Roll Waves Research Articles

Multi-dimensional shear shallow water flows: Problems and solutions

The mathematical model of shear shallow water flows of constant density is studied. This is a 2D hyperbolic non-conservative system of equations that is mathematically equivalent to the Reynolds-averaged model of barotropic turbulent flows. The model has three families of characteristics corresponding to the propagation of surface waves, shear waves and average flow (contact characteristics). The system is non-conservative: for six unknowns (the fluid depth, two components of the depth averaged horizontal velocity, and three independent components of the symmetric Reynolds stress tensor) one has only five conservation laws (conservation of mass, momentum, energy and mathematical ‘entropy’). A splitting procedure for solving such a system is proposed allowing us to define a weak solution. Each split subsystem contains only one family of waves (either surface or shear waves) and contact characteristics. The accuracy of such an approach is tested on 2D analytical solutions describing the flow with linear with respect to the space variables velocity, and on the solutions describing 1D roll waves. The capacity of the model to describe the full transition scenario as commonly seen in the formation of roll waves: from uniform flow to 1D roll waves, and, finally, to 2D transverse ‘fingering’ of the wave profiles, is shown.

INNOVATIVE SOLUTION FOR THE MAINTENANCE OF OPERATING RELIABILITY OF DRIVEN PILES OF A BUILDING IN THE QUAY AREA

Ensuring strength parameters of building elements of residential, domestic and industrial premises, located on the territory of the embankment in continuous operation is a fundamental factor in the sustenance of the population, especially in changing climatic effects of the environment and a massive impact of coastal waves. Maintaining comfortable conditions normalized long stay population in the residential, domestic, and industrial purposes with reduced power consumption and ensuring safe operation, currently carried out in accordance with the implementation of the city's "life support" and is performed in accordance with the adoption of the Federal law of 23 November 2009 "No. 261-FZ. On energy saving and increasing energy efficiency and introducing amendments to certain legislative acts of the Russian Federation." All this underlines the relevance of the authors research and proposed recommendations for implementation are protected by patents of the Russian Federation of technical solutions. Such construction elements such as driven piles are the most intensively exposed to destruction because of being in wet soil, which contributes to the corrosive destruction of the material and periodic seismic effects beginning with the waves at the perimeter of the coast promenade. As shown by the analysis of known emergency residential, public and industrial construction projects, the decline in the standard terms of use driven piles leads to premature destruction of buildings and constructions, which consequently increases the danger of finding the population on the territory of the embankment. A feature of the exploitation of construction objects located on the territory of the embankment is the sum of the effect as the seismic loads due to the periodic power strokes of the rolling waves on the ground bordering the perimeter, and the corrosive destruction of the material driven piles due to constant contact with wet soil components. The proposed technical solutions, which are based on theoretical and experimental studies of the Department of teplogazosnabzhenie southwestern state University to ensure the maintenance of normalized operating life of driven piles in terms of destruction in the territory of the embankments, the novelty of which is protected by patents of the Russian Federation.

Roll Wave Structure in Long Tubes with Compliant Walls

We consider a flow of a fluid in a long vertical tube with elastic walls and show that, for certain parameters of the flow, small perturbations of the flow at the inlet section of the tube give rise to roll waves. Depending on the properties of the closing relation, either regular or anomalous roll waves are formed. In the latter case, a roll wave is characterized by two strong discontinuities that connect regions of continuous flow. We present the results of numerical simulations of the development of a pulsatile flow mode for convex and nonconvex closing relations that demonstrate the formation of regular and anomalous roll waves. We also construct a two-parameter class of exact periodic solutions and obtain existence diagrams for roll waves.

Non-intrusive techniques to measure roll waves level evolving in a flume

An open-channel experimental set-up is presented in this paper as a tool for examining the presence of instabilities on free-surfaces flows of non-Newtonian fluid. When these flows occur in favorable conditions of inclination, discharge and rheological properties, the propagation of instabilities can evolve into a specific type of wave, known as roll waves. The experimental apparatus developed allows study of stabilized roll waves in many scenarios for non-Newtonian rheology fluids, thereby constituting a highly useful tool for the understanding and control of roll waves. The test fluid used in the experiments was carbopol gel which is rheometrically representative of the muddy material from natural disasters, such as mudflows. Two non-intrusive level measurement systems are proposed (ultrasonic transducer and laser-based absorption technique), and the efficiency of each technique is presented and discussed. Both methods presented relatively low-cost implementation, and calibration procedure assured the quality of the results. The results from the experimental set-up were in agreement in shape and amplitude.

A simple non-equilibrium bedload transport equation for the formation of dune in a shallowwater flow over an erodible bed

In this work, we consider the long-standing problem of capturing dune formation in an erodible-bed channel at subcritical speed by using a reduced order model of depth-averaged equations. The pioneering study by Reynolds [1] showed that the standard Saint-Venant-Exner equations are unconditionally stable at subcritical Froude number. Hence, the use of depthaveraged flow equations, which are commonly used by the hydraulic community, prevents the formation of bedforms as dunes. Recently, Cañada-Pereira & Bohorquez [2] have proposed a simple sediment transport formulation able to capture the formation of dune when coupled with the Saint-Venant equations. We replace the standard Exner equation with a non-equilibrium sediment transport equation that includes the following necessary ingredients: first, a phase shift in the particle entrainment rate; second, a particle diffusivity and an eddy viscosity. Subsequently, we solve the linear stability problem of an erodiblebed channel and show that the neutral curve properly captures the bed instability both in subcritical regime (i.e. dune) and supercritical flow (i.e. antidune and roll wave). Finally, we corroborate the capabilities of the model by means of non-linear numerical simulations which reproduce the growth of dune and antidune in agreement with experiments.

Consistent equations for open-channel flows in the smooth turbulent regime with shearing effects

Consistent equations for turbulent open-channel flows on a smooth bottom are derived using a turbulence model of mixing length and an asymptotic expansion in two layers. A shallow-water scaling is used in an upper – or external – layer and a viscous scaling is used in a thin viscous – or internal – layer close to the bottom wall. A matching procedure is used to connect both expansions in an overlap domain. Depth-averaged equations are then obtained in the approximation of weakly sheared flows which is rigorously justified. We show that the Saint-Venant equations with a negligible deviation from a flat velocity profile and with a friction law are a consistent set of equations at a certain level of approximation. The obtained friction law is of the Kármán–Prandtl type and successfully compared to relevant experiments of the literature. At a higher precision level, a consistent three-equation model is obtained with the mathematical structure of the Euler equations of compressible fluids with relaxation source terms. This new set of equations includes shearing effects and adds corrective terms to the Saint-Venant model. At this level of approximation, energy and momentum resistances are clearly distinguished. Several applications of this new model that pertains to the hydraulics of open-channel flows are presented including the computation of backwater curves and the numerical resolution of the growing and breaking of roll waves.

Application of a single wire-mesh sensor in a parabolic trough facility with direct steam generation

The direct steam generation process can contribute to increase the cost-effectiveness of line-focused solar thermal power plants. The current research focuses on the once-through mode as very promising option for large-scale commercial plants. However, the existing pool of knowledge about the steam–water flow in the horizontal receiver pipes reveals knowledge gaps. The present contribution aims to experimentally investigate the two-phase flow in the receiver pipes of the DISS test facility at the Plataforma Solar de Almería, Spain, by an invasive measurement device for the first time. Therefore, a conductance wire-mesh sensor is employed in the low-quality evaporation section of the DISS test facility. This measurement device measures the local instantaneous void fraction that is used to describe the prevailing flow pattern under different pressures and mass flow rates. The results show slug flow, roll waves, wavy flow, and stratified-wavy flow in the horizontal receiver pipes within pressures of 30–80bar. The probability of slug flow or large-amplitude waves decreases with higher pressures. The findings provide a valuable knowledge about the flow structure within the receiver pipes and confirm the proof of function of the wire-mesh sensor under conditions of the direct steam generation process.

Seismic reprocessing and interpretation of a fractured-basement play: Texas Panhandle

The Panhandle-Hugoton field, of Texas, Oklahoma, and Kansas, is a giant oil field and is the largest conventional gas field in North America. Most hydrocarbon production in this field comes from the Wichita Uplift area, where the basement is the most shallow. Although the field has been extensively produced, many local hydrocarbon accumulations have not been fully exploited. Recent drilling activity in the survey indicates that some wells produce directly from basement fractures, suggesting a new play type for the area. Because the target is shallow, the seismic data are heavily contaminated by coherent noise, such as ground roll and head waves, creating challenges for seismic processing. To improve the seismic interpretation, we carefully reprocessed the field gathers resulting in improved correlation within the sedimentary and the basement sections. Correlating well control to seismic attribute volumes indicates that a fractured basement gives rise to lower P-wave impedance and strong amplitude versus azimuth anomalies. The azimuthal anisotropy is strongest in a direction parallel to the regional maximum horizontal stress, suggesting that these fractures are open. Coherence anomalies indicate a rugose basement surface, whereas curvature shows two lineament sets, consistent with the weathering and fractured exposure of basement in the Wichita Mountains to the southeast.

Direct numerical simulations of two-phase flow in an inclined pipe

We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.

Roll waves structure in two-layer Hele–Shaw flows

The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed.

Ground roll wave suppression based on wavelet frequency division and radial trace transform

Ground roll waves interfere with seismic data. The suppression of ground roll waves based on the division of wavelet frequencies considers the low-frequency characteristics of ground roll waves. However, this method will not be effective when the ground roll wave and the effective signal have the same frequency bands because of overlapping. The radial trace transform (RTT) considers the apparent velocity difference between the effective signal and the ground roll wave to suppress the latter, but affects the low-frequency components of the former. This study proposes a ground roll wave suppression method by combining the wavelet frequency division and the RTT based on the difference between the ground roll wave velocity and the effective signal and their energy difference in the wavelet domain, thus making full use of the advantages of both methods. First, we decompose the seismic data into different frequency bands through wavelet transform. Second, the RTT and low-cut filtering are applied to the low-frequency band, where the ground roll waves are appearing. Third, we reconstruct the seismic record without ground roll waves by using the inverse RTT and the remaining frequency bands. The proposed method not only improves the ground roll wave suppression, but also protects the signal integrity. The numerical simulation and real seismic data processing results suggest that the proposed method has a strong ability to denoise while preserving the amplitude.

A Strategy for Passive Control of Natural Roll-Waves in Power-Law Fluids through Inlet Boundary Conditions

The paper investigates the influence of the inlet boundary condition on the spatial evolution of natural roll-waves in a power-law fluid flowing in steep slope channels. The analysis is carried out numerically, by solving the von Kármán depth-integrated mass and momentum conservation equations, in the long-wave approximation. A second-order accurate scheme is adopted and a small random white-noise is superposed to the discharge at the channel inlet to generate the natural roll-waves train. Both shear-thinning and shear-thickening power-law fluids are investigated, considering uniform, accelerated and decelerated hypercritical profiles as the unperturbed condition. Independently of the unperturbed profile and of the fluid rheology, numerical simulations clearly enlighten the presence of coalescence, coarsening and overtaking processes, as experimentally observed. All the considered statistical parameters indicate that the natural roll-waves spatial evolution is strongly affected by the unperturbed profile. Compared with the uniform condition, at the beginning of roll-waves development an accelerated profile reduces the growth of the roll-waves with a downstream shift of the non-linear wave interaction. The opposite behavior is observed if the roll wave train develops over a decelerated profile. The comparison with the theoretical outcomes of the linearized near wave-front analysis allows the interpretation of this result in terms of stability of the base flow. It is shown that once the coarsening process starts to take place, the roll-waves spatial growth rate is independent of the unperturbed profile. Present results suggest that an appropriate selection of the flow depth at the channel inlet may contribute to control, either enhancing or inhibiting, the formation of a roll-waves train in power-law fluids.

Analysis of roll wave characteristics under low liquid loading two‐phase flow conditions

An experimental study is conducted using a 0.152‐m ID facility to investigate the wave characteristics of two‐phase stratified wavy flow in horizontal pipelines. The experiments are conducted under low liquid loading condition, which is very commonly observed in wet gas pipelines. The experiments are conducted with water as the liquid phase, and repeated with 51 wt % of monoethylene glycol (MEG) in the aqueous phase to analyze the effects of MEG presence on wave characteristics. The experimental range of this study covers superficial gas velocity, vSg, values of 9–23 m/s and superficial liquid velocity, vSL, values of 0.01–0.02 m/s. Similar test matrices are completed for the cases with and without MEG in the aqueous phase. A conductivity probe system is used to measure the wave characteristics at the liquid–gas interface. These characteristics include the wave celerity, frequency, amplitude, length, and liquid film thickness. The experimental oil–air wave characteristics data of Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) is also used for comparison purposes. The trends in the resulting wave characteristics with respect to input parameters are investigated, for oil, water, or MEG–water mixture as the liquid phase. Common predictive methods for interfacial wave celerity, including shallow water theory, Watson (Proceedings of the 4th International Conference in Multi‐Phase Flows, Nice, France. 1989:495–512), Paras et al. (Int J Multiphase Flow. 1994;20(5):939–956), Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029), and Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) are evaluated in comparison with the experimental data. The results of the wave frequency correlation of Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029) are also compared with the experimental wave frequency data. Lastly, a correlation is developed to predict the relative wave amplitude, as a function of superficial gas Weber number and liquid velocity number. Most of the commonly used two‐phase stratified flow models are developed with the assumption of steady‐state conditions, and neglect the transient wave effects. This study provides valuable experimental results on wave characteristics of stratified wavy flow for different types of liquid phase. Moreover, a comprehensive analysis of the parameters affecting the wave characteristics of stratified wavy flow is presented. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3177–3186, 2017

Note on the stability of viscous roll waves

In this note, we announce a complete classification of the stability of periodic roll-wave solutions of the viscous shallow water equations, from their onset at Froude number F≈2 up to the infinite Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F and the boundaries of the region of stable periods, which appears potentially useful in hydraulic engineering applications. In the asymptotic regime F→2 (onset), we provide an analytic expression of the stability boundaries, whereas in the limit F→∞, we show that roll waves are always unstable.

Effects of monoethylene glycol (MEG) on three-phase flow characteristics in near-horizontal pipes

An experimental study is conducted using a 0.152-m ID facility to investigate the effects of the presence of monoethylene glycol (MEG) on three-phase stratified wavy flow in horizontal pipelines. The experiments are conducted under low liquid loading condition, which is very commonly observed in wet gas pipelines. The analyzed flow characteristics include wave pattern, liquid holdup, aqueous phase fraction and pressure gradient.The experimental range of this study covers superficial gas velocity, vSg, values from 8 to 23m/s, superficial liquid velocity, vSL, values of 0.01–0.02m/s, and inlet liquid stream aqueous phase fraction, WCMEG, values of 0–100%. Experiments are conducted with 51wt% of MEG in the aqueous phase, and the results are compared to the case with no MEG, presented by Karami et al. (2016). Differential pressure transmitters, a quick closing valve and pigging system, and a high speed camera are used to acquire the measurements. The trends in the resulting data with respect to input parameters are investigated. The performances of common models and predictive tools are compared to liquid holdup, pressure gradient and aqueous phase fraction experimental results.The observed wave patterns include stratified smooth and stratified wavy with 2-D waves, 3-D waves, roll waves, and atomization flow, with transitions varying by changing the liquid phase. The trends of pressure gradient, liquid holdup, and aqueous phase fraction with respect to vSg, vSL, WCMEG, and wt% of MEG are observed and physical justifications are provided. The predictions of OLGAS 7.1, TUFFP unified model v. 2012, Beggs and Brill (1973), Taitel and Dukler (1976), and Xiao et al. (1990) are compared to the acquired experimental data. The liquid holdup experimental data are under-predicted by all the models, especially for higher WCMEG values. However, the results from OLGAS 7.1 and Xiao et al. (1990) model are in better agreement with experimental data. The three-phase aqueous phase fraction trends are not predicted well. The complicated nature of liquid-liquid interactions causes higher prediction uncertainties. In addition, a statistical analysis is conducted to find the best applicable closure relationships in the modeling of two-phase low liquid loading flow.MEG is used continuously in deep water gas production systems as a hydrate inhibitor. However, MEG mixing in multiphase flow and its effects on flow parameters are not well understood. This paper provides with comprehensive data for three-phase stratified flow for a 0.152-m ID pipe, with MEG in the aqueous phase. In addition, the prediction performance of the commonly used predictive tools in the industry is provided.

Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit

We study the spectral stability of roll-wave solutions of the viscous St. Venant equations modeling inclined shallow-water flow, both at onset in the small-Froude number or "weakly unstable" limit $F\to 2^+$ and for general values of the Froude number $F$, including the limit $F\to +\infty$. In the former, $F\to 2^+$, limit, the shallow water equations are formally approximated by a Korteweg de Vries/Kuramoto-Sivashinsky (KdV-KS) equation that is a singular perturbation of the standard Korteweg de Vries (KdV) equation modeling horizontal shallow water flow. Our main analytical result is to rigorously validate this formal limit, showing that stability as $F\to 2^+$ is equivalent to stability of the corresponding KdV-KS waves in the KdV limit. Together with recent results obtained for KdV-KS by Johnson--Noble--Rodrigues--Zumbrun and Barker, this gives not only the first rigorous verification of stability for any single viscous St. Venant roll wave, but a complete classification of stability in the weakly unstable limit. In the remainder of the paper, we investigate numerically and analytically the evolution of the stability diagram as Froude number increases to infinity. Notably, we find transition at around $F=2.3$ from weakly unstable to different, large-$F$ behavior, with stability determined by simple power law relations. The latter stability criteria are potentially useful in hydraulic engineering applications, for which typically $2.5\leq F\leq 6.0$.

Appliance based control for Home Power Management Systems

This study scrutinizes energy-friendly smart home appliances (hereafter ‘smart appliances’), control of these appliances and their effects on the efficient use of energy. To accomplish this, smart appliances and their operation principles are introduced and their energy savings compared to conventional appliances are analyzed using precise measurements. Then, a real-time Appliance-based Home Power Management System (Ab-HPMS) which manages power consumption of smart appliances and that of the house as a whole is proposed. For Ab-HPMS, an appliance control algorithm, called Appliance-based Rolling Wave Planning (Ab-RWP), is developed with the aim of reducing electricity cost and improving energy efficiency while maintaining user comfort. Ab-RWP algorithm interacts with appliances in a priority order based on user comfort which is determined by utilizing their smart operational characteristics. Operations of smart appliances and their integrations with Ab-HPMS are modeled with Petri nets to verify that they meet the requirements expressed in the specifications. Simulation results demonstrate that proposed Ab-HPMS provides improvements in terms of the energy consumption reduction of about 5%–16%, cost reduction of about 10%–24% and peak reduction at high demand period of about 38%–53% compared to conventional appliances usage.

Modeling Water Motion near Seismic Waves Propagating across a Graded Seabed, as Generated by Man-Made Impacts

Seismic interface waves generated by seabed impacts are believed to have biological importance. Various wave types are of interest to seismologists, who can minimize the unwanted, but often dominant, ground roll waves with suitable instrumentation. Waves made by dredging and piling have been measured using geophones and found to be of this interface type, which propagate much more slowly than the pressure waves in the water column above. Short interface wavelets of a few cycles were modeled using transient finite element analysis (FEA). Wavelets with low losses have been modeled using graded sediment data from the literature. They do not radiate energy away from the interface because the evanescent acoustic pressures they generate decay rapidly with distance from the seabed. Associated water particle velocities are much greater than would be expected from similar acoustic pressure measurements in a free field. This motion is significant to aquatic life which is dependent on inertial sensors (otoliths, etc.) to respond to the environment. Additional amplification of the horizontal seabed motion of the adjacent water is predicted for a short seismic wavelet modeled in a graded solid seabed. Further recent analysis studied the distribution of the energy flux within the sediment layers.

Discussion of “Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations” by Ziyi Huang and Jin-Jen Lee

Discussion of “Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations” by Ziyi Huang and Jin-Jen Lee

Roll waves in two-layer Hele-Shaw flows

In this paper we study the emergence and development of roll waves in two-layer fluid flow in a Hele-Shaw cell. We propose the mathematical model of such flow and define the conditions of transition from stable state to instability in the form of the roll waves. We find out the physical parameters of flows at which the roll waves exist. A linear stability analysis and the Whitham criterion of roll waves existence are used for solving the problem and arrive to identical conclusions on depths of upper and lower layers at which violation of flow stability occurs. The numerical calculations for the obtained mathematical model at found ratios of densities, viscosities and depths of layers are performed. They confirm development of the roll waves of finite amplitude from small oscillations of the interface.