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Research Papers: Flows in Complex Systems

# Modeling the Effect of Stability Bleed on Back-Pressure in Mixed-Compression Supersonic Inlets

[+] Author and Article Information
Lv Yongzhao

National Key Laboratory of Science
and Technology on Aero-Engine
Aero-Thermodynamics,
Collaborative Innovation
School of Energy and Power Engineering,
Beihang University,
Haidian District, Beijing 100191, China
e-mail: lvjiuhui@163.com

Li Qiushi

National Key Laboratory of Science
and Technology on Aero-Engine
Aero-Thermodynamics,
Collaborative Innovation
School of Energy and Power Engineering,
Beihang University,
Haidian District, Beijing 100191, China
e-mail: liqs@buaa.edu.cn

Li Shaobin

National Key Laboratory of Science
and Technology on Aero-Engine
Aero-Thermodynamics,
Collaborative Innovation
School of Energy and Power Engineering,
Beihang University,
Haidian District, Beijing 100191, China
e-mail: lee_shaobin@buaa.edu.cn

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 18, 2014; final manuscript received June 4, 2015; published online August 4, 2015. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 137(12), 121101 (Aug 04, 2015) Paper No: FE-14-1456; doi: 10.1115/1.4030811 History: Received August 18, 2014

## Abstract

To stabilize the terminal normal shock on high-static pressure at outlet, called back-pressure $pout$, stability bleed slots are used in the throat of mixed-compression supersonic inlets. In this paper, a model for the functional relation between the bleed flow rate $mbl$ and back-pressure $pout$ is established based on a bleed flow rate model (BFRM) in order to study the effect of stability bleed on the back-pressure in mixed-compression supersonic inlets. Given the inlet flow parameters $Min$, $pin*$, and $Tin*$, the plenum pressure $ppl$ at slots' outlet, the terminal normal shock position $xs$ in this model, the bleed flow rate $mbl$, Mach number $M¯out$, and back-pressure $pout$ were derived one by one from the basic laws of conservation. To study the effect of plenum pressure $ppl$ on subsonic flow of the divergent section behind the terminal normal shock, a correction coefficient $κ$ is introduced to modify the Mach number $M¯out$. Furthermore, numerical simulations based on Reynolds-Averaged Navier–Stokes equations were performed to analyze the functional relation between the bleed flow rate $mbl$ and back-pressure $pout$. Computational fluid dynamics (CFD) results show that the present model agrees with the data.

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## References

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## Figures

Fig. 5

Schematic of the simplified expansion wave

Fig. 4

Schematic of the specified shock positions: (a) xs =  xs2 and (b) xs =  xs1

Fig. 3

Flow field characteristics through the bleed slot

Fig. 2

Physical model

Fig. 1

Axisymmetric mixed-compression inlet

Fig. 6

Schematic of the flow characteristics of the divergent nozzle: (a) xs2<xs<xs3, (b) xs1<xs<xs2, and (c) 0<xs<xs1

Fig. 7

Flow field characteristics through the bleed slot: (a) case (A) and (b) case (B)

Fig. 10

Normalized pressure distribution

Fig. 8

Validation model (m)

Fig. 9

Generated mesh near the bleed slot for numerical solution

Fig. 18

The back-pressure for different plenum pressures (case 2)

Fig. 19

The total pressure for different plenum pressures (case 2)

Fig. 12

Flow domain and Mach number contours (Case 2:M=1.6,ppl=18,000 Pa,pout/pin*=0.72)

Fig. 13

Distribution of the Maher number: (a) x/xs3=0.6 and (b) x/xs3=2.8

Fig. 14

Distribution of the deflection angle: (a) x/xs3=0.6 and (b) x/xs3=2.8

Fig. 15

Comparison of the back-pressure at the outlet (case 1): (a) ppl = 22,000 Pa, (b) ppl = 18,000 Pa, (c) ppl = 14,000 Pa, and (d) ppl = 10,000 Pa

Fig. 16

Comparison of the back-pressure at the outlet (case 2): (a) ppl = 18,000 Pa, (b) ppl = 14,000 Pa, (c) ppl = 10,000 Pa, and (d) ppl = 8000 Pa

Fig. 17

Comparison of the back-pressure at the outlet (case 3): (a) ppl = 14,000 Pa, (b) ppl = 12,000 Pa, (c) ppl = 8000 Pa, and (d) ppl = 6000 Pa

Fig. 11

Mesh independence verification: (a) bleed flow rate and (b) terminal normal shock position

Fig. 20

Comparison of the back-pressure at the outlet: (a) M = 1.5, ppl = 14,000 Pa and (b) M = 1.6, ppl = 10,000 Pa

Fig. 21

Comparison of the Mach number at the outlet: (a) M = 1.5, ppl = 14,000 Pa and (b) M = 1.6, ppl = 10,000 Pa

## Errata

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