Exploratory numerical experiments with a macroscopic theory of interfacial interactions

Abstract

Phenomenological theories of interfacial interactions are founded on the core idea to model macroscopically the thin layer that forms between media in contact as a two-dimensional continuum (surface phase or interface) characterised by physical properties per unit area; the temporal evolution of the latter is governed by surface balance equations whose set acts as bridging channel in between the governing equations of the volume phases. These theories have targeted terrestrial applications since long time and their exploitation has inspired our research programme to build up, on the same core idea, a macroscopic theory of gas-surface interactions targeting the complex phenomenology of hypersonic reentry flows as alternative to standard methods in aerothermodynamics based on accommodation coefficients. The objective of this paper is the description of methods employed and results achieved in the exploratory study that kicked off our research programme, that is, the unsteady heat transfer between two solids in contact in planar and cylindrical configurations with and without interface. It is a simple numerical-demonstrator test case designed to facilitate quick numerical calculations but, at the same time, to bring forth already sufficiently meaningful aspects relevant to thermal protection due to the formation of the interface. The paper begins with a brief introduction on the subject matter and a review of relevant literature within an aerothermodynamics perspective. Then the case is considered in which the interface is absent. The importance of tension (force per unit area) continuity as boundary condition

Thermal Boundary Characteristics of Homo-/Heterogeneous Interfaces

“…At the surface of re-entry vehicles chemical reactions can occur, these reactions contribute to the heating of such vehicles [8,19]. Furthermore, these reactions form a small layer, and influence the heat and mass transport at the surface.…”

“…The elastic and thermal properties, obtained from ReaxFF MD, served as input parameters for the macroscopic level phenomenological-theory (PT) [8]. Temperature profiles of non-reactive interfaces, obtained from both methods, are compared.…”

“…To study the heat transfer between two solids in contact, Giordano et al [8] have proposed a Phenomenological-Theory (PT). With the aim of building up a macroscopic theory of gas–surface interactions targeting the hypersonic re-entry flows.…”

“…This macroscopic theory is founded on momentum conservation and represents a more physically motivated boundary condition. For the mathematical formulation of the phenomenological-theory and further details, readers can refer to the original paper [8]. This method is used to compare the temperature profile non-reactive interfaces studied with MD.…”

“…Molecular characteristics of solids in contact play a key role in various fundamental studies related to heat transfer [1], mechanical behavior [2], micro/nano-fluidics [3], and catalysis [4]. Besides, it plays an important role in applications related to semiconductors [5], microelectronics [6,7] and heat-shielding in re-entry vehicles for aerospace applications [8]. In the latter case, insight into the thermal resistance at an interface of a multilayer structure is crucial for prediction and control of overheating of the thermal protection system used for the re-entry shuttle.…”