Estimation of Turbulent Length Scales at a Turbocharger Inlet using Stereoscopic Particle Image Velocimetry

Stereoscopic Particle Image Velocimetry measurements are carried out at the inlet of a turbocharger compressor at four different shaft speeds from 80,000 rpm to 140,000 rpm and over the entire range of flow rates from choke to mild surge. This paper describes the procedure used in processing the PIV data leading to the estimates of turbulent length scales - integral, Taylor, and Kolmogorov, to enhance the fundamental understanding and characterization of the compressor inlet flow field. The analysis reveals that at most operating conditions the three different length scales have markedly different magnitudes, as expected, while they have somewhat similar qualitative distributions with respect to the duct radius. For example, at 80,000 rpm and at a flow rate of 15.7 g/s (mild surge), the longitudinal integral length scale is of the order of 15 mm, the Taylor scale is around 0.5 mm, and the Kolmogorov scale is about 10 microns. With the onset of flow reversal, the turbulent kinetic energy and turbulent intensity at the compressor inlet are observed to increase rapidly, while the magnitudes of the Kolmogorov scale and to a certain extent, the Taylor scale are found to decrease suggesting that the increased turbulence gives rise to even smaller flow structures. The variation of length scales with compressor shaft speed has also been studied.

Estimation of Turbulent Length Scales at a Turbocharger Inlet Using Particle Image Velocimetry

Stereoscopic Particle Image Velocimetry measurements are carried out at the inlet of a turbocharger compressor at four different shaft speeds from 80,000 rpm to 140,000 rpm and over the entire range of flow rates from choke to mild surge. This paper describes the procedure used in processing the PIV data leading to the estimates of turbulent length scales – integral, Taylor, and Kolmogorov, to enhance the fundamental understanding and characterization of the compressor inlet flow field. The analysis reveals that at most operating conditions the three different length scales have markedly different magnitudes, as expected, while they have somewhat similar qualitative distributions with respect to the duct radius. For example, at 80,000 rpm and at a flow rate of 15.7 g/s (mild surge), the longitudinal integral length scale is of the order of 15 mm, the Taylor scale is around 0.5 mm, and the Kolmogorov scale is about 10 microns. With the onset of flow reversal, the turbulent kinetic energy and turbulent intensity at the compressor inlet are observed to increase rapidly, while the magnitudes of the Kolmogorov scale and to a certain extent, the Taylor scale are found to decrease suggesting that the increased turbulence gives rise to even smaller flow structures. The variation of length scales with compressor shaft speed has also been studied.

Chemical Signaling in the Turbulent Ocean—Hide and Seek at the Kolmogorov Scale

Chemical cues and signals mediate resource acquisition, mate finding, and the assessment of predation risk in marine plankton. Here, we use the chemical properties of the first identified chemical cues from zooplankton together with in situ measurements of turbulent dissipation rates to calculate the effect of turbulence on the distribution of cues behind swimmers as well as steady state background concentrations in surrounding water. We further show that common zooplankton (copepods) appears to optimize mate finding by aggregating at the surface in calm conditions when turbulence do not prevent trail following. This near surface environment is characterized by anisotropic turbulence and we show, using direct numerical simulations, that chemical cues distribute more in the horizontal plane than vertically in these conditions. Zooplankton may consequently benefit from adopting specific search strategies near the surface as well as in strong stratification where similar flow fields develop. Steady state concentrations, where exudation is balanced by degradation develops in a time scale of ~5 h. We conclude that the trails behind millimeter-sized copepods can be detected in naturally occurring turbulence below the wind mixed surface layer or in the absence of strong wind. The trails, however, shorten dramatically at high turbulent dissipation rates, above ~10−3 cm2 s−3 (10−7 W kg−1)

Decaying turbulence in a stratified fluid of high Prandtl number

Decaying turbulence in a density-stratified fluid with a Prandtl number up to $Pr=70$ is investigated by direct numerical simulation. In turbulent flow with a Prandtl number larger than unity, it is well known that the passive scalar fluctuations cascade to scales smaller than the Kolmogorov scale, and show the $k^{-1}$ spectrum in the viscous–convective range, down to the Batchelor scale. In decaying stratified turbulence, the same phenomenon is initially observed for the buoyant scalar of high $Pr~(=70)$, until the Ozmidov scale becomes small and the buoyancy becomes effective even at the Kolmogorov scale. After that moment, however, the velocity components near the Kolmogorov scale begin to show strong anisotropy dominated by the vertically sheared horizontal flow, which reduces the vertical scale of density fluctuations. An analysis similar to that of Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) indeed shows that the vertically sheared horizontal flow reduces the vertical scale of density fluctuations, without changing the horizontal scale.

On the small-scale structure of turbulence and its impact on the pressure field

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length of the second invariant of the velocity gradient is proportional to the Kolmogorov scale. It is also a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.

Conditional damped random surface velocity model of turbulent jet breakup

A turbulent jet breakup model is derived using concepts from probability theory. Velocity fluctuations at the free surface are hypothesized to be the cause of turbulent jet breakup. We formalize this idea by treating the fluctuations as random variables, subject to damping from the free surface. In contrast to previous theories, we use a conditional ensemble average to determine quantities of interest because not all fluctuations produce droplets. An energy balance and a closure model are used to determine the Sauter mean diameter. Similar approaches are used to determine the breakup onset location, breakup length, and spray angle. A criteria for the transition to the turbulent atomization regime is derived under the hypothesis that the cause is a change in the minimum velocity from the Hinze scale to the Kolmogorov scale. To validate the model, we compiled data from previous experimental studies using long pipe nozzles. The little data for rough pipes was used to include turbulence intensity in our study.

A solvable model of Vlasov-kinetic plasma turbulence in Fourier–Hermite phase space

A class of simple kinetic systems is considered, described by the one-dimensional Vlasov–Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan–Batchelor model of chaotic advection. The solution of the model is found in Fourier–Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier–Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wavenumbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wavenumbers ($k$). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

Exact coherent structures in stably stratified plane Couette flow

The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds–Richardson number ($Re$–$Ri_{b}$) space for a fluid of unit Prandtl number $(Pr=1)$ using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge tracking – EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (J. Fluid Mech., vol. 745, 2014, pp. 25–61) – and found to connect with two-dimensional convective roll solutions when tracked to negative $Ri_{b}$ (the Rayleigh–Bénard problem with shear). Both these states and Nagata’s (J. Fluid Mech., vol. 217, 1990, pp. 519–527) original exact solution feel the presence of stable stratification when $Ri_{b}=O(Re^{-2})$ or equivalently when the Rayleigh number $Ra:=-Ri_{b}Re^{2}Pr=O(1)$. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at $Ri_{b}=O(Re^{-2/3})$. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58–85). Increasing the stratification further appears to lead to a third, ultimate regime where $Ri_{b}=O(1)$ in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar–turbulent boundary in the ($Re$–$Ri_{b}$) plane are briefly discussed.