Session S09: Turbulence: Wakes (5:45pm - 6:30pm CST)

Experimental Investigation of Kinetic Energy Transport around a Yawed Tidal Stream Turbine

Tidal Stream Turbines (TST) experience yawed inflows that have a considerable impact on their operational efficiency and wake propagation. We present detailed near-wake measurements using an Acoustic Doppler Velocimetry for a 1:20 scale TST model (three-bladed, constant chord, zero twist) in a uniform inflow at yaw angles of 15\textdegree and 30\textdegree . The results are compared with the baseline no-yaw case. Wake data is collected at hub height up to a downstream location of 4D. The near-wake region is analyzed from the perspective of terms constituting the streamwise momentum and turbulence kinetic energy (TKE) equations in order to better characterize the physical mechanism behind the asymmetric wake due to the yawed inflow. Momentum budget terms elaborate on various factors helping in momentum recovery in the wake. Turbulence kinetic energy (TKE) budget details the relative contribution of physical processes dictating different motions of the turbulent flow that assist in the re-distribution and dissipated of the TKE generated in the shear-layer region.   

Turbulence Kinetic Energy Budget in the Near-Wake Region of a Tidal Stream Turbine at Elevated Levels of Free-Stream Turbulence

Tidal stream turbines (TSTs) are typically deployed at high energetic tidal sites that are characterized by elevated levels of free-stream turbulence (FST). In the current work, the tidal turbulence testing facility at Lehigh University that incorporates an active grid turbulence generator is used to study the effects of elevated FST (turbulence intensity, Ti $=$ 12.6{\%}) on the near-wake characteristics of a 1:20 TST model. The results are compared with a baseline quasi-laminar flow (Ti$=$2.2{\%}). Wake parameters investigated include, energy recovery, swirl, length scales, and turbulence intensity. We also discuss momentum and turbulence kinetic energy (TKE) budgets in the turbine wake under the different inflow conditions to quantify the production, re-distribution, and dissipation of TKE in the near wake high shear regions. The results show that TST wake displays considerable differences at the higher FST, most notably, enhanced energy recovery and swift break up of flow periodicities. The convection term was found to dominate the energy exchange process in the wake. Production of TKE closely correlates to the periodic tip vortices shed from the blade, creating an annular region with prominent shear stresses.   

Into the far wake: simulations of the high-Reynolds-number wake of a slender body

The high-Reynolds-number axisymmetric wake behind a slender 6:1 prolate spheroid with a tripped boundary layer is investigated using a hybrid simulation. The Reynolds number based on the diameter is $10^5$ and the domain spans $x/D=80$. The classic hypotheses that lead to the well-known high-Reynolds-number wake decay exponents are not fulfilled in our domain, despite the presence of broadband turbulence in the near wake and without discernible vortex shedding from the body. Instead, after $x/D \approx 20$ and until the end of the domain, self-similarity with anomalous wake decay is found. At $x/D \approx 20$, a helical wake instability also emerges and the wake transitions into a non-equilibrium scaling of dissipation rate. The effect of density stratification on the wake is also investigated. The decay laws, the generation of gravity waves and the presence of coherent structures are studied in weak ($Fr=10$) and strongly stratified environments ($Fr=2$).   

Dynamics of Coherent Structures in Stratified Wakes at High Reynolds Number

Stratified wakes at high Reynolds number ($Re$) are known to develop organized coherent structures at intermediate to late values of buoyancy time ($Nt$). In the present study, we analyze the dynamics of coherent structures in the wake of a disk at $Re = 50000$ and $Fr = 2, 10$ using large-eddy simulations (LES) and spectral POD (SPOD). SPOD eigenspectra of both wakes show a spectral peak at the vortex shedding frequency ($St \approx 0.13-0.14$) of the unstratified counterpart throughout the domain. With increasing $Nt$, eigenspectra of $Fr = 2$ exhibit increasingly significant low-rank behavior, particularly around the vortex shedding frequency. We also find that the arrival of the $Fr = 2$ wake, at $Nt \approx 20$, into a regime of strongly stratified turbulence (SST) is marked by the dominance of the region with turbulent internal gravity waves (IGWs) to the energy carried by the leading SPOD modes. The onset of turbulent IGW emission in the $Fr = 10$ wake occurs when it enters the intermediate stratified regime (IST). Reconstruction of various turbulent fluxes is also performed to uncover the contribution of different modes towards the statistical descriptors of the flow.   

Characterization of the Far-Wake of an Inclined 6:1 Prolate Spheroid

Despite dramatic advances in computational power seen in the last decades, computational models are unable to predict transition, separation, and wake development for flow over three-dimensional bodies to the desired level of accuracy at acceptable computational cost. Without the ability to predict the forces and moments on the body, critical design parameters such as drag and loads on control surfaces for air- and water-borne vehicles cannot be predicted. The prolate spheroid is a popular body upon which to verify CFD models because of its simple geometry and complex, three-dimensional flow field. Advances in computational speed and experimental capabilities have prompted a renewed interest in related research. An experiment was conducted in the large towing tank facility of the U.S. Naval Academy, using a 6:1 prolate spheroid, measuring 54 in. (1.4 m) in length and 9 in. (0.23 m) in diameter. The spheroid model was inclined by 15\textdegree relative to the undisturbed free surface, and towed at speeds yielding length-based Reynolds numbers from 0.5-4.2x10$^{\mathrm{6}}$. Particle image velocimetry was used to provide two-dimensional velocity maps in two spatial-dimensions (2C2D) at downstream distances of up to 5L. These time histories show the trajectory of the wake as it leaves the tail of the model, the expansion of the wake width, the size, strength, and position of the primary vortical structures shed into the wake. These results will inform follow-on studies focused on measuring turbulent quantities in the far wake.   

Variable-Resolution Partially-averaged Navier-Stokes (PANS) simulations of three-dimensional bluff body wakes

Accurate simulations of complex high Reynolds number turbulent flows of practical interest mandate spatio-temporally varying physical resolution to optimize computational effort. The objective of this study is to develop and demonstrate the closure models required to account for commutation residue due to spatial filter-width variation in the near-wall region of a turbulent flow. A closure model is derived in the context of Partially-averaged Navier-Stokes (PANS) by invoking energy conservation principles and equilibrium boundary layer (EBL) scaling properties of partially-resolved field. The Wall-Modeled PANS (WM-PANS) equations bridge between RANS (Reynolds-averaged Navier-Stokes) method near the wall and required degree of resolution in the interior of the domain. WM-PANS is used to compute three-dimensional bluff body wake flows over a sphere in subcritical (Re $=$ 3700) and supercritical (Re \textasciitilde O(10$^{\mathrm{6}}))$ Reynolds number regimes. One-point statistics and coherent structure behavior are examined. Preliminary results indicate a clear advantage of this approach in capturing key physics of complex wake flows at lower computational effort.   

The topological features of a fully developed turbulent wake flow.

The persistent homology method is used to study the behavior of a turbulent wake field in the phase space. The phase space is constructed using the velocities at 1024 points, and the flow evolution is represented by a trajectory in this space. The trajectory contains many recurrences. The recurrence pattern reflects the interactions among turbulent eddies. Every recurrent section is considered as an interrogation unit. The number of self-crossings in each recurrent loop, which is measured by the first Betti number, reflects the temporal complexity. A significant amount of trajectories have just a few self-crossings, and a small number of complex trajectories contain more than 100 self-crossings. In summary, the homology of recurrent trajectories can be used to characterize a turbulent flow. How to imply higher order Betti numbers needs to be investigated in the future.   

Thermal Effects in the Turbulent Wake of a Heated Bluff Body

We investigate the impact of heat transfer from a triangular prism bluff body on the development of turbulent wake dynamics, and specifically focus on the relative effects of varying fluid density, viscosity, diffusivity and local Reynolds number caused by this heating. We perform three simulations for bluff body temperatures of 310K (the bulk inflow temperature), 900K, and 1500K to examine changes in the flow structure and dynamics over a range of heating intensities. The simulations are performed using the PeleC code, which incorporates adaptive mesh refinement (AMR) to locally resolve the physics of interest. We find that higher bluff body temperatures create strong gradients along the boundary and shear layers, affecting the dynamical importance of specific terms in the turbulence kinetic energy and vorticity transport equations, such as pressure-dilatation and baroclinic torque effects. At the same time, shear layer instabilities drive entrainment and mixing, pulling cold air into the wake and smoothing out initial gradients. We also examine the effects of heat transfer on turbulence intensity, correlations, and anisotropy throughout the wake, and highlight the importance of capturing strong gradients in simulations of such flows, enabled here by the use of AMR.