In this article a number of whole-field blood velocity measurement techniques are concisely reviewed. We primarily focus on optical measurement techniques for in vivo applications, such as laser Doppler velocimetry (including time varying speckle), laser speckle contrast imaging and particle image velocimetry (including particle tracking). We also briefly describe nuclear magnetic resonance and ultrasound particle image velocimetry, two techniques that do not rely on optical access, but that are of importance to in vivo whole-field blood velocity measurement. Typical applications for whole-field methods are perfusion monitoring, the investigation of instantaneous blood flow patterns, the derivation of endothelial shear stress distributions from velocity fields, and the measurement of blood volume flow rates. These applications require individual treatment in terms of spatial and temporal resolution and number of measured velocity components. The requirements further differ for the investigation of macro-, meso-, and microscale blood flows. In this review we describe and classify those requirements and present techniques that satisfy them.

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In vivo whole-field blood velocity measurement techniques

A three-dimensional twenty-seven (D3Q27) discrete velocity multiple-relaxation-time lattice Boltzmann method is developed. The proposed scheme is validated in fully developed turbulent channel, pipe and porous medium flows through direct and large eddy simulations. The direct numerical simulation of the turbulent channel flow confirms that the present scheme is as reliable as the spectrum method for simulating turbulence. Through the large eddy simulations of the pipe and porous medium flows, the present scheme shows its satisfactory accuracy for simulating turbulent flows bounded by circular walls that is failed by the three-dimensional nineteen (D3Q19) model.

A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows

Scaling of turbulence intensity for low-speed flow in smooth pipes

Velocity and turbulence measurements downstream of flow conditioners

Direct numerical simulations of flow in realistic mouth-throat geometries

Fully Developed Turbulent Pipe Flow. - Decay of Disturbances in Turbulent Pipe Flow. - Optimal Characteristic Parameters for the Disturbances in Turbulent Pipe Flow. - Measurement of Velocity and Turbulence Downstream of Flow Conditioners. - Signal processing of Complex Modulated Ultrasonic Signals. - Vortex-Shedding Flow Metering Using Ultrasound. - Ultrasonic Gas-Flow Measurement Using Correlation Methods. - Ultrasound Cross-Correlation Flow Meter: Analysis by System Theory and Influence of Turbulence. - Effect of Area Changes in Swirling Flow. - Errors of Turbine Meters due to Swirl. - Investigation of Unsteady Three-Dimensional Flow Fields in a Turbine Flow Meter. - How to Design a New Flow Meter from Scratch. - Effects of Disturbed Inflow on Vortex Shedding from a Bluff Body. - Correction of the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects. - How to Correct the Error Shift of an Ultrasonic Flow Meter Downstream of Installations.

Fluid mechanics of flow metering

Incompressible pipe flows are fully developed if the velocities are independent of the axial coordinate. The theory of turbulent pipe flows at high Reynolds numbers leads to analytical expressions for the velocity profile and the friction factor, which contain free constants. One of the latter is the well-knownKarman constant. The free constants can be determined from the best available experimental data. Final formulae for the velocity distribution and the friction factor are derived. Further effects on these laws are also considered, such as wall roughness and low Reynolds number effects.

Fully Developed Turbulent Pipe Flow

A method is described that allows the correction of the reading of a flow meter that is exposed to pipe flow disturbed by installations upstream of the meter. The method is aimed at minimizing the distance between installation and meter and is based on characterizing the flow by fundamental disturbances, physically interpretable as vortical structures, and on the detection of these disturbances by a measuring device located slightly upstream of the meter. A functional relationship between fundamental disturbances and error shift of the meter is postulated, and its existence is demonstrated by a number of experiments. It is concluded that the correction method is applicable to any type of installation and flow meter

A Universal, Nonintrusive Method for Correcting the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects

A method is described that allows the correction of the reading of a flow meter exposed to pipe flow disturbed by installations upstream of the meter. The method is aimed at minimising the distance between installation and meter and is based on characterizing the flow by “fundamental” disturbances, physically interpretable as vortical structures, and on the detection of these disturbances by a measuring device located slightly upstream of the meter. A functional relationship between fundamental disturbances and “error shift” of the meter is postulated, and its existence is demonstrated by a number of experiments. It is concluded that the correction method is applicable to any type of installation and flow meter.

Correction of the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects

The basic equations for turbulent flows in circular pipes at high Reynolds numbers are derived. At a certain cross section a three-dimensional velocity field is prescribed that differs only slightly from the fully developed state. The axial decay of the disturbances is investigated by solving the basic equations using an asymptotic expansion of the solutions. The resulting system of linear ordinary differential equations leads to eigenvalue problems. Eigenvalues and eigenfunctions are presented. The general solution can be expanded into series of eigensolutions. The decaying flow consists of various flow structures that fall into two categories: the U -type (ring vortex, sourcesink pair, source-sink quadrupole, etc.) and the W -type (single, double and multiple streamwise vortices). Each of these flow structures has its own decay behavior. Swirl (single streamwise vortex) has the lowest decay followed by the source-sink pair. The strength of the individual flow structure is described by means of characteristic parameters that are the coefficients in the series expansions of the solution. Comparisons of the theory with experimental results from the literature show very good agreement. The different dependence of the decay rate on the Reynolds number for flows with and without swirl can be clarified. The theory is valid for smooth as well as for rough pipe walls.

Klaus Gersten

Papers

Fluid mechanics of flow metering

Fully Developed Turbulent Pipe Flow

A Universal, Nonintrusive Method for Correcting the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects

Correction of the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects

Decay of Disturbances in Turbulent Pipe Flow