Measurement of turbulent spatial structure and kinetic energy spectrum by exact temporal-to-spatial mapping

Abstract

We present a method for converting a time record of turbulent velocity measured at a point in a flow to a spatial velocity record consisting of consecutive convection elements. The spatial record allows computation of dynamic statistical moments such as turbulent kinetic wavenumber spectra and spatial structure functions in a way that completely bypasses the need for Taylor's Hypothesis. The spatial statistics agree with the classical counterparts, such as the total kinetic energy spectrum, at least for spatial extents up to the Taylor microscale. The requirements for applying the method is access to the instantaneous velocity magnitude, in addition to the desired flow quantity, and a high temporal resolution in comparison to the relevant time scales of the flow. We map, without distortion and bias, notoriously difficult developing turbulent high intensity flows using three main aspects that distinguish these measurements from previous work in the field; 1) The measurements are conducted using laser Doppler anemometry and are therefore not contaminated by directional ambiguity (in contrast to, e.g., frequently employed hot-wire anemometers); 2) The measurement data are extracted using a correctly and transparently functioning processor and is analysed using methods derived from first principles to provide unbiased estimates of the velocity statistics; 3) The exact mapping proposed herein has been applied to the high turbulence intensity flows investigated to avoid the significant distortions caused by Taylor's Hypothesis. The method is first confirmed to produce the correct statistics using computer simulations and later applied to measurements in some of the most difficult regions of a round turbulent jet -the non-equilibrium developing region and the outermost parts of the developed jet. The proposed mapping is successfully validated using corresponding directly measured spatial statistics in the fully developed jet, even in the difficult outer regions of the jet where the average convection velocity is negligible and turbulence intensities increase dramatically. The measurements in the developing region reveal interesting features of an incomplete Richardson-Kolmogorov cascade under development.

Creation of turbulence in polyatomic gas flow via an intermolecular potential

“…Both the inlet and outlet are visible in Figure 1 as gaps on the left-and right-hand sides of the plot. The length of the domain, together with the size and shape of the inlet, are consistent with those in the experiment of Buchhave and Velte [13].…”

“…Here, we use the inertial flow equations with the hard sphere mean field potential in (5.24) to simulate the flow of air in a straight pipe, with the parameters similar to those in the experiment by Buchhave and Velte [13]. We use the same computational software as in our previous works [4,5] -namely, OpenFOAM [47].…”

On the energy spectrum of rapidly rotating forced turbulence

“…As far as the isotropic small scales are concerned, we have proposed a model [Eq. (8)] that faithfully captures the behaviour of the kinetic energy spectrum in far dissipation range. Our proposed model is in very good agreement with the numerical results over the wavenumber range k ∈ [k η , k max ].…”

“…It is well known that, Kolmogorov 2,3 proposed an inertial range energy spectrum for homogeneous and isotropic 3D hydrodynamics turbulence: E(k) ∼ 2/3 k −5/3 , where is the constant energy dissipation rate. The Kolmogorov spectrum is quite universal and observed in plethora of other realistic settings, e.g., shear flows 4 , viscoelastic fluids 5 , buoyancy-driven systems 6,7 , and jet flows 8 . On the other hand, the energy cascade for the two-dimensional (2D) turbulence system shows dual behaviour [9][10][11][12][13] : an inverse cascade at large scales with E(k) ∼ k −5/3 and a forward cascade of enstrophy at relatively small scales with E(k) ∼ k −3 .…”

A novel volumetric velocity measurement method for small seeding tracers in large volumes

“…According to measurement result in Buchhave and Velte (2017), for 1 cm jet at Re = 19868, the length Taylor microscales are 2.2mm and the temporal Taylor microscales are 1ms at the center line at 30D downstream location and , which requires particle cut-off frequency higher than 1KHz and camera repetition rate higher than 2KHz. From 13mm radial distance off the jet centerline, the temporal Taylor microscales are 2ms, which requires particle cut-off frequency 500Hz.…”