Determination of the shedding frequency of cavitation cloud in a submerged cavitation jet based on high-speed photography images

To accurately determine the shedding frequency of the cavitation cloud in a submerged cavitation jet,the spectral analysis and the proper orthogonal decomposition(POD)for high-speed photography images are performed.The spectrums of 6 different kinds of image signals(the area-averaged gray level,the line-averaged gray level,the point gray level,the cavitation length,width,and area)are calculated and compared.The line-averaged gray level is found to be optimal in determining the shedding frequency but an accurate frequency can only be obtained in the stable-frequency zone where the cavitation cloud sheds.In repeated experiments,the plateau-shape distribution of the main frequency is established with a deviation of 10.8%.A revised Reynolds number Re'is defined and the shedding frequency can be correlated to Re'by a power law when the cavitation number is less than 0.02.This relationship is validated by the experimental data in literature.The first mode of the POD characterizes the ensemble-average of the cavitation cloud while the second mode is the major part of the cavitation cloud transient components.The modes 2-5 are organized in pairs,which confirms the periodic feature of the cavitation cloud in the submerged cavitation jet.Near the nozzle exit,the modes 2-5 are symmetrically distributed in the jet shear layer.The shedding frequency of the cloud cavitation can also be precisely determined by performing the spectral analysis of the weighting coefficients of the mode 2.This paper shows that the two parameters,namely,the line-averaged gray level and the weighting coefficients of the mode 2,can be confidently used to calculate the shedding frequency of the cavitation cloud in a submerged cavitation jet.

VORTEX SHEDDING FREQUENCY DETERMINED BY SURFACE PRESSURE FLUCTUATIONS OF THREE EQUISPACED CYLINDERS

In his paper, the frequency of vortex shedding from three cylinders of the same diameter in equilateral triangular arrangement is determined experimentally by the spectrum analysis of surface pressure fluctuations at a Reynolds number of 3.0×10 4. For α=0°, there exists ‘bistable’ flow at the spacing 2.0. For α=30°, the vortex shedding of the front cylinder is found at small spacing less than 2.0. It is quite different from the case of two cylinders in tandem arrangement only. The side cylinder has great effects on the flow between the other two cylinders in close arrangement. For α=60°, there exists a critical spacing of about 2.5 that the frequency of each cylinders is nearly half of f s below this spacing and equal to f s above it respectively. The interference among three cylinders was negligible in the spacing range above 3.0 at α=0 and 60 deg., and each cylinder behaves as a single cylinder with the same vortex shedding frequency f s. In these small spacing (spacing<3.0), interference occurs seriously and has great effects in a complex fashion on the flow state around three cylinders.

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.

Hierarchical under frequency load shedding scheme for inter-connected power systems

Severe disturbances in a power network can cause the system frequency to exceed the safe operating range.As the last defensive line for system emergency control,under frequency load shedding(UFLS)is an important method for preventing a wide range of frequency excursions.This paper proposes a hierarchical UFLS scheme of“centralized real-time decision-making and decentralized real-time control”for inter-connected systems.The centralized decision-layer of the scheme takes into account the importance of the load based on the equivalent transformation of kinetic energy(KE)and potential energy(PE)in the transient energy function(TEF),while the load PE is used to determine the load shedding amount(LSA)allocation in different loads after faults in real-time.At the same time,the influence of inertia loss is considered in the calculation of unbalanced power,and the decentralized control center is used to implement the one-stage UFLS process to compensate for the unbalanced power.Simulations are carried out on the modified New England 10-generator 39-bus system and 197-bus system in China to verify the performance of the proposed scheme.The results show that,compared with other LSA allocation indicators,the proposed alloca-tion indicators can achieve better fnadir and td.At the same time,compared with other multi-stage UFLS schemes,the proposed scheme can obtain the maximum fnadir with a smaller LSA in scenarios with high renewable energy sources(RES)penetration.

How Do Water Filled Traffic Barriers Shake a Suspension Bridge?

The present study stems from the realization that the general problem relating to the analysis of wind-induced vibrations in suspension bridges still requires significant attention.Sidewalk railings,overhaul tracks,and deflectors are known to largely affect such dynamics.Here,the influence of a row of water-filled traffic barriers on the response of a sample suspension bridge is investigated numerically.It is shown that the existence of water barriers causes flow separation and non-negligible vortices with respect to the condition with no water barriers.The vortex shedding frequency at the far end is around 41.30 Hz,relatively close to the real vibration frequency.It is also shown how different incoming angles of attack can change the flow field around the bridge cross-section and the vortex detachment frequency.

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.

Vortex shedding in the flow around two side-by-side circular cylinders of different diameters

In this paper,the 3-D turbulent flow around two side-by-side circular cylinders of different diameters,at sub-critical Reynolds number（Re=3 900）,is numerically simulated by the large eddy simulation（LES）.The spacing ratios（T/D）between the two cylinders are considered in four cases（T/D=1.2,1.5,1.8 and 2.7）to study the vortex shedding and turbulent properties in the flow field.The main results are focused on the drag and lift coefficients,the vortex shedding frequency,the coherent structure,and the scale properties.It is shown that when T/D is equal to 1.2,the vortex shedding of the main cylinder is strongly suppressed by the small cylinder,the drag and lift coefficients of the main cylinder are smaller than those in other three cases.While T/D is equal to 1.5,the vortex shedding of the main cylinder can be improved,the drag and lift coefficients of the main cylinder are larger than those in other three cases.The empirical mode decomposition（EMD）method is applied to decompose the velocity signals traced by the LES.It is shown that there is a linear relationship between the mean period and the mode in the semi-log coordinates.The vortex shedding period of the main cylinder is consistent with the period of the restructured coherent structures quantitatively.