Numerical Investigation of the Unsteady Flow in a Transonic Compressor with Curved Rotors

The unsteady 3D flow fields in a single-stage transonic compressor under designed conditions are simulated numerically to investigate the effects of the curved rotors on the stage performance and the aerodynamic interaction between the blade rows. The results show that, compared to the compressor with unurved rotors, the compressor under scrutiny acquires remarkable increases in efficiency with significantly reduced amplitudes of the time-dependent fluctuation. The amplitude of the pressure fluctuation around the stator leading edge decreases at both endwalls, but increases at the mid-span in the curved rotors. The pressure fluctuation near the stator leading edge, therefore, becomes more uniform in the radial direction of this compressor. Except for the leading edge area, the pressure fluctuatinn amplitude declines remarkably in the tip region of stator surface downstream of the curved rotor, but hardly changes in the middle and at the hub.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

Gridless Solution Method for Two-Dimensional Unsteady Flow

The main purpose of this paper is to develop a gridless method for unsteady flow simulation. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. A point-moving algorithm is introduced to ensure the clouds of points following the movements of bodyboundaries. A dual time method for solving the two-dimenslonal Euler equations in Arbitrary Lagrangian-Eulerian （ALE） formulation is presented. Dual time method allows the real-time step to be chosen on the basis of accuracy rather than stability. It also permits the acceleration techniques, which are commonly used to speed up steady flow calculations, to be used when marching the equations in pseudo time. The spatial derivatives, which are used to estimating the inviscid flux, are directly approximated by using local least-squares curve method. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in pseudo time. In order to accelerate the solution to convergence, local time stepping technique and residual averaging are employed. The results of NACA0012 airfoil in transonic steady flow are presented to verify the accuracy of the present spatial discretization method. Finally, two AGARD standard test cases in which NACA0012 airfoil and NACA64A010 airfoil oscillate in transonic flow are simulated. The computational results are compared with the experimental data to demonstrate the validity and practicality of the presented method.

An SOR Implicit Time-accurate Scheme in Calculating Unsteady Flows

A new time-accurate marching scheme for unsteady flow calculations is proposed in the present work. This method is the combination of classical Successive Over-Relaxation （SOR） iteration method and Jacobian matrix diagonally dominant splitting method of LUSGS. One advantage of this algorithm is the second-order accuracy because of no factorization error. Another advantage is the low computational cost because the Jacobian matrices and fluxes are only calculated once in each physical time step. And, the SOR algorithm has better convergence property than Gauss-Seidel. To investigate its accuracy and convergency, several unsteady flow computational tests are carded out by using the proposed SOR algorithm. Roe＇s FDS scheme is used to discritize the inviscid flux terms. Unsteady computational results of SOR are compared with the experiment results and those of Gauss-Seidel, Results reveal that the numerical results agree well with the experimental data and the second-order accuracy can be obtained as the Gauss-Seidel for unsteady flow computations. The impact of SOR factor is investigated for unsteady computations by using different SOR factors in this algorithm to simulate each computational test. Different numbers of inner iterations are needed to converge to the same criterion for different SOR factors and optimal choice of SOR factor can improve the computational efficiency greatly.

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.

Computation of Unsteady Flow Past a Biomimetic Fin

The unsteady hydrodynamics of a biomimetic fin attached to a cylindrical body has been studied numerically using a computational fluid dynamic (CFD) simulator based on an in-house solver of the Navier-Stokes equations, combined with a recently developed multi-block, overset grid method. The fin-body CFD model is based on a mechanical pectoral fin device, which consists of a cylindrical body and an asymmetric fin and can mimic flapping, rowing and feathering motions of the pectoral fins in fishes. First the multi-block, overset grid method incorporated into the NS solver was verified through an extensive study of unsteady flows past a single fin undergoing rowing and feathering motion. Then unsteady flows past the biomimetic fin-body model undergoing the same motions were computed and compared with the measurements of forces of the mechanical pectoral fin, which shows good agreement in both time-varying and time-averaged hydrodynamic forces. The relationship between force generation and vortex dynamics points to the importance of the match in fin kinematics between power and recovery strokes and implies that an optimal selection of parameters of phase lags between and amplitudes of rowing and feathering motions can improve the performance of labriform propulsion in terms of either maximum force generation or minimum mechanical power.

Boundary Element Analysis (Laplace Transform Solution) of Groundwater Unsteady Flow to a Multiple Well System in a Confined Aquifer

The calculations of unsteady flow to a multiple well system with the application of boundary elementmethod (BEM) are discussed. The mathematical model of unsteady well flow is a boundary value problem ofparabolic differential equation. It is changed into an elliptic one by Laplace transform to eliminate time varia-ble. The image function of water head H can be solved by BEM. We derived the boundary integral equation ofthe transformed variable H and the discretization form of it, so that there is no need to discretize the bounda-ries of well walls and it becomes easier to solve the groundwater head H by numerical inversion.

Experimental Study on Calculation of Hydro-Geological Parameters for Unsteady Flow

After the linear analytical method of unsteady flow theory is further improved,an innovative and faster algorithm is introduced.The water storage in a confined aquifer is derived from the water transmissivity coefficient and the water-pressure conductivity coefficient.The water transmissivity coefficient is approximated by a Taylorseries expansion of drawdown,and the water-pressure conductivity coefficient is obtained by the average drawdown.In this algorithm,the distance of the observation points from the pumping well must be short.When the distance is as short as the radius of the main pumping well,the data of the drawdown difference between the sidewall and the center of pumping well are difficult to measure,but the same results can be achieved based on the assumption that the drawdown difference approximates to the drawdown of the observation wells at a radial distance from the pumping well according to the algorithm.Without the help of charts,this algorithm is more concise and efficient,which has been verified by the test of water pumping project in Tianjin Binhai International Airport.

Unsteady Flow Simulations in a Three-lobe Positive Displacement Blower

To improve the performance of the positive displacement blower, it is imperative to understand the detailed internal flow characteristics or enable a visualization of flow status. However, the existing two-dimensional unsteady, three-dimensional steady or quasi-unsteady numerical simulation and theoretical analysis cannot provide the detailed flow information, which is unfavorable to improve the performance of positive displacement blower. Therefore, the unsteady flow characteristics in a three-lobe positive displacement blower are numerically investigated by solving the three-dimensional, unsteady, compressible Navier-Stokes equations coupled with RNG k-e turbulent model. In the numerical simulation, the dynamic mesh technique and overset mesh updating method are adopted. Due to the air being compressed in the process of the rotors rotating, the variation of the temperature field in the positive displacement blower is considered. By comparing the experimental measurements and the numerical results on the variation of flow rate with the outlet pressure, the maximum relative error of the flow rate is less than 2.15% even at the maximum outlet pressure condition, which means that the calculation model and numerical computational method used are effective. The numerical results show that in the intake region, the fluctuations of the inlet flow are greatly affected by the direction of the velocity vectors. In the exhaust region, the temperature changes significantly, which leads to the increase of the airflow pulsation. Through analysis on the velocity, pressure and temperature fields obtained from the numerical simulations, three-dimensional unsteady flow characteristics in the positive displacement blower are revealed. The studied results will provide useful reference for improving the performance and empirical correction in the design of the positive displacement blower.

The Vibration Controllability of 20~# Steel Pipe Excited by Unsteady Flow

An excited experiment system of 20# steel pipe was established with oil cylinder, 20# steel pipe, frequency converter, pump station and wave exciter generating unsteady flow artificially. The experimental results showed that the 20# steel pipe could vibrate with the excitation of unsteady flows, and the vibration was periodic, instead of a harmonic one. Particles on the front and rear positions of pipe vibrated synchronously, and the vibration intensity of the pipe＇s two ends was greater than in the middle. System pressure and wave exciter＇s frequency had much influence upon pipe＇s amplitude. Pipe＇s vibration frequency was little affected by system pressure, and its value was close to the wave exciter＇s. Therefore, the active control of pipe＇s vibration can be realized by setting system pressure and adjusting frequency converter＇s frequency.

Computational fluid dynamics of left ventricular assist device under unsteady flow

Left ventricular assist device( LVAD) in this study is a mechanical tool that is used to support blood flow in the patient with heart disease. It supports left ventricle by building up the pressure to the pump outlet connected to the aorta. This pump was designed based on the magnetic driven centrifugal pump with a unique small washout hole constructed inside the impeller to generate the washout flow passage to prevent the stagnation at the region underneath and around the rotor. Computational fluid dynamics( CFD) was adopted in this study to assess the performance and optimize the design to avoid recirculation and high shear stress which is the main cause of stagnation and blood damage. Transient simulation was used for this study due to the asymmetric design of the washout hole and the complication of the bottom support of the impeller that has a risk of thrombosis,also,it was used to predict the variation of hydraulic performance caused by the rotation of the impeller and pulsed flow at the pump inlet. The simulation results show no excessive stress and no recirculation observed within the computational domain; in addition,the research result also provides information for further optimization and development to the pump.

LES Analysis of the Unsteady Flow Characteristics of a Centrifugal Pump Impeller

Stall phenomena increase the complexity of the internal flow in centrifugal pump impellers.In order to tackle this problem,in the present work,a large eddy simulation(LES)approach is applied to determine the characteristics of these unstable flows.Moreover,a vorticity identification method is used to characterize quantitatively the vortex position inside the impeller and its influencing area.By comparing the outcomes of the numerical simulations and experimental results provided by a Particle Image Velocimetry(PIV)technique,it is shown that an apparent“alternating stall”phenomenon exists inside the impeller when relatively small flow rate conditions are considered.The stall is generated near the suction side of the blade inlet,grows towards the high-pressure side of the blade in the circumferential direction,and gradually attenuates.As the flow rate decreases,the number of stalls remains unchanged,while the related influencing area and strength gradually increase and the circumferential velocity increases.

THEORETICAL DISCUSSION ON UNSTEADY FLOW OF FLUID DURING METAL ATOMIZATION

The expressions of fluid velocity under several conditions during gas atomization according to the unsteady flow mechanics are propsed, and the basic ways to maintain the stability of fluid flow is analyzed

NUMERICAL SIMULATION OF UNSTEADY FLOW AROUND A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS

A Lagrangian-Eulerian hybrid scheme to solve unsteady N-S equation in two-dimensional incompressible fluid at high Reynolds numbers is presented in this paper. A random walk is imposed to simulate the viscous diffusion, the vortex-in-cell method is used to obtain the convection velocity, and nascent vortices are created on a cylinder to satisfy the zero-slip condition. The impulsively started flow around a circular cylinder and the separation induced by a pair of incident vortices symmetrically approaching a circular cylinder have been successfully simulated by the hybrid scheme. The impulsively started flow from rest has been computed at Reynolds numbers 3000 and 9500. Comparisons are made with those results of finite-difference method, vortex method and flow visualization. Agreement is good. The particular attention has been paid to the evolutions of flow pattern. A topological analysis has been proposed in the region of the near wake. The bulge, isolated secondary vortex, a pair of secondary vortices, ' forewake phenomenon and other patterns are simulated numerically. The separation induced by a pair of incident vortices approaching a circular cylinder has been investigated by using the same scheme. The rebounding phenomenon of the incident vortex is observed and is attributed to the effect of the secondary vortex. In particular, we have found that a tertiary vortex can be formed near the surface; this phenomenon has been verified by flow visualization reported recently.

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

ANALYTICAL SOLUTIONS FOR EQUATIONS OF UNSTEADY FLOW OF NON-NEWTONIAN FLUIDS IN TUBE

This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.

Developing Spline Based Overset Grid Assembling Approach and Application to Unsteady Flow Around a Moving Body

Overset or Chimera grid approach is one of methods to cope with complex geometries. A spline based overset grid assembling system has been developed. The system is based on structured grid approach and covers comprehensive features for overset assembling, i.e., grid generation, grid modification, and computing Domain Connectivity Information （DCI） for overset interpolation. Ferguson spline curve is used to compute curves through grid points and cell centers for trimming grids and computing DCI robustly and accurately. Flow simulation around Kriso Container Ship （KCS） with jointed grids shows good continuity of flow field between the grids. The overset grid assembling is enhanced to unsteady problem as dynamic overset approach coupled with a solver which also has been developed in National Maritime Research Institute, Japan. Computed results for pitchup spheroid are compared with measured data and show good agreement in unsteady force acting on the spheroid. It is confirmed that the system has capability to simulate flow field around jointed grids and unsteady flow with dynamic overset assembling approach practically.

UNSTEADY FLOW ANALYSIS IN A CROSS-FLOW FAN WITH A CASING

A numerical analysis method has been developed for the prediction of the flow in across-flow fan with a casing. The method has no simplifying assumptions regarding the geometryof both the impeller blades and the casing Taking into consideration the effect of the boundarylayer on the upper wall surface of the casing, the internal flow is analyzed using both the directboundary element method and the discrete vortex method by assuming that the flow istwo-dimensional. inviscid and incomtressible. In order to satisfy Kelven's theorem, vorticity is sh-ed at the trailing edges of each impeller blade, then the discrete vortex method is used to approxi-mate the convection of the free vorticity. Results are giver for the cross-flow fan with two differ-ent configurations of the casing with an dentical impeller.

DISCONTINUITY-CAPTURING FINITE ELEMENT COMPUTATION OF UNSTEADY FLOW WITH ADAPTIVE UNSTRUCTURED MESH

A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows,which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular,a new testing variable,i.e.,the disturbed kinetic energy E,is suggested and used in the adaptive mesh computation,which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number.Based on several calculated examples,this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.