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

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2013

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Sébastien Duplaa;O. Coutier-Delgosha;A. Dazin;G. Bois;G. Caignaert

火箭发动机涡轮泵的启动一般只需几秒钟。这意味着这些泵仅在几次旋转后就达到其标称操作条件。在叶片的这些第一次旋转期间，泵中的流量演变由瞬态现象决定，主要基于流量和转速演变。当达到稳定行为时，这些现象逐渐变得可以忽略不计。泵瞬态行为引起显著的压力波动，这可能导致部分流汽化，即气穴。LML实验室（法国里尔）已更新了现有的实验测试装置，用于离心泵的启动。研究的重点是泵启动过程中产生的汽蚀。扭矩、流量、入口和出口不稳定压力以及泵转速的瞬时测量能够表征泵在快速启动期间的行为。已经确定了三种不同类型的快速启动行为，并在ISROMAC 12上进行了介绍（Duplaa等人，2008年）。根据最终操作点，启动的特征在于输送静压的单次下降，几次低频下降，或在泵的入口和出口都可以观察到的水锤现象。最近提出了一种物理分析来解释这三种不同类型的瞬态流动行为（Duplaa等人，2010年）。本文提出了汽蚀条件下快速起动的数学模型。它由Dazin等人（2007）提出的非空化条件下的快速启动模型的两步适应组成。为此，在法国原子能机构（CEA）的合作下，在叶轮中进行了快速X射线成像，以确定快速启动期间体积分数的高频演变。虽然这里提出的建模结果不是确定的，但它们是非常有希望的。名称A面积（m）B叶片到叶片通道的高度（m）Cu速度的切向分量（m/s）Cr = Q/（2prB）速度的径向分量（m/s）C扭矩（Nm）H总压头（m）L等效长度（m）Ps泵吸入管中的静压（Pa）Pd泵输送管中的静压（Pa）Pvs蒸汽压（Pa）Q入口体积流量（m3/s）r叶轮半径（m）S通道中流体体积的极限（m2）t时间（s）u叶尖速度= w <$r2（m/s）v入口管速度（m/s）V体积（m3）b相对流动角（-）b体积分数= Vvap/Vw（-）DP泵静压升（Pa）d流量系数：= Q/u2r2 2（-）f流量系数= Q/2pr2b2u2（-）Y压力系数= DP/ru2 2（-）w转速（s-1）ws比转速= wQ 1/2/（gH）（-）t =（Ps +1 ⁄ 2rv2-Pvs）/（1 ⁄ 2 ru22）（-）r密度（kg/m3）下标：1叶轮入口2叶轮出口空腔空化条件d扩散器f最终（快速启动的稳定部分）n标称st稳态tr瞬态v蜗壳w液态水引言空间发射器涡轮泵的特点是快速启动：实际上，轴旋转的开始和标称流动条件之间的时间延迟通常接近一秒。这意味着转速在一秒钟内从零增加到每分钟数万转。这种快速启动导致严重的瞬态效应，主要由速度加速度dw/dt和流速增加dQ/dt控制（Dazin等人，2007年）。离心泵中的瞬态效应已经通过几种方法进行了大约25年的实验研究：阀门的快速打开或关闭（Tanaka和Tsukamoto，1999 a），快速启动和关闭顺序（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 a），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 a），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 a），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 a），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999 b），（Tanaka和Tsukamoto，1999

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

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

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