## 1 Introduction  
The fire turbopump has the special structure with two hydraulic machineries of a turbine and a pump in Figure 1, and plays an important role in supplying the natural water source for handling the fire. When its turbine section is driven by the circulating water from the finite-volume tank of a fire brigade vehicle, its pump section starts to supply continuously natural water to the fire ground. The turbine is hit by the power water during the operating period, which causes different-extent vibrations affecting the steady operation of the pump because of the turbopump structure. Meanwhile, the natural water delivered in the pump is controlled by pump structure and operation condition, and its reaction also results in pump vibration. Due to the special structure of fire turbopump, these flow-induced vibrations are enhanced by the coupled effects of hydraulic forces on the turbine and pump to cause the inconsistent fire-water supply to influence negatively on handling the fire. Turbopump was invented to draw water from the Kushk River to irrigate farmland by the former Soviet Union in 1922 [1]. Due to its lower energy consumption, the turbopump was widely applied in agricultural irrigation with using the water from the streams and rivers by China in 1970s. The Fujian Research Institute of Mechanics [2,3] studied the design calculation, manufacture and applied research for the turbopump. This turbopump is usually installed on the river or stream with a big vertical drop, such as the river dam in a mountainous region, rapids of the river, tidal areas, etc. The water from the upstream drives the turbine, and then the pump draws the water from downstream to irrigate the farmland. Recently, with the fire supply equipment innovating constantly, the turbopump is introduced to be applied in fire-fighting. The fire turbopump belongs to the micro turbopump, due to its length of 60 mm or so; so its design and application are different than the irrigation turbopump. Some studies on the fire turbopump were conducted by our previous research and revealed the design calculation and stability analysis of the fire turbopump [4; 5]. Nevertheless, little research has been conducted for the flow-induced vibration characteristics of the fire turbopump with considering the coupled effects of turbine section and pump section. The turbine vibration is produced when the water impacts on the volute and impeller. The large radial hydraulic force is generated on the turbine because of the asymmetric structure of volute and rotating impeller, and this force was proved to be the main factor producing the vibration [6; 7]. Some unsteady flows have important effects on generating the hydraulic force, such as the non-uniform flow in the volute, two flow-related factors and pressure fluctuations in the impeller passage [8]. Some numerical studies have been conducted to explore unsteady flow characteristics in the impeller and volute [9; 10; 11]. The radial hydraulic force changes with the radial impeller-volute gap varying, due to the rotor-stator interaction. This force under the design flow condition is different from that under the off-design conditions, and its frequency was proved to be consistent with the impeller rotating frequency. As for the pump, the internal flow field is determined by pump structure and operation condition. The pressure fluctuation in the flow channel is formed to induce the unit vibration, due to some different types of unsteady phenomena such as flow separation, vortex shedding, rotor-stator interaction, etc. [12]. The impeller-volute interaction is dominant in the generation of the pressure fluctuation in the hydraulic machinery [13]. This fluctuation was measured on the rotating impeller with a high speed pressure sensor; the result revealed that the pressure variations on the blades were closely related to the static pressures in the volute [14; 15].