Adiabatic Boundary Conditions Research Articles

Adaptive deep homogenization theory for periodic heterogeneous materials

We present an adaptive physics-informed deep homogenization neural network (DHN) approach to formulate a full-field micromechanics model for elastic and thermoelastic periodic arrays with different microstructures. The unit cell solution is approximated by fully connected multilayers via minimizing a loss function formulated in terms of the sum of residuals from the stress equilibrium and heat conduction partial differential equations (PDEs), together with interfacial traction-free or adiabatic boundary conditions. In comparison, periodicity boundary conditions are directly satisfied by introducing a network layer with sinusoidal functions. Fully trainable weights are applied on all collocation points, which are simultaneously trained alongside the network weights. Hence, the network automatically assigns higher weights to the collocation points in the vicinity of the interface (particularly challenging regions of the unit cell solution) in the loss function. This compels the neural networks to enhance their performance at these specific points. The accuracy of adaptive DHN is verified against the finite element and the elasticity solution respectively for elliptical and circular cylindrical pores/fibers. The advantage of the adaptive DHN over the original DHN technique is justified by considering locally irregular porous architecture where pore–pore interaction makes training the network particularly slow and hard to optimize.

Influence of boundary conditions on non-equilibrium heat transport under ultrafast laser action based on the lattice Boltzmann method

Based on the lattice Boltzmann method, this paper simulated the non-equilibrium heat transfer process in nano-silicon thin film under ultrafast laser irradiation. The influence of boundary conditions on heat transport was investigated. Results show that under rebound and diffuse boundary conditions, the energy distribution within the film is non-uniform due to interface effects. However, the specular boundary condition is equivalent to eliminating the interface, resulting in a smooth energy distribution. Under convective boundary conditions, the thermal wave phenomenon disappears owing to the open interface. When the energy tends to be stable, the energy density under convective boundary conditions is reduced to 50% of that under adiabatic boundary conditions. As the film size decreases, the differences between boundary conditions become more significant. Particularly when the film size is smaller than the phonon mean free path, the influence of boundary conditions cannot be neglected. Therefore, boundary conditions and size effects are important for the design of nanodevices. Furthermore, compared with the results obtained by the Cattaneo-Vernotte model, it is found that at smaller Knudsen numbers, the Cattaneo-Vernotte model has a better match with the lattice Boltzmann method.

Lattice Boltzmann simulation of cross diffusion via Soret and Dufour effects on natural convection of experimental data based MWCNTs-H[formula omitted]O nanofluids in an L-shaped enclosure

The cross-diffusion via Soret and Dufour impacts on natural convection in an L-shaped enclosure full of multi-walled carbon nanotubes (MWCNTs)-H2O (water) nanofluids has been studied numerically utilizing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) through graphics processing unit (GPU) computing. The indented part of the L-shape is cold (Tc), while the left and bottom walls of the chamber maintain a heated (Th) temperature. The adiabatic boundary condition is present on the cavity’s remaining walls. The thermal conductivity and viscosity of the nanofluids are the function of fluid temperature, and the corresponding correlation was derived from the experimental data. The current methodology and the experimental data based (MWCNTs)-H2O (water) nanofluids outcomes are wholly noble. Numerical simulations have been done for numeroust relevant pertinent such as Rayleigh number, 3×103≤Ra≤3×105, buoyancy ratio, −2≤Br≤2, volume fraction, 0.0≤ϕ≤0.01, Soret number, 0.0≤Sr≤0.2, Dufour number, 0.0≤Df≤0.2, while Prandtl number, Pr=6.2, and Lewis number, Le=2 are fixed. The results are presented regarding the streamlines, isotherms, isoconcentration, velocity and temperature distribution, local Nusselt and average Nusselt number, local Sherwood and average Sherwood number, and local and total entropy production. It is discovered that with growing Rayleigh numbers, volume fractions, and Soret numbers, the Nu¯ and the Sh¯ rise. For various Rayleigh numbers Ra = (3×103, 3×104, 3×105), the Nu¯ grew by 29.95%, 19.86%, and 1.77% respectively when ϕ increased from 0.0 to 0.01. The Nu¯ graph reaches its maximum for Ra=3×105. The streamlines grow as Ra enhances. In addition, when the volume fraction rises from 0.0 to 0.02, the local Nu rises because of more potent thermal conductivity, but the local Sh falls. The highest entropy formation is found by Ra=(3×105), and the general rate of entropy formation improves with enlarged Rayleigh numbers while the Bejan number stays constant. Finally, a response surface analysis has been done, and the output closely matches the original simulation results.

Effect of variable viscosity, porous walls and mixed thermal boundary condition on the onset of Rayleigh-Bénard convective instability

In this paper, we have studied the criteria for the onset of instability in the Rayleigh-Bénard convection problem, by considering a fluid layer confined between two infinitely extended rough boundaries, which are subjected to mixed-type thermal boundary conditions, physically representing the imperfectly conducting boundaries. The rough boundaries are assumed to be shallow porous layers with different pore size, properties, and permeabilities. Mathematically, it is given by the Saffman type boundary condition. Therefore, we have two generalized forms of boundary conditions, one for the flow field and the other for the thermal field. The two limiting cases of the mixed-type thermal boundary condition correspond to a perfectly conducting boundary and to a perfectly insulating boundary, whereas the two limiting cases of the hydrodynamic boundary condition correspond to a no-slip condition and to a free-surface condition, depending upon the limiting values of the parameters involved in these two generalized boundary conditions. The linear and nonlinear energy stability analyses are performed, and the existence of the region of subcritical instability is checked. Through the principle of exchange of stability analysis, it is found that the instability occurs only in the stationary mode. The adiabatic boundary condition is found to be more restrictive than the isothermal boundary condition. Under given conditions, the instability is observed to be occurring in the infinite wavelength mode for the case of adiabatic boundaries. In the present work, the effect of temperature and pressure dependent viscosity on the stability of the system has been shown and found to be of destabilizing nature. However, the roughness of the boundaries is found to be of stabilizing nature.

Numerical Modeling of Aircraft Fire: Postcrash Fire

The Fire Dynamics Simulator (FDS) model was utilized in this study to replicate a full-scale aircraft postcrash experiment conducted within the C-133 test facility by the Federal Aviation Administration. FDS is a computational fire field model that incorporates submodels for soot formation, pyrolysis, and thermal radiation transport. It solves three-dimensional time-dependent Navier–Stokes equations and is grounded in the large-eddy simulation approach and the eddy dissipation concept, serving as turbulence and combustion models. The obtained results, including the heat release rate and temperature, were validated against experimental data and compared with earlier prediction studies employing different turbulence and combustion models. The results from this simulation closely align with the experiment’s findings. The impact of fire-blocking layers and carry-on baggage on interior material was examined. Moreover, two boundary conditions were imposed on the fuselage structure: 1) the adiabatic wall, and 2) heat loss within the wall. Both the fire-blocking layers and the adiabatic boundary condition played a significant role in the flashover occurrence. The large-eddy simulation and eddy dissipation concept approaches have demonstrated a reliable ability to predict flashover and general fire properties to a considerable extent.

Global stability of Bénard–Marangoni convection in an anisotropic porous medium

Surface tension is essential in many industrial applications, especially where the liquid surface is in contact with the environment, such as crystal growth, semiconductor manufacturing, and welding. The present article reports a numerical analysis of convection induced by the combined effects of buoyancy force and surface tension in an infinitely extended horizontal fluid-saturated anisotropic porous layer with high permeability. We assume that the bottom boundary is rigid and the top is exposed to the air. Biot numbers establish general thermal conditions at both ends instead of commonly used adiabatic and isothermal boundary conditions. The anisotropy of the porous structure results in thermal and mechanical anisotropy parameters while examining layer's stability. The Chebyshev Tau technique yields the critical Marangoni number, MaLc and MaEc, representing linear and energy stability boundaries. We compare the constraints obtained from linear and energy analyses and conclude that the energy bounds for the current problem are less than linear bounds, indicating subcritical instabilities may exist. It is also observed that thermal anisotropy and Biot numbers stabilize the system. In contrast, mechanical anisotropy and the Darcy number advance the onset of convection. The existing results of limiting cases of the present problem are recovered with remarkable accuracy.

Example of thermal retrofitting for the Piedicastello tunnel

Over the last decades, global warming has become one of the major issues to cope with: as it stands, human activities are responsible for a global surface temperature increase of approximately 1.1°C since the pre-industrial age. Climate change is directly linked to the level of global warming, thus affecting different kind of regions around the world in multiple ways, leading not only to increments of heat extremes, but also to changes in rainfall patterns, sea level rise, amplification of the permafrost thawing, ocean acidification and much more [1].
 In this context, carbon dioxide emissions due to heating systems are one of the main enemies in the pathway for reaching the 1.5°C Paris climate goal and energy geostructures could play a relevant role. Among them, the thermal activation of tunnels has raised interest [2, 3, 4] and recent full scale projects have demonstrated the feasibility of such technology [5, 6]. However, so far applications have been related to new tunneling projects, whereas possibilities of implementation in the existing heritage of tunnels have not yet been investigated.
 The Authors are developing investigations for the thermal retrofitting feasibility of existing tunnels. In this abstract the attention is posed on the case study of the Piedicastello tunnel, located in the city of Trento, crossing the city centre through a 100 m high spur of limestone, called Doss Trento. This tunnel used to be part of the Italian roadway network but, following the construction of a new tunnel in 2007, it fell into disuse, being partly transformed into a museum one year later, i.e. the tunnel is now a closed environment.
 One of the design hypotheses identified for thermal retrofitting of the Piedicastello tunnel consists in taking advantage of its 100 m overburden by drilling radial borehole heat exchangers (rBHEs), arranged along several tunnel cross sections. In Figure 1a, a 3D view of the rBHEs solution is shown. This solution leaves the lining intrados visible for future inspection and is essentially unaffected by the internal aerothermal condition of the tunnel.
 In order to assess its thermal performance, some 3D numerical models were built with the Finite Element software Feflow [7]. The above-mentioned models are 200.0 m high and wide, with a thickness that varies as a function of the rBHEs cross section interaxis distance (Figure 1-b). The two horse-shoe shaped tubes of the Piedicastello tunnel have an external equivalent diameter of 12.7 m, with an 80 ÷ 130 cm thick concrete lining. Heat exchanger pipes, instead, were modelled through one-dimensional elements (“discrete features”), with a cross section of 201 mm2, corresponding to an external diameter of 20 mm and a thickness of 2 mm.
 Both thermal and hydraulic boundary conditions were set considering the lack of information about the groundwater regime of the Doss Trento and the internal aerothermal conditions of the Piedicastello tunnel. Nonetheless, given its unusual conditions (absence of moving vehicles and closed environment), the latter would likely have a minor role in the heat exchange process. Accordingly, setting adiabatic boundary conditions at the tunnel contour and considering a dry rock mass, a preliminary sensitivity analysis was performed with the aim of drawing some meaningful conclusions about two key design aspects of the rBHEs solution. To this purpose, three different borehole length setups (short – 12.50 m, mid – 18.75 m and long – 25.00 m) and three cross section interaxis distances (3.0 m, 5.0 m and 7.5 m) were investigated. The results of the preliminary numerical simulations are shown in Table 1.
 From the sensitivity analysis, it seems evident that, in the considered cases and ranges: (i) as expected, the longer the rBHEs, the higher the heat that the system can exploit, accordingly the rBHEs optimal length should be designed considering also the pumping and drilling costs, (ii) two consecutive instrumented cross sections have virtually no interaction if the interaxis distance is set higher than 5.0 m.
 Starting from these valuable evidences, future research will investigate: (i) the influence of the groundwater regime, as well as the internal aerothermal conditions of the tunnel, (ii) new alternatives for the thermal retrofitting of existing tunnels and (iii) the optimal rBHEs length with respect to a cost-benefit analysis that will consider both drilling and pumping costs.

The Effects of Heat Transfer through the Ends of a Cylindrical Cavity on Acoustic Streaming and Gas Temperature

The longitudinal vibrational motion of a cylindrical cavity with gas, in which the acoustic streaming occurs, is considered. The motion is described by the system of equations for the dynamics and thermal conductivity of a viscous perfect gas, written in a cylindrical coordinate system associated with the cavity. The system of equations is solved numerically by the finite volume method with an implicit staggered grid scheme, while the convective–diffusion fluxes are approximated by the power law scheme. According to the boundary conditions, the lateral surface of the cavity is maintained at a constant equal initial temperature. The effects of heat transfer through the ends of the cavity are studied. Heat transfer is given by isothermal boundary conditions. The obtained solutions are compared with the solutions under adiabatic boundary conditions. It is shown for the first time that the effects of heat transfer manifest themselves with an increase in the nonlinearity of the process; when the frequency and amplitude of vibration increase, this is also facilitated by an increase in the radius of the cavity. The effects of heat transfer on the period average temperature, on the streaming velocity and on structure are established.

Experimental and numerical studies on enhanced effusion cooling with shallowly dimpled film holes on double-wall structure surface

This paper presents a flow and heat transfer investigation on multi-row dimpled film cooling in the double-wall configuration, considering important flow and geometrical characteristics including internal narrow jet impingement channel and outer film cooling with shallowly dimpled holes. The film cooling hole has dimpled exit, with the dimple depth to diameter ratio of 0.2. The inclined angle of the film hole is 30 degree and film hole length to diameter ratio is 3.0. The adiabatic film cooling effectiveness and heat transfer characteristics on the external surface are obtained by using transient infrared thermography measurement technique, which is based on the Impulse Response Method. And steady-state numerical computations using the Shear Stress Transport (SST) k-ω turbulence model were carried out respectively with the experimentally related adiabatic wall boundary conditions and with the fluid–solid conjugated boundary conditions, which provides the turbulent flow structure and overall cooling performance of the double-wall structure. The experimental results indicate that compared to the counterpart cylindrical film holes, the dimpled film holes can expand the spanwise coverage of coolant film, and the adiabatic film cooling effectiveness was improved by 66 %, 82 % and 180 % respectively at BR = 0.3, 0.6 and 1.0. Therefore, the dimpled holes can improve the film cooling effectiveness significantly. The numerical simulations indicated that the dimpled film holes influence the jet-in-crossflow structure and film cooling effectiveness significantly through complex interactions of the coolant jets, mainstream flow and dimpled wall. The overall cooling effectiveness of the double-wall structure with dimpled film holes on the thermal barrier coating can be distinctively improved by about 12.8 % over the case with conventional cylindrical film holes, which was indicated in the conjugated simulations under the blowing ratio of 1.0 and the mainstream-coolant temperature ratio of 2.0.

Impact of convective tip condition on the transient thermal behavior of wet porous convective radiative exponential profiled inclined longitudinal fin structures subject to heat generation

AbstractA convective‐radiative fully wet porous inclined longitudinal fin of exponential profile is the focus of the current work. The thermal behavior of the fin under unsteady conditions has been analyzed for adiabatic and convective boundary conditions. The exponential fin and its counterpart inverted exponential fin are simultaneously investigated by considering temperature‐relevant thermal conductivity and heat generation. The modeled governing equation upon nondimensionalization reduces to a partial differential equation which is computed by employing the finite difference approach. The impact of relevant parameters like the convective parameter, radiative parameter, wet porous parameter, dimensionless time, exponential index, dimensionless ambient temperature, generation number, thermal conductivity parameter, and angle of inclination on thermal characteristics of exponential and inverted exponential fin structures with adiabatic and convective boundary restrictions have been examined. One of the main outcomes was that the inverted exponential fin with an adiabatic tip gives rise to the highest thermal curve, and the tapered exponential fin with a convective tip resulted in the lowest thermal curve.

Wavelet-based adaptive large-eddy simulation of supersonic channel flow with different thermal boundary conditions

This work investigates the effect of different thermal wall boundary conditions on the wavelet-based adaptive large-eddy simulation of supersonic turbulent channel flow. The compressible flow governing equations are expressed in terms of wavelet-based Favre-filtered variables and are supplied with the anisotropic minimum dissipation closure model. Various computations are performed, where the resolved temperature field is constrained by either Dirichlet (isothermal) or Neumann (adiabatic) boundary conditions at the walls. The turbulence diagnostics include mean flow features and turbulent fluctuations statistics. The successful comparison with reference direct numerical simulations demonstrates the validity and the efficiency of the wavelet-based adaptive approach for wall-bounded turbulent compressible flow, regardless of the thermal boundary conditions that are imposed.

Thermo-hydrodynamic lubrication analysis of journal bearings using a simplified THL model and prediction of onset speed of instability (Application of adiabatic boundary condition to the journal side)

Thermo-hydrodynamic lubrication analysis of journal bearings using a simplified THL model and prediction of onset speed of instability (Application of adiabatic boundary condition to the journal side)

Theoretical analysis of a two-dimensional multilayer diffusion problem with general convective boundary conditions normal to the layered direction

Theoretical analysis of transient thermal conduction in a two-dimensional multilayer structure has been limited to problems with isothermal or adiabatic boundary conditions along the walls normal to the layered direction. Due to mathematical difficulties pointed out in past work, an analytical solution has not been possible so far for the general case where each layer has a distinct convective boundary condition. This work presents an analytical technique to solve this general problem using Laplace transforms followed by derivation of a sufficient number of linear algebraic equations based on given boundary conditions to determine the coefficients of an eigenfunction-based series solution. This technique makes it possible to solve the problem when each layer may have a different convective heat transfer coefficient along the walls normal to the layered direction. Results from this general analysis are shown to correctly reduce to past work for the special cases of very small or very large Biot number. Good agreement with specific results presented in a past paper is also demonstrated. The technique is used to investigate the impact of key dimensionless parameters on the temperature field. This work significantly generalizes past work that was limited only to adiabatic or isothermal boundary conditions. Results presented here may help improve the theoretical understanding of multilayer diffusion problems, and make theoretical models much more representative of realistic conditions.

Modeling radial turbine performance under pulsating flow by machine learning method

This work presents the development and application of a machine learning model to predict the unsteady performance of a turbocharger radial turbine subject to on-engine pulsating flow conditions. The model proposed, based on a fully connected neural network, predicts the instantaneous turbine torque and circumferentially-averaged relative inflow angle when given, as only inputs, the total pressure and temperature pulses and the time derivative of the total pressure pulse upstream of the turbine. The training data set for the model is obtained from an experimentally-validated Reynolds-averaged Navier-Stokes model and consists of various operating conditions characterized by different pulse amplitudes and frequencies. Heat transfer effects are neglected by the use of adiabatic boundary conditions while the rotational speed of the rotor is otherwise maintained fixed. Based on the results obtained, the model is shown capable of accurately predicting the turbine torque and local properties of the flow, such as the relative inflow angle, with a high degree of accuracy (coefficient of determination larger than 0.98 ). At first, the model is tested for both interpolation and extrapolation conditions. Given a training data set constituted by only three pulses characterized by different amplitudes, the model accurately predicts the turbine performance both for conditions inside and outside the range of amplitudes of the training data set. Lastly, the model is trained with a larger data set, including both variations of the pulse amplitude and frequency, in order to predict the performance of the turbine subject to a more general pulse shape. The error indicators show an improvement with respect to the extrapolation case due to the larger size of the training data set, showing also a great capability of the model to predict the unsteady performance of the turbine for a more general pulse shape. The model represents a fast and efficient approach for predicting the unsteady turbine performance as compared to more complex experimental set-ups and time-consuming 3D numerical simulations and a valid alternative to the more common 0D-1D models.

Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions

Fin is an efficient and straightforward way to enhance heat transfer rate. When the heat source varies dramatically in a very short time, non-Fourier heat conduction should be considered. In the paper, taking advantage of numerical stability and no integral and easy-to-implement features of an element differential method, a numerical model is developed to evaluate the fin efficiency of the convective-radiative fin within non-Fourier heat conduction. In this fin, heat is generated by an internal heat source and dissipated by convection and radiation. Both periodic and adiabatic boundary conditions are considered. The accuracy and efficiency of the element differential method is validated by several numerical examples with analytical solutions. The results indicate that the element differential method has high precision and flexibility to solve non-Fourier heat conduction in convective-radiative fin. Besides, the effects of Vernotte number, dimensionless periodicity, thermal conductivity coefficient, and emissivity coefficient on dimensionless fin tip temperature, instantaneous fin efficiency, and average fin efficiency are comprehensively analyzed.

Thermodynamic characteristics of counter flow and cross flow plate fin heat exchanger based on distributed parameter model

The distributed parameter models of counter flow and cross flow plate fin heat exchanger (PFHE) are constructed to investigate their thermodynamic characteristics. In practical application, the cold end of PFHE may be directly connected to the cold equipment. Therefore, the effect of longitudinal heat conduction (LHC) under different thermal boundary conditions set on two ends of the separating plates (SPs) is investigated based on the model of counter flow PFHE. It is found that LHC effect transmits the effect of boundary condition on two ends of the SPs into the inner domain of PFHE. The LHC effect on the heat transfer performance of PFHE is positive when setting appropriate boundary condition on two ends of the SPs. When considering LHC, compared with the adiabatic boundary conditions on two ends of the SPs, the effectiveness of constant wall temperature boundary conditions increases by 31.7 ∼ 35.8 %, and the effectiveness of constant heat flux boundary conditions increases by 22.8 %. The model of cross flow PFHE is used to investigate the effect of configuration and operation parameters on the heat transfer amount and the pump power. The cross flow PFHE is optimized to arrive at the maximization of heat transfer amount per unit pump power (HTPUP). In the three-stream cross flow PFHE studied, the heat transfer amount almost doesn’t change when the xz projected area is maintained and one projected length (z side length) is changing. The pump power is the lowest and the HTPUP is the largest when z side length of PFHE (z side is the flow direction of the fluid with large mass flowrate) is 0.15 ∼ 0.2 m.

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.

Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.

An Advanced Model for Long-Term Localized Corrosion of Copper

The Nuclear Waste Management Organization (NWMO) is responsible for the implementation of the Adaptive Phased Management (APM) plan, the federally-approved plan for the safe long-term management of Canada’s used nuclear fuel.1 Under the APM plan, used nuclear fuel will ultimately be placed within a deep geological repository (DGR) in a suitable host rock formation. Part of evaluating the long-term performance and safety of the repository system is understanding the behavior of the copper-coated container with respect to localized corrosion. Even though localized corrosion is not expected in the DGR design system, there is still a need to develop a mathematical model for localized corrosion of copper.A 2-D axisymmetric time-dependent model for the localized corrosion of copper was developed using the concept of an Evans droplet.2 The model accounts for three reversible electrochemical reactions on the metal surface (copper dissolution/plating, cuprous ion oxidation (Cu+) /cupric ion (Cu2+) reduction, and hydrogen (H2) evolution/oxidation) and three irreversible electrochemical reactions (cupric ion reduction, oxygen (O2) reduction, and hydroperoxyl ion (HO2 -) reduction). Dissolved cuprous ion reacts in a second chemical step to form the cuprous chloride (CuCl) salt film treated as a diffusion barrier, or it reacts to form the cuprous oxide (Cu2O) film that partially blocked the active area on the metal surface. The model also accounts for fifteen homogeneous reactions involving copper chloride complex, copper hydroxide complex, copper carbonate complex, and superoxide species. The associated equilibrium constants were obtained from PHREEQC thermodynamic software.3 The mathematical model was developed using the finite-element method (COMSOL Multiphysics). The model includes coupled, nonlinear, diffusion equations for ionic species, which include the contribution of migration, local electroneutrality, and homogeneous reactions. The anodic and cathodic regions are not predefined but, instead, are determined by values of local concentration and potential from the simulation results. The growth of nm-scale films was calculated implicitly without using finite-element meshing and surface coverage was expressed in terms of the thickness in units of monolayers. The model also accounted for the effect of porous CuCl film thickness on the surface oxygen concentration and potential applied on electrochemical reactions. The influence of temperature was included on model parameters such as equilibrium rate constant, diffusion coefficient, Henry’s law constant, solubility product constant and kinetic parameters associated with electrochemical reactions. Transient droplet temperature was described by interpolating results from a one-million-year simulation for the temperature change on the used fuel container surface.4 A total of 28 dependent spatial-temporal variables including species’ concentrations, potentials and local corrosion rate were solved in this model.In the current version of model, two extreme conditions were chosen such that droplet boundary has a faster or slower rate of oxygen decay for an initially air-saturated droplet. The model shows a 10-year time-dependent radial distribution of anodic and cathodic current density, surface coverage of CuCl film and Cu2O film, and localized corrosion rates and depths. It also shows a distribution of pH, potential, and concentrations of dissolved gaseous and ionic species through the entire droplet. Temperature and oxygen concentration is shown to have a strong contribution to the simulation results. Simulations show that the depth of corrosion is almost uniform over the elapsed time simulated and the maximum deviation from the average corrosion depth was less than 0.0004% for slower oxygen decay and less than 0.002% for faster oxygen decay in 10 years.References NWMO, “Choosing a Way Forward. The Future Management of Canada’s Used Nuclear Fuel. Final Study,” Nuclear Waste Management Organization, Toronto, Ontario, 2005.R. Evans, The Corrosion of Metals, E. Arnold & Company, London, 1926.PHREEQC Version 3, United States Geological Survey, 202, https://www.usgs.gov/software/phreeqc-version-3Guo, “Thermal response of a Canadian conceptual deep geological repository in crystalline rock and a method to correct the influence of the near-field adiabatic boundary condition”, Engineering Geology, 218 (2017), p50-p62. AcknowledgementThis work was supported by the Nuclear Waste Management Organization, Canada, under project 2000904.

Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow–thermodynamics interactions

Hydrodynamic stability of compressible boundary layers is strongly influenced by the Mach number ( $M$ ), Prandtl number ( $Pr$ ) and thermal wall boundary condition. These effects manifest on the flow stability via the flow–thermodynamics interactions. Comprehensive understanding of stability flow physics is of fundamental interest and important for developing predictive tools and closure models for integrated transition-to-turbulence computations. The flow–thermodynamics interactions are examined using linear analysis and direct numerical simulations in the following parameter regime: $0.5 \leq M \leq 8$ ; and $0.5 \leq Pr \leq 1.3$ . For the adiabatic wall boundary condition, increasing Prandtl number has a destabilizing effect. In this work, we characterize the behaviour of production, pressure–strain correlation and pressure dilatation as functions of the Mach and Prandtl numbers. First and second instability modes exhibit similar stability trends but the underlying flow physics is shown to be diametrically opposite. The Prandtl number influence on instability is explicated in terms of the base flow profile with respect to the different perturbation mode shapes.