Session U27: Turbulence: Shear Layers and Wakes

Turbulent energy distribution in scales and energy transfers in non-homogeneous turbulence

Wakes produced by bluff bodies give rise to intense turbulence whose dynamics cannot be described by the classical Richardson-Kolmogorov cascade; this is not only due to mean flow gradients, responsible for turbulence production, but also due to coherence and inhomogeneity in the turbulence fluctuations. We address this latter aspect of wake turbulence through asymptotic matching of the second order structure function and subsequently examining its governing equation (the Kármán-Howarth-Monin-Hill - KHMH - equation) at inner (small) and outer (large) scales. Through direct numerical simulation of turbulent wakes generated by pairs of prisms, we find that the second order structure functions display clear 2/3 power laws and are self-similar both in terms of inner and outer scales, provided the coherence is not too strong. This is in spite of the non-equilibrium and non-homogeneous nature of the cascade, which gives rise to power law dependencies of the normalised dissipation on the local Reynolds number and which is clearly manifest in the fact that all terms involved in the KHMH equation are active. These terms are found to be self-similar only in terms of inner scales, which is in fact the sole requirement in predicting 2/3 power laws in non-homogeneous turbulence.   

The effects of freestream turbulence on the near- and mid-field wake of circular and square cylinders

Cylindrical objects often appear in both natural and artificial environments, and are often subjected to turbulent incoming flows. Furthermore, they are often found in groups, where the flow field around any particular element will interact with other elements. Thus, it is crucial to understand how the wake behind these cylinders is influenced by different incoming turbulent flows, particularly in the near- to mid-field regions, where interactions with other elements can be expected and do not necessarily follow universal laws. Using planar PIV, we investigated the wake of a circular and a square cylinder up to 20 cylinder diameters downstream, or 1 m in physical length. Four different inflow conditions are generated with an active grid, with the freestream turbulence intensity levels ranging from 2% to 13%. The Reynolds number is approximately 50 000. Preliminary analysis shows that the coherent structures in the wake are suppressed with increasing freestream turbulence level, and that mean velocity recovery in the wake is promoted. The centreline velocity deficit and the wake half-width follow their expected power-laws in the streamwise direction. Subsequent analysis will focus on how the self-similar behaviour of the wake are influenced by the freestream turbulence.   

Tracking fluid particles in subsonic, transonic and supersonic flows past a circular cylinder

Inertial and non-inertial particle-laden flows were very extensively reported in the literature for isotropic turbulence, channel flow, boundary layers, jets and wakes. By contrast, there are very few studies of circular cylinder particle-laden flow, and those only considered the incompressible, nearly two-dimensional, very-low Reynolds number range between 100 and 300, based on diameter and upstream speed. In this work, Eulerian DNS of flows past a circular cylinder for subsonic, transonic and supersonic conditions are first performed at Mach numbers of 0.2, 0.9 and 1.2 and Reynolds numbers 3,900 and 10,000. Lagrangian tracking and sampling of fluid tracer particles are then carried out in a second step. For each flow condition, 200,000 particles are released from the immediate vicinity of the cylinder surface and from a selected upstream plane. An ensemble of 8 different initial release instants are employed to increase sample size. The recorded particle velocity and position fields are used to extract statistics concerning instantaneous flow reversal and dispersion. The multiple sets of oblique and normal shock waves in the transonic and supersonic flows alter the particle behavior in an intriguing manner.   

Turbulence and Recirculation Modulation in a Wall-mounted Cruciform

The investigation presented aims to compare the turbulence and recirculation characteristics of cross-cylinder arrangements. Cross-cylinder structures alter the effect of local ocean currents, fish populations and scouring of the surrounding sediment. Several hydrodynamic environments are home to this type of flow such as in the areas of off-shore oil rigs, reef restoration stations and in the foundations of pier piles. The flow over the body of a cruciform with modified branch angle is used to demonstrate the changes in the flow field impacting the turbulence statistics and the resulting recirculation zone aft of the geometry. During local optimization of the branch angle of the cruciform, the reduction in drag coefficient was associated with changes in the size of the recirculation zone, the coherence of the cross-cylinder's vortex shedding and the wake. The cross-cylinder arrangements with modified branch angle demonstrate lower coefficient of drag at lower branch angle is attributed to a shift in wake size and breakdown in the shedding structure coherency. The turbulence characteristics of the interaction between the recirculation zone and branch shedding vortices is captured through hybrid RANS/LES formulation (IDDES) for a neutral, high and low branch angled cruciform. The work will focus on the cross-cylinder arrangements at a Reynolds number of ~7500 using 0.3 m/s inlet flow. Analysis of the turbulent kinetic energy budget transport, time averaged fluctuations, probability distribution functions and two-point correlations will be utilized to complement the qualitative turbulence structures identified within the flow field of the cruciform.   

Unsteady wake characteristics of unequal-height tandem cylinders submerged in a turbulent boundary layer

The unsteady wake dynamics of two finite wall-mounted cylinders of unequal-height arranged in tandem are investigated using time-resolved particle image velocimetry. The cylinders were submerged in a water tunnel with a turbulent boundary layer (TBL) of thickness 8.7d (where d is the cylinder diameter) and Reynolds number based on d of 5540. The spacing ratio of the cylinders was fixed at 4d. Five height ratios (h/H = 0.1 – 1.0) were studied by varying the aspect ratio (AR) of the upstream cylinder, UC (h/d) while fixing the AR of the downstream cylinder, DC (H/d = 7.0). The height ratio introduced sheltering where part or the whole span of the DC was blocked from direct interaction with the TBL. As the height ratio increases, the downwash from UC impinges on the front of the DC and induces a stronger upwash on the opposite side of the DC. The induced upwash impedes the downwash behind the DC, enhances the Reynolds stresses and significantly modifies the wake topology for increasing height ratio. Spectral analysis and joint-probability density functions of the reverse flow area showed that the attachment of the downwash of the UC on the DC mutually affects the pumping motion of the reverse flow area behind each cylinder.

  

*Natural Sciences and Engineering Research Council.  

    

Scaling patch analysis of planar turbulent wakes

A scaling patch approach is used to investigate the proper scales in planar turbulent \textcolor{black}{wakes}. A proper scale for the mean axial flow is the well-known maximum velocity deficit $U_\mathrm{ref} = U_\infty - U_\mathrm{ctr}$, where $U_\infty$ is the free stream velocity and $U_\mathrm{ctr}$ is the mean axial velocity at the wake centerline. From an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is found as $V_\mathrm{ref} = (d\delta/dx) U_\mathrm{ref}$, where $d\delta/dx$ is the growth rate of the wake width. From an admissible scaling of the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is found as $R_{uv,\mathrm{ref}}= U_\infty V_\mathrm{ref}$, which is a mixed scale of the free stream velocity and the mean transverse flow scale. Expressions are derived for the scaled mean transverse velocity and Reynolds shear stress in the far field of planar turbulent wakes. Using a Gaussian function for the mean axial velocity deficit, approximate functions for the scaled mean transverse velocity and Reynolds shear stress are developed and found to agree well with experimental and simulation data. This work reveals that the mean transverse flow, despite its small magnitude, plays an important role in the scaling and understanding of the planar turbulent wake.   

Length Scales Governing Turbulence Transport and Mass Diffusion in Variable-Density Turbulent Shear-Driven Mixing Layers

Moment equations for quantities characterizing variable-density turbulence in shear-driven mixing layers include terms describing turbulence transport and mass diffusion behavior. Modeling these quantities with common closures (RANS-type modeling, e.g., Schwarzkopf et al., Flow, Turbulence and Combustion, 96, 2016) introduces length scales defining these processes for the moments evolving within the flow. Direct numerical simulations for low-speed mixing of two miscible fluids with Atwood numbers of up to 0.87 (Baltzer and Livescu, J. Fluid Mech, 900, 2020) allow the relevant length scales to be extracted using the actual budget terms. Besides Reynolds stresses and turbulent kinetic energy, which are relevant to all turbulent flows, this variable-density flow also requires that density correlations (turbulent mass flux and density-specific volume correlation) be considered. Analyzing the length scales for the various quantities reveals the degree to which the governing processes are similar between turbulent motions and variable-density effects.   

Direct numerical simulations of a statistically stationary and streamwise periodic turbulent mixing layer

Turbulent mixing layers are one of the most studied turbulent free shear flows and are found in combustion, aerodynamics, and atmospheric applications. Most turbulent mixing layer simulations are computationally inefficient. In temporally evolving (spatially homogeneous) mixing layers, the thickness continuously grows in time and most of the simulation time is wasted resolving the transient behavior. Spatially evolving (temporally stationary) mixing layers grow in space and require a long streamwise domain to develop the desired Reynolds number. To combat these limitations, we propose a method utilizing direct numerical simulation (DNS) of incompressible turbulent mixing layers that normalize the coordinate system under which the Navier-Stokes equations (NS) are solved. Anticipated self-similarity is used to develop this scaling and introduces additional unclosed source terms involving the mixing layer growth rate which are resolved on the fly using the simulation data. This approach is an extension of Ruan (2021) where this technique was originally applied to turbulent flat-plate boundary layers. To validate our approach, we compare mean, extracted growth rates, rms, and Reynolds shear stress profiles with other DNS calculations of turbulent mixing layers.   

Surface-Pressure Measurements of Bi-stability on BeVERLI Hill

Over the past two decades, several experimental campaigns have been conducted with hill geometries in an effort to improve our knowledge on the behaviour of turbulent boundary layer flows subject to pressure gradients and surface curvature effects. The Benchmark Validation Experiments for RANS and LES Investigations (BeVERLI) project is being conducted to collect detailed experimental datasets of the flow over a three-dimensional hill geometry. Mean and unsteady surface-pressure measurements were collected at the Virginia Tech Stability Wind Tunnel and the recirculating wind tunnel at the University of Toronto Institute for Aerospace Studies. Results obtained at the two facilities are compared to evaluate their sensitivity to extrinsic experimental conditions. The results for the 0^? model orientation and model height based Reynolds numbers from 165,000 to 325,000 are presented. For this orientation, the wake is bi-stable in nature. The behaviour of this phenomena is explored by tracking the time elapsed between switching events, conditional averaging of the two modes, and proper orthogonal decomposition of the surface-pressure field. It is shown that the mean surface-pressure distributions of the two modes are symmetrical about the hill centerline. Furthermore, a favouring toward one mode is observed from the measurements collected at Virginia Tech. This is associated with an asymmetry in wall conditions at the test facility indicating the sensitivity of the bi-stable flow to extrinsic conditions.   

Geometrical influence on decay rates of low-order azimuthal modes in turbulent axisymmetric wakes

The dynamics of coherent structures in turbulent wakes are of particular interest in aero- and hydrodynamic applications, as they have a relationship with the drag on a body. Understanding the primary coherent structures within a wake and their dynamics can help us further understand and develop turbulence models. In this work, the influence of initial geometry on the decay of coherent structures in turbulent axisymmetric wakes is investigated at a Reynolds number Re = 26,000. The rate at which the first azimuthal mode decays, associated with vortex shedding, is strongly influenced by initial conditions. The downstream location where the double-helix mode, the second azimuthal mode, dominates for the disk is consistent with those found in the literature, however, it can be moved further downstream by modifying the initial geometry of the wake generating plate.   

Decay of an axisymmetric drag wake at Reynolds number (Re) 105

The problem of axisymmetric drag wakes has been studied for nearly a century (Swain 1929), yet the far-field wake decay scaling law is still not fully understood. Recently, there has been substantial evidence that the previously accepted scaling law is incorrect (Bonnier and Eiff 2002, Nedic et al 2013, Saunders et al 2020).  Here, the drag wake of a dimpled sphere at Re = 10⁵ is studied experimentally using Stereo Particle Image Velocimetry to a downstream distance of ~90 diameters. The data were used to produce estimates of the mean velocity field, velocity fluctuations, and Reynolds stresses. Self-similar decay was observed with the ensemble mean axial velocity defect decaying as x^-1 and the wake size growing as x^1/2 which matched previous dimpled sphere data at Re = 50,000. Due to the difference in Reynolds number, the two spheres have different drag coefficients (0.13 and 0.25, respectively), but these self-similar decay exponents were not observed to depend on drag coefficient or Reynolds number. The results suggest that the self-similar drag wake decay observed at laboratory scales may extrapolate to the larger Re typical of engineering and geophysical flows.