Dimensionless Numbers as an Effective Tool for Validation & Verification
Authors: Saint-Marcoux Jean-François 
Published: April 2019

Abstract

Objectives/Scope
The generalized use of multi-physics software may lead to significant errors when engineering judgement has not been exercised to its full extent. For that purpose ASME has developed Verification and Validation documents for Solid and Fluid Mechanics and is developing one for Energy Systems.
Verification (solving the equation right) benefits from a large body of numerical analysis and theoretical handbooks but validation (solving the right equation) does not always appear to have the same foundation. This is particularly the case when it is necessary to build the confidence in extension to more complex scenarios and where testing is not feasible such as in the offshore industry. The selection of the applicable software or the development of a new one rests on the shoulders of the designer.
Similitude laws state that identical results must be obtained when the dimensionless parameters are the same (n-theorem). In the pre-computer era dimensionless numbers have been extensively used in particular to design relevant experiments.
Dimensionless Numbers are usually the ratio of two values representing two physical phenomena (such as momentum and viscous forces for the Reynolds number). Above a critical value, the numerator phenomenon is dominant whereas it is the denominator phenomenon which is dominant below the critical value. Different sets of equations for either ranges are packaged in a software. The boundaries of their domains of validity may then become blurred to the casual user.
Another example for flow assurance is the case of compressibility effects which may become locally important, although under regular design rules (under the "erosional velocity" limit) they are not. Water-hammer is also an example for pressure fluctuations which are usually ignored unless in specific cases.
It is proposed to define the domain of validity of a software by reference to the use of the Dimensionless Numbers relevant to the phenomena anticipated by the designer, and then to control that the value of the computer derived Dimensionless Numbers remain within the expected range. In essence Dimensionless Numbers must remain essential parameters to contribute to an educated engineering judgment in the computer era.

Methods, Procedures, Process
The following process is proposed when dealing with a new design: -identify the relevant physical phenomena-assess, from Dimensionless Numbers, the applicable model-screen the software for its capacity to solve the computer model under the prescribed conditions-solve the computer model (with appropriate verification)-verify that the results are consistent with the assumptions by generating global and local Dimensionless Numbers.

Results, Observations, Conclusions
As the capacity of software increases to cover different engineering disciplines, there could be a sense that the computer dictates the results without the necessary control of engineering judgment, either because it is simply not available or not voiced at an effective level.
Dimensionless Numbers have played a very important role in many areas of physics for the design of experiments and for defining the domain of validity of the different theories which have now been packaged into software or part thereof. But now that these software are available, Dimensionless Numbers have fallen into disuse.
When software packages are used beyond their limits severe technical and economic consequences may happen. Dimensionless Numbers are relatively simple to manipulate and must be used by the designer to validate seemingly formidable computer results. Software developers should also play their part in the process.

Novel/Additive information
Dimensionless Numbers are not new by any mean but their use should be restored in the validation processes of a new design.