Thickness Of Viscous Sublayer Research Articles

Stomatal transpiration and droplet evaporation on leaf surfaces by a microscale modelling approach

Knowledge on convective water vapour exchange at leaf-air interfaces is required to assess transpiration of leaves via stomata and evaporation of droplets, which can both be considered as microscopic moisture sources, heterogeneously distributed across the leaf. An innovative modelling approach was proposed to investigate such convective mass transport from leaf surfaces, using computational fluid dynamics (shear-stress transport k–ω turbulence model with low-Reynolds number modelling). The main novelty lies in the fact that a large range of spatial scales (10−5–10−1m) was included and that the individual microscopic sources were modelled discretely. The convective exchange from the leaf model was strongly dependent on three parameters: surface coverage, air speed and source size. The relation between the convective flow rate and both the coverage ratio (CR) and the microscopic Sherwood number, i.e., the ratio of the source size to the viscous sublayer thickness, was quantified. It was shown that well-established convective transfer coefficients, obtained from plates or leaf models for a CR of 100%, can result in a significant overprediction of the convective exchange, compared to more realistic, lower CR. Furthermore, small variations in stomatal density (CR), e.g., due to biological variability, were shown to have a large impact on the convective exchange and droplets were found to evaporate more rapidly at low CR. The decrease in mass transfer rate due to stomatal closure was quantified as well. The proposed numerical modelling approach can be applied to increase our understanding of leaf transpiration and droplet evaporation, but also of the leaf boundary-layer microclimate and the transport processes therein. A critical discussion of the modelling assumptions allowed to identify focus points for future model refinement as well as future research.

Peculiarities of deformation of compliant coatings with increased strength

Influence of elasticity module of coating material on the parameters of hard compliant coatings deformation has been analysed. Calculation using two-dimensional model has shown that maximum coating deformation is achieved at the ratio of flow rate U to the parameter Ct0 = (E/3ρ)0.5 approximately equal to 2.5, however, velocity of wall surface motion has first local maximum at U/Ct0≈1. The range of coating parameters’ values at which compromise between its hardness and intensity of interaction with turbulent flow is provided has been determined. For rubbery materials with Poisson coefficient of about 0.5, correlations of the flow velocity and parameter Ct0 shall be in the range 1÷1.5. It is shown that at such parameters, the mean square value of the coating surface deflection/inflection is less than the viscous sublayer thickness, its correlation with the wavelength is very small and equals (1÷5)·10−4. Such form of deformed surface fundamentally differs from the parameters of the wave wall in Kendall’s experiments which results are used for calculation of inverse influence of wall deformation on the flow. It was assumed that solid compliant coatings do not cause instability of interaction with the ambient flow.

Mechanism of wall transfer under steady localized blowing

The scalar transport downstream of a localized blowing is analyzed through direct numerical simulations, in a fully developed low-Reynolds number turbulent channel flow subject to constant wall temperature. The Karman number is 180 and the Prandtl number is 1. The streamwise extend of the blowing spanwise slot is varied in a large range, going from the half channel height to particularly small values that are roughly twice the viscous sublayer thickness, while past published experimental and numerical results focused on significantly larger slots. Detailed data on the flow and temperature fields are reported and discussed. It is shown that, the severity parameter defined as the ratio of injected mass to the mean flow rate considered as the main similarity parameter so far, is no more valid when the streamwise extends of localized wall intervention becomes comparable to the buffer layer thickness. The Reynolds analogy breaks-up and the local wall transfer is significantly enhanced under these conditions.

Roughness enhanced mechanism for turbulent convective heat transfer

The mechanism of turbulent convective heat transfer enhancement was experimentally investigated by measuring the heat transfer in two dimensional roughness tubes with different roughness heights at various Reynolds numbers. The results show that there is a maximum Nusselt number ratio ( Nu/ Nu 0) for a fixed roughness height with increasing Reynolds numbers. For water as working fluid, heat transfer can hardly be increased when the roughness height is lower than the thickness of the viscous sublayer, and both heat transfer and flow friction begin to increase when the roughness height is higher than the viscous sublayer. When the roughness height is more than five times of the viscous sublayer thickness, the flow friction begins to increase sharply but heat transfer is slowly enhanced. So the best heat transfer enhancement for a given pumping power is reached when the roughness height is about three times of the viscous sublayer thickness. The Prandtl number influences to the turbulent heat transfer enhancement by roughness were also analyzed.

Assessment of a One-Equation Turbulence Model for Strongly Heated Gas Flowing Upward in a Vertical Tube

A one-equation near-wall turbulence model is used to predict a strongly heated, low-Mach-number gas flowing upward in a vertical tube. Intense wall heating causes significant and continuous fluid property variation and thickening of the viscous sub-layer. Consequently, a fully developed flow does not evolve. Existing literature reveals that two-equation models with various near-wall approaches generally perform poorly under such conditions. However, the one-equation model considered in this study is shown to accurately predict this flow through adjustment of a model constant related to the viscous sub-layer thickness.

Influence of young's modulus on drag-reduction in turbulent flow using flexible tubes

In order to develop technologies of friction drag reduction with a flexible tube to be used for water transport, experimental studies were carried out on the influence of Young's modulus on the turbulent drag reduction. The friction coefficients of flexible tubes with different Young's modulus were examined by using a sleeve-tube structure. The fluctuating vibration of the outer wall and the fluctuating pressure on the inner wall of the tubes were measured with a laser displacement sensor and a pressure sensor. The results are as follows. The smaller the Young's modulus of a flexible tube and the larger the Reynolds number, the larger the turbulent drag reduction rates become. The transition from laminar flow to turbulent flow can be delayed with an appropriate Young's modulus. Non-dimensional amplitude of fluctuating vibration on the outer wall is smaller than that of a viscous sub-layer thickness, and is positively correlated with the friction drag reduction.

Calculation of a flow in prismatic tubes using the planar flow model

The turbulent flow of a Newton liquid in prismatic tubes was represented as a superposition of planar layers. The hydraulic resistance coefficient was calculated from the calculated rate profile in a planar layer. The only fitting parameter was the Reynolds number determined from the dynamic rate and the thickness of the viscous sublayer. The calculated data are in satisfactory agreement with the experimental data on the flow in tubes with a round, trigonal, square, and rectangular transverse section.

Drag reduction in turbulent flows over superhydrophobic surfaces

In this paper, we demonstrate that periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide laminar flow drag reduction, are capable of reducing drag in the turbulent flow regime. Superhydrophobic surfaces contain micro- or nanoscale hydrophobic features which can support a shear-free air-water interface between peaks in the surface topology. Particle image velocimetry and pressure drop measurements were used to observe significant slip velocities, shear stress, and pressure drop reductions corresponding to drag reductions approaching 50%. At a given Reynolds number, drag reduction is found to increase with increasing feature size and spacing, as in laminar flows. No observable drag reduction was noted in the laminar regime, consistent with previous experimental results for the channel geometry considered. The onset of drag reduction occurs at a critical Reynolds number where the viscous sublayer thickness approaches the scale of the superhydrophobic microfeatures and performance is seen to increase with further reduction in viscous sublayer height. These results indicate superhydrophobic surfaces may provide a significant drag reducing mechanism for marine vessels.

Sediment resuspension and erosion by vortex rings

Particle resuspension and erosion induced by a vortex ring interacting with a sediment layer was investigated experimentally using flow visualization (particle image velocimetry), high-speed video, and a recently developed light attenuation method for measuring displacements in bed level. Near-spherical sediment particles were used throughout with relative densities of 1.2–7 and diameters (d) ranging between 90 and 1600 μm. Attention was focused on initially smooth, horizontal bedforms with the vortex ring aligned to approach the bed vertically. Interaction characteristics were investigated in terms of the dimensionless Shields parameter, defined using the vortex-ring propagation speed. The critical conditions for resuspension (whereby particles are only just resuspended) were determined as a function of particle Reynolds number (based on the particle settling velocity and d). The effects of viscous damping were found to be significant for d/δ<15, where δ denotes the viscous sublayer thickness. Measurements of bed deformation were obtained during the interaction period, for a range of impact conditions. The (azimuthal) mean crater profile is shown to be generally self-similar during the interaction period, except for the most energetic impacts and larger sediment types. Loss of similarity occurs when the local bed slope approaches the repose limit, leading to collapse. Erosion, deposition, and resuspension volumes are analyzed as a function interaction time, impact condition, and sediment size.

Experimental investigation for near-wall lift of coarser particles in slurry pipeline using γ-ray densitometer

Experimental data are collected in 54.9 mm diameter horizontal pipe for concentration profiles using γ-ray densitometer. Two sizes of glass beads with mean diameter and geometric standard deviation of 440 μm and 1.2 and 125 μm and 1.15, respectively, are used. These data are collected for flow velocity up to 5 m/s and overall concentration up to 50% by volume for each velocity. Experimental data measured by sampling probe and pressure gradients in the previous study [D.R. Kaushal, K. Sato, T. Toyota, K. Funatsu, Y. Tomita, Effect of particle size distribution on pressure drop and concentration profile in pipeline flow of highly concentrated slurry, International Journal of Multiphase Flow, 31(7) (2005) 809–823.] are used to compare with γ-ray densitometer measurements and to study slip velocity and near-wall lift of particles in the pipeline. In overall, γ-ray densitometer and sampling probe give quite similar concentration profiles except for few cases of coarser (440 μm) particles at lower flow velocities. Measurements show that, for finer particles, point of maximum concentrations are near the pipe bottom ( y/ D = 0.1) and for coarser particles, maximum points are relatively away from the pipe bottom with decrease in shift as flow velocity increases. Pressure gradient profiles of equivalent fluid for finer particles are found to resemble with water data except for 50% concentration, however, more skewed pressure gradient profiles of equivalent fluid are found for coarser particles. Experimental results indicate absence of near-wall lift for finer particles due to submergence of particles in the lowest layer into the viscous sublayer and presence of considerable near-wall lift for coarser particles due to impact of viscous–turbulent interface on the bottom most layer of particles and increased particle–particle interactions. It is observed that near-wall lift decreases with increase in flow velocity; however, the effect of slip velocity on pressure drop is greater at lower flow velocities and less at higher flow velocities than near-wall lift of coarser particles in slurry pipeline. For finer particles, the departure from equivalent fluid pressure gradient profile at 50% concentration is attributed to the sudden increase of viscous sublayer thickness.

The transient response characteristics of compliant coating to pressure fluctuations

The amplitude and phase lag of surface deformation were determined for a compliant coating under the action of turbulent pressure fluctuations. For this purpose, pressure fluctuations were measured experimentally. The amplitude and duration of coherent wave train of pressure fluctuations were investigated using digital filtration. The transient response was calculated for stabilization of forced oscillations of the coating in approximation of local deformation. The response of coating was analyzed with considerations of its inertial properties and limited duration of coherent harmonics action of pressure fluctuations. It is shown that a compliant coating interacts not with the whole spectrum of pressure fluctuations, but only with a frequency range near the first resonance. According to the analysis, with increasing elasticity modulus of the coating material E, deformation amplitude decreases as 1/E, and dimensionless velocity of the coating surface decreases as 1/√ E. For sufficiently hard coatings, deformation amplitude becomes smaller than the thickness of viscous sublayer, while surface velocity remains comparable to vertical velocity fluctuations of the flow.

Investigation of Microbubble Boundary Layer Using Particle Tracking Velocimetry

Particle tracking velocimetry has been used to measure the velocity fields of both continuous phase and dispersed microbubble phase, in a turbulent boundary layer, of a channel flow. Hydrogen and oxygen microbubbles were generated by electrolysis. The average size of the microbubbles was 15μm in radius. Drag reductions up to 40% were obtained, when the accumulation of microbubbles took place in a critical zone within the buffer layer. It is confirmed that a combination of concentration and distribution of microbubbles in the boundary layer can achieve high drag reduction values. Microbubble distribution across the boundary layer and their influence on the profile of the components of the liquid mean velocity vector are presented. The spanwise component of the mean vorticity field was inferred from the measured velocity fields. A decrease in the magnitude of the vorticity is found, leading to an increase of the viscous sublayer thickness. This behavior is similar to the observation of drag reduction by polymer and surfactant injection into liquid flows. The results obtained indicate that drag reduction by microbubble injection is not a simple consequence of density effects, but is an active and dynamic interaction between the turbulence structure in the buffer zone and the distribution of the microbubbles.

Drag reduction in a flat-plate boundary layer flow by polymer additives

This paper presents a theoretical study on the velocity distribution and the friction factor of boundary layer flows with polymer additives starting from the concept of “stress deficit.” A novel method of order of magnitude analysis is developed, which converts the governing equations of boundary layer flow into a solvable ordinary differential equation, thus the total shear stress distribution is obtained, then the formulas for the mean velocity profiles and the friction factor for a boundary layer flow are derived after introducing appropriate expressions for the “effective viscosity” and the thickness of viscous sublayer. The derived velocity equation is able to depict the velocity from a solid wall to the outer edge of boundary layer with or without polymer additives using only one fitted parameter D* that is a function of polymer species, its concentration, and Reynolds number. By integrating the velocity profiles, the friction factor and the thickness of boundary layer development are obtained. Experimental data agree well with the theoretical results.

Microstructured Surfaces for Drag Reduction Purposes: Experiments and Simulations on Rectangular 2D Riblets

AbstractIt is well established that properly structured surface exhibits a lower friction drag, when exposed to a turbulent boundary layer, than a smooth surface under the same flow conditions. The observed drag decrease is usually attributed to an increased thickness of the viscous sublayer. In this work we examine the friction drag reducing mechanism. Two parallel approaches towards achieving this goal are presented. Photolithography was used to manufacture rectangular riblets in the 10∝m range on a standard 4” silicon wafer. A special compact plane channel system was designed and used for measurements of the frictional drag on structured surfaces in the turbulent flow covering a wide Reynolds number range. Navier-Stokes equation, for the examined drag reducing geometry, was solved in the laminar regime with appropriate boundary conditions. The resulting velocity field was used to extract the protrusion heights difference for streamwise and spanwise flows over the structured surface. The latter was then related to the experimentally measured drag reduction slope. We show that in case of a rectangular riblet, with a size of the order of one wall unit, the observed drag reduction can be accounted for within the above model.

Coefficients of Time and Length Scales of Turbulent Eddies

ABSTRACTThe turbulence time and length scales representing the energy containing eddies are by Tt= CtTk/ε and ℓt= Ctℓk32/ε, respectively, while the Kolmogorov time and length scales representing the energy dissipative eddies are expressed by Tk= CkT(ν/ε)1/2and ℓk= Ckℓ(ν3/ε)1/4, respectively. The available DNS data for fully developed channel flows with and without wall injection / suction are used to determine the coefficients. It is found that, with the typical values of CtT= Ctℓ= 1 which are usually adopted in the turbulence study, ckT= 2 and Ckℓ= 3. However, this set of coefficients lead to underprediction of the thickness of viscous sublayer. By relaxing the usual assumption of CtT= Ctℓ= 1, a new set of coefficients: CtT= Ctℓ= 0.8, CkT= 4, and Ckℓ= 9 is suggested. Thecalculated with this set of coefficients becomes more physically reasonable.

Experimental study on the turbulent boundary layer flow over riblets surface

The laser Doppler velocimeter (LDV) and hydrogen bubble flow visualization techniques have been used to measure the characteristics of turbulent boundary layer flow over riblets surface and to observe its coherent structure in the near wall region. The experimental results indicate that, in comparison with the turbulent boundary layer flow over a smooth surface, greater values are obtained for the thickness of viscous sublayer, the thickness of buffer region and the integral constant C in the log-law. Moreover, the maximum value of turbulent intensity u′/U* is increased by 6.7%, but its position is decreased by 6.4%, the skewness factor and the flatness factor are hardly affected by the riblets surface. The non-dimensional value of low-speed streak spacing is reduced by 20%, this is also an indication of turbulent drag reduction.

Turbulence management using riblets for heat and momentum transfer

Experiments were carried out in a low-speed wind tunnel to investigate the heat-transfer characteristics of triangular-profiled riblet surfaces by comparing them with those of a smooth surface of an identical construction in a thermal turbulent boundary layer. The results of careful heat-transfer measurements indicate that the heat-transfer coefficient over riblet surfaces is increased from that of a smooth surface by 10%. This increase is obtained without incurring the drag penalty usually associated with a modified surface geometry, suggesting that there is an apparent breakdown of the Reynolds analogy over the heated riblet surfaces. The logarithmic temperature profile of the boundary layer over the riblet surface is shifted downward, suggesting that the thickness of the thermal viscous sublayer is reduced. The statistical analysis of the higher moments of temperature fluctuation shows that the effect of riblets on the thermal boundary layer is extended farther away from the wall into the boundary layer than on the momentum boundary layer. These results lead to a conclusion that the turbulent transport mechanism of heat over the riblet surfaces may be quite different from that of momentum even if the temperature is considered a passive contaminant in this investigation.

Power spectrum of tangential stress on a wall in a turbulent flow

The mechanism of formation of the tangential stress spectrum on a wall in a developed turbulent flow is considered. An interpretation of spectra obtained experimentally is proposed. It is shown that the spectrum contains information on the viscous sublayer thickness and enables us to perform nonprecision measurements of tangential stress on the wall in the developed turbulent flow with no precalibration of sensors.

Breakdown of the Reynolds analogy over drag-reducing riblets surface

An experiment was carried out in a low-speed wind tunnel to study the near-wall turbulence structure over a heated riblets surface. The results confirmed the main conclusion of previous study that riblets can enhance the convective heat-transfer rate by as much as 35 percent even within the drag- reducing region. The logarithmic profile of the mean temperature was shifted downwards, indicating that viscous-sublayer thickness of the thermal boundary layer was reduced over a riblets surface. The reason for the apparent breakdown of the Reynolds analogy seems to be related to the difference in the turbulence length scale between the thermal and momentum boundary layers in the near-wall region.

Cohesionless Fine‐Sediment Bed Forms in Shallow Flows

Bed-form data from laboratory experiments using cohesionless, fine silica solids in shallow water flows are analyzed to find dimensionless relationships for geometry and friction factor. With increasing flow discharge over a stationary flat bed, the bed-form sequence is primary ripples, barchanoid and linguoid ripples (secondary ripples), ripples on dunes (for silt grades only), and a moving flat bed. The primaries develop from the incipient transport stress, otherwise called the primary threshold. By extrapolating dimensionless bedform length and height data to this threshold, it is shown that the geometry is proportional to the depth of the viscous sublayer thickness. The secondaries develop from a secondary threshold, which is an approximate constant stress condition at which incipient suspension also begins. The ripples on dune form is associated with a tertiary threshold for which the dimensionless stress ratio \IY\N/\IY\dc\N is about 20. And the moving flat bed form occurs at a transition threshold for which \IY\N/\IY\dc\N appears to be a natural constant at about 15. A single friction factor curve is demonstrated for all these data.