Session G31: Experimental Techniques - PIV-based Pressure and Wind Tunnel

Error Propagation dynamics of PIV-based pressure calculation 2: from Poisson equations to Kirchhoff plates

Little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure calculation. Rather than measure experimental error, we analytically investigate error propagation by examining the properties of the Poisson equation directly. Our results provide two contributions to the PIV community. First, we quantify the error bound in the pressure field by illustrating the mathematical roots of why and how PIV-based pressure calculations propagate. Second, we design the ``worst case error'' for a pressure Poisson solver. In other words, we provide a systematic example where the relatively small errors in the experimental data can lead to maximum error in the corresponding pressure calculations. The 2D calculation of the worst case error surprisingly leads to the classic Kirchhoff plates problem, and connects the PIV-based pressure calculation, which is a typical fluid problem, to elastic dynamics. The results can be used for optimizing experimental error minimization by avoiding worst case scenarios. More importantly, they can be used to design synthetic velocity error for future PIV-pressure challenges, which can be the hardest test case in the examinations.    

Quantification and correction of the error due to limited PIV resolution on the accuracy of non-intrusive spatial pressure measurement using a DNS channel flow database

The effect of the subgrid-scale (SGS) stress due to limited PIV resolution on pressure measurement accuracy is quantified using data from a direct numerical simulation database of turbulent channel flow (JHTDB). A series of 2000 consecutive realizations of sample block data with 512x512x49 grid nodal points were selected and spatially filtered with a coarse 17x17x17 and a fine 5x5x5 box averaging, respectively, giving rise to corresponding PIV resolutions of roughly 62.6 and 18.4 times of the viscous length scale. Comparison of the reconstructed pressure at different levels of pressure gradient approximation with the filtered pressure shows that the neglect of the viscous term leads to a small but noticeable change in the reconstructed pressure, especially in regions near the channel walls. As a contrast, the neglect of the SGS stress results in a more significant increase in both the bias and the random errors, indicating the SGS term must be accounted for in PIV pressure measurement. Correction using similarity SGS modeling reduces the random error due to the omission of SGS stress from 114.5{\%} of the filtered pressure r.m.s. fluctuation to 89.1{\%} for the coarse PIV resolution, and from 66.5{\%} to 35.9{\%} for the fine PIV resolution, respectively, confirming the benefit of the error compensation method and the positive influence of increasing PIV resolution on pressure measurement accuracy improvement.   

Instantaneous Pressure Field Calculation from PIV Data with Least-Square Reconstruction

A method using least-square reconstruction of instantaneous pressure fields from PIV velocity measurements is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated. The pressure field is estimated as the least-square solution of the overdetermined system. The flow acceleration is approximated by the vortex-in-cell procedure, providing the pressure field from a single velocity snapshot. The least-square method is compared against the omni-directional pressure gradient integration and solving the pressure Poisson equation. The results demonstrate that the omni-directional integration and the least-square method are more robust to the noise in velocity measurements than the pressure Poisson solver. In addition, the computational cost of the least square method is much lower than the omni-directional integration, and very easily extendable to volumetric data retaining computational efficiency. The least-square method maintains higher accuracy than the pressure Poisson equation while retaining a similar computational burden.   

GPU-based, parallel-line, omni-directional integration of measured acceleration field to obtain the 3D pressure distribution.

A PIV based method to reconstruct the volumetric pressure field by direct integration of the 3D material acceleration directions has been developed. Extending the 2D virtual-boundary omni-directional method (Omni2D, Liu {\&} Katz, 2013), the new 3D parallel-line omni-directional method (Omni3D) integrates the material acceleration along parallel lines aligned in multiple directions. Their angles are set by a spherical virtual grid. The integration is parallelized on a Tesla K40c GPU, which reduced the computing time from three hours to one minute for a single realization. To validate its performance, this method is utilized to calculate the 3D pressure fields in isotropic turbulence and channel flow using the JHU DNS Databases (http://turbulence.pha.jhu.edu). Both integration of the DNS acceleration as well as acceleration from synthetic 3D particles are tested. Results are compared to other method, e.g. solution to the Pressure Poisson Equation (e.g. PPE, Ghaemi et al. 2012) with Bernoulli based Dirichlet boundary conditions, and the Omni2D method. The error in Omni3D prediction is uniformly low, and its sensitivity to acceleration errors is local. It agrees with the PPE/Bernoulli prediction away from the Dirichlet boundary. The Omni3D method is also applied to experimental data obtained using tomographic PIV, and results are correlated with deformation of a compliant wall.   

Weighted least-squares solver for determining pressure from particle image velocimetry data

Currently, most approaches to determine pressure from particle image velocimetry data are Poisson approaches (e.g. de Kat \& van Oudheusden, 2012, \emph{Exp. Fluids} 52:1089--1106) or multi-pass marching approaches (e.g. Liu \& Katz, 2006, \emph{Exp. Fluids} 41:227--240). However, these approaches deal with boundary conditions in their specific ways which cannot easily be changed---Poisson approaches enforce boundary conditions strongly, whereas multi-pass marching approaches enforce them weakly. Under certain conditions (depending on the certainty of the data or availability of reference data along the boundary) both types of boundary condition enforcement have to be used together to obtain the best result. In addition, neither of the approaches takes the certainty of the particle image velocimetry data (see e.g. Sciacchitano \emph{et al.}, 2015, \emph{Meas. Sci. Technol.} 26:074004) within the domain into account. Therefore, to address these shortcomings and improve upon current approaches, a new approach is proposed using weighted least-squares. The performance of this new approach is tested on synthetic and experimental particle image velocimetry data. Preliminary results show that a significant improvement can be made in determining pressure fields using the new approach.   

On Using Shaped Honeycombs for Experimental Generation of Arbitrary Velocity Profiles in Test Facilities

It is common to use a uniform approach flow in the study of most problems in aerodynamics. Motivated by situations where the approach flow is not uniform, the focus of the current work is on the experimental generation of arbitrary velocity profiles in a flow facility (water tunnel) using the shaped honeycomb technique originally proposed by Kotansky (1966). Employing further refinement of this approach, multiple honeycomb devices are designed and fabricated to produce prescribed velocity profiles. The performance of these devices is assessed in terms of their agreement with the desired velocity profiles and the level of turbulence they produce. Single-component molecular tagging velocimetry (1c-MTV) is used to characterize the resulting mean and fluctuating streamwise velocity profiles and their streamwise development. The shaped honeycomb technique is shown to be effective in producing the desired velocity profiles with high fidelity while maintaining velocity fluctuations level at or below that of the freestream prior to installation of the devices.   

Use of 3D Printing for Custom Wind Tunnel Fabrication

Small-scale wind tunnels for the most part are fairly simple to produce with standard building equipment. However, the intricate bell housing and inlet shape of an Eiffel type wind tunnel, as well as the transition from diffuser to fan in a rectangular tunnel can present design and construction obstacles. With the help of 3D printing, these shapes can be custom designed in CAD models and printed in the lab at very low cost. The undergraduate team at Loyola Marymount University has built a custom benchtop tunnel for gas turbine film cooling experiments. 3D printing is combined with conventional construction methods to build the tunnel. 3D printing is also used to build the custom tunnel floor and interchangeable experimental pieces for various experimental shapes. This simple and low-cost tunnel is a custom solution for specific engineering experiments for gas turbine technology research.