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### GUEST EDITORIAL

J. Fluids Eng. 2007;129(12):1481-1482. doi:10.1115/1.2822659.
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The Navier-Stokes equations (NSE) can be solved directly for laminar flows, but the wide range of eddy scales to be captured prohibits direct numerical simulation for the high Reynolds-number turbulent flows of technological interest. The prevalent remedy to this resolution problem has traditionally involved the Reynolds-averaged Navier-Stokes (RANS) approach, with averaging typically carried out over time or across an ensemble of equivalent flows. The applicability of RANS typically requires that time scales associated with organized unsteady motion be substantially larger than those of turbulent motion. Such statistically steady flow assumptions can be satisfied in many (e.g., low-frequency dominated) unsteady flow applications, but most turbulent flows of interest do not fall into this category.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPERS

J. Fluids Eng. 2007;129(12):1483-1492. doi:10.1115/1.2801684.

Recent progress in understanding the theoretical basis and effectiveness of implicit large eddy simulation (ILES) is reviewed in both incompressible and compressible flow regimes. We use a modified equation analysis to show that the leading-order truncation error terms introduced by certain hybrid high resolution methods provide implicit subgrid scale (SGS) models similar in form to those of conventional mixed SGS models. Major properties of the implicit SGS model are related to the choice of high-order and low-order scheme components, the choice of a flux limiter, which determines how these schemes are blended locally depending on the flow, and the designed balance of the dissipation and dispersion contributions to the numerical solution. Comparative tests of ILES and classical LES in the Taylor–Green vortex case show robustness in capturing established theoretical findings for transition and turbulence decay.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1493-1496. doi:10.1115/1.2801680.

Implicit large eddy simulation (ILES) has provided many computer simulations with an efficient and effective model for turbulence. The capacity for ILES has been shown to arise from a broad class of numerical methods with specific properties producing nonoscillatory solutions using limiters that provide these methods with nonlinear stability. The use of modified equation has allowed us to understand the mechanisms behind the efficacy of ILES as a model. Much of the understanding of the ILES modeling has proceeded in the realm of incompressible flows. Here, we extend this analysis to compressible flows. While the general conclusions are consistent with our previous findings, the compressible case has several important distinctions. Like the incompressible analysis, the ILES of compressible flow is dominated by an effective self-similarity model (Bardina, J., Ferziger, J. H., and Reynolds, W. C., 1980, “Improved Subgrid Scale Models for Large Eddy Simulations  ,” AIAA Paper No. 80–1357; Borue, V., and Orszag, S. A., 1998, “Local Energy Flux and Subgrid-Scale Statistics in Three Dimensional Turbulence  ,” J. Fluid Mech., 366, pp. 1–31; Meneveau, C., and Katz, J., 2000, “Scale-Invariance and Turbulence Models for Large-Eddy Simulations  ,” Annu. Rev. Fluid. Mech., 32, pp. 1–32). Here, we focus on one of these issues, the form of the effective subgrid model for the conservation of mass equations. In the mass equation, the leading order model is a self-similarity model acting on the joint gradients of density and velocity. The dissipative ILES model results from the limiter and upwind differencing resulting in effects proportional to the acoustic modes in the flow as well as the convective effects. We examine the model in several limits including the incompressible limit. This equation differs from the standard form found in the classical Navier–Stokes equations, but generally follows the form suggested by Brenner (2005, “Navier-Stokes Revisited  ,” Physica A, 349(1–2), pp. 60–133) in a modification of Navier–Stokes necessary to successfully reproduce some experimentally measured phenomena. The implications of these developments are discussed in relation to the usual turbulence modeling approaches.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1497-1503. doi:10.1115/1.2801374.

This paper looks at the use of high-resolution and very high-order methods for implicit large-eddy simulation (ILES), with the specific example of simulating the multicomponent two-dimensional single-mode Richtmyer–Meshkov instability for which experimental data is available. The two gases are air and SF6, making stringent demands on the models used in the code. The interface between the two gases is initialized with a simple sinusoidal perturbation over a wavelength of $59mm$, and a shock of strength Mach 1.3 is passed through this interface. The main comparison is between the second-order monotone upwind-centered scheme for conservation law methods of van Leer (1979, “Towards the Ultimate Conservative Difference Scheme  ,” J. Comput. Phys.32, pp. 101–136) and the current state-of-the-art weighted essentially nonoscillatory interpolation, which is presented to ninth order, concentrating on the effect on resolution of the instability on coarse grids. The higher-order methods as expected provide better resolved and more physical features than the second-order methods on the same grid resolution. While it is not possible to make a definitive statement, the simulations have indicated that the extra time required for the higher-order reconstruction is less than the time saved by being able to obtain the same or better accuracy at lower computational cost (fewer grid points). It should also be noted that all simulations give a good representation of the growth rate of the instability, comparing very favorably to the experimental results, and as such far better than the currently existing theoretical models. This serves to further indicate that the ILES approach is capable of providing accurately physical information despite the lack of any formal subgrid model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1504-1513. doi:10.1115/1.2801367.

The paper presents implicit large-eddy simulation (ILES) simulation of a shock tube experiment involving compressible turbulent mixing. A new characteristic-based approximate Riemann solver is derived, and employed in a second-order and fifth-order finite volume Godunov-type ILES framework. The methods are validated against (qualitative) experimental data and then compared and contrasted in terms of resolved turbulent kinetic energy and mixing parameters as a function of grid resolution. It is concluded that both schemes represent the experiment with good accuracy. However, the fifth-order results are approximately equivalent to results gained on double the grid size at second order, whereas the fifth-order method requires only approximately 20% extra computational time.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1514-1523. doi:10.1115/1.2801370.

The present study concerns the application of large eddy simulation (LES) and implicit LES (ILES) to engineering flow problems. Such applications are often very complicated, involving both complex geometries and complex physics, such as turbulence, chemical reactions, phase changes, and compressibility. The aim of the study is to illustrate what problems occur when attempting to perform such engineering flow calculations using LES and ILES, and put these in relation to the issues originally motivating the calculations. The issues of subgrid modeling are discussed with particular emphasis on the complex physics that needs to be incorporated into the LES models. Results from representative calculations, involving incompressible flows around complex geometries, aerodynamic noise, compressible flows, combustion, and cavitation, are presented, discussed, and compared with experimental data whenever possible.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1524-1532. doi:10.1115/1.2801368.

Airborne contaminant transport in cities presents challenging new requirements for computational fluid dynamics. The unsteady flow involves very complex geometry and insufficiently characterized boundary conditions, and yet the challenging and timely nature of the overall problem demands that the turbulence be included efficiently with an absolute minimum of extra memory and computing time requirements. This paper describes the monotone integrated large eddy simulation methodology used in NRL’s FAST3D-CT (CT is contaminant transport) simulation model for urban CT and focuses on critical validation issues that need to be addressed to achieve practical predictability. Progress in validation studies benchmarking with flow data from wind-tunnel urban model simulations and actual urban field studies are reported. Despite inherent physical uncertainties and current model tradeoffs, it is clearly possible to achieve some degree of reliable prediction.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1533-1539. doi:10.1115/1.2801678.

The dynamics of the atmosphere and oceans pose a severe challenge to the numerical modeler, due in large part to the broad range of scales of length and time that are encompassed. Modern numerical methods based on nonoscillatory finite volume (NFV) approximations provide a simple and effective means for mitigating this challenge by reproducing the large scale behavior of turbulent flows with no need for explicit subgrid-scale models. In this paper, we describe the remarkable properties of a particular NFV model, multidimensional positive definite advection transport algorithm, and highlight its application to a variety of meteorological and turbulent flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1540-1546. doi:10.1115/1.2801350.

The inception of leading-edge sheet cavitation on two-dimensional smooth thin hydrofoils at low to moderately high Reynolds number flows is investigated by an asymptotic approach and numerical simulations. The asymptotic theory is based on the work of Rusak (1994, “Subsonic Flow Around Leading Edge of a Thin Aerofoil With a Parabolic Nose  ,” Eur. J. Appl. Mech., 5, pp. 283–311) and demonstrates that the flow about a thin hydrofoil can be described in terms of an outer region, around most of the hydrofoil chord, and an inner region, around the nose, which asymptotically match each other. The flow in the outer region is dominated by the classical thin hydrofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number (ReM ) are used to correctly account for the nonlinear behavior and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model (simplified) problem of a uniform flow past a semi-infinite smooth parabola with a far-field circulation governed by a parameter Ã that is related to the hydrofoil’s angle of attack, nose radius of curvature, and camber. The model parabola problem consists of a viscous flow that is solved numerically for various values of Ã and ReM to determine the minimum pressure coefficient and the cavitation number for the inception of leading-edge cavitation as function of the hydrofoil’s geometry, flow Reynolds number, and fluid thermodynamic properties. The predictions according to this approach show good agreement with results from available experimental data. This simplified approach provides a universal criterion to determine the onset of leading-edge (sheet) cavitation on hydrofoils with a parabolic nose in terms of the similarity parameters Ã and ReM and the effect of hydrofoil’s thickness ratio, nose radius of curvature, camber, and flow Reynolds number on the onset.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1547-1558. doi:10.1115/1.2801361.

The effect of uniform surface blowing and suction on the wake dynamics and the drag and lift forces on a sphere is studied using a high-resolution direct numerical simulation technique. The sphere Reynolds number Re, based on its diameter and the freestream velocity, is in the range 1–300. The onset of recirculation in the sphere wake occurs at higher Re, and the transition to nonaxisymmetry and unsteadiness occurs at lower Re in the presence of blowing. The size of the recirculation region increases with blowing, but it nearly disappears in the case of suction. Wake oscillation also increases in the presence of blowing. The drag coefficient in the presence of blowing is reduced compared to that in uniform flow, in the range $10, whereas it is increased in the presence of suction. The reduction in the wake pressure minimum associated with the enhanced vortical structures is the primary cause for drag reduction in the case of blowing. In the case of suction, it is the increased surface vorticity associated with the reduction of the boundary layer that results into increased drag. The fluctuations in the instantaneous lift and drag coefficients are significant for blowing, and they result from the asymmetric movement of the wake pressure minimum associated with the shedding process.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1559-1564. doi:10.1115/1.2801352.

Adiabatic capillary tubes and short tube orifices are widely used as expansive devices in refrigeration, residential air conditioners, and heat pumps. In this paper, a generalized neural network has been developed to predict the mass flow rate through adiabatic capillary tubes and short tube orifices. The input/output parameters of the neural network are dimensionless and derived from the homogeneous equilibrium flow model. Three-layer backpropagation (BP) neural network is selected as a universal function approximator. Log sigmoid and pure linear transfer functions are used in the hidden layer and the output layer, respectively. The experimental data of R12, R22, R134a, R404A, R407C, R410A, and R600a from the open literature covering capillary and short tube geometries, subcooled and two-phase inlet conditions, are collected for the BP network training and testing. Compared with experimental data, the overall average and standard deviations of the proposed neural network are 0.75% and 8.27% of the measured mass flow rates, respectively.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1565-1576. doi:10.1115/1.2801356.

The incipience of two-phase flow in discharging branches from a stratified gas-liquid region has major implications in industrial applications where safety is of concern. An experimental investigation of the liquid side flow field at the onset of gas entrainment, in a single downward oriented discharging branch, was presented. Particle image velocimetry was used to measure the liquid side flow field in horizontal and vertical planes. Averaged velocity profiles were presented and demonstrated a highly radial flow. The particle image velocimetry data were validated using continuity and showed that the mass flow rate to be in the range of 10–25% of the expected value. Further, the vortex-free flow field assumption, used previously in the development of analytical and empirical models, was found to be reasonable.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(12):1577-1583. doi:10.1115/1.2801365.

The effect of yaw angle and cavity depth on the resulting flow field of cavities with elliptical planform areas embedded in a low velocity turbulent boundary layer was investigated experimentally. A 2:1 elliptical cavity with depth to minor axis ratios ranging from 0.1 to 1.0 was tested in a wind tunnel facility. Surface pressure measurements and wake velocity measurements, using hot-wire anemometry, were conducted to examine the resulting flow regimes. The results indicated several different flow regimes for the different yaw angle and cavity depth configurations. Cellular structures were observed when the minor axis was aligned with the streamwise direction. Yawing the cavity with respect to the streamwise direction resulted in a highly asymmetric flow regime. This flow regime was also associated with high drag for certain cavity depth configurations. A nominally two-dimensional flow regime was observed for large yaw angles, when the major axis of the cavity was aligned with the streamwise direction. The yaw angle had only a minor effect on the flow regimes associated with the shallowest and deepest cavities examined. A strong resemblance was found between the flow regimes associated with elliptical and rectangular cavities for similar yaw and depth configurations. This similarity was also observed in the lift and drag coefficients for the different yaw angles and cavity depths. This indicated that the wall radius of curvature of elliptical cavities has a negligible effect on the resulting flow regimes when compared to rectangular cavities.

Commentary by Dr. Valentin Fuster