Hydrodynamic Resistance Coefficient Research Articles

Control and navigation problems for model bio-inspired microswimmers

Navigation problems for a model bio-inspired micro-swimmer, consisting of a cargo head and propelled by multiple rotating flagella or propellers and swimming at low Reynolds numbers, are formulated and solved. We consider both the direct problem, namely, predicting velocity and trajectories of the swimmer as a consequence of prescribed rotation rates of the propellers, and inverse problems, namely, find the rotation rates to best approximate desired translational and rotational velocities and, ultimately, target trajectories. The equations of motion of the swimmer express the balance of the forces and torques acting on the swimmer, and relate translational and rotational velocities of the cargo head to rotation rates of the propellers. The coefficients of these equations, representing hydrodynamic resistance coefficients, are evaluated numerically through a custom-built finite-element code to simulate the (Stokes) fluid flows generated by the movement of the swimmer and of its parts. Several designs of the propulsive rotors are considered: from helical flagella with different chirality to marine propellers, and their relative performance is assessed.

Experimental Determination of Hydrodynamic Resistance Coefficients and the Lifting Force of Various Pipeline Crossing Methods

Experimental Determination of Hydrodynamic Resistance Coefficients and the Lifting Force of Various Pipeline Crossing Methods

ТЕОРЕТИЧЕСКОЕ ОБОСНОВАНИЕ МИНИМАЛЬНОЙ ВЫСОТЫ ПАДЕНИЯ СФЕРИЧЕСКОЙ ЗЕРНОВКИ В РАСТВОР ПРОТРАВЛИВАТЕЛЯ

Food products made of grain are the main source of human nutrition and feed for farm animals. One of the main reserves for increasing its production is sowing with high-quality material, purified from various impurities and pathogens. To protect it from various diseases, etching is used. The most effective way to implement this technological operation is wet pickling with simultaneous release of grain impurities. For implementation of a corresponding device, an estimate was made of the minimum drop height of a weevil which is necessary to overcome the surface tension of a liquid. Pea seeds with a shape close to a sphere were used as objects of research. Therefore, a spherical caryopsis with density ρз = (1.15…1.45)∙103 kg/m3, diameter 2rз = (3.5…10.9) ∙10-3 m was taken as a model of the seed. We investigated the fall of separately taken spherical caryopses with minimum (2rзmin. = 3.5∙10-3 m), average (2rзmid. = 7.2∙10-3 m) and maximum (2rзmax. = 10.9∙10-3 m) linear dimensions having a density ρз = 1.15; 1.25; 1.35 and 1.45∙103 kg/m3, on the surface of an aqueous solution of the dressing agent with a density of ρж = 1.00; 1.03; 1.06; 1.09; 1.12 and 1.15 ∙ 103 kg/m3 with the corresponding coefficients of surface tension σ = 0.0727; 0.0755; 0.0771; 0.0786; 0.0801 and 0.0816 N/m and hydrodynamic resistance coefficients c = 0.4 (0.5 for ρж = 1.12 and 1.15 ∙ 103 kg/m3). The etching process was considered at a temperature of 20°C. The minimum drop height h for overcoming the surface tension of the dressing solution by all caryopses with physical and mechanical parameters with the indicated values should be 15.5 ∙ 10-3 m

Flexible concrete protective coating resistance to approach flow exposure

In order to protect the bottom and coastal slopes of natural channels and artificial reservoirs from channel deformations, various shore reinforcing structures are often used. One of this structures is the universal flexible protective concrete coating. When using this kind of structures, it is necessary to take into account their interaction with the approach flow. At the flexible protective coatings operating, one of the problems is the “wrapping” of the coating body. To calculate the stability assessment of the surface coating, it is necessary to know the value of the coefficient of hydrodynamic resistance of the protective coatings. It is determined mainly by its shape. Currently, various forms of surface coatings from various materials are used. In most cases, the resistance of such structures is assumed approximately, based on the known values of the resistance coefficients of bodies of various shapes. As a rule, the elements of protective coatings have a specific form, the resistance of which must be established experimentally. The article presents the results of an experimental determination of the hydrodynamic drag coefficient of a universal flexible concrete protective coating (a universal flexible protective mat) on aerodynamic and hydraulic experimental stands. Used laboratory equipment with basic operating characteristics, examples of experimental models, and basic operating conditions during experiments are described. It is shown that the value of the coefficient of hydrodynamic resistance decreases with increasing Reynolds number. The obtained values of the hydrodynamic resistance coefficient in some cases exceed the values recommended for calculating the maximum permissible flow velocity when assessing the stability of a protective coating. It is concluded that it is necessary to experimentally evaluate the hydrodynamic resistance coefficient for each model of protective coatings. The recommended value of the hydrodynamic resistance coefficient for the studied modification of a flexible protective concrete coating is established.

Aerodynamic Characteristics of the Cooling Tower under the Nonuniform Distribution of the Water and Air Flows

At thermal power stations, the rate of the fuel equivalent consumed to generate electric energy, the vacuum level in condensers, and the steam turbine output are determined by the performance of the cooling towers. However, the occurrence of water and air flows' nonuniform distribution may become one of the causes of a reduction in the cooling towers' efficiency. Research into the aerodynamic characteristics of a chimney-type cooling tower under the nonuniform distribution of the water and air flows over the cells of the apparatus has been conducted. The effects of four factors, viz., the drop of the atmospheric air and cooling water temperatures, the hydrodynamic resistance coefficient of a cell, the water concentration in the latter, and the wind velocity in close proximity of the air-intake ports, on the consumption rate of the intake air and its distribution over the cooling tower cells have been analyzed. The effect of the water concentration on the distribution of the air over the cooling tower cells has been studied under laboratory and field conditions. The existence of a correlation relationship between the above parameters has been established. In the course of the experiments, the extreme form of dependence of the wind velocity distribution over the cooling tower cells on the wind velocity field in the vicinity of the air-intake ports has been obtained. The effect of every factor on the air velocity in individual cells and the cooling tower as a whole has been analyzed. Based on the experimental results, both one-dimensional regression equations and a multiple regression equation for all factors have been derived.

ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ МОДЕЛЕЙ ЗАКИДНЫХ НЕВОДОВ В ГИДРОКАНАЛЕ ОАО «МАРИНПО»

The experiment was conducted with three models of beach seines with different values оf continuity in the towing channel of “MariNPO” JSC. Experimental values of tension in the model wing and calculated values of hydrodynamic resistance coefficient depending on Reynolds number Re, continuity and shape of the models ( f / L ratio, blowing θ) have been obtained. The range of characteristic values made 123 ≤ Re ≤ 184; 0.168 ≤ F 0 ≤ 0.202; 0.15 ≤ f/L ≤ 0.77; 0.4 ≤ θ ≤ 0.8. There have been plotted the graphs of dependence of experimental values of force in seine wing on ratio f / L for different Re values. There have been built graphs of dependency of calculated values of hydrodynamic resistance coefficient on relations f / L for different Re values. Approximation of calculated values of hydrodynamic resistance coefficient has been made and the graphs of approximating functions of the dependence of hydrodynamic resistance coefficient on f / L ratio have been plotted for different Re values. Error of approximation of dependence сх = f (Re, F 0, f/L , θ) doesn’t exceed 10 %.

Determination of the Hydrodynamic Resistance Coefficient for Bodies Installed on the Bottom of Turbulent Flow

A method for calculating the hydrodynamic resistance coefficient of bodies of various form installed at the bottom of turbulent flow is examined. Using a power series velocity profile and the proposed calculation plan, which relates the resistance of a freely streamlined body and the object on the screen, a relation was derived between the appropriate coefficients of resistance of these bodies, taking account of the resistance of the screen. The materials in this paper are of timely nature, in connection with hydraulic engineering construction of various structures that interact with water flows, including pipeline systems for different purposes.

Modeling of a clamped–clamped beam vibrating in a fluid for viscosity and density sensing regarding compressibility

A clamped–clamped beam vibrating in a compressible fluid for the measurement of the fluid’s density and viscosity is modeled using the Bernoulli–Euler equation for the beam and the linearized Navier–Stokes equations for the fluid. The adiabatic compressibility coefficient was used to characterize the pressure–density coupling. Based on the method of moments, the flow around the beam and the associated resistance of the fluid on the beam were computed using a 2D-approximation. Hydrodynamic resistance coefficients are determined and compared to the known resistance coefficients for a cylinder vibrating in an incompressible fluid. The influence of the fluid’s compressibility on the resistance on the beam is examined and a critical value of the vibration frequency is determined, over which the beam experiences excessive damping due to the excitation of pressure waves.

Linear heat transfer in a flow around a cylinder or a sphere

It is shown that the relation between the Nusselt and Reynolds numbers determined by the Reynolds analogy is linear with self-similarity of the hydrodynamic resistance coefficient.

Effect of instability on boundary layer detachment

When fluid or gas flows around a body, a thin boundary layers forms near its surface. The behavior of this boundary layer is determined by hydrodynamic resistance. If the boundary layer is detached from the surface, the resistance increases sharply [i, 2]. In order to reduce this resistance, the detachment must be stretched out; that is the boundary layer line detachment must be shifted as far as possible to the aft critical point, so that the region of stagnant flow (the wake) behind the body is narrowed. In this regard, investigations of nonstationary fluid around a body are of current interest. The acceleration of a cylindrical body into a quiescent fluid has been examined [2]. Undetached flow around the body was observed immediately after the acceleration started. Then, after the cylinder traveled a distance s = 0.351 R (where R is the cylinder radius), the flow detached near the aft critical point of the body. The detachment gradually moved forward along the flow and increased the wake behind the body. After a certain time, a pair of vortices appeared behind the body, which grew and continually broke off to form a vortical wake. As measurements show [3], the hydrodynamic resistance coefficient is minimized in the case of undetached flow. This leads to the importance of investigating nonstationary flow around bodies.

Hydrodynamic resistance and refracting effect of a fine-mesh screen

An attempt has been made to carry out a systematic study of the hydrodynamic resistance and refracting properties of screens and screen packs on the basis of both a generalization of the existing data and additional experiments with broad variation of the principal characteristics of the screens and the values of the Reynolds number. A universal law of resistance, valid on the interval 1 < Ree < 105, is obtained for screens and combinations of screens (matrices) is investigated in detail; Gol'dshtik's theoretical relation for the index of refraction of the streamlines is shown to be correct. The relation obtained for the hydrodynamic resistance coefficient and the index of refraction of screens and matrices can be used for apparatus design purposes.

Turbulent-flow resistance for solutions of polymers and micelle-forming surfactants

Calculation method and results are presented for the hydrodynamic-resistance coefficients of solutions of polymers and surfactants.

Hydrodynamic resistance of aqueous solutions of polymers and surface-active substances in rough tubes

Results of measurements of the hydrodynamic resistance coefficient are presented for turbulent flow of polyacrylamide and metaupone solutions in tubes with natural and artificial roughness.

The motion of a particle in a viscous medium discharging as a jet

Motion of a particle is examined during jet discharge of a viscous liquid in the region Re ≤ 300 with a hydrodynamic resistance coefficient which takes account of all the inertial terms.

Determination of molecular dimensions from rheological data

AbstractA survey of the existing possibilities of molecular size and shape determination from rheological experiments is given. Because the hydrodynamic behaviour of particles depends on their size and shape at the conditions of experiment, one obtains by such methods just the dimensions as they are in the chosen solvent, at the temperature, ionization degree, pH, and ionic strength of the experiment. This fact is specially important in investigation of biological material, where one wishes to know the particle properties in natural surrounding or at least in a state as little denaturated as possible.With corpuscular particles, usually represented by spheroids, there are methods enough for obtaining all informations wanted even in the case that, due to swelling and selective adsorption of some solvent components, the particle density appreciably differs from that of dry particle. With linear particles, i.e. statistically coiled chain polymers, the main geometrical parameter is the gyration redius. It may be obtained by combination of translational motion and viscosity with proper consideration of solvent immobilisation inside the coil. The situation in the field, althought not yet elucidated enough, seems to converge rather rapidly to a complete understanding. The porous sphere model yields gyration radii which in nitrocellulose and to a lesser degree in polymethyl methacrylate very well agree with the values from light scattering. But hydrodynamic resistance coefficient of the monomer is highly underestimated. A more realistic approach, removing this discrepancy, is the neck‐lace model with hydrodynamic among all chain elements. For densily packet coils, e.g. in ideal solution (Θ‐point) and not too low molecular weight, one may assume complete solvent immobilisation so that gyration radii R0 are directly calculable from either limiting viscosity number or translational resistance coefficient. In systems not too far from Θ‐point the coil diameter can be calculated from R0 by series expension in powers of second virial coefficient and coil permeability obtained from rheological data. In good solvents, however, but the limiting case of complete solvent immobilisation is sufficiently well treated. Experiments on cellulose demonstrate that the permeability may reach rather high values as consequence of large coil expension. Due to the two parameters involved, the non‐Gaussian character and permeability of the coil, one cannot hope that, on the basis of the neck‐lace model, in such a case gyration radii may be derivable from rheological data only. On the contrary, by use of light scattering radii or eventually of those obtained by the porous sphere model one can test existing thermodynamic and hydrodynamic treatment of isolated polymer molecules in solution.