Flow Equations Research Articles

Managing power balance and reserve feasibility in the AC unit commitment problem

Incorporating the AC power flow equations into unit commitment models has the potential to avoid costly corrective actions required by less accurate power flow approximations. However, research on unit commitment with AC power flow constraints has been limited to a few relatively small test networks. This work investigates large-scale AC unit commitment problems for the day-ahead market and develops decomposition algorithms capable of obtaining high-quality solutions at industry-relevant scales. The results illustrate that a simple algorithm that only seeks to satisfy unit commitment, reserve, and AC power balance constraints can obtain surprisingly high-quality solutions to this AC unit commitment problem. However, a naive strategy that prioritizes reserve feasibility leads to AC infeasibility, motivating the need to design heuristics that can effectively balance reserve and AC feasibility. Finally, this work explores a parallel decomposition strategy that allows the proposed algorithm to obtain feasible solutions on large cases within the two hour time limit required by typical day-ahead market operations.

Optimizing local electricity markets: A bi-level primal-dual approach for integrating price-based demand response and distribution locational marginal pricing

This paper addresses the conundrum of optimizing electricity consumption patterns in response to fluctuations in demand and price, a task managed by both load aggregators and the distribution system operator (DSO). The conventional approaches in the literature to integrate demand response (DR) into optimal power flow (OPF) problems typically overlook the price responsiveness of consumers or simplify power flow equations to account for price-elastic demand.In this paper, we strive to close this gap by introducing a bi-level primal-dual optimization framework that incorporates aggregators' objectives into the market-clearing process while preserving the precision of the OPF equations. At the upper level, the model seeks to minimize both the total payment and peak load. The lower level, structured as a second-order conic (SOC) problem, aims to reduce overall generation costs subject to constraints of the second-order conic (SOC) branch flow model (BFM). The two levels interact through the optimal demand response and distribution locational marginal prices (DLMPs). The principles of convex duality principles together with the strong duality constraint are leveraged to transform the market-clearing problem into a single primal-dual problem. We also circumvent the non-linearity that stems from the DR payment term by incorporating discretizing loads and the big-M method, thus converting the problem into a mixed-integer SOC (MI-SOC) formulation. The merits of the proposed MI-SOC framework are validated through case studies conducted on the IEEE 33-bus test system, showcasing its potential to enforce price-elasticity demand response in distribution system's electricity markets.

An adaptive energy-based sequential method for training PINNs to solve gradient flow equations

Recent developments in numerous scientific computing fields have been made possible by physics-informed neural networks (PINNs), a class of machine learning techniques that incorporate physical knowledge into neural networks. However, PINNs still encounter difficulties in simulating a kind of partial differential equations (PDEs), i.e. gradient flow equations of complex dynamic systems. Through analysis from the neural tangent kernel's (NTK) point of view, we find that directly training PINNs on the large temporal window may lead to failure. To tackle this problem, we utilize one of the gradient flow equations' significant physical properties, the energy dissipation law, to propose an adaptive energy-based sequential training method for PINNs. Specifically, the gradient of free energy is employed to determine the adaptive temporal steps of the training window, which also enhances the training efficiency. Numerical experiments are demonstrated among gradient flow equations including Cahn-Hilliard, heat conduction, and Allen-Cahn equations. Our method not only outperforms PINNs but also preserves the energy dissipation law, which shows the ability to solve complex long-time simulation problems of gradient flow systems.

Nano particle distribution in blood via electroosmotic peristaltic flow in a non-uniform wavy membrane base capillaries

ObjectiveThe primary purpose of this article is to undertake a mathematical investigation into the electro osmotically thermally driven transport of solute particles, which are typically on a micro to nano-meter scale, suspended in blood. The study is conducted within a non-uniform porous channel for a Williamson fluid. The main objective of this research is to explore the interactions and consequences of solute particles and nanoparticles in the Esophagus, particularly regarding their potential applications in drug delivery and biomedical engineering, especially in the context of electroosmotic non-Newtonian fluids. SignificanceThis research also has significant implications for microscale physiological phenomena. In this investigation, blood serves as the base fluid, and a nanofluid is created by introducing Nickel and Cobalt nanoparticles into the blood. Both nanoparticles have critical medical applications, especially in drug delivery and cancer treatment. To delve deeper into the study of nanomedicine delivery, Nickel and Cobalt nanoparticles are introduced into the blood alongside other smaller solute particles. MethodologyThe mathematical modeling is conducted in a rectangular coordinate system, and the governing flow equations are linearized using approximations that consider low Reynolds numbers and large wavelengths. The numerical solution is computed for a coupled set of nonlinear equations that describe the profiles of fluid-particle velocity, temperature, and fluid-particle composition. The study explores the influence of various key parameters and presents these effects through graphical representations. FindingsIt is observed that an increase in the suspension concentration and the Williamson fluid parameter leads to higher fluid velocity, while the temperature distribution exhibits the opposite trend. The introduction of nanoparticles into the fluid decelerates the flow and raises the temperature.

Global existence of entropy solutions for euler equations of compressible fluid flow

Global existence of entropy solutions for euler equations of compressible fluid flow

Combined Effect of Surface Irregularities and Applied Voltage on the Behavior of Hole-Entry Spherical Hybrid Journal Bearings Lubricated with an Electro-Rheological Fluid

Abstract Surface irregularities substantially affect the performance of tribological systems. The influence of three-dimensional surface irregularities has been investigated on the behavior of hole-entry spherical hybrid journal bearings. Recently, smart fluids have been employed in several applications to improve their performance. The interactive effect of electro-rheological (ER) fluid and surface irregularities have also been studied. The modified Reynolds equation and restrictor flow equation have been solved using the finite element technique with appropriate boundary conditions. The results show that consideration of surface irregularities on bearing surface enhances bearing stability. Spherical hybrid journal bearings lubricated by ER fluid increase minimum fluid film thickness and minimize the possibility of metal-to-metal contact. It is found that the combined effect of surface irregularities and ER fluid significantly improved the bearing performance parameters than individual behavior. The bearing designer is anticipated to benefit from the current model.

Multi-parameter modeling for prediction of gas–water production in tight sandstone reservoirs

Tight sandstone reservoirs are significant sources of natural gas reserves. As traditional reserves become increasingly scarce and costly, optimizing the development of these reservoirs becomes crucial. This study introduces a novel two-phase gas–water flow model for single wells, incorporating both Darcy and non-Darcy flow equations. These equations are derived from mass conservation and momentum principles for both gas and water phases. Using data from a real tight gas well, our model, which includes stress-sensitive phases for gas and water, outperforms traditional Darcy flow models. Specifically, the average relative deviations in daily production rates were 0.1815% for gas and − 0.2677% for water, which are significantly smaller compared to traditional Darcy flow models. Further application of the non-Darcy flow model reveals strategies to enhance well performance. For example, mitigating liquid lock damage within a 2 m radius near the well could restore the permeability from 0.045 to 0.143 mD, thereby tripling the daily gas production. This non-Darcy flow model is easy to implement and shows significant potential in forecasting production yields in tight sandstone reservoirs, highlighting its importance in the petroleum and natural gas industry.

Dispatchable region for distributed renewable energy generation in reconfigurable AC–DC distribution networks with soft open points

The dispatchable region (DR) describes the ability of a power system to adapt to the variability of distributed renewable energy (DRE) generation. Switchable devices such as soft open points (SOPs) and tie switches enable the AC–DC distribution network to flexibly cope with DRE power fluctuations. Currently, research on DRs seldom considers the effects of SOPs and reconfiguration with tie switches in AC–DC distribution networks, which prevents accurate evaluation of DR for this type of network. To bridge this gap, this paper formulates DRs for DRE generation in an AC–DC distribution network considering SOPs and reconfiguration with tie switches. The original model for deriving DRs is typically nonconvex, and the DR boundaries are intractable because of nonlinear power flow equations and binary variables of tie switches. Accordingly, this paper employs the outer polyhedral approximation and convex hull relaxation to approximate the original DR. An efficient adaptive constraint generation algorithm is developed to search for boundaries of the approximated DR. The numerical results show that the proposed model can effectively adapt to the DR of reconfigurable AC–DC distribution networks with SOPs and verify the accuracy and computational efficiency of the proposed method.

The Effect of Viscous Dissipation and Joule Heating on Poiseuille Flow of Hyperbolic Tangent Fluid

In this paper, we showed the computer solutions for the Flow of Poiseuille of (MHD) hyperbolic tangent impossible-to-compress fluid Amid a pair of parallel slabs that are sloped at an angle utilizing a uniformly porous medium. Heat transfer attempts and slip boundary conditions are taken into account. In the energy equation, radiation, joule heating, and viscous dissipation are also accounted for. It is presented in a cartesian coordinate system that supplies the model of the governing equations of the hyperbolic tangent fluid flow. The equations of velocity and Temperature are solved numerically by using "ND solver built". The effects of different factors such that Hartmann number, Darcy number, slip parameter, Grashof number, Brinkman number, radiation parameter and others on velocity and temperature profiles are explored and presented in the Mathematica program. It is noticed that the profiles of velocity and Temperature are an increasing function of Darcy number, slip parameter, Grashof number, inclination angle, pressure gradient, Brinkman number, radiation parameter, and index-power parameter while they are a decreasing function of Hartmann and Weissenberg numbers. The research intends to improve our understanding of the thermal behavior of hyperbolic tangent fluids in practical applications by studying the combined effects of viscous dissipation and Joule heating on the Poiseuille flow. The potential ramifications of this phenomenon extend to multiple domains, encompassing engineering, materials science, and fluid dynamics.

Chaotic Vortex-Induced Vibrations of Rigid Cylinders with Nonlinear Snapping Support

Vortex-Induced Vibration (VIV) is a complex fluid–structure interaction in offshore structures. Traditionally, this phenomenon is considered periodic; however, many of its signals show chaotic behavior. The basic model already employed by other researchers is a rigid circular cylinder with linear springs and dampers. In this work, nonlinear snapping support is used to model nonlinearity in the system. To numerically simulate the flow, Reynolds-Averaged Navier–Stokes (RANS) equations for two-dimensional incompressible unsteady flows are applied. The degree of nonlinearity of the system can be changed by manipulating [Formula: see text], which is one of the geometric properties of the spring and takes values between 0 and 1. The 0–1 test, Poincaré section, and Fast Fourier Transform are used to analyze the cylinder and lift force behavior. Also, the Hilbert transform is applied to the signals, and the phase shift between displacement and lift force is obtained. The results show that the system behavior consists of branches: branch I and branch II. The large amplitudes occur in branch II. It is found that chaos emerges at the beginning of branch II, regardless of the value of [Formula: see text]. By raising the [Formula: see text] value, the span of branch II becomes more expansive, and its first point is placed at lower reduced velocities. Also, the wake dynamics becomes more regular at the end of branch I and more irregular at the beginning of branch II with the increase in [Formula: see text]. When the cylinder displacement signal is chaotic, the lift force behavior is also chaotic, but not vice versa.

Numerical simulation on magnetohydrodynamics convection in annulus inclined elliptical enclosure

ABSTRACT The present work numerically demonstrates the uniform magnetohydrodynamics Newtonian, laminar natural convection in elliptical cold enclosure with inner hot circular body considering the influence of its vertical movement on the fluid flow and heat transfer. The gap area between the elliptical enclosure and the inner body had been filled by the Al2O3-water nanofluid in the upper layer, whereas lower layer has been filled by the porous medium that has been saturated by an identical nanofluid. The local thermal equilibrium model had been implemented to model the nanofluid and porous media. Additionally, Darcy–Brinkman model considered in the representation of the porous media. The three governing equations of heat and fluid flow like energy and momentum of fluid, in addition to the continuity equation, had been solved numerically utilising finite element formulation. The parameters under investigation are the Rayleigh number value 10 3 ≤ Ra ≤ 10 6 , Darcy number 10 − 5 ≤ Da ≤ 10 − 1 , and Hartmann number 0 ≤ Ha ≤ 60 . Additionally, two geometrical parameters had been selected, which are the three different locations of inner cylinder (top, middle, bottom), as well as the four different values of the enclosure’s orientation angle γ = 0 ∘ , γ = 90 ∘ , γ = 180 ∘ , γ = 270 ∘ . The results have been presented to reflect the influence of the abovementioned parameters on isotherms and streamlines, besides Nusselt’s number. It has been proved that to improve the heat transfer rate, it is better to locate inner body in bottom region. The Nusselt number increases by 17.44% when it is moved from the top to the bottom. Additionally, the Nusselt number along the elliptical enclosure attached to the nanofluid layer when rotating the elliptical body from γ = 0 ∘ into γ = 180 ∘ leads to lower the Nusselt number by 32.3372%. This result is exactly inverse considering Nusselt number along nanofluid–porous layer which proved that increasing the orientation angle from γ = 0 ∘ to γ = 180 ∘ contributed to enhancing Nusselt number by 24.7009%.

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

Multilayer Commingled Production Effects in Hydrate Reservoirs with Underlying Gas

Multilayer commingled production is a widely used development method to improve the production capacity of gas reservoirs. However, there is currently limited research on the gas production characteristics of multilayer commingled production in hydrate reservoirs with underlying gas. The objective of this study was to analyze the characteristics of multilayer commingled production in order to determine suitable hydrate reservoirs for such a development method. Firstly, we employed analytical solutions to the equations of fluid flow in porous media to determine the factors affecting the production capacity. Then, by employing numerical simulation and depressurization methods, the rates of gas production and gas release from hydrate dissociation in a single production well were estimated. Additionally, the production capacity ratio of multilayer commingled production and separated-layer production was proposed. The influence of different reservoir characteristics on multilayer commingled production yield was determined and plotted. When there is an interlayer between hydrates and the underlying gas, the formation pressure ratio is the decisive factor affecting the multilayer commingled production yield. When there is no interlayer, the multilayer commingled production rate will increase with an increase in the permeability ratio, hydrate saturation, and underlying gas saturation. This study provides a theoretical foundation for predicting the production capacity of hydrate reservoirs, as well as assistance in selecting the hydrate reservoirs most suitable for multilayer commingled production.

An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion

Abstract This article investigates the unsteady mixed convention two-dimensional flow of magnetohydrodynamic Casson hybrid nanofluids (alumina oxide and titanium oxide nanoparticles with base fluid water) flow through porous media over a linearly stretched sheet. We analyzed the heat and mass transfer in mixed convection, thermal radiation, variable thermal conductivity, variable mass diffusivity, and chemical reaction in the presence of thermophoresis and Brownian motion. A system of partial differential equations is reduced to a solvable system of ordinary differential equations by applying a suitable similarity transformation. We used the Runga–Kutta method along with the shooting procedure to solve the flow, heat, and mass transfer equations along with boundary conditions. The results obtained from MATLAB codes are compared with previously published results of the same type in a limiting case. The results of the velocity, temperature, and concentration profile of the hybrid nanofluid for varying different flow parameters are obtained in the form of graphs, while the rate of shear stress, rate of heat, and mass transfer are expressed in tables. We noticed that velocity and temperature diminish as an unsteady parameter increases; however, the reverse trend was observed in the nanoparticle concentration profile. With an increase in the thermal radiation parameter, the resultant velocity and temperature profile improves, while the concentration of nanoparticle profiles decreases. The velocity and temperature increase with higher Brownian motion, while the velocity increases and temperature decreases with higher thermophoresis.

Effects of vibration on natural convection in a square inclined porous enclosure filled with Cu-water nanofluid

PurposeThe purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.Design/methodology/approachThe present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.FindingsThe numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψmax| = 21.415 to |ψmax| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.Originality/valueTo the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

Triple Mixed Integral Transformation and Applications for Initial-Boundary Value Problems

In this paper, we establish a new integral transformation method for solving the initial-boundary value problems of the partial differential equations. The method is a combined expression mainly based on the triple integral transformation of Laplace and Sumudu. We study the basic properties of the triple Laplace-Sumudu transform, and give the triple Laplace-Sumudu transforms of some basic functions. And as applications, we solve some heat flow equations and wave equations with initial-boundary value conditions by using the method. The results show that the triple Laplace-Sumudu transform is more efficient and useful to deal with these problems.

Gravity and [formula omitted] flows in higher dimensions

We study systems in arbitrary space-time dimensions where matter, deformed by TT‾-like irrelevant operators, is coupled to gravity in the Palatini formalism. The dynamically equivalent perspective is investigated, wherein the deformation transitions from the matter action to the gravitational one or vice versa. This alternative viewpoint leads to the emergence of Ricci-based gravity theories, thus providing a high-dimensional generalisation of the well-known equivalence between two-dimensional TT‾ deformations and coupling to Jackiw-Teitelboim gravity. This dynamical equivalence is examined within the framework of the recently introduced Lagrangian flow equation, which notably led to the discovery of a direct link between Nambu-Goto theory and TT‾ in d=2, as well as significant insights into nonlinear electrodynamics models in d=4. The investigation involves explicit examples in d=4 dimensions; it builds upon earlier research concerning the metric interpretation of TT‾-like perturbations, incorporates and extends recent findings in the cosmology-related literature associated to the concept of reframing. We focus on scenarios where the resulting modified gravity theories manifest as Born-Infeld and Starobinsky types.

Modeling of artificial neural network to analyze heat and mass transfer of ternary hybrid nanofluid between two parallel plates with inclined magnetic field

The applications of the artificial neural network (ANN) have become the focus of interest of researchers due to their convenience for accurate modeling, simulation, and efficiency of evaluation. The primary objective of this study is to investigate the characteristics of heat and mass transfer of the ternary hybrid nanofluid flow (THNF), which is squeezed between two parallel plates, using ANN. The plate which lies on x-axis is stretching while the upper plate (UP) can move in upward and downward direction. An inclined magnetic field (MF) is also applied to the lower plate (LP). A system of partial differential equations of flow, energy, and mass transfer is used to simulate the THNF, which is then condensed using similarity substitution to a collection of ordinary differential equations (ODEs). Using the differential transform method (DTM), the resultant nonlinear ODEs in dimensionless form are further solved. The influence of the different varying physical parameters on velocity, temperature, and concentration is graphically presented and discussed. It becomes apparent that the velocity, heat, and mass transfer in squeezing flows are significantly impacted by the inclination angle of the applied MF. To demonstrate the validity of the study, the numerical findings of the Nusselt and the Sherwood numbers are provided. For the accuracy of the used approach, DTM results are compared with results from the numerical approach. The novelty of the current work is to train the neural network with the Levenberg–Marquardt algorithm in the model. To get the estimated output of the model, different scenarios are set for training, testing, and validation. The analysis is done by mean square error (MSE), histogram, fitness curve, and regression (RG). The created ANN model is shown to be reliable due to its exceptional accuracy throughout the training, validation, and testing stages.

Utilization of vortex flow pattern in the design of an efficient solar air heater

In this work, numerical and experimental analyses of a new model of circular solar air heater are carried out to examine the effect of employing vortex flow inside the air vessel of collector for convection enhancement. In three-dimensional numerical CFD-based analysis, the COMSOL Multi-physics is used to solve the flow equations for the turbulent forced convection airflow and conduction equation for the solid parts of the solar heater at different air mass flow rates in the range of 0.003 to 0.012 kg/s. In the calculation of turbulent stresses and heat fluxes, the RNG κ-∊ turbulence model is employed. The surface to surfaces (S2S) radiation model is used to consider the radiations emitted by the hot surfaces in collaboration with the energy equation. For validation, the theoretical findings are evaluated against the experiment. For the studied test cases with different values of solar irradiation and air mass flow rate, thermal efficiencies of up to 80 % are found. In comparison to the conventional rectangular-shaped solar air heaters with smooth ducts, more than 100 % increase in the value of thermal efficiency is delineated from the theoretical and experimental findings. This gain is attributed to the unique flow pattern in the developed solar collector.

Upgrading of the modified Knudsen equation and its verification for calculating the gas flow rate through cylindrical tubes

The modified Knudsen equation was developed to calculate the gas flow rate through a cylindrical tube with arbitrary length-to-diameter ratio in any flow regime including molecular flow, viscous laminar flow, turbulent flow, critical flow, subcritical flow, and their intermediates in our laboratory. Here, it is upgraded for better agreement with literature data, and the upgraded version is compared with 83 literature sources including 31 gas flow equations to verify its reliability. For Kn > 10−5, the modified Knudsen equation mostly agrees with the literature data to within 20%, except for orifice flows with pd/pu ≈ 1.