Hydraulic Drag Coefficient Research Articles

Study of hydraulic resistance of tangential swirlers

This article presents the results of experimental research and simulation of the hydraulic drag of tangential swirlers. Three types of swirler devices made with straight, profiled, and circular channel walls were studied within a wide range of design and process parameters. Simulation modelling on the Comsol Multiphysics platform was used to calculate hydraulic drag and determine the velocity and pressure fields. This allowed obtaining a dependence of the hydraulic drag coefficient of the investigated swirlers and identifying parameters affecting their hydraulic drag.

Determination of a Bubble Drag Coefficient during the Formation of Single Gas Bubble in Upward Coflowing Liquid

Bubble flow is present in many processes that are the subject of chemical engineering research. Many correlations for determination of the equivalent bubble diameter can be found in the scientific literature. However, there are only few describing the formation of gas bubbles in flowing liquid. Such a phenomenon occurs for instance in airlift apparatuses. Liquid flowing around the gas bubble creates a hydraulic drag force that leads to reduction of the formed bubble diameter. Usually the value of the hydraulic drag coefficient, cD, for bubble formation in the flowing liquid is assumed to be equal to the drag coefficient for bubbles rising in the stagnant liquid, which is far from the reality. Therefore, in this study, to determine the value of the drag coefficient of bubbles forming in flowing liquid, the diameter of the bubbles formed at different liquid velocity was measured using the shadowgraphy method. Using the balance of forces affecting the bubble formed in the coflowing liquid, the hydraulic drag coefficient was determined. The obtained values of the drag coefficient differed significantly from those calculated using the correlation for gas bubble rising in stagnant liquid. The proposed correlation allowed the determination of the diameter of the gas bubble with satisfactory accuracy.

Numerical method for identifying the flow model in the line pipe

With high availability of measuring tools and wide opportunities of modern computer technology, the existing methods of predictive estimations of hydraulic parameters for the fluids’ pipeline transport seem to be too approximate. Due to this, it is relevant to adapt the most accurate relationships available in the scientific and technical literature to real conditions. Based on the review of analytical solutions for calculating friction losses in the pressure lines, the structure of relationships most accurately reflecting the experimental data of I. Nikuradze is determined, where the hydraulic drag coefficient ? is described by the piecewise-continuous relations, given by O. M. Ayvazyan. The hydraulic drag coefficient structural relationship shall be selected with the highest capability to summarize the experimental data available in the scientific and technical literature. Using the pressure measurement data, free parameters included in the selected relationship for the hydraulic drag coefficient shall be identified. The numerical computation algorithm is proposed that enables to recover the values of parameters in the structural relationship of hydraulic drag coefficient ? through multiple application of the well-known method of sensitivity functions and pressure measurement data in the line pipe. The procedure is described for generating the computing system of ordinary differential equations that enables for every fixed set of experimental data (pressure and flow rate) to determine (or correct, if necessary) the corresponding parameters in the unified structural relationship for hydraulic drag coefficient ?. The feature of the proposed algorithm is the absence of embedded cycles. Dynamic control of variable parameters in the hydraulic drag coefficient ? based upon the proposed approach enables to improve the predictive estimations accuracy of flow parameters while pumping fluids and to acquire additional data on the state of the fluids filling the inner pipeline space.

Derivation of phenomenological turbulence theory in liquid with small additives of drag reducing agents

Paper considers the issue of deriving the phenomenological turbulence theory in liquids treated with small additives of drag reducing agent. It also proposes the concept that for practical purposes, it is the phenomenological theory, which is relevant, since it determines the parameters of the phenomenon in question in the absence of detailed knowledge of the mechanisms of additives action, which, despite many years of intensive studies, remain either unknown or not fully understood. Different additives have different effects on shear turbulence in pipes and channels and, accordingly, change the integral characteristics of the turbulent flow in different ways. Some additives affect only the narrow wall-bounded areas of the flow without changing the turbulent viscosity in the flow core, while others act throughout the entire flow volume and significantly change the turbulent viscosity. Additives of the first type affect a turbulent flow by changing the boundary conditions in known models without changing the model coefficients. Additives of the second type change both the boundary conditions and the coefficients of the model itself. It is shown that the von Karman modified theory (model) of shear turbulence is equally suitable for describing the turbulent flow of a liquid with additives of the both first and second types. The universal drag equation with experimentally determined transfer coefficients that follows from this model enables calculating the hydraulic drag coefficient depending on the properties of the drag reducing agent used.

Petroleum products interface volume reduction in back-to-back batching

The paper deals with interface mixing in back-to-back batching light petroleum products along the same pipeline. It is known that when one petroleum product is pumped back-to-back in the line without any separating device, a mixture is formed in the interface area of consistently moving batches, which is generally a substandard product. Therefore, the issue of reducing the substandard product volume is an important task that attracts an attention of scientists for many years. Since it is known that the volume of the resulting mixture depends on the intensity of convection and turbulent diffusion processes in the fluid flow in the line, the hydraulic drag reduction, at least in the contact area of petroleum products, can reduce the interface volume. It is shown that drag-reducing agents, usually injected into the flow of the transported liquid, can also be successfully used to reduce the volume of the substandard mixture. Formulas are given for calculating the hydraulic drag coefficient of a liquid with a drag-reducing agent depending on the concentration of this additive, the Reynolds number and the relative equivalent roughness of the inner pipe wall. The main aspects of the drag-reducing agent injection to reduce the petroleum products interface mixing in back-to-back batching are presented.

Hydraulic Resistance to Non-Isothermal Turbulent Gas and Liquid Flows in Pipes

An equation for the hydraulic drag coefficient of friction of stabilized turbulent flows in pipes was obtained based on the boundary layer model and the use of universal relations for the characteristics of boundary layer flows. This equation is in good agreement with experimental data for isothermal flows in the Reynolds number Re range of 5·103–108. The equation contains a structural parameter that can be used to account for the effect of changes in the physical properties of heat transfer fluids on the resistance in the flow cross sections during heating and cooling. For gaseous heat transfer agents, the impact of their atomicity on frictional resistance in non-isothermal conditions is analyzed.

Hydraulic drag of dense beds consisting of particles of different shape

Formulas derived by different researchers for the hydraulic drag of a dense bed consisting of particles of different type (balls, pellets, particles of arbitrary shape) are compared. Similarities in the dependence on the temperature and filtration rate are sought in terms of the reduced hydraulic drag coefficient. The dependence of the hydraulic drag on the porosity is practically unaffected by the shape of the particles. A formula is recommended for the hydraulic drag of a pellet bed with natural packing, with a low content of fines. On that basis, the energy losses in the bed itself and in the whole gas–air channel of roasting machines may be determined.

A two-phase damping model on tube bundles subjected to two-phase cross-flow

An analytical model is developed to estimate the two-phase damping ratio for upward cross-flow through horizontal tube bundles. The present model is formulated based on Feenstra’s model (2000) for void fraction and various models (homogeneous, Levy, Martinelli-Nelson and Marchaterre) for two-phase friction multiplier. The analytical results of drag coefficient on a cylinder and two-phase Euler number are compared with the experimental results by Sim-Mureithi (2013). The correlation factor between frictional pressure drop and the hydraulic drag coefficient is evaluated by considering the experimental results. The two-phase damping ratios given by the analytical model are compared with existing experimental results. The model based on Marchaterre’s model is suitable for air-water mixture, whereas the Martinelli-Nelson’s model is suitable for steam-water and Freon mixtures. The two-phase damping ratio is independent of pitch mass flux for air-water mixture, but is more or less influenced by the mass flux for steam-water/Freon (134) mixtures. The two-phase damping ratios given by the present model agree well with experimental results for a wide range of pitch mass ratio, quality, and p/d ratios.

Experimental Study of the Vertical Hydraulic Drag Force on Regular Tetrahedron

It is well known that the hydraulic drag force on objects cant be ignored in computing the movement of objects in water. And the drag forces on sphere and cuboids have long been studied. While in hydraulic engineering, objects with regular tetrahedron shape are widely used to form the foundation and temporary dam for they can interlock each other to obtain a compacted integral. In this article the vertical hydraulic drag force on regular tetrahedron is studied by indoor experiments, the relation of the vertical hydraulic drag coefficient and the vertical velocity is proposed. And the max vertical speeds of different materials are deduced. The result is helpful to compute the movement of regular tetrahedron in water and estimate the impact effect on the groundwork.

Turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field in the region of hydrodynamic stabilization

Numerical simulation is performed of turbulent pipe flow in the vicinity of entry to longitudinal magnetic field. Use is made of the model of turbulence developed by the present author and previously employed for performing calculations in the region of stabilized flow and heat transfer. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on the hydraulic drag coefficient and longitudinal component of velocity vector.

Refined Formula for Calculating the Hydraulic Drag Coefficient of a Pipeline

It is shown that the hydraulic drag coefficient depends significantly on the ratio of the equivalent hydraulic and geometric roughnesses for developed turbulent pipeline flow in the regime of partial manifestation of roughness. It is proposed to classify roughness types using this ratio. Introducing this parameter into the formula for computing the drag coefficient can considerably extend the domain of applicability of the computational method to different roughness types.

Improving the characteristics of liquid-metal fast breeders using a magnetic field

The known theoretical and experimental investigations of turbulent flow in tubes in a longitudinal magnetic field indicate that the drag coefficient may be reduced by a factor of 5-10 in comparison with turbulent flow in the absence of a magnetic field [3, 4]. Therefore, suppose that a reactor body is surrounded by a solenoid generating a magnetic field, the lines of force of which are parallel to the coolant flow in the active region (Fig. 1). Investigations of the flow around a cylinder and a sphere in the presence of a transverse magnetic field indicate that the hydraulic-drag coefficient may be significantly increased [3]. If, on the basis of these results, it is assumed that applying a longitudinal magnetic field leads to increase in the hydraulic-drag coefficient across the element and decrease in that along the element, then it is possible to replace the walls of the fuel elements in the active region and the blanket by, e.g., a rigid frame. Results of calculations using the ROKBAR optimization complex [5] showed that this leads to increase in the multiplication factor and the energy yield of the fuel while the doubling time may be reduced by 20-25%. Since buckling of the fuel-element casing necessitates an increase in the gaps between them and leads to additional blurring of the neutron spectrum, replacing the casing by a rigid frame would allow these losses to be reduced. The results of calculations indicate that increase in fast-breeder power is possible mainly by increase in radius of the active region. Increase in height of the active region is limited both by the mechanical stress in the walls of the fuel-element casing and by the accompanying heating of the coolant, which reaches 180250~ [5, 6]. The heating may be reduced, e.g., by increasing the rate of coolant flow. However, the maximum rate is limited by a number of factors: the erosional effects of the coolant on the fuel-element casing and other structural components; increase in the injection power, which depends on the hydraulic drag; vibrations of the fuel assemblies in the coolant flow. Applying a longitudinal magnetic field may diminish these limiting factors and hence allow the rate of the coolant flow to be increased. The increase in the erosional effects of the coolant with increase in its flow rate is associated with the accompanying reduction in thickness of the laminar boundary layer at the immersed surfaces [7, 8]. Applying a longitudinal magnetic field leads to increase in thickness of the laminar layer [8]. Rise in injection power with increase in the coolant flow rate is impossible on those sections of the fuel assembly where the field is parallel to the coolant flow. This

An experimental study of hydraulic resistance to the ascending flow in film-type distillers

The hydraulic drag coefficient in an ascending thin air-water film was studied as a function of the wetting rate and of the air velocity. Formulas have been derived for calculating this coefficient.