Feasibility of Deep Neural Network Surrogate Models in Fluid Dynamics

Abstract

This paper studies reduced-order-models for the fluid flow problem of a digital valve, and whether it may efficiently be formulated by a deep Artificial Neural Network (ANN) to model e.g. the valve flow, flowinduced force, stiction phenomena and steep local pressure gradients that arise before plunger impact, which may otherwise require CFD to be accurately modeled. Several methodologies are investigated to evaluate both the required computation time and the accuracy. The accuracy is benchmarked against CFD solutions of flows and forces. As basis for comparison an analytical model is proposed where some fitting parameters are allowed, and the equation is tested outside its fitting range. A similar model is built as a deep ANN which is trained with data from the analytical model to investigate the amount of data required for an ANN and its fitting capabilities. The results show that in higher dimensions the required training data can be maintained low if data is structured by a Latin Hypercube, otherwise the amount becomes infeasible. This makes an ANN surrogate feasible when compared to a look-up table, and may be expanded to higher dimension where dynamical effects are included. However, the required data and computational cost for this is too extensive for the valve design considered as basis for the analysis. Instead, for this specific problem, the derived analytical model is sufficient to describe the valve dynamics and reduces the computation time significantly.

Investigating the Design Parameters’ Influence in a Fast Switching Valve – An Approach to Simplify the Design Process

“…below. Hence, the plunger movement gives rise to a resisting force as discussed in [22] where both stiction and Movement-Induced (MI) parametric relations are described. Thus increasing the contact area between plunger and seat means significantly increasing the stiction force, but also ensures a leak-free design and lowers the mechanical stresses.…”

“…Generally the system is described by complex models using e.g., Navier-Stoke's equations, Maxwell's equations, etc., which are used in the detailed simulation of the system. However, to understand how different parameters are related to the design parameters, simplified models are presented in the following, based on previous studies of the valve [22,25]. These models are used to identify the output parameters considered when investigating various designs parameters sensitivity, cf.…”

“…The fluid velocity will locally cause pressures to decrease, thus potentially affecting the flow force. The following parametric form has been proposed, [22]:…”