Session F39: Turbulence: Wakes

On the decay of stratified wake: A numerical study

In stratified fluids, wakes are longer lived with a significant reduction of mean velocity defect. G.R. Spedding (1997) and K.A. Brucker & S. Sarkar (2010) quantify decay rates in 3 phases, namely a near-wake (NW), a non-equilibrium (NEQ), and a quasi-two-dimensional (Q2D) region. Given $U_0 \propto x^{-m}$, where $U_0$ is centerline mean defect velocity and $m$ is a decay rate, both studies observe $m_{NW} \approx 2/3$, $m_{NEQ} \approx 1/4$, and $m_{Q2D} \approx 3/4$. Here, $U_\infty$, $D$, and $N$ are the free-stream velocity, length scale of a wake generator, and constant background buoyancy frequency, respectively. However, M. Bonnier and O. Eiff (2002) observe $m_{NEQ}=0.38$ in their experiment and K. Chongsiripinyo and S. Sarkar (TSFP10) find $m_{NEQ}\simeq 0.4$ in their simulation. In the far wake, M. Bonnier and O. Eiff (2002) obtain $m_{Q2D}=0.9$ close to the value of $m=0.88$ from Spedding $et \; al.$ (1996) at similar flow conditions. Due to the lack of consistency, more evidence is required. The present study utilizes advantages of both body-inclusive ($BI$) and temporal-model ($TF$) simulations to not only resolve near-body statistics, but also to reduce computational expense needed. Decay rates of mean velocity defect and turbulence dissipation will be presented.   

Hybrid D.N.S. model of the spatially-evolving turbulent wake

A hybrid spatially-evolving D.N.S. model is used to simulate the turbulent wake behind a sphere at Reynolds number, $Re=U_\infty D/\nu=3700$ and Froude numbers, $Fr=U_\infty/ND=\infty, 3$, and $1$. Without a sphere in the domain but inflow conditions generated from a body-inclusive simulation, this method is a hybrid of both body-inclusive and body-exclusive models. To investigate extraction sensitivity, inlet conditions are extracted from three locations in the streamwise direction, $x_1/D=3, 6$, and $10$. It is found that strategic choice in extraction location accounting for local flow physics is required for statistical accuracy. Grid resolution is examined for all Froude numbers. Vorticity contours illustrate good qualitative agreement between the hybrid model and body-inclusive simulations. The two-layered form is captured well while phase lines indicating internal wave propagation are clearly observed. Analysis of turbulent kinetic energy also indicates agreement between the hybrid model and body-inclusive simulations.   

Experimental evaluation of square bar and fractal grid-generated turbulent flow inside recirculating water tunnel

High resolution, two dimensional PIV measurements of grid-generated turbulence in the US Naval Academy's recirculating water tunnel (1.8m test section with 0.41m x 0.41m cross sectional area) are presented for two different grid designs. The first grid is a uniform square bar grid with mesh width, M$=$3.9cm, bar thickness t$_{\mathrm{0}}=$1cm, a streamwise thickness of 1cm and resulting solidity of 44{\%}, similar to the conventional grid used by Krogstad and Davidson (2012). The other is Mazellier {\&} Vassilicos' (2010) square fractal grid, SFG17, with fractal iteration count, N$=$4, thickness ratio t$_{\mathrm{r}}=$17 and length ratio L$_{\mathrm{r}}=$8. Grid patterns differ from the published designs by a circular hole with 4.30cm diameter in the middle that will accept, in future experiments, a shaft connected to an axisymmetric rotating wake generator with diameter, D. Grids were designed to generate turbulence of specific integral length scale of O(D) and intensity of 6{\%} at the prescribed downstream location. Mean tunnel centerline velocity is 2 m/s and measurements are made in a streamwise vertical center plane with nominal individual field of view (FOV) of 12x8 cm$^{\mathrm{2}}$. Spatial coverage in the test section is accomplished by ``tiling'' individual FOV with approximately 2cm overlap. Results will focus on characterizing resulting turbulence in the test section and discussion will include comparison between published results and the present measurements.   

Stratified turbulent wake of a prolate spheroid

Numerical simulations are performed to study the stratified turbulent wake behind a 6:1 aspect ratio prolate spheroid at zero angle of attack. The incompressible Navier-Stokes equations under the Boussinesq approximation are solved along with the density equation. The body is represented using an immersed boundary method. A finite-difference formulation on a staggered, cylindrical grid is implemented with spectral treatment for pressure in the azimuthal direction. Linear and non-linear (pycnocline) density profiles are employed in order to analyze the effects of stratification on flow features such as force coefficients, wake dimensions, coherent structures, first and second order statistics, frequency response and vortex shedding. Differences between the internal gravity waves created by the body and those created by turbulent regions are noted. The benchmark case of flow past a sphere is compared to the prolate spheroid case with particular attention paid to the near wake and non-equilibrium phase.   

Numerical study of ship airwake characteristics immersed in atmospheric boundary-layer flow

Helicopter pilot workload is known to increase substantially in the vicinity of a ship flight deck due to the unsteady flowfield past the superstructure. In this work, the influence of atmospheric turbulence on a ship airwake is investigated. A ship geometry representing the Simple Frigate Shape 2 is immersed into a Large-Eddy-Simulation-resolved Atmospheric Boundary Layer (ABL). Specifically, we aim in identifying the fundamental topology differences between a uniform-inflow model of the incoming wind and those representative of a neutral atmospheric stability state. Thus, airwake characteristics due to a shear-driven ABL are evaluated and compared. Differences in the energy content of the airwakes are identified and discussed. The framework being developed allows for future coupling of flight dynamic models of helicopters to investigate flight envelope testing. Hence, this work represents the first step towards the goal of identifying the effects a modified airwake due to the atmospheric turbulence imposes on the handling of a helicopter and pilot workload.   

Impact of Aspect Ratio, Incident Angle, and Surface Roughness on Windbreak Wakes

Wind-tunnel results are presented on the wakes behind three-dimensional windbreaks in a simulated atmospheric boundary layer. Sheltering by upwind windbreaks, and surface-mounted obstacles (SMOs) in general, is parameterized by the wake-moment coefficient $\tilde{C}_h$, which is a complex function of obstacle geometry and flow conditions. Values of $\tilde{C}_h$ are presented for several windbreak aspect ratios, incident angles, and windbreak-height-to-surface-roughness ratios. Lateral wake deflection is further presented for several incident angles and aspect ratios, and compared to a simple analytical formulation including a near- and far-wake solution. It is found that $\tilde{C}_h$ does not change with aspect ratios of 10 or greater, though $\tilde{C}_h$ may be lower for an aspect ratio of 5. $\tilde{C}_h$ is found to change roughly with the cosine of the incident angle, and to depend strongly on windbreak-height-to-surface-roughness ratio. The data broadly support the proposed wake-deflection model.   

Distinguishing chaotic structures from background turbulence using Benford's law

Unsteady turbulent flow is featured by multi-scale structures. Some of the large-scale structures are caused by periodic boundary motion, unsteady flow separation, or vortex shedding. They are usually deterministic, but their chaotic nature makes them almost undistinguishable from the background turbulence. We attempt to identify the deterministic structures in an unsteady turbulent field and to examine them through the lens of Benford's law. Chaotic signals usually disobey the Benford's law, which claims that the first significant digits of a stochastic sequence follow the probability distribution: P (d) $=$ log (1$+$1/d) and d $=$ 1, 2, ... 9. We decomposed a turbulent wake field downstream a cylinder into large-scale motions and sub-grid-scale fluctuations. In the near wake where the Karman vortex dominated the flow dynamics, the large-scale velocity signal disobeyed the Benford's law; While far downstream the cylinder, the large-scale signal gradually shifted to the Benford distribution. The sub-grid fluctuations in both near and far wakes followed the Benford's law. These results suggested that large energy-containing structures could be isolated from the background turbulence and modeled using lower dimensions.   

Anisotropic character and low dimensional representations of a model wind turbine array versus an array of porous disks

A model turbine array is compared to an array of matched stationary porous disks via stereo particle image velocimetry. Wind tunnel measurements bracket the center turbine in the fourth row of a $4\times3$ model array. The invariants of the normalized Reynolds stress anisotropy tensor and the Proper Orthogonal Decomposition (POD) are employed to characterize the similarities and differences between the near as well as the far wake of the rotor and disk cases. The rotor case illustrates a greater degree of large scale spatial organization and more uniform values of the anisotropy stress invariants than the disk case. The anisotropic invariants of the POD modes are also examined in order to determine how the anisotropic character of the flow varies with turbulent kinetic energy content. Results are relevant in the modeling of rotors using a stationary disk parametrization in computational studies focusing on structural response.   

Measurement of High Reynolds Number Stratified Turbulent Wake of a Towed Sphere

Although aircraft and ships operate at Reynolds numbers significantly greater than one million, there are virtually no extant data on the turbulence of wakes at Re \textgreater 10$^{\mathrm{6}}$, above the drag crisis regime. The present study is designed to characterize the near-field of a stratified wake at large Reynolds numbers, Re \textasciitilde 2 x 10$^{\mathrm{5}}$ - 10$^{\mathrm{6}}$, by towing a large diameter (D \textasciitilde 0.5 m) sphere through a thermally stratified fresh water lake and a thermally stratified large salt water towing tank. Stratification produced BV frequencies, N, up to 0.07 s$^{\mathrm{-1}}$ resulting in Froude numbers F $=$ U/ND $\ge $ 15. Three component turbulent velocities and temperature measurements were obtained using Acoustic Doppler Velocimeters (ADVs) and an array of fast response thermistors at various downstream distances. Turbulence power spectra of both the velocity and temperature signals exhibited a clear -5/3 slope over an order-of-magnitude range in wavenumber, which is generally not clearly evident in lower Re laboratory experiments. This study is sponsored by the Office of Naval Research Turbulence and Stratified Wakes Program.   

Flow past an axially aligned spinning cylinder: Experimental Study

Experimental investigation of flow past a spinning cylinder is presented in the context of its application and relevance to flow past projectiles. A subsonic wind tunnel is used to perform experiments on the flow past a spinning cylinder that is mounted on a forward sting and oriented such that its axis of rotation is aligned with the mean flow. The experiments cover a Reynolds number of range of up to 45000 and rotation numbers of up to 2 (based on cylinder diameter). Time-averaged mean flow and turbulence profiles in the wake flow are presented with and without spin along with comparison to published experimental data.