Buoyancy-driven melting and solidification heat transfer analysis in encapsulated phase change materials

Controlled melting and solidification in encapsulated phase change materials (PCMs) is of practical interest, for example, in latent heat storage applications. The choice of PCMs and the dynamic heat transfer characteristics during phase change - affecting the transient charging/discharging rates - are decisive for the energy and power density of the heat storage option. For example, highly conductive, high melting point (above 700 K) metal alloys have a potential advantage as a high energy and power density latent heat storage, compared to the widely used low conducting molten salt and paraffin wax. This advantage depends on the relative dominance of heat transfer modes that vary depending on the thermal properties of the PCM, shape of the encapsulation, and the load conditions, and must be quantified to warrant a fair comparison. We developed a 2D transient phase change model of encapsulated PCMs, accounting for phase change over a temperature range, volumetric expansion and contraction, and multi-mode heat transfer within the encapsulated PCM. The enthalpy-porosity method was used to model the phase change in a fixed grid. Validation was performed with literature data of low and high-conductivity PCM experiments (RT27 and lead). Two types of PCMs were subsequently investigated in detail: a high-conducting binary-eutectic alloy Al-12.6Si and a low-conducting commercially available RT27 paraffin wax (Rubitherm GmbH). The model was used to compare the phase change process and the strength of the various modes of heat transfer in the PCM filled cylindrical stainless-steel encapsulations in horizontal and vertical orientation with constant temperature walls. A full parameter study and non-dimensional analysis are presented for different PCMs. The results quantified the influence of boundary conditions, thermophysical properties and geometrical parameters on the phase change process and the contribution of the natural convection within the encapsulation. The non-dimensional analysis linked the melt fraction and heat transfer rates to a combination of the Fourier, Stefan, Rayleigh and Nusselt numbers. Fitting of the exponents of non-dimensional number groups to the heat transfer calculations allowed to provide general correlations for melting time, melt fraction, heat transfer rates, and characteristics of melting. Such correlations provide general understanding of the transient heat transfer in phase change media and provide engineering tools for designing, for example, a latent heat storage unit.

Microstructure and embrittlement of leaded copper alloys

Laurent Felberbaum

Mechanisms responsible for the embrittlement of leaded "free-machining" copper alloys at intermediate temperatures (i.e. around 400 °C) are examined using a combination of microstructural and mechanical characterization. Tensile tests are conducted on pure copper and on industrial high-strength Cu-Ni-Sn alloys, comparing leaded and unleaded versions, at strain rates ranging from 10-4 to 10 s-1, and various temperatures between 25 °C and 800 °C. It is found that, in the leaded samples, both liquid metal embrittlement and grain boundary embrittlement operate at intermediate temperature,i.e., near the melting point of lead. Their respective importance depends mainly on the strain rate: fracture at high strain rate (10 s-1) displays characteristic signatures of liquid metal embrittlement, while at low strain rate (10-4 s-1) the ductility trough behaviour can be attributed to grain boundary embrittlement. In leaded copper and copper alloys, lead is mostly present as discrete inclusions, frequently located along grain boundaries. The dihedral angle of intergranular lead inclusions is then the main microstructural parameter besides their size. A new technique is proposed and demonstrated for the measurement of inclusion dihedral angle in a high-purity Cu-1 wt.% Pb alloy, based on room temperature characterization of samples that were held at elevated temperature at times sufficiently long for shape equilibration of the inclusions and then rapidly quenched. Quantitative scanning electron microscopic analysis of metallographic surfaces along which individual inclusions have been dissolved is used to deduce the dihedral angle using a mathematical fit of their solid/liquid interface. For a specific temperature, we show that the dihedral angle is not unique; this reflects the fact that high-angle grain boundary energies are not constant in copper. Existing micromechanical analyses of shape equilibrium for intergranular inclusions in the presence of external stress are adapted to produce an improved description at low stress and to take into account the inclusion bulk compressibility. The derivation is based on minimization of the global capillary and elastic strain energy associated with such inclusions. An adimensional parameter that depends on the applied stress, the inclusion volume, the elastic properties of the solid, and the relevant interfacial energies emerges from the analysis as the sole factor governing the shape of the inclusion. If void nucleation occurs easily within the inclusion, such that its apparent bulk modulus is nil, the inclusion become unstable, degenerating to a crack when this adimensional parameter exceeds a critical value. Measurements of the dihedral angle on samples previously subjected to a remote stress at 400 °C show that applied stress causes a reduction in the apparent dihedral angle of liquid lead inclusions. Calculated critical stresses for both leaded pure copper and leaded copper-nickel-tin alloys that fail at high strain rate by liquid metal embrittlement are calculated for individual inclusions in the metal. These calculated critical stresses correlate relatively well with the measured fracture stress, suggesting that shape instability of the inclusions cause fracture of the alloys. This result is applied towards the suggestion of general strategies for reduction of the susceptibility of leaded copper alloys to liquid metal embrittlement. A case study addressing the problem of quench cracking of leaded Cu-Ni-Sn alloys on the basis of experimentation and finite element thermomechanical simulation, showing how the problem can be alleviated in production, concludes the thesis.

EPFL2005

Grain Boundary Relaxation in 18-carat Gold Alloys

Ann-Kathrin Audren

Grain boundaries (GBs) play an important role for the mechanical properties of metals. In addition to dislocation motion inside the grains, some metal alloys deform along the GBs at high temperatures. GBs can also be the cause of a brittle behaviour of some metallic alloys, where crack propagation along the GBs is observed. This thesis aims to understand the role of GBs on the thermo-mechanical behaviour of metals and especially to define the microscopic mechanism, which leads to a deformation at the GBs. In this thesis, polycrystals, single crystals and bi-crystals of a yellow gold alloy are studied in detail, primarily by mechanical spectroscopy. The analysis and interpretation of the experimental data identifies different anelastic relaxations (internal energy dissipation processes), that produce peaks in the mechanical loss spectrum. The mechanical loss spectrum of polycrystals shows a relaxation peak P2 at about 780K, which is absent in single crystals made from the same alloy. Stepwise deformation of a single crystal causes an increase of the high temperature mechanical loss background and the appearance of a high temperature peak (P3). Above a critical deformation, P3 disappears and the peak P2, which is normally observed in polycrystals, appears. The increase of the exponential background is interpreted as due to the introduction of new dislocations whereas the peak P3 is attributed to a dislocation relaxation mechanism in the sub-grain boundaries. The peak P2 located at intermediate temperatures depends on the grain size: with grain growth, the peak position shifts to higher temperatures. It is shown that the relaxation time is proportional to the grain size d. Such a grains size dependence is in agreement with the Zener model based on geometrical considerations of an assembly of elastic grains, which can slide against each other. The investigations on bi-crystals containing a single GB with a specific misorientation between crystal lattices and a specific boundary plane orientation show that the relaxation peak P2 is closely related to a mechanism taking place at the boundary. The peak height is proportional to the GB density in a bi-crystal, whereas a single crystalline part cut from a bi-crystal does not show a relaxation peak. Molecular dynamics simulations are performed in order to illustrate the potential microscopic mechanisms responsible for the stress relaxation peak P2 in polycrystals. A Sigma5 grain boundary is submitted to a shear deformation parallel to the boundary plane. The grain boundary shows a migration perpendicular to the boundary plane coupled to shear for temperatures below 700K. Above 1000K, only grain boundary sliding is observed. Two models are developed that provide expressions for the relaxation strength and the relaxation time that are compared to experimental measurements performed on polycrystals. The observed grain size dependence favours the sliding model over the migration model. Measurements as a function of stress allow a refinement of the sliding model. The stress amplitude dependence of the peak P2 indicates a depinning mechanism, which is interpreted as due to GB dislocations between zones where sliding of different amount occurred. Obstacles to the sliding movement like steps or extended coincidence sites in the GB plane act as pinning points. The pinning points can be overcome at high temperatures close to the melting point, which results in the onset of local microscopic creep.

EPFL2014

Grain Boundary Relaxation in 18-carat Gold Alloys

Ann-Kathrin Audren

EPFL2014

Microstructure and embrittlement of leaded copper alloys

Laurent Felberbaum

EPFL2005