On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe＇s geometry on the effective flow.

A numerical simulation of unsteady flow in small diameter helical grafts

The application of small diameter arterial grafts is limited due to the fact of relatively poor long-time patency which is caused by thrombosis formation in the short term and intimal hyperplasia(IH) in the medium and long term.Thrombosis,obstructing the flow of blood

HELICAL SYMMETRIC SOLUTION OF 3D NAVIER-STOKES EQUATIONS ARISING FROM GEOMETRIC SHAPE OF THE BOUNDARY

In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface（screw propeller）while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved.

The Conservation of Helicity in Hurricane Andrew(1992)and the Formation of the Spiral Rainband

The characteristics of helicity in a hurricane are presented by calculating the MM5 model output in addition to theoretical analysis. It is found that helicity in a hurricane mainly depends on its horizontal component, whose magnitude is about 100 to 1000 times larger than its vertical component. It is also found that helicity is approximately conserved in the hurricane. Since the fluid has the intention to adjust the wind shear to satisfy the conservation of helicity, the horizontal vorticity is even larger than the vertical vorticity, and the three-dimensional vortices slant to the horizontal plane except in the inner eye. There are significant horizontal vortices and inhomogeneous helical flows in the hurricane. The formation of the spiral rainband is discussed by using the law of horizontal helical flows. It is closely related to the horizontal strong vortices and inhomogeneous helical flows.

Mechanisms and field test of solution mining by self-resonating cavitating water jets

Rapid solution mining is the key to cavern construction in salt formations. Rapid solution mining technology with self-resonating cavitating water jets is described in this paper. It can generate three main physical effects： helical flow dissolution, self-resonating cavitating jet erosion, and ultrasonic waves. A self-resonating cavitating nozzle was also designed with the principles based on theory of fluid transients and hydro-acoustics. Under ambient pressure, the experimental results show that the impulse amplitude of pressure reaches a peak at a standoff distance of 5-13 times the nozzle outlet diameter and the cutting ability of self-resonating cavitating jets is twice that of conventional jets under the same conditions. Compared with the conventional mining method, the field test indicates that rapid solution mining technology with self-resonating cavitating jets can speed the construction by more than 2 times at the pocket stage of cavern development.

Haemodynamic Analysis of the Relationship between the Morphological Alterations of the Ascending Aorta and the Type A Aortic-Dissection Disease

Type A aortic dissection(AD)is one of the most serious cardiovascular diseases,whose risk predictors are controversial.The purpose of this research was to investigate how elongation accompanied by dilation of the ascending aorta(AAo)affects the relevant haemodynamic characteristics using image-based computational models.Five elongated AAos with different levels of dilation have been reconstructed based on the centerlines data of an elderly and an AD patient.Numerical simulations have been performed assuming an inflow waveform and a Windkessel model with three elements for all outflow boundaries.The numerical results have revealed that the elongation of AAo can disturb the systolic helical flow pattern between the root of AAo and the aortic arch.The helical flow inside the AAo starts to develop into a vortex flow when the elongated AAo becomes dilated.The vortex gives rise to a localized oscillatory shear index at the ostia of the brachiocephalic artery(BA)and the inner curve of the aortic arch.This study suggests that abnormal growth of AAo,especially accompanied by its moderate dilation,can be considered as morphological risk factors of AD.

A High-Order Discontinuous Galerkin Solver for Helically Symmetric Flows

We present a high-order discontinuous Galerkin(DG)scheme to solve the system of helically symmetric Navier-Stokes equations which are discussed in[28].In particular,we discretize the helically reduced Navier-Stokes equations emerging from a reduction of the independent variables such that the remaining variables are:t,r,ξwithξ=az+bϕ,where r,ϕ,z are common cylindrical coordinates and t the time.Beside this,all three velocity components are kept non-zero.A new non-singular coordinateηis introduced which ensures that a mapping of helical solutions into the three-dimensional space is well defined.Using that,periodicity conditions for the helical frame aswell as uniqueness conditions at the centerline axis r=0 are derived.In the sector near the axis of the computational domain a change of the polynomial basis is implemented such that all physical quantities are uniquely defined at the centerline.For the temporal integration,we present a semi-explicit scheme of third order where the full spatial operator is splitted into a Stokes operator which is discretized implicitly and an operator for the nonlinear terms which is treated explicitly.Computations are conducted for a cylindrical shell,excluding the centerline axis,and for the full cylindrical domain,where the centerline is included.In all cases we obtain the convergence rates of order O(hk+1)that are expected from DG theory.In addition to the first DG discretization of the system of helically invariant Navier-Stokes equations,the treatment of the central axis,the resulting reduction of the DG space,and the simultaneous use of a semi-explicit time stepper are of particular novelty.

Numerical modelling of supercritical flow in circular conduit bends using SPH method

The capability of 1he smoothed-particle hydrodynamics （SPH） method to model supercritical flow in circular pipe bends is considered. The standard SPH method, which makes use of dynamic boundary particles （DBP）, is supplemented with the original algorithm for the treatment of open boundaries. The method is assessed through a comparison with measured free-surface profiles in a pipe bend, and already proposed regression curves for eslimation of the flow-type in a pipe bend. The sensitivity of the model to different parameters is also evaluated. It is shown that an adequate choice of the artificial viscosity coefficient and the initial particle spacing can lead to correct presentation of the flow-type in a bend. Due to easiness of its implementation, the SPH method can he efficiently used in the design of circular conduits with supercritical flow in a bend, such as tunnel spillways, and bottom outlets of dams, or storm sewers.

Lattice Boltzmann method simulating hemodynamics in the three-dimensional stenosed and recanalized human carotid bifurcations

By using the lattice Boltzmann method(LBM)pulsatile blood flows were simulated in three-dimensional moderate stenosed and recanalized carotid bifurcations to understand local hemodynamics and its relevance in arterial atherosclerosis formation and progression.The helical flow patterns,secondary flow and wall dynamical pressure spatiotemporal distributions were investigated,which leads to the disturbed shear forces in the carotid artery bifurcations.The wall shear stress distributions indicated by time-averaged wall shear stress(TAWSS),oscillatory shear index(OSI),and the relative residence time(RRT)in a cardiac cycle revealed the regions where atherosclerotic plaques are prone to form,extend or rupture.This study also illustrates the point that locally disturbed flow may be considered as an indicator for early atherosclerosis diagnosis.Additionally the present work demonstrates the robust and highly efficient advantages of the LBM for the hemodynamics study of the human blood vessel system.

Hemodynamic evaluation of different stent graft schemes in aortic arch covered stent implantation

Implantation of the left subclavian artery(LSA)stent graft used in fenestration technique of the thoracic endovascular aortic repair(TEVAR)may interfere with the aortic helical blood flow that is believed to have important protective functions against atherogenesis.The present study investigated four different LSA stent graft implantation schemes for their resulted blood flow patterns in the thoracic aortic with hemodynamic computational simulation methods:the flush branch(FB),the protruding branch(PB),the straight cuff branch(SCB)and the cured cuff branch(CCB).The results showed that the PB scheme could slightly enhance helicity of the swirling flow in the aorta,but the other three schemes had less effect on blood flow helicity.The PB scheme produced lowTAWSS,high-OSI and high-RRT around the LSA root,and the FB scheme had similar TAWSS,OSI and RRT in both value and distribution to those in the aorta without LSA stent graft implantation.The SCB and CCB schemes led to less area of high-OSI and high-RRT values along the walls of the LSA branch arteries.The results also showed that the PB scheme would significantly reduce blood supply to the LSA,on the contrary,the CCB scheme enhanced LSA blood supply and less effect on the total blood supply to the three branches of the thoracic aorta.In summary,all of the four schemes have no significant effect on the aortic swirling flow,however,in the terms of TAWSS,OSI,RRT and blood supply to the LSA,the CCB model might be the best option with less area of low-WSS,high-OSI,high-RRT and well blood supply in the LSA.