Unsteady Terms Research Articles

Simulation of solidification for saving energy with using nanomaterial involving conduction heat transfer

The current article studies the improvement of the discharging rate in cold storage systems by modifying the tank configuration and incorporating additives. Specifically, the study inspects how varying the diameter (dp) and fraction (ϕ) of nano-powders affects the process duration. The governing equations, derived under the assumption of negligible slip velocity of nanoparticles and convection terms, were solved using the Galerkin method. The computational grid was modified owing to location of the ice front, and unsteady terms were discretized using an unconditionally stable approach. The results indicate that initially, increasing dp decreases the process duration by approximately 20.01 %, but further increases in dp lead to a 49.53 % rise in the duration. As the process time increases, the amount of ice produced also increases, with nanoparticle loading resulting in a significantly higher ice yield. Specifically, the incorporation of nanoparticles enhances the storage rate by approximately 41.37 %.

Effects of strain and pressure on entropy generation in laminar flames

The mitigation of combustion noise is crucial for preventing thermoacoustic instabilities in rocket and gas turbine engines. Entropy noise, arising from entropy fluctuations within the engine, serves as a prominent noise source. Therefore, understanding the mechanisms governing entropy generation in flames becomes imperative for identifying the roots of indirect combustion noise. While previous studies have broadly examined various pathways of entropy generation under different canonical configurations of laminar flames, surprisingly, the effect of strain and pressure has been overlooked. This aspect is analyzed in the present work. Building upon previous analysis, the entropy source term of the reacting flow is decomposed into three sub-terms: the unsteady heat release term (Se,1), the sensible enthalpy term (Se,2), and the partial entropy term (Se,3). The extent to which these three sub-terms contribute to entropy generation is thoroughly analyzed. Simultaneously, the scaling laws of the three sub-terms with respect to strain rate and pressure are investigated. The inclusion of detailed chemical kinetics as well as flame structure in the simulation dataset allows for in-depth investigation into the mechanism of the strain and pressure effects. Three canonical laminar flame configurations – the freely propagating premixed flame, the premixed counterflow flame, and the counterflow diffusion flame – are investigated. The following main conclusions are drawn: the heat release term is the leading constituent of the entropy source; the sensible enthalpy term is negligible; and the partial entropy term is secondary while non-negligible. Under strain and pressure variations, the contribution of the partial entropy term to total entropy production can greatly off-set the total entropy source or even qualitatively affect the strain/pressure response of the entropy generation, i.e., the strain response of the premixed flame and pressure response of the hydrogen non-premixed flame.Novelty and significance statement1. Conducted a systematic investigation of entropy production due to chemical reactions under the influence of strain and pressure variations.2. Revealed that the partial entropy term, often overlooked in previous studies, can surpass the heat release term in certain configurations, emerging as the leading constituent of the total entropy generation source.3. Identified dominating reactions contributing to entropy production for two different fuels of hydrogen and methane.

Implementation of nanoparticles for expedition of freezing through storage unit involving conduction mechanism

This work employs an approach to examine the effects of adding alumina nanoparticles with varying diameters (dp) to water on the productivity of cold storage. Utilizing a finned geometry with a curved cold wall, the mesh configuration was adapted to the solid front's location, and unsteady terms were discretized using implicit methods. The concentration (ϕ) of alumina nanoparticles was also evaluated as a key parameter. Results indicated that increasing the concentration of nanoparticles improved cold storage efficiency by approximately 42.11 %. Among the various sizes, medium-sized nanoparticles were most effective, yielding a 20 % improvement in freezing efficiency compared to the smallest size. Optimal nanoparticle dispersion significantly reduced the required cooling time from 9383.58 s to 5507.129 s. This study highlights the substantial benefits of combining fins and nanoparticles to enhance cold storage systems, presenting a notable advancement in thermal management technology.

Improvement of cold storage efficiency with loading hybrid nanoparticles and utilizing porous media

The purpose of current article is to develop a more efficient cold storage design by integrating hybrid nanomaterials and permeable foam. The container architecture features two sinusoidal walls containing water, with the addition of hybrid nano-powders to enhance conduction. Additionally, to account for radiation effects, a source term based on Roseland approximation is incorporated into the energy equation. The unsteady source terms for freezing are discretized using an implicit technique, and the model is solved using the Galerkin method. Grid configuration is adjusted based on the position of the solid front to ensure accurate simulation results. Verification against previous data demonstrates reasonable accuracy in the model outputs. The study reveals significant improvements in cold storage efficiency through the adoption of these techniques. Without any enhancements, the required storage time is approximately 1552.28 s. However, the integration of all three techniques results in a remarkable reduction of about 91.64 % in this storage time, emphasizing the substantial impact of the proposed design modifications. Specifically, the addition of hybrid nano-powders enhances the freezing rate by approximately 7.84 %, while saturating the medium with porous foam leads to a decrement in storage time of around 90.69 %. Furthermore, an increase in the radiation factor (Rd) by 1 leads to a notable improvement of approximately 20.02 % in cold storage efficiency.

Unsteady hydrodynamics of a surface piercing and fully submerged body when entering a lock

Ship hydrodynamics in a constant waterway have been well studied. With a coordinate system fixed on the moving ship, the boundary value problem (BVP) is usually treated as a steady one. However, the hydrodynamics of a ship moving in confined waterways with abrupt changes in width or depth are complex due to their unsteady nature. The studies on such unsteady problems are insufficient. In the engineering practice, the hydrodynamic unsteadiness can be fully reflected by a scenario when a ship enters a lock. Prior studies have predominantly focused on predicting the ships' hydrodynamic forces without considering the unsteady terms on the free-surface boundary conditions. Obviously, such steady or quasi-steady methods overlooked the crucial unsteady phenomena on free water surface. To address this gap, the present study introduces a novel three-level difference scheme to discretize the free surface condition, preserving unsteady terms while maintaining temporal continuity of cells on the free surface. With the implementation of such fully unsteady BVP, we observed some interesting unsteady free surface motions, which were not well documented in the existing literature. To verify our new observations, as well as to validate the numerical method proposed in this study, two physical model tests were designed and conducted in a towing tank: a submerged ellipsoid enters a deep lock at relatively high speeds, and a box enters a shallow and narrow lock at very low speeds. The discussion is highlighted on the unsteady waves in front of the moving bodies, as well as the unsteady resistance induced by such waves.

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady inertial effects are important. In this work, we propose a gap-averaged Floquet theory accounting for inertial effects induced by the unsteady terms in the Navier–Stokes equations, a scenario that corresponds to a pulsatile flow where the fluid motion reduces to a two-dimensional oscillating Poiseuille flow, similarly to the Womersley flow in arteries. When gap-averaging the linearised Navier–Stokes equation, this results in a modified damping coefficient, which is a function of the ratio between the Stokes boundary layer thickness and the cell's gap, and whose complex value depends on the frequency of the wave response specific to each unstable parametric region. We first revisit the standard case of horizontally infinite rectangular Hele-Shaw cells by also accounting for a dynamic contact angle model. A comparison with existing experiments shows the predictive improvement brought by the present theory and points out how the standard gap-averaged model often underestimates the Faraday threshold. The analysis is then extended to the less conventional case of thin annuli. A series of dedicated experiments for this configuration highlights how Darcy's thin-gap approximation overlooks a frequency detuning that is essential to correctly predict the locations of the Faraday tongues in the frequency–amplitude parameter plane. These findings are well rationalised and captured by the present model.

Modeling of solidification via Galerkin method within storage unit utilizing nano-powders incorporating unsteady source term

The employed numerical method, which incorporates nanomaterial and fins, represents a noteworthy advancement in simulating enhanced freezing processes. This technique leverages an adaptive grid approach, providing a sophisticated framework for estimating the characteristics of the nanomaterial. A key innovation lies in considering the final material as a homogeneous mixture. Notably, the exclusion of gravity's influence on the freezing process, leading to the omission of velocity terms, adds to the precision of the model. This approach holds substantial promise for a range of applications requiring controlled and efficient freezing. The study's significance lies in its potential to revolutionize freezing technologies, offering improved outcomes across various industrial contexts. The analysis's physical outputs, demonstrating notable reductions in completion time, further underscore the method's efficacy in enhancing freezing processes. The Finite Element Method (FEM) has been employed to obtain a comprehensive solution, allowing for an assessment of the effect of the shape factor “m” and nanoparticle concentration (ϕ) on the freezing process. Notably, the introduction of nanoparticles leads to a significant acceleration of the process, resulting in a remarkable 26.77 % reduction in completion time. This finding underscores the crucial role that nanoparticle dispersion plays in enhancing the efficiency of the solidification process. This insight holds substantial promise for applications where controlled and rapid freezing is paramount. The choice of particles with higher “m” values leads to an enhancement in the conduction mode. Consequently, this results in a nearly 7 % reduction in completion time, demonstrating the efficiency of this selection. The fastest process achieves solidification in a mere 538.98 s, while in the absence of nanomaterial, the process with water alone takes significantly longer at 975.69 s. This showcases the substantial improvement that can be achieved with the incorporation of nanoparticles. This information is vital for industries where rapid, controlled solidification is critical.

Computational aeroacoustics and phase-conjugation technique for localizing flow-induced sources

This paper presents a framework comprising computational aeroacoustics (CAA) solvers and a numerical phase-conjugation technique to localize flow-induced noise sources generated by bodies immersed in low Mach number flows. Two test-cases were considered, namely, flow over a two-dimensional (a) circular cylinder at Reynolds number Re =150 and Mach number M = 0.2 and (b) NACA-0012 airfoil at Re = 5000 and angle of attack (AoA) α = 5 deg. The CAA simulations were carried out in OpenFOAM wherein the two-dimensional unsteady, incompressible Navier–Stokes equations was solved using either the pressure-implicit splitting of operators (PISO) algorithm or large eddy simulation (LES). The near-field aerodynamic sources were extracted in terms of the unsteady Lighthill stress tensor terms, following which the far-field acoustic data were computed on boundary nodes using different methods which include the numerical solution of the Lighthill equation, Curle’s analogy, and Ffowcs Williams and Hawkings (FWH) analogy as well as linearized Euler equations (LEE). Next, the frequency-domain phase-conjugation (PC) method was implemented in the finite-element (FE) based COMSOL software to reconstruct the radiated acoustic pressure field, whereby the dipole source location was readily identified by pair of focal spots at the cylinder or at the airfoil trailing-edge (TE).

On the computation of compressible multiphase flows with heat and mass transfer in elastic pipelines

The present work is motivated by the engineering need to simulate the multiphase flows in the course of the start-up of a long-distance crude oil pipeline. We propose a model for compressible multiphase flows with heat and mass transfer and diffusion processes in elastic pipelines. The model is derived with two approaches, i.e., (a) the spatial averaging procedure of a single phase model and (b) the Arbitrary Lagrangian Eulerian (ALE) formulation of the Baer-Nunziato model with quasi-1D approximation. The diffusion processes include the viscous dissipation, wall friction, heat conduction, and heat exchange with external environment. In particular, the wall friction consists of steady friction term calculated by Darcy-Weisbach formula, and the unsteady friction determined by the instantaneous-acceleration-based (IAB) model. The unsteady friction modifies the characteristic structure of the hyperbolic part of the model. For the solution of the hyperbolic part, we propose a three-wave approximate Riemann solver incorporating the unsteady friction term. Mass and heat transfer are realized via instantaneous relaxations of the chemical potential and temperature, respectively. Efficient iterative relaxation procedures for N-phase flows have been proposed. We have validated the proposed model and numerical methods against some benchmark multiphase problems and applied the model to calculate the start-up of a realistic liquid pipeline with intermediate pump station boundary condition.

Computational Simulation of Unsteady Squeezing Hybrid Nanofluid Flow Through a Horizontal Channel Comprised of Metallic Nanoparticles

The characteristics of hybrid nanofluid flow contained copper (Cu) and cobalt ferrite (CoFe2O4) nanoparticles (NPs) across a squeezing plate have been computationally evaluated in the present report. In biomedical fields, in very rare cases fluid flow through a static channel. Similarly in industrial sights, we are also often observed that the fluid flows through comprising plates rather than fixed plates (flow in vehicle’s engine between nozzles and piston). CoFe2O4 and Cu nanoparticles are receiving huge attention in medical and technical research due to their broad range of applications. For this purpose, the phenomena have been expressed in the form of the system of PDEs with the additional effect of suction/injection, heat source, chemical reaction, and magnetic field. The system of PDEs is simplified to the dimensionless set of ODEs through similarity replacements. Which further deals with the computational approach parametric continuation method. For the validity and accuracy of the outcomes, the results are confirmed with the existing works. The results are displayed and evaluated through Figures. It is detected that the hybrid nanoliquid has a greater ability for the velocity and energy conveyance rate as related to the nanofluid. Furthermore, the energy profile declines with the consequences of unsteady squeezing term, while enhances with the effects of suction factor, heat absorption and generation, and lower plate stretching sheet.

Energy storage analysis during melting in presence of metallic fins via numerical method

The performance of the storage unit during the discharging process can be improved with installing extended surfaces and this study aims to show the effect of two arrangements of fins on solidification. The same area of I and V shaped fins indicates that the volume of paraffin will not change with altering the configuration of the system. Unsteady terms were applied via implicit technique and two dimensional domains were simulated via FVM to show the behavior of the system during discharging. The conductivity of utilized paraffin (RT28) has been improved by loading nanoparticles of CuO. Since the fraction of additives is low, it is logical to use homogeneous model formulation to derive the properties of NEPCM. The both cases were compared and outputs showed that the required time for case 1 is 8.93 % lower than that of case 2. With involving I and V shaped fins, the required time of freezing will be 47.26 min and 51.89 min, respectively.

Interstage difference and deterministic decomposition of internal unsteady flow in a five-stage centrifugal pump as turbine

A five-stage centrifugal pump is utilized to investigate the interstage flow characteristics of the multistage centrifugal pump as turbine (PAT). The simulation results of performance are verified by comparing with the experimental results. Owing to the distinct structural attributes, significant differences in flow occur between the first stage and the other stages of the multistage PAT. To enhance the understanding of these disparities and explore their repercussions, this study focuses on analyzing the flow within the impellers in the first and second stages by a deterministic analysis. The main conclusions are as follows: The discrepancies in the inflow conditions are the major reason for the dissimilarities in the flow of impellers between stages. The impact loss generated by the misalignment between the positive guide vane outlet angle and the impeller inlet angle leads to flow deviation between impeller passages and affects the internal flow pattern. The unsteadiness under low flow rates is mostly produced by the spatial gradient of the blade-to-blade nonuniformities, which is relevant to the relative position between blades and the positive guide vanes. At high flow rates, especially in the second-stage impeller, the pure unsteady term is the primary cause of flow unsteadiness as a result of the flow separation induced by interactions between the blades and the positive guide vanes. This study can provide some references for the practical operation and performance optimization of the multistage PATs in the future.

Analysis of solidification and physical behavior of nanomaterial during unsteady process

Alumina nanoparticles with various shapes have been loaded into water to accelerate the freezing phenomena within closed cavity. The mathematical model contains unsteady conduction equation in the existence of unsteady source terms for phase changing. In this model, three properties of NEPCM are involved and for calculating those parameters, single phase approximation has been utilized. By using FEM, outputs for impact of shape and volume of nanoparticles have been reported. Also, the method was verified by comparing the outputs with the previous data. Increasing the volume of nanoparticles to twice the range makes the needed time decrease by about 13.82%. When [Formula: see text], replacing nanoparticles with [Formula: see text] instead of [Formula: see text] makes freezing time decrease by about 3.92%.

The volumetric thermal capacitor method for nonlinear heat transfer in phase-change materials

Recently, there was an increase in the study of phase change materials mainly due to thermal storage studies or modeling of manufacturing processes. Usually, these problems, which have a moving boundary, are solved with the enthalpy formulation. This paper presents a new methodology to address the unsteady enthalpy term in the heat diffusion equation. The Volumetric Thermal Capacitor method is developed to solve the non-linear heat diffusion equation with the enthalpy function. The alternative method applies the integration by parts rule to divide the enthalpy term into three components. This approach allows the use of non-linear thermal properties without simplifications or generalized considerations. The method is compared to the classical formulation. The routines were implemented and executed in parallel on a CUDA-C in-house code. Simulated and lab-controlled experiments validated the proposed methodology. The results highlighted the differences between the models for experiments with intense heat flux. The proposed model presented a better agreement with the experimental data than the classical model for high-temperature cases. The Volumetric Thermal Capacitor method proved to be more stable and accurate than the classical method.

Implicit numerical method for discharging of energy storage curved container in appearance of nanomaterial evaluating performance

The performance of the system during discharging has been improved in this article involving nano-sized powders. The shapes and concentrations of powders have been supposed as parameters in simulation. To derive the equations, properties of nanomaterial were predicted based on homogeneous mixture and the impact of velocity has been neglected. Galerkin technique for finding the answer of the problem was hired incorporating implicit approach for unsteady terms. Both variables have favorable efficacy on freezing and make the freezing quicker. Time of process declines with an augmenting ϕ and shape factor more than 26 % and 7 % which means that concentration has more sensible efficacy. The minimum time of discharging is 236.77 s which happens if maximum concentrations of powders with greater shape factor have been applied.

Numerical thermal storage analysis within discharging involving nanomaterial

The rate of discharging has been investigated in this article, involving various shapes of additives. The numerical method for analyzing such transient phenomena has been selected with selecting implicit technique for unsteady terms. The fraction of additives is lower than 0.05 which means that selecting a single phase model is logical. The nanoparticles have been added to enhance the speed of the process. The model includes two equations and solutions were achieved by utilizing the Galerkin approach. New styles of geometry involving fins were applied. The freezing increases as nanoparticles were added into base material. The period of process declines with growth of ϕ from 303.74 s to 222.37 s. The period of process for m = 8.6 is 1.075 times bigger than that of m = 4.8.

Thermal storage examination with Galerkin approach involving mixture of water and nanoparticles

With involving homogeneous model for incorporating nanomaterial impact on discharging of PCM, the mathematical models with unsteady terms were derived for this study. In this model, influences of shape of nano-powders were included in properties of nanomaterial. Discharging of water with the container with tilted fin attached to upper circular wall has been simulated and since there is low magnitude of liquid PCM, the associated term was discard and only two equations have been remained. For find more accuracy in solution, FEM with involving variable configuration of grid have been utilized and for validation purpose, published article with same numerical method was selected. The more magnitude of shape factor, the quicker solidification has been obtained. Increase of this factor makes the time of process to decrease around 5.83 % which is about 75.34 % greater impact in comparison to case with ϕ = 0.02. Inclusion of blade shape particle with highest fraction leads to reduction of period of freezing around 23.51 % and this effect for cylinder shape can be 25.23 % lower than the mentioned effect.

Thermophysical improvement of PCM with inclusion of nanoparticles during solidification

Demonstration of heat release phenomenon by employing the numerical approach is the main purpose of current research. Water as PCM was combined by particles and homogeneous mixture was assumed. Various shapes of powder with different concentrations were employed. The unsteady energy equation involving nanomaterial properties and freezing source term has been analyzed and for finding the solution, the Galerkin technique was employed. The adaptive grid generates greater number of elements in solid front region. Implicit formulations for unsteady terms were implemented and automatic time step was employed in software. Solid front changes with alteration of shapes of nanopowder and its fraction. With fraction augmentation, freezing finishes in lower time. The needed time diminishes by about 10.29% and 13.78%, respectively. Changing the shape of particles to the biggest level makes the period decline by less than 4.8% and 8.4%. A greater fraction of nanomaterial leads to a higher effect on the shape of nanomaterial.

Expedition of discharging of energy storage unit with adding nanoparticles using numerical technique

Freezing of paraffin through a channel of air conditioning system was simulated in present study by means of finite volume approach. The sinusoidal air gaps have been imposed within the PCM (phase change material) zone. With inclusion of nanoparticles within RT28, the thermal features have been improved and for estimating the properties, single phase based formulations have been incorporated. The air zone has turbulent regime (Re = 2000 to 3000) and k-ε technique was applied while paraffin zone was laminar. The impact of gravity has been ignored in freezing process and implicit approach for discretization of unsteady terms has been applied. Two levels for fraction of nano-powders and inlet temperature of air have been involved in simulations. The freezing time reduces by 4.58 % with using nanoparticles which is associated with higher conductivity of NEPCM. With reduction of temperature of inlet flow, the solidification time reduces about 27.6 %. With rise of Re from 2e3 to 2.5e3 and 3e3, the freezing rate enhances around 14.3 % and 11.93 %.

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions. An alternative approach

A numerical technique is devised to solve a problem of the steady laminar fluid motion in a straight plane hard-walled duct with two local axisymmetric rectangular constrictions. It uses the stream function, the vorticity and the pressure as the basic variables, has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of a solution, and needs significantly less computational time to obtain a result compared to appropriate techniques available in a scientific literature. The technique consists in: a) introducing the stream function and the vorticity, and subsequent transiting from the non-dimensional governing relations for the fluid velocity and the pressure to the corresponding non-dimensional relations for the stream function, the vorticity and the pressure; b) deriving their discrete counterparts in the nodes of the chosen space-time computational grid; c) integrating the systems of linear algebraic equations obtained after making the discretization. The discretization is based on applying appropriate differencing schemes to the terms of the equations for the basic variables. These are the two-point temporal onward difference for the unsteady term of the vorticity equation, as well as the two-point backward differences (for its convective term) and the five-point approximations (for its diffusive term and for the Poisson’s equations for the stream function and the pressure) in the axial and cross-flow coordinates. As for the velocity components, the appropriate central differences are applied to discretize their expressions. The above-mentioned systems of linear algebraic equations for the stream function and the pressure are integrated by the iterative successive over-relaxation method. The algebraic relation for the vorticity does not need application of any method to be solved, because it is a computational scheme to find this quantity based on the known magnitudes computed at the previous instant of time.