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Analytical and computational studies on the vacuum performance of a chevron ejector

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Abstract

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

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Abbreviations

A :

Cross-sectional area \((\hbox {m}^{2})\)

\(c_\mathrm{p}\) :

Constant pressure specific heat (J/kg K)

\(D_\mathrm{h}\) :

Hydraulic diameter (m)

E :

Specific total energy (J/kg)

f :

Friction factor

H :

Height of the nozzle throat (m)

L :

Length (m)

M :

Mach number

P :

Pressure (Pa)

\(\mathrm{Pr}_\mathrm{t}\) :

Turbulent Prandtl number

R :

Gas constant (J/kg K)

Re:

Reynolds number

Rm:

Entrainment ratio

t :

Time (s, ms)

T :

Temperature (K)

\(u_{i,j,k}\) :

Velocity components (m/s)

\(\overline{u_i } ,u_i^{\prime }\) :

Mean and fluctuating velocity components (m/s)

\(\overline{u_i^{\prime } u_j^{\prime } } \) :

Reynolds stress tensor

V :

Velocity (m/s)

x, y, z :

Cartesian coordinates

\(y^+\) :

Non-dimensional distance

\(\alpha \) :

Thermal conductivity (W/m K)

\(\varepsilon \) :

Roughness height (m)

\(\gamma \) :

Ratio of specific heats

\(\delta _{ij}\) :

Kronecker symbol

\(\delta \) :

Deflection angle (\(^{\circ }\))

\(\theta \) :

Shock angle (\(^{\circ }\))

\(\lambda \) :

Thickness of the chevrons (\(\lambda <\!<{H}\))

\(\dot{m}\) :

Mass flow rate (kg/s)

\(\mu \) :

Dynamic viscosity (Pa s)

\(\mu _{\mathrm{eff}}\) :

Effective viscosity (kg/m s)

\(\rho \) :

Density (\(\hbox {kg}/\hbox {m}^{3}\))

\(\tau _{ij}\) :

Stress tensor

\(\tau _{ij, \mathrm{eff}}\) :

Effective stress tensor

\(\psi _{1,2,3} \) :

Complementary coefficients

0:

Stagnation condition

1:

1st: primary stream

2:

2nd: secondary stream

atm:

Atmosphere

b:

Back pressure

c:

Cross section-c

D:

Diffuser section

e:

Exit of the vacuum ejector-diffuser system

i, j, k :

Unit vectors

m:

Cross section-m

M:

Mixing chamber

o:

Cross section-o

s:

Cross section-s, before the normal shock wave

t:

Primary flow nozzle throat

w:

Cross section-w, after the normal shock wave

CFD:

Computational fluid dynamics

DER:

Dynamic equilibrium region

HAT:

High altitude test

RANS:

Reynolds averaged Navier–Stokes

RSM:

Reynolds stress model

S–A:

Spalart–Allmaras Model

SFR:

Steady flow region

STR:

Starting transients region

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Acknowledgments

This work is supported by the Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) contracted through Advanced Space Propulsion Research Center at Seoul National University (Project Number: 0659-20150012).

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Authors and Affiliations

  1. School of Mechanical Engineering, Andong National University, Andong, 760-749, Korea

    F. S. Kong & H. D. Kim

  2. College of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Y. Z. Jin

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  1. F. S. Kong
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Correspondence to H. D. Kim.

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Communicated by K. Hannemann and A. Higgins.

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Kong, F.S., Jin, Y.Z. & Kim, H.D. Analytical and computational studies on the vacuum performance of a chevron ejector. Shock Waves 26, 771–788 (2016). https://doi.org/10.1007/s00193-015-0618-8

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