Three-dimensional numerical simulations of barchan dune interactions in unidirectional flow

ABSTRACT

In this study, a constitutive model based on fluvial hydrodynamics is coupled with a large eddy simulation to better understand barchan dune interactions from the perspective of morphological dynamics. The results show that the developed model can reproduce crescent-shaped dunes, as well as variations in turbulent flow structures above the dune surface. The interactions between two barchan dunes arranged in coaxial and staggered alignments are simulated by changes in their initial mass ratios. A critical moment of fast erosion is observed for the larger of the two coaxial dunes, and the value of this moment converges to a constant with a linear increase in the mass ratio. The interaction pattern of “coalescence” agrees with that of the experiments. These results provide deep insights into the transition of the barchan dune interaction patterns from “coalescence” to “ejection”, which corresponds to a dynamic mass equilibrium state in large dunes. In addition, one elongated horn created from merged barchans after a staggered collision reaffirms that dune collision and influx asymmetry are two potential mechanisms in barchan asymmetry.     

Prediction and Control of Internal Condensing Flows in the Experimental Context of their Inlet Condition Sensitivities

The reported experimental results involve fully condensing flows of pure FC-72 vapor on a horizontal condensing surface (316 stainless steel) which is the bottom surface (wall) of a rectangular cross-section duct of 2 mm height, 15 mm width, and 1 m length. The sides and top of the duct are made of clear plastic. The experimental system in which this condenser is used is able to control steady-in-the-mean (termed quasi-steady) mass flow rate, exit pressure, and wall cooling conditions. It has been found that, with the condenser mean (time averaged) inlet mass flow rate, exit pressure, and wall cooling condition held fixed at steady values, there is a very strong sensitivity to high amplitude pressure fluctuations and flow rate pulsations at the condenser inlet. This sensitivity often significantly alters the condenser mean inlet pressure, pressure drop, local heat transfer rates (>200% increase at certain locations), and the condensing flow morphology. These effects are representative of fluctuations/pulsations that are typically encountered in applications but are either not accounted for or are not detected. The effects of imposed fluctuations/pulsations, as opposed to cases involving negligible imposed fluctuations/pulsations, are dependent on the amplitude and the frequency content of the imposed fluctuations and this is discussed in a separate paper. A significant upstream annular regime portion of the reported shear/pressure driven fully condensing flows operate under conditions where the laboratory??s transverse gravity effects are negligible and, therefore, the identified sensitivity phenomenon is highly relevant to zero- or micro-gravity conditions. The micro-gravity relevance of this sensitivity for the annular regime phenomenon is currently also being demonstrated with the help of computations and simulations.     

Numerical investigation of conductance of porous media in high vacuum systems

In high vacuum systems or materials that have fine capillaries, the molecular transport can be characterized as being free-molecular flow regime. In this flow regime intermolecular interactions can be ignored and flow is determined entirely by molecule-surface collisions. The transport of gases and volatile compounds through porous media and filters with variety of geometries is of great interest in various industrial applications. Although the effect of porosity on gas flow in the most of the flow regimes has been explored, but there are a few investigations on gas transport in porous media and filers at free-molecular regime. In this investigation gas transport in porous media with various porosities and geometries is explored. Test Particle Monte-Carlo (TPMC) method is employed. The walls are assumed to be diffusive. The skeletal portion of the porous media (frame) is modelled by solid spheres. The developed numerical scheme is validated with non porous cases. The effect of porosity, sphere sizes of frame, porous geometry, gas type and temperature on the conductance is examined. The simulations are performed for a porous pipe and porous nozzle. Results demonstrate that porosity and filtration highly affects the conductance of pipe and nozzle and causes great pressure drop in high vacuum systems. The increase of sphere sizes at constant porosity causes conductance to grow. The gas type and temperature of gas affects the conductance of pipe and nozzle too.     

Numerical investigation of conductance of porous media in high vacuum systems

In high vacuum systems or materials that have fine capillaries, the molecular transport can be characterized as being free-molecular flow regime. In this flow regime intermolecular interactions can be ignored and flow is determined entirely by molecule–surface collisions. The transport of gases and volatile compounds through porous media and filters with variety of geometries is of great interest in various industrial applications. Although the effect of porosity on gas flow in the most of the flow regimes has been explored, but there are a few investigations on gas transport in porous media and filers at free-molecular regime. In this investigation gas transport in porous media with various porosities and geometries is explored. Test Particle Monte-Carlo (TPMC) method is employed. The walls are assumed to be diffusive. The skeletal portion of the porous media (frame) is modelled by solid spheres. The developed numerical scheme is validated with non porous cases. The effect of porosity, sphere sizes of frame, porous geometry, gas type and temperature on the conductance is examined. The simulations are performed for a porous pipe and porous nozzle. Results demonstrate that porosity and filtration highly affects the conductance of pipe and nozzle and causes great pressure drop in high vacuum systems. The increase of sphere sizes at constant porosity causes conductance to grow. The gas type and temperature of gas affects the conductance of pipe and nozzle too.     

Turbulence characteristics of open channel flow over non-equilibrium 3-D mobile dunes

This paper reports velocity measurements over mobile dunes using an acoustic Doppler velocimetry (ADV). Experiments were conducted with two different flow conditions resulting in the formation of two different size mobile dunes. Dunes height, wavelength and velocity of dunes found to be increasing with increase in average flow velocity for a constant flow depth. The quasi-stationary bed condition was assumed while measuring the velocity distribution along the depth. The effect of the non-equilibrium mobile dunes on the flow characteristics and turbulence is examined by computing turbulent intensities, turbulent kinetic energy and Reynolds shear stresses using time averaged and time–space averaged velocity measurements. The magnitudes of transverse velocities are approximately 1/10 of streamwise velocities and vertical velocities are approximately half of the transverse velocities. The considerable magnitudes of transverse velocities over mobile bedforms necessitate measurement of 3-D velocity components to analyze the flow field. Computed turbulence intensities are found to be maximum in the region consisting of the trough and the reattachment point of the dunes. It is observed that streamwise turbulence intensities near the bed are twice the transverse turbulence intensities, and transverse turbulence intensities are twice the vertical turbulence intensities. Reynolds stresses (transverse fluxes of streamwise and vertical momentum) are observed to be high on mobile bedforms which shows mobile dunes reinforce the secondary currents. Peak values of turbulent kinetic energy (TKE) and Reynolds stresses are also found in the region consisting of the trough and the reattachment point. It is visually observed in the present experiments that maximum erosion takes place at the reattachment point and eroded sediment is carried as total load and dropped on the lee slope of the subsequent downstream dune. This phenomenon is caused by flow expansion in the separation zone, and which is also the main reason for mobility of dunes and associated bedload transport. Most importantly, it is found that turbulence anisotropy increases with increase in size of mobile bedforms and anisotropy is extended up to the free surface in the flows over mobile bedforms, which proves the entire depth of flow is being disturbed by the mobile dunes.     

Hyperbolic contraction measuring systems for extensional flow

In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored.     

Study of the origin of shear zones in quasi-static vertical chute flows by using discrete particle simulations

We perform discrete-particle simulations of vertical chute flows in the quasi-static regime using disk-like particles. The velocity profiles show a plug flow in the central region and shear zones next to the walls approximately 6 particle diameters wide regardless of bin width, as was observed experimentally. The stress distributions are in good agreement with the predictions of the continuum mechanics equations even for small systems (15 and 20 particle diameters wide) as those studied in the present work. Large stress fluctuations in space and time have been observed, these are mainly due to the inhomogeneity of the force network. It is observed in the simulations that the wall friction does not act homogeneously but it is concentrated at certain points on the wall depending on the local arrangement of the packing. Large stress zones or arches appear at these points of the wall. It is the formation and the way these arches collapse that seems to generate the shear zones. Based on this, a simple mechanism to explain the formation of the shear zone is proposed. The simulations have revealed other interesting features of the flow, particularly the presence of macroscopic fluctuations of velocity, in which large blocks of material move together showing sudden accelerations (corresponding to the collapse of the arches) and sudden decelerations (corresponding to the formation of the arches).     

Stability of sessile and pendant liquid drops

The solution space of axisymmetric liquid drops attached to a horizontal plane is investigated, and the stability of hydrostatic shapes is assessed by a novel numerical linear stability analysis involving discrete perturbations. For a given contact angle and Bond number, multiple interfacial shapes exist with compact, lightbulb, hourglass, and more convoluted pearly shapes. It is found that more than one solution branch can be stable, and that negative curvature at the contact line of a pendant drop is not a prerequisite for instability. Numerical simulations based on the boundary-integral method for Stokes flow illustrate the process of unstable drop detachment. Unstable drops transform into elongated threads with a spherical head whose volume is determined by a Bond number expressing the significance of surface tension. A complementary investigation of the shape and stability of two-dimensional drops attached to a horizontal or inclined plane reveals that hydrostatic shapes are least stable in the inclined configuration and most stable in the pendant or sessile configuration.     

Sand suspension deposition in horizontal low-concentration slurry pipe flows

Detailed observations in a slurry transparent horizontal loop of the sand transport deposition regime, ranging from fully suspended particles to bed motion as a train of dunes, are reported. Deposition, or scouring, is known as a deleterious sand transport regime in view of pipeline erosion. The two velocity thresholds limiting the deposition regime: the critical sand-carrying velocity threshold or deposition threshold below which particles begin to deposit, and the minimum conveying velocity threshold, below which particles cannot be suspended anymore and self-organize into dunes, span about 20 % of the bulk velocity such that detection of the beginning of the deposition provides a margin of safety before accumulation risks. Observed moving, snaking structures are likely to be the actors of the reckoned erosion on pipelines bottom in this scouring regime. From a digital treatment of the videos of the deposited particles, the deposition regime presents a salient characteristic: a consistent increase in the number of detected entities as the bulk velocity decreases down to a brutal trend inversion once all particles are eventually deposited and self-organise and hide into dunes. The findings are, in a first approximation, independent of the sand size and concentration, for the cases considered, and provide a basis for the design of monitoring methods for systematic detection of the deposition regime.     

Experimental study on the stable morphology and self-attraction effect of subaqueous barchan dunes

The evolutionary process of isolated dunes under the action of a unidirectional steady water flow is recorded from a bottom-up visual angle by optical synchronization imaging measurements. The morphological characteristics of dunes formed from different initial sand pile configurations are analyzed by an image-processing method. Results show that the trend of reproducing the crescent shape of the dune is shown in all sand piles, which is independent of the initial configuration. The triangular initial sand pile is found to be the first to stabilize to a crescent shape, whereas the square initial sand pile takes the longest time to form a stable crescent shape. This finding is essentially due to the shape effect of the triangle, which effectively reduces the amount of transverse moving sand particles. Based on the aspect ratio of the barchan dune that is stable at approximately 1, we determine that the evolution time required for the final stability of barchan dunes reproduced from different initial sand piles is approximately 200 s within the restriction of the present closed-water-tunnel experimental condition. Moreover, a dimensionless comparison of the profile curves of barchan dunes’ stable morphologies reveals a “streamwise–spanwise” dimension of the dune, which essentially synthesizes characteristic information about windward face and two horns. This “streamwise–spanwise” dimension ultimately presents the self-attraction effect of the crescent shape.     

Experimental analysis on particle fluctuation velocity in a horizontal air–solid two-phase pipe flow having a dune model

To further elucidate the mechanism of energy-conserving conveying in horizontal pneumatic conveying with the dune model, the high-speed particle image velocimetry is applied to measure particle fluctuation velocity near the minimum conveying velocity of the conventional pneumatic conveying. This study focuses on the effect of mounting dune models on the horizontal pneumatic conveying in terms of power spectrum, autocorrelation coefficients, two-point correlation coefficients, fluctuation intensity of particle velocity, skewness factor, and probability density function. It is found that the power spectrum peaks with the dune model are larger than those of the nondune system, suggesting the acceleration and suspending efficiency of the dune model, especially dune models mounted at the bottom of the pipe. Meanwhile, the profiles of particle fluctuation velocity intensity indicate that the large particle fluctuating energy is generated due to mounting the dune model so that the particles are more easily accelerated and suspended. This is one of the important reasons why the mounted dune model results in a low pressure drop and low minimum conveying velocity. Based on the distribution of skewness factor and probability density function, it is found that the particle fluctuation velocities of all cases follow the Gaussian distribution in the lower and middle parts of the pipe. The particle fluctuation velocities in the case of the dune models mounted at the bottom of the pipe obey the Gaussian-type fluctuation more.     

The dune size distribution and scaling relations of barchan dune fields

Barchan dunes emerge as a collective phenomena involving the generation of thousands of them in so called barchan dune fields. By measuring the size and position of dunes in Moroccan barchan dune fields, we find that these dunes tend to distribute uniformly in space and follow an unique size distribution function. We introduce an analytical mean-field approach to show that this empirical size distribution emerges from the interplay of dune collisions and sand flux balance, the two simplest mechanisms for size selection. The analytical model also predicts a scaling relation between the fundamental macroscopic properties characterizing a dune field, namely the inter-dune spacing and the first and second moments of the dune size distribution.     

Fingering instability of partially wetting evaporating liquids

A numerical study of the fingering instability of the leading edge of a film of evaporating partially wetting liquid flowing down an inclined solid substrate is presented. The effects of capillarity, gravity, disjoining pressure, and evaporation are included in the formulation of our lubrication-type model. The disjoining pressure is assumed to be a linear combination of two components to account for both van der Waals forces and electrostatic effects. Consistent with previously published results, evaporation has a stabilizing effect on fingering instability and can completely suppress the instability if the evaporation number, a nondimensional measure of evaporation intensity, is above a critical value. The critical evaporation number decreases as the inclination angle is decreased. Increasing the apparent contact angle by suitable changes in the disjoining pressure parameters, has a destabilizing influence on the contact line. Also investigated is the length of the fingers in the regime when the instability develops, and it is found that this length decreases as the evaporation number is increased.     

Enhancing the fluidization quality of nanoparticles using external fields

Fluidization quality of beds containing alumina and iron oxide nanoparticles in the Agglomerate Bubbling Fluidization (ABF) was improved by applying a combination of vibration and magnetic field. Pressure fluctuations were measured and analyzed by Fast Fourier Transform (FFT), Recurrence Plot (RP) and Recurrence Quantitative Analysis (RQA). Results of FFT showed that the wall vibration creates a periodic signal at 100?Hz which is not originated from the bed hydrodynamics. RP of pressure fluctuations before and after applying the assisting forces showed that the white areas in the plot decrease in size, which indicates an increase in the contribution of meso-structures such as agglomerates and small bubbles. The transition in the equilibrium bed hydrodynamics, between the condition in which assisting forces are not applied and condition in which they are applied, was tracked. It was shown by the determinism of pressure fluctuations that when the iron oxide nanoparticles exist alongside with alumina nanoparticles, this transition to the new equilibrium condition was reached in a shorter time. Determinism of pressure fluctuation of beds containing iron oxide decreased after applying the assisting forces. This trend confirms that large bubbles start to disappear and become substituted by smaller structures when magnetic field is applied to the bed. Under this condition, the interphase contact efficiency increases and the bed becomes closer to the Agglomerate Particle Fluidization (APF) regime.     

Melt Flow Instability and Turbulence in Electro-Magnetically Levitated Droplets

This article addresses fluid flow instabilities and flow transition to turbulent chaotic motions through numerical analysis and turbulence in electro-magnetically levitated droplets through direct numerical simulations. Numerical implementation and computed results are presented for flow instability and turbulence flows in magnetically levitated droplets under terrestrial and microgravity conditions. The linear melt flow stability is based on the solution of the Orr-Sommerfeld linearized equations with the base flows obtained numerically using high order numerical schemes. The resulting eigenvalue problems are solved using the linear transformation or Arnold's method. Melt flow instability in a free droplet is different from that bounded by solid walls and flow transits to an unstable motion at a smaller Reynolds number and at a higher wave number in a free droplet. Also, flow instability depends strongly on the base flow structure. Numerical experiments suggest that the transition to the unstable region becomes easier or occurs at a smaller Reynolds number when the flow structures change from two loops to four loops, both of which are found in typical levitation systems used for micro-gravity applications. Direct numerical simulations (DNS) are carried out for an electro-magnetically levitated droplet in a low to mild turbulence regime. The DNS results indicate that both turbulent kinetic energy and dissipations attain finite values along the free surface, which can be used to derive necessary boundary conditions for calculations employing engineering k--ε models.     

APPLICATION OF LIAPUNOV'S SECOND METHOD OF STABILITY TO GAS-SOLID TRANSPORT

Liapunov's second method of stability was applied to two basic equations describing particle and gas velocities during horizontal gas-solid transport. System parameters were then varied to determine which, if any, had a significant effect on the conditions at which the transport system borders between stability and Instability. The regions of asymptotic stability (RAS) increase with an increase in particle diameter, particle density and linear pressure drop but decreases with an increase in fluid density. The line diameter is not a significant parameter for changing the RAS. Actual experimental data must be tested to evaluate the usefulness of the analysis.     

Simulation of single mode Rayleigh–Taylor instability by SPH method

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh–Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace’s law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.     

The SPH method for simulating a viscoelastic drop impact and spreading on an inclined plate

In the present work, the phenomenon of an Oldroyd-B drop impact and spreading on an inclined rigid plate at low impact angles is simulated numerically using the smoothed particle hydrodynamics (SPH) method. In order to remove the unphysical phenomenon of fracture and particle clustering in fluid stretching which is the so-called tensile instability, an artificial stress term is employed which has been successfully proposed in simulations of elastic solids. Particularly, the effects of surface inclination and the different regimes of drop impact and spreading on an inclined surface are investigated. The numerical results show the capability of the proposed scheme in handing the unsteady viscoelastic free surface flows. All numerical results of using the SPH method are in agreement with the available data.