Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

An experimental investigation of a superplastic constitutive equation in Al–Mg–Si alloy composites reinforced with Si3N4 whiskers

Superplastic properties at 818 K were investigated by tensile tests for Al–Mg–Si alloy composites reinforced with Si₃N₄ whiskers whose volume fractions were 0–30%. The 20 and 30 vol.% composites exhibited large elongation of 615 and 285% at a high strain rate of 2×10⁻¹ s⁻¹, respectively. High strain rate superplasticity of the composites is attributed to the very small grain size of less than 3 μm. The stress–strain rate relation for the composites was almost the same as that of the alloy, taking into consideration the influences of threshold stress and grain size, and the relation was independent of the volume fraction of whisker. This is probably because grain boundary sliding was not hampered by the whiskers due to the presence of liquid phase for the composites.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

Nonlinear Dynamics - In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19...     

Influence of nanoprecipitates on the creep strength and ductility of a Fe–Ni–Al alloy

Creep studies of a duplex Fe–Ni–Al intermetallic alloy, in two microstructural states, have been carried out at temperatures between 725 and 800 °C (about 0.6 T_m). In the as-cast state, the alloy contains a large volume fraction of nanoprecipitates (50–100 nm) which confer a very high creep strength with a stress exponent of 3 and an activation energy of 280 kJ/mol. The different microstructure obtained in the second state of the alloy, obtained after annealing at 1000 °C for 24 h, leads to a much lower creep strength with a higher stress exponent as well as a large value of the apparent activation energy. While volume diffusion appears to control creep in the as-cast state, both thermal and athermal processes seem to contribute to the different creep rate of material in the annealed state. The latter also exhibits a much larger ductility (12%) relative to that observed in the as-cast material (3%), due to the presence of large numbers of interfaces between the two phases present where strain incompatibilities can be accommodated.     

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of $30°~90°$. The Reynolds number ranges from 1000 to 50 000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within $30°~45°$under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.     

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

Numerical study of gas–solid two-phase flow and erosion in a cavity with a slope

Gate valve is mainly used to turn on or turn off the pipeline in pneumatic conveying. When the gate valve is fully open, the particles are easy to collide with the cavity rear wall and enter into the cavity, resulting in particles’ accumulation in the cavity. The particles in cavity will accumulate between the cavity bottom and the flashboard bottom wall and prevent the gate from turning off normally. Meanwhile, the particles’ collision with cavity rear wall will cause serious erosion. Both the particles’ accumulation and erosion will cause the poor sealing of the gate valve, further resulting in the leakage of the pipeline system. To reduce the particles’ accumulation in cavity and erosion on cavity when the gate valve is fully open, we simplify the gate valve into a cavity structure and study it. We find that adding a slope upstream the cavity can effectively reduce the particles’ accumulation in the cavity and the erosion on the cavity rear wall. In this work, Eulerian–Lagrangian method in commercial code (FLUENT) was used to study the gas–solid two-phase flow and erosion characteristics of a cavity with a slope. The particle distribution shows that the particles with Stokes number St = 1.3 and St = 13 cannot enter the cavity due to the slope, but the particles with St = 0.13 enter the cavity following the gas. For St = 13, the particles collide with the wall many times in the ideal cavity. Erosion results show that the slope can transfer the erosion on cavity rear wall to the slope and reduce the maximum erosion rate of the wall near the cavity to some degrees.     

Numerical simulation of hydrogen–air reacting flows in rectangular channels with catalytic surface reactions

In this work a prediction was numerically modeled for a catalytically stabilized thermal combustion of a lean homogeneous mixture of air and hydrogen. The mixture flows in a narrow rectangular channel lined with a thin coating of platinum catalyst. The solution using an in-house code is based on the steady state partial differential continuity, momentum and energy conservation equations for the mixture and species involved in the reactions. A marching technique is used along the streamwise direction to solve the 2-D plane-symmetric laminar flow of the gas. Two chemical kinetic reaction mechanisms were included; one for the gas phase reactions consisting of 17 elementary reactions; of which 7 are forward–backward reactions while the other mechanism is for the surface reactions—which are the prime mover of the combustion under a lean mixture condition—consisting of 16 elementary reactions. The results were compared with a former congruent experimental work where temperature was measured using thermocouples, while using PLIF laser for measuring water and hydrogen mole fractions. The comparison showed good agreement. More results for the velocities, mole fractions of other species were carried out across the transverse and along the streamwise directions providing a complete picture of overall mechanism—gas and surface—and on the production, consumptions and travel of the different species. The variations of the average OH mole fraction with the streamwise direction showed a sudden increase in the region where the ignition occurred. Also the rate of reactions of the entire surface species were calculated along the streamwise direction and a surface water production flux equation was derived by calculating the law of mass action’s constants from the concentrations of hydrogen, oxygen and the rate of formation of water near the surface.     

Numerical study of turbulent flow and heat transfer of Al2O3–water mixture in a square duct with uniform heat flux

Turbulent flow and convective heat transfer of a nanofluid made of Al₂O₃ (1–4 vol.%) and water through a square duct is numerically studied. Single-phase model, volumetric concentration, temperature-dependent physical properties, uniform wall heat flux boundary condition and Renormalization Group Theory k-ε turbulent model are used in the computational analysis. A comparison of the results with the previous experimental and numerical data revealed 8.3 and 10.2 % mean deviations, respectively. Numerical results illustrated that Nu number is directly proportional with Re number and volumetric concentration. For a given Re number, increasing the volumetric concentration of nanoparticles does not have significant effect on the dimensionless velocity contours. At a constant dimensionless temperature, increasing the particle volume concentration increases the size of the temperature profile. Maximum value of dimensionless temperature increases with increasing x/D_h value for a given Re number and volumetric concentration.     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.     

The characteristics of plastic flow and a physically-based model for 3003 Al–Mn alloy upon a wide range of strain rates and temperatures

The uniaxial compressive responses of 3003 Al–Mn alloy upon strain rates ranging from 0.001/s to about 10⁴/s with initial temperatures from 77 K to 800 K were investigated. Instron servohydraulic testing machine and enhanced split Hopkinson bar facilities have been employed in such uniaxial compressive loading tests. The maximum true strain up to 80% has been achieved. The following observations have been obtained from the experimental results: 1) 3003 Al–Mn alloy presents remarkable ductility and plasticity at low temperatures and high strain rates; 2) its plastic flow stress strongly depends on the applied temperatures and strain rates; 3) the temperature history during deformation strongly affects the microstructure evolution within the material. Finally, paralleled with the systematic experimental investigations, a physically-based model was developed based on the mechanism of dislocation kinetics. The model predictions are compared with the experimental results, and a good agreement has been observed.     

Numerical simulation of terrain-induced severe slugging coupled by hydrodynamic slugs in a pipeline–riser system

A numerical study based on a one-dimensional two-fluid model is carried out to describe the transient hydrodynamic slugging and terrain-induced severe slugging in a pipeline–riser system. The system of equations is rendered well-posed by interfacial pressure model for the riser. The selected flow conditions are restricted in the well-posed region for the horizontal and the downward inclined pipes to ensure the hydrodynamic slug characteristics are predicted correctly. The validity of the model is examined by water faucet problem and horizontal slug flow experiments. Simulations with and without slug capturing are conducted to address the effect of hydrodynamic slugs on severe slugging. It has been found that more accurate predictions are obtained by taking hydrodynamic slugs into account. At low superficial gas velocity, the simulation without slug capturing tends to overestimate the severe slugging period. When hydrodynamic slugs are captured, the upstream gas expansion is suppressed by the hydrodynamic slugs. At relatively high superficial gas velocity, the simulation without slug capturing tends to underestimate the severe slugging period. When hydrodynamic slugs are captured, the upstream compressible volume is greatly enlarged by the blowout of the hydrodynamic slugs. In both situations, the influences of the hydrodynamic slugs can reduce the errors of the predicted severe slugging characteristics.     

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m³ and a diameter of 5.0 × 10^?4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.     

Numerical simulation of shock–vortex interaction in Schardin’s problem

Shock diffraction over a two-dimensional wedge and subsequent shock–vortex interaction have been numerically simulated using the AUSM $+$ + scheme. After the passage of the incident shock over the wedge, the generated tip vortex interacts with a reflected shock. The resulting shock pattern has been captured well. It matches the existing experimental and numerical results reported in the literature. We solve the Navier–Stokes equations using high accuracy schemes and extend the existing results by focussing on the Kelvin–Helmholtz instability generated vortices which follow a spiral path to the vortex core and on their way interact with shock waves embedded within the vortex. Vortex detection algorithms have been used to visualize the spiral structure of the initial vortex and its final breakdown into a turbulent state. Plotting the dilatation field we notice a new source of diverging acoustic waves and a lambda shock at the wedge tip.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.     

Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid

This paper discusses the results of a study related to natural convection cooling of a heat source located on the bottom wall of an inclined isosceles triangular enclosure filled with a Cu water-nanofluid. The right and left walls of the enclosure are both maintained cold at constant equal temperatures, while the remaining parts of the bottom wall are insulated. The study has been carried out for a Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁶, for a heat source length in the range 0.2 ≤ ε ≤0.8, for a solid volume fraction in the range 0 ≤ ?≤0.06 and for an inclination angle in the range 0° ≤ δ≤45°. Results are presented in the form of streamline contours, isotherms, maximum temperature at the heat source surface and average Nusselt number. It is noticed that the addition of Cu nanoparticles enhances the heat transfer rate and therefore cooling effectiveness for all values of Rayleigh number, especially at low values of Ra. The effect of the inclination angle becomes more noticeable as one increases the value of Ra. For high Rayleigh numbers, a critical value for the inclination angle of δ = 15° is found for which the heat source maximum temperature is highest.