DOI: 10.14278/rodare.3623
title: Data publication: Measurement of liquid foam flow through a diverging nozzle

description: The hydrodynamic theory of pneumatic foam analytically predicts the advective transport of liquid by foam rising continuously in a vertical column or pipe, relying on cross-sectional averaging of the foam velocity and liquid fraction. This experimental study accumulates a database for assessing the pneumatic foam theory in a vertically aligned diverging nozzle, i.e. at increasing cross-sectional area in nominal flow direction. The velocity distribution of the flowing foam and its liquid fraction distribution were measured by means of X-ray, optical and electrical techniques in three different nozzles distinguished by their half angle θ = 5°, 10°, 20°. The experimental setup and the measurements are described in detail in Skrypnik et al. (https://www.hzdr.de/publications/Publ-41024).


 X-ray radiography (XR) has measured the distribution of the liquid fraction (ε<sub>XR</sub>) inside the nozzle as a two-dimensional projection, i.e. integrated in the X-ray beam direction.
 X-ray particle tracking (XPTV) has measured the local velocity u<sub>T</sub> inside the nozzle, along the motion path of each tracer particle described by the radial (r) and vertical position (z) in consecutive frames. The velocity u<sub>T</sub> was normalised by the superficial gas velocity j<sub>g</sub>(z) = Q<sub>g</sub> / (π * R(z)<sup>2</sup>), with Q<sub>g</sub> denoting the gas flow rate of compressed air applied for foam generation, and R(z) denoting the radius of the cross-sectional area depending on the vertical position z. To compare different nozzles, the vertical position z was normalised by the total length L = 25 mm / tan(θ) of the nozzle depending on its half angle θ = 5°, 10°, 20°.
 Optical PIV adapted to foam (FoamPIV) has measured the time-averaged velocity u<sub>W</sub> through the transparent wall of the nozzle, i.e. at the nozzle radius r = R(z) depending on the vertical position z. As described above, the velocity u<sub>W</sub> was normalised by the superficial gas velocity j<sub>g</sub>(z), and the vertical position z was normalised by the total length L of the nozzle.
 Electrode pairs (EP) have measured the cross-sectional average values of the liquid fraction (ε<sub>EP</sub>) upstream and downstream the nozzle, simultaneously to the X-ray radiographic measurement of the liquid fraction distribution (ε<sub>XR</sub>) inside the nozzle.


The experimental data in this repository is structured into different folders and files as follows.


 FoamNozzle_Overview.CSV gives an overview of all measurements runs, nozzles, and techniques.
 Level 1 are folders classified by the measurement technique: 01_XR: X-ray radiography, 02_XPTV: X-ray particles tracking velocimetry, 03_FoamPIV: Optical PIV adapted to foam, 04_EP: Electrode pairs.
 Level 2 are folders classified by the different nozzles, distinguished by the nozzle half angle θ = 5°, 10°, 20°, and divided into bottom and top part in the case of θ = 5°, 10°.
 Level 3 are TIF and CSV files of measurement results.
 
 01_XR: Each TIF image shows the time-averaged distribution of the liquid fraction inside the nozzle; the liquid fraction (0 &lt; ε<sub>XR</sub> &lt; 1) is indicated by the value of each pixel.
 02_XPTV: Each CSV file consists of three columns, namely the radial position (r, in mm), the normalised vertical position (z / L), and the normalised velocity (u<sub>T</sub> / j<sub>g</sub>(z)).
 03_FoamPIV: Each CSV file consists of two columns, namely the normalised vertical position (z / L), and the normalised velocity (u<sub>W</sub> / j<sub>g</sub>(z)).
 04_EP: Each CSV file consists of three columns, namely the cross-sectional average of the liquid fraction (0 &lt; ε<sub>EP</sub> &lt; 1) downstream as well as upstream the nozzle, and the time (in s).
description: The authors gratefully acknowledge the financial support provided by the German Research Foundation (DFG, under grant number HE 7529/3-1, project numbers 431077191 and 551239760), by the German Federal Ministry of Education and Research (BMBF, under grant number 03HY123E), and by the Summer Student Program at the Helmholtz-Zentrum Dresden-Rossendorf.