The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

a cura di

A survey is given of the major developments in three-dimensional velocity field measurements using the tomographic particle image velocimetry (PIV) technique. The appearance of tomo-PIV dates back seven years from the present review (Elsinga et al 2005a 6th Int. Symp. PIV (Pasadena, CA)) and this approach has rapidly spread as a versatile, robust and accurate technique to investigate three-dimensional flows (Arroyo and Hinsch 2008 Topics in Applied Physics vol 112 ed A Schroder and C E Willert (Berlin: Springer) pp 127–54) and turbulence physics in particular. A considerable number of applications have been achieved over a wide range of flow problems, which requires the current status and capabilities of tomographic PIV to be reviewed. The fundamental aspects of the technique are discussed beginning from hardware considerations for volume illumination, imaging systems, their configurations and system calibration. The data processing aspects are of uppermost importance: image pre-processing, 3D object reconstruction and particle motion analysis are presented with their fundamental aspects along with the most advanced approaches. Reconstruction and cross-correlation algorithms, attaining higher measurement precision, spatial resolution or higher computational efficiency, are also discussed. The exploitation of 3D and time-resolved (4D) tomographic PIV data includes the evaluation of flow field pressure on the basis of the flow governing equation. The discussion also covers a-posteriori error analysis techniques. The most relevant applications of tomo-PIV in fluid mechanics are surveyed, covering experiments in air and water flows. In measurements in flow regimes from low-speed to supersonic, most emphasis is given to the complex 3D organization of turbulent coherent structures.

Tomographic PIV: principles and practice

Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

This paper deals with the evolution of infrared (IR) thermography into a powerful optical tool that can be used in complex fluid flows to either evaluate wall convective heat fluxes or investigate the surface flow field behavior. Measurement of convective heat fluxes must be performed by means of a thermal sensor, where temperatures have to be measured with proper transducers. By correctly choosing the thermal sensor, IR thermography can be successfully exploited to resolve convective heat flux distributions with both steady and transient techniques. When comparing it to standard transducers, the IR camera appears very valuable because it is non-intrusive, it has a high sensitivity (down to 20 mK), it has a low response time (down to 20 μs), it is fully two dimensional (from 80 k up to 1 M pixels, at 50 Hz) and, therefore, it allows for better evaluation of errors due to tangential conduction within the sensor. This paper analyses the capability of IR thermography to perform convective heat transfer measurements and surface visualizations in complex fluid flows. In particular, it includes the following: the necessary radiation theory background, a review of the main IR camera features, a description of the pertinent heat flux sensors, an analysis of the IR image processing methods and a report on some applications to complex fluid flows, ranging from natural convection to hypersonic regime.

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Infrared thermography for convective heat transfer measurements

Image deformation methods in particle image velocimetry are becoming more and more accepted by the scientific community but some aspects have not been thoroughly investigated neither theoretically nor with the aid of simulations. A fundamental step in this type of algorithm is reconstruction of the deformed images that requires the use of an interpolation scheme. The aim of this paper is to examine the influence of this aspect on the accuracy of the PIV algorithm. The performance assessment has been conducted using synthetic images and the results show that both the systematic and total errors are strongly influenced by the interpolation scheme used in the reconstruction of the deformed images. Time performances and the influence of particle diameter are also analysed.

Analysis of interpolation schemes for image deformation methods in PIV

Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets

During the past several years infrared thermography has evolved into a powerful investigative means of thermo-fluid-dynamic analysis to measure convective heat fluxes as well as to investigate the surface flow field behaviour over complicated body shapes. The basic concepts that govern this innovative measurement technique together with some particular aspects linked to its use are herein reviewed. Different operating methods together with their implementations are also discussed. Finally, the capability of infrared thermography to deal with several simple, or complex, fluid flow configurations is analysed.

Gennaro Cardone

Papers

Infrared thermography for convective heat transfer measurements

Analysis of interpolation schemes for image deformation methods in PIV

Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets

A survey on infrared thermography for convective heat transfer measurements

Heat transfer rate and uniformity in multichannel swirling impinging jets