Time-averaged Thickness Research Articles

The Effects of Curved Gas-Liquid Interface on Light Reflectance Liquid Film Measurement for an Optical Waveguide Film

This study aims to improve the measurement accuracy of liquid film thickness using a liquid film sensor with an optical waveguide film (OWF). The measurement principle of employing the OWF is based on the detection of light reflection at the liquid film surface with high spatial resolution. Because the curved surface of the liquid film reflects light and increases measurement error, we propose a signal processing method to remove the error factor in the calculation of the time-averaged thickness. This method requires prediction of the surface curvature, and we numerically investigated the characteristics of the output signal related to the reflected light intensity. The analysis results showed that the effect of the curved surface up to the surface curvature of 5.0 mm−1 was negligible because the liquid film thickness showed good agreement with that of the flat liquid film surface within 7% accuracy. Furthermore, we consider the applicable range of liquid film thicknesses under the operating conditions of boiling water reactors (BWRs). We estimated the surface curvature of the liquid film based on the calculation of the critical Weber number and confirmed that the curvature caused under the BWR operating conditions was covered by the analysis conditions of this study. Therefore, our proposed method for signal processing via the OWF enabled us to improve the measurement accuracy of the time-averaged thickness with respect to the base film thickness by extracting accurate surface curvature data.

Air-Water Bubbly Flow by Multiple Vents on a Hydrofoil in a Steady Free-Stream

Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, c, is oriented at the angle of inclination, α = 3.5°. The Froude number, Fn, based on the free-stream velocity, V∞, and air injection vent diameter, dh, is 30.30, 50.51 and 70.71. Air is injected through multiple vents on the hydrofoil at the non-dimensional air injection coefficient, Cq∼16−8917. The air bubble packing per unit area is quantified using spatial density, SD, at various combinations of Fn,Cq based on a high-speed video from the side view. The time-averaged spatial density, <SD>, is observed to increase in a logarithmic manner with an increase in the air injection rate, Q, at various Froude numbers. There is an increase in the mean spatial density of the bubbles with the increase in Cq at all Fn. A power–law relation is shown to exist between the time-averaged spatial density, <SD>, and the non-dimensional flow variables, Reynolds number, Reair, Fn and Cq based on a regression analysis. By tracking individual finite volume bubbles flowing with the free-stream, the bubble dimensions in pixels are quantified using quantities such as the deformation rate, ϵ, and standardization, ϵS, from the side-view videos. It is observed that ϵ and ϵS change with time, even as they become advected with the free-stream. Through high-speed imaging from the top view, we characterize the bubbly flow features’ time-averaged thickness, t, at various combinations of Fn,Cq at α = 3.5°. We obtain a power-law relation between the non-dimensional time-averaged jet thickness, t/c, and the non-dimensional flow parameters such as, Reair, Fn,Cq and the non-dimensional streamwise distance, x/xref, based on a regression analysis, where xref is a reference distance. The results are relevant to engineering applications where the air–water bubbly flow in a free-stream is important.

Characteristic Scales in Shock–Turbulence Interaction

A semi-empirical estimate of the time-averaged thickness of a planar shock embedded in a turbulent mean flow is presented in an effort to quantify the characteristic time and length scales for turbulence modeling. Simplified Favre-averaged Navier–Stokes equations are reformulated and combined with the Rankine–Hugoniot relations to obtain an equation that relates the shock structure and its characteristic thickness to the upstream turbulent and mean flow quantities. The only mean flow and turbulence quantities needed to compute the shock thickness or velocity profile through the shock are upstream Mach number , turbulent Mach number , and the Taylor-based Reynolds number . The accuracy of method for the shock structure is validated against direct numerical simulations of shock–turbulence interaction and shows a very good agreement over a wide range of Mach, Reynolds, and turbulent Mach numbers. Finally, the obtained ratio of characteristic shock time scale to the upstream turbulence time scale is shown to be proportional to the turbulent kinetic energy amplification through the shock and supported through direct numerical simulations.

Simulating disturbance frequency effect on heat transfer enhancement in wavy condensate films

It is of great significance to investigate microscopic mechanisms of heat transfer enhancement in wavy condensate films which are frequently encountered in nuclear power plants. A numerical model, in which the wavy interface is tracked by a non-orthogonal coordinate transformation, is developed to study the disturbance frequency effect on heat transfer enhancement along a vertical wall. A sinusoidal disturbance is introduced by a fictitious body force to sustain waves. A disturbance frequency of 16 Hz associated with the critical film Reynolds number is numerically determined by analyzing the neutral stability curve. Compared with other disturbance frequencies, the wave effect on local heat transfer coefficients is the most significant at 16 Hz. The minimum time-averaged thickness and the maximum proportion of substrate film length in the wave length at 16 Hz proves that the film thinning effect is determined by the length of the film substrate rather than the substrate film thickness. The more notable variation of the normal velocity close to the wall at the wave front at 16 Hz accounts for the convection effect of heat transfer enhancement.

Application results of a prototype ultrasonic liquid film sensor to a 7 MPa steam–water two-phase flow experiment

A prototype ultrasonic liquid film sensor was applied to a high-temperature steam–water two-phase flow experiment. The liquid film sensor was vertically installed in a loop which was connected to HUSTLE, a multi-purpose steam source test facility. The hydraulic diameter of the measurement section was 9.4 mm. The output waveforms of the sensor were acquired with a digital oscilloscope. The fluid temperature and system pressure were kept at 288 °C and 7.2 MPa, respectively, during the experiment. The pulse-echo method was used to calculate the liquid film thickness. The cross-correlation calculation was utilized to determine the time difference between the pulse reflected at the sensor surface and the pulse reflected at the liquid film surface. The time-averaged liquid film thicknesses were less than 0.055 mm in the annular flow condition. The increase of the time-averaged thickness was small with the change of the gas momentum flux. The film thicknesses measured with the sensor were compared with the past experimental results; the former were smaller than one-fourth of the thickness estimated as the mean film thickness. The comparison results suggested that the continuous liquid sublayer thickness was measured with the liquid film sensor.

High pressure low impedance electrostatic transducer

An electrostatic transducer in which two sheets (40, 42) are separated by a gas-filled gap. The sheets have conductive surfaces for imposing electric fields within the gap when an electrical potential is applied across the sheets. A flexible positioning mechanism (43) maintains the gap at a desired time-averaged thickness. The gap is made up of a plurality of thick regions (47) and a plurality of thin regions (48). Both regions have a total projected area which is a substantial portion of the total area of one of the sheets. The average thickness of the gap in the thick regions greatly exceeds (by at least ten times) the gap's average thickness in the thin regions. The electrostatic field energy of the electric fields is concentrated in the thin regions.

Effect of turbulence on extinction of counterflow diffusion flame

A laminar counterflow diffucion flame established in the forward stagnation region of a porous cylinderhas been used widely for the laminar flame studies. In the present study, this flame was applied to investigating the extinction of a diffusion flame due to air stream turbulence. Propane or methane was ejected from a 30-mm porous cylinder. The turbulence was given to the counterflowing air stream by perforated plates. The results of this study show that the air stream turbulence causes large-scale distortions with small amplitude on the apparently laminar diffusion flame, and the time-averaged thickness of this flame is three times as large as the purely laminar flame. Even if the air stream becomes turbulent, there exists a critical stagnation velocity gradient beyond which the flame can never be stabilized, however large the fuel ejection velocity is. Local extinction near the stagnation region always leads to global extinction of the whole flame. As expected, the critical velocity gradient decreases as the turbulence intensity increases. This flame is subjected to the sum of the bulk stretch rate exerted by the mean flow and the turbulent stretch rate exerted by small eddies of Kolmogorov scale. The critical total stretch rate at which the extinction occurs is nearly constant for each fuel for all turbulence conditions tested in the present study and coincides with the critical stagnation velocity gradient of the laminar diffusion flame, that is, the total stretch rate without turbulence. This fact suggests that large-scale eddies are not so effective for the local extinction and that the chemical reaction that occurs in molecular scale is not affected by small eddies of the Kolmogorov scale.

Properties of the liquid layer in horizontal annular flow

Time records have been collected of local liquid film thickness, using parallel-wire conductance probes, in a new 50.8 mm i.d. pipe loop. Statistical analysis of these records allows the study of the circumferential variation of time-averaged thickness, of RMS values and of other quantities. The power spectra show that the dominant frequency associated with large disturbance waves is <10 Hz at low gas velocities, displaying a tendency to increase with gas flow rate. By combining signal cross-correlation data with visual observations, it is shown that the disturbance waves tend to deform rapidly, move on a plane inclined with respect to the vertical and cover an increasingly larger portion of the circumference with increasing gas velocity. The mean large wave height at the pipe bottom is linearly related to the local RMS value. It is also a strong function of gas flow rate, with a moderate dependence on liquid flow rate. The wave steepness shows a similarly strong dependence on gas flow rate. However, the disturbance wave intermittency appears to be almost independent of gas as well as liquid flow rates.

An Investigation of the Liquid Distribution in Annular-Mist Flow

The results of an experimental investigation of the average liquid film thickness are presented for vertical upward annular-mist two-phase flow, with and without heat transfer. The effects on the film thickness for variations in vapor flow rate, liquid flow rate, vapor density, and heat transfer are described. A correlation equation is presented for the local time-averaged thickness and for the droplet size distribution. In addition, an equation is given for the liquid film flow rate as a function of the average film thickness.