Session S7: Tubulent Boundary Layers IX

An experiment to determine the frequency response of hot-wire anemometers to velocity fluctuations

It has proven difficult in the past to test the true response of a hot-wire anemometry system to velocity fluctuations. In this set of experiments, exploiting the unique capabilities of the Princeton Superpipe, a hotwire probe is exposed to a turbulent flow with a known spectral composition, but an adjustable frequency content. By comparing the measured result from the anemometer to the well-defined input, a transfer function (or Bode plot) of the true response to velocity fluctuations is obtained. Results indicate that for most commonly used anemometry systems the response measured by this process is reasonably close to that predicted by the square-wave test. However, in situations where precise measurements of turbulence are desired, we question the suitability of the 3dB drop-off to accurately characterise frequency response. One of the tested anemometers exhibits a measured frequency response to velocity fluctuations that differs substantially to the response indicated from electronic testing. Predicted errors due to frequency response for various anemometry systems will be presented for turbulent boundary layer measurements.   

Turbulent Channel Flow Measurements Using Matched Hot-Wires

We present an experimental study conducted in a turbulent channel flow facility using hot-wire probes with both constant and varying viscous-scaled wire length. The objectives of the study were threefold: first, to validate the flow produced by the channel flow facility; second, to investigate the validity of recently proposed spatial filtering corrections for Reynolds stress profiles; and third, to extend the investigation of the near-wall peak Reynolds number dependence in turbulent pipe flow conducted by Hultmark, Bailey and Smits (see J. Fluid Mech. (2010), vol. 649, pp. 103--113). We found that in channel flow, unlike in the pipe flow experiments, the near-wall peak exhibited the same Reynolds number dependence observed in turbulent boundary layer studies and channel flow DNS. Since the same measurement techniques and procedures were used in the current study as used in the pipe flow study, this demonstrated that the near-wall Reynolds number independence observed in the pipe study was not due to error introduced by measurement methodology. Furthermore, comparison of results from wires of different length verified that spatial filtering corrections work in channel flow as well as pipe and boundary layer flows. Corrected results were in good agreement with channel flow DNS, thus verifying that the flow in the facility approximates one-dimensional turbulent Poiseuille flow.   

Uncertainties in interpretation of data from turbulent boundary layers due to measurement errors

Composite expansions based on log law and power law were used to generate synthetic velocity profiles of ZPG turbulent boundary layers in the range $800 \leq Re_{\theta} \leq 8.6 \times 10^{5}$. Several artificial errors were then added to the velocity profiles to simulate dispersion in velocity measurements, error in determining probe position and uncertainty in measured skin friction. The effects of the simulated errors were studied by extracting log-law and power-law parameters from all these pseudo-experimental profiles, regardless of their original overlap region description. Various techniques were used, including the diagnostic functions ($\Xi$ and $\Gamma$) and direct fits to logarithmic and power laws, to establish a measure of the deviations in the overlap region. The differences between extracted parameters and their expected values are compared for each case, with different magnitudes of error, to reveal when the pseudo-experimental profile leads to {\it ambiguous} conclusions; i.e., when parameters extracted for log law and power law are associated with similar levels of deviations. This {\it ambiguity} was observed up to $Re_{\theta}=16,000$ for a 3$\%$ dispersion in the velocity measurements and $Re_{\theta}=2,000$ when the skin friction was overestimated by only 2$\%$. With respect to the error in the probe position, an uncertainty of 400 $\mu$m made even the highest $Re$ profile ambiguous. The results from the present study are valid for air flow at atmospheric conditions.   

Reimagining the description of the turbulent boundary layer

The turbulent boundary layer has been described from many different perspectives, drawing on physical inference, mathematical interpretation, and even visual observation. Many descriptions, however, lack complete explanation for the various features of the mean flow, or rely heavily on the description of only the streamwise mean velocity without analogous description of the Reynolds stress profiles. Here, a new description is proposed in which three regions of the turbulent boundary layer are identified, each defined by distinct physical phenomena and distinct mathematical solutions. A viscous region is shown to exist nearest the wall, with an extent further from the wall than previously thought. An inertial region, encompassing the potential region of the solution as well as the outermost part of the boundary layer, is proposed to help clearly and uniquely identify the extent of the boundary layer as well as allow for description of other wall-bounded flows, which possess a different outer boundary condition. Finally, the region in which turbulence is dominant is singled out as a separate region, calling into question the classical inner versus outer scaling while better explaining the presence of intermediate regions such as the classical buffer layer and wake region.   

Self-similar vorticity apportionment in turbulent wall-flows

The analytical closure by Fife et al. (\textit{J. Disc. \& Cont. Dyn. Sys.} \textbf{24}, 2009) allows the mean momentum equation for turbulent wall-flows to be represented by an invariant set of nonlinear ordinary differential equations. With appropriate starting conditions, these equations are integrated over an internal domain specified by the theory, and yield solutions for the mean velocity, Reynolds stress and their derivatives. The present talk primarily investigates the affiliated similarity structure of the mean vorticity field, and, in particular, its development as a function of Reynolds number. Existing data from boundary layers ($300 < \delta^+ < 50,000$), pipes ($180 < \delta^+ < 530,000$) and channels ($180 < \delta^+ < 5,000$) are shown to exhibit the theoretically predicted mean vorticity decay rate scalings. The outward movement of the centroid of the mean vorticity distribution (with $\delta^+$) into a region dominated by turbulent inertia is shown to coincide with the onset of the asymptotic (four- layer) dynamical regime. Evidence supporting the emergence of a self-similar relationship between the mean and rms spanwise vorticity is clarified through their relationships to the length scale distribution intrinsic to the mechanism of turbulent inertia. Overall, the results of the theory and data are discussed relative to two physically distinct mechanisms by which the velocity and vorticity field motions exhibit scale separation with increasing Reynolds number.   

A New Scaling for Adverse Pressure Gradient Turbulent Boundary Layers

A new scaling for strong adverse pressure gradient (APG) turbulent boundary layers (TBL) is presented. The new scaling is applied to data from the author's APG TBL experiment as well as several previous experimental studies. Both steady and unsteady flows are considered. The new scaling is shown to provide an excellent collapse of not only the mean velocity but also the turbulent stress profiles. The physical motivation for the scaling is presented in terms of underlying stability mechanisms as evidenced by a series of conditional boundary layer measurements. The implications of the scaling on the physics of strong APG TBL flows is also discussed.   

Non-universal $k_1^{-1} $ laws in pressure-gradient-driven turbulent wall-bounded flows

The scaling laws for the spectra of streamwise velocity fluctuations in turbulent wall-bounded flows are reformulated with inclusion of the streamwise pressure gradient. These laws indicate that the presence of pressure gradient naturally leads to the so-called incomplete similarity of spectra irrespective of the mean flow acceleration. Interestingly however, the corresponding spectral overlap arguments still lead to the inverse-power variation of the power spectral density of streamwise velocity fluctuations i.e. the $k_1^{-1}$ law. These are, however, the non-universal $k_1^{-1} $ laws arising out of incomplete similarity. Experimental evidence in the literature on pipe and channel flows clearly supports this. Striking experimental evidence is presented in favour of the non-universal $k_1^{-1} $ laws for an accelerating turbulent boundary layer flow. It is observed that the prerequisite condition of ``high Reynolds number'' for having substantial spectral overlap in experiments appears to be remarkably relaxed in the presence of streamwise mean flow acceleration.   

Turbulence in Accelerating Boundary Layers

This study focuses on favorable pressure gradient (FPG) turbulent boundary layers. 2D PIV data has been obtained in a sink flow in multiple planes and locations, at two Reynolds numbers and acceleration parameters. FPG decreases the locally normalized stresses over the entire boundary layer, but increases their magnitude close to the wall ($y$/\textit{$\delta $}$<$0.1) and decreases it in outer regions. This turbulence suppression is associated with confinement of coherent structures originated in the inner part of the boundary layer to a narrow near-wall region. Several contributors have been identified: (1) Weaker normalized strength of structures and consequently weaker self-induced wall-normal transport, (2) the negative $\partial $V/$\partial $y and high $\partial $U/$\partial $y, which preferentially orient inclined structures parallel to the wall. In the FPG region, almost all of the small-scale turbulence is confined to low speed streaks, where ejections bring fresh turbulence away from the wall, while sweeps bring in outer layer fluid with low turbulence. Pressure calculations based on integration of material acceleration obtained from time-resolved data show that ejections are associated with negative pressure gradients, as the upward moving fluid accelerates, while the opposite holds for sweeps.   

Direct numerical simulation of turbulent boundary layers under unsteady pressure gradients

Direct numerical simulations are performed to improve the understanding of unsteady separation processes of turbulent boundary layers characterizing the performance and efficiency of many aerodynamic applications such as helicopter rotor blades, wind turbine blades, pitching and flapping airfoils and wings, and rotating turbomachines. A time varying blowing-suction velocity distribution is imposed along the upper boundary to introduce unsteady adverse pressure gradients to the turbulent boundary layer. The distinct characteristics of turbulent boundary layers under unsteady adverse pressure gradients including unsteady boundary-layer detachment and reattachment, and production and dissipation of turbulent kinetic energy and vorticity, are revealed by a systematic comparison with steady attached/separated turbulent boundary layers.   

Turbulent Boundary Layers Absent Mean Shear

In environmental flows, we often observe turbulence levels that far exceed those produced by mean boundary shear (e.g., breaking surface waves), contributing to significant sediment resuspension and turbulent boundary layers that differ strikingly from classic turbulent boundary layer characterizations. We choose to study sediment resuspension in turbulence in the absence of mean shear using a novel laboratory facility that uses a Randomly Actuated Synthetic Jet Array (RASJA), designed to generate homogeneous isotropic turbulence with low mean flows. We use Particle Image Velocimetry (PIV) at both solid glass and sediment boundaries to examine the turbulent structures and nature of the flow at the two bed conditions. The sediment boundary is narrowly graded sand with a median grain size (D50) of 260 microns. Surprisingly, we find that the interaction of turbulence with a sediment boundary results in the formation of ripple patterns, with spacings on the order of the integral length scale. We measure metrics such as the turbulence intensity, turbulent kinetic energy, spectra, and dissipation. Our analysis includes a quadrant-based Reynolds stress analysis and the determination of critical turbulent stresses responsible for sediment resuspension, from which we develop a non-dimensional Shields-like parameter that captures incipient particle motion.