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Register a new userTracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow
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We study the 6-dimensional dynamics -- position and orientation -- of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with 2 high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation `candidates at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the integral range, close to the integral scale of the underlying turbulent flow.
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We study the melting dynamics of large ice balls in a turbulent von Karman flow at very high Reynolds number. Using an optical shadowgraphy setup, we record the time evolution of particle sizes. We study the heat transfer as a function of the particle scale Reynolds number for three cases: fixed ice balls melting in a region of strong turbulence with zero mean flow, fixed ice balls melting under the action of a strong mean flow with lower fluctuations, and ice balls freely advected in the whole flow. For the fixed particles cases, heat transfer is observed to be much stronger than in laminar flows, the Nusselt number behaving as a power law of the Reynolds number of exponent 0.8. For freely advected ice balls, the turbulent transfer is further enhanced and the Nusselt number is proportional to the Reynolds number. The surface heat flux is then independent of the particles size, leading to an ultimate regime of heat transfer reached when the thermal boundary layer is fully turbulent.
In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety of different potentials. In this work, we use the same hypothesis to develop new fluid mechanics equations which model turbulent gas flow on a macroscopic scale. The main difference between our approach and the conventional formalism is that we avoid replacing the potential interaction between particles with the Boltzmann collision integral. Due to this difference, the velocity moment closure, which we implement for the shear stress and heat flux, relies upon the high Reynolds number condition, rather than the Newton law of viscosity and the Fourier law of heat conduction. The resulting system of equations of fluid mechanics differs considerably from the standard Euler and Navier-Stokes equations. A numerical simulation of our system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier spectra of the kinetic energy of this flow exhibit Kolmogorovs negative five-thirds power decay rate.
Three-dimensional particle tracking experiments were conducted in a turbulent boundary layer with friction Reynolds number $Re_tau$ of 700 and 1300. Two finite size spheres with specific gravities of 1.003 (P1) and 1.050 (P2) and diameters of 60 and 120 wall units were released individually from rest on a smooth wall. The spheres were marked with dots all over the surface to monitor their translation and rotation via high-speed stereoscopic imaging. The spheres accelerated strongly after release over streamwise distances of one boundary layer thickness before approaching an approximate terminal velocity. Initially, sphere P1, which had Reynolds numbers $Re_p$ of 800 and 1900, always lifts off from the wall. Similar behavior was observed occasionally for sphere P2 with initial $Re_p$ of 1900. The spheres that lifted off reached an initial peak in height before descending towards the wall. The sphere trajectories exhibited multiple behaviors including saltation, resuspension and sliding motion with small random bouncing depending on both $Re_tau$ and specific gravity. The lighter sphere at $Re_tau=1300$, which remained suspended above the wall during most of its trajectory, propagated with the fastest streamwise velocity. By contrast, the denser sphere at $Re_tau=700$, which mostly slid along the wall, propagated with the slowest streamwise velocity. After the spheres approached an approximate terminal velocity, many experienced additional lift-off events that were hypothesized to be driven by hairpins or coherent flow structures. Spheres were observed to rotate about all three coordinate axes. While the mean shear may induce a rotation about the spanwise axis, near-wall coherent structures and the spheres wake might drive the streamwise and wall-normal rotations. In all cases where the sphere propagates along the wall, sliding motion, rather than forward rolling motion, is dominant.
The unsteady, lineal translation of a solid spherical particle through viscoelastic fluids described by the Johnson-Segalman and Giesekus models is studied analytically. Solutions for the pressure and velocity fields as well as the force on the particle are expanded as a power series in the Weissenberg number. The momentum balance and constitutive equation are solved asymptotically for a steadily translating particle up to second order in the particle velocity, and rescaling of the pressure and velocity in the frequency domain is used to relate the solutions for steady lineal translation to those for unsteady lineal translation. The unsteady force at third order in the particle velocity is then calculated through application of the Lorentz reciprocal theorem, and it is shown that this weakly nonlinear contribution to the force can be expressed as part of a Volterra series. Through a series of examples, it is shown that a truncated representation of this Volterra series, which can be manipulated to describe the velocity in terms of an imposed force, is useful for analyzing specific time-dependent particle motions. Two examples studied using this relationship are the force on a particle suddenly set into motion and the velocity of a particle in response to a suddenly imposed steady force. Additionally, the weakly nonlinear response of particle captured by a harmonic trap moving lineally through the fluid is computed. This is an analog to active microrheology experiments, and can be used to explain how weakly nonlinear responses manifest in active microrheology experiments with spherical probes.
Plane Couette flow presents a regular oblique turbulent-laminar pattern over a wide range of Reynolds numbers R between the globally stable base flow profile at low R<R_g and a uniformly turbulent regime at sufficiently large R>R_t. The numerical simulations that we have performed on a pattern displaying a wavelength modulation show a relaxation of that modulation in agreement with what one would expect from a standard approach in terms of dissipative structures in extended geometry though the structuration develops on a turbulent background. Some consequences are discussed.
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