Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme ( MILU-CG). The effects of surface suction or blowing' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.

NUMERICAL STUDY OF FLOW IN CONICAL DIFFUSER WITH VORTEX GENERATOR JETS

To develop vortex generator jet （VGJ） method for flow control, the turbulence flow in a 14° conical diffuser with and without vortex generator jets are simulated by solving Navier-Stokes equations with k-ε turbulence model. The diffuser performance, based on different velocity ratio （ratio of the jet speed to the mainstream velocity）, is investigated and compared with the experimental study. On the basis of the flow characteristics using computation fluid dynamics （CFD） method observed in the conical diffuser and the downstream development of the longitudinal vortices, attempt is made to correlate the pressure recovery coefficient with the behavior of vortices produced by vortex generator jets.

Steady vortex force theory and slender-wing flow diagnosis

The concept vortex force in aerodynamics is sys- tematically examined based on a new steady vortex-force theory （Wu et al., Vorticity and vortex dynamics, Springer, 2006） which expresses the aerodynamic force （and moment） by the volume and boundary integrals of the Lamb vector. In this paper, the underlying physics of this theory is explored, including the general role of the Lamb vector in non- linear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerody-namic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.

INVESTIGATION OF DOMINANT FREQUENCIES IN TRANSITION REYNOLDS NUMBER RANGE OF FLOW AROUND A CIRCULAR CYLINDER PARTⅡ: THEORETICAL DETERMINATION OF THE RELATIONSHIP BETWEEN VORTEX SHEDDING AND TRANSITION FREQUENCIES AT DIFFERENT REYNOLDS NUMBERS

An attempt has been made to explore whether the power relation can be obtained from theoretical considerations. The classical laminar and turbulent boundary layer concepts have been employed to determine appropriate values of the scaling lengths associated with vortex shedding and shear layer frequencies to predict the power law relationship with Reynolds number. The predicted results are in good agreement with experimental results. The findings will provide a greater insight into the overall phenomenon involved.

INVESTIGATION OF VORTEX SHEDDING INDUCED HYDRODYNAMIC VIBRATION IN VORTEX STREET FLOWMETER

Vortex street flowmeter has been used in steady flow measurement for about three decades The benefits of this type of flowmeter include high accuracy,good linearty,wide measuring range,and excellent reliability However,in unsteady flow measurement,the pressure disturbance as well as the noise from the system or surrounding can reduce the signal to noise ratio of the flowmeter seriously Aimed to use vortex street flowmeters in unsteady flow measurement,the characteristics of the vortex shedding induced hydrodynamic vibration around the prism bluff body in a vortex street flowmeter are investigated numerically and by expriments The results show that the hydrodynamic vibrations with 180° phase shift occur at the axisymmetric points of the channel around the bluff body The most intense vibration occurs at the points on the lateral faces close to the base of the prism The results provide therefore a useful reference for developing an anti interference vortex flowmeter using the different ial sensing technique.

Discussion on Stability Criterion of Inviscid Compressible Swirling Flow

The stability condition for compressible and incompressible swirling flow is discussed and compared. It is found that Eckhoff and Storesletten's necessary condition for stability of inviscid compressible swirling flow seems incorrect.

NUMERICAL INVESTIGATION OF THE MECHANISM OF ASYMMETRIC VORTEX FLOWS

A robust iterative method suitable for the numerical simulation of high angle-of-attack vortex flows is established based upon the multiple line-vortex model(MLVM).With symmetric or asymmetric positions of sep- aration lines given,the first converged solution at an angle of attack as high as 60 degree is obtained by means of the present method.Numerical experiments for a tangent-ogive forebody indicate the viscous onset mechanism of asymmetric vortex flows over a body of revolution at high angles of attack and zero sideslip.

Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)──Theory

The stability of inviscid incompressible swirling flow with slowly divergence is investigated A multiple scale expansion is used to develop a linear stability study of slowly divergent swirling flow with non-axisymmetric disturbances The differental equations of zero-order and first-order disturbance module and governing equation of amplitude variation due to slowly divergent flow are derved The plaschko s equation for slowly divergent swirl-free jet has been extended to slowly divergent flow with swirlin the present study.

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

Receptivity of plane Poiseuille flow to local micro-vibration disturbance on wall

The receptivity of plane Poiseuille flow to local single-period micro-vibration disturbances with different phases at the top and bottom walls was investigated through direct numerical simulation of three-dimensional incompressible Navier-Stokes equations. Results show that the disturbance presents a symmetrical distribution in the spanwise direction when the micro-vibration on the wall ends, and the initial disturbance velocities and spatial distribution of the disturbance structure are different at the top and bottom walls. The disturbance＇s velocity, amplitude, and high- and low-speed streaks increase with time, and the amplitude of streamwise disturbance velocity is larger than those of spanwise and vertical disturbance velocities. However, no significant Tollmien-Schlichting wave was found in the flow field. The number of disturbance vortex cores gradually increases with the disturbance area. High-speed disturbance fluid concentrates near the wall and its normal velocity largely points to the wall, while low-speed disturbance fluid largely deviates from the wall. Furthermore, the streamwise velocity profiles near the top and bottom walls both become plump because of the existence of the disturbances, and the streamwise velocity profiles show a trend of evolving into turbulent velocity profiles. The shear stress near the wall increases significantly. The local micro-vibration disturbance on the wall in plane Poiseuille flow can induce the development of a structure similar to turbulent spots.

Research on Capture Performance of an Induction Type Microplastics Recovery Device

Microplastic wastes in ocean can include the harmful chemical material, and the harmful material is concentrated by marine species. The separation and collecting methods of microplastics in ocean are researched in the world. The authors proposed the microplastics recovery device composed of the plates. Besides, the device consists of the tilted inlet/outlet and the horizontal part. In the water flow such as the tidal and ocean currents, the microplastics can be extracted from the main flow due to the vortex flow generated at the inner part of this device. In this research, the effects of the flow velocity and the inlet/outlet tilt angle on the capture performance were investigated experimentally and numerically. In the numerical simulations using the discrete phase model, the tilt angle was changed in a range between 30 degrees and 150 degrees in increments of 15 degrees, and the particle tracks of plastics were derived in steady condition. On the other hand, the capture performances in three cases of tilt angle 45 degrees, 120 degrees and 150 degrees were compared by circulation type water channel tests in which the plastics denser than the water were swept away 30 times every flow velocity. As the result, it seems that the tilt angle of 120 degrees is suitable for the wide range of the flow velocity in river and ocean.

Numerical Wave Flume Study on Wave Motion Around Submerged Plates

Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.

Analysis of the operating parameters of a vortex electrostatic precipitator

A vortex electrostatic precipitator （VEP） forms a vortex flow field within a precipitator by means of the vertical staggered layout of the double-vortex collecting plate facing the direction of the gas flow. The ion concentrations within the precipitator can be significantly increased. Correspondingly, the charging and coagulation rates of fine particles and particle migration velocity are significantly improved within the VEP. Since it can effectively collect fine particles and reduce precipitator size, VEPs represent a new type of electrostatic precipitator with great application potential. In this work the change curve of the external voltage, gas velocity, row spacing and effective collecting area influencing the precipitation efficiency were acquired through a single-factor experiment. Using an orthogonal regression design, attempts were made to analyze the major operating parameters influencing the collecting efficiency of fine particles, establish a multiple linear regression model and analyze the weights of factors and then acquire quantitative rules relating experimental indicators and factors. The regression model was optimized by MATLAB programming, and we then obtained the optimal factor combination which can enhance the efficiency of fine particle collection. The final optimized result is that： when gas velocity is 3.4 m s-1, the external voltage is 18 kV, row spacing is 100 mm and the effective collecting area is 1.13 m2, the rate of fine particle collection is 89.8867%. After determining and analyzing the state of the internal flow field within the VEP by particle image velocimetry （PIV）, the results show that, for a particular gas velocity, a vortex zone and laminar zone are distinctly formed within the VEP, which increases the ion transport ratio as well as the charging, coagulation and collection rates of fine particles within the precipitator, thus making further improvements in the efficiency of fine particle collection.

Simulation of the plasticizing behavior of composite modified doublebase(CMDB)propellant in grooved calendar based on adaptive grid technology

The frequent occurrence of safety accidents during the calendering process is caused by the flammable and explosive properties of composite modified double-base(CMDB)propellant.Optimization of process parameters with the aid of fluid simulation technology could effectively ensure the safety of the calendering process.To improve the accuracy of the simulation results,material parameters and model structure were corrected based on actual conditions,and adaptive grid technology was applied in the local mesh refinement.In addition,the rheological behavior,motion trajectories and heat transfer mechanisms of CMDB propellant slurry were studied with different gaps,rotational rates and temperatures of two rollers.The results indicated that the refined mesh could significantly improve the contour clarity of boundaries and simulate the characteristics of CMDB propellant slurry reflux movement caused by the convergent flow near the outlet.Compared with the gap,the increased rotational rate of roller could promote the reflux movement and intensify the shear flow of slurry inside the flow region by viscous shear dragging.Meanwhile,under the synergistic effect of contact heat transfer as well as convective heat exchange,heat accumulated near the outlet and diffused along the reflux movement,which led to the countercurrent heat dissipation behavior of CMDB propellant slurry.The plasticizing mechanism of slurry and the safety of calendering under different conditions were explored,which provided theoretical guidance and reference data for the optimization of calendering process conditions.Based on the simulation results,the safety of the CMDB propellant calendering process could be significantly improved with a few tests conducted during a short research and development cycle.

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.

Measurement of surface shear stress vector distribution using shear-sensitive liquid crystal coatings

The global wall shear stress measurement tech- nique using shear-sensitive liquid crystal （SSLC） is extended to wind tunnel measurements. Simple and common every- day equipment is used in the measurement; in particular a tungsten-halogen light bulb provides illumination and a saturation of SSLC coating color change with time is found. Spatial wall shear stress distributions of several typical flows are obtained using this technique, including wall-jet flow, vortex flow generated by a delta wing and junction flow behind a thin cylinder, although the magnitudes are not fully calibrated. The results demonstrate that SSLC technique can be extended to wind tunnel measurements with no complicated facilities used.

Tomographic PIV investigation on coherent vortex structures over shark-skin-inspired drag-reducing riblets

Nature has shown us that the microstructure of the skin of fast-swimming sharks in the ocean can reduce the skin friction drag due to the well-known shark-skin effect.In the present study,the effect of shark-skin-inspired riblets on coherent vortex structures in a turbulent boundary layer（TBL） is investigated.This is done by means of tomographic particle image velocimetry（TPIV） measurements in channel fl ws over an acrylic plate of drag-reducing riblets at a friction Reynolds number of 190.The turbulent fl ws over drag-reducing riblets are verifie by a planar time-resolved particle image velocimetry（TRPIV） system initially,and then the TPIV measurements are performed.Two-dimensional（2D） experimental results with a dragreduction rate of around 4.81% are clearly visible over triangle riblets with a peak-to-peak spacing s＋of 14,indicating from the drag-reducing performance that the buffer layer within the TBL has thickened;the logarithmic law region has shifted upward and the Reynolds shear stress decreased.A comparison of the spatial topological distributions of the spanwise vorticity of coherent vortex structures extracted at different wall-normal heights through the improved quadrant splitting method shows that riblets weaken the amplitudesof the spanwise vorticity when ejection（Q2） and sweep（Q4） events occur at the near wall,having the greatest effect on Q4 events in particular.The so-called quadrupole statistical model for coherent structures in the whole TBL is verified Meanwhile,their spatial conditional-averaged topological shapes and the spatial scales of quadrupole coherent vortex structures as a whole in the overlying turbulent fl w over riblets are changed,suggesting that the riblets dampen the momentum and energy exchange between the regions of near-wall and outer portion of the TBL by depressing the bursting events（Q2 and Q4）,thereby reducing the skin friction drag.

COMPUTATIONAL AND EXPERI-MENTAL STUDY ON TIP LEAKAGE VORTEX OF CIRCUMFERENTIAL SKEWED BLADES

In the steady operation condition, the experiments and the numerical simulations are used to investigate the tip leakage flow fields in three low pressure axial flow fans with three kinds of circumferential skewed rotors, including the radial rotor, the forward-skewed rotor and the back- ward-skewed rotor. The three-dimensional viscous flow fields of the fans are computed. In the experiments, the two-dimensional plane particle image velocimetry （PIV） system is used to measure the flow fields in the tip region of three different pitchwise positions of each fan. The results show that the computational results agree well with the experimental data in the flow field of the tip region of each fan. The tip leakage vortex core segments based on method of the eigenmode analysis can display clearly some characteristics of the tip leakage vortex, such as the origination position of tip leak- age vortex, the development of vortex strength, and so on. Compared with the radial rotor, the other two skewed rotors can increase the stability of the tip leakage vortex and the increment in the forward-skewed rotor is more than that in the backward-skewed one. Among the tip leakage vortices of the three rotors, the velocity of the vortex in the forward-skewed rotor is th6 highest in the circumferential direction and the lowest in the axial direction.