Abstract
A method is proposed to determine the instantaneous pressure field from a single tomographic PIV velocity snapshot and is applied to a flat-plate turbulent boundary layer. The main concept behind the single-snapshot pressure evaluation method is to approximate the flow acceleration using the vorticity transport equation. The vorticity field calculated from the measured instantaneous velocity is advanced over a single integration time step using the vortex-in-cell (VIC) technique to update the vorticity field, after which the temporal derivative and material derivative of velocity are evaluated. The pressure in the measurement volume is subsequently evaluated by solving a Poisson equation. The procedure is validated considering data from a turbulent boundary layer experiment, obtained with time-resolved tomographic PIV at 10 kHz, where an independent surface pressure fluctuation measurement is made by a microphone. The cross-correlation coefficient of the surface pressure fluctuations calculated by the single-snapshot pressure method with respect to the microphone measurements is calculated and compared to that obtained using time-resolved pressure-from-PIV, which is regarded as benchmark. The single-snapshot procedure returns a cross-correlation comparable to the best result obtained by time-resolved PIV, which uses a nine-point time kernel. When the kernel of the time-resolved approach is reduced to three measurements, the single-snapshot method yields approximately 30 % higher correlation. Use of the method should be cautioned when the contributions to fluctuating pressure from outside the measurement volume are significant. The study illustrates the potential for simplifying the hardware configurations (e.g. high-speed PIV or dual PIV) required to determine instantaneous pressure from tomographic PIV.
Highlights
In only a decade, techniques that determine the fluid flow pressure based on PIV measurements have come to a degree of maturity that justifies their application in practical problems
Padding boundary conditions: when the vorticity outside of the measurement volume is small compared to the vorticity contained within the measurement volume, the measurement volume may be padded with an extension region of zero vorticity and a homogeneous boundary condition on the acceleration is prescribed on the enlarged domain, which allows the temporal velocity derivative on the measurement domain volume to become non-zero
The approximated pressure fluctuations at the microphone location are compared to the simultaneous instantaneous microphone surface pressure measurements (Fig. 8), where both the PIV and microphone results are band-pass-filtered for 300 Hz < f < 3 kHz
Summary
Techniques that determine the fluid flow pressure based on PIV measurements have come to a degree of maturity that justifies their application in practical problems. The problem of the flat-plate boundary layer is considered, which has been studied in recent studies employing time-resolved tomographic PIV for pressure determination (Ghaemi and Scarano 2011, 2013; Schröder et al 2011; Pröbsting et al 2013, amongst others). These studies follow two decades of literature on turbulent boundary layer flows as reviewed in Marusic et al (2010). It is proposed to approximate the velocity material derivative from a single tomographic PIV snapshot by a vortex-in-cell (VIC) simulation (Sect. 2.1)
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