) flowing down an incline. The stability analysis has been performed theoretically by using the long-wave approximation method. The critical Reynolds number at which the instability arises depends on the material parameters, on the tilt angle as well as on the prescribed inlet discharge. In particular, the results show that the regularized Casson flow has stability characteristics different from the regularized Bingham. Indeed, for the regularized Casson flow an increase in the yield stress of the fluid induces a stabilizing effect, while for the Bingham case an increase in the yield stress entails flow destabilization. Full article

A ground-penetrating radar (GPR) technology was developed to study the process of water drainage in sand layers with an insignificant concentration of dusty and clayey particles when moistened from above. The technology includes a method of calibration of the GPR equipment, algorithms for processing the GPR information, and their software implementation. The technology was used to process the results of laboratory GPR measurements obtained during draining of water through sand layers from different quarries for 100 h. The absolute values and the changes in the refractive index and specific conductivity near the sand layer upper boundary and on average over the layer depth were calculated. The results show that the developed technology makes it possible to determine electrophysical properties with an accuracy of up to 10%. The developed method for calculating relative reflectivity and its derivative with respect to the depth of the layer made it possible to visualize the information contained in the radargrams on the distribution of water near the surface and deep in the sand layers. The application of the method makes it possible to quantitatively estimate the moisture content near the upper boundary of the layer and the depth of the location of the most moistened areas of the layer depending on the duration of water drainage. Full article

The interaction of waves and currents with marine structures finds interesting applications, including the study of offshore and shoreline protection systems, as in the case of permeable breakwaters. The latter systems exhibit various benefits, including a decrease in wave run-up, reflected wave energy and load excitation, allowing for the propagation of part of the incident flow to the lee side, facilitating the improvement of water quality in the protected areas. The present work focuses on the modelling and numerical simulation of wave fields, interacting with arrays of vertical cylinders in the presence of currents. The problem is treated in the framework of potential theory in the frequency domain, assuming waves of small steepness, in conjunction with boundary integral formulation. Numerical results are presented and discussed, concerning the structure of the reflected and transmitted 3D flow fields, making the model suitable for optimization purposes; however, it presents increased computational cost. On the other hand, for small current velocities the problem can be approximately considered on the horizontal plane, modelled by the 2D Helmholtz equation with variable coefficients, which is numerically treated by a coupled BEM–FEM scheme. Numerical examples are presented, demonstrating that the latter model is cost-efficient, providing reasonable predictions, and can be used for the preliminary study of the hydrodynamic characteristics of the considered configurations and the support of the design. Full article

A Buckley–Leverett analysis with capillary pressure to model the oil displacement in fractal porous media is herein presented. The effective permeability for a non-Newtonian micellar fluid is calculated by a constitutive equation used to describe the rheological properties of a displacement fluid. The main assumption of this model involves a bundle of tortuous capillaries with a size distribution and tortuosity that follow fractal laws. The BMP model predicts two asymptotic (Newtonian) regions at low and high shear and a power-law region between the two Newtonian regions corresponding to a stress plateau. Both the stress at the wall and the fluidity are calculated using an imposed pressure gradient in order to determine the mobility of the solution. We analyze different mobility ratios to describe the behavior of the so-called self-destructive surfactants. Initially, the viscosity of the displacing fluid (micellar solution) is high; however, interactions with the porous media lead to a breakage process and degradation of the surfactant, producing low viscosity. This process is simulated by varying the applied pressure gradient. The resulting equation is of the reaction–diffusion type with various time scales; a shock profile develops in the convective time scale, as in the traditional Buckley-Leverett analysis, while at longer times diffusion effects begin to affect the profile. Predictions include shock profiles and compressive waves. These results may find application when selecting surfactants for enhanced oil recovery processes in oilfields. Full article

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation. Full article

Due to the high complexity of some treatments, there is a need to develop drug-delivery systems that can release multiple drugs/bioactive agents at different stages of treatment. In this study, a thermoresponsive injectable dual-release system was developed with gellan gum/alginate microparticles (GG:Alg) within a thermoresponsive Pluronic hydrogel composed of a mixture of Pluronic F127 and F68. The increase in F68 ratio and decrease in F127 lead to higher transition temperatures. The addition of the GG:Alg microparticles decreased the transition temperatures with a linear tendency. In Pluronic aqueous solutions (20 wt.%), the F127:F68 ratios of 16:4 and 17:3 (wt.%:wt.%) and the addition of microparticles (up to 15 wt.%) maintained the sol–gel transition temperatures within a suitable range (between 25 °C and 37 °C). Microparticles did not hinder the injectability of the system in the sol phase. Methylene blue was used as a model drug to evaluate the release mechanisms from microparticles, hydrogel, and composite system. The hydrogel delayed the release of methylene blue from the microparticles. The hydrogel loaded with methylene blue released at a faster rate than the microparticles within the hydrogel, thus demonstrating a dual-release profile. Full article

Wildland fires have become a major research subject among the national and international research community. Different simulation models have been developed to prevent this phenomenon. Nevertheless, fire propagation models are, until now, challenging due to the complexity of physics and chemistry, high computational requirements to solve physical models, and the difficulty defining the input parameters. Nevertheless, researchers have made immense progress in understanding wildland fire spread. This work reviews the state-of-the-art and lessons learned from the relevant literature to drive further advancement and provide the scientific community with a comprehensive summary of the main developments. The major findings or general research-based trends were related to the advancement of technology and computational resources, as well as advances in the physical interpretation of the acceleration of wildfires. Although wildfires result from the interaction between fundamental processes that govern the combustion at the solid- and gas-phase, the subsequent heat transfer and ignition of adjacent fuels are still not fully resolved at a large scale. However, there are some research gaps and emerging trends within this issue that should be given more attention in future investigations. Hence, in view of further improvements in wildfire modeling, increases in computational resources will allow upscaling of physical models, and technological advancements are being developed to provide near real-time predictive fire behavior modeling. Thus, the development of two-way coupled models with weather prediction and fire propagation models is the main direction of future work. Full article

This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal. Full article

On the basis of previous experimental and numerical studies, the windage operation of low-pressure turbine rear stage is investigated. The state of the steam within the rotor channel was correlated to measurements carried out downstream of the blades for different ventilation regimes. Considering very-low-volume flow conditions, the ventilation power was related to the drag force acting on the moving blades. A correlation was identified between the drag coefficient and a Reynolds number relative to the reverse flow height. This correlation can be used in order to predict the power loss of a last-stage moving blade operating at low load. Full article

With the improvement in wind turbine (WT) operation and maintenance (O&M) technologies and the rise of O&M cost, fault diagnostics in WTs based on a supervisory control and data acquisition (SCADA) system has become among the cheapest and easiest methods to detect faults in WTs.Hence, it is necessary to monitor the change in real-time parameters from the WT and maintenance action could be taken in advance before any major failures. Therefore, SCADA-driven fault diagnosis in WT based on machine learning algorithms has been proposed in this study by comparing the performance of three different machine learning algorithms, namely k-nearest neighbors (kNN) with a bagging regressor, extreme gradient boosting (XGBoost) and an artificial neural network (ANN) on condition monitoring of gearbox oil sump temperature. Further, this study also compared the performance of two different feature selection methods, namely the Pearson correlation coefficient (PCC) and principal component analysis (PCA), and three hyperparameter optimization methods on optimizing the performance of the models, namely a grid search, a random search and Bayesian optimization. A total of 3 years of SCADA data on WTs located in France have been used to verify the selected method. The results showed the kNN with a bagging regressor, with PCA and a grid search, provides the best R² score, and the lowest root mean square error (RMSE). The trained model can detect the potential of WT faults at least 4 weeks in advance. However, the proposed kNN model in this study can be trained with the Support Vector Machine hybrid algorithm to improve its performance and reduce fault alarm. Full article

Passive flow control techniques are needed to reduce flow separation and enhance aerodynamic performance. In this work, the effect of a knitted wire mesh on the flow separation of a backward-facing ramp was numerically investigated for a Reynolds number of 3000. A grid independence study and a RANS turbulence model sensitivity analysis were conducted. The CFD simulations exhibited counter-rotating streamwise vortices emerging from the knitted wire mesh, and the reattachment length was significantly reduced. A variation of the knitted wire rows revealed a maximum reduction of the reattachment length of 25.7% for the case of four rows. A comparison with a different knitted wire mesh geometry yielded a decreased reattachment length reduction. Full article

The numerical calculation of local mass distributions in membrane systems by computational fluid dynamics (CFD) offers indispensable benefits. However, the concept to calculate such distributions in response to separate variations of operation conditions (OCs) makes it difficult to address overall, flow-physics-related questions, which require the consideration of the collective interaction of OCs. It is shown that such understanding-related relationships can be obtained by the analytical solution of the advection–diffusion equation considered. A Fourier series model (FSM) is presented, which provides exact solutions of an advection–diffusion equation for a wide range of OCs. On this basis, a new zeroth-order model is developed, which is very simple and as accurate as the complete FSM for all conditions of practical relevance. Advection-dominated blocked and diffusion-dominated unblocked flow regimes are identified (depending on a Péclet number which compares the flow geometry with a length scale imposed by the flow), which implies relevant requirements for the use of lab results for pilot- and full-scale applications. Analyses reveal the equivalence of variations of OCs, which offers a variety of options to accomplish desired flow regime changes. Full article

Hybrid RANS-LES methods are supposed to provide major contributions to future turbulent flow simulations, in particular for reliable flow predictions under conditions where validation data are unavailable. However, existing hybrid RANS-LES methods suffer from essential problems. A solution to these problems is presented as a generalization of previously introduced continuous eddy simulation (CES) methods. These methods, obtained by relatively minor extensions of standard two-equation turbulence models, represent minimal error simulation methods. An essential observation presented here is that minimal error methods for incompressible flows can be extended to stratified and compressible flows, which opens the way to addressing relevant atmospheric science problems (mesoscale to microscale coupling) and aerospace problems (supersonic or hypersonic flow predictions). It is also reported that minimal error methods can provide valuable contributions to the design of consistent turbulence models under conditions of significant modeling uncertainties. Full article

The demand for wind energy harvesting has grown significantly to mitigate the global challenges of climate change, energy security, and zero carbon emissions. Various methods to maximize wind power efficiency have been proposed. Notably, neural networks have shown large potential in improving wind power efficiency. In this paper, we provide a review of attempts to maximize wind power efficiency using neural networks. A total of three neural-network-based strategies are covered: (i) neural-network-based turbine control, (ii) neural-network-based wind farm control, and (iii) neural-network-based wind turbine blade design. In the first topic, we introduce neural networks that control the yaw of wind turbines based on wind prediction. Second, we discuss neural networks for improving the energy efficiency of wind farms. Last, we review neural networks to design turbine blades with superior aerodynamic performances. Full article

The development of energy-efficient solutions for large-scale fermenters demands a deep and comprehensive understanding of hydrodynamic and heat and mass transfer processes. Despite a wide variety of research dedicated to measurements of mass transfer intensity in bubble flows, this research subject faces new challenges due to the topical development of new innovative bioreactor designs. In order to understand the fluid dynamics of the gas–liquid medium, researchers need to develop verified CFD models describing flows in the bioreactor loop using a progressive physical and mathematical apparatus. In the current paper, we represent the results of evaluating the key performance indicator of the bioreactor, namely the volumetric mass transfer coefficient (${\mathrm{k}}_{\mathrm{L}}\mathrm{a}$) known as a parameter of dominant importance for the design, operation, scale-up, and optimization of bioreactors, using the developed thermometry method. The thermometry method under consideration was examined within a series of experiments, and a comparative analysis was provided for a number of various regimes also being matched with the classical approaches. The methodology, experiment results, and data verification are given, which allow the evaluation of the effectiveness and prediction of the fluid flows dynamics in bioreactors circuits and ultimately the operational capabilities of the fermenter line. Full article

Bubble formation and dissolution have a wide range of industrial applications, from the production of beverages to foam manufacturing processes. The rate at which the bubble expands or contracts has a significant effect on these processes. In the current work, the hydrodynamics of an isolated bubble expanding due to mass transfer in a pool of supersaturated gas–liquid solution is investigated. The complete scalar transportation equation (advection–diffusion) is solved numerically. It is observed that the present model accurately predicted bubble growth when compared with existing approximated models and experiments. The effect of gas–liquid solution parameters such as inertia, viscosity, surface tension, diffusion coefficient, system pressure, and solubility of the gas has been investigated. It is found that the surface tension and inertia have a very minimal effect during the bubble expansion. However, it is observed that the viscosity, system pressure, diffusion, and solubility have a considerable effect on bubble growth. Full article

Numerous problems occur during engine operation, such as start-up, lack of lubrication, and overheating, resulting in engine components’ wear, power loss, and fuel consumption. Nanomaterials dispersed in engine oil can play an important role in improving the tribological properties of oil lubricants. This study investigated the influence of multi-walled carbon nanotubes (MWCNTs) and aluminum oxide nanoparticles (Al₂O₃ NPs) as nano-additives for lubricants. Different engine oil samples were loaded with 0.5–2.0 wt% Al₂O₃ NPs and 0.5–1.0 wt% MWCNTs and compared with unmodified oil. The tribological performance of the nano lubricants was investigated using the four-ball test method. In addition, the wear scar in the engine was evaluated using 3D micrographs and scanning electron microscopy (SEM). The results of the sliding surfaces with hybrid MWCNTs/Al₂O₃ NPs showed better friction performance and wear resistance. The coefficient of friction (COF) and wear scar width were improved by 47.9% and 51.5%, respectively, compared with unmodified oil. Full article

Supercavitation technology has important application value in military and national defence fields because of its huge potential in drag reduction, while the cavitation around underwater moving objects may be affected by the surface properties of objects. In this paper, the supercavitation characteristics and hydrodynamics of a projectile with hydrophobic and hydrophilic surface coatings were experimentally studied using a high-speed camera. The supercavitation evolution, cavitation size, velocity change, drag force coefficient, and ballistic deflection of projectiles in different water depths are compared and analyzed. The results show that the length and diameter of the supercavity increase with the decrease in water depth. At the same water depth and cavitation number, the length and diameter of the supercavitation of the projectile with hydrophobic coating were greater than those of the projectile with hydrophilic coating, and the drag force coefficient of the hydrophobic projectile was obviously smaller than that of the hydrophilic projectile. Under the working conditions of 6.67D, 16.7D, and 33.3D, the drag force coefficient of the hydrophobic projectile could be reduced by about 20–40% compared with that of the hydrophilic projectile. The maximal reduction in drag force coefficient was up to 40% at $\sigma$ = 0.34 under a water depth of 33.3D. The velocity attenuation of hydrophobic projectile was about 20% slower than that of hydrophilic projectile. In addition, the ballistic stability of hydrophobic coated projectiles was better than that of hydrophilic coated projectiles in the different water depths observed in the paper. Full article

Characterization of unsteady loads is critical for the development of control systems for next-generation air vehicles. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) methods are prohibitively expensive, and existing Reynolds-Averaged Navier-Stokes (RANS) approaches have been shown to be inadequate in predicting both mean and unsteady loads. In recent years, scale-resolving methods, such as Partially Averaged Navier-Stokes (PANS) and Detached Eddy Simulation (DES), have been gaining acceptance and filling the gap between RANS and LES. In this study, we focus on a new variant of the PANS method, namely blended PANS or BPANS, which was shown to perform well in the incompressible regime for both wall-bounded and free shear flows. In this paper, we extend BPANS to compressible supersonic flows by adding a compressibility correction, leading to a new model called BPANS CC. The new model is tested using a well-known supersonic mixing layer case, and the results show good agreement with experimental data. The model is then used on a complex supersonic retropropulsion case and the results are in good agreement with experimental data. Full article

Nonlinear free convection in an inclined rectangular porous cavity heated from below has been studied using a two-dimensional spectral decomposition. The code uses pseudo-arclength continuation to follow solution curves around fold bifurcations. The evolution with inclination of the pattern of convection is complicated and it relies strongly on both the Darcy–Rayleigh number and the aspect ratio of the cavity. When the inclination is large it is generally true that only one cell appears, and that it has a circulation that is consistent with the direction of the buoyancy forces along the heated and cooled boundaries. However, as the inclination decreases back towards the horizontal, this unicellular pattern evolves, sometimes initially via fold bifurcations, into patterns with different numbers of cells. Such evolutions always conserve the parity of the number of cells (such as one cell becoming three and then five, or two cells becoming four), but bifurcations also arise between patterns with different parities. These phenomena are illustrated using a suitable selection of solution curves that show the dependence of the Nusselt number on the inclination. Full article

The oleo-pneumatic shock absorber involves a complex two-phase flow in the working process. In this paper, a simple oleo-pneumatic shock absorber model was established, and the volume-of-fluid (VOF) two-phase flow model was adopted to accurately simulate the distribution of the two-phase flow field in the shock absorber through the commercial software FLUENT 2020 R2. The accuracy of the simulation model was verified by the method of engineering damping force estimation, and the error of the numerical simulation results compared with the engineering estimation results was 7–8%. By numerical simulation, the influence of different orifice lengths and diameters on the maximum pressure, temperature, velocity and oil damping force inside the shock absorber was studied. The results showed that with the increase of the orifice length, the maximum pressure, flow rate and oil damping force in the shock absorber decreased. The temperature decreased first and then increased, but the overall effect was small. However, according to the oil volume fraction contour, the gas–liquid distribution in the shock absorber with an orifice larger than 15 mm was more chaotic. Increasing the diameter of the orifice had a great impact on the shock absorber. The maximum pressure, flow rate and damping force of the oil inside the shock absorber were sharply reduced, and the temperature continued to rise. These research results can provide reference for the optimization design of oleo-pneumatic shock absorbers. Full article