Session H33: Boundary Layers: General Topics

Reexamination of the Classical View of how Drag-Reducing Polymer Solutions Modify the Mean Velocity Profile: Baseline Results

Recent numerical and experimental data have shown that the classical view of how drag-reducing polymer solutions modify the mean turbulent velocity profile is incorrect. The classical view is that the log-region is unmodified from the traditional law-of-the-wall for Newtonian fluids, though shifted outward. Thus the current study reexamines the modified velocity distribution and its dependence on flow and polymer properties. Based on previous work it is expected that the behavior will depend on the Reynolds number, Weissenberg number, ratio of solvent viscosity to the zero-shear viscosity, and the ratio between the coiled and fully extended polymer chain lengths. The long-term objective for this study includes a parametric study to assess the velocity profile sensitivity to each of these parameters. This study will be performed using a custom design water tunnel, which has a test section that is 1 m long with a 15.2 cm square cross section and a nominal speed range of 1 to 10 m/s. The current presentation focuses on baseline (non-polymeric) measurements of the velocity distribution using PIV, which will be used for comparison of the polymer modified results. Preliminary polymeric results will also be presented.   

Scaling properties and turbulence modulation of flows with variable density and viscosity

In order to identify the effect of variable density and viscosity on turbulence, we have performed DNS of canonical channel flows. The channel walls are isothermal and the flow is heated volumetrically to obtain gradients in temperature and thus in density and viscosity. Several constitutive relations for density $\rho$ and viscosity $\mu$ as a function of temperature are used to create a database. We parametrize the influence of density and viscosity in terms of gradients in semi-local Reynolds number $Re_\tau^*=\frac{\sqrt{{\overline{\rho}}/{\overline{\rho}_w}}}{\overline{\mu}/\overline{\mu}_w}Re_\tau$ (bar denotes Reynolds averaging, subscript $w$ denotes wall value and $Re_\tau$ is the friction Reynolds number). The dominant factors that influence the turbulence are then attributed first to changes in viscous length scales and second to structural changes in turbulence. While the change in viscous length scales is accounted for by the semi-local scaling, structural changes remain for cases with gradients in $Re_\tau^*$. Additionally, budgets of streamwise and spanwise vorticity equations are studied and the role of terms that are not accounted for by the semi-local framework, e.g. baroclinic torque, are also discussed.   

PIV Measurements of Turbulent Pipe Flow with Drag-Reducing Megasupramolecules

Toms (1948) was the first to observe that dissolving small amounts of high-molecular weight (HMW) polymers into a liquid can drastically reduce turbulent drag. Ever since, studying polymers in turbulence has been of great fundamental interest, as it can potentially provide insight into the self-sustaining mechanisms of wall turbulence. HMW polymers commonly employed for drag-reduction studies are plagued by chain scission due to the high shear rates accompanying turbulent flow at practical Reynolds numbers (Re); this shear degradation reduces the length of the polymer molecules, diminishing their effectiveness for drag-reduction. However, Wei et al. (2015) have recently developed ``megasupramolecules'' that perform comparably to traditional HMW polymers and circumvent the shear degradation problem by using end-associating polymers that can break and reassociate reversibly. Particle image velocimetry is used in specialized turbulent pipe flow experiments in the range~Re~$\approx $~7.5x10$^{\mathrm{4}}$-1.2x10$^{\mathrm{5}}$~to investigate and compare the drag and turbulence characteristics of the (Newtonian) baseline, traditional HMW polymer solutions, and megrasupramolecules.   

Stability analysis of two immiscible fluids in a shear driven flow: a DNS study

Numerical studies of the flow over either super hydrophobic surfaces or liquid infused surfaces have shown that a large drag reduction ($>$10\%) can be obtained if the flow remains in the Cassie state, thus stability of the interface plays a crucial role to achieve drag reduction. Direct Numerical Simulations of two immiscible fluids have been performed to assess how the stability of the interface depends on the viscosity ratio, thickness and Reynolds number of the two-layer flow. The flow is driven by the motion of one plate at constant velocity while the other plate is at rest. A finite difference code, based on a Runge-Kutta and fractional step method, has been combined to a level set method for tracking the interface between the two fluids. Results agree well with the linear theory until the nonlinear saturation. Once the fluctuations become large, a halving of the wavelength in the streamwise direction is observed for the least stable mode. The interaction between Tollmien-Schlichting waves and interfacial instabilities will be discussed at the meeting.   

Turbulent drag reduction over liquid infused surfaces

Numerical Simulations of two superposed fluids in a turbulent channel with a textured surface made of either longitudinal square bars or staggered cubes have been performed. The viscosity of the fluid inside the substrate is ten times smaller than that of the main stream ($m=\mu_1/\mu_2= 0.1$ where the subscripts 1 and 2 indicate the fluid in the cavities and the overlying fluid respectively). The interface between the two fluids can move due to the turbulent pressure fluctuations and it is modeled with a Level Set Approach. Two cases are compared: $We=0$, implying an interface sustained by the surface tension which can slip only in the horizontal direction, and $We=\infty$ where the interface can be displaced vertically and deform subject to wall normal stress. The textured surface made of staggered cubes is the most sensitive to the value of the surface tension, providing a drag reduction ranging between $15-30\%$ for $We=0$ and approximately $40\%$ drag increase when $We=\infty$ . On the other hand, longitudinal square bars, even with $We=\infty $ present a drag smaller than that over a smooth wall.   

Thermal transport due to buoyant flow past a vertical, heated superhydrophobic surface with uniform stream-wise slip

An analytical investigation of thermal transport due to a steady, laminar, buoyancy-driven flow past a vertical superhydrophobic(SHPo) surface was performed. The surface temperature was constant and uniform and exceeded the temperature of the surrounding liquid. Uniform stream-wise hydrodynamic slip and temperature jump are imposed at the wall to model the SHPo surface. Applying an integral analysis within the boundary layer results in a system of differential equations which are solved numerically to obtain boundary layer thickness, maximum velocity in the profile, and local and average values of both the friction coefficient and the Nusselt number. The classical smooth hydrophobic scenario with no-slip and no temperature jump showed excellent agreement with previous analysis of the same problem. The influence of varying temperature jump length on the local and average values of the friction coefficient and the Nusselt number was obtained for Rayleigh number ranging from 10$^{\mathrm{4}}$ to 10$^{\mathrm{9}}$ and Prandtl number ranging from 2 to 11. Local and average Nusselt numbers decrease dramatically, concomitant with a decrease in the maximum fluid velocity, as the temperature jump length increases.   

Two-Phase Flow Hydrodynamics in Superhydrophobic Channels

Superhydrophobic surfaces have been shown to reduce drag in single-phase channel flow; however, little work has been done to characterize the drag reduction found in two-phase channel flow. Adiabatic, air-water mixtures were used to gain insight into the effect of hydrophobicity on two-phase flows and the hydrodynamics which might be present in flow condensation. Pressure drop in a parallel plate channel with one superhydrophobic wall (cross-section 0.5 x 10 mm) and a transparent hydrophilic wall were explored. Data for air/water mixtures with superficial Reynolds numbers from 20-215 and 50-210, respectively, were obtained for superhydrophobic surfaces with three different cavity fractions. Agreement between experimentally obtained two-phase pressure drops and correlations in the literature for conventional smooth control surfaces was better than 20 percent. The reduction in pressure drop for channels with a single superhydrophobic wall were found to be more significant than that for single phase flow. The effect of cavity fraction on drag reduction was within experimental error.   

Magnetic Resonance Velocimetry Measurements of a Three-Dimensional Disturbance in a Laminar Boundary Layer

Magnetic Resonance Velocimetry (MRV) is a modern flow diagnostic technique with unique advantages including the ability to efficiently capture volumetric measurements of velocity fields in complex geometry without the need for optical access. In the present work, MRV is employed to provide boundary-layer-resolved measurements of a 3D disturbance created by a roughness element in a laminar boundary layer. Three-component mean-velocity-filed data are captured over a volume of approximately 100 x 100 x 250 mm$^{\mathrm{3}}$ with a voxel size of 1 mm$^{\mathrm{3}}$. The reported measurements are similar to those presented at the APS-DFD meeting last year, after improvement of the acrylic test section of the water-flow loop used in the experiments. The roughness element is mounted through the test-section's side wall where the boundary layer Reynolds number is 162, based on displacement thickness. The experiments are designed to investigate the effect of the roughness element's shape (cylindrical versus hemi-spherical) and height (for the cylindrical element). Details of the 3D velocity and vorticity fields in the disturbed boundary layer will be presented.   

Study of laminar boundary layer instability noise study on a controlled diffusion airfoil

Detailed experimental study has been carried out on a Controlled Diffusion (CD) airfoil at $ 5^{\circ}$ angle of attack and at chord based Reynolds number of $1.5 \times 10^{5}$. All the measurements were done in an open-jet anechoic wind tunnel. The airfoil mock-up is held between two side plates, to keep the flow two-dimensional. PIV measurements have been performed in the wake and on the boundary layer of the airfoil. Pressure sensor probes on the airfoil were used to detect mean airfoil loading and remote microphone probes were used to measure unsteady pressure fluctuations on the surface of the airfoil. Furthermore the far field acoustic pressure was measured using an $\frac{1}{2}$ inch ICP microphone. The results confirm very later transition of a laminar boundary layer to a turbulent boundary layer on the suction side of the airfoil. The process of transition of laminar to turbulent boundary layer comprises of turbulent reattachment of a separated shear layer. The pressure side of the boundary layer is found to be laminar and stable. Therefore tonal noise generated is attributed to events on suction side of the airfoil. The flow transition and emission of tones are further investigated in detail thanks to the complementary DNS study.   

Flow Field Classification Using Critical Point Matching

Classification of flow fields according to topological similarities can help reveal features of the flow generation and evolution for bluff body flows, and characterize different swimming maneuvers in aquatic locomotion, to name a few. Rigorous classification can be challenging, however, especially when complex flows are distorted by measurement uncertainties or variable flow generating conditions. The present work uses critical points of the velocity field to characterize the global flow topology. Flow fields are compared by finding a best match of critical points in two flow fields based on topological and location characteristics of the critical points together with general point set distance measures. The similarity between the flow fields is quantified based on the matched critical points. Applying clustering algorithms to a set of flow fields with quantified similarity can then be used to group flows with similar characteristics. This approach has been applied to generic 2D flow fields constructed using potential flow results and is able to correctly identify similar flow fields even after large distortions (up to 20{\%} of the vortex separation) have been applied to the flows.