Marek Morzynski

Poznan University of Technology · Chair of Virtual Engineering

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier–Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of...

We propose the first least-order Galerkin model of an incompressible flow undergoing two successive supercritical bifurcations of Hopf and pitchfork type. A key enabler is a mean-field consideration exploiting the symmetry of the base flow and the asymmetry of the fluctuation. These symmetries generalize mean-field theory, e.g. no assumption of slo...

We present the first application of a Smith predictor in the model-based feedback control of a convectively unstable flow. The two-dimensional incompressible mixing layer is chosen as a plant and integrated with a finite-element Navier-Stokes solver. The flow is actuated by a modulation of the inflow mimicking a pulsed jet actuator. The state is mo...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of...

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised data comparison. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric quantifies the overlap between these attractors in three steps. First, all states are clustered into dis...

The paper aims to build a reduced order model (ROM) of the left and right ventricle of a human heart. The input heart model is build from 3D sets of registered, flexible surface meshes for the left and right ventricle, resulting from the MRI data. Spatial and temporal variables are separated using Proper Orthogonal Decomposition. It enables data re...

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer t...

Characterizing and controlling nonlinear, multi-scale phenomena play important roles in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic mod...

A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$ th mode is defined recursively in an analogous manner bas...

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit...

In this paper, we propose a novel framework to extract features such as vortex cores and saddle points in two-dimensional unsteady flows. This feature extraction strategy generalizes critical points of snapshot topology in a Galilean-invariant manner, allows to prioritize features according to their strength and longevity, enables to track the temp...

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional,...

Reduced order models allow quickly predict fluid behaviour and to better understand flow phenomena. They are the key enablers of closed-loop flow control. In this paper, reduced-order model (ROM) of an incompressible flow around a wall-mounted cylinder is constructed, by means of Galerkin projection of Navier-Stokes equations onto space spanned by...

A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N-1 modes. The...

The method for computation of stability modes for two- and three-dimensional flows is presented. The method is based on the Dynamic Mode Decomposition of the data resulting from Direct Numerical Simulation of the flow in the regime close to stable flow (fixed-point dynamics, small perturbations about steady flow). The proposed approach is demonstra...

In the IDIHOM Project three aeroelastic testcases have been calculated. Two of them - LANN Wing and DLR-F6 wing-body configuration - have been conducted by PUT. The last one, the HART II rotor has been prepared by NLR. Each partner has used different technology and software tools, hence each of the testcases describes the results of the simulation...

Article presents the development process of aeroelastic system basing on finite volume CFD solver for higher order methods. The main aspect is interpolation tools which allows application of Discontinuous Galerkin solution of CFD solver. There is also described the elastic analogy deformation tool for curvilinear mesh. To summarize, the two testcas...

The article presents elastic analogy approach of deformation curvilinear meshes applied in aeroelastic simulations. The details of algorithm used in developed software with the new metrics designated for high-order mesh quality assessment are presented. The article ends the example of LANN wing deformed by featured tool. Presented software allows c...

In this paper analysis of scalability of the solver UNS3, dedicated to direct numerical simula-tion (DNS) of Navier-Stokes equations, is presented. Efficiency of parallel computations has been examined with the use of a PC cluster built by the Division of Virtual Engineering. Tests have been carried out on a different number of partitions, in the r...

Cluster-based reduced-order modelling (CROM) builds on the pioneering works of Gunzburger's group in cluster analysis [1] and Eckhardt's group in transition matrix models [2] and constitutes a potential alternative to reduced-order models based on a proper-orthogonal decomposition (POD). This strategy frames a time-resolved sequence of fl...

This article presents application of modal analysis for the computation of biometric data base (3D faces) and extraction of three dimensional geometrical features. Traditional anthropometric database contains information only about some characteristic points recorded as linear or angular dimensions. The current face recognition systems are also bas...

Physical flow modes are of particular interest for Reduced Order Flow Control-Oriented Models. Computation of physical modes as the eigensolution of linearized Navier-Stokes equations is a cumbersome and difficult task, especially for large, 3D problems. Instead we propose the solution of Navier-Stokes equation in the frequency domain and investiga...

Phenomena occurring in the flows are very complex. Their interpretation, as well as an effective impact on them in the flow control is often only possible with the use of modal analysis and low-dimensional models. In this paper, the selected modal decomposition techniques, namely Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DM...

Principal Component Analysis, a statistical tool allowing to create a low dimensional subspace basing on input data, finds many applications in biomechanics. The PCA requires the same topology (mesh connectivity, number of nodes) for all objects in database. To achieve this, each new object added to database must be registered. In this article the...

Flow-induced de§ections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like §utter or bueting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the §ow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto s...

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model...

We propose a general framework for parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in traditional approaches. The proposed formulation relies on variational data assimilation using measurement da...

Expansion of computer technologies allow using numerical simulation in the early stages of aircraft design more and more often. The role of both wind tunnels and initial test flights used to verify the validity of solutions seems to be diminishing. Big systems for three-dimensional simulations of Fluid-Structure Interactions (FSI) constitute highly...

In the current study, Reduced Order Models (ROMs) targeting strategies for experimental feedback flow control are discussed. For practical reasons, such models should incorporate a range of flow operating conditions with a small number of degrees of freedom. Standard POD Galerkin models are challenged by overoptimization at one operating condition...

Galerkin Projection is one of the most popular methods of flow model’s reduction. Mode basis used in Galerkin expansion allows reconstruction of the flow for a given set boundary and operating conditions. In the case of changing flow conditions, used mode basis has to be adjusted, for example using mode parametrization [1] or Continuous Mode Interp...

Expansion of computer technology enables use of computer simulation for prediction of aircraft characteristics in early stages of design. These simulation nowadays include highly sophisticated and reliable aerodynamics computations as well as solutions of coupled aeroelastic interactions. In this paper we consider numerical simulation of the full...

Low order Galerkin models were originally introduced as an effective tool for stability analysis of fixed points and, later, of attractors, in nonlinear distributed systems. An evolving interest in their use as low complexity dynamical models, goes well beyond that original intent. It exposes often severe weaknesses of low order Galerkin models as...

This article presents application of modal analysis for the computation of data base of biological objects set and extraction of three dimensional geometrical features. Traditional anthropometric database contains information only about some characteristic points recorded as linear or angular dimensions. The current face recognition systems are als...

Low-dimensional models, allowing quick prediction of fluid behaviour, are key enablers of closed-loop flow control. Reduction of the model's dimension and inconsistency of high-fidelity data set and the reduced-order formulation lead to the decrease of accuracy. The quality of Reduced-Order Models might be improved by a calibration procedure. It le...

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow...

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability ana...

Global stability analysis of fluid flows is presented as a method of extracting physical eigenmodes with associated linear dynamic models. These reduced-order models (ROM) are optimal for the transients near the onset of instability. We describe the computational aspects of the eigenmode extraction in detail. This outline includes (i) the discretiz...

A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirica...

The natural and periodically forced flow around a two-dimensional bluff body with a blunt rear end are numerically investigated using an unsteady Reynolds-averaged Navier-Stokes (URANS) calculation. The applied zero-net-mass-flux forcing at the rear end corners of the body leads to a drag reduction due to a significantly higher pressure at the ster...

We propose a system reduction strategy for spectral and Galerkin models of incompressible fluid flows. This approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced models, slow dynamics are incorporated as non-linear manifold consistent with mean-field theory. Fast dynamics are stochast...

The necessity to include dynamic mean field representations in low order Galerkin models, and the role and form of such representations, are explored along natural and forced transients of the cylinder wake flow. The shift mode was introduced by Noack et al. J. Fluid Mech. 497, 335 2003 as a least-order Galerkin representation of mean flow variatio...

The Navier-Stokes equations are the trusted description for many flows of practical relevance. Ample physical and engineering expertize is necessary to accommodate this description to an industrial setting. Presently and in predictable future there will be no CFD method to simulate the flow ranging from large coherent structures to the Kolmogorov s...

This article presents application of the PCA (Principal Component Analysis) method for analysis and computation of three dimensional biometric description of 3D objects. As the data input the geometrical data sets (threedimensional points coordinates) of faces are used. Authors apply 3D version of PCA method for numerical estimation of similarity a...

ABSTRACT In this paper fluid-structure interaction, taking into account the nonlinearity of structural models, is concerned. This phenomenon has important influence in many aeronautical applications. The method and developed system is demonstrated on NACA-0012 wing mounting, made of nonlinear springs and include structures with nonlinear materials,...

Landau's (1944) celebrated amplitude equation dA/dt = sigmaA - betaA^3 for a supercritical Hopf bifurcation connects linear instability with a nonlinear amplitude saturation mechanism, thereby describing the transient and post-transient phase of oscillations. This model is significantly generalized for a much larger class of laminar to turbulent sh...

In the paper the structural optimization method based on trabecular bone surface adaptation is presented. The basis for numerical algorithm formulation was the phenomenon of bone adaptation to mechanical stimulation, whereas the theoretical ground for the method is based on the mechanical theory of the stiffest design. The resulting optimization sy...

Solution of the global flow stability problem delivers not only information about the growth rate of disturbances and respective frequencies. Eigenvectors of this system constitute physical modes space useful in Low Dimensional Modeling of the flow and flow control design. The 3D global stability solutions are rare and mostly limited to structured...

An approximate POD algorithm provides an empirical Galerkin approximation with guaranteed a priori lower bound on the required resolution. The snapshot ensemble is partitioned into several sub-ensembles. Cross correlations between these sub-ensembles are approximated in terms of a far smaller correlation matrix. Computational speedup is nearly line...

Turbulentfluidhasoftenbeenconceptualizedasatransientthermodynamicphase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The pro- posed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dimensional...

Three-dimensional global flow stability analysis generates very large complex generalized eigenvalue problem. Solution of the global flow stability problem delivers not only information about the growth rate of disturbances and respective frequencies. Eigenvectors of this system constitute physical modes space necessary in Low Dimensional Modeling...

The construction of low‐dimensional models of the flow, containing only reduced number of degrees of freedom, is the essential prerequisite of closed‐loop control of that flow. Presently used models usually base on the Galerkin method, where the flow is approximated by the number of modes and coefficients. The velocities are computed from a system...

Model reduction based on Galerkin projection is a key technique used in feedback flow control. It significantly accelerates the flow computations, and thus it can be suitable for the aeroelastic simulations or, generally, in the flow analysis of changing configurations and boundaries. The present paper concerns the reduced-order Galerkin modelling...

This article presents application of the Principal Component Analysis method for analysis of geometry of biological objects and computation of three dimensional anthropometric database. In this work as the biological objects the fifteen human femur bones were used. The geometry of each bone was obtained by using 3D structural light scanner. For PCA...

Turbulent fluid has often been conceptualized as a transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The proposed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dim...

We propose a nonlinear flow control strategy using a low-dimensional Galerkin model. This control design is successfully applied to the stabilization of the flow around a circular cylinder by a transverse local volume force. This wake stabilization problem is a well-established flow control benchmark. A state estimation is needed, since the informa...

The generalized mean field model has been introduced by Noack & al. (JFM, 2003) as a critical enabler for very low dimensional Galerkin fluid models of transient dynamics. As originally introduced, it uses a shift mode to resolve the global state space direction of natural transient changes in the base flow. Here we highlight a physics interpretati...

A finite-time thermodynamics (FTT) formalism (Andresen, Salamon & Berry 1977) is proposed to compute the mean flow and fluctuation levels of unsteady, incompressible, shear flows. That formalism yields a definition for a thermodynamic degree of freedom of the velocity fluctuation as well as conditions for local thermal equilibrium. In general, the...

In the current study, a hierarchy of control-oriented Galerkin models is proposed targeting least-dimensional representations at different operating conditions. These models are employed for passive as well as active actuation. In passive control, a linearised model is shown to reproduce a wake stabilization experiment of Strykowski & Sreenivasan (...

The objective of this paper is twofold. One is to explore extensions of the generalized mean-field empirical Galerkin model, previously developed for wake instabilities1 to sin- gularly actuated 2D airfoils, including a high lift configuration and a single airfoil at a high angle of attack. We present a minimum order mean field model, explore the r...