A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

Size-Dependent Stability of a Cantilevered Piezoelectrically Actuated Micropipe Conveying Fluid

Size-dependent effects of a cantilevered piezoelectrically actuated micropipe conveying fluid are investigated. Based on the modified strain gradient beam theory, the model of system is obtained using Hamilton's principle. The motion equation is discretized into ordinary differential equations by Generalized Differential Quadrature Method (GDQM). A stability analysis of the system is completed through eigenvalue analysis. Numerical results show the effect of geometrical shape size, and length scale parameters on critical flow velocity, and critical voltage. Results prove that the modified strain gradient theory (MSGT) has a higher critical flow velocity and critical voltage than predicted by modified couple stress theory (MCST) and classical theory (CT).

A New Model for Predicting Liquid Loading in Shale Gas Horizontal Wells

Current critical flow rate models fail to accurately predict the liquid loading statuses of shale gas horizontal wells. Therefore, a new critical flow rate model for the whole wellbore of shale gas horizontal wells is established. The results of the new model are compared to those of current models through the field case analysis. The new model is based on the dynamic analysis and energy analysis of the deformed liquid-droplet, which takes into account the liquid flow rate, the liquid-droplet deformation and the energy loss caused by the change of buildup rate. The major axis of the maximum stable deformed liquid-droplet is determined based on the energy balance relation. Meanwhile, the suitable drag coefficient equation and surface tension equation applied to shale gas horizontal wells are chosen. Finally, the critical flow rate equation is established and the maximum critical flow rate of the whole wellbore is chosen as the criterion for liquid loading prediction. The precision of liquid loading prediction of the new model is compared to those of the four current models, including Belfroid's model, modified Li's model, liquid film model and modified Wang's model. Field parameters of 29 shale gas horizontal wells are used for the comparison, including parameters of 18 unloaded wells, 2 near loaded-up wells and 9 loaded-up wells. Field case analysis shows that the total precision of liquid loading prediction of the new model is 93.1%, which is higher compared to those of the current four models. The new model can accurately predict the liquid loading statuses of loaded-up wells and near loaded-up wells, while the prediction precision for unloaded wells is high enough for the field application, which is 88.9%. The new model can be used to effectively estimate the field liquid loading statuses of shale gas horizontal wells and choose drainage gas recovery technologies, which considers both the complex wellbore structure and the variation of flowback liquid flow rate in shale gas horizontal wells. The results of the new model fill the gap in existing studies and have a guiding significance for liquid loading prediction in shale gas horizontal wells.

Hydrodynamic model of fish orientation in a channel flow

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we make an essential step to elucidate the hydrodynamic underpinnings of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are validated against experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

Numerical Study of Thermal Effect on the Stability of Carbon Nanotubes Resting on a Viscoelastic Foundation Subjected to Magnetic Field

Carbon nanotubes (CNTs) have emerged as efficient tools in drug delivery systems; therefore, it is essential to refer to the importance of the magnetic field, in addition to the fluid flow on the dynamic behavior of CNTs. Additionally, in such medical applications, the actual working environment of nanotube often contains temperature changes, and CNTs are surrounded by soft tissues with viscoelastic mechanical properties. In this study, the vibrational behavior of CNTs conveying magnetic-fluid flow and resting on a viscoelastic foundation is investigated under various temperature variations. To incorporate the influence of slip velocity at the nanoscale, a correction factor is employed on the basis of the Beskok–Karniadakis model. The nanotube is modeled by the Euler–Bernoulli beam theory, and governing equations of motion are derived by implementing Hamilton’s principle based on Eringen’s nonlocal elasticity theory. Results indicate that by applying a magnetic field with an intensity of 30[Formula: see text]T, the dimensionless critical flow velocity increases from 4.345 to 12.603. Also, the critical flow velocity shows an increase from 4.345 to 5.854 in the presence of a viscoelastic foundation. Furthermore, a temperature variation equal to 20[Formula: see text]K reduces the critical flow velocity dramatically from 4.345 to 1.802 at low temperatures, while an increase from 4.345 to 5.443 is observed at high temperatures. Consequently, while the magnetic field and the viscoelastic foundation affect the system stability, the temperature variation may improve or deteriorate the stability. Therefore, to plan for a medical application, the inclusion of temperature variation is required.

Assessment of the flow behavior and structural performance of open-cell aluminum foams at critical flow conditions of pressure and temperature

Open-cell Al foams were produced by the replication casting technique in three different pore sizes. All produced foams were physically characterized, determining their relative density, porosity, and pores per inch, as well as their mean pore surface area and diameter. Permeability tests were carried out by means of the injection of a highly pressurized gasoline additive at room temperature and 200 °C, at pressures of up to 25,000 psi. The structural capacity of the studied specimens to conduct fluids at these critical experimental conditions was assessed by means of compression tests in order to determine their mechanical properties after the permeability tests, e.g., energy absorption capacity, Young’s modulus, and plateau stress. It was found that the produced open-cell Al foams were able of conducting the gasoline additive at critical flow conditions of pressure and temperature, without suffering important physical nor structural damage. Graphic abstract

CRITICAL FLOW PREDICTION MODELS FOR THE COOLANT AT SUPERCRITICAL PARAMETERS

An interest of the problems of various thermophysical and hydrodynamic phenomena in the nuclear industry, determined by the real application in the field of analysis of the accident scenarios related to the loss of coolant accident. For the generic super critical water reactor the meaning of the problem at the initial stage of the critical flow process, is the existing of the uncertainty in the accepting boundary conditions to predict the flow characteristics. The article provides an analytical review of existing approaches for describing the critical flow phenomenon of the medium and to focus on the current predictive models. A description of the physical nature of such a phenomenon is provided. The scope of consideration includes information from the literature for single and two-phase flow, taking into account their physical basis and the assumptions made. The task of the work was to analyze the information found and to evaluate and update the data on the application of the models to obtain the critical characteristic. It was supposed to highlight the physical aspects and peculiarities of this phenomenon, as applied to the coolant at supercritical parameters. To formulate important requirements to the representative critical flow model for the possibility of its use in the system codes for evaluation of the nuclear safety problems of promising fourth generation nuclear reactors.