蛙又結節網地の抗力係数におよぼすレイノルズ数の影響

New methods for studying the effect of gas injection from the surface of a solid spherical particle on its drag coefficient in the transient and self-similar regimes of flow around the particle have been presented. An advantage of the proposed methods is the ability to isolate in a pure form the effect of the mass flux from the particle surface (without the effect of other factors, for example, particle acceleration) on the drag coefficient. New results of an experimental study of the effect of air flow blowing on the drag coefficient of a solid perforated sphere in the Reynolds number range Re = 133÷9900 have been presented. It has been shown that the drag coefficient decreases when air is blown from the particle surface. As the Reynolds number Re increases, the drag coefficient CD upon gas injection in the transient flow regime decreases to a certain critical value corresponding to the onset of the self-similar regime. At the onset of the selfsimilar regime (reaching the critical value of CD), the drag coefficient increases with an increase in the Reynolds number and asymptotically tends to a constant value CD = 0.44. However, the opposite effect has been found for a small diameter of the particle (D = 1 cm) at a blowing velocity ue ≥ 1.3 m/s: an increase in the drag coefficient of the particle CD at air efflux from the particle surface in comparison with the drag coefficient value in the absence of gas flow injection (ue = 0 m/s). This is apparently associated with a change in the characteristics of the boundary layer of the particle due to the rearrangement of the flow profile near the spherical particle surface caused by a decrease in its size. An empirical dependence of the drag coefficient of a solid sphere on the ratio of the velocity of injection from the surface of the particle to the velocity of blowing CD = 0.15 + (0.44 - 0.15)/ (1 + 9ū/53.8) (with the coefficient of determination R2 = 0.89) has been obtained for a self-similar particle regime flow. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder

It is well-known the dimples on the surface of a golf ball increase in flying distance and the drag force of the pipe jumper that used as the conductor of the high-voltage transmission is decreased by the grooves on the surface of the pipe jumper. But it has not been clarified completely how dimples and grooves manipulate the flow. The final goal of our research is to make clear the drag reduction mechanism of grooves and dimples and the detailes of the related flow structures. As the first stage of this research, this paper deals with the influence of the depth of grooves on the cross-flow around a circular cylinder. Pressure distribution and drag and lift coefficients were measured in a uniform flow in the Reynolds number range of 8.6×103≤Re≤5×105. The Reynolds number regime was classified by the variation in the drag coefficient with Reynolds number. Pressure distributions and drag and lift coefficients showed the characteristic changes for subcritical, critical, and supercritical Reynolds number ranges, respectively. As the depth of grooves decreased, drag coefficient became lower, and the critical points shifted into the high Reynolds number range. Lift was generated in the range of critical Reynolds number, even though a circular cylinder was not rotating.

Effect of cable surface characteristics and flow turbulence on the aerodynamic behaviour of stay cables in dry conditions

Purpose This paper aims to introduce a numerical investigation of aquatic locomotion using the smoothed particle hydrodynamics (SPH) method. Design/methodology/approach To model this problem, a simple improved SPH algorithm is presented that can handle complex geometries using updatable dummy particles. The computational code is validated by solving the flow over a two-dimensional cylinder and comparing its drag coefficient for two different Reynolds numbers with those in the literature. Findings Additionally, the drag coefficient and vortices created behind the aquatic swimmer are quantitatively and qualitatively compared with available credential data. Afterward, the flow over an aquatic swimmer is simulated for a wide range of Reynolds and Strouhal numbers, as well as for the amplitude envelope. Moreover, comprehensive discussions on drag coefficient and vorticity patterns behind the aquatic are made. Originality/value It is found that by increasing both Reynolds and Strouhal numbers separately, the anguilliform motion approaches the self-propulsion condition; however, the vortices show different pattern with these increments.

The purpose of this thesis is to investigate the drag coefficient of spheres in free motion, falling and rising, in water. Following the introduction the test set-up, sphere release mechanism, spheres and timing device and recorder are described. Section 3 gives the results of the drag coefficient measurements for free falling spheres which show good agreement with the known measurements, quoted, for instance, in the Handbuch der Experimentalphysik. Section 4 deals with the measurement of drag coefficients of free-rising spheres. It was found that the freely rising spheres move in an oscillatory path of which wavelength and amplitude depend on the ratio of sphere density and water density. The local drag coefficient of the spheres was measured to be the same as for falling spheres. It was found to be independent of the sphere motion. No critical Reynolds number was found for the onset of the oscillatory motion of the sphere. The oscillatory motion appeared to be independent of initial disturbances of the sphere motion. From photographs of the sphere paths Strouhal numbers were formed which are about one third the value given for circular cylinders in the same Reynolds number range. A theoretical oscillatory force coefficient, based on a force balance on the sphere, was obtained. It was found to be of the same order of magnitude as the correspondent, actually measured oscillatory force coefficient on a circular cylinder. The Strouhal number based on the main theoretical frequency was found to be four times as high as the one calculated from the frequency of the sphere path. It could be, dependent on the sphere density, as high as twice the Strouhal number found for circular cylinders in the same Reynolds number range.

The square lattice tower with tubular members (SLTTM) is widely used in civil engineering. Wind load is the primary factor affecting the stability of these structures. This paper presents the wind loads of the SLTTM at different Reynolds numbers (Re) through wind tunnel testing and large eddy simulation (LES). A series of wind tunnel tests with four segment models were first conducted to discuss the effects of wind direction, turbulence intensity, and solidity ratio on the aerodynamic force under low and subcritical Reynolds numbers. The LES method was subsequently employed to determine the aerodynamic force coefficient at Re = 191–1.34 × 106 in both the smooth and uniform turbulent wind fields. The results from wind tunnel tests indicate that the mean and fluctuating drag coefficients at low Reynolds numbers are somewhat different from those at subcritical Reynolds numbers. The solidity ratio and wind direction exert a notable influence on the mean drag coefficient, whereas their impact on the fluctuating drag coefficient is relatively minimal. As the turbulence intensity increases, both the mean and fluctuating drag coefficients exhibit a notable rise. The results of the LES at Re = 191–1.34 × 106 show that an increase in turbulence intensity can markedly elevate the fluctuating drag coefficient. However, the effect on the mean drag coefficient is found to depend on the Reynolds number range. The Reynolds number effect on the mean and fluctuating drag coefficients of the SLTTM may be primarily attributed to the members without and with a shielding effect, respectively.

Numerical simulation of the thermal and hydraulic characteristics of the flow in the initial sections of tubes with corrugated inserts “blocking up” the cross section of the tube was carried out. The structure of the flow and the process of disturbance`s generation with a concomitant change in heat exchange at different degrees of clamping of the tube cross section in the range of transitional Reynolds numbers are investigated. The change in the thermal and hydraulic characteristics of tubes with corrugated inserts was shown depending on the degree of cross section local blocking and the Reynolds number in the considered ranges of geometric parameters in a transient flow regime. The features of the disturbances formation in the flow and their relationship with the energy efficiency of the heat exchange surface`s structuring were considered. The influence of the Reynolds number on the stagnant fluid zone formation in the goffers of considered amplitude and length ratio, as well as the effect of this zone on heat exchange processes, was determined. A comparison of the heat transfer intensity and the hydraulic resistance values of partially corrugated tubes with similar parameters in smooth tubes was made. The effect of perturbation generation beginning on the energy efficiency of tubes with a partially corrugated surface compared to smooth tubes in the range of transition Reynolds numbers was shown. The threshold values of the parameter k = a 2 / R 0 and the Reynolds number, at which it is possible to achieve the highest heat transfer intensity with minimal hydraulic losses in the considered range of Reynolds numbers, Prandtl numbers and geometrical parameters were determined.

Validation of a new methodological approach for the selection of wire-coil inserts in thermal equipment

Experiments examining the effect of surface roughness on vortex-induced vibration (VIV) and drag of flexible cylinders at critical and supercritical Reynolds numbers have been conducted. Four levels of surface roughness were tested for their effect on VIV and drag of a circular cylinder that was 20 diameters upstream of a downstream cylinder (i.e. effectively an isolated cylinder). The rougher cylinders experienced vibrations of up to 3rd mode (in transverse bending). A surprising discovery was that the smooth cylinder experienced low drag and virtually no VIV as the boundary layers became turbulent in the critical Reynolds number range. Introduction and Background The study of flow separation and vortex shedding past a circular (or approximately circular) cylinder has a long history. Simple observation of flow past a vertical stick or reed in a stream indicates that man has probably observed this phenomenon well before recorded history. Similarly, vortexinduced vibration (VIV), which results when something free to move experiences vortex shedding, has an equally long history. The vibration felt when attempting to move one's arm through the water as fast as possible is evidence that VIV was also observed in antiquity. A parameter that strongly influences flow past a circular cylinder is the Reynolds number (Re), which represents the ratio of the convective forces to the diffusive forces, defined as Re=V*D/?. Another important parameter, for the purposes of this paper, is the surface roughness k/D, where k is the average "peak to trough" height of the surface protrusions. Figure 1 illustrates the basics of flow past a circular cylinder. As the fluid approaches the cylinder, a thin boundary layer (exaggerated in the figure for illustration purposes) forms on each side of the cylinder (shown on only one side). The fluid closest to the cylinder wall is impeded by friction on the cylinder's surface, hence the region between the wall and where the velocity is close to that of the free stream is known as the boundary layer. As the boundary layer fluid proceeds around the cylinder surface, the retardation of the fluid near the surface eventually causes it to come to a halt, thereby resulting in separation of the boundary layer into a "shear layer". Because the outer fluid in the shear layer is moving faster than the inner fluid of the shear layer, the layer rolls up into a vortex. For Reynolds numbers larger than about 40, the vortex pattern is unstable, and thus there is an alternating vortex street that is shed from the cylinder. Numerous studies have been made of flow past a stationary circular cylinder, most of these with air as the flowing fluid1–6. These studies have covered Reynolds numbers well exceeding 1×107. Figure 2 illustrates the general relationship that these studies have found between drag coefficient (defined as Cd = Fd/(0.5*?*V2*D*L) and Reynolds number for flow past a stationary cylinder. This figure shows that, at a Reynolds number of about 1×105 (the "critical" Reynolds number range), the drag coefficient diminishes dramatically, a phenomenon known as the "drag crisis". This corresponds to a change in the boundary layers from laminar to turbulent.

The drag coefficient of a sphere immersed in turbulent air flow in the Reynolds number (Re = U ∞ d/ν ∞) range up to 250 and turbulence intensity (u ∞′/U ∞) up to 60% is computed numerically. Reynolds-averaged Navier-Stokes equations (RANS) are solved in Cartesian coordinates by using a blocked-off technique. To our knowledge, the present work is the first to employ the blocked-off technique for flow over a sphere. Closure for the turbulence stress term is accomplished by testing four different turbulence closure models. The main findings of the present investigation are that the laminar numerical data compare well with numerical and experimental published work. However, different turbulence closure models produce different trends in the range of Reynolds number up to Re = 100, and this difference is demarcated by the nonagreement between the turbulent predictions and the “standard” drag coefficient results. However, the results obtained using Menter's SST turbulence model show fair agreement with the well-known sphere “standard” drag over the range of test conditions explored here. Thus, the present results confirm recently published findings, which suggest that the free-stream turbulence intensity does not have a significant effect on the sphere mean drag.

The relationship between the coefficient of drag and the Reynolds number on a sphere in the polymer solutions was studied experimentally through on the measurement of terminal velocity and the observation of flow about a falling sphere. And then, the effectiveness of Stokes's law and Perry's curve for the concentrated polymer solutions (CMC & PED) in the range of low Reynolds numbers (less than 103) was examined using Re* instead of Re and the drag reduction of very dilute polymer solutions (PEO) in the range of high Reynolds numbers (more than 5×103) was confirmed. Besides, it was shown that such a drag reduction was characterized by two dimensionless numbers, Reynolds number (Re) and Weissenberg number (Rn*: Reiner-Rivlin model or Ne*: Combination model).

Predicting aerodynamic forces on bluff bodies remains to be a challenging task due to the unpredictable flow behavior, specifically at higher Reynolds numbers. Experimental approaches to determine aerodynamic coefficients could be costly and time consuming. In the meantime, use of numerical techniques could also require a considerable computational cost and time depending on complexity of the flow behavior. The research focusses on developing an effective deep learning technique to predict aerodynamic force coefficients acting on elliptical bluff bodies for a given aspect ratio and given flow condition. Collecting data for drag and lift coefficients of several aspect ratios for flow conditions starting from onset of vortex shredding to verge of subcritical region is conducted by an accurate full order model. The specified region will provide a transient flow behavior and thus lift coefficient will be represented in terms of root mean square value and drag coefficient in terms of a mean value. With variations in flow behavior and vortex shredding frequencies, it requires to select an appropriate turbulence model, optimum discretization of fluid domain and time step to obtain an accurate result. Flow simulations are conducted primarily using Unsteady Reynolds Averaged Navier-Stokes Equations (URANS) model and Detached Eddy Simulations (DES) model. Effectiveness in using different turbulence models for specified flow regimes are also explored in comparison to available experimental results. At lower Reynolds numbers, aerodynamic force coefficients for a specified body will only depend on Reynolds number. But after a certain specific Reynolds number, aerodynamic forces are dependent on the Mach number in addition to Reynolds number. Therefore, for higher Reynolds numbers, aerodynamic force coefficients are recorded for multiple Mach numbers with same Reynolds number and will be fed to the neural network. With the development of the machine learning and neural network modelling, many of the fields have nourished and created effective and efficient technologies to ease complex functions and activities. Our goal is to ease the complexity in the computational fluid dynamic field with a deep neural network tool created to predict drag and lift coefficient of elliptical bluff bodies for a given aspect ratio with an acceptable accuracy level. Researchers have developed deep neural network tools to predict various flow conditions and have succeeded with sufficient accuracy and a satisfying reduction of computational cost. In our proposed deep learning neural network, we have chosen to model the network with inputs as the geometry setup and the flow conditions with validated drag and lift coefficients. The model will extract the necessary flow features into filters with the convolution operation performed on the inputs. Our main directive is to create a deep learned neural network tool to predict the target values within an acceptable range of accuracy while minimizing the computation cost.

Flow around a cube for Reynolds numbers between 500 and 55,000

In many chemical processes, the settling of solid particles in a suspension is of fundamental importance. In this work, the terminal settling velocity of spherical particles is experimentally investigated in cylindrical columns in the range of Reynolds numbers 2 ≤ Ret∞ ≤ 185 and of particle-to-column diameter ratios, λ, of ≤ 0.9. Finding that none of the existing equations relating the terminal settling velocity to the diameter ratio is fully satisfactory, the authors propose two new empirical calculation methods which enable the terminal settling velocity to be determined in the whole range of both Reynolds number, Ret∞, and diameter ratio, λ