A COMPUTER MODEL OF PULSE WAVE AND INPUT IMPEDANCE IN HUMAN ARTERIES

To predict the propagation of pressure and fiow pulses in arterial system and the variation of vascular input impedance, a branched and tapered tube model is studied through one-dimensional transient flow analysis. Coupling the continuity and momentum equations yields a group of quasilinear hyperbolic partial differential equations which can be solvednumerically by using the method of characteristics. Several boundary conditions of the arterial system are also simplified suitably. The propagation of the pulses of the arterial system and the vascular input impedance is calculated on computer by using the dimensions and the physiological data of the arterial system. The results point out that the pressure and flow pulses of the arterial system and the vascular input impedance produced by this theoretical model is consistent quite well with the experimental results published.     

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

Computation of pressure drop for dilute gas-solid suspension across thin and thick orifices

The present work deals with the computation of the gas-solid two-phase flow pressure drop across thin and thick orifices for a vertically downward flow configuration at the higher limits of a dilute phase flow situation(0.01≤αs,in≤0.10).The Eulerian-Eulerian(two-fluid)model has been used in conjunction with the kinetic theory of granular flow with a four-way coupling approach.The validation of the solution process has been performed by comparing the computational result with the existing experimental data.It is observed that the two-phase flow pressure drop across the orifice increases with an increase in the thickness of the orifice,and the effect is more prominent at higher solid loading.The pressure drop is found to increase with an increase in the solid volume fraction.An increase in the Reynolds number or the area ratio increases the pressure drop.An increase in the size of the particles reduces the pressure drop across the orifice at both small and relatively large solid volume fractions.Finally,a two-phase multiplier has been proposed in terms of the relevant parameters,which can be useful to evaluate the gas-solid two-phase flow pressure drop across the orifice and can subsequently help to improve the system performance.     

Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow

This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.     

Exact solutions for nonlinear transient flow model including a quadratic gradient term

The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform.Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.     

Flow structures of gaseous jets injected into water for underwater propulsion

Gaseous jets injected into water are typically found in underwater propulsion,and the flow is essentially unsteady and turbulent.Additionally,the high water-to-gas density ratio can result in complicated flow structures;hence measuring the flow structures numerically and experimentally remains a challenge.To investigate the performance of the underwater propulsion,this paper uses detailed Navier-Stokes flow computations to elucidate the gas-water interactions under the framework of the volume of fluid(VOF) model.Furthermore,these computations take the fluid compressibility,viscosity,and energy transfer into consideration.This paper compares the numerical results and experimental data,showing that phenomena including expansion,bulge,necking/breaking,and back-attack are highlighted in the jet process.The resulting analysis indicates that the pressure difference on the rear and front surfaces of the propulsion system can generate an additional thrust.The strong and oscillatory thrust of the underwater propulsion system is caused by the intermittent pulses of the back pressure and the nozzle exit pressure.As a result,the total thrust in underwater propulsion is not only determined by the nozzle geometry but also by the flow structures and associated pressure distributions.     

Turbulence,vortex and external explosion induced by venting

The process of explosion venting to air in a cylindrical vent vessel connected to a duct, filling with a stoichiometric methane-oxygen gas mixture, was simulated numerically by using a colocated grid SIMPLE scheme based on k-epsilon turbulent model and Eddydissipation combustion model. The characteristics of the combustible cloud, flame and pressure distribution in the external flow field during venting were analyzed in terms of the predicted results. The results show that the external explosion is generated due to violent turbulent combustion in the high pressure region within the external combustible cloud ignited by a jet flame. And the turbulence and vortex in the external flow field were also discussed in detail. After the jet flame penetrating into the external combustible cloud, the turbulent intensity is greater in the regions with greater average kinetic energy gradient, rather than in the flame front ; and the vortex in the external flow field is generated primarily due to the baroclinic effect, which is greater in the regions where the pressure and density gradients are nearly perpendicular.     

PRESSURE AND PRESSURE GRADIENT IN AN AXISYMMETRIC RIGID VESSEL WITH STENOSIS

Based on an improvement of the Karman-Pohlhausen's method, using nonlinear polynomial fitting and numerical integral, the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained, and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed. It shows that with the increasing of stenotic degree or Reynolds number, the fluctuation of pressure and its gradient in stenotic area is intense rapidly, and negative pressure occurs subsequently in the diverging part of stenotic area. Especially when the axial range of stenosis extends, the flow of blood in the diverging part will be more obviously changed. In higher Reynolds number or heavy stenosis, theoretical calculation is mainly in accordance with nast experiments.     

Viscous falling film instability around a vertical moving cylinder

The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity.After studying the linear conditions,a generalized nonlinear kinematic model is then derived to present the physical system.Applying the boundary conditions,analytical solutions are obtained using the long-wave perturbation method.In the first step,the normal mode method is used to characterize the linear behaviors.In the second step,the nonlinear film flow model is solved by using the method of multiple scales,to obtain Ginzburg-Landau equation.The influence of some physical parameters is discussed in both linear and nonlinear steps of the problem,and the results are displayed in many plots showing the stability criteria in various parameter planes.     

An investigation on internal thermal flow of non-Newtonian fluid

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the fiow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied, For the flow into mould cavity the constitutive equation of power-law fluid is used as a rheological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid fiow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting differen     

A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid

A general solution for 3D Stokes flow is given which is different from, and more compact than the existing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape translating along the direction normal to it in an unbounded fluid.The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the velocity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and elliptic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.     

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density(PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.     

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed.Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model(DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density.The pressure propagation is slower in the direction of larger fracture density.     

PRESSURE DROP ACROSS A FIXED BED REACTOR WITH MECHANICAL FAILURE OF CATALYST PELLETS DESCRIBED BY SIMPLIFIED ERGUN＇S EQUATION

The pressure drop across a laboratory-scale catalyst packed bed with mechanical failure of catalyst pellets has been examined. It was found that the increased pressure drop can be described by a simplified model deduced from Ergun‘s equation. The pressure drop is determined mainly by the term of viscous energy loss.     

Inertial migration of aerosol particles in three-dimensional microfluidic channels

In recent years,manipulation of particles by inertial microfluidics has attracted significant attention.However,most studies focused on inertial focusing of particles suspended within liquid phase,in which the ratio of the density of the particle to that of the medium is O(1).The investigation on manipulation of aerosol particles in an inertial microfluidics is very limited.In this study,we numerically investigate the aerosol particle's motion in a 3D straight microchannel with rectangular cross section by fully resolved simulation of the particle-air flow.The air flow is modeled by the Navier-Stokes equations.The particle's motions,including translation and rotation,are governed,respectively,by the Newton's second law and the Euler equations without using any approximation models for the lift and drag forces.The coupled mathematical model is numerically solved by combining immersed boundary with lattice Boltzmann method(IB-LBM).We find that the Reynolds number(Re),the particle's initial position,particle's density and diameter are the influential parameters in this process.The equilibrium positions and their stabilities of aerosols are different from those suspended in liquid.     

Towards multi-fidelity simulation of flows around an underwater vehicle with appendages and propeller

Flow around a real-life underwater vehicle often happens at a high Reynolds number with flow structures at different scales from the boundary layer around a blade to that around the hull. This poses a great challenge for large-eddy simulation of an underwater vehicle aiming at resolving all relevant flow scales. In this work, we propose to model the hull with appendages using the immersed boundary method, and model the propeller using the actuator disk model without resolving the geometry of the blade. The proposed method is then applied to simulate the flow around Defense Advanced Research Projects Agency(DARPA) suboff. An overall acceptable agreement is obtained for the pressure and friction coefficients. Complex flow features are observed in the near wake of suboff. In the far wake, the core region is featured by a jet because of the actuator disk, surrounded by an annular region with velocity deficit due to the body of suboff.     

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10 species surrogate based on the principle of extended corresponding states (ECS). Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly different from those of ideal gases. A two-stage fuel heating and delivery system is used to heat the kerosene up to a temperature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle (Laval nozzle) have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

SUPG finite element method based on penalty function for lid-driven cavity flow up to $$Re = 27500$$

A streamline upwind/Petrov–Galerkin(SUPG)finite element method based on a penalty function is proposed for steady incompressible Navier–Stokes equations.The SUPG stabilization technique is employed for the formulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pressure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.     

Boundary layer flow over a moving surface in a nanofluid with suction or injection

An analysis is performed to study the heat transfer characteristics of steady two-dimensional boundary layer flow past a moving permeable flat plate in a nanofluid. The effects of uniform suction and injection on the flow field and heat transfer characteristics are numerically studied by using an implicit finite difference method. It is found that dual solutions exist when the plate and the free stream move in the opposite directions. The results indicate that suction delays the boundary layer separation, while injection accelerates it.