Abstract: To investigate the new measurement method of the cryogenic propellant flow rate of the rocket engine， e.g.， the flow rate of the liquid hydrogen (LH2) and the liquid oxygen (LO₂)， the performance of the V-cone flowmeter when measuring the cryogenic fluid was investigated by numerical simulation. The Realizable κ-ε model was used to describe the turbulence. The Schnerr-Sauer cavitation model was used to investigate the effects of cavitation on the performance of the V-cone flowmeter. A UDF was also added to take into account the effects of latent heat of vaporization. The discharge coefficient and pressure loss coefficient of the V-cone flowmeter were discussed when the fluids were cryogenic fluids and water. The measurement error of the flowmeter was also analysed. The results show that the discharge coefficient and pressure loss coefficient are almost constant when the Reynolds number in a ‘stable region’， where the average discharge coefficient of both the cryogenic fluids and the water around the room temperature is essentially equal. It is also found that the lower limits of the Reynolds number for the constant discharge coefficient is very close for each fluid， while the upper limits of Reynolds number are quite different. The cryogenic fluids， especially LH2， have wider stable Reynolds number ranges than the water. In addition， there is little effect of cavitation on the discharge coefficient and pressure loss coefficient at the initial stage of cavitation. When the cavitation occurred downstream of V-cone affects the pressure around the low pressure tapping， the discharge coefficient decreases rapidly with Reynolds number increasing， while the pressure loss coefficient rises quickly. Under the Reynolds number range of the ‘stable region’， the V-cone flowmeter can accurately predict the flow rate of LH2， LO₂ and water， whose relative errors are with ±0.5%. The measurement of LH2 and LO₂， in particular， has high accuracy over a wide range of Reynolds number. The results also demonstrate that the effects of cavitation on the measurement error of the flow rate are small. This study opens a new avenue for measuring the cryogenic propellant flow rate of the liquid rocket engine.

Key words: Liquid rocket engine；Propellant；Cryogenic fluid；Liquid hydrogen and liquid oxygen；V-cone flowmeter；Discharge coefficient；Pressure loss coefficient；Flow rate measurement

摘要： 为探究火箭发动机液氢液氧低温推进剂流量测量新方法，通过数值模拟研究了V锥流量计低温流体的测量性能。湍流模型采用Realizable κ-ε模型，空化模型为Schnerr-Sauer模型，并通过自行编写UDF程序，在能量方程中考虑汽化潜热等热力学效应的影响。获得了V锥流量计流出系数和压力损失系数的变化规律，并分析了V锥流量计的测量误差。研究结果表明，存在一个雷诺数“稳定区”，该区域内流出系数和压力损失系数基本为常数，液氢液氧和常温水对应的平均流出系数基本相等，且稳定区雷诺数下限值也基本相同；不同流体稳定区的平均流出系数对应的雷诺数范围差别较大，低温流体尤其是液氢的雷诺数上限值明显高于常温水。此外，空化较轻时，对流出系数和压力损失系数影响较小，当空化区域对锥尾低压口附近的压力分布产生较大影响时，则会导致流出系数迅速下降和压力损失系数增大。在稳定区对应的雷诺数范围内，液氢、液氧和水的质量流量均具有较高的测量精度，其相对误差在±0.5%之内，尤其对于液氢和液氧，其在很宽的测量范围内也可以保持较高的测量精度，空化的产生亦对V锥流量计测量精度影响较小。

关键词: 液体火箭发动机；推进剂；低温流体；液氢液氧；V锥流量计；流出系数；圧力损失系数；流量测量