Turbulent Boundary Layer In Air Research Articles

A posteriori uncertainty quantification of PIV-based pressure data

A methodology for a posteriori uncertainty quantification of pressure data retrieved from particle image velocimetry (PIV) is proposed. It relies upon the Bayesian framework, where the posterior distribution (probability distribution of the true velocity, given the PIV measurements) is obtained from the prior distribution (prior knowledge of properties of the velocity field, e.g., divergence-free) and the statistical model of PIV measurement uncertainty. Once the posterior covariance matrix of the velocity is known, it is propagated through the discretized Poisson equation for pressure. Numerical assessment of the proposed method on a steady Lamb–Oseen vortex shows excellent agreement with Monte Carlo simulations, while linear uncertainty propagation underestimates the uncertainty in the pressure by up to 30 %. The method is finally applied to an experimental test case of a turbulent boundary layer in air, obtained using time-resolved tomographic PIV. Simultaneously with the PIV measurements, microphone measurements were carried out at the wall. The pressure reconstructed from the tomographic PIV data is compared to the microphone measurements. Realizing that the uncertainty of the latter is significantly smaller than the PIV-based pressure, this allows us to obtain an estimate for the true error of the former. The comparison between true error and estimated uncertainty demonstrates the accuracy of the uncertainty estimates on the pressure. In addition, enforcing the divergence-free constraint is found to result in a significantly more accurate reconstructed pressure field. The estimated uncertainty confirms this result.

Impacts of Free-Tropospheric Temperature and Humidity on Nocturnal Nonprecipitating Marine Stratocumulus

Abstract Marine stratocumulus (MSc) cloud amount can decrease with an increase in the cloud-top instability parameter κ, based on the cloud-top entrainment instability (CTEI) theory. Notice that if boundary layer temperature and humidity remain the same, a given κ can correspond to different combinations of free-tropospheric temperature and humidity. By employing large-eddy simulations coupled with bin microphysics, this study investigates the characteristics of three nocturnal nonprecipitating MSc systems with the same κ but different free-tropospheric conditions. It is found that the spread of liquid water path (LWP) among the three cases is large. The LWPs of these three cases are also compared with the base case where κ is smaller. One of the three cases even has larger LWP than the base case, which is not expected by the CTEI theory. Results indicate that the thermodynamic properties of the free-tropospheric air are important. For the three cases with the same κ, cooler and moister free-tropospheric air leads to a cooler and moister boundary layer through entrainment, hence a lower cloud base. A cooler and moister free troposphere also allows the turbulent boundary layer air parcels to overshoot to a higher height, leading to a higher cloud top. Therefore, there is a spread in LWPs among systems with the same κ. The spread can be so large that sometimes systems with larger κ may have larger LWPs than systems with smaller κ. More simulations are also performed covering other free tropospheric conditions and aerosol concentrations.

EFFECTS OF FREE STREAM VELOCITY ON TURBULENT NATURAL CONVECTION FLOW OVER A VERTICAL FORWARD-FACING STEP

Measurements of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection over an isothermal two-dimensional, vertical forward-facing step are reported. The upstream and downstream walls and the step itself were heated to a uniform and constant temperature. Air velocity and temperature distributions and their turbulent fluctuations are measured simultaneously using a two-component laser-Doppler velocimeter (LDV) and a cold wire anemometer, respectively. The present study treats buoyancy-dominated mixed convection over a vertical forward-facing step and examines the effect of a small free stream velocity on turbulent natural convection. The experiment was carried out for a step height of 22 mm, for a range of free stream air velocities 0 m/s ⋚ u∞ ⋚ 0.55 m/s (corresponding to a range of Reynolds numbers of 0 ⋚ Re\\abinf{s} ⋚ 712), and a temperature difference, ΔT, of 30°C between the heated walls and the free stream air (corresponding to a local Grashof number Grxi = 6.45 × 1010). It was found that the reattachment length increases while the heat transfer rate from the downstream heated wall decreases as the small free stream velocity increases.

高温熱駆動乱流境界層のPIV計測

The instantaneous velocity vectors in the thermally driven turbulent boundary layer in air along a vertical plate heated at high temperatures were measured by using a PIV to accumulate experimental data for the velocity field. The effects of PIV parameters on the experimental results were investigated, especially paying attention to the large-scale fluid motions in the outer layer, which play a predominant role in the generation of turbulence. The turbulent statistics revealed that the transverse velocity fluctuation (perpendicular to flat plate) depended on the PIV parameters, while the mean streamwise velocity did not change with the parameters. In addition, it was found that a discontinuous distribution appeared in instantaneous velocity fluctuations measured without the sub-pixel algorithm.

EFFECTS OF FREE-STREAM VELOCITY ON TURBULENT NATURAL-CONVECTION FLOW ALONG A VERTICAL PLATE

A detailed measurement of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection adjacent to an isothermal vertical flat plate are reported. A cold-wire anemometer and laser Doppler velocimeter were used, respectively, to measure simultaneously the time-mean turbulent temperature and velocity distributions and their turbulent fluctuations. In this experimental study, measurements of the flow and thermal fields were carried out at one streamwise location, x

Flow visualization of the three-dimensional, time-evolving structure of a turbulent boundary layer

Experiments were performed using volumetric flow visualization to study the evolution of three-dimensional boundary layer turbulence, and the interactions between inner and outer layer coherent structures. In the experiment, the inner and outer layers of a low Reynolds number (Rθ=705) turbulent boundary layer in air were seeded with smoke. A section of the boundary layer was rapidly scanned with a high intensity pulsed laser sheet, and the individual images were recorded using a high-speed video camera. The video images were digitized and assembled into three-dimensional volumes. A variety of image processing techniques and conditional sampling and statistical methods were then used to extract quantitative information from the three-dimensional, time-evolving visualization data.

Roughness element shape effects on heat transfer and skin friction in rough-wall turbulent boundary layers

Stanton number and skin friction coefficient results are presented for zero pressure gradient incompressible turbulent boundary layer air flows over two rough surfacescomposed of 1.27 mm base diameter by 0.635 mm high truncated cones spaced in staggered arrays two ( L/d 0 = 2) and four diameters( L/d 0 = 4)

Heat Transfer Measurements and Calculations in Transitionally Rough Flow

Experimental data on a rough surface for both transitionally rough and fully rough turbulent flow regimes are presented for Stanton number distribution, skin friction coefficient distribution, and turbulence intensity profiles. The rough surface is composed of 1.27-mm-dia hemispheres spaced in a staggered array four base diameters apart on an otherwise smooth wall. Special emphasis is placed on the characteristics of heat transfer in the transitionally rough flows. Stanton number data are reported for zero pressure gradient incompressible turbulent boundary layer air flow for nominal free-stream velocities of 6, 12, 28, 43, 58, and 67 m/s, which give x-Reynolds numbers up to 10,000,000. These data are compared with previously published rough surface data, and the classification of a boundary layer flow into transitionally rough and fully rough regimes is explored. Moreover, a new heat transfer model for use in the previously published discrete element prediction approach is presented. Computations using the discrete element model are presented and compared with data obtained from two different rough surfaces. The discrete element predictions for both surfaces are found to be in substantial agreement with the data.

The effect of small particles on fluid turbulence in a flat-plate, turbulent boundary layer in air

This paper describes the result of both an experimental and an analytical investigation of the response of a two-dimensional, turbulent boundary layer in air to the presence of particles. Copper shot, 70 μm in diameter, were uniformly introduced into a vertical boundary layer, at a momentum thickness Reynolds number of about 1000. The particle mass flux was set at 20% of the fluid mass flux, and all measurements were made using a single-component, forward-scatter laser Doppler anemometer. The measurements clearly demonstrated that the particles damped fluid turbulence, apparently affecting all scales equally. The measurements further showed a strong correlation between the degree of damping and the particle concentration in the log region of the boundary layer.

Measurements and calculations of rough-wall heat transfer in the turbulent boundary layer

Experimental Stanton number results from aerodynamically smooth, transitionally rough, and fully rough turbulent boundary layer flows are presented for four surfaces—three rough and one smooth. The rough surfaces are composed of 1.27 mm diameter hemispheres spaced in staggered arrays 2, 4, and 10 base diameters apart, respectively, on otherwise smooth walls. Stanton number data are reported for zero pressure gradient incompressible turbulent boundary layer air flows which give Re x up to 10000 000. These data are compared with previously published results on another, similar rough surface, and it is shown that some conclusions about heat transfer behavior based on data from that single rough surface do not extend to these new surface geometries. A refined roughness element energy transport model for use in the previously published discrete element prediction method is also presented. Calculations are compared with data from the four rough surfaces with well-defined roughness elements for both constant pressure and accelerated flow cases, and it is shown that the predictions are in excellent agreement with the data.

The behavior of solid particles in a vertical turbulent boundary layer in air

This paper presents the results of an experimental investigation on the response of solid particles to a zero-pressure gradient, vertical, turbulent boundary layer in air. Two different size classified glass beads, 50 and 90 μm dia (Re ≈ 1 and 4, respectively), were independently dispersed in the air flow with a 2% mass loading. Velocities of both the contaminant particles and the seeded air flow were measured using laser Doppler anemometry. The data show that the light particle loading had no effect on either the mean flow or the turbulence properties of the air boundary layer. The measured r.m.s. velocity fluctuations of both particle sizes nearly equaled the flow turbulence intensity in the streamise direction but were strongly attenuated in the normal direction. This paper presents a model for predicting the mean particle behavior to within 2% and the particle r.m.s. velocities to within 50%.

Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes

Measurements in the viscous sublayer of a flat-plate turbulent boundary layer in air, using single hot-wire sensors with lengths from 1–60 viscous length scales show that, at a given distance from the surface, the turbulence intensity, flatness factor, and skewness factor of the longitudinal velocity fluctuation are nearly independent of wire length when the latter is less than 20–25 times the viscous length scale (i.e. 20–25 “wall units”), and decrease significantly and abruptly for larger wire lengths. This conclusion is consistent with other workers' probability density functions of streak spacing: the lateral spacing of “streaks” in the viscous sublayer is 80–100 wall units on average with minimum spacing of 20–25 wall units, which implies that signals would be strongly attenuated by wires whose length exceeds 20–25 wall units. To achieve wire lengths of less than 20–25 wall units, subminiature hot wire probes like those described by Ligrani and Bradshaw (1987), having lengths as small as 150 μm, are necessary for sublayer measurements in typical laboratory wind tunnels. As well as the measurements mentioned above, dissipation spectra are presented, to show the effect of spanwise averaging on the high-frequency motions, which is necessarily more severe than the effect on overall intensities.

Spectral characteristics of turbulent pressure fields

Wall pressure fluctuations associated with equilibrium turbulent boundary layer air flow have been measured in two anechoic flow facilities over a range of flow rates. The pressure field was probed with arrays of microphones. The multichannel signal data from the microphones was synchronously digitized and digitally processed to resolve the dependence of the turbulent pressure field on both (temporal) frequency and (spatial) wavenumber. Spectral estimates of the wall pressure field around the convective ridge and in the low‐wavenumber region will be presented. Contributions of observed coherent pressure structures to the spectral estimates will be discussed. [Research sponsored by ONR.]

Further results related to the turbulent boundary layer with slot injection of helium

Data from an experiment involving the slot injection of helium into a turbulent boundary layer in air are analyzed in terms of unconditioned and conditioned Favre averages. The conditioning is based on two levels of helium concentration so that the contributions to the unconditioned statistics from air, helium, and a mixture of these two gases can be determined. The distributions of intermittency associated with the two helium levels establish the domains of influence of air, helium, and the mixture.

The ‘bursting’ phenomenon in a turbulent boundary layer

Using a hot wire in a turbulent boundary layer in air, an experimental study has been made of the frequent periods of activity (to be called ‘bursts’) noticed in a turbulent signal that has been passed through a narrow band-pass filter. Although definitive identification of bursts presents difficulties, it is found that a reasonable characteristic value for the mean interval between such bursts is consistent, at the same Reynolds number, with the mean burst periods measured by Kline et al. (1967), using hydrogen-bubble techniques in water. However, data over the wider Reynolds number range covered here show that, even in the wall or inner layer, the mean burst period scales with outer rather than inner variables; and that the intervals are distributed according to the log normal law. It is suggested that these ‘bursts’ are to be identified with the ‘spottiness’ of Landau & Kolmogorov, and the high-frequency intermittency observed by Batchelor & Townsend. It is also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and outer layers.

Relationship between temperature and velocity profiles in a turbulent boundary layer along a supersonic nozzle with heat transfer

Turbulent boundary layer air flow through supersonic convergent-divergent nozzle with heat transfer, considering relationship between temperature and velocity profiles