A Review of Measurement-Integrated Simulation of Complex Real Flows

Abstract

In spite of the inherent difficulty, reproducing the exact structure of real flows is a critically important issue in many fields, such as weather forecasting or feedback flow control. In order to obtain information on real flows, extensive studies have been carried out on methodology to integrate measurement and simulation, for example, the four-dimensional variational data assimilation method (4D-Var) or the state estimator such as the Kalman filter or the state observer. Measurement-integrated (MI) simulation is a state observer in which a computational fluid dynamics (CFD) scheme is used as a mathematical model of the physical system instead of a small dimensional linear dynamical system usually used in state observers. A large dimensional nonlinear CFD model makes it possible to accurately reproduce real flows for properly designed feedback signals. This review article surveys the theoretical formulations and applications of MI simulation. Formulations of MI simulation are presented, including governing equations of a flow field observer, those of a linearized error dynamics describing the convergence of the observer, and stabilization of the numerical scheme, which is important in implementation of MI simulation. Applications of MI simulation are presented ranging from fundamental turbulent flows in pipes and Karman vortices in a wind tunnel to clinical application in diagnosis of blood flows in a human body.

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

“…is visualized. In a previous study, the MI simulation was performed in two-dimensional analysis and the operation described above was performed in real time [8]. In the present study, we dealt with three-dimensional analysis, and the MI simulation was performed off-line with pre-measured pressure because of increased computational time.…”

“…Recently, the methodology combining measurement and simulation has been used to obtain the velocity in regions where no velocity information is available in particle image velocimetry (PIV) [5], and to estimate time-resolved velocity fields from non-time-resolved PIV data [6]. The present authors have also studied measurement-integrated (MI) simulation, which is a kind of the state observer in dynamical system theory employing the CFD scheme as a model instead of a linear differential equation [7] [8]. The validity of the MI simulation has been shown for several flow related problems.…”

Calculation of the Pressure Field for Turbulent Flow around a Surface-Mounted Cube Using the SIMPLE Algorithm and PIV Data

“…State observers can be defined as functions aiming to reconstruct the state of a system from an incomplete set of measurements [22]. The principal motive behind the integration of measurements is the necessity of reproducing the exact structure of real complex flows, especially in disciplines such as meteorology and feedback flow control [23]. The inherent difficulty in calculating adequately real complex flows is directly linked to the uncertainty with regard to the boundary conditions [23].…”

“…The principal motive behind the integration of measurements is the necessity of reproducing the exact structure of real complex flows, especially in disciplines such as meteorology and feedback flow control [23]. The inherent difficulty in calculating adequately real complex flows is directly linked to the uncertainty with regard to the boundary conditions [23]. The creation of a state observer for the integration of three-dimensional PIV velocity measurements into a CFD simulation has recently been accomplished [24].…”

Nudging-based data assimilation of the turbulent flow around a square cylinder

“…Exploring a cost-efficient alternative data assimilation methodology focusing on state estimation, we here consider the so-called nudging technique (Hoke & Anthes 1976;Lakshmivarahan & Lewis 2013). It may also be referred to as the state observer technique in the framework of control theory, or more specifically measurement-integrated simulation (Hayase 2015a) in the context of computational fluid dynamics (CFD). Nudging consists of adding a feedback term to the flow governing equations that acts at specified measurement locations (nudging points) and is directly proportional to the difference between reference data and numerical prediction.…”