An upper bound on the steady flow velocity of solvent-free nanofluids

The rheological properties and limited flow velocities of solvent-free nanofluids are crucial for their technologically significant applications.In particular,the flow in a solvent-free nanofluid system is steady only when the flow velocity is lower than a critical value.In this paper,we establish a rigid-flexible dynamic model to investigate the existence of the upper bound on the steady flow velocities for three solvent-free nanofluid systems.Then,the effects of the structural parameters on the upper bound on the steady flow velocities are examined with the proposed structure-preserving method.It is found that each of these solvent-free nanofluid systems has an upper bound on the steady flow velocity,which exhibits distinct dependence on their structural parameters,such as the graft density of branch chains and the size of the cores.In addition,among the three types of solvent-free nanofluids,the magnetic solvent-free nanofluid poses the largest upper bound on the steady flow velocity,demonstrating that it is a better choice when a large flow velocity is required in real applications.

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.

Energy analysis of geosynthetic-reinforced slope in unsaturated soils subjected to steady flow

Soils are actually unsaturated in nature. In the present study, a stability analysis of a geosynthetic-reinforced slope in unsaturated soils subjected to various steady flow conditions is conducted based on limit analysis. Work rate by apparent cohesion due to matric suction is calculated based on the effective stress-based equation. Analytical expression of the required cohesion/stability number of slope is derived from the energy balance equation. An optimization code is programmed to capture the optimized solution of the stability number. Comparison is made to verify the present work and a parametric analysis is conducted to investigate the effects of soil type, infilitration rate, reinforcement strength and soil suction on slope stability afterwards. A set of numerical solutions is presented at the end of the paper for preliminary design purposes.

Behavior of Vortex-Induced Vibration of A Circular Cylinder Near A Deformable Wall with Two Degrees of Freedom in Steady Flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder＇s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number

ON ANALYSIS OF THE STEADY FLOW IN AN IRRECTANGULARPARALLEL-PLATE FLOW CHAMBER

The parallel-plate flow chamber (PPFC), of which the height is far smaller than its own length and width, is one of the main apparatus for the in vitro study of the mechanical behaviors of cultured cells at the bottom of PPFC undergoing shear stress. The PPFC of which the upper and lower plates are rectangular is usually used by research workers, and the flow field in this kind of PPFC (except for the regions near the entrance and exit) is uniform([1]), so only the effect the shear stress with one value has on cultured cells can be observed during each experiment. A kind of PPFC of which the upper and lower plates are not rectangular is proposed in this paper. The distributions of the velocities inside and the shear stresses at the bottom of the chamber are given by analyzing the flow field of the steady flow in the PPFC. The results show that the mechanical behaviors of cultured cells undergoing the shear stresses with various values may be simultaneously observed by the use of this kind of irrectangular PPFC. The theoretical and experimental results obtained by Ultrasonic Doppler Technique show good agreement.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.

MOLECULAR MODELS AND FLOW CALCULATIONS Ⅱ.SIMULATION OF STEADY PLANAR FLOW

A multibead-rod model is used to replace the constitutive equation of continuum me- chanics in solving flow problems of steady-state planar flows of rigid-rodlike molecular suspensions.The governing equations then constitute a set of differential equations of the elliptic type,which is more ame- nable to numerical treatment than those of the mixed type.The conservation equations of the flow fields are solved by the boundary element method with linear boundary elements in physical space and the diffusion equation of the distribution function is solved separately by the Galerkin method in phase space. The solution to the flow problem is obtained when the convergence of the iteration procedure between the two spaces has been reached.Several numerical examples are shown and the interesting features of the present method are discussed in this paper.

Numerical Investigation of Flow Motion and Performance of A Horizontal Axis Tidal Turbine Subjected to A Steady Current

Horizontal axis tidal turbines have attracted more and more attentions nowadays, because of their convenience and low expense in construction and high efficiency in extracting tidal energy. The present study numerically investigates the flow motion and performance of a horizontal axis tidal turbine with a supporting vertical cylinder under steady current. In the numerical model, the continuous equation and incompressible Reynolds-averaged Navier-Stokes equations are solved, and the volume of fluid method is employed to track free surface motion. The RNG k-ε model is adopted to calculate turbulence transport while the fractional area/volume obstacle representation method is used to describe turbine characteristics and movement. The effects of installation elevation of tidal turbine and inlet velocity on the water elevation, and current velocity, rotating speed and resultant force on turbine are discussed. Based on the comparison of the numerical results, a better understanding of flow structure around horizontal axis tidal turbine and turbine performance is achieved.

Debye-Hckel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary

Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hiickel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the mi- crocapillary, while the couple stress tensor is uniform across the cross-section.

Precision calculation of crustal deformation induced by radial steady laminellar flow of underground water from single well in multi-layered structural aquifers

According to both the general formula of ground surface displacement by drainage from a well for radial permeable flow of underground water and the drawdown expressions for the flow in multilayered structural aquifers, we have derived the analytical expressions of surface displacement induced by steady flow withdrawal from a full penetrating well on phreatic water and confined water in multilayered structural aquifers and discussed the numerial integration scheme of these analytical expressions. And by means of Hermite′s quadrature formula with 20 nodes, we have made calculational programs and examples to show that the methods mentioned in this paper are effective. We think that these methods lay a foundation to study quantitatively crustal deformation due to groundwater drainage when we are engaged in high precision dynamic geodetic measurement on the area of steady flow of multilayered aquifers.

THE STEADY/PULSATILE FLOW AND MACROMOLECULAR TRANSPORT IN T-BIFURCATION BLOOD VESSELS

A numerical analysis of the steady and pulsatile, macromolecular(such as low density lipopotein (LDL), Albumin) transport in T-bifurcation was proposed. The influence of Reynolds number and mass flow ratio etc. parameters on the velocity field and mass transport were calculated. The computational results predict that the blood flow factors affect the macromolecular distribution and the transport across the wall, it shows that hemodynamic play an important role in the process of atherosclerosis. The LDL and Albumin concentration on the wall varies most greatly in flow bifurcation area where the wall shear stress varies greatly at the branching vessel and the atherosclerosis often appears there.

Fourier neural operator with boundary conditions for efficient prediction of steady airfoil flows

An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator(FNO),which is a new framework of neural networks.Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO,which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions.The proposed approach runs several orders of magnitude faster than the traditional numerical methods.The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach.Furthermore,the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids,thereby improving the accuracy in the near-wall region.There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.

A COMPLETE BOUNDARY INTEGRAL FORMULATION FOR STEADY COMPRESSIBLE INVISCID FLOWS GOVERNED BY NONLINEAR EQUATIONS

A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.

Dispersion of Dynamic Biochemical Signals in Steady Flow in a Shallow Y-type Microfluidic Channel

This paper presents an analysis of dispersion of dynamic biochemical signals in steady flow in a shallow Y-type microfluidic channel. A method is presented to control the flow widths of two steady flows in the Y-type microchannel from two inlets.The transfer function for the Y-type microchannel is given by solving the governing equation for the Taylor-Aris dispersion in the microchannel. The amplitude-frequency and phase-frequency relations are provided which show that a shallow Y-type microchannel acts as a low-pass filter. The transports of different dynamic biochemical signals are investigated. In comparison with a fully mixing microfluidic channel, the magnitudes of the dynamic signals at the outlets in a Y-type microchannel are much smaller than those in a fully mixing microchannel, which demonstrates that the amplitude attenuation in a Y-type microchannel is larger than that of a fully mixing microchannel due to the transverse molecular diffusion. In order to control the desired signal in a microchannel, the solution of the inverse problem for the channel is also presented.

Numerical Simulation of CFD and Fluid-Structure-Interaction (FSI) of Steady Flow in a Stenotic Vessel

This paper is concerned with the computational results of two-dimensional axisymmetric rigid and elastic wall formulation. In this paper, steady flow in a stenotic vessel is simulated and compared to available numerical data with COMSOL Multiphysics software. Numerical results for a 2D axisymmetric vessel of 45% area reduction indicate that as the area is reduced with the decreasing of cross-section, the maximum axial velocity at post stenotic decreases until the end of the artery but the radial velocity increases upto 4 mm from the stenosis throat and then decreases. Overall, comparison is carried out on hemodynamics for elastic and rigid wall of steady flow. Our investigated findings may enable risk factor for patients with attacked cardiovascular diseases and can play an important role to detect a solution to such kinds of diseases.

Numerical Study of a Three-Dimensional Laminar Flow in a Rectangular Channel with a 180-Degree Sharp Turn

This study presents a numerical analysis of three-dimensional steady laminar flow in a rectangular channel with a 180-degree sharp turn. The Navier-Stokes equations are solved by using finite difference method for Re = 900. Three-dimensional streamlines and limiting streamlines on wall surface are used to analyze the three-dimensional flow characteristics. Topological theory is applied to limiting streamlines on inner walls of the channel and two-dimensional streamlines at several cross sections. It is also shown that the flow impinges on the end wall of turn and the secondary flow is induced by the curvature in the sharp turn.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

ON MULTI-DIMENSIONAL SONIC-SUBSONIC FLOW

In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional （n ≥ 2） Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy Hloc^-1（Ω） compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional （n ≥ 2） Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension （n ≥ 3）.

An experimental study on the choked flow characteristics of CO_(2) pipelines in various phases

High pressure pipeline transportation has been an established technology for economically transporting large amounts of CO_(2).However,there are still issues and associated risks that have to be effectively addressed and adequately understood.It is well known that a strong JouleThomson Cooling effect can occur when pressurized CO_(2) flows through a choke valve.Thus,to investigate the choking characteristics especially the temperature drop of high pressure CO_(2),a new laboratory scale experimental setup(total length of 14.85 m and the inner diameter of 15 mm)was constructed.Steady choked flow and transient choked flow tests were carried out respectively for pressurized CO_(2) in various initial phases.The phase transitions and temperature drop characteristics were then studied following the choked flow and the results show that the phase transitions in steady choked flow differs significantly from that in transient choked flow.For transient choked flow of various initial phases,all the flows downstream would transfer from single phase to gas-liquid twophase flow.Furthermore,the effect of water on transient choked flow of supercritical CO_(2) pipeline was investigated,and the phenomena of solid particles deposition was captured which was paramount importance of ensuring the safety operation of CO_(2)pipelines when throttling by the choke valves.

UNSTEADY/STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.