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Technical Brief

Determination of the Pressure Field Using Three-Dimensional, Volumetric Velocity Measurements

[+] Author and Article Information
Hansheng Pan, Sheila H. Williams, Paul S. Krueger

Department of Mechanical Engineering,
Southern Methodist University,
P.O. Box 750337,
Dallas, TX 75275

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 31, 2013; final manuscript received March 8, 2016; published online May 19, 2016. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 138(8), 084502 (May 19, 2016) (9 pages) Paper No: FE-13-1760; doi: 10.1115/1.4033293 History: Received December 31, 2013; Revised March 08, 2016

Methods to determine the pressure field of vortical flow from three-dimensional (3D) volumetric velocity measurements (e.g., from a TSI V3VTM system) are discussed. The boundary pressure was determined where necessary using the unsteady Bernoulli equation for both line integration and pressure Poisson equation methods. Error analysis using computational fluid dynamics (CFD) data was conducted to investigate the effects of spatial resolution, temporal resolution, and velocity error levels. The line integration method was more sensitive to temporal resolution, while the pressure Poisson equation method was more sensitive to boundary flow conditions. The latter was generally more suitable for V3VTM velocity measurements.

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Figures

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Fig. 1

Computational domain used for CFD simulations of vortex ring formation and evolution

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Fig. 2

Contour plots for CFD simulations of axisymmetric flow: (a) velocity magnitude when the vortex ring is in the middle of the domain, (b) pressure field when the vortex ring is in the middle of the domain, (c) velocity magnitude when the vortex ring is on the edge, and (d) pressure field when the vortex ring is on the edge

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Fig. 3

The effect of spatial resolution on pressure estimation errors: (a) maximum bias error in the middle of the domain, (b) maximum bias error on the edge of the domain, (c) RMS error in the middle of the domain, and (d) RMS error on the edge of the domain

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Fig. 4

The effect of temporal resolution on pressure estimation errors: (a) maximum bias error in the middle of the domain, (b) maximum bias error on the edge of the domain, (c) RMS error in the middle of the domain, and (d) RMS error on the edge of the domain

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Fig. 5

The effect of velocity error level on the accuracy of maximum bias error when the vortex ring is (a) in the middle of the domain and (b) on the edge of the domain

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Fig. 6

The effect of velocity error level on the RMS error when the vortex ring is (a) in the middle of the domain and (b) on the edge of the domain

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Fig. 7

Schematic of vortex ring generator mechanism: (a) piston–cylinder vortex ring generator cross section, (b) top view of the entire setup showing the arrangement of the laser and camera, and (c) photograph of the setup

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Fig. 8

A single vortex ring plotted from raw velocity data: (a) velocity magnitude, (b) Q-criterion, (c) isosurface of pressure at P* = −0.15 computed by the line integration method, (d) isosurface of pressure at P* = −0.15 computed by the pressure Poisson equation method, (e) pressure distribution in the X–Y plane through the middle of the vortex ring computed by the line integration method, and (f) pressure distribution in the X–Y plane through the middle of the vortex ring computed by the pressure Poisson equation method

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Fig. 9

A single vortex ring plotted from smoothed velocity data: (a) velocity magnitude, (b)Q-criterion, (c) isosurface of pressure at P* = −0.2 computed by the line integration method, (d) isosurface of pressure at P* = −0.15 computed by the pressure Poisson equation method, (e) pressure distribution in the X–Y plane through the middle of the vortex ring computed by the line integration method, and (f) pressure distribution in the X–Y plane through the middle of the vortex ring computed by the pressure Poisson equation method

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Fig. 10

Comparison of the standard deviation of the line integration results (ε) with RMS errors: (a) when the vortex ring is in the middle of the domain and (b) when the vortex ring is on the edge of the domain

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