Uncertainty Quantification and Modelling of CFD Simulations of a Swirling Turbulent Jet Created by a Rotating Pipe for Application to Heat Transfer From a Heated Solid Flat Plate

Abstract

Swirling turbulent flows created by the rotation of pipes and applications for heat transfer can have interesting industrial purposes. As such physical phenomenon is under some physical uncertainties, it is interesting to understand their impact on the relevant parameters. In the present paper, the Stochastic Collocation method with Sparse Grids is developed, in order to study how the uncertainties are propagated from the Computational Fluid Dynamics (CFD) simulations of a Swirling jet created by the rotation of a pipe to the CFD simulations of the heat transfer from a flat plate by the impingement of the generated swirling jet. In addition, some mathematical models for the velocity profile and turbulent parameters are given, and their uncertainties studied, in order to facilitate this two-step process for industrial applications.

Propagation of uncertainty in a rotating pipe mechanism to generate an impinging swirling jet flow for heat transfer from a flat plate

“…Nevertheless, this modelling was also tried with a cubic polynomial in v z /U (3) , which requires only three constants to estimate, but had a poor performance. Amongst v z /U (1) and v z /U (2) there are some clear differences. A cubic power factor in v z /U (1) is introduced to deal with the non linearity, which is not introduced in v z /U (2) , undergoing a bad fit.…”

“…It is specially relevant for the proper modelling of the boundary layer, since this plays an important role in the further development of the flow. This led to select a parametric function with a hyperbolic tangent for v z /U (1) , v z /U (2) , v z /U (best) . This is consistent with the past work of [82,16] that reports boundary layer of flows under rotation having a hyperbolic tangent shape.…”

“…It is well known that Computational Fluid Dynamics (CFD) is a powerful tool in fluid-related fields such as optimisation [1,2], aerospace & aerodynamics industry [3,4,5], fire safety modelling [6], heat transfer [7] or nuclear energy [8], amongst many others. Much effort has been spent to develop numerical algorithms for CFD, leading to more reliable simulations for decision-making and validation purposes, where uncertainty plays an important role.…”

“…This is because the stochastic variance of some parameters is taken into account in the simulation and may have effect on the performance. To our knowledge, there is no previous literature on the effect of simulating impinging jet flows for heat transfer under uncertain conditions, apart from the early stage work presented by the authors in a conference [34]. This is a motivation to provide a framework for these complex problems, since the quantification of uncertainties should be an important common practice in computational engineering.…”

On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust

“…One of the key aspects of CFD is that they are, generally, a cheaper option for product design and development than experiments. Actually, CFD simulations are routinely used in fields like optimisation [88,37], aerospace & aerodynamic industry [55], fire safety modelling [94], heat transfer [65] or nuclear energy [54], amongst many others. Much effort has been spent to develop such techniques, leading to the most reliable simulations for decision-making purposes.…”