Effect of Divergent Section Contour of Supersonic Nozzle on Oscillation Characteristics of Underwater Jet Propulsion

doi:10.12382/bgxb.2024.0103

Abstract

Abstract:

The effect of the divergent section contour of supersonic nozzle on the multiphase flow and propulsion performance of underwater rocket propulsion nozzle is studied by a series of numerical simulations.The underwater flow processes of conical and parabolic nozzles with different divergent section contours under still water,variable depth and over-expanded conditions are simulated.A numerical model of underwater supersonic gas jet is established based on the volume of fluid(VOF)multiphase model.The influence laws of the contour types and key parameters of divergent section on the nozzle near-field flow structure,flow separation characteristics,and thrust oscillation characteristics are analyzed.The results show that the separation shock structure in the nozzle operating in deep water is highly unstable.The gas-liquid separation may also occur at the separation point in the divergent section,and the nozzle thrust oscillates on the basis of the full-flow value.There is a dynamic transition of flow separation patterns in parabolic nozzles,and the gas-liquid separation phenomenon is not significant under the restricted shock separation(RSS)pattern.The effect of contour type is more pronounced than that of contour parameters,with the parabolic nozzles having more moderate thrust oscillations than the conical nozzles,and the difference is more significant at greater water depths.At a depth of 90 m,the maximum difference in average thrust of the nozzles with different contours reaches 10.13% of that of the basic parabolic nozzle.

Key words: underwater jet propulsion, supersonic gas jet, nozzle contour, flow separation, thrust oscillation

CLC Number:

TJ610.1

WANG Deyou, LI Shipeng, GUO Baojun, ZHANG Beichen, WANG Ningfei. Effect of Divergent Section Contour of Supersonic Nozzle on Oscillation Characteristics of Underwater Jet Propulsion[J]. Acta Armamentarii, 2025, 46(2): 240103-.

Figures/Tables 22

Fig.1 Computational domain and boundary conditions

Fig.2 Schematic diagram of thrust calculation of underwater rocket motor

Fig.3 Meshing

Table 1 Parameter setting for conical nozzles

参数	C-1	C-2	C-3	C-4	C-5
β/(°)	9	12	15	18	21
L/mm	158.24	118.14	93.96	77.73	66.05

Table 2 Parameter setting for parabolic nozzles

参数	P-1	P-2	P-3	P-4	P-5
θ_n/(°)	26	30	30	30	34
θ_e/(°)	5	1	5	9	5
L/mm	77.73	77.73	77.73	77.73	77.73

Fig.4 Comparison of gas bubble morphologies during initial evolution

Fig.5 Location-time curves of gas bubble vertex

Fig.6 Wall pressure distributions and Mach number contours of nozzle divergent section under different NPRs

Fig.7 Flow structures near the basic conical nozzle at typical moments

Fig.8 Flow structures near the conical nozzles at 10ms at 90m depth

Fig.9 Internal shock structures in a parabolic nozzle during different separation patterns[36]

Fig.10 Flow structures near the basic parabolic nozzle at typical moments

Fig.11 Gas bubble morphologies at the first necking time for different nozzles at 90m depth

Fig.12 Wall pressure distributions in divergent section for the basic parabolic nozzle at 90m depth

Fig.13 Locations of pressure probing points

Fig.14 Oscillation patterns of shock separation point for conical nozzle

Fig.15 Oscillation patterns of shock separation point for parabolic nozzle

Fig.16 Nozzle thrust-time curves of the basic conical and parabolic nozzles

Fig.17 Thrust component spectrum analysis for basic nozzles at 90m depth

Fig.18 Change rule of nozzle thrust increment at 90m depth

Table 3 Average thrusts of conical nozzles

扩张型面	平均喷管推力/kN
扩张型面	满流	H=50m	H=90m
C-1	6.399	7.091	7.863
C-2	6.397	7.019	8.035
C-3	6.345	6.968	7.876
C-4	6.342	6.923	7.818
C-5	6.311	6.804	7.795

Table 4 Average thrusts of parabolic nozzles

扩张型面	平均喷管推力/kN
扩张型面	满流	H=50m	H=90m
P-1	6.399	6.813	7.421
P-2	6.374	6.732	7.385
P-3	6.395	6.774	7.296
P-4	6.405	6.825	7.488
P-5	6.382	6.839	7.500

References 38

[1]	ZHANG X Y, LI S P, YANG B Y, et al. Flow structures of over-expanded supersonic gaseous jets for deep-water propulsion[J]. Ocean Engineering, 2020, 213:107611.
[2]	黄楠, 陈志华, 王争论. 水下超声速气体射流线性稳定性研究[J]. 推进技术, 2021, 42(3):550-559.
	HUANG N, CHEN Z H, WANG Z L. Linear stability of underwater supersonic gas jet[J]. Journal of Propulsion Technology, 2021, 42(3):550-559. (in Chinese)
[3]	HUANG N, CHEN Z H, WANG Z L. Main characteristics of underwater supersonic gas jet flows[J]. Mathematical Problems in Engineering, 2022(5):1191938.
[4]	SHI H H, WANG B Y, DAI Z Q. Research on the mechanics of underwater supersonic gas jets[J]. Science China Physics,Mechanics & Astronomy, 2010, 53(3):527-535.
[5]	SHI H H, GUO Q, WANG C, et al. Oscillation flow induced by underwater supersonic gas jets[J]. Shock Waves, 2010, 20:347-352.
[6]	汤龙生, 刘宇, 吴智锋, 等. 水下超声速燃气射流气泡的生长及压力波传播特性实验研究[J]. 推进技术, 2011, 32(3):417-420.
	TANG L S, LIU Y, WU Z F, et al. Experimental study on characteristics of bubble growth and pressure wave propagation by supersonic gas jets under water[J]. Journal of Propulsion Technology, 2011, 32(3):417-420. (in Chinese)
[7]	贾有军, 张胜敏, 尤俊峰, 等. 固体发动机水下点火尾流变化过程试验研究[J]. 固体火箭技术, 2015, 38(5):660-663,678.
	JIA Y J, ZHANG S M, YOU J F, et al. Experimental research on the changing process of underwater ignition wake of solid rocket motor[J]. Journal of Solid Rocket Technology, 2015, 38(5):660-663,678. (in Chinese)
[8]	朱卫兵, 陈宏, 黄舜. 水下高速射流气泡变化过程数值研究[J]. 推进技术, 2010, 31(4):496-502.
	ZHU W B, CHEN H, HUANG S. Numerical study of the process of the evolution of bubble of high-speed jet underwater[J]. Journal of Propulsion Technology, 2010, 31(4):496-502. (in Chinese)
[9]	唐云龙, 李世鹏, 刘筑, 等. 水下固体火箭发动机的推力特性[J]. 航空动力学报, 2017, 32(2):477-485.
	TANG Y L, LI S P, LIU Z, et al. Underwater thrust characteristic of solid rocket motor[J]. Journal of Aerospace Power, 2017, 32(2):477-485. (in Chinese)
[10]	乌岳, 李卓, 江晓瑞. 水下点火固体火箭发动机两相流流场数值分析[J]. 航空动力学报, 2018, 33(10):2508-2514.
	WU Y, LI Z, JIANG X R. Numerical analysis for underwater ignition two-phase flow field of solid rocket motor[J]. Journal of Aerospace Power, 2018, 33(10):2508-2514. (in Chinese)
[11]	TANG J N, WANG N F, SHYY W. Flow structures of gaseous jets injected into water for underwater propulsion[J]. Acta Mechanica Sinica, 2011, 27:461-472.
[12]	张小圆, 李世鹏, 杨保雨, 等. 潜航飞行体深水超音速气体射流的流动稳定性研究[J]. 兵工学报, 2019, 40(12):2385-2398. doi: 10.3969/j.issn.1000-1093.2019.12.001
	ZHANG X Y, LI S P, YANG B Y, et al. Analysis of the flow instability of supersonic gaseous jets for submarine vehicles working in deep water[J]. Acta Armamentarii, 2019, 40(12):2385-2398. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.12.001
[13]	张小圆, 李世鹏, 杨保雨, 等. 水下固体火箭发动机垂直气体射流结构和推力影响研究[J]. 推进技术, 2021, 42(5):961-969.
	ZHANG X Y, LI S P, YANG B Y, et al. Flow structures of vertical gaseous jets and effects of thrust of underwater solid rocket motor[J]. Journal of Propulsion Technology, 2021, 42(5):961-969. (in Chinese)
[14]	张春, 郁伟, 王宝寿. 水下超声速燃气射流的初期流场特性研究[J]. 兵工学报, 2018, 39(5):961-968. doi: 10.3969/j.issn.1000-1093.2018.05.016
	ZHANG C, YU W, WANG B S. Research on the initial flow field characteristics of underwater supersonic gas jets[J]. Acta Armamentarii, 2018, 39(5):961-968. (in Chinese) doi: 10.3969/j.issn.1000-1093.2018.05.016
[15]	张春, 郁伟, 王宝寿. 水下超声速过膨胀燃气射流的流场特性[J]. 航空动力学报, 2022, 37(8):1633-1642.
	ZHANG C, YU W, WANG B S. Flow field characteristics of underwater supersonic over-expanded gas jet[J]. Journal of Aerospace Power, 2022, 37(8):1633-1642. (in Chinese)
[16]	GONG Z X, LU C J, LI J, et al. The gas jet behavior in submerged Laval nozzle flow[J]. Journal of Hydrodynamics, 2017, 29(6):1035-1043.
[17]	张磊. 大水深火箭发动机尾流场数值模拟[J]. 固体火箭技术, 2019, 42(2):159-163.
	ZHANG L. Numerical simulation of tail flow field for underwater solid rocket motor[J]. Journal of Solid Rocket Technology, 2019, 42(2):159-163. (in Chinese)
[18]	FRONZEO M, KINZEL M. An investigation of compressible gas jets submerged into water[C]// Proceedings of the 46th AIAA Fluid Dynamics Conference.Washington,D.C., US:AIAA, 2016:4253.
[19]	唐云龙, 李世鹏, 刘筑, 等. 水下火箭水平射流初期特征研究[J]. 物理学报, 2015, 64(23):234702.
	TANG Y L, LI S P, LIU Z, et al. Horizontal jet characteristics of an underwater solid rocket motor at the beginning of working[J]. Acta Physica Sinica, 2015, 64(23):234702. (in Chinese)
[20]	许海雨, 罗凯, 刘日晨. 水下超声速气流流场非定常特性研究[J]. 推进技术, 2019, 40(11):2618-2625.
	XU H Y, LUO K, LIU R C. Research on unsteady characteristics of underwater supersonic gas jet[J]. Journal of Propulsion Technology, 2019, 40(11):2618-2625. (in Chinese)
[21]	JANA A, HOSKOTI L, SUCHEENDRAN M M. A numerical study of the flow field driven by a submerged,high-speed,gaseous jet[J]. Journal of Fluids Engineering, 2022, 144(11):111208.
[22]	王利利, 刘影, 李达钦, 等. 固体火箭发动机水下超音速射流数值研究[J]. 兵工学报, 2019, 40(6):1161-1170. doi: 10.3969/j.issn.1000-1093.2019.06.006
	WANG L L, LIU Y, LI D Q, et al. Numerical study of underwater supersonic gas jets for solid rocket engine[J]. Acta Armamentarii, 2019, 40(6):1161-1170. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.06.006
[23]	王德友, 李世鹏, 金戈, 等. 耦合尾喷管堵盖运动的水下固体火箭发动机点火启动过程特性[J]. 兵工学报, 2023, 44(6):1665-1676. doi: 10.12382/bgxb.2022.0136
	WANG D Y, LI S P, JIN G, et al. Characteristics of ignition start-up process of underwater solid rocket motor with the effect of nozzle closure[J]. Acta Armamentarii, 2023, 44(6):1665-1676. (in Chinese) doi: 10.12382/bgxb.2022.0136
[24]	FERGUSON J D. Experimental data from underwater conical nozzles exhausting N₂ gas[J]. Journal of Hydronautics, 1969, 3(4):200.
[25]	权晓波, 王占莹, 刘元清, 等. 水环境下喷管流动分离数值研究[J]. 固体火箭技术, 2020, 43(1):8-15.
	QUAN X B, WANG Z Y, LIU Y Q, et al. Numerical simulation research on the flow separation of solid rocket motor in water environment[J]. Journal of Solid Rocket Technology, 2020, 43(1):8-15. (in Chinese)
[26]	GROSS A, WEILAND C. Numerical simulation of separated cold gas nozzle flows[J]. Journal of Propulsion and Power, 2004, 20(3):509-519.
[27]	SCHOMBERG K, OLSEN J, NEELY A, et al. Effect of the contour shock on restricted shock separation in rocket nozzles[J]. Journal of Propulsion and Power, 2018, 34(2):556-560.
[28]	王一白, 梁远舰, 赵宇辉, 等. 抛物线喷管型面参数对流动分离影响的数值模拟[J]. 航空动力学报, 2017, 32(4):955-960.
	WANG Y B, LIANG Y J, ZHAO Y H, et al. Numerical simulation of effect of parabolic nozzle contour parameters on flow separation[J]. Journal of Aerospace Power, 2017, 32(4):955-960. (in Chinese)
[29]	穆旭, 田维平, 董新刚, 等. 固体火箭发动机喷管扩张段型面参数对其性能影响仿真分析[J]. 固体火箭技术, 2021, 44(2):254-263.
	MU X, TIAN W P, DONG X G, et al. Study on the effect of divergence contour parameters on performance of solid rocket motor nozzle[J]. Journal of Solid Rocket Technology, 2021, 44(2):254-263. (in Chinese)
[30]	何淼生, 覃粒子, 刘宇. 环喉型圆锥塞式喷管的水下流动分离特性[J]. 推进技术, 2015, 36(1):37-46.
	HE M S, QIN L Z, LIU Y. Numerical investigation of flow separation in an annular conical aerospike nozzle for underwater propulsion[J]. Journal of Propulsion Technology, 2015, 36(1):37-46. (in Chinese)
[31]	HE M S, QIN L Z, LIU Y. Oscillation flow induced by underwater supersonic gas jets from a rectangular Laval nozzle[J]. Procedia Engineering, 2015, 99:1531-1542.
[32]	TANG Y L, LI S P. The mechanism for the quasi-back-attack phenomenon of gas jets submerged in water[J]. International Journal of Aeronautical and Space Sciences, 2019, 20:165-171.
[33]	许海雨, 罗凯, 刘富强, 等. 水下超声速射流对上浮水雷受力特性影响研究[J]. 推进技术, 2020, 41(11):2623-2629.
	XU H Y, LUO K, LIU F Q, et al. Effects of underwater supersonic jet on force characteristics of floating mine[J]. Journal of Propulsion Technology, 2020, 41(11):2623-2629. (in Chinese)
[34]	öSTLUND J, DAMGAARD T, FREY M. Side-load phenomena in highly overexpanded rocket nozzles[J]. Journal of Propulsion and Power, 2004, 20(4):695-704.
[35]	öSTLUND J. Flow processes in rocket engine nozzles with focus on flow separation and side-loads,TRITA-MEK-02-09[R]. Stockholm, Sweden: Royal Institute of Technology,Department of Mechanics, 2002.
[36]	BAARS W J, TINNEY C E, RUF J H, et al. Wall pressure unsteadiness and side loads in overexpanded rocket nozzles[J]. AIAA Journal, 2012, 50(1):61-73.
[37]	何成军, 李建强, 黄江涛, 等. 非对称超声速喷管内流动分离非定常特性[J]. 航空学报, 2022, 43(1):124930. doi: 10.7527/S1000-6893.2020.24930
	HE C J, LI J Q, HUANG J T, et al. Unsteadiness of flow separation in an asymmetric supersonic nozzle[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(1):124930. (in Chinese) doi: 10.7527/S1000-6893.2020.24930
[38]	张磊, 佘湖清. 固体火箭发动机水下工作推力特性的实验研究[J]. 含能材料, 2020, 28(12):1184-1189.
	ZHANG L, SHE H Q. Experimental research on thrust characteristics of solid rocket engine working underwater[J]. Chinese Journal of Energetic Materials, 2020, 28(12):1184-1189. (in Chinese)