Nonlinear Flow Model Research Articles

Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Numerical simulations on focused wave propagation are carried out by using three types of numerical models, including the linear potential flow, the nonlinear potential flow and the viscous fluid flow models. The wave—wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined, by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated. The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed, including the increased focused wave crest, delayed focused time and downstream shift of focused position with the increase of input amplitude. It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models. However, only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed, implying the insignificant effect of fluid viscosity on focused wave behavior. Therefore, the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.

Effect of mesoscopic structure on hydro-mechanical properties of fractures

Geothermal extraction usually requires reservoir fracturing to realize economic exploitation and fluid flow in hot-dry rock fractures has become a research hotspot. In the present study, gas flow through shear and tensile granite fractures was investigated to comparatively study effect of fracture mesoscopic structure evolution on fracture hydro-mechanical characteristics under confining stress ranging from 1 to 40 MPa and inlet pressure ranging from 0.005 to 3.6 MPa. Four major findings are reported herein. First, the conductivity of shear fractures is much higher than that of tensile fractures and the ratio of the former to the latter can be up to around 265 under the stress of 40 MPa. The second finding was that the Z2 values of tensile fractures are higher than shear fractures, indicating that the fracture surface of tensile fractures is rougher and has more mesoscopic asperities. When the two surfaces get to contact, tip contact and stress concentration happen, resulting in higher deformation in tensile fractures. The cluster coefficient characterizes fracture contact cluster property. Higher cluster coefficient indicates lower fracture deformation and lower viscous loss. Shear fractures have higher cluster coefficient than that of tensile fractures so shear fractures are weakly deformable. However, high flow velocity and Reynolds number easily occur in shear fractures, so transitional and turbulent flow dominates in shear fractures while laminar and transitional flow in tensile fractures. Third, a mechanical model relates the average imbedded depth to loading stress and lacunarity, a hydraulic aperture model based on void space and lacunarity and a friction factor model based on Reynolds number and lacunarity were built, respectively, based on the experimental data. Then a nonlinear flow model was proposed. The fourth finding was that parametric analysis on the cluster coefficient shows that the higher the cluster coefficient, the lower of fracture deformation is and the higher of hydraulic aperture is. When the cluster coefficient is high, less viscous loss occurs; however, the fluid velocity may be high, so the friction factor will be high since more inertial loss happens.

Distributed Optimal Voltage Control With Asynchronous and Delayed Communication

The increased penetration of volatile renewable energy into distribution networks necessities more efficient distributed voltage control. In this paper, we design distributed feedback control algorithms where each bus can inject both active and reactive power into the grid to regulate the voltages. The control law on each bus is only based on local voltage measurements and communication to its physical neighbors. Moreover, the buses can perform their updates asynchronously without receiving information from their neighbors for periods of time. The algorithm enforces hard upper and lower limits on the active and reactive powers at every iteration. We prove that the algorithm converges to the optimal feasible voltage profile, assuming linear power flows. This provable convergence is maintained under bounded communication delays and asynchronous communications. We further numerically test the performance of the algorithm using the full nonlinear AC power flow model. Our simulations show the effectiveness of our algorithm on realistic networks with both static and fluctuating loads, even in the presence of communication delays.

Numerical simulation of Joule heating and Arrhenius activation energy for nonlinear radiative flow of Casson nanofluid with Cattaneo–Christov heat flux model

This article explores the novel features of Cattaneo–Christov heat flux model for nonlinear radiative flow of Casson nanofluid over an inclined permeable stretched cylinder with joule heating mechanism. The novelty of the present study is to account for the effect of activation energy, dual stratification, nonlinear mixed convection, non-uniform heat generation/absorption, binary chemical reaction and Joule heating effect. The velocity and thermal slips are also accounted for present flow model instead of no-slip condition. Casson fluid nanomaterial model is measured that refers to the significant slip mechanism such as Brownian and thermophoresis diffusions. Suitable similarity transformations are employed to get the required coupled ODEs system. The developed nonlinear system is unravelled through shooting technique along with Runge–Kutta–Fehlberg (RK-45) approach. Physical quantities of interest are investigated through graphs and tables. From the present analysis, we will see the conflicting effect of chemical reaction parameter to that of activation energy parameter Further it will be also analyzed that the heat transfer rate at the cylindrical surface and thermal boundary layer thickness enhances within the frame thermal radiation It will also be observed that both thermophoresis and activation energy parameter become a source of enhancement in concentration frame. A validation of the work is offered by comparing the current results with published literature. Casson flow model as deliberated in the paper finds practical applications in polymer engineering, blood flow, silicon suspensions, and lithograph industry.

Experimental and Numerical Modelling of Nonlinear Flow Behavior in Single Fractured Granite

In this study, the hydromechanical behavior was experimentally investigated by conducting fracture geometry evolution-based gas flow tests on single fractured granite. The traditional fracture roughness value (Rp) of a single surface cannot adequately explain the intrinsic permeability in multiple samples. Instead, the permeability is better explained by aperture distribution, and it is positively correlated with the mean aperture size. The permeability is also affected by a combination of contact area and void space under changing confining stress. The average embedded depth increases rapidly under low-loading stress (less than 8 MPa) and slowly under high-loading stress (higher than 8 MPa). A simplified Hertz contact model was used to fit the experimental data. The model uses the reciprocal of the standard deviation of the aperture as the average curvature radius of the fracture. Good agreement was found between the experimental and theoretical results. A modified smooth parallel-plate model to describe flow friction in fractures was developed, which takes fracture contact and void space into account. A new friction model was also developed that takes both the nonlinear effect and the influence of fracture relative roughness into account by multiplying the ideal model by two power-law functions. This new model is effective in predicting the friction factor. Finally, taking into consideration the built permeability, mechanical, and friction models, a nonlinear flow model was proposed. The flow rate can be estimated based on the 3D fracture topography data, the applied loading stress, and the pressure gradient. The influence of four types of aperture distribution on the friction factor was investigated. The results showed that a high mean aperture size would result in a low friction factor. In addition, the influence of the mean aperture size on the friction factor is obvious, even under a very high-loading stress while the effect of the standard deviation is negligible when the loading stress is very high.

Analysis of higher harmonics in a focused water wave group by a nonlinear potential flow model

This work analyses the higher harmonic wave elevations of focused wave groups based on the assumption of a Stokes-type nonlinear structure. A fully nonlinear potential flow model is employed to generate nonlinear wave groups by the NewWave theory, which represents an extreme event in a random sea state. We present a methodology to generate high-quality nonlinear wave groups of a narrow-banded wave spectrum in a numerical wave tank. A phase-manipulation approach is employed to accurately extract the higher harmonic elevations. The elevation spectra show clean separation of the first four harmonics. Comparisons with the experimental data show remarkably good agreements for the higher harmonics. We confirm the Stokes-type underlying nonlinear structure of the harmonic elevations in focused wave groups. This is found by simulating wave groups with varying wave steepness and calculating the corresponding elevation coefficients of the higher harmonics. The harmonic coefficients are found almost constant against varying steepness. An implication of the Stokes-type structure for the nonlinear wave elevations is that, it allows us to estimate the higher harmonics based only on the linear component. This is successfully demonstrated by reconstructing a nonlinear focused wave group using the linear NewWave model and the coefficients at its higher harmonics.

Investigation of Focusing Wave Properties in a Numerical Wave Tank with a Fully Nonlinear Potential Flow Model

Nonlinear wave interactions and superpositions among the different wave components and wave groups in a random sea sometimes produce rogue waves with extremely large wave heights that appear unexpectedly. A good understanding of the generation and evolution of such extreme wave events is of great importance for the analysis of wave forces on marine structures. A fully nonlinear potential flow (FNPF) model is proposed in the presented paper to investigate the different factors that influence the wave focusing location, focusing time and focusing wave height in a numerical wave tank. Those factors include wave steepness, spectrum bandwidth, wave generation method, focused wave spectrum, and wave spreading functions. The proposed model solves the Laplace equation together with the boundary conditions on a σ -coordinate grid using high-order discretisation schemes on a fully parallel computational framework. The model is validated against the focused wave experiments and thereafter used to obtain insights into the effects of the different factors. It is found that the wave steepness contributes to changing the location and time of focus significantly. Spectrum bandwidth and directional spreading affect the focusing wave height and profile, for example, a wider bandwidth and a wider directional spread lead to a lower focusing wave height. A Neumann boundary condition represents the nonlinearity of the wave groups better than a relaxation method for wave generation.

Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al. (2000)’s eddy-viscosity approach originally developed for Boussinesq-type wave models. In this approach, an extra term, constructed to conserve the horizontal momentum for waves propagating over a flat bottom, is added in the dynamic free-surface condition. In the second method, a pressure distribution is introduced at the free surface that dissipates wave energy by analogy to a hydraulic jump (Guignard and Grilli, 2001). The modified Hamiltonian systems are implemented using the Hamiltonian Coupled-Mode Theory, in which the velocity potential is represented by a rapidly convergent vertical series expansion. Wave energy dissipation and conservation of horizontal momentum are verified numerically. Comparisons with experimental measurements are presented for the propagation of a breaking dispersive shock wave following a dam break, and then incident regular waves breaking on a mildly sloping beach and over a submerged bar.

Security region of natural gas network in electricity-gas integrated energy system

The strengthening interdependency between electricity network and natural gas network not only promotes the renewable energy integration and flexibility of electricity-gas integrated energy system (IES) operation, but also escalates the operation risk of the IES. Security region (SR) is a powerful tool to improve the situational awareness of IES security. However, the concept and application of SR for the natural gas network in IES is rare. This paper presents a SR of natural gas network in IES considering the influence of the electricity network and natural gas network. Firstly, the concepts of the SR, pressure security region (PSR) and transmission security region (TSR) of the natural gas network in the IES are defined by referring the definitions of electricity network SR. Then, the general nonlinear optimization energy flow (OEF) models are developed to form the SR, PSR and TSR of natural gas network in the IES, and the frameworks for constructing the SR of natural gas network in multi-dimensional space are also proposed. Results for the IES 30-20 and IES 118-3 × 20 test systems indicate that the proposal approach can construct the SR of natural gas network in IES with high accuracy.

Market Evaluation of Energy Storage Systems Incorporating Technology-Specific Nonlinear Models

A generic constant-efficiency energy flow model is commonly used in techno-economic analyses of grid energy storage systems. In practice, charge and discharge efficiencies of energy storage systems depend on state of charge, temperature, and charge/discharge powers. Furthermore, the operating characteristics of energy storage devices are technology specific. Therefore, generic constant-efficiency energy flow models do not accurately capture the system performance. In this work, we propose to use technology-specific nonlinear energy flow models based on nonlinear operating characteristics of the storage devices. These models are incorporated into an optimization problem to find the optimal market participation of energy storage systems. We develop a dynamic programming method to solve the optimization problem and perform two case studies for maximizing the revenue of a vanadium redox flow battery (VRFB) and a Li-ion battery system in Pennsylvania New Jersey Maryland (PJM) interconnection's energy and frequency regulation markets.

Unit Commitment With an Enhanced Natural Gas-Flow Model

The interdependency of electric power and natural gas systems requires co-ordinated operational planning. We propose a unit commitment model that integrates a second-order-cone relaxation of a non-convex nonlinear natural-gas flow model that considers pipeline line pack. The model is enhanced by using convex envelopes of bilinear terms, which tighten the relaxation. By fixing the binary variables at their optimal values and linearizing the natural gas-flow-balance equations around the solution that is obtained, we obtain electricity and natural gas locational marginal prices as the dual variables of electricity- and natural gas-flow-balance equations, respectively. The interdependence between these sets of prices is discussed. Numerical results from two test systems validate the solution-quality and computational-efficiency benefits of the proposed modeling methodology.

An Efficient Hybrid Model for Nonlinear Two-Phase Flow in Fractured Low-Permeability Reservoir

The staged fracturing horizontal well has proven to be an attractive alternative for improving the development effect of a low permeability waterflood reservoir. Due to the coexistence of matrix, fracture, and horizontal wellbore, it remains a great challenge to accurately simulate the nonlinear flow behaviors in fractured porous media. Using a discrete fracture model to reduce the dimension of the fracture network, a two-parameter model is used to describe the nonlinear two-phase flow behavior, and the equivalent pipe flow equation is selected to estimate the horizontal wellbore pressure drop in the fractured low-permeability reservoir. A hybrid mathematical model for the nonlinear two-phase flow, including the effect of horizontal wellbore pressure drop in fractured porous media, is developed. A numerical scheme of the hybrid model is derived using the mimetic finite difference method and finite volume method. With a staggered five-spot flood system, the accuracy of the proposed model and the effect of fracture properties on nonlinear two-phase flow behaviors are further investigated. The results also show that with an increase of fracture length near injectors, the breakthrough time of injected water into the horizontal wellbore will be shorter, indicating a faster rise of the water cut, and a worse development effect. The impact of shortening fracture spacing is consistent with that of enlarging fracture length. Successful practice in modeling the complex waterflood behaviors for a 3-D heterogeneous reservoir provides powerful evidence for the practicability and reliability of our model.

Bookings in the European gas market: characterisation of feasibility and computational complexity results

As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special long-term capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookings-namely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.

Energy Trading and Market Equilibrium in Integrated Heat-Power Distribution Systems

The increasing utilization of cogeneration plants and energy conversion facilities accelerates the integration of energy systems, which introduces both opportunities and challenges into system operation and management. Thorough mathematical models and analytical methods that take into account the energy flow interdependence and strategic behaviors in multi-carrier energy systems are highly desired. This paper studies an integrated heat-power distribution system from the market perspective. The nonlinear AC optimal power flow (OPF) model is used to clear the distribution power market, which exactly accounts for network losses. To facilitate computation, convex relaxation is applied and polyhedral outer approximation of second-order cone is performed, leading to a linear market clearing model. An optimal thermal flow (OTF) model is employed to clear the heat market. Energy consumptions of heating devices are charged according to locational marginal prices. The market equilibrium is interpreted by a fixed point between OPF and OTF and reformulated as a mixed-integer linear program. Dedicated optimization models are set forth to investigate the market impact of strategic providers and elastic demands in which the market equilibrium condition serves as constraint. Case studies validate the effectiveness of the proposed model and method.

Linear Data-Model Based Adaptive ILC for Freeway Ramp Metering without Identical Conditions on Initial States and Reference Trajectory

Although freeway traffic system is conducted with a repeatable pattern day-to-day, the initial volume/or speed and the desired density of the traffic flow may vary with days due to the external disturbances. In this paper, a new linear data-model based adaptive ILC (LDM-AILC) is proposed to address ramp metering in a macroscopic level freeway environment. A linear data-model is developed for the nonlinear macroscopic traffic flow model by introducing an equivalent dynamical linearization approach in the time domain. Then the LDM-AILC is designed with a feedback control law and a parameter updating law. The proposed scheme is data-driven intrinsically, where only the I/O data is required for the controller design and analysis. The convergence is shown by rigorous analysis without any identical conditions exposed on both the initial state and the reference trajectory. Extensive simulation results are provided to verify the effectiveness of the proposed LDM-AILC.

Adaptive reduced basis method for the reconstruction of unsteady vortex-dominated flows

A local adaptive Reduced Basis approach is presented with a focus on the accuracy in reconstructing unsteady vortex-dominated flow fields generated by impulsively started lifting surfaces and bodies. The adaptive approach is built on the combination of methods based on Proper Orthogonal Decomposition, Spectral Orthogonal Decomposition, Dynamic Mode Decomposition and Recursive Dynamic Mode Decomposition and aims at making possible to explicitly take into account the temporal correlation between available snapshots of the problem. The latter has proven to be a critical element when building a Reduced Model for complex non-periodic and nonlinear unsteady flows. For a given instant of time in which the reconstruction is needed, the most accurate Reduced Model is automatically selected on the basis of an estimation of the error of the various methods in reconstructing the entire flow field. The impulsive start of a 2D symmetric airfoil, which evolves towards a periodic limit cycle, and the impulsive start of a three element airfoil and a 3D wing in high-lift configurations will be considered as demonstration cases.

Spectral Element FNPF Simulation of Focused Wave Groups Impacting a Fixed FPSO-type Body

A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretizedusing high-order prismatic – possibly curvilinear – elements using a spectral ...

A Robust Assessment Model of the Solar Electrical-Thermal Energy Comprehensive Accommodation Capability in a District Integrated Energy System

As effective utilization of solar resources is a significant way to address the imbalance between energy supply and demand. Therefore, reasonably assessing the accommodation capability of solar energy is important. A two-stage robust evaluation model is proposed for the solar electricity-thermal energy comprehensive accommodation capability in a district integrated energy system. The accommodation capability index is constructed based on the second law of thermodynamics. A robust optimization model was adopted to deal with the uncertainty of solar irradiance. In the solution procedure, the non-convex non-linear power flow model is transformed into a second-order cone model to effectively fit the proposed two-stage robust evaluation model. Finally, a case study verifies the effectiveness of the proposed model and the solution method. The influence of irradiance fluctuation range, gas boiler, and energy storage is discussed in detail.

A Nonlinear Analytical Algorithm for Predicting the Probabilistic Mass Flow of a Radial District Heating Network

This paper develops a nonlinear analytical algorithm for predicting the probabilistic mass flow of radial district heating networks based on the principle of heat transfer and basic pipe network theory. The use of a nonlinear mass flow model provides more accurate probabilistic operation information for district heating networks with stochastic heat demands than existing probabilistic power flow analytical algorithms based on a linear mass flow model. Moreover, the computation is efficient because our approach does not require repeated nonlinear mass flow calculations. Test results on a 23-node district heating network case indicate that the proposed approach provides an accurate and efficient estimation of probabilistic operation conditions.

Supersonic Starting Flow by Accelerated Sinking Movement to Large Angle of Attack

The classic linear Heaslet–Lomax problem, which is concerned with the indicial response of a supersonic airfoil experiencing a sudden small step motion, was recently extended to nonlinear cases where the sudden step motion is of high amplitude or equivalently a high angle of attack is suddenly achieved. Here in this paper, the more practical case of starting flow is considered where the high angle of attack is achieved through an accelerated sinking movement over a finite time interval. The problem is classified into fast sinking motion, middle-speed sinking motion, and slow sinking motion, for which the flow and force evolution exhibit different behaviors. The acceleration is shown to generate unsteady pressure waves that feed the major shock wave and expansions wave. A nonlinear indicial approach based on application of weighted Duhamel superposition principle to nonlinear starting flow model is built. This nonlinear model is shown to compare well with computational fluid dynamics simulation. The physics related to various stages of force evolution is discussed.