Energy cascades in active-grid-generated turbulent flows

Abstract

The energy cascade and diverse turbulence properties of active-grid-generated turbulence were studied in a wind tunnel via hot-wire anemometry. To this aim, two active grid protocols were considered. The first protocol is the standard triple-random mode, where the grid motors are driven with random rotation rates and directions, which are changed randomly in time. This protocol has been extensively used due to its capacity to produce higher values of Re λ than its passive counter part, with good statistical homogeneity and isotropy. The second protocol was a static or open grid mode, where all grid blades were completely open, yielding the minimum blockage attainable with our grid.Centreline streamwise profiles were measured for both protocols and several inlet velocities. It was found that the turbulent flow generated with the triple-random protocol evolved in the streamwise direction consistently with an energy dissipation scaling of the form ε = C ε u 3 /L, with C ε being a constant, L the longitudinal integral length-scale, and u the rms of the longitudinal velocity fluctuations.Conversely for the open-static grid mode, the energy dissipation followed a non-equilibrium turbulence scaling, namely, C ε ∼ Re G /Re L , where Re G is a global Reynolds number based on the inlet conditions of the flow, and Re L is based on the local properties of the flow downstream the grid. Furthermore, this open-static grid mode scaling exhibits important differences with other grids, as the downstream location of the peak of turbulence intensity is a function of the inlet velocity, a remarkable observation not previously reported, as it would allow to study the underlying principles of the transition between equilibrium and non-equilibrium scalings, which are yet to be understood.It was also found that a rather simple theoretical model can predict the value of C ε based on the number density of zero-crossings of the longitudinal velocity fluctuations. A theory, which is valid for both active grid operating protocols (and therefore two different energy cascades).

Pitfalls Measuring 1D Inertial Particle Clustering

“…This polydispersity was previously quantified by means of a PDI (see [1,2]), and the measurements for this study are illustrated in figure 1b. The turbulence within the measuring region (3 in figure 1a) has been experimentally found to be very close to a statistically homogeneous isotropic state [24,25] under similar conditions (Re λ , and η) as the ones reported here [21]. Figure 1c shows the energy spectrum, taken at this measuring station via hot-wire anemometry, with a mild region where statistically isotropic turbulence (see -5/3 power-law in the figure) was recovered.…”

“…A schematic sketch of the experimental setup is shown in figure 1a. Turbulence is produced by means of an active grid [20] operated in triple random or open mode [21] (using both grid protocols, we recovered K41 [22,23] turbulence at the measuring locations), downstream of which a rack of 36 spray nozzles generate inertial water droplets with a polydisperse diameter distribution. This polydispersity was previously quantified by means of a PDI (see [1,2]), and the measurements for this study are illustrated in figure 1b.…”

Experimental estimation of turbulence modification by inertial particles at moderateReλ

“…However, in order to the latter argument to hold there should be sufficient particles to sample the fluid flow (see figure2a for criteria). These two observations give credence to extend the mentioned approach to particle laden flows considering that the cut-off wave number 2π/η C , after which Vassilicos and collaborators [14,15] found a plateau in the density of zero crossings n s , was at least one order of magnitude larger than the Kolmogorov length-scale, i.e., a low-pass filtered particle velocity record could still be able to resolve the value of λ.…”

“…Hence, the particle field velocity is a low-pass filtered version of the carrier phase one, and being the filter a function of the Stokes number (St = τ p /τ η , with τ η = (ν/ε) 1/2 the Kolmogorov time scale of the flow) with a cut-off frequency of f c = τ −1 p /2π, or f c τ η = (2πSt) −1 . Several authors [12][13][14][15] starting from Liepmann, have proposed and extended a way to estimate the Taylor microscale (λ) in an unladen flow from the density of zero crossings n s of the longitudinal velocity fluctuation component u (x) [13][14][15] where the temporal measurements are translated into space by means of the Taylor hypothesis. These zero crossings follow a powerlaw function dependent on the ratio between the flow integral lengthscale (L), and the size of a low pass filter η C (not to be confused with the Kolmogorov length-scale η) applied to the 'raw' signal.…”

“…This wind tunnel has been extensively used to study particle-turbulence interaction under homogeneous isotropic turbulent (HIT) conditions (more experimental details are described in [22][23][24]). The measuring station was located three meters (3m) downstream the active grid, and at the center line of the wind tunnel, where HIT and the classical scalings from K41 theory have been recovered [15]. At this position we set a PDI device (Artium Technologies PDI-200), with an experimental setup, which was almost identical as the one described in Sumbekova [21], with the only difference being two circular holes of ten centimeters (10cm) on each window.…”