VIBRATING VELOCITY RECONSTRUC-TION USING IBEM AND TIKHONOV REGULARIZATION

The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate solution possible, the indirect boundary element method(IBEM) code for investigating vibration velocity reconstruction and Tikhonov regularization methodby means of singular value decomposition (SVD) are used. The amount of regularization is determinedby a regularization parameter. Its optimal value is given by the L-curve approach. Numerical resultsindicate the reconstructed normal surface velocity is a good approximation to the real source.

Structure normal velocity reconstruction withsparse measurement points

To achieve normal velocity reconstruction of a vibrating surface with sparse mea- surement points, a reconstruction method is proposed by exploiting of acoustic radiation modes as expansion functions, which are capable of describing the geometric shape of a vibrating surface. Firstly, acoustic radiation modes of the vibrating surface are calculated and the rela- tionship between normal velocity and acoustic radiation modes is built. Then actual measured normal velocity values are expressed by corresponding acoustic radiation modes and the expan- sion coefficients are calculated. Subsequently, all normal velocity values can be reconstructed by the obtained expansion coefficients. Experimental validations have been performed by a double-layer steel cylindrical shell with enclosed ends in an anechoic water tank. Two cases with different wavenumber components distribution were designed by a vibration shaker and a rotor device respectively. Two experimental results both show that actual vibration distribution cannot be revealed exactly by the sparse measurement points, which corresponds to severe loss of vibration related wavenumber components. On the other hand, normal velocity and corresponding wavenumber components can be restored accurately in both two wavenumber components distribution cases according to the proposed method, which demonstrates obvious effectiveness of the proposed method.

A Study of the Velocity Field of Liquid Sodium in a Toroidal Channel

The velocity field of liquid sodium in a toroidal channel is studied.Velocity measurements are made using the magnetic induction method.The proposed technique involves two steps:an external alternating magnetic field of certain frequency is induced in the channel;then the measurements of the resulting magnetic field are used to reconstruct the velocity profile.

Characterization of gas-liquid-solid fluidized beds by S statistics

The hydrodynamics of a gas-liquid-solid fluidized bed was investigated by applying the S statistics method to pressure fluctuations measured under various operating conditions in a laboratory-scale bed. S statistics tests reveal the existence of three transition velocities, especially at low gas velocities. Four distinct fluidization regimes, namely, the compacted bed, agitated bed and coalesced and discrete bubble regimes were detected. A comparison of reconstructed attractors of pressure fluctuations measured at different axial positions along the riser and with various solid loadings showed significant differences in the signals compared before fluidization, especially at minimum liquid agitation velocity. Close to the minimum liquid fluidization velocity and high liquid velocities, the variation in particle size has an insignificant effect on the bed hydrodynamics. Therefore, S statistics is a reliable method to demar- cate different fluidization regimes and to characterize the influence of various operating conditions on the hydrodynamics of gas-liquid-solid fluidized beds. The method is applicable in large-scale industrial installations to detect dynamic changes within a bed, such as regime transitions or agglomeration.