两级膨胀喷管设计方法及数值模拟

doi:10.7527/S1000-6893.2024.31009

Abstract

Abstract:

To enhance the performance of the nozzle in a wide airspace （0–24 km） and wide speed domain （Mach number 0–5）， a two-stage expansion nozzle design methodology is investigated by utilizing altitude compensation and inverse design concepts. Firstly， the design method and steps of the two-stage expansion nozzle are introduced. The two-stage expansion nozzle profiles are divided into the base section and extension section profiles. The base section profiles are generated by the reverse design method based on the wall pressure， which is used to shorten the negative thrust surface of the nozzle by changing the position and strength of the shock wave and to improve the thrust performance of the nozzle under the low-speed flight condition. The nozzle extension profile adopts the maximum thrust nozzle design method based on strong geometric constraints to meet the purpose of hypersonic vehicle afterbody integration design. Secondly， the validity of the proposed design methodology is verified using numerical simulation， in which the numerical calculation methodology is introduced and verified， and the grid resolution is determined. Further， the design method for the reverse design of nozzle base profile for controlling wall pressure distribution is validated， and the goal of forward/backward shifting of the shock wave is achieved. At the same time， a study is conducted on the influence of the two key design parameters， i. e.， the position control factor and the pressure control factor， on the the performance of the nozzle. Finally， comparative analysis of the proposed method and the maximum thrust nozzle design method with full geometric constraints is performed to verify the effectiveness and superiority of the new method. The results show that compared to the fully geometrically constrained maximum-thrust nozzle， the nozzle designed with the proposed method improves the thrust performance by 7.86% in the over-expansion state and decreases the thrust performance by only 0.75% in the under-expansion state under typical design conditions， which provides a theoretical basis for the design of the exhaust system of hypersonic vehicles.

Key words: two-stage expansion, forward and reverse design, method of characteristics, full geometric constraint, maximum thrust theory

CLC Number:

V231.3

Wenqian PEI, Kaikai YU, Zengxu LIU, Qiyue NING, Jinglei XU. Two-stage expansion nozzle design method and numerical simulation[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(8): 631009.

Figures/Tables 24

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 1

Low pressure ratio condition

NPR	$L / m m$	$R o u t / m m$	$M a i n$	$P 0 / P a$	$T 0 / K$	$H / k m$	$P b / P a$	$M a ∞$
5.3	490	178	1.139	95 200	1 281	1.5	17 933	2
5.0	490	178	1.139	95 200	1 281	1.5	19 040	2

Table 1

Fig.9

Fig.10

Fig.11

Table 2

Intra-nozzle shock wave positions obtained from designs with different position control factors for NPR=5.3 and NPR=5.0

$n$	$β$	激波位置
$n$	$β$	NPR=5.3	NPR=5.0
1.0	1.0	300	277
1.1	1.0	345	336
0.8	1.0	212	196
0.6	1.0	136	148
0.4	1.0	95	84

Table 2

Table 3

Design conditions

$N P R$	$L / m m$	$R o u t / m m$	$M a i n$	$P 0 / P a$	$T 0 / K$	$H / k m$	$P b / P a$	$M a ∞$
138.8	490	178	1.764 9	402 402	2 635	24.2	2 899.482	5

Table 3

Fig.12

Fig.13

Fig.14

Fig.15

Table 4

Intra-nozzle shock wave positions and thrust performance obtained by designs with different position control factors

$β$	基础段末端压力/Pa	$n$	基础段长度/mm	$N P R = 5.3$ 激波位置/mm	$N P R = 5.3$ 推力/N	推力增长/%	$N P R = 138.8$ 推力/N	推力增长/%
1.00	1 854.8	1.00	394	300	-1 024.0		837.4
0.13	13 946.3	0.11	45	261	-950.4	7.19	833.0	-0.53
0.13	13 946.3	0.10	40	257	-943.6	7.86	831.1	-0.75
0.13	13 946.3	0.09	35	253	-937.1	8.49	828.9	-1.02

Table 4

Fig.16

Fig.17

Fig.18

Fig.19

Table 5

Intra-nozzle shock wave positions and thrust performance of nozzle designed with different pressure control factors

$n$	基础段长度/mm	$β$	基础段末端压力/Pa	$N P R = 5.3$ 激波位置/mm	$N P R = 5.3$ 推力/N	推力增长百分比/%	$N P R = 138.8$ 推力/N	推力增长百分比/%
1.00	394	1.00	1 854.8	300	-1 024.0		837.4
0.10	40	0.13	13 946.3	257	-943.6	7.86	831.1	-0.75
0.10	40	0.17	10 648.9	243	-889.8	13.10	820.8	-1.98
0.10	40	0.21	8 910.1	227	-855.3	16.47	811.9	-3.05

Table 5

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Two-stage expansion nozzle design method and numerical simulation

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