Mass Conservation Research Articles

Thermodynamic Analysis of Gas Turbine Power Plant of PT PLN Belawan Generation Implementation Unit

The low quality of the thermodynamic process in a gas turbine power plant results in the waste of potential energy and impacts the power plant's efficiency. Analysing the thermodynamic performance of a gas turbine power plant is crucial to evaluating its efficiency in converting fuel energy into useful work. This analysis helps identify opportunities for improvement and optimise the plant's design for better performance by examining the components (e.g., the compressor, combustion chamber, and turbine). This study aims to evaluate the performance of a Gas Turbine Power Plant (GTPP) through thermodynamic analysis considering the variation of cycle loads. The study was conducted based on the field survey data obtained from the GTPP PT PLN Belawan generation implementation unit. The collected operation data was used to perform a thermodynamic analysis by applying the principles of conservation of mass and energy, along with the laws of thermodynamics. The study examined five cycle load variations: 31.7 MW, 34.3 MW, 48.1 MW, 60.7 MW, and 71.7 MW. Results showed a consistent reduction in the gas turbine heat rate as the load increased, with a significant 53.3% drop in heat rate from 34.3 MW to 71.7 MW. Higher cycle loads also correlated with increased turbine and compressor work, with the turbine producing 55.8% more work than the compressor at 71.7 MW. The turbine's thermal efficiency ranged from 40% to 44%, with potential for a 5% efficiency increase.

A generalized scalar auxiliary variable approach for the Navier–Stokes-[formula omitted]/Navier–Stokes-[formula omitted] equations based on the grad-div stabilization

In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes-ω/Navier–Stokes-ω equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed scheme is almost unconditionally stable and requires solving only the linear equation with constant coefficient at each time step. It can also penalize for lack of mass conservation and improve the accuracy. Finally, a series of numerical experiments are carried out to illustrate the stability and effectiveness of the proposed scheme.

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks.

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI. The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints. The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels. The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations

This paper proposes and analyzes a fully discrete scheme for nonlinear biharmonic Schrödinger equations. We first write the single equation into a system of problems with second-order spatial derivatives and then discretize the space variable with an ultraweak discontinuous Galerkin scheme and the time variable with the Crank–Nicolson method. The proposed scheme proves to be computationally more efficient compared to the local discontinuous Galerkin method in terms of the number of equations needed to be solved at each single time step, and it is unconditionally stable without imposing any penalty terms. It also achieves optimal error convergence in L2 norm both in the solution and in the auxiliary variable with general nonlinear terms. We also prove several physically relevant properties of the discrete schemes, such as the conservation of mass and the Hamiltonian for the nonlinear biharmonic Schrödinger equations. Several numerical studies demonstrate and support our theoretical results.

Optimal error bounds of the time-splitting sine-pseudospectral method for the biharmonic nonlinear Schrödinger equation

We propose a time-splitting sine-pseudospectral (TSSP) method for the biharmonic nonlinear Schrödinger equation (BNLS) and establish its optimal error bounds. In the proposed TSSP method, we adopt the sine-pseudospectral method for spatial discretization and the second-order Strang splitting for temporal discretization. The proposed TSSP method is explicit and structure-preserving, such as time symmetric, mass conservation and maintaining the dispersion relation of the original BNLS in the discretized level. Under the assumption that the solution of the one dimensional BNLS belongs to Hm with m≥9, we prove error bounds at O(τ2+hm) and O(τ2+hm−1) in L2 norm and H1 norm respectively, for the proposed TSSP method, with τ time step and h mesh size. For general dimensional cases with d=1,2,3, the error bounds are at O(τ2+hm) and O(τ2+hm−2) in L2 and H2 norm under the assumption that the exact solution is in Hm with m≥10. The proof is based on the bound of the Lie-commutator for the local truncation error, discrete Gronwall inequality, energy method and the H1- or H2-bound of the numerical solution which implies the L∞-bound of the numerical solution. Finally, extensive numerical results are reported to confirm our optimal error bounds and to demonstrate rich phenomena of the solutions including rapidly dispersion in space of high frequency waves and soliton collisions.

An improved Arbitrary Lagrangian–Eulerian thermal-fluid model by considering powder deposition effects on melting pool during Direct Energy Deposition processes

Directed Energy Deposition (DED) has emerged notably by offering new possibilities for (re-)manufacturing parts. The multi-phase thermal-fluid models that simulate powder stream deposition are computationally too expensive. The mono-phase Arbitrary Lagrangian–Eulerian (ALE) method are limited in prediction due to exclusion of powder deposition parameters. To address this, we propose an improved 3D mono-phase thermal-fluid model that incorporates powder deposition effects and employs a Moving Thermal-Fluid (MTF) framework to accelerate simulations. Mass, energy, and momentum conservation equations are solved using the finite element method (FEM) and an implicit time integration algorithm, and the ALE method tracks the free surface during deposition. The improved ALE allows considering enthalpy and momentum related to powder deposition through the implementation of new source terms in the energy and momentum conservation equations, leading to more accurate predictions without significantly increasing computing time. Numerical investigations into powder deposition parameters, such as powder distribution, powder enthalpy, and powder momentum, are conducted to identify their impact on melting pool prediction. The in-situ and ex-situ measurements of the melting pool are also performed to check the efficiency of the proposed model. The applications highlight the importance of incorporating powder stream effects and demonstrate the proposed model’s computational efficiency compared to the classical ALE model.

A coupled phase-field model for sulfate-induced concrete cracking

The performance of concrete will decrease when subjected to external sulfate corrosion, and numerical models are effective means to analyze the mechanism. Most models cannot efficiently consider the effect between cracks and ionic transport because crack initiation and propagation are ignored. In this paper, a coupled chemical-transport-mechanical phase-field model is developed, in which the phase-field model is applied for the first time to predicate the cracking of sulfate-eroded concrete. The chemical-transport model is established based on the law of conservation of mass and chemical kinetics. The phase-field model equivalents the discrete sharp crack surface into a regularized crack, making it convenient to couple with the chemical-transport model. The crack driving energy in the phase-field model is computed by the expansion strain, which can be obtained from the chemical-transport model. The coupling of crack propagation and ionic transport is achieved by a theoretical equation, which considers both the effects of cracking and porosity. Complex erosion cracks can be automatically tracked by solving the phase-field model. The simulation results of the multi-field coupling model proposed in this paper are in good agreement with the experimental data. More importantly, the spalling phenomenon observed in physical experiments is reproduced, which has not been reported by any other numerical models yet, and new insight into the spalling mechanism is provided.

A numerical model for solitary wave breaking based on the phase-field lattice Boltzmann method

This study presents a numerical investigation of a solitary wave breaking over a slope by using the phase-field lattice Boltzmann method. The incompressible two-phase flow equations are solved by using a velocity-based formulation of the two-phase lattice Boltzmann method with a central-moment collision model to accurately simulate wave breaking problems. For interface capture, a phase-field lattice Boltzmann method that ensures mass conservation is employed. The validity of the proposed method is confirmed through solitary wave propagation and transformation problems, and the obtained results are in good agreement with the experimental and calculated results. The proposed method is then employed to analyze wave breaking on a slope, demonstrating strong concordance with experimental data and existing computational findings. By analyzing the instantaneous flow characteristics and the temporal evolution of the variation in kinetic, potential, and total energy from deep to shallow water, the model can reveal the macroscopic characteristics of solitary wave breaking. Because the phase-field model effectively simulates wave breaking and air entrainment, it can depict wave energy dissipation more accurately than the single-phase lattice Boltzmann method with free surface tracking.

Thermal dynamics of nanoparticle aggregation in MHD dissipative nanofluid flow within a wavy channel: Entropy generation minimization

This paper examines how nanoparticle aggregation and a consistent magnetic field influence the peristaltic movement of a dissipative nanofluid, which is caused by the sinusoidal deformation of the boundary. The viscosity of TiO2/H2O nanofluids is accurately determined by the Krieger-Dougherty model with nanoparticle aggregation, while thermal conductivity (TC) is estimated through the Bruggeman model. The set of governing equations are modeled in a fixed frame by utilizing the conservation laws of energy, mass and momentum. Galilean transformation is utilized to transform the system of equations into a wave frame, which is then converted into a dimensionless form. The assumption of a small Reynolds number and long wavelength serve to further simplify the set of equations, which are subsequently addressed through the implementation of the differential quadrature method (DQM), a highly effective numerical technique. Quantities of interest, namely velocity, pressure gradient, temperature, trapping phenomena, heat transfer, and volumetric entropy generation are analyzed across a range of physical parameters, including the solid volume fraction (Φ=0.01−0.04), Eckert number (Ec=0.0−0.1), Hartman number (Mh=0.2−2.2), Grashof number (Gr=1.0−3.0) and temperature ratio parameter (θd=0.5−2.5). A comparative analysis is conducted between the scenario involving aggregation and the one without aggregation. It is observed that nanoparticle aggregation significantly alters these quantities.

Comparison of novel physics-guided machine learning models with empirical equations for predicting longitudinal dispersion coefficient in diverse natural river systems

Accurate calculation of the longitudinal dispersion coefficient (LDC) is crucial for assessing river fate and transport processes. Traditional methods, including experimental, analytical, and empirical equations, each have their challenges, such as complexity and susceptibility to errors. This study introduces and evaluates advanced physics-guided machine learning (ML) models, including hybrid hydrodynamic-particle simulation (HHPS), physics-enhanced ML (PEML), and physics-regularized regression trees (PRRT). Our dataset includes hydraulic and geometric parameters collected from 50 diverse rivers across the US and the UK, encompassing variables such as river width (W), flow depth (H), average flow velocity (U), flow shear velocity (U*), concentration of the solute (μgL) and LDC (ε). Input parameters were dimensioned using the UU∗ and WHratios, while the dimensionless LDC (εHU∗) served as the model output. By embedding core hydrodynamic principles such as continuity, mass and momentum conservation, and Navier-Stokes equations into the ML algorithms, these models achieved high predictive accuracy. Specifically, the HHPS model reached a coefficient of determination of 0.997, and both PEML and PRRT demonstrated Nash-Sutcliffe efficiencies exceeding 0.950, significantly outperforming traditional empirical equations. Additionally, SHapley Additive exPlanations (SHAP) sensitivity analysis revealed the substantial influence of channel width and flow conditions on LDC predictions. Our study highlights the superior performance of physics-guided ML models in providing accurate and reliable tools for river water quality management, demonstrating their substantial improvements over traditional methods and their potential broader applications in environmental studies.

A free-energy based multiple-distribution-function lattice Boltzmann method for multi-component and multi-phase flows

This study presents the development of a multiple-distribution-function lattice Boltzmann model (MDF-LBM) for the accurate simulation of multi-component and multi-phase flow. The model is based on the diffuse interface theory and free energy model, which enable the derivation of hydrodynamic equations for the system. These equations comprise a Cahn-Hilliard (CH) type mass balance equation, which accounts for cross diffusion terms for each species, and a momentum balance equation. By establishing a relationship between the total chemical potential and the general pressure, the momentum balance equation is reformulated in a potential form. This potential form, together with the CH type mass balance equation, is then utilized to construct the MDF-LBM as a coupled convection–diffusion system. Numerical simulations demonstrate that the proposed MDF-LBM accurately captures phase behavior and ensures mass conservation. Additionally, the calculated interface tension exhibits good agreement with experimental data obtained from laboratory studies.

An estimation method for bias error of measurements by utilizing process data, an incidence matrix and a reference instrument for data validation and reconciliation: Part 2 Extension to the energy balance relation

Abstract Ensuring data reliability is becoming increasingly important for further applications of AI, IoT, and digital twins. One promising technology for ensuring data reliability is data validation and reconciliation (DVR), which minimizes the uncertainty of measurements based on statistics. DVR has been widely used for the operation and maintenance of nuclear power plants in Europe and the United States in recent years. The most important input for DVR analysis is measurement uncertainty. The catalog value provided by sensor manufacturers includes the measurement uncertainty, but in reality, the actual measurement uncertainty is often smaller. Previous studies have proposed several methods for evaluating the actual measurement uncertainty based on process data, which have been confirmed to be effective for evaluating random errors. It is important to note that bias errors also contribute significantly to the measurement uncertainty. In our previous paper, we proposed a method for estimating bias error using process data, an incidence matrix, and a reference instrument. The proposed method was limited to a mass balance relation, i.e., flow rate measurements. In this paper, we extend the method to include an energy balance relation by considering energy conservation in addition to mass conservation. This extension enables the evaluation of measurement uncertainty for flow rate and temperature. The proposed method was validated with two benchmark problems. It was found to be applicable to various flow conditions, including physically fluctuating flow, such as that observed in the feedwater flow in nuclear power plants.

Analysis on transient wave propagation in the soft matter of hydrogels

The precise control and structural design of the soft matter of the hydrogel subjected to dynamic loading require an in-depth understanding of its transient wave characteristics. However, for the complex solid–liquid coupling effects of the soft matter of hydrogels, the traditional single-phase wave model is no longer applicable. In this study, a transient wave propagation model that considers the solid–liquid coupling effects and its computational method is proposed. The wave-governing equations of hydrogels are derived based on the mass conservation and dynamic equilibrium equations, where the motions of solid and liquid phases are independently described. After transforming the governing equations into the equivalent weak form, numerical solutions for transient wave propagation in one- and two-dimensional hydrogels are calculated. The accuracy of the proposed model is verified by a comparison between semi-analytical and commercial finite element method solutions. We observe that the travelling and reflection processes of the two types of compression waves, P1 and P2, with different wave speeds are captured when the dynamic coefficient of permeability kf increases. Furthermore, the influence of solid–liquid coupling effects on the transient responses of hydrogels is discussed. The results show that the hydrogels exhibit the dynamic characteristics of a single-phase medium to a certain extent when kf is sufficiently small.

Study on the macro-mechanical behavior and micro-structure evolution law of broken rock mass under triaxial compression

Study on the macro-mechanical behavior and micro-structure evolution law of broken rock mass under triaxial compression

A sub-grid gas–solid interaction model for coarse-grained CFD–DEM simulations

Computational fluid dynamics has been coupled with coarse-grained discrete element method (CFD–CGDEM) to study industrial-scale gas–solid fluidized beds. However, solving the fluid flow at a grid size of several coarse-grained particles (CGPs) cannot accurately predict the gas–solid interaction, and thus reasonable correction model is required. This study develops a sub-grid model to correct the gas–solid interaction and thereby improve the accuracy of coarse-grid CFD–CGDEM simulation. First, the fluid grids with the size of several CGPs are divided into the auxiliary three-dimensional sub-grids. Then, the CGPs are mapped onto the sub-grids by the weight function to reconstruct the local solid velocities and solid fractions of the sub-grids. After that, the simplified mass and momentum conservation equations are solved to resolve the local gas velocities of sub-grids. Finally, the drag on each CGP is corrected based on the local gas-phase hydrodynamics of sub-grids. Results show that the sub-grid model resolving the local gas velocity in all the three directions works better than that just in the main stream direction. The coarse-grid CFD–CGDEM simulations with this sub-grid model agree well with the experiment for the bubbling, turbulent and rapid fluidized beds. Besides, by solving the simplified conservation equations with graphics processing units, the coarse-grid CFD–CGDEM coupled with the sub-grid model achieves 674 times speedup compared to the fine-grid simulation, demonstrating a much more efficient method to study industrial-scale gas–solid fluidized beds.

Role of periodic oscillating flow modulators on mixed convection in a long horizontal channel

Present study explores mixed convection characteristics in a long horizontal channel subjected to multiple periodically distributed flow modulators. The flow modulators are represented by oscillating blades placed along a centerline of the channel whose lower and upper walls are kept at constant high and low temperatures respectively. In replicating the blade oscillation, moving mesh approach has been adopted within Arbitrary Lagrangian–Eulerian (ALE) framework for a representative periodical unit. The corresponding non-dimensional governing mass, momentum and energy conservation equations have been solved through Galerkin finite element solver for a wide variations of modulator's dynamic condition (oscillating frequency and maximum angular displacement) for different fluids represented by Prandtl number. Heat transfer performance of the system has been demonstrated in terms of spatially-averaged transient as well as time-averaged Nusselt number while qualitative analysis of fluid flow and thermal field has been presented as streamline and isotherm plots. Present study indicates that the time averaged Nusselt number undergoes significant variation with blade oscillating frequency and maximum angular displacement depending on both the Prandtl number and Reynolds Number. Power spectrum analysis obtained through Fast Fourier Transformation (FFT) of the imposed blade frequency and induced thermal frequency reveals different correlation depending on the blade frequency. Blade friction power requirement has been found to increase at higher blade frequency as well as maximum angular displacement. However, contrary to power consumption, increase in frequency does not result in a significant rise in heat transfer. Consequently, specific heat transfer decreases at higher blade oscillating frequency and maximum angular displacement.

Model-free chemomechanical interfaces: History-dependent damage under transient mass diffusion

This paper presents a data-driven framework based on distance functional for chemo-mechanical cohesive interfaces to capture transient diffusion and resulting interfacial damage evolution. The framework eliminates reliance on complex constitutive models and phenomenological assumptions, especially avoiding the coupling tangent terms with a given material database. The interfacial chemical potential and its jumps are used to expand the phase space for describing the chemical states of interfaces. Subsequently, a novel chemo-mechanical distance norm, including traction-separation pair, interfacial chemical potential-concentration pair and corresponding chemical potential jump-flux pair, is presented. Momentum conservation law for interfacial tractions and mass conservation law for interfacial concentration are enforced via Lagrange multipliers. For tracking the history-dependent state of the interface damage, an internal variable, termed interface integrity, is introduced to condition the interfacial database and manage the subsets mapping strategies, following physically motivated evolution constraints. Numerical examples are conducted to investigate the efficiency and capability of the present framework. A monotonic loading test validates a good numerical convergence relative to the number of data points. Subsequent cyclic loading simulations, compared with the reference solutions, show that the algorithm is well suitable to predict the history-dependent interface damage evolution under complex loading paths. Finally, the chemo-mechanically coupled examples capture phenomena such as interfacial swelling and interface degradation induced by transient diffusion and stress-driven diffusion. The current work provides a promising tool for understanding chemo-mechanical behaviors of interfaces within heterogeneous composites.

Physics–dynamics–chemistry coupling across different meshes in LFRic‐Atmosphere: Formulation and idealised tests

AbstractThe main components of an atmospheric model for numerical weather prediction are the “dynamical core,” which describes the resolved flow, and the “physical parametrisation,” which capture the effects of non‐fluid and non‐resolved fluid processes. Additionally, models used for air quality or climate applications may include a component that represents the evolution of chemicals and aerosols within the atmosphere. Though, traditionally, all these components use the same mesh with the same grid spacing, we present a formulation for the different components to use a series of nested meshes, with different horizontal grid spacings. This gives the model greater flexibility in the allocation of computational resources, so that resolution can be targeted to those parts that provide the greatest benefits in accuracy. The formulation presented here concerns the methods for mapping fields between meshes and is designed for the compatible finite‐element discretisation used by LFRic‐Atmosphere, the Met Office's next‐generation atmosphere model. Key properties of the formulation include the consistent and conservative transport of tracers on a mesh that is coarser than the dynamical core, and the handling of moisture to ensure mass conservation without generation of unphysical negative values. Having presented the formulation, it is then demonstrated through a series of idealised test cases that show the feasibility of this approach.

Non-Fourier heat and mass transport enhancement by hybrid nanofluid-flow over a non-linearly stretchable surface having variable thickness

This article uses non-classical Fick's law, non-Fourier's law, and conservation laws for mass and thermal transport. The hybrid nanoparticles Cu and Al2O3 are considered. The new correlations among the thermo-physical properties of base fluid, Cu and Al2O3 are coupled with simplified nonlinear mathematical models. The resulting models are solved numerically by the finite element method (FEM). The linear shape functions are chosen for the approximation of residual equations. This approximation leads to a nonlinear algebraic system that is linearized by the Picard scheme. The numerical results are ensured to be grid-independent, and convergence is analyzed. The results are validated, and an excellent agreement is obtained between available benchmarks and current outcomes. Thermal solutal relaxation phenomena are responsible for a significant reduction in the transport of heat and mass in Newtonian fluids. These non-Fourier's and non-classical Fick's laws are capable of capturing thermal and solutal elastic phenomena, respectively. Cu and Al2O3 simultaneously act as good conductors of heat, and their simultaneous dispersion in base fluid results in a significant rise in thermal conductivity. Numerical experiments have shown that the transport of heat can be optimized by simultaneous suspension of Cu and Al2O3.

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.