MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers

Flow over an impulsively started low-aspect-ratio flat plate at angle-of-attack is investigated for a Reynolds number of 300. Numerical simulations, validated by a companion experiment, are performed to study the influence of aspect ratio, angle of attack, and planform geometry on the interaction of the leading-edge and tip vortices and resulting lift and drag coefficients. Aspect ratio is found to significantly influence the wake pattern and the force experienced by the plate. For large aspect ratio plates, leading-edge vortices evolved into hairpin vortices that eventually detached from the plate, interacting with the tip vortices in a complex manner. Separation of the leading-edge vortex is delayed to some extent by having convective transport of the spanwise vorticity as observed in flow over elliptic, semicircular, and delta-shaped planforms. The time at which lift achieves its maximum is observed to be fairly constant over different aspect ratios, angles of attack, and planform geometries during the initial transient. Preliminary results are also presented for flow over plates with steady actuation near the leading edge

Supersonic Jet Noise from Round and Chevron Nozzles: Experimental Studies

High speed exhaust noise reduction continues to be a research challenge for supersonic cruise business jets as well as for current and future tactical military aircraft. Significant noise reduction may be possible from advanced concepts for controlling instability generated large-scale turbulence structures in the jet shear layer, generally accepted to be the source of aft-angle noise. In response to this opportunity, our team is focused on experimental diagnostic studies and unique instability modeling suited for identifying control strategies to reduce large scale structure noise. The current paper benchmarks the jet noise from supersonic nozzles designed to provide the supporting experimental data and validation of the modeling. Laboratory scale jet noise experiments are presented for a Mach number of Mj = 1.5 with stagnation temperature ratios ranging from Tr = 0.75 to 2. The baseline configuration is represented by a round converging-diverging (CD) ideal expansion nozzle. A round CD nozzle with chevrons is included as the first of several planned non-circular geometries directed at demonstrating the impact on large scale structure noise and validating noise prediction methods for geometries of future technological interest. Overexpanded and underexpanded conditions were tested on both nozzle configurations. The resulting data base provides an opportunity to benchmark the statistical characteristics of round and chevron nozzle data. The current paper examines far field spectra, directivity patterns, and overall sound pressure level dependence comparing observed characteristics with the fine scale turbulence noise and large-scale turbulence structure noise characteristics identified by Tam. In addition, the paper probes the effect of chevrons on the developing flow field and suppression of screech tones. Measurements are also reported from a far-field narrow aperture phased array system used to map the acoustic source distribution on the jet axis. The dominant source region, situated between the end of the potential core and the sonic point, was found to agree with the peak amplitude location of the jet near field wavepackets measured using a unique near field array. This observation supports the cause-effect link between large-scale turbulence structures in the shear layer and their dominant contribution to aft radiated far field noise

Unstructured Large Eddy Simulation Technology for Prediction and Control of Jet Noise

Development of concepts for reduction of jet noise has relied heavily on expensive experimental testing of various nozzle designs. For example, the design of nozzle serrations (chevron) and internal mixer/ejector nozzles have relied largely on laboratory and full-scale testing. Without a deeper understanding of the sources of high-speed jet noise it is very difficult to effectively design configurations that reduce the noise and maintain other performance metrics such as nozzle thrust. In addition, the high complexity of the flow limits the success of a parametric black-box optimization

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the 6-equation model of Saurel et al. [3] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model of Allaire et al. [1] for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [2] for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of pressure-disequilibrium models. Lastly, the performance of pressure disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed

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.Comment: 19 pages, 9 figures, submitted to J. Comp. Phy