Session LB: Turbulent Boundary Layers VI

Boundary layer flow over streamwise grooves

We use the Reduced Navier-Stokes (RNS) equations for the simulation of the nonlinear evolution of a zero pressure gradient boundary layer flow over a grooved bottom wall. The RNS formulation provides Reynolds independent solutions that are asymptotically exact in the limit $Re \gg 1$. It requires much less computational effort than DNS and it is numerically more robust than nonlinear PSE. We present results for the different flow patterns that appear depending on the spanwise period of the grooves and their cross section profile. And we discuss the idea of using the grooves to induce transversal motion in the boundary layer in order to produce a stabilization effect similar to the one induced by the streaks in a flat plate boundary layer.   

Characteristics of Turbulent flow over Superhydrophobic Surfaces

Recent research has suggested significant modification in the structure of turbulent flow of water over a superhydrophobic surface. The changes, which may include large reductions in skin friction, are due to the modification of the no-slip boundary condition at the liquid-solid interface. We present experimental and computational results from an ongoing exploration of this system. Experimental results include new measurements of laminar flow friction coefficients, as well as high-resolution PIV over a number of superhydrophobic geometries. To complement the experimental investigations, direct numerical simulations of turbulent channel flow are performed. The no-slip boundary layer is modified with Navier slip boundary conditions in the streamwise and spanwise flow directions. The effect of compliance at the air-water interface between microstructures is investigated numerically using a simple model to calculate out-of-plane wall deflections and allow for non-zero wall-normal velocities. Mean and fluctuating velocity statistics as well as flow structures are examined, and compared with the experimental measurements.   

Analysis of the Mean Momentum Balance in Polymer Drag Reduced Turbulent Boundary Layers

Mean momentum balances (MMB) in polymer drag reduced turbulent channel and zero-pressure gradient boundary layer flows are examined using experimental and numerical data available in the literature. For each data set, three flow cases are examined: Newtonian, low drag reduction (LDR), and high drag reduction (HDR). The Newtonian case is used as a baseline for comparison, while LDR and HDR flows are chosen since turbulent statistics trend differently between LDR and HDR flows. The results show that important qualitative features of the layer structure that exists for flows of a Newtonian fluid exist for flows of drag reducing polymer solutions. However, with increasing drag reduction: the stress gradient balance layer extends further from the wall, the Reynolds stress gradient contribution to the MMB decreases, and the polymer stress gradient contribution to the MMB increases. The latter finding demonstrates that polymers have a significant effect on the mean dynamics of HDR flows.   

Air-Induced Drag Reduction at High Reynolds Numbers: Velocity and Void Fraction Profiles

The injection of air into a turbulent boundary layer forming over a flat plate can reduce the skin friction. With sufficient volumetric fluxes an air layer can separate the solid surface from the flowing liquid, which can produce drag reduction in excess of 80{\%}. Several large scale experiments have been conducted at the US Navy's Large Cavitation Channel on a 12.9 m long flat plate model investigating bubble drag reduction (BDR), air layer drag reduction (ALDR) and the transition between BDR and ALDR. The most recent experiment acquired phase velocities and void fraction profiles at three downstream locations (3.6, 5.9 and 10.6 m downstream from the model leading edge) for a single flow speed ($\sim $6.4 m/s). The profiles were acquired with a combination of electrode point probes, time-of-flight sensors, Pitot tubes and an LDV system. Additional diagnostics included skin-friction sensors and flow-field image visualization. During this experiment the inlet flow was perturbed with vortex generators immediately upstream of the injection location to assess the robustness of the air layer. From these, and prior measurements, computational models can be refined to help assess the viability of ALDR for full-scale ship applications.   

Local suppression of turbulent noise by passively inducing relaminarization

Direct numerical simulations of turbulent channel flow were performed to study potential means of locally suppressing wall pressure noise by passively driving the flow towards relaminarization. The noise reduction is achieved by altering the surface geometry along a wall of the channel. Two separate geometries were investigated, namely a wedge-shaped protrusion and an inverted wedge-shaped depression. In both configurations, the wedge remains stationary and spans the width of the channel. The flow tends toward relaminarization due to local convective acceleration along the upslope of the wedge (in the case of the protrusion) and due to the gradual unstalled expansion along the downslope of the wedge (in the case of the depression). Simulations were performed at a Reynolds number based on friction velocity of 180. The no-slip condition along the surface of the protrusion/depression was enforced using an immersed boundary method. Profiles of turbulence statistics and wall- pressure intensity, as well as the wall-pressure spectra along the front face of the two different wedges are compared in relation to those of the undisturbed approach boundary layer.   

The coherent structure of atmospheric surface layers

The structure of two-point correlation statistics in the atmospheric surface layer are studied from measurements on the western Utah salt flats at the SLTEST facility. Large-scale features in the stable, neutral and unstable surface layers that adhere to Monin-Obukhov similarity ($-10 [Preview Abstract]

Very-Large-Scale Coherent Structures in the Wall Pressure Field Beneath a Supersonic Turbulent Boundary Layer

Previous wind tunnel experiments up to Mach 3 have provided fluctuating wall-pressure spectra beneath a supersonic turbulent boundary layer, which essentially are flat at low frequency and do not exhibit the theorized $\omega ^{2}$ dependence. The flat portion of the spectrum extends over two orders of magnitude and represents structures reaching at least 100 $\delta $ in scale, raising questions about their physical origin. The spatial coherence required over these long lengths may arise from very-large-scale structures that have been detected in turbulent boundary layers due to groupings of hairpin vortices. To address this hypothesis, data have been acquired from a dense spanwise array of fluctuating wall pressure sensors, then invoking Taylor's Hypothesis and low-pass filtering the data allows the temporal signals to be converted into a spatial map of the wall pressure field. This reveals streaks of instantaneously correlated pressure fluctuations elongated in the streamwise direction and exhibiting spanwise alternation of positive and negative events that meander somewhat in tandem. As the low-pass filter cutoff is lowered, the fluctuating pressure magnitude of the coherent structures diminishes while their length increases.   

Vortex convection velocities in wall parallel planes of a turbulent boundary layer

The organization and convection velocity of vortices in wall parallel planes of a zero-pressure gradient turbulent boundary layer are investigated using time resolved digital particle image velocimetry (DPIV) at a moderate Reynolds number ($Re_\tau=470$). Time resolved DPIV provides a means for tracking vortical structures in the flow giving their trajectories, velocities, and relation to other turbulent structures in the flow. Measurements are taken at three different wall normal locations ($y/\delta$ = 0.07, 0.23, and 0.59) and comparisons of the vortex populations and convection velocities are made between the three planes. Vortical structures captured in these planes may be interpreted as signatures of hairpin-like structures which have been proposed to play a key role in turbulent boundary layer dynamics.   

Analysis of vortex populations in turbulent boundary layers based on tomographic PIV

Vortex populations in the logarithmic region of turbulent boundary layers were investigated using results from tomographic PIV. The experiments were carried out in a water channel facility with $\delta \approx $ 125 mm and Re$_{\tau }\approx $ 2500 (Re$_{\theta }\approx $ 6200). Measurement volumes were about 90 x 80 x 9mm$^{3}$ (1650 x 1470 x 130 viscous units) spanning a wall-normal range from z$^{+}$ = 150 to 280. Four 2K x 2K cameras were mounted above the channel and aimed at the measurement volume with tilt angle about 30 degrees to the wall normal direction. The magnification was 0.07 mm/pixel. Correlations were performed on 48 x 48 x 48 voxel volumes with 75{\%} overlap yielding a vector spacing of 17 x 17 x 17 viscous units. Swirl strength and swirl direction were used to identify and characterize vortices in terms of orientation, circulation, size, and convection velocity. The results showed that swirl direction was a better indicator than vorticity of eddy orientation. Eddy circulation was found to increase approximately quadratically with eddy radius. The advantages and limitations of tomographic PIV vs. dual plane PIV will be discussed.   

Coherent Structures in a Thermally Stable Boundary Layer

Experiments were conducted in thermally stable boundary layers to examine the reduction in heat and momentum fluxes, the effects of buoyancy on the turbulence statistics, and the interaction between turbulent coherent structures and internal gravity waves. This experiment was conducted in a 5 m long, 1.2 m by 0.6 cross-section, open-return wind tunnel. The measurements were conducted on the surface of the tunnel, which is heated using strips of heating tape. The plate was isothermal, and a wide range of stabilities were investigated, with Richardson numbers ranging from 0 to 0.5, covering both the weakly and strongly stable regimes. Additionally, it was attempted to identify significant features of the turbulence that could be used to identify clearly delineating features between weak and strong regimes. This work was made possible by support received through Princeton University's Grand Challenges-Energy program, supported by the Thomas and Stacey Siebel Foundation.