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Research Papers: Fundamental Issues and Canonical Flows

# Investigation of the Flow Structures in Supersonic Free and Impinging Jet Flows

[+] Author and Article Information
C. Chin

e-mail: chincc@unimelb.edu.au

A. Ooi

Department of Mechanical Engineering,
The University of Melbourne,
Parkville, VIC, 3010, Australia

A. Risborg

Department of Mechanical and Aerospace Engineering,
Monash University,
Clayton, VIC, 3800, Australia

J. Soria

Department of Mechanical and Aerospace Engineering,
Monash University,
Clayton, VIC, 3800, Australia;
Department of Aeronautical Engineering,
King Abdulaziz University,
Jeddah, 22254, Saudi Arabia

1Corresponding author.

Manuscript received February 14, 2012; final manuscript received August 22, 2012; published online February 22, 2013. Assoc. Editor: Meng Wang.

J. Fluids Eng 135(3), 031202 (Feb 22, 2013) (12 pages) Paper No: FE-12-1077; doi: 10.1115/1.4023190 History: Received February 14, 2012; Revised August 22, 2012

## Abstract

A numerical study of compressible jet flows is carried out using Reynolds averaged Navier–Stokes (RANS) turbulence models such as $k-ɛ$ and $k-ω-SST$. An experimental investigation is performed concurrently using high-speed optical methods such as Schlieren photography and shadowgraphy. Numerical and experimental studies are carried out for the compressible impinging at various impinging angles and nozzle-to-wall distances. The results from both investigations converge remarkably well and agree with experimental data from the open literature. From the flow visualizations of the velocity fields, the RANS simulations accurately model the shock structures within the core jet region. The first shock cell is found to be constraint due to the interaction with the bow-shock structure for nozzle-to-wall distance less than 1.5 nozzle diameter. The results from the current study show that the RANS models utilized are suitable to simulate compressible free jets and impinging jet flows with varying impinging angles.

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## Figures

Fig. 1

Supersonic impinging jet setup

Fig. 2

(a) Experimental setup for supersonic impinging jet using Schlieren photography. (b) Zoomed-in view of the impinging jet region.

Fig. 3

Specifications for Schlieren field mirrors

Fig. 4

3D view of the mesh employed for RANS simulations of a supersonic free-jet

Fig. 5

Computational domain and boundary conditions employed for supersonic free jet simulations

Fig. 6

Computational domain and boundary conditions employed for supersonic impinging jet simulations

Fig. 7

Grid resolution in the core region where shock occurs: (a) for free jet flow and (b) for impinging jet flow. Color contours of pressure gradient (color contours are rescaled for better illustration of shock structures).

Fig. 8

Flow visualization of the axial velocity distribution of the supersonic free jet with RANS k-ɛ model. (a) Color contours of Mach number 0≤M≤ 2.5. (b) Normalized pressure gradient distribution 0.5≤dP/dP| max≤ 1.

Fig. 9

Centerline Mach number of the supersonic free jet simulations comparing with experimental results of Troutt and McLaughlin [8]. k-ɛ (solid-line), k-ω-SST (dashed-line) and experiment (°).

Fig. 10

Comparison of the streamwise Mach number profiles in the radial direction at different axial locations. (a) Zn/D = 1, (b) Zn/D = 5, (c) Zn/D = 10, and (d) Zn/D = 15. k-ɛ (solid-line), k-ω-SST (dashed-line) and experiment (°).

Fig. 11

Streamwise velocity profiles in the radial direction at various axial locations comparing with the Gaussian curve defined by Troutt and McLaughlin [8]. Axial locations are (a) Zn/D = 1, (b) Zn/D = 5, (c) Zn/D = 10, and (d) Zn/D = 15. Lines are as in Fig. 9. The dot-dashed line corresponds to Eq. (13).

Fig. 12

Flow visualization of shock structure using RANS simulations and shadowgraphy for nozzle-to-wall distance Zn/D= 2.5 at various impingement angles. (a) θ=0 deg, (b) θ=10 deg, (c) θ= 30 deg, and (d) θ= 45 deg.

Fig. 13

Flow visualization of shock structure using RANS simulations and shadowgraphy for nozzle-to-wall distance Zn/D= 1.5 at various impingement angles. (a) θ= 0 deg, (b) θ=10 deg, (c) θ= 30 deg, and (d) θ= 45 deg.

Fig. 14

Comparison of the length of the first shock cell between experiment and simulation for various nozzle-to-wall distances Zn/D and impingement angles θ. Open symbols denote simulation results using RANS k-ɛ model and solid symbols correspond to experimental results. Symbols in red represent Zn/D≈ 1.5 and black for Zn/D≈ 2.5.

Fig. 15

Distribution of the normalized pressure profiles (P˜) for RANS model k-ɛ (solid line) comparing with experimental results of Donaldson and Snedeker [17] (°) for varying impinging angles θ; (a) 0 deg, (b) 15 deg, (c) 30 deg, and (d) 45 deg

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