Transfer function estimation with SMC method for combined heat transfer: insensitivity to detail refinement of complex geometries

Abstract

The optimization of thermal transfers in engineering systems such as heat exchangers requires the analysis of the influence of heat sources upon the temperature at various positions of interest in the studied system. In order to achieve the resolution of the combined modes of heat transfer through these systems, their couplings and the complex 3D geometries involved need to be integrated with full accuracy. Recent developments in probabilistic formulations in the context of transient combined heat transfer (linearized conduction-radiation-convection) have opened a new route to solving such problems with Monte Carlo (MC) algorithms, using state-of-the-art computer graphics digital libraries to handle complex geometries. To estimate the temperature at a probe point of interest, random paths are generated from its position and propagated through the geometry until a known temperature is reached. From a single MC calculation to sample the path statistics, the Symbolic Monte Carlo (SMC) method is used to express the probe temperature as a linear function of the sources. This function can then be used to estimate the probe temperature for any source values, alleviating the need to repeat Monte-Carlo simulations for each source condition, resulting in greatly reduced computation time. This approach is applied to the case of an open-cavity porous medium and computation time insensitivity to the complexity and fineness of the geometry is demonstrated.

Path integrals formulations leading to propagator evaluation for coupled linear physics in large geometric models

“…• the power density throughout the solid phase ψ. 12 gathers all the computation times, illustrating that the benefits of using the stored propagation information, instead of running the Monte Carlo, is a computation time reduction by a factor 10 3 to 10 4 [22].…”

Coupled heat transfers resolution by Monte Carlo in urban geometry including direct and diffuse solar irradiations

“…For conciseness, the derivation of Eq. 3 and the integral formulation of θ R is not replicated but may be found in the work of Penazzi et al [24] and Bati et al [3] (and also in Tregan et al [29] for semi-transparent media). The absorbed solar irradiation is also unknown and its expression is given in Eq.…”

“…Indeed, this new approach has benefited practically from the computer graphics advances in image synthesis with MCM techniques [22] by the public release of efficient free software which guaranty independence between the MCM algorithm and the complex data representation while insuring fast access to data and the ability to manage large and complex three-dimensional (3D) geometry [32]. In addition, Penazzi et al [24] showed that the MCM algorithms developed to solve coupled heat transfers may be used to estimate and store propagators when heterogeneous and transient sources are known. This enables reusing propagators to evaluate their corresponding probe temperatures when the sources are different leading to a drastic reduction of computation time.…”

“…However, in the specific application of urban physics, the outdoor and indoor absorbed solar irradiations are unknown sources that originate from direct and diffuse solar irradiations but also from multiple reflections within the complex geometry. Thus, to solve coupled heat transfers in urban environments with a single MCM algorithm that is insensitive to geometrical refinements, the existing theoretical framework [29,17,24] should be enriched with a model for solar sources and their coupling to thermal heat transfers.…”

Monte Carlo functional estimation of the radiative source term in a semi-transparent medium: A faster coupled conductive–radiative model resolution

“…This function can therefore be directly used at each iteration of the FDM algorithm, resulting in a significant reduction in computational time in comparison to a standard direct model resolution in which the MCM computation is performed at each iteration. The estimation of a function of physical quantities with the MCM was initially referred to as Inverse Monte Carlo and Symbolic Monte Carlo in the field of radiative transfer [6,7,13,27] and has only recently been applied to coupled heat transfer [35,34,33].…”