Researches On The Characteristics Of High-Velocity Flow And Flow-Induced Vibration Based On Chaotic Theory

The phenomenons of high-velocity flow (HVF) and flow-induced vibration (FIV) are common and important problems in the field of water resources and hydropower engineering. In the building of projects with high water head and large flow, It’s easy to make the HVF and FIV harmful phenomenons if we don’t take care of in the course of design, construction, operation and management. Given this, it’s very necessary to study the phenomenons of HVF and FIV. Researching on these two aspects, it has accumulated rich achievements and experience at home and abroad. But these achievements and experience vast majority are in engineering sense, which means the test data analysis and numerical simulation are both based on the theory of Reynolds number average thinking. Although this kind of treatment method can satisfy the engineering demand in a certain extent, it ignores the complex regularity which are contained in the phenomenons of HVF and FIV. So it’s very necessary to introduce the chaotic theory into the research of HVF and FIV. This theory returns to the nature sources of turbulent flow and fluid-solid coupling in the research of turbulence and vibratio, which is a new idea. The idea can provide certain theory to project planner, which can help them to comprehend the complexity in the phenomenons of HVF and FIV preferably. So it’s of a great significance.The paper firstly studies the impact of boundary conditions on gate vibration, then based on the chaotic theory and measured data in the model test, the paper studies the complexity law of fluctuating pressure and vibration acceleration in HVF under four specific situations which are slit-type energy dissipater, step energy dissipater, stilling pool dissipation of underflow and FIV in bulkhead gate. Meanwhile, the paper reveals chaotic characteristics in phenomenons of HVF and FIV.This study used the deep-hole bulkhead gate of Longkaikou hydropower station as research object to evaluate the effect of boundary support conditions and fluid-solid interaction on the characteristics of natural vibration by means of constraint stiffness variation and added mass using Block Lanczos modal analysis. Results showed that the variation of forward flow, transverse and vertical constraint stiffness is substantially effective on the characteristics of natural vibration in a certain range. Its rule is in accordance with the rule of transverse vibration of rectangle thin plate. The natural frequencies are closely related to the restraints of the modal vibration direction, and have nothing to do with other directions. Therefore, the corresponding direction of vibration modes can be obtained by analysing the rule of gate’s natural frequency changing with the restraints. In considering the effect of fluid-solid interaction, water in front of the gate is simulated by added mass, the result shows that the impact created by upstream water level changing within a certain range on gate’s natural frequency can be neglected, and therestraints have a relatively small impact.Then, in the chaotic characteristic analysis of the experimental data measured from four various model experiments, it could generally get the following two conclusions:(1) Overall, it was entirely feasible to adopt the Principal Component Analysis method and 0-1 test method when initially discriminated chaotic characteristics of data time series. Moreover, the two methods were with simple concept, strong operability and visually effective discriminated method. However, they could qualitatively discriminate whether the time series was of chaotic characteristics, not to quantitatively distinguish the intensity differences of chaotic degree.(2) Using Cao method to calculate the embeddingdimension of phase space reconstruction, studies found that the measured data contains a certain level of noise, which might affect the recurrence of chaotic attractors and the calculation of Lyapunov exponent. Nevertheless, literature pointed that the method Cao was of better robustness to noise for the high dimensional time evolution process. So it was entirely feasible to adopt Cao method in the application of chaotic analysis of the measured fluctuating pressure data.(3) Because of noise, K entropy and λ1 can only identify the chaotic identification in qualitative for the measured fluctuating pressure sequence, rather than the level of chaos and complexity of size. However, the distribution law of λ1 is obvious in the analysis of the acceleration signal.In the two distribution regularity aspects of phase space reconstruction and chaotic characteristic quantity, certain disparities existed in various model tests. The main conclusions were as follows.(1) Select two types of one-stage contraction scheme (FC) and two-stage contraction scheme (SC) to measure pressure data of every type of slit-type energy dissipater in every condition. Collectively, the range of embedding parameters of phase space reconstruction τ is from 6 to 13, and m is from 6 to 13. In FC scheme, τ and m have certain regularity with flow direction. Saturated correlation dimension D2 can reflect more regularity. With the upstream water level higher, the flow structure will be more complicated, turbulent randomicity will be higher. And in the SC scheme of the second contraction section near the floor, flow turbulence does not depend on initial conditions, for instance, water level, flow rate and so on, but depend on suddenly turning of two-stage contraction wall. In the slit-type energy dissipater suddenly turning in the side wall makes more complexity and turbulent flow structure near the floor dynamic degree than the side wall near the water. But the contraction section did not change the flow dynamic structure in essence, which is only small perturbations.(2) This paper studied the chaotic characteristics of step energy dissipater with the two step combination schemes through controlling the discharge per unit width and Froude number to control flow conditions. The study shows that the best embedding parameters of phase space reconstruction are like this:τ is from 7 to 18, and m is from 8 to 17. Using the regularity of correlation dimension with the variation of flow conditions, it is easy to find in the stepped energy dissipater, the evolvement process of internal flow structure does not directly depend on the flow conditions or step shape, but depends on the flow pattern in the step. The different evolution pattern makes the different flow state. The fluctuating pressure sequence of vertical convex corner may exist noise or the flow field near the high is complex, it is probably due to drop flow, cavity exists in the vertical convex corner. The cavity is more complicated than the fluctuation of flow. The distribution of λ1 shows fluctuating pressure sequence of vertical convex corner in nappe flow have more random than skimming flow, while the fluctuating pressure sequence of horizontal space in the skimming flow are larger than drop flow in the level of chaos. Through the study of distribution law in D2 under the same flow, it is certain that in the skimming flow, measuring points of vertical and horizontal plane convex corner have the downward trend.(3) This paper drew up three test conditions to study on the chaotic characteristic of stilling pool depends on a new energy dissipation structure. It turns out that τ at point of bottom is bigger than at central pier of stilling pool, but m is the opposite. D2 ranges between 5.238～8.854, on the whole, D2 at bottom of stilling pool is bigger than at central pier. In condition with high flow (2%),D2 at bottom has the tendency of increase along flow. In the condition with small flow (50%), D2 has the tendency of decrease along flow. D2 at central pier has nothing to do with flow condition, and with the decrease of flow, D2 before central pier reduces and then increases, and after central pier, it reduces, which apply to the energy dissipation mechanism of this prioritization scheme. The analysis result of distribution law of λ1 also suggests that energy dissipation effect of prioritization scheme under small flow is better.(4) This paper studied on gate vibration acceleration of Longkaikou hydropower station,7 gate openings of 1/8～7/8 are studied out, and the upper level is design level. The m of transverse vibration is bigger than other directions except the gate opening of 1/8. In addition, m of gate opening 1/8 and 7/8 in any vibration directions is bigger than other gate openings. The vertical and forward flow direction vibration of gate appears low dimension (3.342～5.130) chaotic attractor which shows that less independent control variables can describe the complexity and nonlinearity principle during gate vibration when modeling flow-induced vibration of gate. The distribution law of λ1 shows principle of "small at side and big in the middle" along the change of gate opening. Therefore, the complexity of vibration of gate under flow-induced vibration is bigger except gate opening 1/8 and 7/8. It shows that in practical engineering, the vibration of gate opening between 2/8～6/8 is not certain, including strong vibration.