Reliable modelling of non-Newtonian sludge flows using novel computational fluid dynamics

The project is interdisciplinary in two dimensions because it brings together experiments and simulations as well as solid and fluid mechanics.  The integration of concepts and technology across these boundaries brings a level of adventure to the project which is countered by building on well-established research in solid mechanics on quantitative comparisons of measurements and predictions using orthogonal decomposition[i]^,[ii] leading to validation metrics based on relative error[iii] and assessment of measurement of uncertainty[iv]; and in fluid dynamics using experimental techniques to understand turbulent flow regimes[v]^,[vi],[vii].  IAEA considers the use of CFD and associated validation data in various nuclear design issues and has identified gaps in verification and validation procedures[viii].  The goal of the project will be to develop techniques that allow volumetric, time-varying, flow data from both measurements and predictions to be represented as feature vectors that can be compared using the validation metrics already established in solid mechanics for dynamic events. 

In fluid mechanics, Lumley and his co-workers[ix]^,[x] were probably amongst the first to use orthogonal decomposition to characterise the coherent structure of turbulence.  More recently, weighted orthogonal decomposition has been used to generate reduced order models of, for instance, swirling flow from a turbine[xi] and LES-derived bed shear stress data in a rectangular channel[xii]; and dynamic mode decomposition[xiii]^,[xiv] has been applied to turbulent flows in cavities[xv]^,[xvi].  However, the resultant low-dimensional descriptions do not appear to have been used in quantitative validation processes of the type pioneered in computational solid mechanics; instead validation tends to take the form of comparisons along one-dimensional sections, e.g. Oliva & Held[xvii], or qualitative comparisons of flow patterns, e.g. Shi et al[xviii]; so, this project will attempt to address this technology gap.

Hypotheses

Turbulent Newtonian and non-Newtonian fluid flows can be represented, or characterised, by feature vectors using decomposition and that this will allow quantitative comparison of predicted and measured flows for the purposes of validation and updating of computational fluid dynamics models.

Aims

To generalise a validation metric based on relative errors to allow integration with orthogonal decomposition and, or dynamic mode decomposition of predicted and measured data, thereby unifying quantitative validation approaches in solid and fluid mechanics, for the first time.

Objectives

• To acquire and evaluate suitable sets of measured and predicted data from fluid flows using the literature, on-going research and performing experiments and simulations.
• To establish algorithms for the application of orthogonal decomposition and dynamic mode decomposition to fluid flows.
• To demonstrate the application of the algorithms for decomposition of fluid flow data from both measurements and predictions.
• To develop a quantitative validation method based using a probabilistic assessment of the congruence of the measurements and predictions.
• To apply the algorithm and method to a number of case studies relevant to the nuclear industry.

The initial task for the PhD student will be to conduct a review on the computational and experimental studies of Newtonian and non-Newtonian fluid flow regimes from a range of disciplines, including the nuclear, water and wastewater, and process industries, and the validation procedures applied to them.  These insights will permit decisions to be made on the appropriate selection of measured and predicted datasets for comparison in a validation procedure.  It is anticipated that some new computational fluid dynamics (CFD) simulations will be required in order to produce comparable datasets, and it might be necessary to commission or undertake some limited experiments using synthetic sludge to ensure appropriate comparisons are being made.

In the second phase of the project, the PhD student will establish algorithms for orthogonal decomposition of predicted and measured fluid flows and also for dynamic mode decomposition.  Orthogonal decomposition[xix] can be construed as a more generalised form of the image decomposition used to represent strain fields in recent work² as well as the CEN validation procedure[xx] and has been used to identify the salient features of open flows^10,11.  While dynamic mode decomposition has been shown to be well-suited to identifying the spatial coherent features of flow^15,16, it is proposed to use the modes obtained from these decomposition techniques to characterise the predicted and measured flows and compare the modal values via the updated relative error metric that has been developed for strain fields.  In simple terms, this can be considered as replacing the Chebyshev (or Tchebichef) moments obtained from the decomposition of a strain field with the singular values from an orthogonal decomposition, such as those for the open cavity flow found by Guéniat et al¹⁶.  The efficacy of orthogonal decomposition and dynamic mode decomposition will be compared.  The final innovative step will be the implementation of the more suitable decomposition approach within the validation methodology developed for solid mechanics models, in order to allow a probabilistic statement to be made about the reliability of a computational fluid dynamics model.  The whole process will be demonstrated in a number of case studies based on flow regimes relevant to nuclear plant that will be selected in collaboration with the National Nuclear Laboratory.