Session MB: Turbulent Boundary Layers VIII

Status Update of the Flow Physics Facility at the University of New Hampshire

The Flow Physics Facility at UNH is a unique high Reynolds number boundary layer wind tunnel. The facility uses a long length test section (72 m long, with a 2.5m x 6m cross section) to obtain a Reynolds number of about 50,000 based on boundary layer thickness and friction velocity. Since the tunnel uses a large development length and low speed (15-30 m/s) to create the boundary layer, the small scales of turbulence remain large enough to be measured with currently available instrumentation, enabling resolution of the entire turbulent spectrum at real-world scale Reynolds numbers. Phase I of the project has been constructed, enabling a test section speed of 15 m/s using an open-circuit design. Phase II has undergone preliminary design, with a funding request submitted, and would add a closed circuit and raise the maximum speed to 30 m/s. An adjustable ceiling allows is used to maintain a zero pressure gradient as the boundary layer grows down the length of the tunnel. A description of the facility's attributes as well as preliminary measurements characterizing the test section flow will be presented.   

Large-eddy simulation of the zero pressure gradient, turbulent boundary layer

Large-eddy simulations (LES) of the zero-pressure gradient, smooth-wall, flat-plate turbulent boundary layer are presented. The LES combines the stretched-vortex, subgrid-scale (SGS) model with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. Specifically, an approximate analytic integration of the stream-wise momentum equation across the near-wall layer, with inner-scaling used to reduce inertial terms, leads to a hyperbolic partial differential equation for the wall shear stress. This is coupled to an SGS model of streamwise, attached vortices in the presence of the wall, constructed to capture the principal dynamical behavior of longitudinal vortices in wall-normal transport of streamwise momentum. The result is an effective slip-velocity boundary condition for the LES at a raised ``virtual wall'' together with a dynamical calculation of the K\'arm\'an constant. Presently we demonstrate LES of the spatially developing, turbulent boundary layer at Reynolds numbers $Re_\theta$ based on the free-stream velocity and the momentum thickness in the range $Re_\theta = 10^3 -10^{12}$. At large $Re_\theta$, the calculated skin-friction coefficient agrees well with the Coles-Fernholz relation.   

Combined Compact Difference Numerical Method for Simulation of Boundary Layer Turbulence Transition in the Non-Linear Stage

The non-linear stage of boundary layer turbulence transition is investigated by solving the Vorticity Transport Equation using a 12th-order discretization of the spatial derivatives in uniform grids and a 4th-order 5-6 alternating stages Runge-Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the downstream convective term to achieve better spectral resolution. In this method, the downstream wave number spectrum is divided into two parts: the first part preserves low dispersion and dissipation errors for accurate simulations of the physical waves; the second part generates strong numerical dissipation to suppress numerical grid-mesh oscillations. In addition, a multigrid method is used to accelerate the convergence of solving the velocity Poisson's equation. Results of the simulations show that nonlinear wave interactions, generation, and amplification can be realized.   

Numerical simulation of negative Magnus force on a rotating sphere

Flow characteristics and fluid force on a sphere rotating along with axis perpendicular to mean air flow were investigated using Large Eddy Simulation at two different Reynolds numbers of 10,000 and 200,000. As a result of simulation, opposite flow characteristics around the sphere and displacement of the separation point were visualized depending on the Reynolds number even though the sphere rotates at the same rotation speed according to the Reynolds number. When Reynolds number is 10,000, flow characteristics agree with the flow field explained in the Magnus effect. However sphere rotates at the same rotation speed while increasing Reynolds number to 200,000, separation point moves in opposite direction and wake appears in the different direction. The reason of the negative Magnus force was discussed in terms of the boundary layer transition on the surface.   

Comparison of Intermittency Detection Algorithms in a Transitional Boundary Layer

Intermittency algorithms evaluate the maturity of the laminar-to-turbulent transition process by assessing how often a flow is turbulent. This work compares four different intermittency algorithms using thermal anemometry data sets. These data were acquired above the suction surface of a transitional low-pressure turbine airfoil at three chord Reynolds numbers of 2.5x10$^{4}$, 5.0x10$^{4}$, and 7.5x10$^{4}$. Comparisons between the Hedley-Keffer, Volino-Hultgren, Clark, and MTERA algorithms show that using one algorithm over another could lead to an improper interpretation of the transition physics occurring throughout the flowfield. Algorithms appear to signal the onset of transition in similar locations, although the surface-normal and surface-tangential extents and magnitudes of intermittency can vary considerably throughout the transitional region. Comparisons of the anemometry data to Coles' Law of the Wake turbulent similarity velocity profiles also provide insight into the degree of correlation between algorithm intermittencies and accepted turbulent velocity profiles.   

Mean Dynamics of Channel Flow Transition

The redistribution of mean momentum and vorticity are explored for laminar-to-turbulent transition in fully developed channel flow. A central aim is to better understand how the mean dynamical mechanisms representative of the fully turbulent regime are first established. Specifically, the mean dynamics of channel flow transition evolve from a simple balance of two differential forces at every point to a balance involving three terms that forms into a complex four layer structure. Primary considerations stem from the emergence of the effects of turbulent inertia as reflected by the appearance of the Reynolds stress gradient in the mean dynamical equation. The experimental and DNS results presented support a scenario in which the initial instabilities lead to a Reynolds stress distribution that is generally localized in space, and that subsequently spreads both inward and outward from the peak value. A characteristic feature of this distribution is the juxtaposition of positive and negative Reynolds stress gradients -- a dynamical feature that persists for all higher Reynolds numbers. Connections are drawn between the mechanisms initiated during transition and those responsible for mean profile behaviors at much high Reynolds numbers.   

Mean momentum balance evolution in boundary layer transition

The mean momentum balance in the high Reynolds number turbulent boundary layer has a four layer structure. This structure reflects a specific magnitude ordering of the underlying dynamical mechanisms. The observed properties of the mean velocity and Reynolds stress profiles follow directly from this ordering of terms. The recent DNS of Wu and Moin (\textit{JFM} \textbf{630}, 2009) is used to explore how the four-layer structure first forms. Specific and mathematically well-justified criteria are employed to identify the minimum Reynolds number at which the ordering of terms characteristic of the high Reynolds number state is first established. Physically, this ordering occurs owing to the inward localization of the mean viscous force in concert with the outward localization of mean inertia. Comparisons indicate that, while the characteristic four layer structure for boundary layers and channels is very similar at high Reynolds numbers, the approach to the these similar states occurs by a different route and at significantly different rates.   

Kelvin-Helmholtz-like instability of turbulent flows over riblets

The turbulent drag reduction due to riblets is a function of their size and, for different configurations, collapses well with a length scale $l_g^+ =(A_g^+)^{1/2}$, based in the groove cross-section $A_g$. The initially linear drag reduction breaks down for $l_g^+ \approx 11$, which agrees in our DNS with the previously reported appearance of quasi-two-dimensional spanwise rollers immediately above the riblets. They are similar to those found over porous surfaces and plant canopies, and can be traced to a Kelvin-Helmholtz-like instability associated with the relaxation of the impermeability condition for the wall-normal velocity. The extra Reynolds stress associated with them accounts quantitatively for the drag degradation. An inviscid model for the instability confirms its nature, agreeing well with the observed perturbation wavelengths and shapes. The onset of the instability is determined by a length scale $L_w^+$ that, for conventional riblet geometries, is proportional to $l_g^+$. The instability onset, $L_w^+ \geq 4$, corresponds to the empirical breakdown point $l_g^+ \approx 11$.   

The Role of Turbulent Scales in a Rough and Smooth Surface Wind Turbine Blade

In the present research, a 2-D (constant chord) wind turbine blade section based on an S809 airfoil was manufactured and tested at Johns Hopkins University in the closed return subsonic Corrsin wind tunnel. The blade was covered with a 24-grit aluminum oxide abrasive sheet for the rough surface measurements. Smooth-wall blade measurements were also performed. Turbulence was generated using an active grid placed 5.5 m upstream of the blade. A free stream velocity of 10 m/s corresponding to a Reynolds number of 1.68x10$^{5}$ and angles of attack of 0 and 16 degrees (before and after flow separation) were selected, in order to study the effects of free stream turbulence on the aerodynamics and development of turbulent scales on the wind turbine. Global flow measurements such as mean velocity and Reynolds stresses were taken using Particle Image Velocimetry (PIV) and the pressure distribution around the suction and pressure surfaces of the 2-D blade with and without turbulence was acquired for angles of attack of 0 and 16 degrees. Initial results suggest that for the smooth surface blade at an angle of attack of 0 degrees, turbulence decreases lift production from a lift coefficient of 0.067 to 0.018, while at 16 degrees, turbulence enhances lift from 0.82 to 0.92.   

Subgrid Scale (SGS) Flow Structures and Energy Flux in a Rough-wall Channel Flow

This study examines interactions among turbulence structures of different scales based on high resolution PIV data obtained in a rough-wall channel flow, with $\delta $/$k$=50 ($k$ is roughness height), $k_{s}^{+}$=90-150 and Reynolds numbers of \textit{Re}$_{\tau }$=3520-5360. Top-hat spatial filtering with filter length scale of $\Delta $=1$k$, 3$k$, 6$k$ divide the turbulence to roughness, intermediate and large scale motions, respectively. The SGS energy flux increases substantially with length scale and decreasing distance from the wall, especially in the roughness sublayer. The latter persist even when this flux is scaled with the local TKE production rate, which also peaks near the wall. Dissipation of energy is particularly high in the 1-3$k$ range everywhere, especially in the roughness sublayer. Non-local transport, i.e. direct energy flux from large to roughness scales, which circumvents the typical cascading process, also increases rapidly near the wall. Conditional sampling indicates that this non-local flux is associated with inclined large scale shear layers (coherent structures) residing in the outer part of the boundary layer, which as our earlier data indicate, transport roughness scale turbulence to the outer layer.