This work deals with stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.
In the chemical, petroleum and nuclear industries, pipelines are often used to transport fluids from one process site to another one. The understanding of the fluids behavior inside the pipelines is the most important consideration for the engineers and scientists. From the previous studies, there are several two-phase flow patterns in horizontal pipe. One of them is stratified flow pattern, which is characterized by the liquid flowing along the bottom of the pipe and the gas moving above it cocurrently. Another flow patterns are slug and plug flow patterns. This kind of flow triggers the dama…
Simultaneous Particle Image Velocimetry (PIV) measurements of stratified turbulent air/water flow in a horizontal pipe have been performed using water droplets as tracers in the gas-phase. The use of water droplets as tracers ensures that the water surface tension remains unaffected and thus allows small-scale interfacial structures, such as capillary waves to occur naturally. Experiments have been conducted in a 31 m long, 100 mm diameter PVC pipe using air and water as test fluids. For the purpose of validation of the experimental set-up and the suggested seeding technique, single-phase meas…
Experimental series of stratified gas-liquid two-phase flows had been carried out in a 26 mm i.d. transparent acrylic horizontal pipe. The study was aimed to determine the interfacial wave characteristics of the flow and to develop a high quality database of it. The longitudinal section of the pipe was used as the reference section of image recording. Air and water were used as the test fluids, flowing co-currently inside the pipe. The flow behavior was recorded by using a high-speed video camera around 5 m in axial distance from the inlet pipe to ensure the fully-developed stratified gas-liqu…
The present article investigates the interactions between the pilot and main flames in a novel stratified swirl burner using both experimental and numerical methods. Experiments are conducted in a test rig operating at atmospheric conditions. The system is equipped with the BASIS (Beihang Axial Swirler Independently-Stratified) burner fuelled with premixed methane-air mixtures. To illustrate the interactions between the pilot and main flames, three operating modes are studied, where the burner works with: (i) only the pilot flame, (ii) only the main flame, and (iii) the stratified flame (with …
Lakes and many other geophysical flows are shallow, density stratified, and contain a free-surface. Conventional studies on stratified shear instabilities make Boussinesq approximation. Free-surface arising due to large density variations between air and water cannot be taken into consideration under this approximation. Hence the free-surface is usually replaced by a rigid-lid, and therefore has little effect on the stability of the fluid below it. In this paper we have performed non-Boussinesq linear stability analyses of a double circulation velocity profile prevalent in two-layered density …
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the associated eigenproblem. The neutral stability boundary and the corresponding critical wave number are obtained for liquid - liquid and air - water systems. Depending on the problem parameters, the instability sets in owing to short, intermediate, of long wave most unstable perturbations. Patterns of the most unstable disturbances are reported and discussed…
According to the classical Helmholtz picture, an organ pipe while generating its eigentone has two anti-nodes at the two open ends of a cylinder, the anti-nodes being taken as boundary condition for the corresponding sound. Since 1860 it is also known that according to the classical picture the pipe actually sounds lower, which is to say that the pipe so-to-speak sounds longer than it is, a long-standing enigma. As for the pipe's end, we have resolved this acoustic enigma by detailing the physics of the airflow at the pipe's open end and showing that the boundary condition is actually the pipe…
This article examines the use of characteristic methods in stratified two-phase pipe flow simulations for obtaining non-dissipative flow predictions. A Roe scheme and several methods based on the principle of characteristics are presented for the two-fluid model. The main focus is finding numerically efficient ways of capturing wave dynamics and flow regime transitions through direct simulation. Characteristic methods offer the possibility of simulating hyperbolic systems without numerical dissipation. These methods do however lack certain fundamental conservation properties. Challenges relate…
Experiments and numerical simulations were conducted to investigate the dispersion of turbulent jets issuing from realistic pipe geometries. The effect of jet densities and Reynolds numbers on vertical buoyant jets were investigated, as they emerged from the side wall of a circular pipe, through a round orifice. Particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques were employed simultaneously to provide time-averaged flow velocity and concentrations fields. Large eddy simulation (LES) was applied to provide further detail with regards to the three-dimensiona…
Here we have considered the effects of shallowness of the domain as well as the air-water free surface on the stratified shear instabilities of the fluid underneath. First, we numerically solve the non-Boussinesq Taylor-Goldstein equation for smooth velocity and density profiles of a model shear layer with a free surface. When the depth of the fluid is relatively shallow compared to the shear layer thickness, the surface gravity waves existing at the free surface come closer to the waves existing in the shear layer. This can lead to resonant wave interactions, making the flow unstable to more …
We consider a simplified physics of the could interface where condensation, evaporation and radiation are neglected and momentum, thermal energy and water vapor transport is represented in terms of the Boussinesq model coupled to a passive scalar transport equation for the vapor. The interface is modeled as a layer separating two isotropic turbulent regions with different kinetic energy and vapor concentration. In particular, we focus on the small scale part of the inertial range as well as on the dissipative range of scales which are important to the micro-physics of warm clouds. We have nume…
We study experimentally temperature fluctuations in stably stratified forced turbulence in air flow. In the experiments with an imposed vertical temperature gradient, the turbulence is produced by two oscillating grids located nearby the side walls of the chamber. Particle Image Velocimetry is used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with sensitive thermocouples is employed to measure the temperature field. We found that the ratio $\big[(\ell_x \nabla_x \bar{T})^2 + (\ell_y \nabla_y \bar{T})^2 + (\ell_z \nabla_z \bar{T})^2\big] / <θ^2…
The LES/PDF methodology is applied to the Cambridge/Sandia turbulent stratified flame series under swirling conditions. The methane/air chemistry is represented by a 16-species reduced ARM1 mechanism, and the in situ adaptive tabulation method is adopted to accelerate the chemistry calculation. Effects of differential diffusion and heat loss through the bluffbody surface are taken into account. The simulations are conducted for premixed (SwB3), moderately and highly stratified (SwB7 and SwB11, respectively) cases under swirling conditions. The results from LES/PDF simulations are compared with…
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme in which a special treatment for the "missing" boundary condition is performed. Several numeric…
Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified multiphase flow model (Chang & Liou, JCP 2007). In this method, each face is divided into gas-gas, gas-liquid, and liquid-liquid parts via reconstruction of volume fraction, and the corresponding fluxes are calculated by Riemann solvers. Viscosity and heat transfer models are included. The effects of frequency (below the natural frequency of bubbles), volume fraction, visc…
Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability of flow predictions are however strongly dependent upon the numerics within these simulator tools, the scheme type and resolution in particular. A Kelvin-Helmholtz stability analysis for the differential two-fluid model is in the present work presented and extended to discrete representations of said model. This analysis provides algebraic expressions which…
Twisted tapes are used to induce swirling flow and improve mixing. The flow induced by a 180 degree twisted tape with length (pitch) 60 mm and diameter 25.4 mm in a circular pipe was investigated using Laser Doppler Velocimetry (LDV) measurements. Tangential velocity profiles downstream of the twisted tape swirler were measured at multiple locations along the pipe axis, across the horizontal diameter of the pipe. The profiles showed an unexpected transition along the pipe axis from regular swirling flow to an apparent counter-rotation near the pipe axis, and then reverting back to regular swir…
Combustion modes in locally stratified dual-fuel (DF) mixtures are numerically investigated for methanol n-dodecane blends under engine-relevant pressures. In the studied constant-volume numerical setup, methanol acts as a background low-reactivity fuel (LRF) while n-dodecane serves as high-reactivity fuel (HRF), controlling local ignition delay time. The spatial distribution of n-dodecane is modeled as a sinusoidal function parametrized by stratification amplitude (Y) and wavelength (0.01 mm<$λ$<15 mm). In contrast, methanol is assumed to be fully premixed with air at equivalence ratio 0.8. F…
This study aims to experimentally investigate the two-group interfacial area transport in small diameter pipes. Experimental data focusing on the bubbly to slug transition regime, namely one-group to two-group transport region, are collected in a 12.7 mm vertical pipe under adiabatic, air-water conditions. The result shows the intergroup transfer in the small diameter pipe can be drastic, especially under low superficial liquid velocities. The cause of this phenomenon is mainly due to the large relative bubble size comparing to the pipe cross-sectional area. The wake entrainment effect could b…
We consider two common heat transfer processes and perform a through sensitivity study of the variables involved. We derive and discuss analytical formulas for the heat transfer coefficient in function of film velocity, air temperature and pipe diameter. The according plots relate to a qualitative analysis of the multi-variable function $h$, according to functional optimization. For each process, we provide with graphs and tables of the parameters of interest, such as the Reynolds number. This method of study and the specific values can constitute a useful reference for didactic purposes.
This paper presents a one-dimensional time-dependent numerical model of a sea organ, which generates music driven by the motion of the sea. The governing equations are derived by coupling hydrodynamic and thermodynamic equations for water level and air pressure oscillations in a sea organ pipe system forced by irregular waves. The model was validated by comparing numerical results to experimental data obtained from a scaled physical model. Furthermore, the models' capabilities are presented by simulating internal oscillations in the Sea Organ in Zadar, Croatia. The response of the Sea Organ va…
Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number $\sim 10^8$. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, that corresponds to the stably stratified flow. In the experiments with a wavy heated bottom wall, we detect large-scale standing internal gravity waves excited in the regions with the stably stratified flow. The wavelength and the period of these waves are much larger than the turbulent spatial and time scales, respectively. In particular, the frequenc…
