to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Driven by functionality and purity demand for applications of inorganic nanoparticle colloids in optics, biology, and energy, their surface chemistry has become a topic of intensive research interest. Consequently, ligand-free colloids are ideal reference materials for evaluating the effects of surface adsorbates from the initial state for application-oriented nanointegration purposes. After two decades of development, laser synthesis and processing of colloids (LSPC) has emerged as a convenient and scalable technique for the synthesis of ligand-free nanomaterials in sealed environments. In addition to the high-purity surface of LSPC-generated nanoparticles, other strengths of LSPC include its high throughput, convenience for preparing alloys or series of doped nanomaterials, and its continuous operation mode, suitable for downstream processing. Unscreened surface charge of LSPC-synthesized colloids is the key to achieving colloidal stability and high affinity to biomolecules as well as support materials,...

Laser Synthesis and Processing of Colloids: Fundamentals and Applications

Cavitation and Bubble Dynamics: Preface

We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence statistics that are very similar to the implicit LES results. However, while the explicit LES requires a tailored high-order low-dissipative numerical method that applies numerical dissipation only in shock normal direction, no such ad hoc adjustments are necessary with the proposed implicit LES method.

Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction

We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics. The thermodynamic model is embedded into an implicit large-eddy simulation (LES) environment. The considered configuration follows the general setup of a reference experiment and is a generic reproduction of a scaled-up fuel injector or control valve as found in an automotive engine. Due to the experimental conditions, it operates, however, at significantly lower pressures. LES results are compared to the experimental reference for validation. Three different operating points are studied, which differ in terms of the development of cavitation regions and the jet break-up characteristics. Observed differences between experimental and numerical data in some of the investigated cases can be caused by uncertainties in meeting nominal parameters by the experiment. The investigation reveals that three main mechanisms promote primary jet break-up: collapse-induced turbulent fluctuations near the outlet, entrainment of free gas into the nozzle, and collapse events inside the jet near the liquid-gas interface.

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Large-eddy simulation of cavitating nozzle flow and primary jet break-up

Cavitation erosion is the consequence of repeated collapse-induced high pressure-loads on a material surface. The present paper assesses the prediction of impact load spectra of cavitating flows, i.e., the rate and intensity distribution of collapse events based on a detailed analysis of flow dynamics. Data are obtained from a numerical simulation which employs a density-based finite volume method, taking into account the compressibility of both phases, and resolves collapse-induced pressure waves. To determine the spectrum of collapse events in the fluid domain, we detect and quantify the collapse of isolated vapor structures. As reference configuration we consider the expansion of a liquid into a radially divergent gap which exhibits unsteady sheet and cloud cavitation. Analysis of simulation data shows that global cavitation dynamics and dominant flow events are well resolved, even though the spatial resolution is too coarse to resolve individual vapor bubbles. The inviscid flow model recovers increasingly fine-scale vapor structures and collapses with increasing resolution. We demonstrate that frequency and intensity of these collapse events scale with grid resolution. Scaling laws based on two reference lengths are introduced for this purpose. We show that upon applying these laws impact load spectra recorded on experimental and numerical pressure sensors agree with each other. Furthermore, correlation between experimental pitting rates and collapse-event rates is found. Locations of high maximum wall pressures and high densities of collapse events near walls obtained numerically agree well with areas of erosion damage in the experiment. The investigation shows that impact load spectra of cavitating flows can be inferred from flow data that captures the main vapor structures and wave dynamics without the need for resolving all flow scales.

Cavitation erosion prediction based on analysis of flow dynamics and impact load spectra

The objective of this paper is the assessment of the numerical predictability of erosive events arising in cavitating flows. First, a numerical method and an efficient thermodynamic model for the simulation of cavitating flows are briefly described. The prediction of typical flow details is evaluated by simulating the 3-D flow around a quasi 2-D NACA hydrofoil. We find that the maximum length of the attached cavity, the Strouhal number, and the average diameter of detached clouds are essentially grid independent. Scale enrichment and enhanced 3-D flow details are observed on refined grids. Even delicate flow features, such as cavitating vortices and irregular 3-D break-up patterns, are reproduced, provided that the spatial resolution is sufficiently high. The simulation of cloud collapses and resulting instantaneous peak pressures is assessed in a second investigation. Here, we analyze the effect of the computational grid resolution with respect to typical collapse characteristics, such as the collapse duration, and the instantaneous maximum pressure within the flow field and at walls. The proposed methodology is confirmed by a third investigation, where an experimental setup to investigate cavitation erosion is simulated, and regions of experimentally observed cavitation damage are compared with numerical predictions of strong collapses. The excellent agreement of numerically predicted collapse positions and experimentally observed damage justifies the proposed methodology.

Assessment of Erosion Sensitive Areas via Compressible Simulation of Unsteady Cavitating Flows

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben et al. [1]. While a diesel-like test fuel was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for water and vapor and a simple phase-change model based on equilibrium assumptions. Our LES resolve all wave dynamics in the compressible fluid and the turbulence production in shear layers. 1. INTRODUCTION Turbulence modeling and the numerical discretization of the Navier-Stokes equations are strongly coupled in Large Eddy Simulations (LES). Since subgrid-scale (SGS) models generally operate on scales that are only marginally resolved by the underlying numerical method, the truncation error of common approximations for the convective terms can out-weigh the effect of even physically sound models. This interference is especially severe in LES of cavitating flows, as numerical errors of robust discretizations increase notably at discontinuities such as phase boundaries and shock waves that are generated by vapor-bubble collapses. A different approach is to exploit this link by developing discretization methods from subgrid-scale models, or vice versa. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). SGS effects are modeled explicitly if the underlying conservation law is modified and subsequently discretized. The filtering concept of Leonard [2] is commonly employed for deriving explicit SGS models without reference to a computational grid and without taking into account a discretization scheme. As implicit modeling we denote the situation when the unmodified conservation law is discretized and the numerical truncation error acts as an SGS model. Since this SGS model is implicitly contained within the discretization scheme, an explicit computation of model terms becomes unnecessary. Most previous approaches to implicit SGS modeling have relied on the application of pre-existing discretization schemes to fluid-flow turbulence. Consequently, methods with suitable implicit SGS models have usually been found by trial and error, which has led to the common belief that an implicit subgrid-scale model is merely inferred by the choice of discretization. Comparative studies have shown that stabilizing under-resolved simulations by upwind or non-oscillatory schemes is insufficient for accurately representing SGS turbulence. For example, Honein and Moin [3] found that traditional ILES required differently tuned parameters to predict the correct decay rates of different quantities. Employing implicit LES for prediction requires numerical methods that are specially designed, optimized and validated for the particular differential equation to be solved. A full coupling of the SGS model and the discretization scheme cannot be achieved without incorporating physical reasoning into the design of the implicit SGS model. Implicit SGS modeling requires procedures for design, analysis, and optimization of nonlinear discretization schemes. We have proposed such a systematic framework that resulted in the adaptive local deconvolution method (ALDM), see Refs. [4,5]. ALDM is a nonlinear finite volume scheme based on a solution adaptive deconvolution operator and a numerical flux function. Free parameters inherent to the discretization allow to control the truncation error and have been calibrated in such a way that the truncation error acts as a physically motivated SGS model. The compressible version of ALDM, see Ref. [5], is asymptotically consistent with incompressible turbulence theory, which is essential for cavitating low Mach number flows. Yet, the numerical discretization is robust enough to survive strong shock waves [6]. In this paper, we present the first implicit LES of a compressible cavitating two-phase flow. The thermodynamic model and the numerical method are derived in Sections 2 and 3, respectively. A validation of the novel method is presented in Section 4. As the test case we chose a micro channel with a step-like restriction, which is representative for typical cavitating-flow situations in fuel injectors. This setup follows closely an experimental study of Iben et al. [1]. While a diesel-like fuel with confidential properties was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for vapor and water and a simple phase-change model.

Implicit Large Eddy Simulation of Cavitation in Micro Channel Flows

A compressible 2D Euler CFD code is utilised for the numerical simulation of compressible cavitating liquids with a density-based numerical scheme which has been proved to capture shock-induced dynamics that are the origin of erosion damages [22]. A barotropic cavitation model is applied on planar micro throttles where the qualitative impact of the following parameters on the location and strength of erosion is evaluated and compared to experimental data:  Channel inlet geometry, round versus sharp inlet shape  Channel inlet and outlet pressure  Fluid inlet temperature While the erosion strength and location in the experiment is evaluated by temporal sequences of the material erosion, an erosion probability based on pressure thresholds is extracted from the simulation results which quantifies the magnitude of the stress on the wall. By comparing the wall stress magnitude (simulation) and the material erosion (experiment), the qualitative influence of the channel inlet geometry as well as the inlet and outlet pressure can be well captured. The temperature impact on erosion can not be predicted by the barotropic model. NOMENCLATURE

Numerical simulation of collapse induced shock dynamics for the prediction of the geometry, pressure and temperature impact on the cavitation erosion in micro channels

M. Mihatsch

Papers

Cavitation erosion prediction based on analysis of flow dynamics and impact load spectra

Assessment of Erosion Sensitive Areas via Compressible Simulation of Unsteady Cavitating Flows

Implicit Large Eddy Simulation of Cavitation in Micro Channel Flows

Numerical simulation of collapse induced shock dynamics for the prediction of the geometry, pressure and temperature impact on the cavitation erosion in micro channels

Assessment of the Prediction Capability of a Thermodynamic Caviation Model for the Collapse Characteristics of a Vapor-Bubble Cloud