Two-dimensional Numerical Simulations Research Articles

Ignition studies of hydrogen-air mixtures over hot wire

Hot surface ignition of combustible gas mixtures poses a safety threat in many engineering applications. Gaseous mixtures ignite when hot surface temperature reaches the ignition threshold. In the present work, two-dimensional numerical simulations with detailed reaction mechanism are performed to simulate the flow of stoichiometric hydrogen-air mixture over a stationary hot wire. The effect of heating rates, wire diameters, mixture inlet velocities, and mixture equivalence ratios on the ignition threshold is investigated. In all the cases investigated, ignition is found to occur at the rear stagnation point, and wire heating rate did not influence the ignition phenomenon significantly. With an increase in mixture inlet velocity and mixture equivalence ratio, the ignition threshold increases, whereas the threshold has been found to decrease with increasing wire diameters. The role of the local equivalence ratios at the ignition point and reaction rates prior to the ignition process has been studied to help better understand the ignition phenomenon under different conditions.

Dynamics of FREI with/without cool flame interaction

The interactions between cool flames and flames with repetitive extinction and ignition (FREI) of stoichiometric n-heptane/air mixture were studied using a micro flow reactor with a controlled temperature profile from 373 to 1300 K. Two different flame dynamics with and without cool flames were observed in reactors with inner diameters dinner of 1 and 2 mm. Cool flames and FREI are spatially separated at dinner= 1 mm, whereas interactions between cool flames and FREI are observed at dinner= 2 mm. At dinner= 1 mm, the brightness intensity from cool flames depends on the inlet velocity (uinlet). Approximately above uinlet= 10 cm/s, the brightness intensity from cool flames decreases with increasing inlet velocity, despite a large amount of mixture input. This is because before low temperature ignition occurs under higher inlet velocity conditions, the mixture archives temperature where negative temperature coefficient is dominant. Reaction front propagation speed of FREI decreases monotonically due to heat loss because the extinction points of FREI are located in higher temperatures than the cool flame region. At dinner= 2 mm, the acceleration of the reaction front in the cool flame region is confirmed experimentally, as predicted in our previous two-dimensional numerical simulations. Additionally, the instantaneous reaction front speed after autoignition is analyzed at dinner= 1 mm. The instantaneous reaction front speed decreases as the time from extinction to ignition tex_ig becomes longer because a moderate mixing zone of reactants and products is formed.

The electrohydrodynamic plumes evolution in viscoelastic fluids with energy transfer process

Two-dimensional direct numerical simulation was carried out to investigate the various dynamic characteristics of electrohydrodynamic plumes in viscoelastic fluids in a complex blade-plate configuration. Here, the effects of different elasticities (Weissenberg number, Wi) and the maximum possible extension lengths (L) of polymer are studied. The results show that a new stem expansion process is found for viscoelastic plumes, which is explained by the transport mechanism of free charges. The rise and spread of plumes are promoted with an increase in elasticity and L, which we interpret from both an energy perspective and through the concept of the first principal normal stress difference (Np) for the first time. Our results suggest that when elasticity is weak, the total currents in the system are slightly enhanced due to the denser charge density, and above a certain value of Wi they are considerably inhibited maximum by 11.8% with the increasing of Wi or L mainly because of the variation in Uy.

A study on flow control in a hypersonic inlet using a plasma synthetic jet actuator

The plasma synthetic jet actuator (PSJA) has been proven to have potential for shock wave control in the supersonic/hypersonic flow. To evaluate the possibility for the PSJA applied in the hypersonic inlet under a Mach number greater than the design value and provide a deeper understanding of its control mechanism, the relevant two-dimensional numerical simulations are carried out. Based on the discussions about the numerical results, the effects are clear of the actuations generated by the PSJAs, including diffracted waves, synthetic jets, and discharged heat, on the oblique shock waves induced by the compression ramps and the aerodynamic performance of the hypersonic inlet. Concretely, the shapes of the oblique waves are changed by propagations of the diffracted waves, whose starting point moved due to the synthetic jets. A deceleration occurs near the surface of the hypersonic inlet caused by the movement of the discharged heat, leading to a thickener boundary layer. Furthermore, the incremental analysis about the total pressure recovery coefficient at the throat shows that the diffracted waves can increase the static pressure at the throat achieving a higher total pressure recovery coefficient, while the discharged heat makes the total pressure recovery coefficient drop due to a lower local Mach number at the throat. The effect of the discharged heat is more obvious than that of the diffracted waves.

A Comparative Study on 2D CFD Simulation of Flow Structure in an Open Channel with an Emerged Vegetation Patch Based on Different RANS Turbulence Models

Aquatic plants widely exist in rivers, which can affect the flow structure in rivers and have an important impact on the evolution of river morphology. The emerged vegetation is an important member of aquatic vegetation in the river, so studying the flow structure around the emerged vegetation patches is of great significance. Computational fluid dynamics (CFD) simulation provides support for the related research works. Applying the appropriate turbulence model is crucial to achieving realistic numerical simulation results. In this study, two-dimensional numerical simulations were carried out and compared with experimental data by six different Reynolds-Averaged Navier–Stokes (RANS) turbulence models, i.e., Standard k-ε model, Renormalization group (RNG) k-ε model, Realizable k-ε model, Standard k-ω model, Shear-stress transport (SST) k-ω Model, and the Reynolds stress model (RSM). CFD is an effective research method, and the results showed that there are different simulation performances with different turbulence models. The shear stress transport k-ω model achieves the most consistent numerical simulation results with the experimental data for the longitudinal mean flow velocity distribution at the centerline, and the Reynolds stress model provides the least consistent numerical simulation with the experimental data. Then the performance of the six models in simulating the flow field characteristics and longitudinal outflow after vegetation patch was compared.

Anguilliform and carangiform fish-inspired hydrodynamic study for an undulating hydrofoil: Effect of shape and adaptive kinematics

This work is motivated by the fact that the thinner-anguilliform and thicker-carangiform types of fish adapt to each other's kinematics under certain conditions. Our two-dimensional hydrofoil model-based numerical simulations demonstrate that the adaptive kinematics increases thrust force for the thinner-fish while it increases propulsive efficiency for the thicker-fish; as found in nature. Further, hydrodynamic reasons are discussed for such adaptive behavior. This bioinspired and biomimetics study may assist need-based efficient design of underwater-vehicles.

Near-wall dynamics of premixed methane/air flames

This work focuses on sidewall quenching (SWQ) for premixed methane/air flames that are forced by a periodic oscillatory inflow with excitation frequency f = 100 Hz. The effects of steady-state and transient flame stretch on the near-wall flame dynamics are evaluated using two-dimensional direct numerical simulation (2D-DNS) and the GRI 3.0 reaction mechanism. The velocity fluctuations lead to significant changes in flame speed and flame stretch, as well as the associated Markstein numbers. The phenomenon of SWQ is analyzed using flame quenching distance, wall heat flux and heat release rate. For steady-state conditions, there is a strong correlation between the maximum wall heat flux WHFmax and the flame quenching Peclet Number (Peq), as well as between the flame speed and the flame stretch; for transient conditions, the flame quenching distance (dq) increases continuously from phase angles of 1/4f−1 to 3/4f−1 in one cycle as time progresses, and the fluctuation of the quenching distance (Δdq) decreases gradually with increasing equivalence ratio (∅). The flame stretch changes from negative to positive in the process from 1/4f−1 to 3/4f−1, while the heat release rate and fuel reaction rate near the wall gradually decrease. Furthermore, the FWI region is dominated by negative flame stretch while positive flame stretch is present at the base of the flame. Moreover, the methane/air flame has a nearly twofold increase in the consumption speed during the oscillation from phase angle 3/4f−1 to the next cycle at 1/4f−1 at ∅ = 0.5 and ∅ = 1.0. These results show that flow field perturbations are not negligible in elucidating the effects of flame-wall interactions.

A diffuse interface model for low solubility binary flows in porous media

Dissolution-driven convection of low solubility fluids separated by a free interface in a porous medium is analyzed via two-dimensional numerical simulations and scaling considerations. Towards this end, we employ a low solubility Darcy-Cahn-Hilliard model with a Helmholtz free energy. The momentum equations are solved in the stream function-vorticity formulation with a pseudospectral method, so that continuity is automatically satisfied, while the diffusion equation is integrated in time by an explicit Runge-Kutta procedure, combined with high order compact finite differences. We validate the simulation approach by comparing the growth rate of the standard deviation of the surface location with experimental measurements for a CO2-water system in a Hele-Shaw cell. The numerical results for the evolving interfacial shape in density-driven convection flow of low solubility fluids agree significantly better with experimental observations than corresponding fully soluble results. The temporal evolution of the interfacial plumes is accurately captured, and distinct stages with different plume features are identified. The differences in plume features and solute flux of CO2 between low solubility and fully soluble fluids are discussed, and it is found that the low solubility simulation approach offers clear advantages for the investigation of CO2-dynamics in porous rock.

Solution approaches for evaporation-driven density instabilities in a slab of saturated porous media

This work considers the gravitational instability of a saline boundary layer formed by an evaporation-induced flow through a fully saturated porous slab. Evaporation of saline waters can result in the formation of salt lakes as salt accumulates near the top surface. As gravitational instabilities can impede the accumulation of salt, establishing a relation between their occurrence and the value of physical parameters such as evaporation rate is crucial. One step toward determining when gravitational instabilities can arise is to compute the ground-state salinity. In this work, this ground state is analytically derived within the framework of Sturm–Liouville theory. Then, a linear stability analysis in conjunction with the quasi-steady state approach is employed to investigate the occurrence of instabilities. These instabilities can develop and grow over time depending on the Rayleigh number and the dimensionless height of the porous medium. To calculate the critical Rayleigh number, which is used to determine the stability of a particular system, the eigenvalues of the linear perturbation equations have to be computed. Here, a novel fundamental matrix method is proposed to solve this perturbation eigenvalue problem and shown to coincide with an established Chebyshev–Galerkin method in their shared range of applicability. Finally, a two-dimensional direct numerical simulation of the full equation system via the finite volume method is employed to validate the time of onset of convective instabilities predicted by the linear theory. Moreover, the fully nonlinear convection patterns are analyzed.

Swimming in density-stratified fluid: study on a flapping foil

It is of interest to investigate how a swimming animal performs in a density-stratified fluid. This paper studies a simplified swimmer, a pitching NACA0015 airfoil, considering its locomotion in both homogeneous, or unstratified, and stratified fluid flows. A direct comparison is made between these two conditions through two-dimensional numerical simulations. Our numerical results show that the stratification modifies the dynamics of the pitching foil in both its wake structures and the drag force, or thrust, as well as its propulsive performance. We suggest that the effects of stratification on flapping performance or propulsive efficiency can be categorized according to the Froude number, or the level of stratification. First, in the range of high Froude numbers, notable modification of the flow structure can be observed, which however does not greatly affect the propulsive performance. Second, at a very low Froude number, i.e., Fr = 1, the propulsive efficiency drops markedly compared to its homogeneous counterpart, attributed to the pronounced internal waves induced by the strong stratification. Moreover, at a moderate Froude number Fr = 2, we find an increase in the propulsive efficiency, which can be explained by the unique variation in the wake structure. At A D = 2.50, the propulsive efficiency peaks at Fr = 2, with its efficiency 18.3% higher than its homogeneous counterpart, exhibiting a favourable influence of the stratification on a swimmer.

Geomorphic response of outburst floods: Insight from numerical simulations and observations––The 2018 Baige outburst flood in the upper Yangtze River

Outburst floods related to glacial or landslide damming are a major agent of geomorphic change in mountain rivers. Although the evidence between outburst flooding and riverine landscapes has been gradually recognized, the lack of hydraulics to the extent that there has still not been quantified on the relationship of how the amount and spatial distribution of these changes relate quantitatively to the hydraulic conditions and durations of these catastrophic events. This study combined remote and field observations of the 2018 Baige outburst flood with two-dimensional numerical simulation using the diffusive wave equation. By feeding the measured dam-breach hydrograph and comparing three different Manning coefficients in numerical experiments, the simulation results show that when n = 0.055, the time of peak flow was only 0.5 h different from that indicated by measured data in Yebatan, 54 km downstream of the Baige landslide dam. Under high shear stress over several hours at sustained ~20 m water depth, lateral erosion caused by these outburst floods contributed to the adjacent landslide, which was activated in association with intermittent water velocity waves of approximately 17 m/s. Sustained high stream power (>50 kW m2) from the outburst flood eroded slope toes and accelerated slippage of six slopes. Combining simulation and observations, we also developed a physical model related to hillslope instability caused by high hydrodynamic erosion of riverbanks generated by flow waves lasting several hours, which explained the hydrodynamic response of the outburst flood to the canyon geomorphology. Furthermore, we suggest that the pattern of channel widening erosion and deposition is governed by the variation in shear stress and Froude number as the high-energy flood flows from a wide channel into a narrow river valley. Our findings highlight that the hydraulics of high-magnitude outburst floods and sediment transport play crucial roles in reshaping canyon geomorphology.

Applicability of two-dimensional numerical simulation associated with vortex-induced vibration response of the circular cylinder

ABSTRACT The VIV responses of the circular cylinder at low and moderate Reynolds numbers are calculated according to two-dimensional numerical simulation and the fourth-order Runge–Kutta algorithm. The first part of the study is focused on the applicability of 2D numerical simulation between the response of 2D numerical simulation and the actual response, which can guide the preliminary engineering studies by vortex shedding. The reasonable vortex shedding mode of each branch, and the change process of the trajectory from the ‘8’ type to the ‘droplet’ type, are discussed in the second part of the study. And independent calculations under different speed reduction conditions are employed to suit practical application scenarios. The comparison shows the applicability of the 2D numerical simulations at low Reynolds numbers. Although the amplitude calculation results at moderate Reynolds numbers are inconsistent with the experimental results, the two-dimensional numerical simulation has good reliability in the trailing vortex capture.

Estimation method of coal channel Q value based on frequency shift phenomenon of transmitting channel wave

Currently, the transmitting channel wave technique mainly uses the attenuation coefficient of the channel wave total energy to explore the geological structure of the coal seam face. In the case of weak geophone coupling and intense geological anomaly, the channel wave energy will be attenuated severely, which significantly affects the stability and accuracy of the result. The Q value of the coal channel is a critical parameter to evaluate the energy attenuation characteristics of the channel wave. The Q value is typically estimated by using the attenuation coefficient of the body wave, but the special coal channel model hinders the estimation of the Q value of the coal seam. According to the linear attenuation characteristics of the centroid frequency of the transmitting channel wave, a new method was proposed to assess the quality factor (Q) of the coal channel by using the centroid frequency change of the channel wave signal. The expected frequency was calculated as its centroid frequency according to the energy ratio of each frequency point through the spectral analysis of the channel wave signal. Combined with the transmission tomography technology, the imaging of the coal seam face based on the transmitting channel wave Q value was established. According to the sudden change of the Q value of the coal channel near the geological structure of the coal seam face, a geological interpretation method based on the abnormal Q value was proposed. The two-dimensional numerical simulation demonstrated that the centroid frequency of the transmitting channel wave signal decayed linearly with the propagation distance and the geological structure increased the frequency shift. Furthermore, three-dimensional numerical simulation validated the feasibility and effectiveness of the Q value inversion method. Field Experimental results showed that the algorithm exhibited improved stability and accuracy. This work proposed a novel frequency-domain inversion method of the transmitting channel wave that directly uses the frequency shift characteristics of the channel wave to estimate the Q value of the coal channel, which offers a new strategy in the data processing of channel wave.

Analytical study for wave-induced submarine groundwater discharge in subtidal zone

Both tide and wave are significant coastal driving forces of submarine groundwater discharge (SGD). The hydrodynamic process of tidal SGD is well studied while wave induced part is still challenging to quantify. In this paper, an analytical study was performed to investigate wave-induced SGD in a subtidal aquifer extending horizontally infinitely with impermeable horizontal bottom. The loading effect of seawater weight overlying the seabed was taken into account. The analytical solution was validated by two-dimensional numerical simulations with modeling domains of finite horizontal extension length. Sensitivity analyses of the analytical solution showed that the amplitude of groundwater head fluctuations generally decayed exponentially with the aquifer thickness, and the decay rate decreased with increasing loading efficiency. Loading effect can decrease the head gradients between seawater and porewater. Wave-induced SGD generally increased with the aquifer’s thickness, permeability, wavenumber, wave period, and decreased with the loading efficiency and specific storage of the aquifer. The analytical and simulated results may provide guidance for assessing the wave-induced SGD and shed light on modeling the biogeochemistry process in wave dominated porous seabed environment.

Critical tube diameter for quasi-detonations

The critical tube diameter problem for quasi-detonations is studied via experiments and two-dimensional numerical simulations based on the reactive Euler equations. In the experiments, quasi-detonation in stoichiometric acetylene-oxygen mixtures is generated in rough-walled tubes with three different diameters, where the wall roughness is introduced by using spiral inserts with different wire diameters. Photodiodes are placed along the rough tubes to record the detonation time-of-arrival to deduce the velocity, and a high-speed schlieren system is used to observe the diffraction processes. Near the critical regime of detonation diffraction, the quasi-detonation emerging from the rough tube is again shown to first fail and subsequently re-initiate from a local explosion center in the spherical deflagration reaction zone. For quasi-detonations, stronger turbulence and instabilities produce stronger local hot spots, which balances the significant velocity deficit as much as approximately 15% in the rough tube, resulting in the critical pressure remaining relative constant. The cell sizes for quasi-detonation in rough tubes are directly measured, and the ratio of critical tube diameters (dc) to these determined cell sizes (λ) is used to quantify the critical criterion of detonation initiation. In rough tubes with coil springs, the previous criterion of dc/λ≧ 13 for detonation re-initiation appears invalid, and the critical initiation regime for quasi-detonation in rough tubes is found approximately as dc/λ≧ 8. Despite the cell enlargement and the lower propagation velocity for quasi-detonation, it is hypothesized that the increase in cell irregularities or instabilities can in turn benefit the transmission process. These unstable features of quasi-detonation are supported by the two-dimensional numerical simulations, also showing a higher degree of cell irregularities, a wider spectrum of induction rate, and the generation of shocked reactive pockets.

Investigation of liquid n-heptane/air spray detonation with an Eulerian-Eulerian model

A two-dimensional numerical simulation of detonation in a reactive dispersed liquid droplet cloud is performed with an Eulerian-Eulerian method. This study aims to investigate the model and the effects of two-phase sub-models on the propagation of a detonation through an n-heptane spray. Firstly, the simulations are compared to the experiments conducted in the thesis of Mohamed El-Amine Benmahammed [1]. Three simulations are carried out for a mono-dispersed/one sample cloud of droplets with a mass corresponding to equivalence ratios of 0.8, 1.0, and 1.3. The Eulerian-Eulerian method predicted the experimental detonation velocity and gaseous phase thermodynamic properties with reasonable accuracy. Secondly, an investigation of the effects of the mobilization of the droplet size poly-dispersity on the detonation properties was carried out. For a droplet Sauter mean diameter of 30 µm, the effect of the number of droplet samples used for modeling the poly-dispersity modifies the front structure and detonation properties. For instance, comparing 15 samples of droplet size to a unique sample, the detonation velocity decreases by 2.0 %, and the mean detonation cell width increases by 10 %.

Hydrodynamic shape optimization of an auxiliary structure proposed for circular bridge pier based on a developed adaptive surrogate model

Reducing the hydrodynamic force for a cylindrical structure is extremely important in oceanic engineering applications. In this study, an auxiliary structure, shaped by two controlling parameters, is proposed to be placed in front of a typical circular bridge pier, desiring to mitigate the hydrodynamic loads on the pier. Two-dimensional numerical simulations are carried out through the open source CFD (computational fluid dynamics) program OpenFOAM to optimize the shape of the auxiliary structure by using a developed adaptive surrogate model, where the optimal auxiliary structure is identified by searching optimal hydrodynamic indexes, i.e., the drag and lift coefficients. The salient observations show that: (1) High efficiency is embodied in the whole optimization procedure by way of adopting the developed adaptive model; (2) The optimal auxiliary structure is featured with convex surfaces and can reduce the vortex scale and accelerate the vortex dissipation; (3) Investigation of the hydrodynamic performance proves that the optimal auxiliary structure can effectively decrease the drag and lift coefficients; and (4) The excellent performance emanating from the optimal auxiliary structure retains for a large range of the Reynolds numbers. It is hoped that the presented concept of the optimal auxiliary structure can provide guidance on mitigating the hydrodynamic loads for other oceanic engineered structures.

Unconditionally energy-stable time-marching methods for the multi-phase conservative Allen–Cahn fluid models based on a modified SAV approach

In this study, we add nonlocal Lagrange multipliers to the Allen–Cahn (AC) equation to establish the N-component conservative Allen–Cahn (CAC) system and the ternary conservative Allen–Cahn–Navier–Stokes (CACNS) system which conserve the mass for each phase. Then, we construct linear, totally decoupled, and energy dissipative methods for those multi-component phase-field. In the classical scalar auxiliary variable (SAV) approach, the phase variables and the scalar auxiliary variables are coupled, which need extra computational time to decouple. In this paper, we adopt a variant of SAV approach in which all variables are totally decoupled and can be calculated in a step-by-step manner. The linear multigrid algorithm is adopted to accelerate convergence. We further analytically prove the unique solvability, modified energy dissipation law, and mass conservation in time-discretized version. We demonstrate the performance of the proposed scheme via various two-dimensional (2D) and three-dimensional (3D) numerical simulations. Contrast tests between the N-component CAC model and the N-component Cahn–Hilliard (CH) model show that the N-component CAC model is efficient.

Diurnal and semidiurnal internal waves on the southern slope of the Yermak Plateau

The Yermak Plateau (YP) is located across the Arctic–Atlantic gateway in the northwest of the Svalbard archipelago. In this region, internal waves are believed to cause intense turbulent mixing and hence influence the heat budget in the Arctic Ocean. Based on year-long observations from three moorings, the characteristics and energetics of diurnal and semidiurnal internal waves on the southern slope of the YP are investigated in this study. Diurnal internal waves induce large isothermal displacements exceeding 100 m, which are nearly one order of magnitude greater than those of semidiurnal internal waves. In addition, diurnal internal waves are strong in winter but weak in summer, while the semidiurnal internal waves exhibit complicated temporal variation. For the diurnal internal waves, their available potential energy is greater than the horizontal kinetic energy; whereas the situation is opposite for the semidiurnal ones. This feature is further clarified with two-dimensional numerical simulations. Due to the larger tidal excursion, diurnal tidal forcing yields the generation of stronger higher harmonics, i.e., the semidiurnal internal waves. In contrast, higher harmonics are rather weak under the semidiurnal forcing. Moreover, a large proportion of energy for both diurnal and semidiurnal internal waves is dissipated locally. Results of this study can provide useful insight on the dynamics of internal waves in the Arctic Ocean.

Unmanned aerial vehicle transport of frozen blood samples using phase change materials

Appropriate cryopreservation of blood samples during transit from the point of collection to testing sites is an important element of quality sample management in clinical and veterinary diagnostics and research. Here, a heat-insulated design that employs 23.3% w/w salt water as the phase change material (PCM) for encapsulating a 1.5-mL vial of frozen blood sample was studied to assess its efficacy in maintaining sub-zero temperatures during transport. A two-dimensional finite element numerical simulation model with 5457 elements was found to exhibit mesh independence with 10% convergence error. For the PCM pre-cooled in dry ice and vial sample kept initially at 20 °C before flight, this model is predicted to maintain a stable transport temperature of −20 °C for at least 70 min. It also predicted to have uniform temperature distribution across the PCM holder, PCM, sample vial and sample. Experimental data obtained using a thermocouple confirmed the accuracy of the simulation model. Sensor data collected from a bespoke unmanned aerial vehicle (UAV) allowed mapping of the acceleration forces during flight and facilitated the development of a mechanical setup to experimentally show that frozen samples are protected from shear forces generated under mimicked transport conditions. The capability of real-time sample temperature monitoring with feedback control on UAV flight path demonstrates the viability of the drone delivery system for quality transport of thermal-sensitive samples. • UAV transport of frozen blood samples done here with salt water phase change material. • 2D finite element model achieved mesh independence with 10% convergence error. • 70 min stable transfer at −20 °C attained after 30 min of dry ice pre-cooling. • Sensor data from UAV mimicked the flight conditions in a sloshing test setup. • Preliminary tests with frozen sheep's blood show lower coagulation from sloshing.