An empirical model of the surface pressure spectrum beneath a two-dimensional, zero-pressure-gradient boundary layer is presented that is based on the experimental surface pressure spectra measured by seven research groups. The measurements cover a large range of Reynolds number, 1.4 × 10 3 < Reθ < 2.34 × × 10 4 . The model is a simple function of the ratio of the timescales of the outer to inner boundary layer. It incorporates the effect of Reynolds number through the timescale ratio and compares well to experimental data. It is proposed that the effect of Reynolds number is more aptly described as the effect of the range of relevant scales. Spectral features of the experimental data and the scaling behavior of the surface pressure spectrum are also discussed.

Empirical Spectral Model of Surface Pressure Fluctuations

The overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity. The composite profile incorporates κ, B, and Π as the varying parameters and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers. The von Karman coefficient in channel flow is smaller than the well-established value for zero pressure gradient turbulent boundary layers of 0.384, while in pipe flows it is consistently higher. In contrast, the estimates of the wake parameter Π are the smallest for channel flows and largest for boundary layers. Further, the Superpipe data are reanalyzed to reveal that κ=0.41 is a better value for the von Karman constant in pipe flow. The collective behavior of κ in boundary layers, pipes, and channels reveals that the von Karman coefficient is not universal and exhibits dependence not only on the pressure gradient but also on the flow geometry.

Variations of von Kármán coefficient in canonical flows

A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers, \({Re_{\tau}\sim\mathcal{O}(10^6)}\) . It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.

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Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory

Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations accurately describe the local Cf behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, H, shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of D and d asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter, P, is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.

Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

Turbulent boundary layer skin friction in liquid flows may be reduced when bubbles are present near the surface on which the boundary layer forms. Prior experimental studies of this phenomenon reached downstream-distance-based Reynolds numbers (m. At the lowest test speed and highest air injection rate, buoyancy pushed the air bubbles to the plate surface where they coalesced to form a nearly continuous gas film that persisted to the end of the plate with near-100% skin-friction drag reduction. At the higher two flow speeds, the bubbles generally remained distinct and skin-friction drag reduction was observed when the bubbly mixture was closer to the plate surface than 300 wall units of the boundary-layer flow without air injection, even when the bubble diameter was more than 100 of these wall units. Skin-friction drag reduction was lost when the near-wall shear induced the bubbles to migrate from the plate surface. This bubble-migration phenomenon limited the persistence of bubble-induced skin-friction drag reduction to the first few metres downstream of the air injector in the current experiments.

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

Accurate measurements of the turbulent wall pressure have been difficult to achieve due to signal contamination at low frequencies by background facility noise and/or attenuation at high frequencies due to sensor averaging effects. The current study utilizes a new noise cancellation scheme based on an optimal filtering technique to capture the noise-canceled time series. Furthermore, to address the high-frequency attenuation problem, a number of pinholes are utilized along with high-sensitivity micropbones to obtain measurements of the wall pressure at a resolution down to d + = du τ /v ≅2. The results show that the maximum allowable nondimensional sensing diameter to avoid spectral attenuation for frequencies up to f + = fv/u τ 2 = 1 is in the range of 12.0 ≤d + < 18.0. Additionally, it is shown that the wall-pressure rms level when scaled on the wall-shear stress seems to increase slowly with increasing Reynolds number, apparently due to the influence of large-scale structures in the outer part of the boundary layer. On the other hand, it is demonstrated that, even though √p '2 /q 0 appears to become invariant with increasing Reynolds number, p' is not generated by structures whose velocity scale is U 0 .

Characterization of the Pressure Fluctuations Under a Fully Developed Turbulent Boundary Layer

Accurate measurements of pressure beneath turbulent wall-bounded flows are generally difficult to achieve due to signal contamination resulting from facility-induced noise, sensor vibration, etc. This is particularly true at low Reynolds numbers where the noise signature overwhelms the low-level turbulent fluctuations. In the current work a noise-cancellation technique based on an optimal filtering approach is developed. This technique is particularly useful for conditions of low signal-to-noise ratio and therefore it is well suited for low to moderate Reynolds number measurements. Unlike the conventional, subtraction-based, noise-cancellation methods, the utility of the optimal-filter scheme is not limited to the extraction of the turbulent statistics but it can be used to obtain the noise-canceledtime-series. Furthermore, the energy of the low-frequency turbulent motion lost due to the application of the noise-cancellation scheme is an order of magnitude smaller in the case of the optimal filter as compared to the subtraction scheme. Employment of the technique developed here is not confined to two-dimensional flows and therefore it is also useful for measurements in applications involving non-equilibrium flows.

Extraction of turbulent wall-pressure time-series using an optimal filtering scheme

Recent improvements in three techniques for measuring skin friction in two- and three- dimensional turbulent wall-bounded shear flows are presented. The techniques are: oil-film interferometry, hot wires mounted near the wall, and surface hot-film sensors based on MEMS technology. First, we demonstrate that the oil-film interferometry technique can be used to measure the skin friction magnitude and its direction in two- and three-dimensional wall-bounded shear flows. The results also demonstrate that accurate measurements of the mean skin friction with MEMS sensors are possible. Second, fluctuating skin friction is measured in two- and three-dimensional turbulent boundary layers using a MEMS sensor and a wall-wire as reference. Statistics like skewness, flatness and spectra of the turbulent skin friction are presented to demonstrate the potential and limitations of the MEMS sensor. Finally, the skin friction is measured using the oil film technique with an accuracy of about 1.5%, over the range of Reynolds numbers 10,000 < Reθ < 70,000, in a zero pressure-gradient boundary layer. The results are very well represented by the log-law with κ = 0.38, C = 4.1.

Can We Ever Rely on Results from Wall-Bounded Turbulent Flows without Direct Measurements of Wall Shear Stress?

Method for injection of liquid reductant into an exhaust gas evaporating and decomposing the liquid reductant at elevated temperature includes providing an exhaust pipe having an interior surface disposing the exhaust pipe in fluid communication with and upstream of a catalyst. The method includes steps disposing an internal cone within the exhaust pipe generally parallel to the exhaust pipe, mounting an injector to the exterior of the exhaust pipe in fluid communication with the internal cone, injecting liquid reductant into the internal cone, directing the exhaust gas in a passage between the interior surface of the exhaust pipe and the internal cone. Exhaust gas is directed within the internal cone. Flow of exhaust gas has an elevated temperature compared to an ambient. A further step includes creating a drag force on the injected liquid reductant to increase travel time of the injected liquid reductant from the injector to the catalyst.

Method, system and apparatus for liquid injection into a gas system

A control system for engine braking for a vehicle powered by a turbocharged engine uses a supercharger to assist a turbocharger compressor to boost turbocharger air flow into the engine cylinders. An engine driven air pumping device draws ambient air, or alternately exhaust gas through the pump inlet, compresses the air, and delivers the compressed air through the pump outlet to the turbocharger compressor inlet or alternately the turbocharger compressor outlet. The increased air flow into the cylinders and out of the cylinder exhaust valves increases retarding power of the vehicle.

Steve Gravante

Papers

Characterization of the Pressure Fluctuations Under a Fully Developed Turbulent Boundary Layer

Extraction of turbulent wall-pressure time-series using an optimal filtering scheme

Can We Ever Rely on Results from Wall-Bounded Turbulent Flows without Direct Measurements of Wall Shear Stress?

Method, system and apparatus for liquid injection into a gas system

Supercharged boost-assist engine brake