Isothermal Case Research Articles

Analysis of a Wind-Driven Air Compression System Utilising Underwater Compressed Air Energy Storage

The increasing push for renewable penetration into electricity grids will inevitably lead to an increased requirement for grid-scale energy storage at multiple time scales. It will, necessarily, lead to a higher proportion of the total energy consumed having been passed through storage. Offshore wind is a key technology for renewable penetration, and the co-location of energy storage with this wind power provides significant benefits. A novel generation-integrated energy storage system is described here in the form of a wind-driven air compressor feeding underwater compressed air energy storage. A direct drive compressor would require very high intake swept volumes. To overcome this difficulty, some prior compression is introduced. This paper discusses the constituent technologies for this concept, as well as the various configurations that it might take and the logic behind operating it. Special consideration has been given to the differences resulting from utilising a near-isothermal wind-driven compressor versus a near-adiabatic one. Multiple iterations of the system have been simulated. This has been done using a price-matching algorithm to optimise the system operation and using volumetric air flow rates to calculate exergy flow. Simulated operation has been performed for a year of real wind and electricity price data. This work has been performed in order to clarify the relationships between several key parameters in the system, including pressure and work ratios, volumetric flowrates, storage costs and profit rates. An additional objective of this paper was to determine whether the system has the potential for economic viability in some future energy grid, especially when compared with alternative wind and energy storage solutions. The results of the simulation indicated that, with proper sizing, the system might perform competitively with these alternatives. Maximum one-year return on investment values of 9.8% for the isothermal case and 13% for the adiabatic case were found. These maxima were reached with ~15–20 h of output storage. In all cases, it was found that maximising the power of the wind-driven compressor compared with the initial compressor was favourable.

Role of odd viscosity in falling viscous fluid

The aim of the present study is to investigate the linear and nonlinear wave dynamics of a falling incompressible viscous fluid when the fluid undergoes an effect of odd viscosity. In fact, such an effect arises in classical fluids when the time-reversal symmetry is broken. The motivation to study this dynamics was raised by recent studies (Ganeshan & Abanov, Phys. Rev. Fluids, vol. 2, 2017, p. 094101; Kirkinis & Andreev, J. Fluid Mech., vol. 878, 2019, pp. 169–189) where the odd viscosity coefficient suppresses thermocapillary instability. Here, we explore the linear surface wave and shear wave dynamics for the isothermal case by solving the Orr–Sommerfeld eigenvalue problem numerically with the aid of the Chebyshev spectral collocation method. It is found that surface and shear instabilities can be weakened by the odd viscosity coefficient. Furthermore, the growth rate of the wavepacket corresponding to the linear spatio-temporal response is reduced as long as the odd viscosity coefficient increases. In addition, a coupled system of a two-equation model is derived in terms of the fluid layer thickness $h(x,t)$ and the flow rate $q(x,t)$. The nonlinear travelling wave solution of the two-equation model reveals the attenuation of maximum amplitude and speed in the presence of an odd viscosity coefficient, which ensures the delay of transition from the primary parallel flow with a flat surface to secondary flow generated through the nonlinear wave interactions. This physical phenomenon is further corroborated by performing a nonlinear spatio-temporal simulation when a harmonic forcing is applied at the inlet.

On the polytropic Bondi accretion in two-component galaxy models with a central massive BH

ABSTRACT In many investigations involving accretion on a central point mass, ranging from observational studies to cosmological simulations, including semi-analytical modelling, the classical Bondi accretion theory is the standard tool widely adopted. Previous works generalized the theory to include the effects of the gravitational field of the galaxy hosting a central black hole and of electron scattering in the optically thin limit. Here, we apply this extended Bondi problem, in the general polytropic case, to a class of new two-component galaxy models recently presented. In these models, a Jaffe stellar density profile is embedded in a dark matter halo such that the total density distribution follows a r−3 profile at large radii; the stellar dynamical quantities can be expressed in a fully analytical way. The hydrodynamical properties of the flow are set by imposing that the gas temperature at infinity is proportional to the virial temperature of the stellar component. The isothermal and adiabatic (monoatomic) cases can be solved analytically; in the other cases, we explore the accretion solution numerically. As non-adiabatic accretion inevitably leads to an exchange of heat with the ambient, we also discuss some important thermodynamical properties of the polytropic Bondi accretion and provide the expressions needed to compute the amount of heat exchanged with the environment as a function of radius. The results can be useful for the subgrid treatment of accretion in numerical simulations, as well as for the interpretation of observational data.

A self‐consistent mean‐field model for turbulent particle and heat transport in 2D interchange‐dominated electrostatic ExB turbulence in a sheath‐limited scrape‐off layer

AbstractIn this paper, a self‐consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange‐dominated electrostatic ExB drift turbulence in sheath‐limited scrape‐off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy (). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for through the interchange source. A series decomposition of the sheath term in the equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath‐driven conducting‐wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self‐saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean‐field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the ‘divertor-type’ and ‘limiter-type’ free boundaries in the tokamak cylindrical coordinate. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a 0 (a 0 is the minor radius) for M 0 = 0.2 (the toroidal Alfvén Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125a 0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M 0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.

Influence of a Central Jet on Isothermal and Reacting Swirling Flow in a Model Combustion Chamber

We studied flow dynamics in a model combustion chamber using Large-eddy simulations (LES) and Particle image velocimetry (PIV) at the Reynolds number Re of 15,000. The swirl is produced using a Turbomeca swirler and air flow, while combustion is supported by a central methane/air jet. We compared four flow regimes, assessing the effect of the central jet for isothermal and lean reacting conditions. A detailed comparison for isothermal and reactive cases without the central jet is described, validating the LES results against PIV. We observe that unsteady dynamics are governed by global instability in the form of a well-known precessing vortex core (PVC). The central jet slightly changes the dynamics of PVC in the isothermal case where a strong recirculation zone is still formed. However, for the reacting case, the bubble is completely destroyed with no signs of strong vortical structures in the inner shear layer. These observations are confirmed using spectral analysis and proper orthogonal decomposition, describing the contribution of different flow modes in terms of azimuthal harmonics.

A damage phase-field model for fractional viscoelastic materials in finite strain

This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials following the strategy developed by Boldrini et al. (Methods Appl Mech Eng 312:395–427, 2016). Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the assumption of finite strain, in terms of fractional derivatives. A novel degradation function, which properly couples stress response and damage evolution for viscoelastic materials, is proposed. We obtain a set of differential equations that accounts for the evolution of motion, damage, and temperature. In the present work, for simplicity, this model is numerically solved for isothermal cases by using a semi-implicit/explicit scheme. Several numerical tests, including fitting with experimental data, show that the developed model accounts appropriately for damage in viscoelastic materials for small and finite strains. Non-isothermal numerical simulations will be considered in future works.

Effect of Ti addition on crystallization behavior of a Zr-based bulk metallic glass

The isochronal and isothermal crystallization characteristics of (Zr54Al10.2Ni9.4Cu26.4)100-xTix (x = 0∼0.5 at.%) bulk metallic glasses (BMGs) were investigated by differential scanning calorimetry. The isochronal crystallization indicates that both crystallization activation energy and local activation energy Eα of the Ti-free BMG are larger than those of the BMGs (x = 0.2 and 0.4), while smaller than those of the BMGs (x = 0.1, 0.3 and 0.5). The isothermal crystallization shows that the Eαs decrease with increasing crystallization fraction for the first crystallization process and nearly maintain a constant for the second crystallization process. Moreover, the crystallization phases are ZrNi and Zr2Ni7 nanocrystals for the partially and/or fully crystallized BMGs in isochronal and isothermal cases. The crystallization mechanism nearly depends on the Ti content and the heating rate for the isochronal crystallization and the Ti content and the annealling temperature for the isothermal crystallization, respectively.

Hyperbolic discretization of simplified Euler equation via Riemann invariants

We are interested in numerical schemes for the simulation of large scale gas networks. Gas transport is described by a simplified Euler equation with a general equation of state for the pressure, including in particular the isentropic as well as the isothermal case. The numerical scheme is based on transformation of conservative variables in Riemann invariants and its corresponding numerical discretization. A novelty of the proposed method is the possibility to allow for an efficient discretization of the boundary and coupling conditions at nodal points of the network, as well as obtaining well balanced schemes. The proposed discretization is analysed in view of its property to correctly recover steady states as well as to resolve possible analytic solutions. Comparisons with existing methods are presented.

Non-isothermal effects in the slippage condition and absolute viscosity for an electroosmotic flow

In this work, we have developed a novel asymptotic analysis using perturbation techniques for an electroosmotic flow in a rectangular microchannel, considering that the absolute viscosity η is a function of temperature; a situation that affects also the slip condition at the walls of the microchannel, u=−sη∂u∂n. The physical importance of this temperature dependence is based on the presence of the applied external electric field on the electrolyte solution, which originates the Joule heating effect that disturbances the isothermal hydrodynamic behavior. The above leads to a significant increase of the volumetric flow rate for this non-isothermal condition in comparison to the purely isothermal electroosmotic flow. This result is simultaneously controlled by the heat losses to the ambient and the slip effect: the lower the presence of the heat dissipation mechanism on the outer walls of the microchannel and the higher the sliding condition, the higher the values of the volumetric flow rate. The above trend differs substantially from the isothermal case and finds its justification in the recognition of the presence of the Joule heating effect that induces significant longitudinal and transverse temperature gradients along the microchannel. Considering the proper limitations of the asymptotic analysis, we compare the present asymptotic results with a full numerical solution of the governing equations, which are composed of the continuity, momentum, and energy equations for the electrolyte flow, together with the Poisson–Boltzmann.

A Comparative Study of the Buoyancy-Opposed Wall Jet using Different Turbulent Models

A comparative study of the buoyancy-opposed wall jet has been carried out using RANS methods (including RNG model, Realizable k-ε model, and two low Reynolds number k-ε models) and LES methods (including the subgrid scale model developed by Smagorinsky et al.(1963), Germano et al. (1991) and Kim et al. (1997)). The capability of each turbulence model to predict the flow field and temperature field in mixing stage was investigated. The results show that the k-ε series model can accurately predict the velocity distribution of flow field under isothermal case. However, in the case of buoyancy, due to the assumption of turbulent normal stress isotropy, the trend of temperature change in the mixing region and transition position existed an obvious deviation with experimental data. The LES methods, solved directly the large scale vortices, take into account the influence of turbulence stress anisotropy in the mixing region on the temperature change and capture the temperature change trend over the whole domain accurately. Due to the application of the subgrid kinetic energy transport equation, KET model has certain advantages in numerical simulation of similar engineering flow phenomenon.

Empirical model of the viscosity of an epoxy binder at the initial stage of the polymerization process

This article presents the results of an experimental study and numerical simulation of the kinetics of curing of an epoxy binder at the initial stage of the polymerization process. Object of research: two-component composition of epoxy resin L and hardener EPH 161, certified as a binder for composite materials for aerospace purposes. The ordinary differential equation is used as the basic model for describing the polymerization process. The values of the material parameters required to perform the calculation operations were obtained by the rheological method using the analysis of changes in the viscosity of the binder depending on the time and temperature of polymerization. Isothermal and non-isothermal polymerization cases are considered. The modes in which the increase in the temperature of the process leads to a decrease in the viscosity of the epoxide composition, despite the polymerization process, were highlighted. The estimates of the model parameters obtained by processing the data of full-scale experiments are also given.

Rapid simulation of airborne contaminant transport: Coupling concentration response factor method into a Markov chain model

The Markov chain model has been proved viable for the airborne contaminant transport simulation. However, its performance should be further validated and improved when there is a contaminant source in the airflow field. This study proposed a novel method that couples the concentration response factor method into a Markov chain model, termed the CRFMC method, to simulate the release and transport of airborne contaminant. The accuracy of the proposed CRFMC method was validated based on two example flow fields, i.e., a 2D isothermal case and a 3D ventilated chamber case. Different contaminant source types, including point, line, area, and volume source (in 3D case only) with constant, linear, exponential, and periodic release strengths were considered. Furthermore, the influence of the pulse type in the CRFMC method on accuracy was evaluated. Results revealed that the CRFMC method is sufficiently accurate for the airborne contaminant transport simulation with a source release. The L2 relative error between the CRFMC method and scalar transport simulation ranges from 9.4% to 16.1% in 2D cases and from 14.9% to 33.4% in 3D cases. This study can aid the development of a Markov chain model for airborne contaminant transport.

Flow behind an exponential shock wave in a perfectly conducting mixture of micro size small solid particles and non-ideal gas with azimuthal magnetic field

Unsteady adiabatic and isothermal flows behind an exponential spherical or cylindrical shock wave in a perfectly conducting mixture of micro size small solid particles and non-ideal gas under the influence of azimuthal magnetic field is investigated. The moving piston drives the shock wave. The azimuthal magnetic field in the ambient medium is assumed to be varying according to exponential laws. In our study, micro size solid particles are taken to be pseudo-fluid with the supposition that the equilibrium conditions for flow are maintained in the entire flow- field region, and the heat conduction and the viscous-stress of the conducting mixture are negligible. In both the isothermal and adiabatic cases, similarity solutions are obtained by taking into consideration the magnetic field and compressibility. The effects on the shock wave propagation and on the flow variables by the ratio of the density of micro size solid particles to the initial density of the gas Ga as well as by the non-idealness parameter δ of the gas in the conducting mixture, by the mass concentration λp of micro size solid particles in the conducting mixture and by the adiabatic exponent γ are worked out in detail. A relationship between the solutions in the cases of isothermal and adiabatic flows is made. It is found that due to the thought of zero temperature gradient the flow variables fluid velocity, density and magnetic field and shock strength decrease. Also, it is important to note down that the shock wave strength enhances with an increase in Gaor due to change in geometry from cylindrical to spherical; whereas it decreases with an increase in the non-idealness parameterδ or the strength of ambient magnetic field MA−2or the adiabatic exponent γ .

Nature-inspired triply periodic minimal surface-based structures in sheet and solid configurations for performance enhancement of a low-thermal-conductivity phase-change material for latent-heat thermal-energy-storage applications

Low-thermal-conductivity phase-change materials (PCMs) are often hybridized with high-thermal-conductivity metal matrices to achieve improved heat-transfer performance in latent-heat thermal-energy-storage (LHTES) applications. Owing to recent developments in additive-manufacturing technology that allow any complicated topology to be manufactured with ease, triply periodic minimal surfaces (TPMS) have gained considerable attention. These nature-inspired TPMS structures have already shown promising results in a variety of applications. TPMS structures can be developed in either sheet or solid configurations, both of which exhibit distinct architectures. Herein, a numerical study is presented whereby an organic PCM (docosane) is hybridized with two TPMS structures, namely, gyroids and I-graph-and-wrapped-packages (IWPs) in both sheet and solid configurations. The effective thermal conductivity of each resulting TPMS-PCM composite was calculated using steady-state simulations. Moreover, transient simulations were conducted under isothermal and isoflux conditions to assess the structures' heat-transfer performance. The obtained results were compared with those obtained using PCM only, and the incorporation of gyroid and IWP structures in both sheet and solid configurations was found to significantly improve the PCM's heat-transfer performance. For isothermal case under pure conduction, sheet-based configurations outperformed the solid-based ones with IWP sheet configuration being the best configuration with a PCM melting time of 118 s. However, upon taking buoyancy into account, IWP solid showed best performance with a PCM melting time of 108 s. Furthermore, the performance of each TPMS-PCM composite was found to depend on the type of structure incorporated into it and the value of the applied boundary condition. For isoflux case, IWP sheet showed the best performance in terms of temperature homogeneity in PCM domain as compared to the rest of the TPMS structures under both pure conduction case and the case with buoyancy effects. The PCM melting time in isoflux case was not found to have a strong dependence on TPMS structure type. In both isothermal and isoflux cases, Gyroid solid based TPMS-PCM composite showed the least performance. Moreover, the effects of PCM buoyancy are more pronounced in solid configurations than the sheet ones. Therefore, this study may serve as a design guideline to select appropriate TPMS configuration based on the applied boundary conditions/application.

Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling.

Modeling a turbulent multicomponent fluid with variable density using a two-fluid approach

In this study, we present a technique for modeling a turbulent multicomponent fluid with variable density using a two-fluid approach. This method extends an existing two-fluid turbulence model for handling multi-component fluids with variable density. We verified the model by applying it to circular jets of helium, air, or carbon dioxide injected into the ambient air. The numerical results obtained for these isothermal cases were compared with previously reported experimental data. The results demonstrate that the two-fluid turbulence model accurately describes the dynamics and mass transfer in a turbulent multicomponent fluid with variable density.

Flow and heat transfer in the wake of a triangular arrangement of spheres

This research work seeks to investigate the influence of spacing and heat transfer on the wake behavior of a triangular arrangement of spheres. Four experimental configurations have been investigated at three Reynolds numbers, Re1 = 350, Re2 = 700, and Re3 = 1050. Two isothermal cases were investigated with spacing between the spheres of zero and one sphere diameter, and two cases were investigated with an applied heat flux at the same spacing conditions. The time resolved particle image velocimetry results revealed various flow phenomena including flow separations, von Karman vortex shedding, and Kelvin–Helmholtz instabilities. The turbulent statistics reveal the effect of proximity and heat transfer on the time averaged values of the wake size, turbulent strengths, and Reynolds shear stress in the wake of each sphere, namely, the laminarization effects from the addition of heat and the suppression of the lead sphere wake from the proximity of the trailing spheres. These results are complemented by the application of proper orthogonal decomposition (POD) to the flow fields, which extracts the coherent structures from the flow. The modes that describe the coherent structures are extracted and described in detail, which provide further insight into effects of the experimental conditions on the temporal behavior of the flow. Many of the low order modes are found to be associated in pairs, corresponding to asymmetric structures or advection of a given structure downstream. The capability of POD to produce reduced order models of the flow is then utilized to facilitate vortex identification analysis. A turbulent kinetic energy based mode truncation criteria, which has been found to enhance vortex identification capability, is applied to select the POD modes and temporal coefficients to be used in the reduced order modeling. The reconstructed velocity fields are then analyzed with vortex identification algorithms to extract the vortex cores and boundaries. The combination of these approaches allows the study of the effect of proximity and heat transfer on the vortex characteristics, such as size, strength, and distribution.

Effects of an Axial Magnetic Field on Vortex Breakdown and Fluid Layer

The effects of an axial magnetic field on both the vortex breakdown process and fluid layers development in a cylindrical container filled with a conducting viscous fluid are numerically analyzed by using the Generalized Integral Transform Technique (GITT) with a stream function-only formulation. A temperature gradient is imposed in the axial direction on the swirling flow which is advanced by the rotation of the bottom disk under the stabilizing effect of the external magnetic field. Flows are studied for a range of parameters: the Richardson number, Ri, 0 ≤Ri ≤2.0; and three values of the Prandtl number are investigated, Pr = 0.025 (liquid Mercury), 0.032 ( PbLi 17 alloy), and 0.065 (the molten lithium). Three combinations of aspect ratios (H/R) and Reynolds numbers are compared: (case A: Re=1500, H/R=1.5); (case B: Re=1855, H/R=2.0) and (case C: Re=2400, H/R=2.5). The results reveal that the increase in the values of Hartmann number, Ha suppresses the vortex breakdown in the isothermal case and reduces the number of fluid layers in the layering case. The stability diagram (Hacr–Ri) corresponding to the transition from the multiple fluid layers zone to the one fluid layer zone for increasing Prandtl number is obtained‎.

Numerical investigation on similarity of isothermal and thermal flow mixing in a horizontal T-junction configuration

Turbulent and stratified mixing flows can cause thermal fatigue in nuclear power plant piping systems. An isothermal Mixed-Fluid-Interaction (MFI) test rig is used to investigate mixing phenomena related to High Cycle Thermal Fatigue in nuclear power plant piping systems. Here, the cold heavy branch pipe fluid of the thermal mixing Fluid Structure-Interaction (FSI) facility is modeled by a sugar or salt solution. Due to limited optical accessibility of the FSI facility a numerical similarity comparison of the flow phenomena occurring in both experimental setups (MFI/FSI) is essential. Thus, Large-Eddy Simulations are carried out which are experimentally validated by applying the Wire-Mesh-Sensor measurement technique (MFI) and temperature measurements (FSI). Numerical LES investigation on similarity between two isothermal cases, three thermal mixing cases, and one geometrically similar scaled-up thermal mixing case is performed when the momentum ratio MR and the Richardson number Ri is kept constant. A very good agreement in the spatial distribution of the time averaged mean and rms values as well as statistical fluctuations is observed between the isothermal and thermal cases. Non-dimensional power spectrum density (PSD) of the mixing scalar fluctuation showed an almost unique profile, indicating the same origin for the occurring periodical fluctuation in all cases. The non-dimensional magnitude of the dominant frequency of the mixing scalar fluctuations in terms of the Strouhal number is in the range of 0.38<Sr<0.40. In the context of similarity, it is shown that the momentum ratio and the Richardson number are mainly responsible for the jet-formation and thus for the down- and upstream flow behaviour. The influence of the inlet Reynolds numbers Rem and Reb as well as the density ratio ΓR on the normalized flow characteristics seem to be negligible in comparison.