SIMULATION STUDY ON FLOW-INDUCED VIBRATION OF  MAN-WAN OVERFLOW POWERHOUSE

Peng Xinmin and Cui Guangtao

Tianjin University

Tianjin, 300072, CHINA,

Fax: 86-22-27406390

Tel: 86-22-27406390

Abstract: The vibration problems of the overflow hydropower house in conjunction with the dam with ski-jumping type dissipation is discussed in this paper. Prediction of the flood safety of low weir overflow is also mentioned. During construction period, the powerhouses have stood the test of sluice impact as long as thirteen hours, with the powerhouses slightly vibrating and units running well. Practices indicate the engineering feasibility of hydro-elastic vibration models.

1    INTRODUCTION

Man-wan hydropower station is located on the middle reach of Lancangjiang River, with a total reservoir capacity of 920 million cubic meters and a generating capacity of 1500 MW. The project includes powerhouses, outlets and gravity dam which is 418 meters in length and 132 meters in height. The powerhouses are located in the middle of the river canyon behind the dam, as shown in Fig. 1. The discharge structures include five surface outlets (in the front of powerhouses), double line discharge tunnel at middle level (in the left side of the canyon), discharge tunnels (in both side of the canyon), scour outlets (in both sides of the canyon) and a cushion pool (behind the dam). The maximum discharge is 22300 m³/s when using the 1000-year frequency flood for design and 5000-year frequency for emergency. Because the spillway gates have not been installed before the completion of the project, a free overflow will occur when a flood comes, which is the main condition discussed in this paper.

2    PRINCIPLE AND DESIGN OF HYDRO-ELASTIC VIBRATION MODEL

2.1    Principle of modeling

A hydro-elastic vibration model studies the liquid-solid combined system including powerhouses, impounded water and the foundation. The model is well suited to simulate the dynamic response of powerhouses under the pulsating load of spillway overflow, when the scale requirements of hydraulics and structure kinetics are met. In terms of model law, model materials must comply with the following criteria: bulk density scale λ_r = 1, elastic modulus scaleλ_E =λ_l (λ_l is the geometric scale of models), flow resistance scaleλ_ξ= 1, Poisson’s ratio scaleλ_μ= 1. The essential of hydraulic similarity is to produce fluctuating stress similarity between models and prototypes under the similarity of gravitation. For the intense turbulent flow discussed in the paper, the prototype observation dictated the feasibility of neglecting the impact of viscous force.

2.2    Model design

The prototype is locally modeled with a model scale of 1/75, with two surface outlets among sluice piers. One section of the powerhouse in prototype is 26 meters in width, 25 meters in span length and 4 meters of the crown thickness. The modeling depth of foundation of the powerhouse is half of its height. The sketch of the model is shown in Fig.1. The model material is weighting rubber, whose physical and mechanical characteristics are compared with those of prototype in Table 1.

Fig. 1 

    Table 1  Physical and mechanical characteristics in prototype and model

By the Table 1, the bulk density scale and elastic modulus scale comply with the model law well, however, for the flow resistance scale and Poisson’s ratio scale, there exist some error, which is be ignored or rectified in the modeling.

3    CHARACTERISTICS OF THE FLUCTUATING LOADS

In order to study the overall responses of impacting flow, to estimate horizontal and vertical random loads of the forced vibration, pressure sensors are placed on the top of powerhouse model. Both horizontal loads and vertical fluctuating loads grow with the water stage, until they arrive at their root-mean-square (rms) maximums --- 281.94 KN and 625.88 KN respectively at the water stage 977.12 meters. While the stage exceed 977.12, the water nappe will jump over the powerhouses. With the water level lowing, the loads will reduce, however, the maximum occurs at the water stage 976.27 meters. (Fig. 2) In terms of normal distribution character of the fluctuating loads, the possible maximum instant load is about three times of the RMS value, that is, 1877.64 KN in vertical direction and 845.82 KN in horizontal direction. The maximum pressure on the top of powerhouses model is 2.09 KPA (in vertical direction), equivalent to 0.21 meter water column. In terms of the prototype measure in Aug. 1993, the maximum fluctuating point pressure is 80.42 KPA (RMS), which can deduce that the possible maximum instant load is 241.26 KPA, equivalent to 24.6 meters water column. The conversion coefficient of point-area load is 0.009. In terms of the model and prototype measure, the amplitude of load fluctuation is limit due to the concentration of the water nappe.

Fig. 2

The frequency of fluctuating load is usually described by power spectrum. (shown in Fig.3) It can be seen that the dominant frequency of dynamic loads in model is below 3.0HZ, which is agreed with the prototype measure.

Fig. 3

4    SYSTEM SIMULATION ANALYSIS ON THE HYDRO-ELASTIC BIVRATION OF POWERHOUSES

The measuring point grid is layout as Fig. 4 shows. Shock excitation is made from single-point, and the acceleration responses are measured on multi-points. The transfer function can be calculated with HP5434A dynamic analyzer.

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Fig. 4

The inherent vibration frequencies in the first ten steps are measured in the model without water downstream (shown in Table 2)  Fig. 5 shows the first three steps of vibration.

Table 2  The inherent frequency of powerhouse system

Fig. 5

Table 3 dictates the comparison of self-oscillation frequency between dry and wet mode of powerhouses. It can be seen that the frequency is greater when there are water downstream, which is in contrast to theory, because the downstream water will reduce the vibration frequency by hydrodynamic pressure. According to the finite element analysis, the error lies in the improper modeling of the gaps between the dam and powerhouses.

The measure dictates that the vibration frequency in the first step is 6.27 HZ, which is much higher than that of fluctuating press and impossible for random resonance.

 Table 3    Self-oscillation frequency

5    FLOW-INDUCED VIBRATION OF POWER HOUSE

Fig. 6 shows the layout of measuring points. Fig. 7 shows the typical power spectrum of the vibration displacement. It is the low step vibration that induces displacement of hydraulic structures. It can be seen from Table 4 that the mean square value of vibration displacement of powerhouse system is 24.15μm in vertical direction and 17.03μm in horizontal direction under the free overflow condition at water level 9677.12 meters, which is no harm to the powerhouses.

Fig. 6

 Table 4  The mean square value of vibration displacement

6    PROTOTYPE OBSERVATION

The powerhouses stood the test of sluice impact as long as thirteen hours in 1993, with the total water discharge 3000 m³/s. The prototype measurement is made by Kunming institute of exploration and designing. It dictates that the maximum mean square value of vibration displacement is 10 μm in vertical direction and 13μm in horizontal direction, which is smaller than model measure due to the increment of steel reinforcements and the increase of concrete hardness in the construction period.

7    CONCLUSIONS

It is feasible to modeling the flow-induced vibration of powerhouses by hydro-elastic models. In terms of the model and prototype observation, the amplitude of load fluctuation is limit due to the concentration of the water nappe, and the frequency of fluctuating pressure is lower than the self-oscillation frequency of powerhouse, which dictate the impossible for random resonance and the safety of power plant.

References

[1]    CUI Guangtao, PENG Xinmin et al, 1990, hydro-elastic model study on flow-induced vibration of the Arch Dam in ER_TAN hydropower station, Journal of Tianjin University (in Chinese).

[2]    GAO Yingying et al, 1994, Prototype measurement of the Man-wan powerhouse system in flood season, Yunnan Hydropower Engineering, No.2 (in Chinese).