- 1-EXPERIMENTAL CHARACTERIZATION AND MODELLING OF A CAVITATING CENTRIFUGAL PUMP OPERATING IN FAST START-UP CONDITIONS

The start-up of rocket engine turbopumps is generally performed only in a few seconds. It implies that these pumps reach their nominal operating conditions after only a few rotations. During these first rotations of the blades, the flow evolution in the pump is governed by transient phenomena, based mainly on the flow rate and rotation speed evolution. These phenomena progressively become negligible when the steady behavior is reached. The pump transient behaviour induces significant pressure fluctuations which may result in partial flow vaporization, i.e. cavitation. An existing experimental test rig has been updated in the LML laboratory (Lille, France) for the start-ups of a centrifugal pump. The study focuses on cavitation induced during the pump start-up. Instantaneous measurement of torque, flow rate, inlet and outlet unsteady pressures, and pump rotation velocity enable to characterize the pump behaviour during rapid starting periods. Three different types of fast start-up behaviours have been identified and have been presented at ISROMAC 12 (Duplaa et al, 2008). According to the final operating point, the start-up is characterized either by a single drop of the delivery static pressure, by several low-frequency drops, or by a water hammer phenomenon that can be observed both a the inlet and outlet of the pump. A physical analysis to explain these three different types of transient flow behaviour has been recently proposed (Duplaa et al, 2010). In the present paper, a modelling of the fast start ups in cavitating conditions is proposed. It consists of a two steps adaptation of fast start-up model in non cavitating conditions proposed by Dazin et al (2007). For that, fast X-rays imaging has been performed in the impeller with the collaboration of the French Atomic Agency (CEA) in order to determinate the high frequency evolution of the volume fraction during fast the start-ups. Although the results of the modelling presented here are not definitive, they are very promising. NOMENCLATURE A area (m) b height of the blade to blade channels (m) Cu tangential component of the velocity (m/s) Cr = Q / (2prb) radial component of the velocity (m/s) C torque (Nm) H Total head (m) L equivalent length (m) Ps static pressure in the pump suction pipe (Pa) Pd static pressure in the pump delivery pipe (Pa) Pvs vapor pressure (Pa) Q Inlet volume flow rate (m3/s) r impeller radius (m) S limit of the fluid volume in the channels (m2) t time (s) u tip velocity =w ́ r2 (m/s) v inlet pipe velocity (m/s) V Volume (m3) b relative flow angle (-) b Volume fraction = Vvap/Vw (-) DP pump static pressure rise (Pa) d flow rate coefficient : = Q / u2r2 2 (-) f flow rate coefficient = Q / 2pr2b2u2 (-) Y pressure coefficient = DP / ru2 2 (-) w rotation speed (s-1) ws specific speed = wQ 1/2 / (gH) (-) t = (Ps + 1⁄2rv2 – Pvs)/(1⁄2 ru22) (-) r density (kg/m3) Subscripts : 1 impeller inlet 2 impeller outlet cav cavitating conditions d diffuser f final (steady part of the fast start up) n nominal st steady tr transient v volute w Liquid water INTRODUCTION Space launcher turbopumps are characterized by fast start-ups: actually, the time delay between the inception of the shaft rotation and the nominal flow conditions is usually close to one second. It means that the rotation speed increases from zero up to several tens of thousands of rotations per minute during a single second. Such fast start-up results in severe transient effects that are mainly governed by the speed acceleration dw/dt and the flow rate increase dQ / dt (Dazin et al, 2007). Transient effects in centrifugal pumps have been studied experimentally by several means for about 25 years: fast opening or closure of valves (Tanaka and Tsukamoto, 1999a), fast start-up and shutdown sequences (Tanaka and Tsukamoto, 1999b), (Tanaka and