Roughness Reynolds Number Research Articles

Application of power law to the currents in a tidal channel

In most cases, the velocity profiles of tidal currents are expressed by the classical logarithmic (log) law, through which various important friction parameters, such as the friction velocity and roughness length, can be obtained conveniently. However, the power law is not used as much as the log law in tidal current surveys because of the difficulty in obtaining the friction parameters as well as the lack of a theoretical basis. Through theoretical improvements of the power law in recent years, its advantages have been validated based on measurements in pipe and river flows. For a better understanding of the power law in tidal flow, an assessment of the power law from three aspects, namely, the mean velocity profiles, the velocity gradient distribution and the Reynolds shearing stress distribution, is performed through a comparison with measurements within a tidal cycle, which are collected from some previous literature. The power law demonstrates a better correlation with the near-bed velocity profiles and gradient distribution compared with the log law. The auxiliary shearing stress distribution caused by tidal acceleration and deceleration can also be well described by the power law. Moreover, the relationships between the power index and other parameters, such as roughness length, Reynolds number and friction velocity, are investigated according to the tidal current profiles.

乱流境界層の平均量特性に及ぼす粗さの影響

The roughness sublayer beneath a turbulent boundary layer has been investigated analytically and experimentally, and the effect has been discussed on the mean velocity profile throughout the layer. The rough surface consists of two-dimensional square roughness elements. The roughness height is proportional to streamwise distance. It is one of conditions of an equilibrium boundary layer proposed by Rotta J.C. The roughness pitch ratio is 4. The measurement within/outside the roughness sublayer was made using LDV and CTA, respectively. The Reynolds number based on the momentum thickness is 6000. The roughness Reynolds number is 149 and the roughness is in complete rough regime. The analytical solutions of streamwise mean velocity and Reynolds shear stress profiles were derived from the space averaged Reynolds equation in the cavity region between roughness elements and the mixing length model. The solutions were well consistent with the experimental results. By use of the solutions and experimental results, the center height of drag moment and the constant of the roughness function can be represented as a function of the roughness pitch ratio for the equilibrium boundary layer. Also, from the momentum integral equation, Coles's wake law, solution and experimental results, the wake parameter will be given as a function of the friction parameter and relative roughness height. Finally, the local skin friction coefficient will be formulated with a function of the roughness pitch ratio and relative roughness height.

壁面せん断乱流の対数層に対する粗さの影響

The roughness sublayer beneath a turbulent boundary layer has been investigated analytically and experimentally, and its effect has been discussed on the logarithmic velocity profile. The rough surface consists of two-dimensional square roughness elements. The roughness height is proportional to streamwise distance. It is one of conditions of an equilibrium boundary layer. The roughness pitch ratio is 4. The free stream velocity is about 9m/s. The experiments were made in zero pressure gradient. The velocity measurement within/outside the roughness sublayer was made using LDV and CTA, respectively. The momentum thickness and roughness Reynolds numbers are 6000 and 149, respectively. From the analytical solutions of streamwise mean velocity and Reynolds shear stress profiles in the cavity region between roughness elements and experimental results , the center height of drag moment and the constant of the roughness function can be represented as a function of the roughness pitch ratio. These functions are well consistent with the experimental and DNS results.

Observation and simulation of lake‐air heat and water transfer processes in a high‐altitude shallow lake on the Tibetan Plateau

AbstractLakes are an important part of the landscape on the Tibetan Plateau. Most of the Plateau lakes' area has been expanding in recent years, but lake‐atmosphere energy and water interaction is poorly understood because of a lack of observational data and adequate modeling systems. Based on the eddy covariance observation over a high‐altitude shallow and small lake (the small Nam Co Lake) during an ice‐free period from 10 April to 30 August 2012, this study analyzes the lake‐air heat and water vapor turbulent transfer processes and evaluates two popular lake‐air exchange models: a bulk aerodynamic transfer model (B model) and a multilayer model (M model). Our main results are as follows: (1) observations show that the bulk transfer coefficient (CE) and roughness length (zoq) for water are higher than those for heat (CH and z0h), especially under low wind speed; (2) both models underestimate turbulent fluxes due to inaccurate values of the Charnock coefficient (α) and the roughness Reynolds number (Rr) which are both important parameters for calculating the roughness length for momentum (z0m) over water; (3) α within a reasonable range of 0.013–0.035 for rough flow and Rr for smooth flow (Rr = 0.11) are 0.031 and 0.54, respectively, by our observation. The wave pattern of shorter wavelength gives a larger z0m in the small and shallow lake; and (4) the B model and the M model gave consistent results, and both models are more suitable for simulation of turbulent flux exchange after z0m optimization.

Transitional flow in the wake of a moderate to large height cylindrical roughness element

The effect of an isolated, cylindrical roughness on the stability of an airfoil boundary layer has been studied based on particle image velocimetry and hot-wire anemometry. The investigated roughness elements range from a sub-critical to a super-critical behavior with regard to the critical roughness Reynolds number. For the sub-critical case, the nonlinear disturbance growth in the near wake is governed by oblique Tollmien–Schlichting (TS) type modes. Further downstream, these disturbance modes are, however, damped with the mean flow stabilization and no dominant modes persist in the far wake. By contrast, in the transitional configuration the disturbance growth is increased, but still associated with a TS-type instability in the near-wake centerline region of the low-aspect (height-to-diameter) ratio element. That is, the disturbances in the centerline region show a similar behavior as known for 2D elements, whereas in the outer spanwise domain a Kelvin–Helmholtz (KH) type, shear-layer instability is found, as previously reported for larger aspect ratio isolated elements. With increasing height and, thereby, aspect ratio of the roughness, the KH-type instability domain extends toward the centerline and, accordingly, the TS-type instability domain decreases. For high super-critical cases, transition is already triggered in the wall-normal and spanwise shear layers upstream and around the roughness. In the immediate wake, periodic shear-layer disturbances roll up into a—for isolated elements characteristic—shedding of vortices, which was not present at the lower roughness Reynolds number cases due to the decreased aspect ratio and, thereby, different instability mechanism.

Turbulent flow in rough wall channels: Validation of RANS models

Two kinds of a generic roughness on plane channel walls have been investigated by standard RANS turbulence models. The objective was to accurately predict mean flow quantities for steady incompressible flows through rough wall channels. Seven turbulence models have been used in a special validation procedure based on direct numerical simulation (DNS) results for several values of the roughness spacing and the Reynolds number (which here are the free parameters). In addition to single RANS solutions also a parameter expansion method (PEM) is examined with respect to its capability to accurately predict rough wall channel flows for an extended range of parameters, i.e. for various roughness heights and Reynolds numbers. Those methods that could be validated were then used to predict results for parameters beyond the validation range. Their accuracy can be assessed by comparison with reasonably extended DNS results. The final conclusion is that RANS solutions only with certain turbulence models and over some parameter ranges can be used to predict turbulent channel flows influenced by wall roughness.

Experimental and CFD-based thermal performance prediction of solar air heater provided with chamfered square rib as artificial roughness

An experimental and two-dimensional computational fluid dynamics (CFD) analysis of a solar air heater has been carried out using chamfered square rib as artificial roughness on the absorber plate. The relative roughness pitch (P/e = 7.14–17.86), chamfer angle (α = 0°–40°), Reynolds number (Re = 3800–18,000) and relative roughness height (e/D = 0.042) are chosen as design variables for analysis. A uniform heat flux of 1000 W/m2 is maintained on the surface of absorber plate. CFD code, ANSYS FLUENT 14.5 with renormalization group k-e model was chosen. An enhancement in Nusselt number and friction factor with decrease in relative roughness pitch (P/e) is presented and discussed with reference to experimental and CFD analysis. The effect of chamfer angle and Reynolds number on enhancement of Nusselt number and friction factor is also presented. Optimum configuration of roughness element for artificially roughened solar air heater has been determined in terms of thermo-hydraulic performance parameter. The chamfer angle of 20° on square rib and relative roughness pitch of 7.14 provide best thermo-hydraulic performance of 2.047 considering the maximum heat transfer and minimum pressure drop.

A computational investigation of the effect of surface roughness on heat transfer on the stator endwall of an axial turbine

A numerical investigation of the effect of stochastic surface roughness on vane endwall heat transfer was conducted. The effect of equivalent sand grain roughness height was explored and compared with available experimental data. Steady-state computations using ANSYS CFX 14.0 in conjunction with the shear stress transport turbulence model were performed. Computations were conducted for fully turbulent flow conditions, since this best reproduces the conditions for the corresponding measurements. Roughness measurements were conducted at different locations along the vane passage. Exploration of these measurements indicated roughness Reynolds number values from the transitional and fully rough regime. The roughness model supplied in CFX was applied to explore the impact of surface roughness on heat transfer. Numerical heat transfer results in the vane passage were determined from a set of computations at the same operating point consisting of an adiabatic and a heat flux calculation. Calculations were conducted with a systematic variation of equivalent sand grain roughness heights and compared with experimental data. Results are presented for smooth and rough wall calculations at two different flow conditions.

Experimental and CFD-based thermal performance prediction of solar air heater provided with right-angle triangular rib as artificial roughness

An experimental and two-dimensional computational fluid dynamics (CFD) analysis of a solar air heater has been carried out using right-angle triangular ribs as artificial roughness on the absorber plate as a convenient method for enhancement of thermal performance of solar air heater. The relative roughness pitch (P/e = 7.14–35.71), Reynolds number (Re = 3800–18000), and relative roughness height (e/D = 0.021–0.042) have been selected as design variables for both analysis. ANSYS FLUENT 14.5 with renormalization group k–e turbulence model is selected for the analysis of computational domain of solar air heater during CFD analysis. An enhancement in Nusselt number and friction factor with a decrease in relative roughness pitch (P/e) and increase in relative roughness height are presented and discussed with reference to experimental investigation and CFD analysis. The results of roughened solar air heater duct have been compared with smooth duct under similar flow condition. The optimum value of rib configuration based on constant pumping power requirement has been derived using thermo-hydraulic performance parameter and has been found 2.03 at P/e = 7.14. e/D = 0.042 and at a Reynolds number of 15,000 for the investigated range of parameters.

Roughness receptivity and shielding in a flat plate boundary layer

Surface roughness can affect boundary layer transition by acting as a receptivity mechanism for transient growth. While experiments have investigated transient growth of steady disturbances generated by discrete roughness elements, very few have studied distributed surface roughness. Some work predicts a ‘shielding’ effect, where smaller distributed roughness displaces the boundary layer away from the wall and lessens the impact of larger roughness peaks. This work describes an experiment specifically designed to study this effect. Three roughness configurations (a deterministic distributed roughness patch, a slanted rectangular prism, and the combination of the two) were manufactured using rapid prototyping and installed flush with the wall of a flat plate boundary layer. Naphthalene flow visualization and hotwire anemometry were used to characterize the boundary layer in the wakes of the different roughness configurations. Distributed roughness with roughness Reynolds numbers ($\mathit{Re}_{kk}$) between 113 and 182 initiated small-amplitude disturbances that underwent transient growth. The discrete roughness element created a pair of high- and low-speed steady streaks in the boundary layer at a sub-critical Reynolds number ($\mathit{Re}_{kk}=151$). At a higher Reynolds number ($\mathit{Re}_{kk}=220$), the discrete element created a turbulent wedge 15 boundary layer thicknesses downstream. When the distributed roughness was added around the discrete roughness, the discrete element’s wake amplitude was decreased. For the higher Reynolds number, this provided a small but measurable transition delay. The distributed roughness redirects energy from longer spanwise wavelength modes to shorter spanwise wavelength modes. The presence of the distributed roughness also decreased the growth rate of secondary instabilities in the roughness wake. This work demonstrates that shielding can delay roughness-induced transition and lays the ground work for future studies of roughness-induced transition.

A fast direct numerical simulation method for characterising hydraulic roughness

We describe a fast direct numerical simulation (DNS) method that promises to directly characterise the hydraulic roughness of any given rough surface, from the hydraulically smooth to the fully rough regime. The method circumvents the unfavourable computational cost associated with simulating high-Reynolds-number flows by employing minimal-span channels (Jiménez & Moin,J. Fluid Mech., vol. 225, 1991, pp. 213–240). Proof-of-concept simulations demonstrate that flows in minimal-span channels are sufficient for capturing the downward velocity shift, that is, the Hama roughness function, predicted by flows in full-span channels. We consider two sets of simulations, first with modelled roughness imposed by body forces, and second with explicit roughness described by roughness-conforming grids. Owing to the minimal cost, we are able to conduct direct numerical simulations with increasing roughness Reynolds numbers while maintaining a fixed blockage ratio, as is typical in full-scale applications. The present method promises a practical, fast and accurate tool for characterising hydraulic resistance directly from profilometry data of rough surfaces.

Investigation on drag performance of anti-fouling painted flat plates in a cavitation tunnel

The flat plate coated with silicone-type Tin–free self-polishing co-polymer (SPC) or the conventional metal-type Tin-free SPC is prepared to investigate the drag performance of the anti-fouling SPC. The local skin friction of anti-fouling paints is evaluated by a flat plate model test method in the cavitation tunnel. The properties of the boundary layer and the drag performance are investigated by flow and force measurement techniques. The silicone-type SPC paint shows better drag performance than the metal-type paint in the high speed regime. The silicone-type SPC paints also show decreasing roughness function (ΔU+) with the increase of displacement thickness Reynolds number (Reδ⁎) and roughness Reynolds number (ks+). Even in the same silicone-type SPC paints with similar roughness function, drag performance appears differently. The different drag performance in the silicone-type SPC painted surfaces is considered to be affected by different turbulent vortical structures caused by the surface roughness. Y-directional peak position of streamwise turbulence intensity is utilized to estimate the existence of vortical structure. To investigate the reason of the different drag performance in the silicone-type SPC painted surfaces, the POD analysis, extracting the most energetic flow fields, is adopted to find the effects of cross-flow velocity component caused by the turbulent vortical structure.

An intermittency model for predicting roughness induced transition

An intermittency transport equation for RANS modeling, formulated in local variables, is extended for roughness-induced transition. To predict roughness effects in the fully turbulent boundary layer, published boundary conditions for k and ω are used. They depend on the equivalent sand-grain roughness height, and account for the effective displacement of wall distance origin. Similarly in our approach, wall distance in the transition model for smooth surfaces is modified by an effective origin, which depends on equivalent sand-grain roughness. Flat plate test cases are computed to show that the proposed model is able to predict transition onset in agreement with a data correlation of transition location versus roughness height, Reynolds number, and inlet turbulence intensity. Experimental data for turbine cascades are compared to the predicted results to validate the proposed model.

Clogging of Fine Sediment within Gravel Substrates: Dimensional Analysis and Macroanalysis of Experiments in Hydraulic Flumes

AbstractAn understanding of the clogging of fine sediments within gravel substrates is advanced through use of dimensional analysis and macroanalysis of previously conducted clogging experiments in hydraulic flumes. Dimensional analysis via the Buckingham pi theorem is used to suggest that the dimensionless clogging depth can be potentially collapsed using the original and adjusted bed-to-grain ratios, i.e., ratio of substrate diameter to fine sediment diameter, substrate porosity, roughness Reynolds number, and Peclet number. Macroanalysis and statistical analysis is performed using 10 previously published studies that include a total of 146 different test conditions reporting noncohesive, fine sediment clogging, or deposition in porous gravel-beds with hydraulically rough turbulent open channel flow. Results suggest that the adjusted bed-to-grain ratio is a reliable predictor of the initiation of clogging with clogging occurring below 27 for the fine fluvial sediment clogging in a gravel bed substrate f...

Near-field flow structures about subcritical surface roughness

Laminar flow over a periodic array of cylindrical surface roughness elements is simulated with an immersed boundary spectral method both to validate the method for subsequent studies and to examine how persistent streamwise vortices are introduced by a low Reynolds number roughness element. Direct comparisons are made with prior studies at a roughness-based Reynolds number Rek (=U(k) k/ν) of 205 and a diameter to spanwise spacing ratio d/λ of 1/3. Downstream velocity contours match present and past experiments very well. The shear layer developed over the top of the roughness element produces the downstream velocity deficit. Upstream of the roughness element, the vortex topology is found to be consistent with juncture flow experiments, creating three cores along the recirculation line. Streamtraces stemming from these upstream cores, however, have unexpectedly little effect on the downstream flowfield as lateral divergence of the boundary layer quickly dissipates their vorticity. Long physical relaxation time of the recirculating wake behind the roughness remains a prominent issue for simulating this type of flowfield.

HIFiRE-1 Ascent-Phase Boundary-Layer Transition

The Hypersonic International Flight Research Experimentation (HIFiRE) program is a hypersonic flight test program. The primary experiment for flight one, launched in March 2010, was to measure boundary-layer transition in hypersonic flight on a nonablating, 7 deg half-angle axisymmetric cone with a small bluntness of 2.5 mm radius. The flight gathered pressure, temperature, and heat transfer measurements during ascent and reentry. Although the vehicle reentered the atmosphere at a higher-than-intended angle of attack, the ascent portion of the flight provided smooth-body boundary-layer transition data at freestream Mach numbers greater than 5, where transition was presumed to be dominated by second-mode instability. The angle of attack during this portion of the flight was less than 1 deg. The end of turbulent-to-laminar transition occurred at Reynolds numbers between and , based on -location and freestream conditions. Transition was correlated with second-mode -factors of approximately 14. Smooth-body transition showed good azimuthal uniformity. High-bandwidth transducers indicated some intermittency in the transition process. Fluctuating pressures, relative to the cone mean pressure, were relatively constant beneath the turbulent boundary layer, but peaked in amplitude just before transition. A diamond-shaped trip retained turbulent flow through ascent until reaching a roughness Reynolds number .

Pressure Gradient Effects on Smooth and Rough Surface Turbulent Boundary Layers—Part I: Favorable Pressure Gradient

The effects of the pressure gradient and surface roughness on turbulent boundary layers have been experimentally investigated. In Part I, smooth- and rough-surface turbulent boundary layers with and without favorable pressure gradients (FPG) are presented. All of the tests have been conducted at the same Reynolds number (based on the length of the flat plate) of 900,000. Streamwise time-mean and fluctuating velocities have been measured using a single-sensor hot-wire probe. For smooth surfaces, the FPG decreases the mean velocity defect and increases the wall shear stress; however, the friction coefficient hardly changes due to the increased freestream velocity. The FPG effect on the streamwise normal Reynolds stress has been examined. The FPG increases the streamwise normal Reynolds stress for y less than 0.6 times the boundary layer thickness. With the zero pressure gradient (ZPG), the roughness increases the mean velocity defect throughout the boundary layer and increases the normal Reynolds stress for y greater than twice the average roughness height. The roughness effect on the mean velocity defect is stronger under the FPG than under the ZPG for y less than 30 times the average roughness height. For y less than 25 times the average roughness height, the roughness effect of increasing normal Reynolds stress is also stronger under the FPG than under the ZPG. Consequently, for a rough surface, the FPG increases the integrated streamwise turbulent kinetic energy, friction coefficient, roughness Reynolds number, and roughness shift. Furthermore, the FPG increases the roughness effects on the integral boundary layer parameters—the boundary layer thickness, momentum thickness, ratio of the displacement thickness to the boundary layer thickness, and shape factor. Thus, the FPG augments the roughness effects on turbulent boundary layers.

Pressure Gradient Effects on Smooth- and Rough-Surface Turbulent Boundary Layers—Part II: Adverse Pressure Gradient

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

A CFD model for the frictional resistance prediction of antifouling coatings

The fuel consumption of a ship is strongly influenced by her frictional resistance, which is directly affected by the roughness of the hull׳s surface. Increased hull roughness leads to increased frictional resistance, causing higher fuel consumption and CO2 emissions. It would therefore be very beneficial to be able to accurately predict the effects of roughness on resistance. This paper proposes a Computational Fluid Dynamics (CFD) model which enables the prediction of the effect of antifouling coatings on frictional resistance. It also outlines details of CFD simulations of resistance tests on coated plates in a towing tank. Initially, roughness functions and roughness Reynolds numbers for several antifouling coatings were evaluated using an indirect method. Following this, the most suitable roughness function model for the coatings was employed in the wall-function of the CFD software. CFD simulations of towing tests were then performed and the results were validated against the experimental data given in the literature. Finally, the effects of antifouling coatings on the frictional resistance of a tanker were predicted using the validated CFD model.

A practical study of the aerodynamic impact of wind turbine blade leading edge erosion

During operation wind turbine blades are exposed to a wide variety of atmospheric and environmental conditions; inspection reports for blades that have been operating for several years show varying degrees of leading edge erosion. It is important to be able to estimate the impact of different stages of erosion on wind turbine performance, but this is very difficult even with advanced CFD models. In this study, wind tunnel testing was used to evaluate a range of complex erosion stages. Erosion patterns were transferred to thin films that were applied to 18% thick commercial wind turbine aerofoils and full lift and drag polars were measured in a wind tunnel. Tests were conducted up to a Reynolds number of 2.20 × 106 scaling based on the local roughness Reynolds number was used in combination with different film thicknesses to simulate a variety of erosion depths. The results will be very useful for conducting cost/benefit analyses of different methods of blade protection and repair, as well as for defining the appropriate timescales for these processes.