Function Of Roughness Research Articles

Effect of straight riblets of the underlying surface on wall bounded flow drag

Direct numerical simulations of thin, straight riblets were conducted to investigate the physical mechanisms involved when the inertial effects within the ribs become important. The main parameter that we assess here is the ribs’ height to spacing ratio (a=h/s). In all cases, ‘k’-type behaviour was observed despite the absence of the pressure drag component. This trend also refers to the destruction of the near-wall cycles and was indicated by the shortening of Reynolds stress structures, mimicking the flows over rough walls. Closely-packed ribs with large h/s have a tendency to generate Kelvin–Helmholtz (KH) like structures at the tips, inducing large pressure fluctuations. Conversely, sparser ribs with low h/s trigger the formation of large mean secondary flows that suppress the pressure fluctuations. We further split the drag contribution of these distinct flow features by decomposing the roughness function into the dispersive and the Reynolds-stress terms. This analysis concludes that the fully-rough (logarithmic) scaling within the drag-increasing regime is transitional, and as the Reynolds number increases, deviates to a more gradual power-law scaling due to the drag increasing mechanism of streamwise aligned secondary motions.

Effects of soldering and wear of die-casting die during ejection: Surface roughness and casting temperature

In the process of high pressure die casting, the soldering of aluminum alloy to dies is a concern. This soldering behavior will cause surface abrasion during the ejection of the casting by ejector rods, which deteriorates the surface quality of the casting and the die. Although the soldering can be mitigated by mold release agents and coating technologies, the die surface roughness and casting temperature also have a significant impact on the soldering problem. This study evaluates the soldering tendency for different casting temperatures and surface roughness by measuring the force of pulling the samples out of the casting, aiming to thoroughly investigate the effects of casting temperatures and die surface roughness on the soldering and wear during ejection for die-casting dies. After casting, the aluminum alloy and the sample surface interlocked. With the surface roughness increased from Ra 0.6 μm to Ra 1.2 μm, the maximum extraction force increased by 26.4 % in the 5th pullout. The high roughness surface induced the formation of surface cracks during the pullout process, which damaged the surface quality of the sample. As the casting temperature increased from 650 °C to 750 °C, the growth rate of maximum extraction force was 8.1 % in the 10th pullout. The severity of surface damage is related to the sample hardness. Therefore, the low surface roughness and casting temperature are beneficial to reduce the soldering and wear of the aluminum alloy on the die. Finally, the correlation function of surface roughness and the number of pullouts to maximum extraction force was obtained.

Influence of skewed three-dimensional sinusoidal surface roughness on turbulent boundary layers

The impact of roughness skewness (ksk) on turbulent boundary layer (TBL) flow with a zero pressure gradient over three-dimensional (3D) sinusoidal rough surfaces was experimentally investigated using a single hotwire anemometer. Nine 3D sinusoidal profiles were manufactured with positive, negative, and zero roughness skewness values. Measurements were taken at three different freestream velocities for each surface and compared with smooth wall TBL results. This study covered a range of friction Reynolds numbers (Reτ) from approximately 1000 to 4000, with δ/k≈20 ± 2, where δ represents the local boundary layer thickness, and k is the maximum height of the roughness, measured from the valley to peak. The results indicate that the wall-unit normalized streamwise mean velocity profiles for all rough surfaces exhibit a downward shift compared to the smooth wall profiles. Surfaces with positive roughness skewness produced the highest drag, leading to the largest downward shift. The friction coefficient (Cf) decreased as ksk decreased. The percentage increase in Cf and ΔU+ (the roughness function) was much larger when moving from negative to zero roughness skewness than when moving from zero to positive roughness skewness. The small differences in turbulence intensity profiles and higher-order turbulence statistics in the outer region of the TBL support the outer layer similarity hypothesis for the roughness considered in this study. The autocorrelation study revealed that surfaces with positive roughness skewness tend to shorten the average length of turbulence structures in the near-wall region.

Influence of Realistic, Cyclic Atmospheric Cycles on the Pitting Corrosion of Austenitic Stainless Steels

Pitting corrosion was evaluated on stainless steels 304H, 304, and 316L the surfaces of which had ASTM seawater printed on them as a function of surface roughness after exposure to an exemplar realistic atmospheric diurnal cycle for up to one year. Methods to evaluate pitting damage included optical imaging, scanning electron microscopy imaging, profilometry analysis, and polarization scans. The developed cyclic exposure environment did not significantly influence pitting morphology nor depth in comparison to prior static exposure environments. Cross-hatching was observed in a majority of pits for all material compositions with the roughest surface finish (#4 finish) and in all surface finishes for the 304H composition. Evidence is provided that cross-hatched pit morphologies are caused by slip bands produced during the grinding process for the #4 finish or by material processing. Additionally, micro-cracking was observed in pits formed on samples with the #4 surface finish and was greatly reduced or absent for pits formed on samples with smooth surface finishes. This suggests that both a low RH leading to an MgCl2-dominated environment and a rough surface containing significant residual stress are necessary for micro-cracking. Finally, the use of various characterization techniques and cross sectioning was employed to both qualitatively and quantitatively assess pitting damage across all SS compositions and surface finishes.

RE-ESTABLISHING CONTEXT OF "ORPHANED" MUSEUM OBJECTS THROUGH SCIENTIFIC INVESTIGATION. A CASE STUDY FROM THE MUSEUM OF JORDANIAN HERITAGE

Many objects in museum collections have no or inadequate information on their origin and archaeological evidence. These objects which are classified as unprovenanced or "Orphaned" represent a big ethical and technical challenge for the museums. Re-establishing the context of these objects by scientific research proves to be the best option for museums. This study main aim is to present a testing protocol that can be used to reestablish the context and determining the provenance of unprovenanced museum objects. The testing protocol was applied on a rare copper-based cauldron from the collection of the Museum of Jordanian Heritage. The object rough date, function, provenance and manufacturing technology were determined by employing an array of scientific techniques: Optical microscopy inductively coupled plasma, optical emission spectroscopy (ICP-OES), reflected microscopy and lead isotopes analysis. The obtained results enabled the museum to transfer the object from the neglect of the storeroom to its main exhibition hall.

Effect of the number of ribbed walls on the thermal performance in rectangular channels with 45-deg parallel or criss-cross ribs

Regionally averaged heat transfer distributions and friction characteristics are experimentally investigated for fully developed, turbulent flow in a rectangular channel with a width-to-height aspect ratio (AR=3). 45-deg angled rib turbulators are placed on one, two, and four sides of the channel in parallel and criss-cross configurations with a pitch-to-height ratio(P/e=10) and a rib blockage ratio(eDh=4.1%). For a roughness Reynolds number range(e+=25−500), results show that increasing the number of ribbed walls improves the overall channel heat transfer for the 45-deg parallel ribs. Results reveal that four-sided ribbed channels provided the greatest thermal performance followed by the two-sided and one-sided ribbed channels, respectively, for both angled rib designs. On the basis of the law of wall similarity, friction and heat transfer roughness functions are derived using the four-sided data reported in this work. Furthmore, friction factors and heat transfer coefficients of similar angled rib designs were obtained from open literature and similarly correlated to derive more robust friction and heat transfer correlations over the roughness Reynolds number range. Thermal designers can use these proposed correlations to predict friction and heat transfer in rectangular cooling channels (AR=1-5) with various numbers of ribbed walls. The measured friction factor and heat transfer coefficient of this study can be predicted using these semi-empirical correlations with maximum errors of 9% and 7%, respectively.

Intelligent Height Adjustment Method of Shearer Drum Based on Rough Set Significance Reduction and Fuzzy Rough Radial Basis Function Neural Network

The intelligent adjustment method of the shearer drum is the key technology to improve the intelligent level and safety degree of fully mechanized mining face. This paper proposes a shearer drum intelligent height adjustment model based on rough set significance attribute reduction (AR) and fuzzy rough radial basis function neural network (FRRBFNN) optimized by adaptive immune genetic algorithm (AIGA). The model first selects the parameters of shearer process monitoring based on the importance attribute reduction algorithm of rough set, and establishes the attribute reduction set of shearer operation characteristic parameters and the drum height decision rule base. Next, a fuzzy rough radial basis function neural network determined by the decision rule space is proposed. By introducing the fuzzy rough membership function as the connection weight, the network can accurately describe the complex nonlinear relationship between the working characteristic parameters of the attribute shearer and the drum height, and measure the uncertainty of the coal seam distribution. Finally, to further optimize the performance of FRRBFNN, the adaptive immune genetic algorithm is introduced to optimize its parameters, to build a high-precision shearer drum height prediction system. For the evaluation method of the model, we use three indicators: mean absolute error, mean absolute percentage error, and root mean square error. Based on the measured data in Yujialiang area, Shaanxi Province, the experimental results show that—compared with the FRRBFNN and support vector regression (SVR) models, a gated current neural network (GRU), a radial basis function neural network (RBF), the memory strengthen long short-term memory (MSLSTM) model, and the adaptive fuzzy reasoning Petri net (AFRPN)—the MAE of the AR-AIGA-FRBFNN model for predicting the height of the left and right rollers are 18.3 mm and 17.2 mm, respectively; the MAPE is 0.96% and 0.93%, respectively; and the RMSE is 21.2 mm and 22.4 mm, respectively. The AR-AIGA-FRBFNN model is therefore more effective than the other considered methods.

Effect of high skewness and kurtosis on turbulent channel flow over irregular rough walls

The skewness of the roughness height distribution is one of the key topographical parameters that govern roughness effects on wall-bounded turbulence. In this paper mathematical bounds for realisable values of skewness and kurtosis are discussed in the context of irregular multi-scale rough surfaces, which are representative of typical forms of engineering roughness. The properties of a set of irregular rough surfaces fully covered by roughness features with very high positive and negative skewness and high kurtosis are investigated using direct numerical simulations of turbulent channel flow at . While an increase of the roughness function is observed at moderate skewness values in line with empirical predictions and previous results for moderately skewed surfaces, the roughness function saturates at extreme values of skewness. Overall, the roughness effect is found to be more sensitive to skewness over the negative skewness range compared to the positive skewness range. Surface pressure statistics show that for surfaces with extreme skewness fully covered by roughness features extreme pits or peaks do not dominate the roughness effect and that surrounding roughness features (‘background’ roughness) retain a significant influence. This is because, while extreme roughness features emerge as skewness approaches high positive or negative values, they tend to be sparse decreasing their overall impact on the wall-bounded flow.

On the effect of streamwise and spanwise spacing to height ratios of three-dimensional sinusoidal roughness on turbulent boundary layers

A developing zero pressure gradient (ZPG) turbulent boundary layer (TBL) over different three-dimensional (3D) sinewave roughnesses is investigated experimentally using single hot-wire anemometry. Seven different sinewave profiles are fabricated with the same amplitude and with different wavelengths in the streamwise (sx) and spanwise (sz) directions. The effects of varying sx and sz on turbulence statistics and the drag coefficient (Cf) are assessed. The wall-unit normalized streamwise mean velocity profile is shifted downward compared with the smooth wall profile for all roughnesses. The streamwise spacing to height ratio sx/k has a more significant effect on the roughness function ΔU+ and Cf compared with the spanwise spacing to height ratio sz/k. However, sz/k has a large impact on the streamwise turbulence intensities in the log and outer layer. An excellent collapse is observed among the mean streamwise velocity profiles plotted in defect form in the outer region. However, a lack of similarity between TBLs over different rough surfaces is observed in the outer region for the turbulence intensities profiles. For isotropic 3D sinusoidal roughness (equal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing spacing to height ratios. For anisotropic 3D sinusoidal roughness (unequal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing sz/sx from half to two in this study.

Experimental testing of solar-based air heater roughed with discrete V-down rib and staggered element.

A rough rectangular channel of solar-based air heater (SBAH) is made and tested. The work consists of an effort to perceive the proportion of heat discharge and frictional behavior of air passing over a roughened rectangular channel. The absorber surface of SBAH is roughed with discrete V-down rib and staggered element roughness having different values of relative rib pitch (P/e) that ranged from 6 to 14. Fixed parameters such as relative gap size (g/e), relative staggered element pitch (P'/P), numeral of gaps (Ng), relative staggered element size (r/g), and relative rib height (e/D) are considered 4, 0.4, 3,1, and 0.0433, respectively, all throughout the study. The flow Reynolds number (Re) changes from 4000 to 14,000; consequently the Nusselt number (Nu) and friction factor (f) reach up to 2.16 and 2.73 times, respectively, with respect to plane surface. The optimum rise in terms of thermal-hydraulic performance (THP) is gained analogous to a P/e of 10. The correlation for heat transfer function, R(e+), and roughness function, G(e+), is given to anticipate the performance of roughness.

Accuracy measure of rough membership multiset functions with application

In this paper, the notion of rough membership function has been introduced in the multiset context. As a consequence, we introduced the lower and upper approximations in terms of the rough membership multiset functions. Finally, an application about how to select the best possible suppliers of chemicals has been presented.

Neural Network Approximation of Refinable Functions

In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there exists a variety of results which show that a wide range of functions can be approximated with sometimes surprising accuracy by these outputs. For example, it is known that the set of functions that can be approximated with exponential accuracy (in terms of the number of parameters used) includes, on one hand, very smooth functions such as polynomials and analytic functions and, on the other hand, very rough functions such as the Weierstrass function, which is nowhere differentiable. In this paper, we add to the latter class of rough functions by showing that it also includes refinable functions. Namely, we show that refinable functions are approximated by the outputs of deep ReLU neural networks with a fixed width and increasing depth with accuracy exponential in terms of their number of parameters. Our results apply to functions used in the standard construction of wavelets as well as to functions constructed via subdivision algorithms in Computer Aided Geometric Design.

More properties of δ β -rough continuous functions on topological approximation spaces

Using the notion of \(\delta \beta \)-open set, we intend to do more research on rough continuous functions. The ideas of \(\delta \beta \)-totally rough continuous functions and \(\delta \beta \)-strongly rough continuous functions are proposed and researched. The notions of \(\delta \beta \)-internally and \(\delta \beta \)-totally functions are discussed, as well as some of their characterizations. Finally, the composition of \(\delta \beta \)-internally and totally functions is discussed.

Predicting the Effect of Hull Roughness on Ship Resistance Using a Fully Turbulent Flow Channel

The consequences of poor hull surface conditions on fuel consumption and emissions are well-known. However, their rationales are yet to be thoroughly understood. The present study investigates the hydrodynamics of fouling control coatings and mimicked biofouling. Novel experimental roughness function data were developed from the “young” fully turbulent flow channel facility of the University of Strathclyde. Different surfaces, including a novel hard foul-release coating, were tested. Finally, the performance of a benchmark full-scale containership was predicted using Granville’s similarity law scaling calculations. Interestingly, the numerical predictions showed that the novel hard foul-release coating tested had better hydrodynamic performance than the smooth case. A maximum 3.79% decrease in the effective power requirements was observed. Eventually, the results confirmed the practicality of flow channel experiments in combination with numerical-based methods to investigate hull roughness effects on ship resistance and powering. The present study can also serve as a valuable guide for future experimental campaigns using the fully turbulent flow channel facility of the University of Strathclyde.

Heat Transfer and Friction in a Rectangular Channel With Varying Numbers of Walls Roughened With 90-Deg Transverse or 45-Deg V-Shaped Ribs

Abstract An experimental investigation was performed to measure the regionally averaged heat transfer distributions and friction factors for fully developed turbulent flow in a rectangular channel with a width-to-height aspect ratio (AR = 3). Data for transverse 90-deg and 45-deg V-shaped, carbon steel ribs placed on one, two, or four sides of the channel were reported for a Reynolds number range (Re = 5,000–60,000). The pitch-to-rib height ratio (P/e) was set at 10 while the rib height-to-channel hydraulic diameter (e/Dh) is 0.041. This corresponds to a roughness Reynolds number range (e+=25−500). For both rib configurations, results show the highest thermal performance was achieved in the channels with four-ribbed wall followed by the two and one-ribbed wall channels, respectively. Using the law of the wall similarity, friction roughness functions (R) and heat transfer roughness functions (G) were developed based on four-sided friction and heat transfer data. Moreover, friction and heat transfer data of similar rib designs were obtained from literature and correlated to the corresponding friction and heat transfer roughness functions. Covering a wide range of roughness Reynolds numbers, more robust heat transfer and friction correlations were developed which can be used by designers to accurately predict both heat transfer and friction in ribbed channels with different numbers of ribbed walls. Using these correlations, one can predict the measured friction and heat transfer data of this study with maximum errors of 9% and 7%, respectively.

Measurement of High Density Electrons Above a Helium Film on an Amorphous Metal Substrate

We have measured two-dimensional electron systems bound to a thin helium film supported by a metallic substrate. We report on our measurement of electron density obtained via a Kelvin probe technique. The underlying metallic substrate is an amorphous metallic alloy (TaWSi), which can support large uniform densities due to its low surface roughness and homogeneous work function. We find that this substrate is able to support high enough densities that the electrons are expected to be Fermi-degenerate.

From drag-reducing riblets to drag-increasing ridges

Small drag-reducing riblets and larger drag-increasing ridges are longitudinally invariant and laterally periodic surface structures that differ only in the details of their lateral periodicity and their size in viscous units. Due to their different drag behaviour, typically riblets and ridges have been analysed separately. By studying experimentally trapezoidal-grooved surfaces of different sizes, we address systematically the transition from riblet-like to ridge-like behaviour in a unified framework. The structure height and lateral wavelength are varied both physically, by considering eight different surfaces, and in their viscous-scaled form, by spanning a wide range of bulk Reynolds number$Re_b$. The effective skin-friction coefficient$C_f$is determined via pressure-drop measurement in a turbulent channel flow facility designed for accurate drag measurements. An unexpectedly rich drag behaviour is unveiled, in which different drag regimes are distinguished depending on the value of$l_g^+$, the viscous-scaled square root of the groove area. The well-known drag-reducing regime of riblets that spans up to$l_g^+=17$is followed by a regime in which the roughness function${\rm \Delta} U^+$increases logarithmically with$l_g^+$, indicating an apparent fully rough behaviour up to$l_g^+\approx 40$. Further increase of$l_g^+$leads to a clear departure from the fully rough regime, and an unexpected non-monotonic behaviour of the roughness function${\rm \Delta} U^+$for$50< l_g^+<200$is reported for the first time. For sufficiently large$Re_b$and$l_g$, it is shown that a single parameter, similar to the classical hydraulic diameter, is sufficient to describe the drag behaviour of ridges. We find that an appropriate definition of the effective channel height is crucial for interpreting the drag behaviour. When the longitudinal protrusion height of the structured surface is accounted for in the channel height definition, a laminar flow exhibits the same$C_f(Re_b)$relation known for flat surfaces. This approach thus allows us to discern the modification of$C_f$induced by turbulence. We provide predictive correlations for the fully rough regime and the high Reynolds number range of trapezoidal-grooved surfaces that become possible thanks to the chosen channel height definition.

Construction of Rough Graph through Rough Membership Function

Rough membership function defines the degree of relationship between conditional and decision attributes of an information system. It is defined by <img src=image/13429145_01.gif> where <img src=image/13429145_07.gif> is the subset of <img src=image/13429145_08.gif> under the relation <img src=image/13429145_09.gif> where <img src=image/13429145_08.gif> is the universe of discourse. It can be expressed in different forms like cardinality form, probabilistic form etc. In cardinality form, it is expressed as <img src=image/13429145_02.gif> where as in probabilistic form it can be denoted as <img src=image/13429145_03.gif> where <img src=image/13429145_04.gif> is the equivalence class of <img src=image/13429145_10.gif> with respect to <img src=image/13429145_09.gif>. This membership function is used to measure the value of uncertainty. In this paper we have introduced the concept of graphical representation of rough sets. Rough graph was introduced by He Tong in 2006. In this paper, we propose a novel method for the construction of rough graph through rough membership function <img src=image/13429145_05.gif>. We propose that there is an edge between vertices if <img src=image/13429145_06.gif>. The rough graph is being constructed for an information system; here objects are considered as vertices. Rough path, rough cycle, rough ladder graph are introduced in this paper. We develop the operations on rough graph and also extend the properties of rough graph.

Passive fluidic control on aero-optics of transonic flow over turrets with rough walls

In the transonic flow over a hemisphere-on-cylinder turret, strong aero-optical effects can be caused by local shock/boundary-layer interactions and separation shear layers at the turret's zenith. The effects of an annular rough wall on the passive control of fluid and aero-optics are investigated by experimental measurements and numerical simulations. The local shock/boundary-layer interaction and separated shear layer at the zenith of the turret are recorded using shadowing and Mach–Zehnder interferometer measurements. The aero-optics are measured using a Shack–Hartmann wavefront sensor. The experimental results show that the annular rough wall on the turret weakens the local shock wave, moves the flow separation point forward, and reduces the wavefront distortion at the zenith. The rough wall functions for the shear stress transport (SST) k-ω turbulence model proposed by B. Aupoix [“Roughness corrections for the k–ω shear stress transport model: Status and proposals,” J. Fluids Eng. 137, 021202 (2014)] and C.-H. Lee [“Rough boundary treatment method for the shear-stress transport k–ω model,” Eng. Appl. Comput. Fluid 12, 261–269 (2018)] are used to further study the control effect of different roughnesses. Numerical simulations based on both rough wall functions show good agreement with the experimental measurements. For various transonic flows, the steady wavefront distortions at the zenith with the rough wall at roughness ks=1 mm are 21%–50% smaller than those with smooth walls. The smaller the supersonic region, the more effective the rough wall is in reducing wavefront distortion.

Numerical Simulation of Roughness Effects of Ice Accretion on Wind Turbine Airfoils

One of the emerging problems in modern computational fluid dynamics is the simulation of flow over rough surfaces. A good example of these rough surfaces is wind turbine blades with ice formation on its leading edge. Instead of resolving the airflow field using a fine computational grid near the wall, rough wall functions (RWFs) can be used to model the flow behavior in case of the presence of roughness. This work aims to investigate the performance of state-of-the-art RWFs to show which of these models can provide the most accurate results with the lowest computational cost possible. This aim is achieved by comparing coefficients of lift and pressure resulting from CFD simulations with wind tunnel results of an airfoil with actual ice profiles collected from the site. The RWFs are used to simulate airflow field over the airfoil profiles with ice profile attached to its leading edge using OpenFOAM CFD framework. The comparison of the numerical simulations and the wind tunnel measurements showed that the Colebrook RWF provided the best agreement between simulation and experimental results while using about 20% of the number of cells used with smooth RWF.