arXiv subjects

Markus Uhlmann

Publications and source records attributed to Markus Uhlmann.

At least 37 records · Page 2Linked to original sources

arXiv2020

On the ice-nucleating potential of warm hydrometeors in mixed-phase clouds

The question whether or not the presence of warm hydrometeors in clouds may play a significant role in the nucleation of new ice particles has been debated for several decades. While the early works of Fukuta and Lee (1986) and Baker (1991) indicated that it might be irrelevant, the more recent study of Prabhakaran et al. (2019) [arXiv:1906.06129] suggested otherwise. In this work, we are aiming to quantify the ice-nucleating potential using high-fidelity flow simulation techniques around a single hydrometeor and use favorable considerations to upscale the effects to a collective of ice particles in clouds. While we find that ice nucleation may be enhanced in the vicinity of a warm hydrometeor by several orders of magnitude and that the affected volume of air is much larger than previously estimated, it is very unlikely that this effect alone causes the rapid enhancement of ice nucleation observed in some types of clouds, mainly due to the low initial volumetric ice concentration. Nonetheless, it is suggested to implement this effect into existing cloud models in order to investigate second-order effects such as ice nucleus preactivation or enhancement after the onset of glaciation.

physics.ao-ph↗

arXiv2020

Can preferential concentration of finite-size particles in plane Couette turbulence be reproduced with the aid of equilibrium solutions?

This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on Nagata's upper-branch equilibrium solution (Nagata, 1990) at low Reynolds numbers where this solution is linearly stable. When adding a single heavy particle with a diameter equivalent to 2.5 wall units, we observe that the solution remains stable and is essentially unchanged away from the particle. This result demonstrates that it is technically feasible to utilize exact coherent structures in conjunction with particle-resolved DNS. While translating in the streamwise direction, the particle migrates laterally under the action of the quasi-streamwise vortices until it reaches the region occupied by the low-speed streak, where it attains a periodic state of motion. As a result of the ensuing preferential particle location, the time-average streamwise particle velocity differs from the plane-average fluid-phase velocity at the same wall-distance as the particle center, as previously observed in experiments and in numerical data for fully turbulent wall-bounded flows. Additional constrained simulations where the particle is maintained at a fixed spanwise position while freely translating in the other two directions reveal the existence of two equilibria located in the low-speed and in the high-speed streak, respectively, the former being an unstable point. A parametric study with different particle to fluid density ratios is conducted which shows how inertia affects the spanwise fluctuations of the periodic particle motion. Finally, we discuss a number of potential future investigations of solid particle dynamics which can be conducted with the aid of invariant solutions (exact coherent structures) of the Navier-Stokes equations.

physics.flu-dyn↗

arXiv2019

Interface-resolved direct numerical simulations of sediment transport in a turbulent oscillatory boundary layer

The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating Navier-Stokes and continuity equations. The bottom is made up of spherical particles, free to move, which mimic sediment grains. The approach allows to fully-resolve the flow around the particles and to evaluate the forces and torques that the fluid exerts on their surface. Then, the dynamics of sediments is explicitly computed by means of Newton-Euler equations. For the smallest value of the flow Reynolds number presently simulated, the flow regime turns out to fall in the intermittently turbulent regime such that turbulence appears when the free stream velocity is close to its largest values but the flow recovers a laminar like behaviour during the remaining phases of the cycle. For the largest value of the Reynolds number turbulence is significant almost during the whole flow cycle. The evaluation of the sediment transport rate allows to estimate the reliability of the empirical predictors commonly used to estimate the amount of sediments transported by the sea waves. For large values of the Shields parameter, the sediment flow rate during the accelerating phases does not differ from that observed during the decelerating phases. However, for relatively small values of the Shields parameter, the amount of moving particles depends not only on the bottom shear stress but also on flow acceleration. Moreover, the numerical results provide information on the role that turbulent eddies have on sediment dynamics.

physics.flu-dyn↗

arXiv2019

Heat and water vapor transfer in the wake of a falling ice sphere and its implication for secondary ice formation in clouds

We perform direct numerical simulations of the settling of an ice sphere in an ambient fluid accounting for heat and mass transfer with the aim of studying in a meteorological context the case of falling graupel in humid air. The study is motivated by the fact that falling graupels in clouds are heated by the latent heat released during the accretion of liquid water droplets. They may therefore be considerably warmer than their surrounding and evaporate water vapor, which mixes with the surrounding air in the wake of the graupel, thereby creating transient zones of supersaturation there. The problem of a falling graupel is modeled as that of a heated sphere falling in a quiescent ambient fluid under the action of gravity. The coupling between the temperature and velocity fields is accounted for by the Boussinesq approximation. This problem can be parameterized by four parameters: the particle/fluid density ratio, the Galileo number, the Prandtl number, and the Richardson number. A separate scalar transport equation accounts for the vapor transport. Typical cloud conditions involve small temperature differences between the sphere and the surrounding, yielding relatively small Richardson numbers for both heat and mass transport. We give a special emphasis to the Galileo numbers 150, 170, 200 and 300 in order to analyze the specificities of each settling regime. The questions addressed in this study are mainly methodological and concern the influence of the settling regime and the mobility of the sphere on the structure of the scalar fields, the possible influence of modest Richardson numbers on the structure of the wake, and the possible application of this simulation framework to the investigation of the saturation in the wake of a falling graupel.

physics.flu-dyn↗

arXiv2018

Direct numerical simulations of ripples in an oscillatory flow

Sea ripples are small-scale bedforms which originate from the interaction of an oscillatory flow with an erodible sand bed. The phenomenon of sea ripple formation is investigated by means of direct numerical simulation in which the sediment bed is represented by a large number of fully-resolved spherical grains. Two sets of parameter values are adopted which are motivated by laboratory experiments on the formation of laminar rolling-grain ripples. The knowledge on the origin of ripples is presently enriched by insights and by providing fluid- and sediment-related quantities that are difficult to obtain in the laboratory. Detailed analysis of flow and sediment bed evolution has confirmed that ripple wavelength is determined by the action of steady recirculating cells which tend to accumulate sediment grains into ripple crests. The ripple amplitude is observed to grow exponentially consistent with established linear stability analysis theories. Particles at the bed surface exhibit two kinds of motion depending on their position with respect to the recirculating cells: particles at ripple crests are significantly faster and show larger excursions than those lying on ripple troughs. In analogy with segregation phenomenon of polydisperse sediments the non-uniform distribution of the velocity field promotes the formation of ripples. The wider the gap between the excursion of fast and slow particles, the the larger the resulting growth rate of ripples. Finally, it is revealed that, in the absence of turbulence, the sediment flow rate is driven by both the bed shear stress and the wave-induced pressure gradient, the dominance of each depending on the phase of the oscillation period. In phases of maximum bed shear stress, the sediment flow rate correlates more with the Shields number while the pressure gradient tends to drive sediment bed motion during phases of minimum bed shear stress.

physics.flu-dyn↗

arXiv2018

An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows

We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta Numerica 11 (2002) 1] into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations while at the same time avoiding strong restrictions of the time step. This technique was implemented in a finite-difference and fractional-step context. A variety of two- and three-dimensional simulations are presented, ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles. The accuracy and efficiency of the current method are clearly demonstrated.

physics.flu-dyn↗

arXiv2017

Direct numerical simulation of open-channel flow over a fully-rough wall at moderate relative submergence

Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully-rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, 441) for an open-channel flow in the transitionally-rough regime, the present purpose is to show how the flow structure changes as the fully-rough regime is attained and, for the first time, to enable a direct comparison with experimental observations. The results indicate that, in the vicinity of the roughness elements, the average flow field is affected both by Reynolds number effects and by the geometrical features of the roughness, while at larger wall-distances this is not the case, and roughness concepts can be applied. The flow-roughness interaction occurs mostly in the region above the virtual origin of the velocity profile, and the effect of form-induced velocity fluctuations is maximum at the level of sphere crests. The spanwise length scale of turbulent velocity fluctuations in the vicinity of the sphere crests shows the same dependence on the distance from the wall as that observed over a smooth wall, and both vary with Reynolds number in a similar fashion. Moreover, the hydrodynamic force and torque experienced by the roughness elements are investigated. Finally, the possibility either to adopt an analogy between the hydrodynamic forces associated with the interaction of turbulent structures with a flat smooth wall or with the surface of the spheres is also discussed, distinguishing the skin-friction from the form-drag contributions both in the transitionally-rough and in the fully-rough regimes.

physics.flu-dyn↗

arXiv2017

Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution

The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant scales of the problem. The numerical approach employed and the flow configuration considered is identical to our previous study (Kidanemariam and Uhlmann J. Fluid Mech., vol. 750, 2014, R2), the only difference being the length of the computational domain. By successively reducing the streamwise length, the minimum box dimension which accommodates an unstable sediment bed is revealed, thus determining the lower threshold of the unstable modes. For the considered parameter point, the cutoff length for pattern formation lies in the range 75-100 particle diameters (3-4 times the clear fluid height). We also simulate the flow in a very long streamwise box with a size of 48 times the clear fluid height (featuring over one million particles), accommodating approximately 11 initial ripple units with a wavelength of 100-110 particle diameters. The amplitude of the patterns exhibits two regimes of growth: an initial exponential regime, with a growth rate independent of the chosen domain size, and a subsequent non-linear regime which is strongly constrained by the domain length. In the small domain cases, after the initial exponential regime, the ripples evolve steadily maintaining their shape and migration velocity, at a mean wavelength equal to the length of the domain. The asymmetric ripple shape is characterized by a spectrum which exhibits a power-law decay over the first few dominant non-dispersive modes propagating at the mean dune migration velocity. The particle flowrate and the mean interface shear stress exhibited an increase with increasing ripple dimensions. Nevertheless, the relationship between the two was observed to be approximately described by the empirical power law formula for sediment transport by Wong & Parker (2006).

physics.flu-dyn↗

arXiv2016

Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence

We have performed interface-resolved direct numerical simulations of forced homogeneous-isotropic turbulence in a dilute suspension of spherical particles in the Reynolds number range Re-lambda=115-140. The solid-fluid density ratio was set to 1.5, gravity was set to zero, and two particle diameters were investigated corresponding to approximately 5 and 11 Kolmogorov lengths. Note that these particle sizes are clearly outside the range of validity of the point-particle approximation, as has been shown by Homann & Bec (2010). At the present parameter points the global effect of the particles upon the fluid flow is weak. We observe that the dispersed phase exhibits clustering with moderate intensity. The tendency to cluster, which was quantified in terms of the standard deviation of Voronoi cell volumes, decreases with the particle diameter. We have analyzed the relation between particle locations and the location of intense vortical flow structures. The results do not reveal any significant statistical correlation. Contrarily, we have detected a small but statistically significant preferential location of particles with respect to the `sticky points' proposed by Goto & Vassilicos (2008), i.e. points where the fluid acceleration field is acting such as to increase the local particle concentration in one-way coupled point-particle models under Stokes drag. The presently found statistical correlation between the `sticky points' and the particle locations further increases when focusing on regions with high local concentration. Our results suggest that small finite-size particles can be brought together along the expansive directions of the fluid acceleration field, as previously observed only for the simplest model for sub-Kolmogorov particles. We further discuss the effect of density ratio and collective particle motion upon the basic Eulerian and Lagrangian statistics.

physics.flu-dyn↗

arXiv2016

Columnar structure formation of a dilute suspension of settling spherical particles in a quiescent fluid

The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers ($110 \leq \text{Ga} \leq 310$) for a fixed density ratio of $Γ= ρ_p/ρ_f = 2.5$. In this regime the particles are known (M. Jenny, J. Dušek and G. Bouchet, Journal of Fluid Mechanics 508, 201 (2004).) to show a variety of motions. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively: vertical, oblique, oblique oscillating, and finally chaotic. Not only does this change the trajectory of single, isolated, settling particles, but it also changes the dynamics of a swarm of particles as collective effects become important even for dilute suspensions, with volume fraction up to $Φ_V = \mathcal{O}\left(10^{-3}\right)$, which are investigated in this work. Multi-camera recordings of settling particles are recorded and tracked over time in 3 dimensions. A variety of analysis are performed and show a strong clustering behavior. The distribution of the cell areas of the Voronoï tessellation in the horizontal plane are compared to that of a random distribution of particles and shows clear clustering. Moreover, a negative correlation was found between the Voronoï area and the particle velocity; clustered particles fall faster. In addition, the angle between two adjacent particles and the vertical is calculated and compared to a homogeneous distribution of particles, clear evidence of vertical alignment of particles is found. The experimental findings are compared to simulations.

physics.flu-dyn↗

arXiv2015

Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity

We consider the case of finite-size spherical particles which are settling under gravity in a homogeneous turbulent background flow. Turbulence is forced with the aid of the random forcing method of Eswaran and Pope [Comput. Fluids, 16(3):257-278, 1988], while the solid particles are represented with an immersed-boundary method. The forcing scheme is used to generate isotropic turbulence in vertically elongated boxes in order to warrant better decorrelation of the Lagrangian signals in the direction of gravity. Since only a limited number of Fourier modes are forced, it is possible to evaluate the forcing field directly in physical space, thereby avoiding full-size transforms. The budget of box-averaged kinetic energy is derived from the forced momentum equations. Medium-sized simulations for dilute suspensions at low Taylor-scale Reynolds number $Re_λ=65$, small density ratio $ρ_p/ρ_f=1.5$ and for two Galileo numbers $Ga=0$ and 120 are carried out over long time intervals in order to exclude the possibility of slow divergence. It is shown that the results at zero gravity are fully consistent with previous experimental measurements and available numerical reference data. Specific features of the finite-gravity case are discussed with respect to a reduction of the average settling velocity, the acceleration statistics and the Lagrangian auto-correlations.

physics.flu-dyn↗

arXiv2014

Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow

A numerical method based upon the immersed boundary technique for the fluid-solid coupling and on a soft-sphere approach for solid-solid contact is used to perform direct numerical simulation of the flow-induced motion of a thick bed of spherical particles in a horizontal plane channel. The collision model features a normal force component with a spring and a damper, as well as a damping tangential component, limited by a Coulomb friction law. The standard test case of a single particle colliding perpendicularly with a horizontal wall in a viscous fluid is simulated over a broad range of Stokes numbers, yielding values of the effective restitution coefficient in close agreement with experimental data. The case of bedload particle transport by laminar channel flow is simulated for 24 different parameter values covering a broad range of the Shields number. Comparison of the present results with reference data from the experiment of Aussillous et al. (J. Fluid Mech. 2013) yields excellent agreement. It is confirmed that the particle flow rate varies with the third power of the Shields number once the known threshold value is exceeded. The present data suggests that the thickness of the mobile particle layer (normalized with the height of the clear fluid region) increases with the square of the normalized fluid flow rate.

physics.flu-dyn↗

arXiv2014

Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion

Direct numerical simulation of the gravity-induced settling of finite-size particles in triply-periodic domains has been performed under dilute conditions. For a single solid-to-fluid density ratio of 1.5 we have considered two values of the Galileo number corresponding to steady vertical motion (Ga=121) and to steady oblique motion (Ga=178) in the case of one isolated sphere. For the multi-particle system we observe strong particle clustering only in the latter case. The geometry and time scales related to clustering are determined from Voronoi tesselation and particle-conditioned averaging. As a consequence of clustering, the average particle settling velocity is increased by 12% as compared to the value of an isolated sphere; such a collective effect is not observed in the non-clustering case. By defining a local (instantaneous) fluid velocity average in the vicinity of the finite-size particles it is shown that the observed enhancement of the settling velocity is due to the fact that the downward fluid motion (with respect to the global average) which is induced in the cluster regions is preferentially sampled by the particles. It is further observed that the variance of the particle velocity is strongly enhanced in the clustering case. With the aid of a decomposition of the particle velocity it is shown that this increase is due to enhanced fluid velocity fluctuations (due to clustering) in the vicinity of the particles. Finally, we discuss a possible explanation for the observation of a critical Galileo number marking the onset of clustering under dilute conditions.

physics.flu-dyn↗

arXiv2014

Direct numerical simulation of pattern formation in subaqueous sediment

We present results of direct numerical simulation of incompressible fluid flow over a thick bed of mobile, spherically-shaped particles. The algorithm is based upon the immersed boundary technique for fluid-solid coupling and uses a soft-sphere model for the solid-solid contact. Two parameter points in the laminar flow regime are chosen, leading to the emergence of sediment patterns classified as `small dunes', while one case under turbulent flow conditions leads to `vortex dunes' with significant flow separation on the lee side. Wavelength, amplitude and propagation speed of the patterns extracted from the spanwise-averaged fluid-bed interface are found to be consistent with available experimental data. The particle transport rates are well represented by available empirical models for flow over a plane sediment bed in both the laminar and the turbulent regimes.

physics.flu-dyn↗

arXiv2013

The motion of a single heavy sphere in ambient fluid: a benchmark for interface-resolved particulate flow simulations with significant relative velocities

Detailed data describing the motion of a rigid sphere settling in unperturbed fluid is generated by means of highly-accurate spectral/spectral-element simulations with the purpose of serving as a future benchmark case. A single solid-to-fluid density ratio of 1.5 is chosen, while the value of the Galileo number is varied from 144 to 250 such as to cover the four basic regimes of particle motion (steady vertical, steady oblique, oscillating oblique, chaotic). This corresponds to a range of the particle Reynolds number from 185 to 365. In addition to the particle velocity data, extracts of the fluid velocity field are provided, as well as the pressure distribution on the sphere's surface. Furthermore, the same solid-fluid system is simulated with a particular non-boundary-conforming approach, i.e. the immersed boundary method proposed by Uhlmann (JCP 2005), using various spatial resolutions. It is shown that the current benchmark case allows to adjust the resolution requirements for a given error tolerance in each flow regime.

physics.flu-dyn↗

arXiv2013

Spatial and temporal scales of force and torque acting on wall-mounted spherical particles in open channel flow

Data from direct numerical simulation of open channel flow over a geometrically rough wall at a bulk Reynolds number of 2900, generated by Chan-Braun et al. ["Force and torque acting on particles in a transitionally rough open-channel flow", J. Fluid Mech. 684, 441--474 (2011), 10.1017/jfm.2011.311] are further analysed with respect to the time and length scales of force and torque acting on the wall-mounted spheres. For the two sizes of spheres in a square arrangement (11 and 49 wall units in diameter, yielding hydraulically smooth and transitionally rough flow, respectively), the spatial structure of drag, lift and spanwise torque is investigated. The auto-correlation and spectra in time as well as the space-time correlation and convection velocities are presented and discussed. It is found that the statistics of spanwise particle torque are similar to those of shear stress at a smooth wall. Particle drag and lift are shown to differ from spanwise particle torque, exhibiting considerably smaller time and length scales; the convection velocities of drag and lift are somewhat larger than those of spanwise torque. Furthermore, correlations between the flow field and particle-related quantities are presented. The spatial structure of the correlation between streamwise velocity and drag/spanwise torque features elongated shapes reminiscent of buffer-layer streaks. The correlation between the pressure field and the particle drag exhibits two opposite-signed bulges on the upstream and downstream sides of a particle.

physics.flu-dyn↗

arXiv2013

DNS of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction

We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of 1.7 times the fluid density and a solid volume fraction of 0.0005. The value of the Galileo number is set to 16.5, while the Shields parameter measures approximately 0.2. Under these conditions, the particles are predominantly located in the vicinity of the bottom wall, where they exhibit strong preferential concentration which we quantify by means of Voronoi analysis and by computing the particle-conditioned concentration field. As observed in previous studies with similar parameter values, the mean streamwise particle velocity is smaller than that of the fluid. We propose a new definition of the fluid velocity "seen" by finite-size particles based on an average over a spherical surface segment, from which we deduce in the present case that the particles are instantaneously lagging the fluid only by a small amount. The particle-conditioned fluid velocity field shows that the particles preferentially reside in the low-speed streaks, leading to the observed apparent lag. Finally, a vortex eduction study reveals that spanwise particle motion is significantly correlated with the presence of vortices with the corresponding sense of rotation which are located in the immediate vicinity of the near-wall particles.

physics.flu-dyn↗

arXiv2012

DNS of vertical plane channel flow with finite-size particles: Voronoi analysis, acceleration statistics and particle-conditioned averaging

We have performed a direct numerical simulation of dilute turbulent particulate flow in a vertical plane channel, fully resolving the phase interfaces. The flow conditions are the same as those in the main case of "Uhlmann, M., Phys. Fluids, vol. 20, 2008, 053305", with the exception of the computational domain length which has been doubled in the present study. The statistics of flow and particle motion are not significantly altered by the elongation of the domain. The large-scale columnar-like structures which had previously been identified do persist and they are still only marginally decorrelated in the prolonged domain. Voronoi analysis of the spatial particle distribution shows that the state of the dispersed phase can be characterized as slightly more ordered than random tending towards a homogeneous spatial distribution. It is also found that the p.d.f.'s of Lagrangian particle accelerations for wall-normal and spanwise directions follow a lognormal distribution as observed in previous experiments of homogeneous flows. The streamwise component deviates from this law presenting significant skewness. Finally, a statistical analysis of the flow in the near field around the particles reveals that particle wakes present two regions, a near wake where the velocity deficit decays as 1/x and a far wake with a decay of approximately 1/(x*x).

physics.flu-dyn↗