An extended rough-wall model for an integral boundary layer model intended for ice accretion calculations

Use of a Two-Dimensional Finite Volume Integral Boundary-Layer Method for Ice-Accretion Calculations

“…The computation of θ on a rough wall precludes the use of a simplified integral method. Consequently, model 5 is generally fed with a smooth-wall momentum thickness, which is not so obvious from a theoretical perspective, but seems to be rather effective [22].…”

“…The use of more evolved or more recent rough-wall models for h tc than the Makkonnen model is also expected. For instance, the article [22] described an adaptation of Aupoix's model to the framework of integral boundary layer methods. One important conclusion of the latter work was that the rough-wall momentum thickness should be used as an input of the new h tc model (socalled integral Aupoix-Grigson-Colebrook model).…”

Comparison of turbulent Prandtl number correction models for the Stanton evaluation over rough surfaces

“…Although useful for model calibration, these experiments are based on spherical roughness elements that are not necessarily representative of ice accretion roughness. The experimental results of Dukhan et al (1999) are more relevant for icing, and have been used by Radenac et al (2018) for extended rough wall model validation.…”

Theory and validation of a 2D Finite-Volume integral boundary layer method intended for icing applications

“…Although not fully satisfying, the method consisting of post-processing the integral quantities produced by the present integral model, including the use of relations (24) and (25), would thus be in line with the state-of-the-art. For improved modelling of the physics, equations (24) and (25) should be changed to include the effect of roughness (with usual relations like the ones of Kays and Crawford [29] or upgraded relations as proposed in [31]), so that the integral model solves the rough-wall-condition boundary layer equations.…”

“…This non-consistency can be corrected by adding a corrective source term in the right hand side of equation (31) to offset the error which appears in the left hand side of equation (31). The corrective source term must therefore be equal to the discretization of Er.…”