Three-dimensional Numerical Simulations Research Articles

A Comparison Between Conventional and MILD Combustion Processes of Turbulent Stratified Mixtures

ABSTRACT The relative enhancements of volume-integrated burning rate and flame surface area under turbulence and heat release rate contributions due to different combustion and flame propagation modes have been compared between conventional and Moderate or Intense Low Oxygen Dilution (MILD) combustion of stratified mixtures (for a global mean equivalence ratio of 0.8) for the first time using three-dimensional Direct Numerical Simulation (DNS) data. The burning rate enhancement under turbulence is found to be comparable to the enhancement of flame surface area for the conventional stratified flames considered here, whereas the burning rate enhancement is found to be considerably greater than flame area augmentation in the MILD cases analyzed here. It has been found that almost all the heat release rate arises due to the lean-premixed mode of combustion for the conventional stratified flame cases considered here. In contrast, the lean premixed mode of combustion accounts for about 50% of the total heat release rate for the MILD cases where rich-premixed and non-premixed modes of combustion contribute significantly to the overall heat release rate. Under the conditions analyzed here, more than 75% of heat release rate arises from the propagation-dominated regions for both MILD combustion and stratified flame cases, but the trend is stronger in the conventional stratified mixture combustion. More than 80% of heat release rate in the globally lean conventional stratified flame cases considered here originates from back-supported flame propagation, whereas both front and back-supported flame propagation modes have comparable contributions to heat release in the MILD combustion cases. The non-premixed mode of combustion has been found to play a more important role in the MILD combustion cases than in the case of conventional stratified flames. This implies that the closures, which work reasonably well for MILD combustion of homogeneous mixtures, may not be sufficient for modeling of MILD combustion of stratified/inhomogeneous mixtures.

Investigation of torsion in asymmetric mid-rise structures on the pile-raft system considering soil-structure interaction

The adverse conditions of the soil such as soft soil can have seismic consequences that may either amplify seismic response or render the structure vulnerable. On one hand, the design and construction of asymmetric structures have become prevalent due to aesthetic considerations and structural space limitations. Studies indicate that structures with geometric irregularities are susceptible to seismic forces, leading to non-uniform distribution of floor drifts, excessive torsional behavior, and more, depending on the degree of irregularity. In this research, the main goal was to investigate the effect of soil and structure interaction on the torsion of asymmetric Mid-Rise Structures. To achieve this goal two asymmetric Steel moment frame system 15-story structures aim to address the effect of interaction between soil and structure on the seismic performance, one with a rigid base and the other with a flexible base, one with a rigid base and the other with a flexible base. To mitigate the settlement of soil-associated structures, a pile-raft system is employed, considering the softness of the soil. Additionally, to study the torsional behavior of these structures, their planes are asymmetrically designed in L-shape and C-shape configurations, subjected to four ground motion excitations in both far and near-field scenarios. Three-dimensional finite element numerical simulations are performed using Abaqus software. Various configurations of the pile-raft system for the asymmetric C-shape structure are examined to assess the effects of pile diameter and length on the torsional irregularity coefficient. The results show that the soil-structure interaction increases the maximum floor rotation angle, placing these structures in critical conditions concerning torsional irregularity under near-field and far-field seismic excitations.

Ammonia energy fraction effect on the combustion and reduced NOX emission of ammonia/diesel dual fuel

With stringent regulations of internal combustion engine on reducing CO2 emission, ammonia has been used as an alternative fuel. Investigating how engine-related performance is affected by partial ammonia replacement of diesel fuel is essential for understanding the combustion. Therefore, in this study, a three-dimensional numerical simulation model is developed for the burning of two fuels of diesel and ammonia based on relevant parameters (i.e., compression ratio, load, ammonia energy fraction, etc.) in a lab-made diesel engine. The consequences of load and compression proportion on combustion and pollutant emissions are investigated for ammonia energy fractions between 50% and 90%. When the ammonia portion rises, the increased ammonia equivalent ratio causes ammonia to move away from the dilute combustion boundary and accelerates the combustion rate of ammonia. An increase in compression ratio significantly increases the specified thermal performance and combustion efficacy. When the compression ratio is 16, as the ammonia energy fractions increases, due to the increase in the proportion of ammonia, that is, the proportion of nitrogen atoms increases, more NOx is generated during the combustion process. When the ammonia substitution rate is 90%, as the compression ratio increases, the cylinder pressure and temperature increase. The combustion efficiency of ammonia increases, generating more NOx and NOx emissions can reach 0.66 mg/m3. At a compression ratio of 18, the NOx emissions can reach 1.59 mg/m3. However, under medium and low load conditions, as the ammonia fraction increases, the total energy of fuel decreases, and the combustion efficiency of ammonia decreases, resulting in a decrease in the heat released during combustion and a decrease in NOx emissions. When the ammonia substitution rate is 90% and the load is 25%, NOx emissions reach 0.1 mg/m3. This research provides theoretical suggestions for the profitable and use ammonia fuel in internal combustion engines in a clean manner.

Influence of porous media and substrate rotation on AlN growth in MNVPE reactors based on CFD simulations

AlN is an important III-V wide-bandwidth semiconductor material. Its maximum (ultra-wide) direct bandgap of up to 6.2 eV at room temperature and excellent physical properties make it have great application prospects in the fields of high-power high-frequency electronics and high-efficiency optoelectronic devices. In this paper, based on Computational Fluid Dynamics (CFD), the finite volume method was employed to investigate the process of growing AlN thin films by MNVPE using CFD simulation software for three-dimensional numerical simulation. By optimizing the chamber structure, it was devoted to improving the growth rate and uniformity of AlN thin films. Different thicknesses of porous media were placed in front of the substrate respectively, and the flow field analysis showed that the presence of eddy currents can be effectively suppressed to reduce the pre-reaction, and the best growth effect was achieved when the thickness reached 7 cm. With the increasing of porosity, more gas reached the substrate surface and improved the growth rate of AlN films. Secondly, for the 90° substrate, substrate rotation created a pumping effect and the growth rate was higher with the increase of the rotation speed. At 160 rpm, the growth rate reached 11.29 μm/h and the coefficient of variation decreased to less than 5 %.

Influence of porous media and substrate rotation on AlN growth in MNVPE reactors based on CFD simulations

AlN is an important III-V wide-bandwidth semiconductor material. Its maximum (ultra-wide) direct bandgap of up to 6.2 eV at room temperature and excellent physical properties make it have great application prospects in the fields of high-power high-frequency electronics and high-efficiency optoelectronic devices. In this paper, based on Computational Fluid Dynamics (CFD), the finite volume method was employed to investigate the process of growing AlN thin films by MNVPE using CFD simulation software for three-dimensional numerical simulation. By optimizing the chamber structure, it was devoted to improving the growth rate and uniformity of AlN thin films. Different thicknesses of porous media were placed in front of the substrate respectively, and the flow field analysis showed that the presence of eddy currents can be effectively suppressed to reduce the pre-reaction, and the best growth effect was achieved when the thickness reached 7 cm. With the increasing of porosity, more gas reached the substrate surface and improved the growth rate of AlN films. Secondly, for the 90° substrate, substrate rotation created a pumping effect and the growth rate was higher with the increase of the rotation speed. At 160 rpm, the growth rate reached 11.29 μm/h and the coefficient of variation decreased to less than 5 %.

Chaotic Transport of Solutes in Unsaturated Porous Media.

Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Three-dimensional numerical simulation of a cylindrical oscillating water column (OWC) device placed in a wave flume

A three-dimensional computational fluid dynamic (CFD) model is developed for simulating a cylindrical Oscillating Water Column (OWC) device for harvesting wave energy. The single-phase CFD model solves the Reynolds-Averaged Navier-Stokes (RANS) equations using the finite element method for simulating the wave motion and uses an aerodynamic model to simulate the flow through the air turbine. The model is implemented to simulate wave energy harvesting of a cylindrical OWC device. Through harmonic decomposition, it is found that the first harmonic wave surface elevation oscillates like a piston in the OWC chamber. However, both the amplitude and phase of the second harmonic wave surface elevation vary significantly along the wave direction in the OWC chamber, demonstrating a sloshing mode of the second harmonic. This study further proved the reduction of the capture width ratio caused by the transverse sloshing mode when the wavelength is the same as the wave flume width. The effect of the width of the wave flume on the peak CWR is found to be negligibly small when the wave flume width is three times the OWC diameter.

Research on the influence of system drainage holes on the head loss of water transmission systems

Abstract To ensure the structural safety of the thin lining structure of the tailwater tunnel, this study used three-dimensional flow field numerical simulation technology to conduct an in-depth analysis of the drainage holes set along the tunnel body, to evaluate the impact of drainage holes on the overall and local head loss of the tunnel under different system layout types. It aims to provide scientific theoretical support and practical reference for engineering design and achieve more efficient and stable tunnel hydraulic operation conditions.

Direct numerical simulations of pure and partially cracked ammonia/air turbulent premixed jet flames

Ammonia has been identified as a promising fuel to diminish greenhouse gas emission. However, ammonia combustion presents certain challenges including low reactivity and high NO emission. In the present study, three-dimensional direct numerical simulations (DNS) of ammonia/air premixed slot jet flames with varying Karlovitz numbers (Ka) and cracking ratios were performed. Three cases were considered, including two pure ammonia/air flames with different turbulence intensities and one partially cracked ammonia/air flame with high turbulence intensity. The effects of turbulence intensity and partial ammonia cracking on turbulence–flame interactions and NO emission characteristics of the flames were investigated. It was shown that the turbulent flame speed is higher for the flames with high turbulence intensity. In general, the flame displacement speed is negatively correlated with curvature in negative curvature regions, while the correlation is weak in the positive curvature regions for highly turbulent flames. Most flame area is consumed in negatively curved regions and produced in positively curved regions. It was found that the NO mass fraction is higher in the flame with partial ammonia cracking compared to the pure ammonia/air flames. The NO pathway analysis shows that the NH → NO pathway is enhanced, while the NO consumption pathway is suppressed in the partially cracked ammonia/air flame. The NO mass fraction is higher in regions of negative curvature than positive curvature. Interestingly, the NO mass fraction is found to be negatively correlated with the local equivalence ratio, which is consistent in both the DNS and the corresponding laminar premixed flames.

Analysis of damage characteristics of the rectangular steel container under near-earth explosion loading

In this study, the dynamic response of a semi-buried steel vessel under a near-surface explosion shock load was investigated through full-scale model tests. A three-dimensional precise numerical simulation model of the semi-buried steel vessel structure was established, and the dynamic response and damage consequences under different load conditions were analyzed. The influence of the thickness of corrugated steel on the dynamic damage and antiknock properties of the structure was studied. The results show that the weak part of the rectangular steel vessel structure is mainly located at the connection between the blast-facing panel and the beam column under near-surface explosion conditions. The peak stress and displacement of the blasting surface decrease with the increase in the horizontal angle of the incident wave, whilst/while increase with the height of the explosion. Under the same explosive yield, the main failure mode of the structure is the tearing of the plate and beam under plastic deformation. Increasing the thickness of the corrugated steel can significantly restrain the plastic deformation and acceleration of the plate. When the thickness is increased from 2mm to 6mm, the antiknock performance is significantly improved. However, when the thickness is increased from 6mm to 8mm, the improvement in antiknock performance slows down. Increasing the height of the enclosing soil can also effectively improve the explosion-proof performance of the structure, with full burial providing the best effect. The research results provide a theoretical basis for the application of rectangular steel vessel structures in the field of protection engineering.

Study on the Influence of Working Characteristics of Centripetal Pump Based on VOF/Mixture Model

Aviation fuel contamination can seriously affect aircraft flight safety, and the centripetal pump is the core component of aviation fuel purification equipment. The performance of centripetal pumps is highly demanded for purification equipment. The operating parameters of centripetal pumps significantly affect the internal flow characteristics, which affects the performance of centripetal pumps. However, the flow characteristics of a centripetal pump influenced by the operating parameters have not yet been elaborated upon. In this research, a three-dimensional numerical simulation of the air-fuel two-phase flow field inside a centripetal pump was carried out using the VOF/Mixture model to investigate the effects of three relatively independent physical quantities, namely, fuel flow, outlet fuel discharge pressure, and rotational speed, on the operating characteristics of the centripetal pump. The flow law inside the flow channel of a centripetal pump was analyzed based on a rotating fluid pressure model, the free liquid surface radius of air-fuel, and the total pressure recovery coefficient. It was found that centripetal pumps have a steady working state and an unsteady working state. In a steady working state, the proportion of separated zones in the flow channel of the centripetal pump is small, the flow coefficient C of the flow channel is greater than 1, and the total pressure recovery coefficient of the centripetal pump is high. In an unsteady working state, the separation zone in the flow channel of the centripetal pump accounts for a large proportion, the flow channel flow coefficient C is less than 1, and the total pressure recovery coefficient of the centripetal pump is low. An unsteady working state can easily occur in small flow, high-speed conditions. By analyzing the working state and flow characteristics of the centripetal pump, the mechanism of the influence of the flow, outlet fuel discharge pressure, and rotational speed on the working state of the centripetal pump is revealed, which provides a basis for the stable operation of the centripetal pump.

The Spatial Development Characteristics of High-Pressure Methane Jet Impinging on Methane Lean-Burn Premixed Flame

This work investigated the effect of high-pressure (10 MPa) methane gas jet impinging on the methane lean-burn premixed flame (equivalent ratio of 0.7) based on a three-dimensional numerical simulation by CONVERGE software. The results show that laminar premixed flame is accelerated to develop into a stable turbulent flame under the action of the methane jet, the whole process of flame front development is divided into three stages: laminar (Reynolds number maintains stable, 1–1.3 ms), transition (Reynolds number shows an increasing trend, 1.4–8 ms), and turbulent (Reynolds number tends to stabilize at a high value, 1.9–3 ms). The effect of high-pressure jet on flame development along jet direction (Z axis) is greater than that on vertical direction (Y axis). During turbulence stage, the momentum and kinetic energy of Z axis are 2.7 and 6.3 times greater than that of Y axis, respectively. The high-pressure methane jet causes a change in heat distribution, resulting in local flameout. The rate of change in the local flameout area is greater than that in the flame area, causing a temperature drop in Z axis. This temperature drop increases with the increase in equivalence ratio and with the decrease in distance between cross-section position and ignition center.

Nonlinear spatiotemporal characteristics of wind–rain flow around the trains passing through the tunnel entrance during rainstorms

Tropical storms present a significant risk to the safety of high-speed trains due to the extreme wind and rainfall they bring. This study employs Eulerian multiphase and Shear-Stress Transport k-ω turbulence models for three-dimensional numerical simulations, focusing on wind–rain interactions involving tunnels, embankments, and trains. The reliability of the numerical analysis method for train slipstream pressure is verified by dynamic model test. Based on the scenario of single train running on the embankment and train intersection at the tunnel portal, the train flow around and wake are analyzed successively with different rainfall intensity. The characteristics of nonlinear wind–rain-train flow field are analyzed from the aspects of velocity field, pressure field and turbulent flow. Finally, the mechanism of the influence of rain on the relative flow field is revealed by the spatiotemporal distribution characteristics of rain phase. With the increase of rainfall intensity, the increase of rain phase distribution on the leeward side of the single train strengthened the backflow on the leeward side of the train. Under the condition of the trains intersecting at the tunnel portal, the relatively closed area between the train and the water film weakened the slipstream effect of the train.

Interaction characteristics between the large ship-rubber fenders-wharf structure in deep-water considering the flexibility of the wharf structure

High pile-supported wharf structures in offshore deep water have significant flexibility due to long free ends and large slenderness ratios of the pile bodies, resulting in substantial deformation of the pile body under kinds of loads. In the design of this new type of wharves, it is expected to consider the characteristic of elastic deformation of pile body absorbing a portion of the ship impact energy reasonably. However, the existing calculation method still adopts the theoretical formulas of traditional wharf structures, failure to incorporate this advanced design concept fully. In order to solve this, firstly, a comprehensive three-dimensional numerical simulation model encompassing large ship, rubber fenders and wharf structure, was developed using Ansys/LS-Dyna, and the calculation model was validated against the existing research results. Subsequently, dynamic response characteristics of wharf structures during the normal berthing of ships were examined meticulously, and the variations in absorption energy and reaction forces of rubber fenders and wharf structures were analyzed systematically. And then the analysis results were compared with previous research, the limitations of the existing design code for wharf structures were discussed as well. Finally, the findings demonstrate that peak values of absorption energy and energy transfer times increase with the increase of ship loading capacities. And the elastic deformation of the wharf structure indeed absorbs considerable partial of the impact energy effectively, with about 30 % for conditions in this study, leading to lower impact forces acted on the wharf structure. Moreover, the maximum pile top displacement of the wharf structure is also smaller than that reported in the existing literature in the same load condition, indicating that considering the structural flexibility in the design of this new type of wharf structure is more in line with reality, and it is more reasonable and economical as well.

Fingering convection in a spherical shell

We use $123$ three-dimensional direct numerical simulations to study fingering convection in non-rotating spherical shells. We investigate the scaling behaviour of the flow length scale, the non-dimensional heat and compositional fluxes $Nu$ and $Sh$ and the mean convective velocity over the fingering convection instability domain defined by $1 \leq R_\rho < Le$ , $R_\rho$ being the ratio of density perturbations of thermal and compositional origins and $Le$ the Lewis number. We show that the chemical boundary layers are marginally unstable and adhere to the laminar Prandtl–Blasius model, hence explaining the asymmetry between the inner and outer spherical shell boundary layers. We develop scaling laws for two asymptotic regimes close to the two edges of the instability domain, namely $R_\rho \lesssim Le$ and $R_\rho \gtrsim 1$ . For the former, we develop novel power laws of a small parameter $\epsilon$ measuring the distance to onset, which differ from theoretical laws published to date in Cartesian geometry. For the latter, we find that the Sherwood number $Sh$ gradually approaches a scaling $Sh\sim Ra_\xi ^{1/3}$ when $Ra_\xi \gg 1$ ; and that the Péclet number accordingly follows $Pe \sim Ra_\xi ^{2/3} |Ra_T|^{-1/4}$ , $Ra_T$ and $Ra_{\xi}$ being the thermal and chemical Rayleigh numbers. When the Reynolds number exceeds a few tens, we report on a secondary instability which takes the form of large-scale toroidal jets which span the entire spherical domain. Jets distort the fingers, resulting in Reynolds stress correlations, which in turn feed the jet growth until saturation. This nonlinear phenomenon can yield relaxation oscillation cycles.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

The vortex-induced vibrations of two side-by-side flexible cylinders in a uniform flow were studied using a three-dimensional direct numerical simulation at Reynolds number Re = 350 with an aspect ratio of 100, and a center-to-center spacing ratio of 2.5. A mixture of standing-traveling wave pattern was induced in the in-line (IL) vibration, while the cross-flow (CF) vibration displayed a standing-wave characteristic. The ninth vibration mode prominently occurred in both IL and CF directions, along with competition between multiple modes. Proximity effects from the neighboring cylinder caused the primary frequency to be consistent between IL and CF vibrations for each cylinder, deviating from the IL to CF ratio of 2:1 in isolated cylinder conditions. Repulsive mean lift coefficients were observed in both stationary and vibrating conditions for the two cylinders due to asymmetrical vortex shedding in this small gap. Comparatively, lift and drag coefficients were notably increased in the vibrating condition, albeit with a lower vortex shedding frequency. Positive energy transfer was predominantly excited along the span via vortex shedding from the cylinder itself and the neighboring one, leading to increasing lower-mode vibration amplitudes. The flip-flopping (FF) wake pattern was excited in the stationary and vibrating cylinders, causing spanwise vortex dislocations and wake transition over time, with the FF pattern being more regular in the stationary cylinder case.

Cavitation mitigation via curvilinear barriers in centrifugal pump

Cavitation is a significant problem in hydraulic machinery that leads to the deterioration of hydraulic performance, material damage, and flow instability. While current methods partially address cavitation instability, there is a lack of comprehensive understanding of the control mechanisms. This study focuses on controlling cavitation flow instability in a centrifugal pump by proposing an active method using obstacles on the blade's surface. A low-specific speed centrifugal pump was chosen as the research object, and a three-dimensional unsteady full-flow channel numerical simulation was conducted. The findings indicate that in the absence of cavitation, the wake vortex induced by obstacles increases energy loss in the centrifugal pump, resulting in a slight drop in efficiency. However, when cavitation occurs, the obstacles effectively improve the flow field, reduce the vortex strength near the back of the blade in the flow channel, and significantly reduce the growth rate of cavitation volume. This reduction is observed in both the cavitation volume and its first derivative. Thus, the obstacles optimize the flow structure, reduce vortex strength, and slow the growth rate of cavitation. The main control mechanism involves inducing high-pressure waves to collapse cavities and improving flow transition characteristics. To solve the inverse problem of cavitation control with obstacles inside a centrifugal pump, dimensionless geometric parameters are studied to determine better suppression effects.

Numerical study of a CO2 swirl ejector with lubricating oil

At present, most simulations of ejectors ignore the presence of lubricating oil, which may affect the accuracy of the results. Additionally, there has been less research conducted on the influence of motive nozzles with swirl generators on the performance of ejectors. In this study, a heterogeneous mixture model was developed for a three-phase swirl ejector equipped with a motive nozzle featuring a swirl generator. This article examines the performance of swirl ejectors under supercritical conditions using three-dimensional numerical simulations conducted in ANSYS. The study explores swirl ejectors with varying helical angles of 77°, 64°, 58°, 50°, 37° . The study also takes into account the influence of lubricating oil to enhance the practicality of the research. Firstly, lubricating oil with a volume fraction of 2 % was introduced into both the motive and suction streams, followed by conducting an ejection analysis. The results indicate that the swirl enhances the entrainment ratio, and the swirl strength can be modified by changing the helical angle. A smaller helical angle results in greater swirl strength and a higher entrainment ratio. When the helical angle is 37° and the helical pitch is 20 mm, a swirl number of 0.42, an entrainment ratio of 0.998, and an effective entrainment ratio of 0.863 is achieved. However, when the oil circulation ratio in the suction stream is increased from 2 % to 10 % while keeping the oil circulation ratio of the motive stream constant, the entrainment ratio decreases.

Optimization Design Method of 2D + 3D Slope Shape for Landslide Prevention in Open-Pit Coal Mine

In order to improve the stability of the slope and prevent the occurrence of landslide disasters, taking the east slope of the first mining area of Zhundong Open-pit Coal Mine as the engineering background, a combination of the two-dimensional limit equilibrium method and three-dimensional numerical simulation is used to optimize the shape of the east slope. By selecting a typical calculation profile based on the Bishop method and the residual thrust method in the two- dimensional rigid body limit equilibrium method, the stability analysis of the profile slope is carried out, and the slope shape of the profile position meeting the requirements of the safety reserve coefficient and stripping ratio is preliminarily designed. Based on the three-dimensional finite element strength reduction method, aiming at the slope shape that does not meet the requirements of safety reserve coefficient and stripping ratio, the width of the transport plate is reasonably changed, and a three-dimensional numerical simulation model of various schemes is established. The influence of different tracking distances and slope angles on slope stability is studied. The three-dimensional stability of the slope under different spatial forms is calculated, and the optimal tracking distance and optimal slope angle are determined. The slope stability and stripping ratio are further optimized. The results show that when the width of the transport plate of the DBS3 section slope is 8meters, it does not meet the requirements of safety reserve coefficient 1.2. When the width of the transport plate is set to 24 meters, it meets the requirements of a safety reserve coefficient of 1.2 and an economic stripping ratio of not more than 8.0 m3/t. The three- dimensional numerical simulation results show that the optimal tracking distance on the east side is 50 meters, and the optimal slope angle is 35°. After the optimization design of a two-dimensional and three-dimensional slope shape, 2.456 million tons of coal resources were mined, creating a profit of about 21.1268 million yuan. While preventing landslide disasters, the recovery rate of coal resources was further improved.

Three-dimensional numerical simulation and theoretical model of a hollow droplet impacting on a solid surface

The phenomenon of a hollow droplet impacting on a solid surface is widely found in various fields. The dynamic characteristics of hollow diesel droplets impacting on a solid surface are studied by combining numerical simulation and theoretical analysis. The dynamic contact angle model presented in this paper couples the advantages of existing dynamic contact angle models for simulating both the spreading and retracting stages. It also considers the continuous variation of the contact angle during the maximum spreading state. Compared to existing models, the maximum error has been reduced from 14.9% to 4.6%. The effects of impact velocity, impact angle, and volume ratio of a hollow droplet on the spreading and jetting characteristics are investigated by three-dimensional numerical simulations. It is found that air entrainment occurred in the counter-jet, and the presence of the impact angle increased the asymmetry of the counter-jet and spreading liquid film, promoting fingerlike splashing at the front liquid film. Based on energy conservation law, the theoretical prediction models of the maximum spreading coefficient of the hollow droplet impacting on the surface and the velocity of the counter-jet at the maximum spreading state are established using the multi-regional modeling method and the energy distribution principle. Compared with existing hollow droplet theoretical models, the proposed theoretical models exhibit a more concise expression, higher accuracy, and wider applicability range.