arXiv subjects

Tim Colonius

Publications and source records attributed to Tim Colonius.

At least 37 records · Page 2Linked to original sources

arXiv2023

Linear Analysis of Boundary-Layer Instabilities on a Finned-Cone at Mach 6

Boundary-layer instabilities for a finned cone at Mach=6, $Re=8.4 \times 10^6$ [m$^{-1}$], and zero incidence angle are examined using linear stability methods of varying fidelity and maturity, following earlier analysis presented in [doi.org/10.2514/6.2022-3247]. The geometry and laminar flow conditions correspond to experiments conducted at the Boeing Air Force Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. Where possible, a common mean flow is utilized among the stability computations, and comparisons are made along the acreage of the cone where transition is first observed in the experiment. Stability results utilizing Linear Stability Theory (LST), planar Parabolized Stability Equations (planar-PSE), One-Way Navier Stokes (OWNS), forced direct numerical simulation (DNS), and Adaptive Mesh Refinement Wavepacket Tracking (AMR-WPT) are presented. A dominant three-dimensional vortex instability occurring at $\approx$ 250 kHz is identified that correlates well with experimental measurements of transition onset. With the exception of LST, all of the higher-fidelity linear methods considered in this work were consistent in predicting the initial growth and general structure of the vortex instability as it evolved downstream. Some of the challenges, opportunities, and development needs of the stability methods considered are discussed.

physics.flu-dyn↗

arXiv2023

A quantitative comparison of phase-averaged models for bubbly, cavitating flows

We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh-Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.

physics.flu-dyn↗

arXiv2022

Global receptivity analysis: physically realizable input-output analysis

In the context of transition analysis, linear input-output analysis determines worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically-realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic, and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations (DNS) for a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

physics.flu-dyn↗

arXiv2021

Conditional moment methods for polydisperse cavitating flows

The dynamics of cavitation bubbles are important in many flows, but their small sizes and high number densities often preclude direct numerical simulation. We present a computational model that averages their effect on the flow over larger spatiotemporal scales. The model is based on solving a generalized population balance equation (PBE) for nonlinear bubble dynamics and explicitly represents the evolving probability density of bubble radii and radial velocities. Conditional quadrature-based moment methods (QBMMs) are adapted to solve this PBE. A one-way-coupled bubble dynamics problem demonstrates the efficacy of different QBMMs for the evolving bubble statistics. Results show that enforcing hyperbolicity during moment inversion (CHyQMOM) provides comparable model-form accuracy to the traditional conditional method of moments and decreases computational costs by about ten times for a broad range of test cases. The CHyQMOM-based computational model is implemented in MFC, an open-source multi-phase and high-order-accurate flow solver. We assess the effect of the model and its parameters on a two-way coupled bubble screen flow problem.

physics.flu-dyn↗

arXiv2021

Efficient global resolvent analysis via the one-way Navier-Stokes equations. Part 2. Optimal response

In this study, we develop an efficient approach for approximating resolvent modes via spatial marching. Building on the methodology from Part 1, we leverage the ability of the projection-based formulation of the one-way Navier-Stokes equations (OWNS) to efficiently and accurately approximate the downstream response of the linearized Navier-Stokes equations to forcing for problems containing a slowly varying direction. Using an adjoint-based optimization framework, forcings that optimally excite a response in the flow are computed by marching the forward and adjoint OWNS equations in the downstream and upstream directions, respectively. This avoids the need to solve direct and adjoint globally-discretized equations, therefore bypassing the main computational bottleneck of a typical global resolvent calculation. The method is demonstrated for a supersonic turbulent jet at Mach 1.5 and a transitional zero-pressure-gradient flat-plate boundary layer flow at Mach 4.5, and the optimal OWNS results are validated against corresponding global calculations.

physics.flu-dyn↗

arXiv2021

Efficient global resolvent analysis via the one-way Navier-Stokes equations. Part 1. Forced response

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equation describing the downstream-traveling waves supported by the linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier-Stokes equations, approximates the action of the resolvent operator on a forcing vector. This capability is leveraged in part 2 of the paper to compute approximate resolvent modes. The method is validated and demonstrated using the examples of a simple acoustics problem and a supersonic turbulent jet.

physics.flu-dyn↗

arXiv2021

Resolvent-based modeling of turbulent jet noise

Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate resolvent analysis as an acoustic analogy that relates the near-field resolvent forcing to the near- and far-field pressure. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, $r/D = [5,6]$, while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We find that a single resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, $St = [0-1]$, and azimuthal wavenumbers, $m=[0,2]$. Finally, we present a simple function that results in a rank-1 resolvent model agreeing within 2dB of the peak noise for both jets.

physics.flu-dyn↗

arXiv2021

Hybrid quadrature moment method for accurate and stable representation of non-Gaussian processes and their dynamics

Solving the population balance equation (PBE) for the dynamics of a dispersed phase coupled to a continuous fluid is expensive. Still, one can reduce the cost by representing the evolving particle density function in terms of its moments. In particular, quadrature-based moment methods (QBMMs) invert these moments with a quadrature rule, approximating the required statistics. QBMMs have been shown to accurately model sprays and soot with a relatively compact set of moments. However, significantly non-Gaussian processes such as bubble dynamics lead to numerical instabilities when extending their moment sets accordingly. We solve this problem by training a recurrent neural network (RNN) that adjusts the QBMM quadrature to evaluate unclosed moments with higher accuracy. The proposed method is tested on a simple model of bubbles oscillating in response to a temporally fluctuating pressure field. The approach decreases model-form error by a factor of 10 when compared to traditional QBMMs. It is both numerically stable and computationally efficient since it does not expand the baseline moment set. Additional quadrature points are also assessed, optimally placed and weighted according to an additional RNN. These points further decrease the error at low cost since the moment set is again unchanged.

math.NA↗

arXiv2021

Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity resolvent model, with a single coefficient, provides substantial agreement between SPOD and resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.

physics.flu-dyn↗

arXiv2020

Lift Coefficient Estimation for a Rapidly Pitching Airfoil

We develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. The approach assimilates four surface pressure measurements with a modified nonlinear state space model (Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient estimates based only on a weighted-sum of the measured pressures are found to be noisy and biased, which leads to inaccurate estimates. The estimate is improved by including the predictive model in an conventional Kalman filter. The Goman-Khrabrov model is shown to be a linear parameter-varying system and can therefore be used in the Kalman filter without the need for linearization. Additional improvement is realized by modifying the algorithm to provide more accurate estimate of the lift coefficient. The improved Kalman filtering approach results in a bias-free lift coefficient estimate that is more precise than either the pressure-based estimate or the Goman-Khrabrov model on their own. The new method will enable performance enhancements in aerodynamic systems whose performance relies on lift.

physics.flu-dyn↗

arXiv2020

Acoustic Cavitation Rheometry

Characterization of soft materials is challenging due to their high compliance and the strain-rate dependence of their mechanical properties. The inertial microcavitation-based high strain-rate rheometry (IMR) method [Estrada et al., J. Mech. Phys. Solids, 2018, 112, 291-317] combines laser-induced cavitation measurements with a model for the bubble dynamics to measure local properties of polyacrylamide hydrogel under high strain-rates from $10^3$ to $10^8$ s$^{-1}$. While promising, laser-induced cavitation involves plasma formation and optical breakdown during nucleation, a process that could alter local material properties before measurements are obtained. In the present study, we extend the IMR method to another means to generate cavitation, namely high-amplitude focused ultrasound, and apply the resulting acoustic-cavitation-based IMR to characterize the mechanical properties of agarose hydrogels. Material properties including viscosity, elastic constants, and a stress-free bubble radius are inferred from bubble radius histories in $0.3\%$ and $1\%$ agarose gels. An ensemble-based data assimilation is used to further help interpret the obtained estimates. The resulting parameter distributions are consistent with available measurements of agarose gel properties and with expected trends related to gel concentration and high strain-rate loading. Our findings demonstrate the utility of applying IMR and data assimilation methods with single-bubble acoustic cavitation data for measurement of viscoelastic properties.

cond-mat.soft↗

arXiv2020

Multi-resolution lattice Green's function method for incompressible flows

We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.

physics.comp-ph↗

arXiv2020

Dynamics and decay of a spherical region of turbulence in free space

We perform direct numerical simulation (DNS) and large eddy simulation (LES) of an initially spherical region of turbulence evolving in free space. The computations are performed with a lattice Green's function method, which allows the exact free-space boundary conditions to be imposed on a compact vortical region. LES simulations are conducted with the stretched vortex sub-grid stress model. The initial condition is spherically windowed, isotropic homogeneous incompressible turbulence. We study the spectrum and statistics of the decaying turbulence and compare the results with decaying isotropic turbulence, including cases representing different low wavenumber behavior of the energy spectrum (i.e. k^2 versus k^4). At late times the turbulent sphere expands with both mean radius and integral scale showing similar time-wise growth exponents. The low wavenumber behavior has little effect on the inertial scales, and we find that decay rates follow Saffman (1967) predictions in both cases, at least until about 400 initial eddy turnover times. The boundary of the spherical region develops intermittency and features ejections of vortex rings. These are shown to occur at the integral scale of the initial turbulence field and are hypothesized to occur due to a local imbalance of impulse on this scale.

physics.flu-dyn↗

arXiv2020

QBMMlib: A library of quadrature-based moment methods

QBMMlib is an open source Mathematica package of quadrature-based moment methods and their algorithms. Such methods are commonly used to solve fully-coupled disperse flow and combustion problems, though formulating and closing the corresponding governing equations can be complex. QBMMlib aims to make analyzing these techniques simple and more accessible. Its routines use symbolic manipulation to formulate the moment transport equations for a population balance equation and a prescribed dynamical system. However, the resulting moment transport equations are unclosed. QBMMlib trades the moments for a set of quadrature points and weights via an inversion algorithm, of which several are available. Quadratures then closes the moment transport equations. Embedded code snippets show how to use QBMMlib, with the algorithm initialization and solution spanning just 13 total lines of code. Examples are shown and analyzed for linear harmonic oscillator and bubble dynamics problems.

physics.comp-ph↗

arXiv2020

Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations

Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D--Var method (En4D--Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin--Voigt material. Results show that En4D--Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D--Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the viscosity is reduced in some cases due to material damage occurring at bubble collapse.

physics.comp-ph↗

arXiv2020

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes, and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as $St/m \rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.

physics.flu-dyn↗

arXiv2020

Dynamics of an inverted cantilever plate at moderate angle of attack

The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle ($α\leq 30^{\circ}$) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The dynamics are shown to differ significantly from the zero-angle-of-attack case, commonly called the inverted-flag configuration. Four distinct dynamical regimes arise at finite angles: a small oscillation around a small-deflection equilibrium (deformed regime), a small-amplitude flapping motion, a large-amplitude flapping motion and a small oscillation around a large-deflection equilibrium (deflected regime). The small-amplitude flapping motion appears gradually as the flow speed is increased and is consistent with a limit-cycle oscillation caused by the quasi-steady fluid forcing. The large-amplitude flapping motion is observed to appear at a constant critical flow speed that is independent of angle of attack. Its characteristics match those of the large-amplitude vortex-induced vibration present at zero angle of attack. The flow speed at which the plate enters the deflected regime decreases linearly as the angle of attack is increased, causing the flapping motion to disappear for angles of attack greater than $α\approx 28^{\circ}$. Finally, the effect of aspect ratio on the plate dynamics is considered, with reduced aspect ratio plates being shown to lack sharp distinctions between regimes.

physics.flu-dyn↗

arXiv2020

On the formation and recurrent shedding of ligaments in droplet aerobreakup

The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as capillary effects. After thorough validation of the simulations with respect to the experiments, we elucidate the ligament formation process and the effect of surface tension. By Fourier decomposition of the flow field, we observe the development of specific azimuthal modes, which destabilize the liquid sheet surrounding the droplet. Eventually, the liquid sheet is ruptured, which leads to the formation of ligaments. We further observe the ligament formation and shedding to be a recurrent process. While the first ligament shedding weakly depends on the Weber number, subsequent shedding processes seem to be driven primarily by inertia and the vortex shedding in the wake of the deformed droplet.

physics.flu-dyn↗