The Evaluation Method of the Hydrodynamic Frictional Resistance for the Painted Rough Surface

2018 ◽  
Author(s):  
Tokihiro Katsui ◽  
Hisao Tanaka
Keyword(s):  
Reynolds Number ◽  
Evaluation Method ◽  
Wave Length ◽  
Frictional Resistance ◽  
Momentum Equation ◽  
Frictional Stress ◽  
Linear Ordinary Differential Equations ◽  
Painted Surface ◽  
Length Fraction ◽  
Surface Profiles

The present study shows a method to evaluate the performance of the paints to reduce the additional frictional resistance in full scale ship Reynolds number. Simultaneous non-linear ordinary differential equations are developed to calculate the hydrodynamic frictional resistance of flat plate based on the momentum equation and Coles’ wall wake law which is the similarity law of the velocity distribution in the turbulent boundary layer. Roughness influence of painted surface is taken into account by adding the roughness function to Coles’ wall wake law. The expression of the roughness function should be determined based on the experimental results of the additional frictional resistance for various kinds of paints. The obtained roughness function depends on the roughness Reynolds number, and it also depends on both the roughness wave height and wave length fraction to its height which are obtained FFT analysis for measured paint surface profiles. The calculated local frictional stress coefficients on the painted surfaces well agreed with the measured ones. The total frictional resistance coefficients of painted surface in the actual ship scale Reynolds number can be evaluated considering influence of surface roughness.

Laser Velocity and Surface Measurements Toward the Prediction of Turbulent Frictional Resistance on Irregular Rough Surface in Higher Reynolds Number Range

2019 ◽  
Author(s):  
Kyohei Okubo ◽  
Shunpei Suzuki ◽  
Yusuke Kuwata ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Rough Surface ◽  
Empirical Formula ◽  
Rough Surfaces ◽  
Frictional Resistance ◽  
Frictional Stress ◽  
Mean Velocity ◽  
Number Range ◽  
High Reynolds

Abstract In this research, we consider the relationship between roughness of the wall and frictional resistance in the range of high-Reynolds number regime which is important for practical use, and its goal is to build a more accurate and highly versatile formula for predicting the frictional resistance acting on the complex surface with irregular roughness. In addition to the parameter corresponding to the distribution of the roughness used in a conventional and empirical formula, we aim to construct an empirical formula including the parameter representing the wavelength of the rough surface. In this study, we conduct laboratory experiments of Taylor-Couette flow, using the cylindrical test specimens roughly sprayed with an actual ship paint, and investigate the influence of irregular roughness on flow field and the surface frictional stress based PIV (Particle Image Velocimetry) measurements and torque measurements in high Reynolds numbers. The azimuthal mean velocity for rough surfaces increased in the entire flow field in comparing to the flow for a smooth surface, and this tendency is remarkable in a bulk region. Also, we measure the rough surfaces of the specimens using a laser type one-shot three-dimensional measurement device. Based on the results of above measurements, we propose the direct relationship between the parameter of a rough surface and frictional resistance.

The Relationship Between Frictional Resistance and Roughness for Surfaces Smoothed by Sanding

2002 ◽  
Vol 124 (2) ◽  
pp. 492-499 ◽  
Author(s):  
Michael P. Schultz
Keyword(s):  
Reynolds Number ◽  
Frictional Resistance ◽  
Resistance Coefficient ◽  
Polished Surface ◽  
Average Height ◽  
Freestream Velocity ◽  
Number Range ◽  
Test Fixture ◽  
Plate Length ◽  
The Relationship

An experimental investigation has been carried out to document and relate the frictional resistance and roughness texture of painted surfaces smoothed by sanding. Hydrodynamic tests were carried out in a towing tank using a flat plate test fixture towed at a Reynolds number ReL range of 2.8×106−5.5×106 based on the plate length and freestream velocity. Results indicate an increase in frictional resistance coefficient CF of up to 7.3% for an unsanded, as-sprayed paint surface compared to a sanded, polished surface. Significant increases in CF were also noted on surfaces sanded with sandpaper as fine as 600-grit as compared to the polished surface. The results show that, for the present surfaces, the centerline average height Ra is sufficient to explain a large majority of the variance in the roughness function ΔU+ in this Reynolds number range.

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

scholarly journals A finite-difference convective model for Jupiter's equatorial jet

2006 ◽  
Vol 2 (S239) ◽  
pp. 230-232 ◽  
Author(s):  
Kwing L. Chan
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Finite Difference ◽  
Spherical Shell ◽  
Reynolds Stress ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Zonal Momentum Balance ◽  
Zonal Momentum ◽  
Convective Model

AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

A MEASUREMENT OF ULTRASONIC ATTENUATION COEFFICIENT BY FREQUENCY RESPONSE IN STEELS WITH DIFFERENT GRAIN SIZES

2003 ◽  
Vol 26 (4) ◽  
pp. 389-402
Author(s):  
Kyung-Cho Kim
Keyword(s):  
Frequency Response ◽  
Attenuation Coefficient ◽  
Evaluation Method ◽  
Ultrasonic Attenuation ◽  
Wave Length ◽  
Structural Behavior ◽  
Response Property ◽  
Sound Waves ◽  
Grain Sizes ◽  
Plate Specimen

A new evaluation method of ultrasonic attenuation in materials is proposed based on the frequency response property of the material evaluated by employing the sound impulse of a wide frequency band. Borrowing from ordinary system theory, the material to be tested is considered to have a characteristic impulse response, representing its micro-structural non-uniformities and thus resulting in the sound attenuation of the material. The concept is resumed as an attenuation system that simulates the material’s micro-structural behavior. Experimental results on a series of specimens, having different grain sizes but all made of a single austenitic stainless steel, showed that the attenuation could properly be evaluated from a single bottom echo in a plate specimen. The attenuation coefficient α, was corrlated in this case to the grain size, D, by the equation, αD=H(πD/λ)n, where λ is wave length and H and n are constants. It was also shown that the micro structural change of materials could be evaluated by the energy loss of sound waves passing through the attenuation systems.

Experimental Investigation of Turbulent Boundary Layer Over Smooth Flat Plate With Towing Tank: Attempt of Measurement of Frictional Stress

2007 ◽  
Author(s):  
Kiyoto Mori ◽  
Hiroki Imanishi ◽  
Yoshiyuki Tsuji ◽  
Masashi Kashiwagi ◽  
Masaru Inada ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Frictional Resistance ◽  
Reynolds Numbers ◽  
Sufficient Accuracy ◽  
Frictional Stress ◽  
Towing Tank ◽  
High Reynolds Numbers ◽  
Pressure Resistance ◽  
High Reynolds

The purpose of this study is to evaluate the frictional resistance with sufficient accuracy and to evaluate the drag coefficient at high Reynolds numbers. We have measured the resistance of flat plate with using a towing tank. Correcting the wave-making resistance, pressure resistance, and drag on turbulence simulator, it is found that the measured frictional resistance is smaller than the Karman-Schoenherr formula. But it agrees with the values suggested by Osaka et. al and Osterlund et. al.

Analysis of the swimming of long and narrow animals

1952 ◽  
Vol 214 (1117) ◽  
pp. 158-183 ◽  
Keyword(s):  
Reynolds Number ◽  
Wave Length ◽  
Constant Speed ◽  
Forward Speed ◽  
Constant Amplitude ◽  
Flexible Cylinder ◽  
Cylinder Diameter ◽  
Wide Range ◽  
The Waves ◽  
Marine Worms

The swimming of long animals like snakes, eels and marine worms is idealized by considering the equilibrium of a flexible cylinder immersed in water when waves of bending of constant amplitude travel down it at constant speed. The force of each element of the cylinder is assumed to be the same as that which would act on a corresponding element of a long straight cylinder moving at the same speed and inclination to the direction of motion. Relevant aerodynamic data for smooth cylinders are first generalized to make them applicable over a wide range of speed and cylinder diameter. The formulae so obtained are applied to the idealized animal and a connexion established between B / λ , V / U and R 1 . Here B and λ are the amplitude and wave-length, V the velocity attained when the wave is propagated with velocity U , R 1 is the Reynolds number Udρ / μ , where d is the diameter of the cylinder, ρ and μ are the density and viscosity of water. The results of calculation are compared with James Gray’s photographs of a swimming snake and a leech. The amplitude of the waves which produce the greatest forward speed for a given output of energy is calculated and found, in the case of the snake, to be very close to that revealed by photographs. Similar calculations using force formulae applicable to rough cylinders yield results which differ from those for smooth ones in that when the roughness is sufficiently great and has a certain directional character propulsion can be achieved by a wave of bending which is propagated forward instead of backward. Gray’s photographs of a marine worm show that this remarkable method of propulsion does in fact occur in the animal world.

scholarly journals Analysis of Aspect Ratio in a Miniature Rectangle Channel for Low Frictional Resistance

Micromachines ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1580
Author(s):  
Takashi Fukuda ◽  
Makoto Ryo Harada
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Rectangular Channel ◽  
Frictional Resistance ◽  
Experimental System ◽  
Cross Sectional ◽  
Friction Resistance ◽  
Calculation Results ◽  
Volume Range

We conducted a theoretical investigation of the cross-sectional aspect ratio of a rectangular channel to have sufficiently low frictional resistance under less than 150 of the Reynolds number. From the theoretical consideration, it was clarified that 3.40 or more is recommended as a criterion for determining the aspect ratio. This addresses the problem of determining the interval of rectangle channels, installed in a plate reactor. There is a concern that the real system does not follow the analytical solution, assuming laminar flow, since the higher aspect ratio leads to disturbances of the flow such as the emergence of vortices. However, in the channel’s volume range of (W × H × L) = (7.0 mm × 0.38 mm × 0.26 m), such a turbulence was not observed in the detailed numerical calculation by CFD, where both calculation results were in agreement to within 3% accuracy. Moreover, even in an experimental system with a surface roughness of ca. 7%, friction resistance took agreement within an accuracy of ±30%.

scholarly journals Capsules Rheology in Carreau–Yasuda Fluids

Nanomaterials ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 2190
Author(s):  
Alessandro Coclite ◽  
Giuseppe Coclite ◽  
Domenico De Tommasi
Keyword(s):  
Reynolds Number ◽  
Shear Zones ◽  
Shear Thinning ◽  
Lateral Position ◽  
Momentum Equation ◽  
Viscosity Model ◽  
Immersed Boundary ◽  
Forcing Term ◽  
Neutrally Buoyant ◽  
The Revolution

In this paper, a Multi Relaxation Time Lattice Boltzmann scheme is used to describe the evolution of a non-Newtonian fluid. Such method is coupled with an Immersed-Boundary technique for the transport of arbitrarily shaped objects navigating the flow. The no-slip boundary conditions on immersed bodies are imposed through a convenient forcing term accounting for the hydrodynamic force generated by the presence of immersed geometries added to momentum equation. Moreover, such forcing term accounts also for the force induced by the shear-dependent viscosity model characterizing the non-Newtonian behavior of the considered fluid. Firstly, the present model is validated against well-known benchmarks, namely the parabolic velocity profile obtained for the flow within two infinite laminae for five values of the viscosity model exponent, n = 0.25, 0.50, 0.75, 1.0, and 1.5. Then, the flow within a squared lid-driven cavity for Re = 1000 and 5000 (being Re the Reynolds number) is computed as a function of n for a shear-thinning (n < 1) fluid. Indeed, the local decrements in the viscosity field achieved in high-shear zones implies the increment in the local Reynolds number, thus moving the position of near-walls minima towards lateral walls. Moreover, the revolution under shear of neutrally buoyant plain elliptical capsules with different Aspect Ratio (AR = 2 and 3) is analyzed for shear-thinning (n < 1), Newtonian (n = 1), and shear-thickening (n > 1) surrounding fluids. Interestingly, the power law by Huang et al. describing the revolution period of such capsules as a function of the Reynolds number and the existence of a critical value, Rec, after which the tumbling is inhibited in confirmed also for non-Newtonian fluids. Analogously, the equilibrium lateral position yeq of such neutrally buoyant capsules when transported in a plane-Couette flow is studied detailing the variation of yeq as a function of the Reynolds number as well as of the exponent n.

scholarly journals Mean dynamics of transitional boundary-layer flow

2011 ◽  
Vol 682 ◽  
pp. 617-651 ◽  
Author(s):  
J. KLEWICKI ◽  
R. EBNER ◽  
X. WU
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Boundary Layer Flow ◽  
Layer Structure ◽  
Momentum Equation ◽  
Stress Profile ◽  
Transitional Regime ◽  
The Mean ◽  
Layer Flow

The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional two-dimensional boundary-layer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the four-layer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Self-consistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the four-layer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U∞ θ/ν ≃ 780. The first-principles-based theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and four-layer regimes. As in channel flow, the transitional regime is marked by a non-negligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the four-layer regime. Empirical and theoretical evidence suggests that the formation of the four-layer structure also underlies the emergence of the mean dynamical properties characteristic of the high-Reynolds-number flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to $y_m^+ {\,\simeq\,} 1.9 \sqrt{\delta^+}$.

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