Time-averaged Equations Research Articles

Development and validation of an acoustic-electrical joint testing system for hydrate-bearing porous media

Acoustic and electrical properties are fundamental and important physical properties to characterize hydrate-bearing sediments. A new experimental system called Ultrasound Combined with Electrical Impedance was developed for jointly testing the ultrasonic wave parameters and electrical impedance of hydrate-bearing porous media in the hydrate formation and decomposition processes. The Ultrasound Combined with Electrical Impedance system features its novel ultrasonic-electrical compound sensors and sensor array, fully controllable instruments, variety of sampled data, and flexible working modes. Experiment was carried out with methane gas as the hydrate former, meanwhile the acoustic/electrical parameters were derived. The acoustic/electrical properties were characterized with the aid of typical models such as the time-average equation, Wood’s equation, weighted equation, and Archie’s formula. It has been shown by the results that key parameters such as the sound velocity and electrical impedance can be used to characterize the acoustic and electrical properties of hydrate-bearing sediments conjointly, demonstrating the applicability of the proposed Ultrasound Combined with Electrical Impedance system. The wavelet-analysis based denoising approach and singularity detection method are effective denoising methods to filter the ultrasound signals and to identify the arriving time of the ultrasonic wave. The weighted equation and Archie’s formula with a segmented regression method are recommended for modeling the relations between the hydrate saturation and sound velocity/impedance modulus, respectively.

Exhausting the background approach for bounding the heat transport in Rayleigh–Bénard convection

We revisit the optimal heat transport problem for Rayleigh–Benard convection in which a rigorous upper bound on the Nusselt number, , is sought as a function of the Rayleigh number, . Concentrating on the two-dimensional problem with stress-free boundary conditions, we impose the time-averaged heat equation as a constraint for the bound using a novel two-dimensional background approach thereby complementing the ‘wall-to-wall’ approach of Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662). Imposing the same symmetry on the problem, we find correspondence with their maximal result for but, beyond that, the results from the two approaches diverge. The bound produced by the two-dimensional background field approaches that produced by the one-dimensional background field from below as the length of computational domain . On lifting the imposed symmetry, the optimal two-dimensional temperature background field reverts to being one-dimensional, giving the best bound compared to in the non-slip case. We then show via an inductive bifurcation analysis that introducing two-dimensional temperature and velocity background fields (in an attempt to impose the time-averaged Boussinesq equations) is also unable to lower the bound. This then exhausts the background approach for the two-dimensional (and by extension three-dimensional) Rayleigh–Benard problem with the bound remaining stubbornly while data seem more to scale like for large . Finally, we show that adding a velocity background field to the formulation of Wen et al. (Phys. Rev. E., vol. 92, 2015, 043012), which is able to use an extra vorticity constraint due to the stress-free condition to lower the bound to , also fails to further improve the bound.

Development and testing of a model for turbulence-radiation interaction effects on the radiative emission

A new model to account for turbulence-radiation interaction on the radiation emission in the framework of Reynolds-Averaged Navier-Stokes simulations is proposed and tested. The model’s development is based on Reynolds decompositions of the temperature T and the Planck-mean absorption coefficient κ in the time-averaged radiative emission and on a multi-variable Taylor-series expansion of κ as a function of temperature and species concentration. The relative importance of the terms that arise from these processes are assessed using statistics extracted from high-resolution, fully-coupled large eddy simulations (LES) of large-scale pool fires. All high-order terms are related to resolved quantities or to quantities for which models are already available by curve fitting the LES-generated data. The model presents a total error in directly estimating the radiative emission of about 25%, offering a considerable improvement over existing approximations, which, at best, have total errors above 40%. An expression introduced for the mean absorption coefficient also shows a good accuracy, with an associated total error of 16%. When applied to the solution of the time-averaged radiative transfer equation, the new model again outperforms other approximations, especially in the flame region.

Influence of blade number on flow-induced noise of centrifugal pump based on CFD/CA

In order to study the influence of blade number on flow-induced noise of the centrifugal pump, a computational method based on the combination of computational fluid dynamics and computational acoustics was proposed to numerically calculate the acoustic field of the centrifugal pump. Taking the principle of single variable, the number of different blades was selected as the research variable, and the three-dimensional unsteady constant value of the flow field in the centrifugal pump was calculated by using the Reynolds time-average equation of SST k-ω turbulence model. Combining with the results of flow field calculation, the acoustic calculation was carried out by using the idea of acoustic-vibration coupling. The results showed that the baffle tongue was the main noise source of the centrifugal pump. The main reason was that due to the interaction between the impeller and the tongue during the operation of the centrifugal pump, the acoustic pressure values of the model pumps at the tongue position were maximized. With the increase of the number of blades, the acoustic pressure level of the model pump first decreased and then increased, and reach the minimum value when the number of blades was 6, which indicated that the number of 6 blades was the optimal value for reducing the flow-induced noise of the centrifugal pump. In order to verify the reliability of numerical calculation, a centrifugal pump flow-induced noise test platform was set up to carry out verification tests on each model pump. The error between the test value and the simulated value was analyzed, and the acoustic pressure level curves at each monitoring point of each model pump under different working conditions were obtained. The test results showed that the acoustic pressure level curves of the test and simulated values had the same trend, which further verified the accuracy and feasibility of the proposed joint calculation method.

Effect of RANS Turbulence Model on Aerodynamic Behavior of Trains in Crosswind

The numerical simulation based on Reynolds time-averaged equation is one of the approved methods to evaluate the aerodynamic performance of trains in crosswind. However, there are several turbulence models, trains may present different aerodynamic performances in crosswind using different turbulence models. In order to select the most suitable turbulence model, the inter-city express 2 (ICE2) model is chosen as a research object, 6 different turbulence models are used to simulate the flow characteristics, surface pressure and aerodynamic forces of the train in crosswind, respectively. 6 turbulence models are the standard k-ε, Renormalization Group (RNG) k-ε, Realizable k-ε, Shear Stress Transport (SST) k-ω, standard k-ω and Spalart–Allmaras (SPA), respectively. The numerical results and the wind tunnel experimental data are compared. The results show that the most accurate model for predicting the surface pressure of the train is SST k-ω, followed by Realizable k-ε. Compared with the experimental result, the error of the side force coefficient obtained by SST k-ω and Realizable k-ε turbulence model is less than 1 %. The most accurate prediction for the lift force coefficient is achieved by SST k-ω, followed by RNG k-ε. By comparing 6 different turbulence models, the SST k-ω model is most suitable for the numerical simulation of the aerodynamic behavior of trains in crosswind.

On the Reynolds time-averaged equations and the long-time behavior of Leray–Hopf weak solutions, with applications to ensemble averages

We consider the three dimensional incompressible Navier–Stokes equations with a non stationary source term , chosen in a suitable space. We prove the existence of global Leray–Hopf weak solutions and also that it is possible to characterize (up to sub-sequences) their long-time averages, which satisfy the Reynolds averaged equations, involving the additional Reynolds stress. Moreover, we show that the turbulent dissipation is bounded by the sum of the Reynolds stress work and the external turbulent fluxes, without any additional assumption, other than that of using Leray–Hopf weak solutions.Finally, in the last section we consider ensemble averages of solutions, associated to a set of different forces and we prove that the fluctuations continue to have a dissipative effect on the mean flow.

More about Q-ball with elliptical orbit

Q-balls formed from the Affleck-Dine field have rich cosmological implications and have been extensively studied from both theoretical and simulational approaches. From the theoretical point of view, the exact solution of the Q-ball was obtained and it shows a circular orbit in the complex plane of the field value. In practice, however, it is reported that the Q-ball that appears after the Affleck-Dine mechanism has an elliptical orbit, which carries larger energy per unit U(1) charge than the well-known solution with a circular orbit. We call them “elliptical” Q-balls. In this paper, we report the first detailed investigation of the properties of the elliptical Q-balls by 3D lattice simulation. The simulation results indicate that the elliptical Q-ball has an almost spherical spatial profile with no nodes, and we observed a highly elliptic orbit that cannot be described through small perturbations around the ground state Q-ball. Higher ellipticity leads to more excitation of the energy, whose relation is also derived as a dispersion relation. Finally, we derive two types of approximate solutions by extending the Gaussian approximation and considering the time-averaged equation of motion and we also show the consistency with the simulation results.

Real-Time Bilevel Energy Management of Smart Residential Apartment Building

This article elucidates a real-time energy management strategy for a smart residential apartment building having nonidentical occupants at the dwelling units (DUs). The aim of the present article is to design a distributed energy management algorithm, which can optimize the real-time demand of the entire building against abruptly updated rooftop solar generation and real-time price (RTP) of energy. The proposed energy management strategy differentiates among the DUs by considering a new parameter named load criticality level, which is defined as the value imposed by the DU residents to their power consumption. The optimization portfolio is developed as a novel bilevel, stochastic, multiobjective optimization problem where the maximization of utility of the consumed power is considered simultaneously with the cost minimization. To this end, a virtual energy trading platform is designed in this article between central building management system and the DUs, where they interact with each other by following the directives of single-leader multifollower Stackelberg game. The solution strategy is proposed as a Lyapunov optimization, which needs only the current values of the uncertain parameters, such as load variation, renewable generation, and energy price, and do not require any knowledge about their probabilistic variation, to eliminate the complexities regarding time average stochastic equations. Strenuous simulation on real-time data of four DUs, it is proved that the proposed framework can track the abrupt change in RTP and solar generation efficiently. Comparing with two benchmark methods viz. centralized process and greedy algorithm, the superiority of the designed energy management portfolio is established.

The mean suspended sediment concentration profile of silty sediments under wave-dominant conditions

Suspended sediment concentration (SSC) is one of the fundamental topics in sediment study. The parameterization of the SSC profile of silty sediments is still under-researched. This study focuses on the mean SSC profile for silty sediments under non-breaking wave-dominant conditions. First, inspired by a 1DV model, different types of the distribution of mean eddy viscosity were proposed, i.e., a toe-type distribution over flat bed and a constant-toe type distribution over rippled bed. Then, the time-averaged diffusion equation for suspended sediment transport was analytically solved, and expressions for the mean SSC profiles were derived. The expressions involve several basic physical processes, including the effects of bed forms, stratification, hindered settling and mobile bed. Verification using a number of experimental datasets showed that the proposed expressions can properly calculate the mean SSC for silt and are applicable for sand as well. In conclusion, this research provides an approach to estimate the mean SSC for silty sediments under wave-dominant conditions, which is expected to be applicable for engineering practice and numerical modelling.

Study on the equivalence between gas hydrate digital rocks and hydrate rock physical models

According to the filling modes of gas hydrate in the permafrost, combined with rock physical method, two types of hydrate rock physical models are established by the method of elastic modulus model, including skeleton type hydrate rock physical model and fluid type hydrate rock physical model. Besides, based on the CT scanning images of hydrate reservoir rocks, combined with the numerical simulation method of hydrate distribution, two types of hydrate digital rock models are constructed, which correspond to the hydrate rock physical models. Firstly, time average equations are used to estimate several physical properties of hydrate rocks, the velocities of the hydrate rock are calculated on different models, in order to verify the equivalence between hydrate rock physical models and hydrate digital rock models, and compare the difference between different hydrate filling modes. Secondly, different models are appliedto the characteristics analysis of hydrate reservoir rocks. Finally, the theoretical calculation curve is compared with the data of the actual sampling point of the hydrate reservoir, which used to the recognition of hydrate filling modes. It can be seen from the results that there is a good equivalence relationship between the hydrate rock physical models and hydrate digital rock models, and the filling modes of hydrate in this area is more in accordance with the skeleton type models, which means that this method can be used to determine the hydrate filling modes in hydrate reservoirs.

A Study on the Causes and the Treatment Measures of Slack Line Flow at the Crossing-over Points of the Oil Pipeline

This paper points out the definition of the oil pipeline crossing-over points, and thereby identifies the existence and the position of crossing-over points by applying the graphical method and the analytical method. Besides, this paper analyzes the phenomenon of slack line flow from the perspectives of thermodynamics, structural mechanics and fluid mechanics. In order to analyze the motion characteristics of slack line flow, this study divides the control volume in stratified flow into several sections, and then carries out a mechanical analysis of the accelerating and the uniform flow section. Based on the analysis, the equations of the gas-liquid two-phase volume and other parameters in the pipeline are worked out. What’s more, with the time-averaged continuum equation, momentum equation, energy equation for turbulent flow, and RNG k − ε two-equation turbulence modeling, this paper works out closed-form simultaneous equations for gas-liquid two-phase flow in order to establish the calculation model of slack line flow section. This paper also introduces the calculation methods of fluid motion equations and some common simulation software. Furthermore, taking into account the fast velocity and instability of slack line flow, and its buffering effect, this paper points out its hazards, and puts forward the application of its buffering effect and the energy dissipation measures to prevent and control slack line flow.

PHENOMENOLOGICAL ANALYSIS OF A CONCEPTUAL WATERJET PROPULSOR BASED ON THE COANDA EFFECT

This work is part of a research project conceived at the Federal University of Rio Grande. The project aims to create and develop mechanical devices that use the Coanda effect to enhance their overall efficiency. The focus herein is analyzing the physical phenomenon occurring in a conceptual water-jet propulsor. In the proposed concept, a water-jet propulsor has its impeller replaced by injectors that produce the so-called Coanda effect, increasing thereby the mass flow rate. In order to simulate the flow through the propulsor, a numerical model was developed. In this model the time-averaged conservation equations of mass and momentum were solved numerically by the finite volume method, more precisely with the commercial package ANSYS FLUENT (version 14.0). For the closure of the constitutive equations, the k-ω URANS turbulence model was employed. The simulation was performed for a transient state with a timestep of ∆t = 1×10-3 s and a total physical time of t = 6.0 s. Static pressure fields, streamlines and speed profiles are used to analyze the equipment performance and the phenomenon occurrence. The results show that the Coanda Effect is able to generate thrust in a waterjet propulsion device without impeller. The study suggests that the employment of this principle has promising applicability in marine propulsion and deserves attention on future works.

Transient dynamics of pulse-driven memristors in the presence of a stable fixed point

Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the transient dynamics of two types of memristors characterized by a stable fixed point using a time-averaged evolution equation. Time-averaged trajectories of the Biolek window function memristor and resistor-threshold type memristor circuit (an effective memristor) are determined analytically, and the times of relaxation to the stable fixed point are found. Our analytical results are in perfect agreement with the results of numerical simulations.

Bouncing phase variations in pilot-wave hydrodynamics and the stability of droplet pairs

We present the results of an integrated experimental and theoretical investigation of the vertical motion of millimetric droplets bouncing on a vibrating fluid bath. We characterize experimentally the dependence of the phase of impact and contact force between a drop and the bath on the drop’s size and the bath’s vibrational acceleration. This characterization guides the development of a new theoretical model for the coupling between a drop’s vertical and horizontal motion. Our model allows us to relax the assumption of constant impact phase made in models based on the time-averaged trajectory equation of Moláček and Bush (J. Fluid Mech., vol. 727, 2013b, pp. 612–647) and obtain a robust horizontal trajectory equation for a bouncing drop that accounts for modulations in the drop’s vertical dynamics as may arise when it interacts with boundaries or other drops. We demonstrate that such modulations have a critical influence on the stability and dynamics of interacting droplet pairs. As the bath’s vibrational acceleration is increased progressively, initially stationary pairs destabilize into a variety of dynamical states including rectilinear oscillations, circular orbits and side-by-side promenading motion. The theoretical predictions of our variable-impact-phase model rationalize our observations and underscore the critical importance of accounting for variability in the vertical motion when modelling droplet–droplet interactions.

Simulation of combustion of sesame and broad bean stalks in the freeboard zone inside a pilot-scale bubbling fluidized bed combustor using CFD modeling

A two-dimensional numerical model has been developed to simulate combustion of sesame and broad bean stalks in the freeboard zone of a pilot-scale Bubbling Fluidized Bed Combustor (BFBC). Eulerian–Lagrangian approach is used so, the gas phase is treated as a continuum by solving the time-averaged Navier-Stokes equations and a Discrete Phase Model (DPM) is used to model the solid phase. The combustion in the freeboard was simulated to be consistent with the experimental conditions and the real combustor work. Prediction of composition for gas and solid phases at the freeboard inlet was performed. A series of simulations have been performed to examine the effect of chemical kinetic parameters, solid phase parameters, gas phase parameters and heat flux through walls on the numerical results. The model results were validated by comparing with experimental results obtained from the BFBC. The maximum absolute deviations corresponding to the numerical results of the mole fraction of flue gas species at the exit were 3.07% for the sesame stalks and 10.89% for the broad bean stalks. The numerical results of the axial temperature distribution have maximum absolute deviations 14.77% and 14.69% for the sesame stalks and broad bean stalks, respectively. It was found that the model simulation results are in a good agreement with the experimental data obtained from the experiments. In the present model, the deviations of the flue gas species and axial temperature distribution along the freeboard height are found within the literature limits.

Vibrational convection in a heterogeneous binary mixture. Part 1. Time-averaged equations

High-frequency vibrations of a container filled with a fluid generate pulsation flows that however are barely visible with the naked eye, and induce the slow but large-amplitude averaged flows that are important for various practical applications. In this work we derive a theoretical model that gives the averaged description of the influence of uniform high-frequency vibrations on an isothermal mixture of two slowly miscible liquids. The miscible multiphase system is described within the framework of the phase-field approach. The full Cahn–Hillard–Navier–Stokes equations are split into the separate systems for the quasi-acoustic, pulsating and averaged flow fields, eliminating the need for the resolution of the short time scale pulsation motion and thus making the analysis of the long-term evolution much more efficient. The resultant averaged model includes the effects of concentration diffusion and barodiffusion, the dynamic interfacial stresses and the generation of the hydrodynamic flows by non-homogeneities of the concentration field (when they are combined with the effects of gravity and vibrations). The resultant model for the vibrational convection in a heterogeneous mixture of two fluids separated by diffusive boundaries could be used for the description of processes of mixing/de-mixing, solidification/melting, polymerisation, etc. in the presence of vibrations.

Prediction of porosity and gas saturation for deep-buried sandstone reservoirs from seismic data using an improved rock-physics model

In recent years, many important discoveries have been made in global deep oil and gas exploration, which indicates that deep exploration has gradually become one of the most important areas in current and future hydrocarbon exploration. However, the prediction of deep reservoirs is very challenging due to their low porosity and complex pore structure characteristics caused by the burial depth and diagenesis. Rock physics provides a link between the geologic reservoir parameters and seismic elastic properties and has evolved to become a key tool of quantitative seismic interpretation. Based on the mineral component and pore structure analysis of studied rocks, we propose an improved rock-physics model by introducing a third feldspar-related pore for deep-buried sandstone reservoirs to the traditional Xu–White model. This modelling process consists of three steps: first, rock matrix modelling using time-average equations; second, dry rock modelling using a multi-pore analytical approximation; and third, fluid-saturated rock modelling using a patchy distribution. It has been used in total porosity estimation, S-wave velocity prediction and rock-physics template establishment. The applicability of the improved rock-physics model is verified by a theoretical quartz-water model test and a real data total porosity estimation compared with the traditional Xu–White model and the density method. Then, a rock-physics template is generated by the improved rock-physics model for porosity and gas saturation prediction using seismic data. This template is carefully calibrated and validated by well-log data at both the well-log scale and seismic scale. Finally, the feasibility of the established rock-physics template for porosity and gas saturation prediction is validated by a deep-buried sandstone reservoir application in the East China Sea.

Examination of the physical assumptions of a quasi-steady vector model using the integral momentum equation

Quasi-Steady (QS) vector models have served as a convenient and effective tool for wind load estimations for low-rise buildings in the wind engineering community. In order to understand the applicability for practice, the physical assumptions of a QS vector model are investigated in this paper. The derivation is done through algebraic manipulation of the time-averaged integral momentum equation, which is used to relate mean, area-averaged, roof surface pressures to the mean flow and turbulence field above a roof. The two main assumptions of the QS model are revealed through this process: (i) The streamlines of an instantaneous flow near the roof are assumed to be the mean streamlines so that the instantaneous direction of the flow measured at the reference point is equivalent to the mean direction; (ii) The magnitude of the instantaneous flow is obtained by amplifying the magnitude of the mean flow at a spatially uniform rate such that the amplified magnitude of mean velocity is equivalent to the instantaneous magnitude measured at the reference point. Missing terms in the QS model are used to develop correction terms to improve QS model performance.

Desenvolvimento de um modelo numérico para a predição de um escoamento em bocal do tipo H.O.M.E.R

No presente estudo é desenvolvido um modelo numérico para a abordagem de escoamentos turbulentos no regime permanente em bocais do tipo H.O.M.E.R (do inglês: High-speed Orienting Momentum with Enhanced Reversibility) que consiste na mistura de dois jatos incidentes sobre superfícies de Coanda. Essa superfície causa uma deflexão no escoamento permitindo que o bocal atue como um dispositivo de manobra em aplicações aeronáuticas. O principal objetivo é avaliar o modelo numérico desenvolvido comparando com resultados numéricos da literatura. As equações de conservação de massa e quantidade de movimento médias no tempo são resolvidas numericamente através do método de volumes finitos. Para resolver o problema do fechamento da turbulência foi empregada modelagem clássica (RANS – do inglês: Reynolds Averaged Navier Stokes) com modelo k – ε. Primeiramente, um teste de independência de malha será realizado, com o intuito de dispender menos recursos computacionais e obter resultados precisos. Em seguida, serão feitas as simulações em regime permanente, com o objetivo de obter os ângulos de deflexão (α) gerados com a diferença das vazões mássicas injetadas em cada um dos canais do bocal H.O.M.E.R (m*). Posteriormente, esses resultados são comparados com os obtidos numericamente na literatura. Os resultados obtidos tiveram o mesmo comportamento obtido na literatura, onde o aumento da diferença entre os jatos de entrada conduziu a um aumento no ângulo de deflexão do jato no bocal. Com exceção de um valor específico (m* = 0.2) os resultados obtidos no presente trabalho apresentaram uma boa concordância com os preditos numericamente na literatura.

Numerical Study of Turbulent Air and Water Flows in a Nozzle Based on the Coanda Effect

In the present work it is performed a numerical study for simulation of turbulent air and water flows in a nozzle based on the Coanda effect named H.O.M.E.R. (High-Speed Orienting Momentum with Enhanced Reversibility). The main purposes of this work are the development of a numerical model for simulation of the main operational principle of the H.O.M.E.R. nozzle, verify the occurrence of the physical principle in a device using water as working fluid and generate theoretical recommendations about the influence of the difference of mass flow rate in two inlets and length of septum over the fluid dynamic behavior of water flow. The time-averaged conservation equations of mass and momentum are solved with the Finite Volume Method (FVM) and turbulence closure is tackled with the k-ε model. Results for air flow show a good agreement with previous predictions in the literature. Moreover, it is also noticed that this main operational principle is promising for future applications in maneuverability and propulsion systems in marine applications. Results obtained here also show that water jets present higher deflection angles when compared with air jets, enhancing the capability of impose forces to achieve better maneuverability. Moreover, results indicated that the imposition of different mass flow rates in both inlets of the device, as well as central septum insertion have a strong influence over deflection angle of turbulent jet flow and velocity fields, indicating that these parameters can be important for maneuverability in marine applications.