Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law

In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re.

On the equilibrium and stability of a fluidized bed as a thermodynamic system

The transfer of the dispersed layer into a fluidized state makes it possible to intensify the drying process. The small size of the particles leads to an increase in the surface of their contact with the coolant at a relatively low hydrodynamic resistance. Other positive qualities of fluidization are listed, which is very important when carrying out exothermic processes. We studied the behavior of the fluidized bed during the drying process. The curve of fluidization of beet chips is shown. The suspended state of the material began when the forces of the hydrodynamic layer were equal to the weight of all its particles per unit area of the cross-section of the working chamber. The region of existence of the fluidized bed is marked. In this area, the flow was relatively equilibrium (fluidized). On the surface of the layer, small waves were observed with different frequencies and amplitudes of oscillations, as well as with spontaneous fluctuations. This mode of operation was achieved as a result of the study of the structures of the support - gas distribution grid and the drying chamber. The flow velocity profile in the working chamber is investigated. An efficient equalization of velocities with the help of flat stamped grids has been established. The results were confirmed by the spectra of the flow in the drying chamber. Oscillations on the free surface of a fluidized bed are considered. The Euler equation was written, which made it possible, as a result of various transformations, to obtain a formula for calculating the oscillation frequency of the fluidized bed. The studies carried out made it possible to establish the regimes of pseudo-fluidization, to a certain extent minimizing the heterogeneity of the layer, which is of significant practical importance. However, the operating parameters need to be adjusted depending on the type of material to be dried and other indicators. The research results do not obscure the general provisions of nonequilibrium thermodynamics. The fluidized bed cannot be in an equilibrium state, since the transfer of substances is obvious: energy, mass and momentum. It is correct to regard the fluidized bed as unstable. Small and spontaneous fluctuations always exist in the layer. The absence of conditions for their decay becomes a condition for the instability of the process.

An Analytic Study of the Effect of a Vane on the Hydraulic Field around a Cylinder

The flow pattern around the cylinder body is a very serious problem and this problem may become more serious and sensitive, when we place a vane neighboring to the cylinder. The present paper deals with the vane impact on the flow pattern around the cylinder. To investigate this problem the ANSYS fluent software is employed in order to achieve the two dimensional numerical analysis. Here, Reynolds Average Navier Stokes model is adopted. The investigation comprises the following hydraulic variables, like eddy viscosity, turbulent intensity, turbulent kinetic energy, turbulent dissipation rate, flow velocity profile, static pressure and pressure coefficient. The constant flow velocity, cylinder diameter and vane dimension are adopted in this analysis, while the different certain distance between the vane and the cylinder is considered. The used vane has a rectangular shape. In this analysis, it is clear that the vane plays a sensitive vital role in the hydraulic behavior of the flow pattern around the cylinder. The study has taken up four distances between the vane and the cylinder, these distances is a function of the cylinder diameter, in addition to the direct touch that happens between the vane and the cylinder. The analysis also shows that when the cylinder has direct touch with the vane, the dramatic reduction will occur in hydraulic variables.

Specific features of coordinated variations in friction resistance and flow velocity profile in tubes at Toms effect

Object and purpose of research. Relationships between friction resistance coefficient and velocity distributions in the turbulent boundary layer of low-concentrated polymer solutions are investigated. These relationships are different from water because in polymer solutions the friction resistance at constant Reynolds numbers is additionally changed with solution concentrations. Materials and methods. The known experimental data on variations of the friction resistance coefficient and the velocity profiles in turbulent flows in circular tubes at changes in polymer solution concentrations. Main results. The general law of coordinated variations in friction resistance coefficient λ and flow velocity profile in the turbulent boundary layer depending on Reynolds number and polymer solution concentration. The flow models are validated, which describe the laws of velocity variations in all characteristic sections of boundary layer: laminar sublayer, buffer and logarithmic flow areas. A new non-dimensional number is introduced, which characterizes the ability of low concentrated water solutions of polymers to reduce the friction resistance. It is called the Toms effect parameter in the work. Conclusion. Results of the investigation will be useful in developing the theoretical methods for estimation of boundary layer characteristics in polymer solutions.

Optimized Vegetation Density to Dissipate Energy of Flood Flow in Open Canals

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

Experimental Investigation of Mean Flow Profile Effects on Impedance Eduction

The results of experimental and computational studies of the three-dimensional mean flow velocity profile influence on the impedance eduction are presented. In order to measure the three-dimensional velocity profile, the TsAGIâ€(tm)s “Interferometer with flow†facility was upgraded so that additional holes were made in one cross section of the rectangular duct. As a result, it became possible to measure the longitudinal flow velocity in this cross section along 6 lines using a Pitot tube or a hot wire anemometer. The full three-dimensional velocity profile is determined by interpolating the values measured.Experimental results of the velocity profile for various experiment conditions are presented. Based on the numerical solution of the three-dimensional Pridmore-Brown equation by means of Finite Element Method and the gradient descent method, the problem of impedance eduction are investigated. The influence of the flow velocity profile and the form of functional on the obtained impedance values are discussed. The impedance values educted by means of this approach are compared with the impedance values obtained using two-dimensional impedance eduction methods, which didnâ€(tm)t taking into account the three-dimensional non homogeneity of the flow velocity field.

Realistic boundary conditions in SimVascular through inlet catheter modeling

Objective This study aims at developing a pipeline that provides the capability to include the catheter effect in the computational fluid dynamics (CFD) simulations of the cardiovascular system and other human vascular flows carried out with the open-source software SimVascular. This tool is particularly useful for CFD simulation of interventional radiology procedures such as tumor embolization where estimation of a therapeutic agent distribution is of interest. Results A pipeline is developed that generates boundary condition files which can be used in SimVascular CFD simulations. The boundary condition files are modified such that they simulate the effect of catheter presence on the flow field downstream of the inlet. Using this pipeline, the catheter flow, velocity profile, radius, wall thickness, and deviation from the vessel center can be defined. Since our method relies on the manipulation of the boundary condition that is imposed on the inlet, it is sensitive to the mesh density. The finer the mesh is (especially around the catheter wall), the more accurate the velocity estimations are. In this study, we also utilized this pipeline to qualitatively investigate the effect of catheter presence on the flow field in a truncated right hepatic arterial tree of a liver cancer patient.

Experiment based calibration of k − ε turbulence model in OpenFOAM package for mountain slope flows using machine learning techniques

We calibrate the k − ε turbulence model for free surface flows in the channel or on the slope. To calibrate the turbulence model, an experiment is carried out in an inclined rectangular research tray. In the experiment, the pressure values in the flow are measured at different distances from the bottom using a Pitot tube; after transforming data, the flow velocity profile is obtained. The k − ε turbulence model is calibrated based on experimental data using the Nelder-Mead optimization algorithm. The calibrated turbulence model is then used to calculate the outburst of a lake near the glacier Maliy Azau on the Elbrus (Central Caucasus).