Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

4D-Flow MRI在肥厚型心肌病左室流出道血流评估中的价值探索

目的 探索四维血流(four-dimensional flow,4D-Flow)磁共振成像(magnetic resonance imaging,MRI)技术在左心室腔内应用的可行性。材料与方法 本研究为前瞻性、横断面研究,纳入2022年8月至2023年1月于我院接受心脏MRI检查的21例肥厚型心肌病患者,采用3.0 T MRI扫描仪进行二维血流(tow-dimensional flow,2D-Flow)及4D-Flow成像,收集患者一周内进行的超声心动图检查结果。采用组内相关系数(inter-class correlation coefficient,ICC)、变异系数(coefficients of variation,COV)及Bland-Altman分析比较2D-Flow、4D-Flow评估左室流出道峰值流速的可重复性及一致性,并通过Pearson相关性分析探究二者与超声心动图测量结果的关系。结果 2D-Flow和4D-Flow观察者内/观察者间的ICC分别为0.999/0.999和0.995/0.992,COV分别为0.5%/0.5%和2.4%/2.6%。4D-Flow与超声心动图的测量结果呈中度相关,相关系数r值为0.574(P=0.006),但一致性较差,ICC为0.375(P=0.013)。2D-Flow与4D-Flow和超声心动图间无显著的一致性及相关性。结论 4D-Flow技术能够可视化心腔内血流模式,对左室流出道峰值流速的测量具有高度可重复性,且与超声心动图的测量结果具有显著的一致性。

Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

To simulate the transonic atomization jet process in Laval nozzles,to test the law of droplet atomization and distribution,to find a method of supersonic atomization for dust-removing nozzles,and to improve nozzle efficiency,the finite element method has been used in this study based on the COMSOL computational fluid dynamics module.The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric,three-dimensional and three-dimensional symmetric models,but it can be calculated with the transformation dimension method,which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model.The visualization of this complex process,which is difficult to measure and analyze experimentally,was realized in this study.The physical process,macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation.The rationality of the simulation was verified by experiments.A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided,and a numerical platform for the study of supersonic atomization dust removal has been established.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

Numerical simulation on fluid flow behavior during 3-dimensional dendrite growth with random preference angle

The flow behavior of three-dimensional(3D)dendrite growth with random preferred angle under natural convection was studied by using the Lattice Boltzmann-Cellular Automata(LB-CA)method with dynamic and static grids.In this model,the temperature field,flow field and solute field calculated by Lattice Boltzmann method(LBM)and dendrite growth calculated by CA method were carried out in static and dynamic grids respectively,and the coupling between LBM and CA was performed by interpolation of calculation parameters between dynamic and static grids.Results show that the asymmetry of solid phase distribution makes the streamline distribution more complex.At the initial stage of multiple dendrites growth,the fluid flow is relatively free.When dendrites grow close to each other,the fluid flow is blocked and can only flow along the gap between dendrites.During the wall equiaxed-columnar-central equiaxed crystals transformation(ECET)process,dense eddy current is formed at the wall equiaxed crystals at first.Then,when the wall equiaxed crystals gradually develop into columnar crystals,the eddy current moves with the solid-liquid interface.When the central equiaxed crystals are formed,the eddy current at the front of the columnar crystals gradually disappears.New eddies appear as the central equiaxed crystal grows.

MHD three-dimensional flow of Jeffrey fluid with Newtonian heating

The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field.

基于4D Flow CMR技术评价心肌纤维化对肥厚型心肌病患者左室舒张功能障碍的影响

目的采用四维血流(four-dimensional flow,4D Flow)心脏磁共振成像(cardiac magnetic resonance,CMR)技术对肥厚型心肌病(hypertrophic cardiomyopathy,HCM)患者是否存在左心室舒张功能障碍进行评估,探讨心肌纤维化对HCM患者左心室舒张功能的影响。材料与方法前瞻性纳入44例HCM患者,根据患者是否合并晚期钆增强(late gadolinium enhancement,LGE)分为HCM LGE(+)组(25例)和HCM LGE(-)组(19例),同期纳入31例健康对照者。三组人群进行3.0 T磁共振稳态自由进动序列及4D Flow序列扫描。采用CVI42后处理软件进行分析,包括心功能参数、二尖瓣血流速度参数。使用单因素方差分析或Mann-Whitney U检验对三组受试者临床资料及影像学参数进行比较;并对二尖瓣水平舒张早期平均血流速度(E)与舒张期整体室壁峰值厚度(global peak wall thickness,GPWT)、左心室质量(left ventricular mass,LVmass)进行相关性分析。结果HCM患者的LVmass及GPWT均大于健康对照组,且伴有心肌纤维化较不伴有心肌纤维化的HCM患者的GPWT增大更加明显[HCM LGE(+)组vs.HCM LGE(-)组vs.健康对照组];[LVmass:157.34(122.24,194.38)g vs.148.29(131.79,189.83)g vs.85.73(73.00,94.02)g;GPWT:20.04(16.76,24.99)mm vs.17.46(16.19,19.99)mm vs.9.47(8.35,10.92)mm](P<0.001);伴有心肌纤维化的HCM患者舒张早期平均血流速度峰值(E峰)低于不伴有心肌纤维化的HCM患者,且均较健康对照组低[HCM LGE(+)组vs.HCM LGE(-)组vs.健康对照组:(30.03±11.33)cm/s vs.(38.05±12.03)cm/s vs.(47.44±10.82)cm/s](P<0.001);而舒张晚期平均血流速度峰值(A峰)在三组间均无显著性差异;且伴有心肌纤维化的HCM患者较健康对照组的E/A值明显减低(1.10±0.61 vs.1.74±0.85)(P<0.05)。舒张期早期二尖瓣水平的平均血流速度与GPWT和LVmass均呈负相关(r=-0.593/r=-0.371,P<0.001/P=0.001)。结论基于4D Flow CMR不仅可以从三维角度对血流速度进行准确测量,同时能从血流动力学方面定量评估HCM患者的左室舒张功能障碍及心肌纤维化对HCM患者左心室舒张功能的影响。

CHAOTIC MOTIONS AND LIMIT CYCLE FLUTTER OF TWO-DIMENSIONAL WING IN SUPERSONIC FLOW

Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.

Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate

In this communication a generalized three- dimensional steady flow of a viscous fluid between two infinite parallel plates is considered. The flow is generated due to uniform stretching of the lower plate in x- and y-directions. It is assumed that the upper plate is uniformly porous and is subjected to constant injection. The governing system is fully coupled and nonlinear in nature. A complete analytic solution which is uniformly valid for all values of the dimensionless parameters β Re and λ is obtained by using a purely analytic technique, namely the homotopy analysis method. Also the effects of the parameters β Re and λ on the velocity field are discussed through graphs.

Four-dimensional flow magnetic resonance imaging incirrhosis

Since its introduction in the 1970’s,magnetic resonance imaging(MRI)has become a standard imaging modality.With its broad and standardized application,it is firmly established in the clinical routine and an essential element in cardiovascular and abdominal imaging.In addition to sonography and computer tomography,MRI is a valuable tool for diagnosing cardiovascular and abdominal diseases,for determining disease severity,and for assessing therapeutic success.MRI techniques have improved over the last few decades,revealing not just morphologic information,but functional information about perfusion,diffusion and hemodynamics as well.Four-dimensional(4D)flow MRI,a time-resolved phase contrast-MRI with three-dimensional(3D)anatomic coverage and velocity encoding along all three flow directions has been used to comprehensively assess complex cardiovascular hemodynamics in multiple regions of the body.The technique enables visualization of 3D blood flow patterns and retrospective quantification of blood flow parameters in a region of interest.Over the last few years,4D flow MRI has been increasingly performed in the abdominal region.By applying different acceleration techniques,taking 4D flow MRI measurements has dropped to a reasonable scanning time of 8 to 12 min.These new developments have encouraged a growing number of patient studies in the literature validating the technique’s potential for enhanced evaluation of blood flow parameters within the liver’s complex vascular system.The purpose of this review article is to broaden our understanding of 4D flow MRI for the assessment of liver hemodynamics by providing insights into acquisition,data analysis,visualization and quantification.Furthermore,in this article we highlight its development,focussing on the clinical application of the technique.

One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient

Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.

TURBULENT SEPARATED REATTACHED FLOW IN A TWO-DIMENSIONAL CURVED-WALL DIFFUSER

A turbulent separation-rcattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter.The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel.At the inlet of the diffuser,Reynolds number based on the diffuser height is 1.2×10~5 and the velocity is 25.2m/s.The re- sults of experiments are presented and analyzed in new defined streamline-aligned coordinates.The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress.A scale is formed using the maximum Reynolds shear stresses.It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law ex- ists in the forward shear flow.Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model.The length scale is taken from that developed by Schofield and Perry.The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield Perry velocity scale as well as the edge velocity of the boundary layer.The results of these experiments are presented in this paper

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Real-time Three-Dimensional Color Doppler Flow Imaging： An Improved Technique for Quantitative Analysis of Aortic Regurgitation

The recently introduced real-time three-dimensional color Doppler flow imaging （RT-3D CDFI） technique provides a quick and accurate calculation of regurgitant jet volume （RJV） and fraction. In order to evaluate RT-3D CDFI in the noninvasive assessment of aortic RJV and regurgitant jet fraction （RJF） in patients with isolated aortic regurgitation, real-time three-dimensional echocardiographic studies were performed on 23 patients with isolated aortic regurgitation to obtain LV end-diastolic volumes （LVEDV）, end-systolic volumes （LVESV） and RJV, and then RJF could be calculated. The regurgitant volume （RV） and regurgitant fraction （RF） calculated by two-dimensional pulsed Doppler （2D-PD） method served as reference values. The results showed that aortic RJV measured by the RT-3D CDFI method showed a good correlation with the 2D-PD measurements （r= 0.93, Y=0.89X＋ 3.9, SEE= 8.6 mL, P〈0.001 ）; the mean （SD） difference between the two methods was - 1.5 （9.8） mL. % RJF estimated by the RT-3D CDFI method was also correlated well with the values obtained by the 2D-PD method （r=0.88, Y=0.71X＋ 14.8, SEE= 6.4 %, P〈0. 001）; the mean （SD） difference between the two methods was -1.2 （7.9） %. It was suggested that the newly developed RT-3D CDFI technique was feasible in the majority of patients. In patients with eccentric aortic regurgitation, this new modality provides additional information to that obtained from the two-dimensional examination, which overcomes the inherent limitations of two-dimensional echocardiography by depicting the full extent of the jet trajectory. In addition, the RT-3D CDFI method is quick and accurate in calculating RJV and RJF.

Three-dimensional boundary layer flow of Maxwell nanofluid:mathematical model

The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlin- ear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

In this paper,to simulate the three dimensional turbulent flow in suddenly expanded rectangular duct numerically,the SIMPLEC algorithm is employed to solve the incompressible Navier-Stckes equation with k-εturbulence model.The numerical resulis show well the three dimensional turbulent flow field in the rectangular duct behind the sudden expansion cross-section. and agree.fairly well with the experimental result of the length of the main circumfluence.The numerical method of this paper can be applied to numerical analysis of this kind of turbulent flow.

Three-dimensional cellular automata based particle flow simulations of mechanical properties of talus deposit

Based on three-dimensional cellular automata （CA）, a new stochastic simulation model to simulate the microstructures and particle flow of talus deposit is proposed. Ill addition, an auto-modeling program CARS is developed, with which nunaerical simulations can be conducted conveniently. For the problem of simulating mechanical behaviors of talus deposit, spatial anangement or sphere shapes should be considered. In the new modeling method, four sphere anangement models are developed for the particle flow simulation of talus deposit. Numerical results show that the talus deposit has the mechanical characteristics of typical stress-strain curves, as other rock-like materials. The cohesion of talus deposit decreases with increasing rock content, while the internal friction angle increases with increasing rock contents. Finally, numerical simulation is verified with the results of field test.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.

2023年SCMR 4D Flow心血管磁共振共识声明解读

血流动力学评估对于心血管疾病的诊断和治疗十分重要,四维心血管磁共振血流成像(four-dimensional cardiovascular magnetic resonance flow imaging,4D Flow CMR)可在一次采集中全面、准确地评估血流。2023年心血管磁共振学会(Society for Cardiovascular Magnetic Resonance,SCMR)在2015版4D Flow CMR共识声明的基础上更新发布了新版共识声明,为4D Flow CMR的采集参数的选择、后处理工作流程、整合入临床实践、推荐的出版标准提供建议,并定义了临床中心的最低质量保证和验证标准,以及对其局限性和未来展望进行讨论。笔者对新版共识声明进行解读与分析,旨在为未来4D Flow CMR广泛应用于临床及该领域研究方向提供参考。