VALIDATION: WHAT, WHY AND HOW

Offshore and Naval engineering have relied on physical models, i.e. experimental fluid dynamics (EFD), for several decades. Although the role of experiments in engineering is still unquestionable, some of the limitations of physical models, as for example domain size (blockage and scale effects), can be addressed using mathematical models, i.e. computational fluid dynamics (CFD). However, to gain confidence in the use of CFD it is fundamental to determine the modelling accuracy, i.e. to determine the difference between the "physical reality" and the selected mathematical model. The quantification of the modelling error is the goal of Validation. It must be emphasized that Validation applies to the mathematical model (and not the code) and is performed for selected flow quantities (the so-called quantities of interest). Ideally, Validation would be performed comparing an exact measurement of the "physical reality" with the exact solution of the selected mathematical model. However, exact measurements do not exist and mathematical models for turbulent flows do not have analytical solutions. Therefore, procedures must be developed to take into account experimental and numerical uncertainties. Furthermore, the exact values of the flow parameters as for example Reynolds number, fluid viscosity or inlet turbulence quantities are often unknown, which leads to the so-called parameter uncertainty that also has to be dealt within the assessment of the modelling error. The main goal of this paper is to demonstrate that the very popular designation of "code X is validated" is meaningless without saying what is the mathematical model embedded in the code, what are the quantities of interest for the specific application and what is the Validation uncertainty imposed by the experimental, numerical and parameter uncertainties. Furthermore, we also illustrate that Validation is not a pass or fail exercise. A modelling error of 10% may be acceptable for a given application, whereas I% may not be enough for a different one. To this end, we present the application of the ASME V&V 20 Validation procedure for local set points and the metric for multiple set points to several practical test cases: prediction of transition from laminar to turbulent regime for the flow over a flat plate; flow around a circular cylinder; flow around the KVLCC2 tanker and current loads in shallow water for a LNG carrier. In most of these exercises, parameter uncertainty is assumed to be zero, which is an assumption often required for the so-called practical calculations due to the computational effort required to address it. Nonetheless, as an illustration of its application, the flow over the flat plate includes parameter uncertainty for the specification of the inlet turbulence quantities.