Papers by Santiago Madruga
arXiv (Cornell University), Nov 21, 2017
We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octad... more We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octadecane in horizontal layers of several sizes heated from below. This configuration allows to cover a wide range of effective Rayleigh numbers on the liquid PCM phase, up to ∼ 10 9 , without changing any external parameter control. We identify four different regimes as time evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime and (iv) turbulent regime. The first two regimes appear at all domain sizes. However the third and fourth regime require a minimum advance of the solid/liquid interface to develop, and we observe them only for large enough domains. The transition to turbulence takes places after a secondary instability that forces the coarsening of the thermal plumes. Each one of the melting regimes creates a distinct solid/liquid front that characterizes the internal state of the melting process. We observe that most of the magnitudes of the melting process are ruled by power laws, although not all of them. Thus the number of plumes, some regimes of the Rayleigh number as a function of time, the number of plumes after the primary and secondary instability, the thermal and kinetic boundary layers follow simple power laws. In particular, we find that the Nusselt number scales with the Rayleigh number as N u ∼ Ra 0.29 in the turbulent regime, consistent with theories and experiments on Rayleigh-Bénard convection that show an exponent 2/7.
Thermal heat storage and convective melting dynamics of phase change materials in inclined square enclosures: Effect of the Prandtl number
Applied Thermal Engineering, 2023
Journal of Fluid Mechanics, Feb 1, 2006
While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold... more While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold (i.e. for Rayleigh numbers R ≈ R c), it has often been assumed that they are always unstable to rolls already for slightly higher Rayleigh numbers. Using the incompressible Navier-Stokes equations for parameters corresponding to water as a working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime (ǫ ≡ R − R c /R c = O(1)). We find 'reentrant' behavior of the hexagons, i.e. as ǫ is increased they can lose and regain stability. This can occur for values of ǫ as low as ǫ = 0.2. We identify two factors contributing to the reentrance: i) the hexagons can make contact with a hexagon attractor that has been identified recently in the nonlinear regime even in Boussinesq convection (Assenheimer & Steinberg (1996); Clever & Busse (1996)) and ii) the non-Boussinesq effects increase with ǫ. Using direct simulations for circular containers we show that the reentrant hexagons can prevail even for side-wall conditions that favor convection in the form of the competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons become stable even over the whole ǫ-range considered, 0 ≤ ǫ ≤ 1.5. Contents 1 Introduction 1 2 Basic Equations 3 3 Linear Stability of Hexagons 8 3.1 Amplitude Instabilities 8 3.2 Side-Band Instabilities 10 4 Origin of Reentrant Hexagons 12 5 Numerical Simulations 16 6 Conclusions 18
Physical Review Letters, Feb 22, 2006
We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussines... more We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non-Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscillations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.
Introducing a new concept for enhanced micro-energy harvesting of thermal fluctuations through the Marangoni effect
Applied Energy, 2022
International Journal of Heat and Mass Transfer, Nov 1, 2018
We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octad... more We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octadecane in horizontal layers of several sizes heated from below. This configuration allows to cover a wide range of effective Rayleigh numbers on the liquid PCM phase, up to ∼ 10 9 , without changing any external parameter control. We identify four different regimes as time evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime and (iv) turbulent regime. The first two regimes appear at all domain sizes. However the third and fourth regime require a minimum advance of the solid/liquid interface to develop, and we observe them only for large enough domains. The transition to turbulence takes places after a secondary instability that forces the coarsening of the thermal plumes. Each one of the melting regimes creates a distinct solid/liquid front that characterizes the internal state of the melting process. We observe that most of the magnitudes of the melting process are ruled by power laws, although not all of them. Thus the number of plumes, some regimes of the Rayleigh number as a function of time, the number of plumes after the primary and secondary instability, the thermal and kinetic boundary layers follow simple power laws. In particular, we find that the Nusselt number scales with the Rayleigh number as N u ∼ Ra 0.29 in the turbulent regime, consistent with theories and experiments on Rayleigh-Bénard convection that show an exponent 2/7.
International Communications in Heat and Mass Transfer, Nov 1, 2018
We carry out a comparative analysis of experimental results and numerical simulations on the melt... more We carry out a comparative analysis of experimental results and numerical simulations on the melting of the Phase Change Material tetracosane contained within a cube and heated from below. Simulations employ a Stefan number Ste = 0.65, Prandtl number Pr = 54, and Rayleigh number covers a range up to 10 8. The simulations show distinct regimes of the melting process: (i) conductive regime, (ii) stable growth regime, (iii) coarsening regime, (iv) turbulent regime. We show how the solid/liquid interface easily observed in the experiment is enough to identify these regimes and so the internal state of the velocity and temperature fields.
Scaling laws during melting driven by thermocapillarity
International Journal of Heat and Mass Transfer, Dec 1, 2020
Abstract We study the melting dynamics of a phase change material by the action of thermocapillar... more Abstract We study the melting dynamics of a phase change material by the action of thermocapillary driving. The geometry corresponds to squares and rectangles with a top free flat surface. We simulate a phase change material with Prandtl number Pr ~ 60 in the liquid phase and two Stefan numbers S t e = 0.67 and S t e = 0.33 . The interplay between conduction and convection dominated regions within the liquid phase of the PCM determines the melting dynamics. We find that some magnitudes follow simple power laws; such as the position of the melting front, the time to full melting, and the input of energy into the system. In addition, we find that the dynamic Marangoni number scales with the Nusselt number as a power-law Nu ~ Maα, where the exponent α depends on the aspect ratio of the geometry and position of the melting fronts at the surface and bottom. These scalings prevail in a wide range of Marangoni numbers and are only slightly affected by the Stefan number.
Chaos, Mar 1, 2006
Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biolog... more Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems we present an approach that aims at characterizing quantitatively spiral-like elements in complex stripe-like patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arclength and their winding number. In addition, it yields the number of pattern components (Betti number), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh-Bénard convection and find that the arclength of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is non-monotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers (P r 1). In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.
Heat transfer performance and thermal energy storage in nano-enhanced phase change materials driven by thermocapillarity
International Communications in Heat and Mass Transfer, Dec 1, 2021
Journal of Non-Equilibrium Thermodynamics, 2004
The stability of a liquid layer with an undeformable interface open to the atmosphere, subjected ... more The stability of a liquid layer with an undeformable interface open to the atmosphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature difference applied on the system. Depending on the liquid depth, this basic flow is destabilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturbations are driven by the basic flow and therefore one must distinguish between convective and absolute thresholds. The instability mechanisms as well as the di¤erent regimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr ¼ 10Þ. In particular, it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally.
IOP conference series, Oct 1, 2019
We present a model and simulations of harvesting of thermal fluctuations occurring in the fuselag... more We present a model and simulations of harvesting of thermal fluctuations occurring in the fuselage of an aircraft during a flight and their transformation into electricity using the thermoelectric effect. The model couples a Thermoelectric Generator with a Phase Change Material as a heat reservoir to boost the generation of electricity. We show how introducing a metallic foam within the PCM enhance the production of electric power, and how it occurs through shorter and higher sprouts of voltage generation.
Physics of Fluids, Jun 1, 2009
We study the linear stability with respect to lateral perturbations of free surface films of poly... more We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.
European Physical Journal-special Topics, Apr 1, 2017
We carry out simulations of the melting process on the phase change material n-octadecane in squa... more We carry out simulations of the melting process on the phase change material n-octadecane in squared geometries in the presence of natural convection and including thermocapillary effects. We show how the introduction of thermocapillary effects enhances the heat transfer rate, being the effect especially relevant for small Bond numbers. Thus induction of Marangoni flows results in a useful mechanism to enhance the typical slow heat transfer rate of paraffin waxes in applications of energy storage or passive control management.
International Journal of Heat and Mass Transfer, Jun 1, 2017
We carry out extensive numerical simulations on the melting of the Phase Change Material n-octade... more We carry out extensive numerical simulations on the melting of the Phase Change Material n-octadecane subjected to thermocapillary driving at a free surface on geometries with the form of circular sections of radius in order of centimeters. Simulations employ Stefan numbers Ste = 0.22 and Ste = 0.67. We compare the heat transfer performance with melting induced only by conduction and find a reduction of melting times by thermocapillarity up to a factor five for semicircular geometries. As a consequence, we propose the use of this mechanism in applications of thermoregulation in microgravity that require fast charge and discharge cycles. We show how a longer free surface enhances the effect of thermocapillarity on the heat transfer performance due to a greater contact area of solid PCM with regions of melted PCM dominated by thermocapillary flows. The length of the free surface has more impact on the heat transfer performance than the contact area between PCM and heat source in the geometries studied in this work. Besides, we observe as well how greater thermal gradients for higher Stefan number augment the importance of thermocapillary effects on the heat transfer performance.
arXiv (Cornell University), Jul 26, 2005
We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussines... more We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as a working fluid. We identify two regimes. For weak non-Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscillations exhibit localized chaotic bursting, which can be modeled by a quintic complex Ginzburg-Landau equation.
arXiv (Cornell University), 2008
We study the stability and dynamics of non-Boussinesq convection in pure gases (CO$_2$ and SF$_6$... more We study the stability and dynamics of non-Boussinesq convection in pure gases (CO$_2$ and SF$_6$) with Prandtl numbers near $Pr\simeq 1$ and in a H$_2$-Xe mixture with $Pr=0.17$. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For $Pr \simeq 1$ and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF$_6$ we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H$_2$-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of target-like components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.
Modeling of enhanced micro-energy harvesting of thermal ambient fluctuations with metallic foams embedded in Phase Change Materials
Renewable Energy, May 1, 2021
Abstract We present an enhanced micro-energy harvester to transform ambient thermal fluctuations ... more Abstract We present an enhanced micro-energy harvester to transform ambient thermal fluctuations into electricity. The design consists of a Thermoelectric Generator (TEG) joined to a thermal storage unit improved with a Phase Change Material within a metallic foam (pPCM). We show how the augmented effective conductivity of the heat storage unit multiplies the production of electric power through voltage generation in higher and shorter sprouts. The porosity of the metallic foam accelerates the heat transfer and permits higher volumes of the heat storage unit to be effective in harvesting more energy from the surroundings. The pPCM/TEG device is a robust and cost-effective means to optimize the output of TEG based systems to power low-consumption electronics. The potential of this design is demonstrated with examples of micro-energy harvesting under ambient thermal conditions in an aircraft and ground solar irradiation. In these applications, a single TEG module with a moderate merit figure is used and found that pPCM allows a substantial optimization of energy conversion. As an example, the pPCM/TEG devices produce about twenty times more electric energy at even small volume fractions of the foam e = 0.95 than PCM/TEG systems in solar micro-energy harvesting on ground conditions with low thermal gradients.
Applied Thermal Engineering, Sep 1, 2017
We carry out extensive numerical simulations on the melting of the Phase Change Material n-octade... more We carry out extensive numerical simulations on the melting of the Phase Change Material n-octadecane subjected to thermocapillary driving at a free surface on geometries with the form of circular sections of radius in order of centimeters. Simulations employ Stefan numbers Ste = 0.22 and Ste = 0.67. We compare the heat transfer performance with melting induced only by conduction and find a reduction of melting times by thermocapillarity up to a factor five for semicircular geometries. As a consequence, we propose the use of this mechanism in applications of thermoregulation in microgravity that require fast charge and discharge cycles. We show how a longer free surface enhances the effect of thermocapillarity on the heat transfer performance due to a greater contact area of solid PCM with regions of melted PCM dominated by thermocapillary flows. The length of the free surface has more impact on the heat transfer performance than the contact area between PCM and heat source in the geometries studied in this work. Besides, we observe as well how greater thermal gradients for higher Stefan number augment the importance of thermocapillary effects on the heat transfer performance.
A function based on the characteristics of the alpha-particle lines obtained with silicon semicon... more A function based on the characteristics of the alpha-particle lines obtained with silicon semiconductor detectors and modi"ed by using cubic splines is proposed to parametrize the shape of the peaks. A reduction in the number of parameters initially considered in other proposals was carried out in order to improve the stability of the optimization process. It was imposed by the boundary conditions for the cubic splines term. This function was then able to describe peaks with highly anomalous shapes with respect to those expected from this type of detector. Some criteria were implemented to correctly determine the area of the peaks and their errors. Comparisons with other well-established functions revealed excellent agreement in the "nal values obtained from both "ts. Detailed studies on reliability of the "tting results were carried out and the application of the function is proposed. Although the aim was to correct anomalies in peak shapes, the peaks showing the expected shapes were also well "tted. Accordingly, the validity of the proposal is quite general in the analysis of alpha-particle spectrometry with semiconductor detectors.
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Papers by Santiago Madruga