进气道流动中SST湍流模型参数的不确定度量化

doi:10.7527/S1000-6893.2023.29429

Abstract

Abstract:

The inlet， as one of the key components of the air-breathing high Mach number vehicle， is significant to the performance of the whole propulsion system. In the numerically simulated inlet flow for engineering applications， RANS （Reynolds Averaged Navier-Stokes） still plays an irreplaceable role. However， the turbulence model frequently used in RANS would affect the reliability of the numerical results due to its parameter uncertainty. The purpose of this paper is to carry out quantitative analysis on parameter uncertainty in the SST （Shear Stress Transport） turbulence model， and evaluate the influence on the inlet flow. The hysteresis loop of the inlet start performance was firstly predicted by the SST turbulence model， the uncertainty of QoIs （Quantity of Interests） caused by the parameter uncertainty was then quantified by Non-Intrusive Polynomial Chaos （NIPC） method， and the key parameters were identified by the sensitivity analysis for both the start and unstart states of the inlet. The results show that the uncertainty of model parameters leads to a large uncertainty in the prediction results of the shock wave structure for the inlet start state and the separation flow for the inlet unstart state， further resulting in a 10% non-negligible uncertainty of the inlet performance parameters. According to the parameter sensitivity analysis， σ_ω₁ and a₁ are the key model parameters contributing most to the QoIs uncertainty.

Key words: turbulence model, inlet, hysteresis loop, uncertainty quantification, sensitivity analysis

CLC Number:

V211.3

Kailing ZHANG, Siyi LI, Yi DUAN, Chao YAN. Uncertainty quantification of parameters in SST turbulence model for inlet simulation[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729429-729429.

Figures/Tables 15

Table 1

Normal values and uncertainty intervals for parameters of SST turbulent model

封闭参数	基准值	区间下界	区间上界
$σ ω 1$	0.5	0.3	0.7
$σ ω 2$	0.856	0.7	1.0
$σ k 1$	0.85	0.7	1.0
$σ k 2$	1.0	0.8	1.2
$β 1$	0.075	0.06	0.09
$β 2$	0.082 8	0.07	0.1
$β *$	0.09	0.078 4	0.102 4
$a 1$	0.31	0.31	0.40
$κ$	0.41	0.38	0.42

Table 1

Fig.1

Fig.2

Table 2

Details for grid independence analysis

网格编号	G1	G2	G3
网格雷诺数	10	20	30
进气道内网格量	733 $×$ 143	626 $×$ 129	519 $×$ 114

Table 2

Fig.3

Fig.4

Fig.5

Fig.6

Table 3

Fig.7

Table 4

Table 5

Fig.8

Fig.9

Table 6

Key parameters of model

物理量	关键参数及Sobol值
物理量	起动状态	不起动状态
总压恢复系数	$σ ω 1$ （0.67）	$σ ω 1$ （0.52）
质量流量	$σ ω 1$ （0.66）	$a 1$ （0.35）
轴向力系数	$σ ω 1$ （0.74）	$σ ω 1$ （0.34）
法向力系数	$σ ω 1$ （0.81）	$a 1$ （0.34）

Table 6

References 26

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位置	物理量	不确定度/%
上壁面	分离点位置	7.51
	峰值1大小	1.35
	峰值2大小	3.27
	峰值3大小	5.78
	再附点位置	5.61
	峰值1位置	4.68
	峰值2位置	2.77
	峰值3位置	2.8
下壁面	峰值1大小	2.36
	峰值2大小	4.59
	峰值3大小	6.65
	峰值1位置	3.19
	峰值2位置	2.14
	峰值3位置	2.95

位置	物理量	不确定度/%
上壁面	分离点位置	24.08
	峰值1大小	6.86
	峰值2大小	15.47
	峰值3大小	11.0
	再附点位置	6.46
	峰值1位置
	峰值2位置	9.38
	峰值3位置	8.99
下壁面	分离点位置	9.87
	峰值1大小	15.99
	峰值2大小	12.9
	峰值3大小	11.82
	再附点位置	7.32
	峰值1位置	4.49
	峰值2位置	10.18
	峰值3位置	8.49

物理量	不确定度/%
物理量	起动状态	不起动状态
总压恢复系数	10.52	8.53
质量流量	1.85	9.72
轴向力系数	9.83	7.13
法向力系数	7.57	2.88

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Uncertainty quantification of parameters in SST turbulence model for inlet simulation

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