Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

Abstract

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle$ , is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol {U} \rangle$ , for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol {\nabla }\boldsymbol {\cdot } \langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated with entrained fluid particles. By considering a classical advection–diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$ ) and momentum (through the turbulent viscosity $\nu _T$ ) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu _T$ (and hence of the turbulent Prandtl number $\sigma _T = \nu _T/K_T$ ) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets.

Compensation of seeding bias for particle tracking velocimetry in turbulent flows

“…Equation ( 10) is a usual approximation for the mean axial velocity V z = V z (r, z)/V z (0, z) for a turbulent jet. As already discussed in a previous work [15], there is no apparent bias from nonhomogeneous seeding for the axial velocity component in a turbulent jet and then V z = V z .…”

“…An ensemble of trajectories is recorded using a stereoscopic visualization technique at frame rate of 6 kHz with three high-speed cameras. More details about the experimental configuration and the particle tracking method can be found in previous works using the same configuration [15,44].…”

“…This solution was obtained in a previous work [15] and aims at describing the mean radial velocity of the tracers if the tracers are injected by the nozzle (the subscript N is for nozzle). If the tracers are injected by the nozzle, then the tracer concentration verifies the same self-similar properties than the axial velocity itself [46], which allows us to compute the solution (12).…”

“…With the example of turbulent jets with particles injected from the nozzle, there is a significant mismatch between the measured radial velocities from the particle tracking analysis and the expected radial velocities [14]. In recent a work [15], it was shown that this radial velocity mismatch is consistent with the particle dispersion by the turbulent jet which can be formulated as a compressible expansion flow for the tracers resulting in an enhanced radial flow.…”

Dose-Response Relationship of Therapeutic Oxygen: More Is Not Necessarily Better and May Be Inferior to No Supplemental Oxygen – Part 1: Proof and Nature

“…In addition, the 1990 study by Barth et al [61] introduced previously in this report, demonstrates that the holes drilled in proximal and distal metaphyses of rat femurs filled in 3 weeks through primary ossification when HBO 2 was administered once a day, in 4 weeks through enchondral ossification without HBO 2 , and in 5 weeks through enchondral ossification when HBO 2 was administered twice a day. In prior research conducted by Bassett and Herrmann [125], it was determined that in vitro connective tissue cells, cut free from a clot of such cells and exposed to modestly elevated levels of oxygen (i.e., 35% with 5% CO 2 and balance N 2 ) would compact and differentiate directly to osseous tissue (primary ossification). Connective tissue cells cut free from the larger mass and exposed to reduced levels of oxygen (i.e., 5% with 5% CO 2 and balance N 2 ) would compact and differentiate to cartilage (enchondral ossification).…”