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Research Papers: Flows in Complex Systems

Nondimensional Parameter for Characterization of Wall Shear Stress From Underexpanded Axisymmetric Impinging Jets

[+] Author and Article Information
Patrick Fillingham

Department of Mechanical Engineering,
University of Washington,
Seattle, WA 98105

Harikrishnan Murali

Department of Aeronautics and Astronautics,
University of Washington,
Seattle, WA 98105

Igor V. Novosselov

Department of Mechanical Engineering,
University of Washington,
Seattle, WA 98105
e-mail: ivn@uw.edu

1The authors contributed equally to this work.

2Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 16, 2016; final manuscript received April 20, 2017; published online August 2, 2017. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 139(11), 111102 (Aug 02, 2017) (9 pages) Paper No: FE-16-1611; doi: 10.1115/1.4037035 History: Received September 16, 2016; Revised April 20, 2017

Wall shear stress is characterized for underexpanded axisymmetric impinging jets for the application of aerodynamic particle resuspension from a surface. Analysis of the flow field resulting from normally impinging axisymmetric jets is conducted using computational fluid dynamics (CFD). A normally impinging jet is modeled with a constant area nozzle while varying the height to diameter ratio (H/D) and the inlet pressures. Schlieren photography is used to visualize the density gradient of the flow field for validation of the CFD. A dimensionless jet parameter (DJP) is developed to describe flow regimes and characterize shear stress. The DJP is defined as being proportional to the jet pressure ratio divided by the H/D ratio squared. Maximum wall shear stress is examined as a function of DJP with three distinct regimes: (i) subsonic impingement (DJP < 1), (ii) transitional (1 < DJP < 2), and (iii) supersonic impingement (DJP > 2). It is observed that wall shear stress is limited to a finite value due to jet energy dissipation in shock structures, which become a dominant dissipation mechanism in the supersonic impingement regime. Additionally, the formation of shock structures in the wall flow was observed for DJP > 2, resulting in difficulties with dimensionless analysis. In subsonic impingement and transitional regimes, equations as a function of the DJP are obtained for the maximum wall shear stress magnitude, maximum shear stress location, and shear stress decay. Using these relationships, wall shear stress can be predicted at all locations along the impingement surface.

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Figures

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Fig. 1

Schematic diagram of a normal impinging jet. The flow consists of the free jet region, stagnation zone, and wall jet region. The boundary layer develops as jet impinges on the surface and creates the flow parallel to the surface.

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Fig. 2

Computational domain (not to scale). Note that only half the domain is modeled due to the presence of symmetry. The inlet is supplied with gauge pressure, plate follows the model of a no slip wall, and outlet represents the open atmosphere (0 psig).

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Fig. 3

Schematic of experimental impinging jet setup. Supply pressure was regulated through the supply pressure gauge and measured precisely using an electronic pressure transducer. The flow was regulated using an alternating current solenoid. The flow field was then captured using Schlieren imaging.

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Fig. 4

Schematic of the z-type Schlieren setup used to visualize the flow field of the underexpanded impinging jet

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Fig. 5

Schematic of underexpanded impinging jet. Key characteristics are outlined. The presence of supersonic flow extending to the impingement point results in a normal plate shock, which dissipates energy resulting in less efficient removal. If the pressure in the recirculation zone is high enough a shockwave in the wall jet region may form.

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Fig. 6

Density contours of CFD model and Schlieren images at a height to diameter ratio of 5. The number of shock cells decreases with increasing pressure, but they get stronger. The oblique shock cells and the plate shocks produced by CFD are in agreement with the Schlieren images.

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Fig. 7

Experimental verification of H/D as a similarity parameter. Normally impinging jets of similar H/D, supplied with the same inlet pressure, produce the same flow pattern.

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Fig. 8

Experimental verification of H/D as a similarity parameter. Normally impinging jets of similar H/D, supplied with the same inlet pressure of 40 psi, produce the same shear stress profiles but different maximum values.

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Fig. 9

Wall shear stress distribution for H/D of 10, 20, and 30 at gauge pressures of 20, 40, 60, 80, and 100 psig. The plots show the change in maximum wall shear stress magnitude and location.

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Fig. 10

Maximum wall shear stress versus DJP with lines separating the subsonic, transitional, and supersonic wall regions. For DJP greater than 1, the maximum shear stress asymptotically approached the maximum value limit.

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Fig. 11

Plot of the variation of peak wall shear stress with the dimensionless jet parameter with data using the equations developed by Phares et al. [12]

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Fig. 12

Plot showing the effect of the dimensionless jet parameter on the peak wall shear location

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Fig. 13

Effect of dimensionless jet parameter on exponential jet decay factor

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