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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The dynamic velocity range of particle image velocimetry (PIV) is determined by the maximum and minimum resolvable particle displacement. Various techniques have extended the dynamic range, however flows with a wide velocity range (e.g., impinging jets) still challenge PIV algorithms. A new technique is presented to increase the dynamic velocity range by over an order of magnitude. The multiple pulse separation (MPS) technique (i) records series of double-frame exposures with different pulse separations, (ii) processes the fields using conventional multi-grid algorithms, and (iii) yields a composite velocity field with a locally optimized pulse separation. A robust criterion determines the local optimum pulse separation, accounting for correlation strength and measurement uncertainty. Validation experiments are performed in an impinging jet flow, using laser-Doppler velocimetry as reference measurement. The precision of mean flow and turbulence quantities is significantly improved compared to conventional PIV, due to the increase in dynamic range. In a wide range of applications, MPS PIV is a robust approach to increase the dynamic velocity range without restricting the vector evaluation methods.

In particle image velocimetry (PIV), a flow is seeded with tracer particles and illuminated by a pulsed light sheet, yielding a series of image pairs with a pulse separation _{V}_{V}_{s}_{V}_{s}_{s}_{bias}

To avoid loss of correlation due to excessive in-plane displacement, Keane and Adrian [_{I}

Raffel _{s}

Westerweel _{rms}

Scarano and Riethmuller [^{−3} px [_{g}d_{I}_{I}_{g}

For the same final window (_{I}_{V}_{g}_{s}_{s}^{(s)}/_{s}^{(m)} ≅ 3 for discrete window shifting and _{s}^{(s)}/_{s}^{(m)} ≅ 10 for subpixel window shifting and deformation, respectively. However, these values are obtained for noiseless artificial images and the uncertainty increases for more realistic conditions, e.g., non-zero gradients [

In the remainder of the paper, ‘conventional’ PIV refers to the current state of art multi-grid cross-correlation using subpixel window shifting and deformation.

Increasing the pulse separation to enhance the dynamic range is generally not preferred. However some studies present satisfactory results when the increase is applied locally [

Fincham and Delerce [

Hain and Kähler [_{τ}δt_{τ}δt_{τ}_{τ}

Multi-frame PIV is most suitable for low speed flows. Hain and Kähler [_{max}_{max}_{max}_{max}

This paper proposes a new multiple pulse separation (MPS) technique to increase the dynamic velocity range of PIV. The technique is based on double-frame imaging, thus avoiding the low speed restriction and excessive pulse separations of MF PIV [

Consider a flow field with a wide range in velocity magnitude (e.g., a jet or wake flow), where _{max}_{min}_{max}_{min}_{V}_{τ}τ_{V}_{s}_{τ}τ_{V}_{τ}

Contrary to the multi-frame approach [_{τ}_{,1}_{τ}_{,2}_{τ,i}τ_{τ,}_{1}, _{τ,}_{2}, … _{τ,N}_{j}_{i}_{j}_{i}_{τ,i}τ_{opt}_{j}

The peak ratio _{s}_{s}_{s}_{s}

The pulse separation optimality criterion is based on the local maximum of _{i}_{i}_{s}_{i}_{s}_{s}_{s}

A selector operator is defined based on the maximum

The optimal pulse separation, displacement and velocity fields are determined as

Based on _{i}_{i}_{i}_{i}_{i}

Using

The optimality criterion based on the relaxed maximum (

In choosing the pulse separation multipliers _{τ,i}_{τ,}_{1} = 1) should limit the correlation loss in the high velocity region, based on e.g., the 1/4 window rule [_{τ,N}_{τ,N} ≅ _{max}_{min}

Compared to conventional PIV, the maximum increase in dynamic velocity range is
_{τ,}_{max} < _{τ,N}_{opt}_{s}

Mann and Picard [

The MPS PIV technique proposed in this paper shows some analogies to HDR imaging. In both cases, a high dynamic range composite field is generated from a set of low dynamic range fields with different ‘exposure times’. Similarities persist in the optimality criterion used to construct the composite field. In HDR imaging, continuous weighting functions are used to provide a gradual transition between dark (underexposed) and bright (overexposed) regions. Thus each pixel contains information from all images in the set. MPS PIV also uses continuous weighting functions based on the local weighted peak ratio

The contribution of data from sub-optimal pulse separations should be limited in MPS PIV due to the strongly nonlinear nature of the correlation peak detection in PIV. Spurious vectors for excessive pulse separation values must not be allowed to propagate into the composite velocity field. As for any other technique, MPS PIV should be applied with good judgment.

Similar to conventional PIV, MPS PIV is applicable to stationary or non-stationary flows. MPS PIV correlates double-frame images separated by _{i}_{F}_{F}_{,}_{max}

For temporal or spectral analyses, the common limitation for MPS and MF techniques is that a single recording duration _{F}

For amplitude domain analysis, no restrictions apply for single-point statistics (e.g., mean, variances and Reynolds stresses, higher order moments, probability density functions). For two-point statistics (e.g., spatial correlation) only point pairs acquired at the same measurement time should be considered.

MPS PIV is not an alternative but an addition to multi-grid techniques, without restricting the use of advanced methods such as window shifting and deformation. For the validation results (Section 3), the technique is implemented as a set of macro functions in LaVision Davis 7.2.2, using its multi-grid algorithms with deformation for vector evaluation.

The proposed methodology is validated based on experimental PIV data, obtained in an axisymmetric impinging jet. Two references are used for this validation: (i) Firstly, the precision of the mean and rms velocity is compared against laser-Doppler velocimetry (LDV). Secondly, the accuracy of the radial mass flux is verified against the mass conservation law.

A single round stationary jet of air impinges perpendicularly onto a flat surface (_{m}

The PIV system comprises a New Wave Solo-II Nd:YAG twin cavity laser (30 mJ, 15 Hz) and a LaVision FlowMaster 3S (PCO SensiCam) thermo-electrically cooled CCD camera (1,280 × 1,024 px^{2}, 12 bit) with 28 mm lens. The image magnification is 1:3.4 (_{p}^{2} to 32 × 32 px^{2} and a 75% overlap. The validation is based only on amplitude domain statistics (mean flow and turbulence intensities). As such, a low speed PIV system can be used in this stationary flow configuration.

The LDV system comprises a 500 mW Ar^{+} laser and a dual beam Dantec optics with 488 nm (blue) and 514 nm (green) wavelengths to measure axial (along

_{min}_{max}^{−1}, the threshold yields _{min}_{I}_{p}

_{min}_{min}_{min}

The MPS technique proposes the weighted peak ratio _{s}_{min}_{min}

_{s}_{min}_{min}

_{opt}_{min}_{min}_{min}_{min}_{min}

_{s}_{s}_{min}_{s}

Comparing _{s}

Based on _{τ}_{opt}_{min}_{τ}^{1.6} times compared to the conventional multi-grid PIV approach. Determining the exact dynamic range based on _{s}^{(m)} ≅ 0.1 px and _{g}d_{I}_{V}^{(m)} ≅ 160:1 (= 10^{2.2}). With this assumption, the dynamic range of MPS PIV is DR_{V}^{(mps)} ≅ 6,400:1 (= 10^{3.8}).

Although data was available at a higher pulse separation (_{min}_{min}_{min}

A dynamic velocity range of four orders of magnitude (10^{4}:1) has already been quoted in the literature for multi-grid algorithms using a single pulse separation [_{V}^{(mps)} ≅ 6,400:1 (or 3.8 orders of magnitude) is obtained in laboratory conditions for a real jet flow.

_{j}_{min}_{s}_{m}

In

The difference is even clearer for the rms velocity fluctuations

Radial turbulence intensity profiles intersecting the wall jet region (

This validation against LDV shows that conventional PIV overestimates the turbulence intensity because the displacement magnitude reduces to the minimum resolvable level _{s}_{V}_{s}_{opt}

The increase in accuracy when applying MPS PIV can be quantified by verifying the conservation of mass in the flow field. For an axisymmetric impinging jet, the net mass flow rate _{jet}_{jet}_{jet}

_{jet}_{jet}

By contrast, the thick solid line (case (iv)) represents the mass flow rate for the MPS PIV flow field, which is the only result showing a reasonable agreement with _{jet}_{jet}

Multi pulse separation (MPS) PIV is presented as a new methodology to increase the dynamic velocity range of PIV, based on a combination of data obtained at multiple pulse separation values. The methodology applies to flow configurations with large variations in velocity magnitude within the field of interest, of the order of the dynamic velocity range.

The pulse separation optimality criterion is based on a weighted peak ratio defined as _{s}_{s}_{s}

The MPS technique has been validated on an impinging jet flow, featuring strong velocity gradients and a wide range in velocity magnitude between the jet core, stagnation, wall jet and entrainment regions. Compared to laser-Doppler velocimetry (LDV) as a reference, conventional PIV significantly overpredicts the turbulence intensity by 7.5% (relative to _{m}

The increase in dynamic velocity range also improves the accuracy, which is verified against the conservation of mass in a control volume around the impinging jet flow. An rms deviation below 7% is obtained using MPS PIV, compared to over 20% using conventional PIV.

The enhancement using MPS PIV in terms of accuracy and precision of mean flow and turbulence quantities is due to the significant increase in dynamic velocity range. Here, the actual dynamic velocity range has increased by 40 times, to 3.8 orders of magnitude (DR_{V}^{(mps)} ≅ 6,400:1).

In other configurations with a wide velocity range, MPS has contributed to the understanding of heat transfer mechanisms e.g., in synthetic jet flows [

hydraulic diameter of the jet nozzle (m)

_{V}

dynamic velocity range

_{I}

interrogation window size (px)

_{p}

particle image diameter (px)

_{F}

frame rate (Hz)

distance between the jet nozzle exit and impingement surface (m)

_{g}

_{τ}

grid refinement factor and pulse separation multiplier

image pixel scaling (m/px)

mass flow rate (kg/s)

number of acquired image pairs

number of pulse separation values

exponent in relaxed maximum selector (see

unweighted and weighted correlation peak ratio (_{s}

jet Reynolds number, based on

radial coordinate in impinging jet (m)

particle image displacement (px)

in-plane velocity (m/s)

in-plane coordinates (m)

camera inter-frame time (frame rate = 1/δ

absolute displacement error or uncertainty (px)

fluid density (kg/m^{3})

_{s}

_{V}

minimum resolvable displacement (px) and velocity (m/s)

pulse separation time between exposures (s)

index of pulse separation values

index of image pair in sequence

uncertainty (

bias (

single-pass correlation

multi-grid correlation

multiple pulse separation PIV

Tim Persoons is a Marie Curie Fellow of the Irish Research Council for Science, Engineering and Technology (IRCSET), co-funded by Marie Curie Actions under FP7. The authors wish to thank Darina B. Murray (Department of Mechanical Engineering, Trinity College Dublin, Ireland) for the elucidating discussions.

Flowchart for

Description and nomenclature of the test case: Axisymmetric impinging jet flow.

Conventional PIV results at pulse separation (a,c) _{min}_{min}

MPS PIV results (_{s}_{min}_{min}_{opt}_{min}

MPS PIV results with (a,c) _{s}_{s}_{min}_{opt}_{min}

Comparison of (a,c,e) conventional PIV and (b,d,f) MPS PIV (_{s}_{m}_{m}_{m}

Radial profile of the mass flow rate _{jet}_{min}_{min}_{min}