Relaxation Redistribution Method for model reduction

The Relaxation Redistribution Method (RRM) is based on the notion of slow invariant manifold (SIM) and is applied for constructing a simplified model of detailed multiscale combustion phenomena. The RRM procedure can be regarded as an efficient and stable scheme for solving the film equation of dynamics, where a discrete set of points is gradually relaxed towards the slow invariant manifold (SIM). Here, the global realization of the RRM algorithm is briefly reviewed and used for auto-ignition and adiabatic premixed laminar flame of a homogeneous hydrogen-air ideal gas mixture

The global relaxation redistribution method for reduction of combustion kinetics

An algorithm based on the Relaxation Redistribution Method (RRM) is proposed for constructing the Slow Invariant Manifold (SIM) of a chosen dimension to cover a large fraction of the admissible composition space that includes the equilibrium and the initial state. The manifold boundaries are determined with the help of the Rate Controlled Constrained Equilibrium (RCCE) method, which also provides the initial guess for the SIM. The latter is iteratively refined until convergence and the converged manifold is tabulated. A criterion based on the departure from invariance is proposed to find the region over which the reduced description is valid. The global realization of the RRM algorithm is applied to constant pressure auto-ignition and adiabatic premixed laminar flames of hydrogen-air mixture

Optimal sensor location and reduced order observer design for distributed process systems

9 páginas, 8 figurasThis paper presents a systematic approach to efficiently reconstruct the infinite dimensional field in distributed process systems from a limited, and usually reduced, number of sensors. To that purpose, two basic tools are employed: on the one hand, a reduced order representation of the system which, based on proper orthogonal decomposition (POD) expansions, captures the most relevant dynamic features of the solution. On the other hand, the selection of the most appropriate type (and number) of measurements by the solution of a max–min optimization problem. These ideas will be illustrated on the problem of field reconstruction for unstable tubular reactorsA.A.A. acknowledges the generous support from Xunta de Galicia and Universidade de VigoPeer reviewe

Optimal sensor placement for state reconstruction of distributed process systems

15 páginas, 15 figuras, 2 apéndicesIn this contribution we propose a systematic approach to field reconstruction of distributed process systems from a limited and usually reduced number of measurements. The method exploits the time scale separation property of dissipative processes and concepts derived from principal angles between subspaces, to optimally placing a given number of sensors in the spatial domain. Basic ingredients of the approach include the identification of a low-dimensional subspace capturing most of the relevant dynamic features of the distributed system, and the solution of a max–min optimization problem through a guided search technique. The low-dimensional subspace can be defined either through a spectral basis (eigenfunctions of a linear or linearized part of the operator) or through a semiempirical expansion known in the engineering literature as the Proper Orthogonal Decomposition (POD) or Karhunen–Loeve expansion. For both cases, the optimal sensor placement problem will be solved by taking advantage of the underlying algebraic structure of the low-dimensional subspace. The implications of this approach for dynamic observer design will be discussed together with examples illustrating the proposed methodology.A.A.A. acknowledges the generous support from Xunta de Galicia and Universidade de Vigo; I.G.K. acknowledges support from the National Science Foundation and the AFOSR (Dynamics and Control Program, Dr. Marc Jacobs).Peer reviewe

On the Dynamics and Global Stability Characteristics of Adaptive Systems

We consider the dynamics of some representative adaptively- controlled systems and focus on situations where the desired operating point is locally, but not globally, stable. Perturbations which drive the system from the set point are quantified by computing the boundaries separating the basin of attraction of the set point from the basins of attraction of the other, undesirable attractors. The basins are found to sometimes consist of complicated, disconnected structures in phase space. This results from the nonunique reverse-time dynamics often exhibited by these systems and can be studied by considering the behavior of the reverse-time map along the basin boundaries. The effect of noninvertibility on the forward-time dynamical behavior is also explored

A 2-D DNS study of the effects of nozzle geometry, ignition kernel placement and initial turbulence on prechamber ignition

A parametric direct numerical simulation study was conducted to investigate the effects of the initial flow field (quiescent or turbulent), nozzle inlet sharpness and width, main chamber composition (lean and stoichiometric), and ignition kernel placement in a two-dimensional prechamber (PC) ignition system. The strongly coupled operating and geometric parameters determine the time at which the flame exits the prechamber, the transient structure and penetration of the initially cold and subsequently hot reactive jet and their impingement on the lower main chamber (MC) wall, affecting the combustion mode and the fuel consumption rate. The temperature of the flame reaching and crossing the nozzle is affected by the flame exit time and is significantly lower than the adiabatic flame temperature of the planar flame, although no quenching is observed. Interaction with the flow field (strong small scale vortices for narrow and sharp entry nozzles, large vortices for wide nozzles) generated close to the exit increases the surface area of the flame and its interaction with the MC mixture. Jet penetration and impingement on the lower MC wall is determined by combustion in the PC and the flow field it generates in the main chamber. Impingement results in large scale vortical structures, which further contribute to the flame area increase and accelerate the consumption of the MC charge at later times. For the conditions studied, budget analysis shows that the main combustion mode is premixed deflagration with locally enhanced or reduced reactivity. Local flame–flame interactions which are more pronounced close to the nozzle exit and the lower MC wall can increase the propagation speed up to six times compared to the planar flame. The evolution of the probability density functions of different quantities is used to characterize the strongly transient process. © 2020 The Combustion Institute

Kinetically reduced local Navier-Stokes equations: an alternative approach to hydrodynamics

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers