V锥流量计火箭发动机液氢液氧推进剂测量性能
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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Realizableκ-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。
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(LH_2)and the liquid oxygen(LO_2),the performance of the Vcone flowmeter when measuring the cryogenic fluid was investigated by numerical simulation. The Realizable κ-εmodel 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 LH_2,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 LH_2,LO_2 and water,whose relative errors are with ±0.5%. The measurement of LH_2 and LO_2,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.
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(LH_2)and the liquid oxygen(LO_2),the performance of the Vcone flowmeter when measuring the cryogenic fluid was investigated by numerical simulation. The Realizable κ-εmodel 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 LH_2,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 LH_2,LO_2 and water,whose relative errors are with ±0.5%. The measurement of LH_2 and LO_2,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.
引文
[1] Cecere D,Giacomazzi E,Ingenito A. A Review on Hydrogen Industrial Aerospace Applications[J]. International Journal of Hydrogen Energy, 2014, 39(20):10731-10747.
[2]谭永华.大推力液体火箭发动机研究[J].宇航学报,2013,34(10):1303-1308.
[3]宋伟荣,汪娟娟.低温流量测量[J].低温与超导,2001,29(2):21-25.
[4]李建军.涡轮流量计在火箭发动机试验中的应用[J].火箭推进,2007,33(3):52-55.
[5]周磊,耿卫国,朱子环,等.低温涡街流场特性数值仿真研究[J].低温工程,2010,(6):37-40.
[6] Jin T,Tian H,Gao X,et al. Simulation and Performance Analysis of the Perforated Plate Flowmeter for Liquid Hydrogen[J]. International Journal of Hydrogen Energy,2017,42(6):3890-3898.
[7]田红,高旭,汤珂,等.结构参数对多孔板低温流量计性能影响分析[J].低温工程,2015,(6):43-48.
[8] Liu H,Tian H,Chen H,et al. Numerical Study on Performance of Perforated Plate Applied to Cryogenic Fluid Flowmeter[J]. Journal of Zhejiang University-Science A,2016,17(3):230-239.
[9] ASMEMFC. Wet Gas Flowmetering Guideline[R].ASME MFC-19G-2008.
[10] He D H,Bai B F. Gas-Liquid Two Phase Flow with High GVF Through a Horizontal V-Cone Throttle Device[J]. International Journal of Multiphase Flow,2017,91:51–62.
[11] Steven R N. Horizontally Installed Cone Differential Pressure Meter Wet Gas Flow Performance[J]. Flow Measurement and Instrumentation,2009,20(4-5):152–167.
[12] He D H,Bai B F,Xu Y,et al. A New Model for the VCone Meter in Low Pressure Wet Gas Metering[J]. Measurement Science and Technology,2012,23(12).
[13] Tan C,Wu H,Dong F. Mass Flow Rate Measurement of Oil-Water Two-Phase Flow by a Long-Waist Cone Meter[J]. IEEE Transactions on Instrumentation and Measurement,2013,62(10):2795–2804.
[14] McCrometer Inc.. Advanced Differential Pressure Flowmeter Technology[M]. Hemet:McCrometer Inc.,2008.
[15] Stephen A I. V-Cone:an Alternative to Orifice Meter in Wet Gas Applications[C]. Haugesund:the 17th North Sea Flow Measurement Workshop,1999.
[16] Hollingshead C L. Discharge Coefficient Performance of Venturi Standard Concentric Orifice Plate, V-Cone,and Wedge Flow Meters at Small Reynolds Numbers[D]. Utah:Utah State University,2011.
[17] Stephen A I. Permanent Pressure Loss Comparison Among Various Flowmeter Technologies[M]. Hemet:McCrometer Inc.,2010.
[18] He D H,Bai B F. Two-Phase Mass Flow Coefficient of V-Cone Throttle Device[J]. Experimental Thermal and Fluid Science,2014,57:77–85.
[19]徐英,于中伟,张涛,等. V形内锥流量计关键参数对流出系数的影响[J].机械工程学报,2008,44(12):105-111.
[20]侯克峰,张虎,占成,等.取压孔位置及锥角变化对V锥流量计的影响分析[J].计量技术,2012,2:3-5.
[21] Tan C,Wu H,Wei C,et al. Experimental and Numerical Design of a Long-Waist Cone Flow Meter[J]. Sensors and Actuators A:Physical,2013,199(17):9-17.
[22] Singh R K,Singh S N,Seshadri V. CFD Prediction of the Effects of the Upstream Elbow Fittings on the Performance of Cone Flowmeters[J]. Flow Measurement and Instrumentation,2010,21(2):88–97.
[23] Singh R K,Singh S N,Seshadri V. Study on the Effect of Vertex Angle and Upstream Swirl on the Performance Characteristics of Cone Flowmeter Using CFD[J]. Flow Measurement and Instrumentation,2009,20(2):69–74.
[24] Peters R,Steven R N,Caldwell S,et al. Testing the Wafer V-Cone Flowmeters in Accordance with API 5.7-Testing Protocol for Differential Pressure Flow Measurement Devices in the CEESI Colorado Test Facility[J]. Flow Measurement and Instrumentation,2006,17(4):247–254.
[25] Hodges C,Britton C,Johansen W. Cone Meter Calibration Problems[C]. Norway:The 27th International North Sea Flow Measurement Workshop,2009.
[26] Brennen C E. Cavitation and Bubble Dynamics[M].UK:Oxford University Press,2013.
[27] Numachi F,Yamabe M,Oba R. Cavitation Effects on the Discharge Coefficient of the Sharp-Edged Orifice Plate[J]. Journal of Fluids Engineering,1960,82(1):1–6.
[28] Numachi F,Kobayashi R,Kamiyama S. Effect of Cavitation on the Accuracy of Herschel-Type Venturi Tubes[J]. Journal of Fluids Engineering,1962,84(3):351–360.
[29] Ramamurthi K,Nandakumar K. Characteristics of Flow Through Small Sharp Edged Cylindrical Orifices[J].Flow Measurement and Instrumentation,1999,10(3):133–143.
[30] Ebrahimi B,He G,Tang Y,et al. Characterization of High-Pressure Cavitating Flow Through a Thick Orifice Plate in a Pipe of Constant Cross Section[J]. International Journal of Thermal Sciences,2017,114:229-240.
[31] Ashrafizadeh S M,Ghassemi H. Experimental and Numerical Investigation on the Performance of Small-Sized Cavitating Venturis[J]. Flow Measurement and Instrumentation,2015,42:6–15.
[32] Tomov P,Khelladi S,Ravelet F,et al. Experimental Study of Aerated Cavitation in a Horizontal Venturi Nozzle[J]. Experimental Thermal and Fluid Science,2016,70:85–95.
[33] Long X,Zhang J,Wang J,et al. Experimental Investigation of the Global Cavitation Dynamic Behavior in a Venturi Tube with Special Emphasis on the Cavity Length Variation[J]. International Journal of Multiphase Flow,2017,89:290–298.
[34]姜映福,刘中祥,褚宝鑫.低温流体汽蚀的数值计算及可视化实验研究[J].推进技术,2017,38(12):2771-2777.(JIANG Ying-fu,LIU Zhong-xiang,CHU Bao-xin. Numerical Simulation and Visualized Experimental Study on Cavitating of Cryogenic Fluids[J].Journal of Propulsion Technology,2017,38(12):2771-2777.)
[35] Brinkhorst S,Lavante E,Wendt G. Numerical Investigation of Cavitating Herschel Venturi-Tubes Applied to Liquid Flow Metering[J]. Flow Measurement and Instrumentation,2015,43:23–33.
[36] Sun Z Y,Li G X,Chen C,et al. Numerical Investigation on Effects of Nozzle’s Geometric Parameters on the Flow and the Cavitation Characteristics within Injector’s Nozzle for a High-Pressure Common-Rail DI Diesel Engine[J]. Energy Conversion&Management,2015,89(9):843–861.
[37] Rodio M G,Congedo P M. Robust Analysis of Cavitating Flows in the Venturi Tube[J]. European Journal of Mechanics-B/Fluids,2014,44(2):88–99.
[38] Yuan W,Sauer J,Schnerr G H. Modeling and Computation of Unsteady Cavitation Flows in Injection Nozzles[J]. Mécanique and Industries,2001,2(5):383–394.
[39] Zhu J K,Chen Y,Zhao D F,et al. Extension of the Schnerr-Sauer Model for Cryogenic Cavitation[J]. European Journal of Mechanics,2015,52:1-10.
[40]贺登辉.内置V锥管内气液两相流动特性及其在湿气双参数测量中的应用[D].西安:西安交通大学,2015.
[41] Hord J,Anderson L M,Hall W J. Cavitation in Liquid Cryogens III-Ogives[R]. NASA-CR-2156,1973.
[42] Huang S F,Ma T Y,Wang D,et al. Study on Discharge Coefficient of Perforated Orifices as a New Kind of Flowmeter[J]. Experimental Thermal and Fluid Science,2013,46:74–83.
[43] Idelchik I E. Hand Book of Hydraulic Resistance(4th Edition)[M]. USA:Begell House,2008.
[2]谭永华.大推力液体火箭发动机研究[J].宇航学报,2013,34(10):1303-1308.
[3]宋伟荣,汪娟娟.低温流量测量[J].低温与超导,2001,29(2):21-25.
[4]李建军.涡轮流量计在火箭发动机试验中的应用[J].火箭推进,2007,33(3):52-55.
[5]周磊,耿卫国,朱子环,等.低温涡街流场特性数值仿真研究[J].低温工程,2010,(6):37-40.
[6] Jin T,Tian H,Gao X,et al. Simulation and Performance Analysis of the Perforated Plate Flowmeter for Liquid Hydrogen[J]. International Journal of Hydrogen Energy,2017,42(6):3890-3898.
[7]田红,高旭,汤珂,等.结构参数对多孔板低温流量计性能影响分析[J].低温工程,2015,(6):43-48.
[8] Liu H,Tian H,Chen H,et al. Numerical Study on Performance of Perforated Plate Applied to Cryogenic Fluid Flowmeter[J]. Journal of Zhejiang University-Science A,2016,17(3):230-239.
[9] ASMEMFC. Wet Gas Flowmetering Guideline[R].ASME MFC-19G-2008.
[10] He D H,Bai B F. Gas-Liquid Two Phase Flow with High GVF Through a Horizontal V-Cone Throttle Device[J]. International Journal of Multiphase Flow,2017,91:51–62.
[11] Steven R N. Horizontally Installed Cone Differential Pressure Meter Wet Gas Flow Performance[J]. Flow Measurement and Instrumentation,2009,20(4-5):152–167.
[12] He D H,Bai B F,Xu Y,et al. A New Model for the VCone Meter in Low Pressure Wet Gas Metering[J]. Measurement Science and Technology,2012,23(12).
[13] Tan C,Wu H,Dong F. Mass Flow Rate Measurement of Oil-Water Two-Phase Flow by a Long-Waist Cone Meter[J]. IEEE Transactions on Instrumentation and Measurement,2013,62(10):2795–2804.
[14] McCrometer Inc.. Advanced Differential Pressure Flowmeter Technology[M]. Hemet:McCrometer Inc.,2008.
[15] Stephen A I. V-Cone:an Alternative to Orifice Meter in Wet Gas Applications[C]. Haugesund:the 17th North Sea Flow Measurement Workshop,1999.
[16] Hollingshead C L. Discharge Coefficient Performance of Venturi Standard Concentric Orifice Plate, V-Cone,and Wedge Flow Meters at Small Reynolds Numbers[D]. Utah:Utah State University,2011.
[17] Stephen A I. Permanent Pressure Loss Comparison Among Various Flowmeter Technologies[M]. Hemet:McCrometer Inc.,2010.
[18] He D H,Bai B F. Two-Phase Mass Flow Coefficient of V-Cone Throttle Device[J]. Experimental Thermal and Fluid Science,2014,57:77–85.
[19]徐英,于中伟,张涛,等. V形内锥流量计关键参数对流出系数的影响[J].机械工程学报,2008,44(12):105-111.
[20]侯克峰,张虎,占成,等.取压孔位置及锥角变化对V锥流量计的影响分析[J].计量技术,2012,2:3-5.
[21] Tan C,Wu H,Wei C,et al. Experimental and Numerical Design of a Long-Waist Cone Flow Meter[J]. Sensors and Actuators A:Physical,2013,199(17):9-17.
[22] Singh R K,Singh S N,Seshadri V. CFD Prediction of the Effects of the Upstream Elbow Fittings on the Performance of Cone Flowmeters[J]. Flow Measurement and Instrumentation,2010,21(2):88–97.
[23] Singh R K,Singh S N,Seshadri V. Study on the Effect of Vertex Angle and Upstream Swirl on the Performance Characteristics of Cone Flowmeter Using CFD[J]. Flow Measurement and Instrumentation,2009,20(2):69–74.
[24] Peters R,Steven R N,Caldwell S,et al. Testing the Wafer V-Cone Flowmeters in Accordance with API 5.7-Testing Protocol for Differential Pressure Flow Measurement Devices in the CEESI Colorado Test Facility[J]. Flow Measurement and Instrumentation,2006,17(4):247–254.
[25] Hodges C,Britton C,Johansen W. Cone Meter Calibration Problems[C]. Norway:The 27th International North Sea Flow Measurement Workshop,2009.
[26] Brennen C E. Cavitation and Bubble Dynamics[M].UK:Oxford University Press,2013.
[27] Numachi F,Yamabe M,Oba R. Cavitation Effects on the Discharge Coefficient of the Sharp-Edged Orifice Plate[J]. Journal of Fluids Engineering,1960,82(1):1–6.
[28] Numachi F,Kobayashi R,Kamiyama S. Effect of Cavitation on the Accuracy of Herschel-Type Venturi Tubes[J]. Journal of Fluids Engineering,1962,84(3):351–360.
[29] Ramamurthi K,Nandakumar K. Characteristics of Flow Through Small Sharp Edged Cylindrical Orifices[J].Flow Measurement and Instrumentation,1999,10(3):133–143.
[30] Ebrahimi B,He G,Tang Y,et al. Characterization of High-Pressure Cavitating Flow Through a Thick Orifice Plate in a Pipe of Constant Cross Section[J]. International Journal of Thermal Sciences,2017,114:229-240.
[31] Ashrafizadeh S M,Ghassemi H. Experimental and Numerical Investigation on the Performance of Small-Sized Cavitating Venturis[J]. Flow Measurement and Instrumentation,2015,42:6–15.
[32] Tomov P,Khelladi S,Ravelet F,et al. Experimental Study of Aerated Cavitation in a Horizontal Venturi Nozzle[J]. Experimental Thermal and Fluid Science,2016,70:85–95.
[33] Long X,Zhang J,Wang J,et al. Experimental Investigation of the Global Cavitation Dynamic Behavior in a Venturi Tube with Special Emphasis on the Cavity Length Variation[J]. International Journal of Multiphase Flow,2017,89:290–298.
[34]姜映福,刘中祥,褚宝鑫.低温流体汽蚀的数值计算及可视化实验研究[J].推进技术,2017,38(12):2771-2777.(JIANG Ying-fu,LIU Zhong-xiang,CHU Bao-xin. Numerical Simulation and Visualized Experimental Study on Cavitating of Cryogenic Fluids[J].Journal of Propulsion Technology,2017,38(12):2771-2777.)
[35] Brinkhorst S,Lavante E,Wendt G. Numerical Investigation of Cavitating Herschel Venturi-Tubes Applied to Liquid Flow Metering[J]. Flow Measurement and Instrumentation,2015,43:23–33.
[36] Sun Z Y,Li G X,Chen C,et al. Numerical Investigation on Effects of Nozzle’s Geometric Parameters on the Flow and the Cavitation Characteristics within Injector’s Nozzle for a High-Pressure Common-Rail DI Diesel Engine[J]. Energy Conversion&Management,2015,89(9):843–861.
[37] Rodio M G,Congedo P M. Robust Analysis of Cavitating Flows in the Venturi Tube[J]. European Journal of Mechanics-B/Fluids,2014,44(2):88–99.
[38] Yuan W,Sauer J,Schnerr G H. Modeling and Computation of Unsteady Cavitation Flows in Injection Nozzles[J]. Mécanique and Industries,2001,2(5):383–394.
[39] Zhu J K,Chen Y,Zhao D F,et al. Extension of the Schnerr-Sauer Model for Cryogenic Cavitation[J]. European Journal of Mechanics,2015,52:1-10.
[40]贺登辉.内置V锥管内气液两相流动特性及其在湿气双参数测量中的应用[D].西安:西安交通大学,2015.
[41] Hord J,Anderson L M,Hall W J. Cavitation in Liquid Cryogens III-Ogives[R]. NASA-CR-2156,1973.
[42] Huang S F,Ma T Y,Wang D,et al. Study on Discharge Coefficient of Perforated Orifices as a New Kind of Flowmeter[J]. Experimental Thermal and Fluid Science,2013,46:74–83.
[43] Idelchik I E. Hand Book of Hydraulic Resistance(4th Edition)[M]. USA:Begell House,2008.