0

### Editorial

J. Fluids Eng. 2014;136(6):060201-060201-1. doi:10.1115/1.4027341.

This special section of the Journal of Fluids Engineering is dedicated to Professor M. Yousuff Hussaini's 70th birthday. It is a great honor to bring out this issue to honor this eminent scholar and scientific leader. Professor Hussaini is among those scientists who have made pioneering and innovative contributions in fluid dynamics, scientific computing research, and provided key scientific leadership in critical NASA research efforts.

Commentary by Dr. Valentin Fuster

### Special Section Articles

J. Fluids Eng. 2014;136(6):060901-060901-5. doi:10.1115/1.4025674.

Fourier analysis of incompressible, homogeneous magnetohydrodynamic (MHD) turbulence produces a model dynamical system on which to perform numerical experiments. Statistical methods are used to understand the results of ideal (i.e., nondissipative) MHD turbulence simulations, with the goal of finding those aspects that survive the introduction of dissipation. This statistical mechanics is based on a Boltzmannlike probability density function containing three “inverse temperatures,” one associated with each of the three ideal invariants: energy, cross helicity, and magnetic helicity. However, these inverse temperatures are seen to be functions of a single parameter that may defined as the “temperature” in a statistical and thermodynamic sense: the average magnetic energy per Fourier mode. Here, we discuss temperature and entropy in ideal MHD turbulence and their use in understanding numerical experiments and physical observations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060902-060902-5. doi:10.1115/1.4023787.

Flows over airfoils and blades in rotating machinery for unmanned and microaerial vehicles, wind turbines, and propellers consist of different flow regimes. A laminar boundary layer near the leading edge is often followed by a laminar separation bubble with a shear layer on top of it that experiences transition to turbulence. The separated turbulent flow then reattaches and evolves downstream from a nonequilibrium turbulent boundary layer to an equilibrium one. Typical Reynolds-averaged Navier–Stokes (RANS) turbulence modeling methods were shown to be inadequate for such laminar separation bubble flows (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Direct numerical simulation (DNS) is the most reliable but is also the most computationally expensive alternative. This work assesses the capability of large eddy simulations (LES) to reduce the resolution requirements for such flows. Flow over a flat plate with suitable velocity boundary conditions away from the plate to produce a separation bubble is considered. Benchmark DNS data for this configuration are generated with the resolution of 59 × 106 mesh points; also used is a different DNS database with 15 × 106 points (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Results confirm that accurate LES are possible using O(1%) of the DNS resolution.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060903-060903-8. doi:10.1115/1.4026234.

Accurate simulation of the fuel-air mixing environment is crucial for high-fidelity scramjet calculations. We compute the velocity fields of jet into supersonic freestream flow and cavity flow typical of scramjet flame-holding applications at different scale resolutions using the partially-averaged Navier–Stokes (PANS) method. We present a sequence of variable resolution computations to demonstrate the potential of PANS method for high-speed mixing environment calculations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060904-060904-7. doi:10.1115/1.4026868.

We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDFs) of order $p≥2$, for the numerical solution of two-dimensional, time-dependent, nonlinear, convection-diffusion partial differential equation (PDE) systems in Cartesian domains. The proposed algorithms, which do not require the solution of nonlinear systems, additionally produce solutions of spectral accuracy in space through the use of Chebyshev approximations. In particular, these methods give rise to minimal artificial dispersion and diffusion and they therefore enable use of relatively coarse discretizations to meet a prescribed error tolerance for a given problem. A variety of numerical results presented in this text demonstrate high-order accuracy and, for the particular cases of $p=2,3$, unconditional stability.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060905-060905-12. doi:10.1115/1.4025866.

A new time domain methodology for Computational Aeroacoustics (CAA) is proposed. The time domain wave packet (TDWP) method employs a temporally compact broadband pulse for acoustic sources. As the radiation and transmission of acoustic waves of all frequencies within the numerical resolution are embedded in the propagation of the wave packet, acoustic solution of the full spectrum become available at once. In addition, it becomes possible to separate the acoustic and instability waves in shear flows in the time domain wave packet method due to the compactness of the wave packet. The instability waves can further be suppressed by a source filtering technique, applied after the acoustic wave packet has propagated through the shear layers. Details on the source filtering technique used in the paper are presented. The TDWP method has been validated using a CAA Benchmark problem. The TDWP method is also applied to the NASA/GE Fan Noise Source Diagnostic Test (SDT) exhaust radiation problem.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060906-060906-12. doi:10.1115/1.4024809.

This article presents Large Eddy Simulations of thermal boundary layer spatial development in a low-Mach number turbulent channel flow. A coupling between isothermal biperiodic channel and anisothermal open channel is done to obtain a fully developed turbulent inlet. The interaction between a high temperature gradient and a turbulent flow is studied during the thermal boundary layer development. Turbulence and temperature quantities are analyzed for both streamwise and wall-normal directions. The results show how the asymmetrical heating modifies the velocity of the flow. The correlation between turbulence and heat transfers is studied. The mean and the fluctuation profiles are found to be asymmetrical. They evolve along the channel and are perturbed by the thermal gradient. Fluctuation destruction and creation areas in the length of the channel are highlighted.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060907-060907-10. doi:10.1115/1.4025254.

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060908-060908-8. doi:10.1115/1.4025657.

Nested numerical simulations of ionospheric plasma density structures associated with nonlinear evolution of the Rayleigh–Taylor (RT) instability in equatorial spread F (ESF) are presented. The numerical implementation of the nested model uses a spatial discretization with a C grid staggering configuration where normal velocities of ions and electrons are staggered one-half grid length from the density of charged particles. The advection of charged particles is computed with a fifth order accurate in space weighted essentially nonoscillatory (WENO) scheme. The continuity equation is integrated using a third-order Runge–Kutta (RK) time integration scheme. The equation for the electric potential is solved at each time step with a multigrid method. For the limited area and nested simulations, the lateral boundary conditions are treated via implicit relaxation applied in buffer zones where the density of charged particles for each nest is relaxed to that obtained from the parent domain. The high resolution in targeted regions offered by the nested model was able to resolve secondary RT instabilities, and to improve the resolution of the primary RT bubble compared to the coarser large domain model. The computational results are validated by conducting a large domain simulation where the resolution is increased everywhere.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060909-060909-8. doi:10.1115/1.4025936.

It is accustomed to think that turbulence models based on solving the Reynolds-averaged Navier–Stokes (RANS) equations require empirical functions to accurately reproduce the behavior of flow characteristics of interest, particularly near a wall. The current paper analyzes how choosing a model for pressure-strain correlations in second-order closures affects the need for introducing empirical functions in model equations to reproduce the flow behavior near a wall correctly. An axially rotating pipe flow is used as a test flow for the analysis. Results of simulations demonstrate that by using more physics-based models to represent pressure-strain correlations, one can eliminate wall functions associated with such models. The higher the Reynolds number or the strength of imposed rotation on a flow, the less need there is for empirical functions regardless of the choice of a pressure-strain correlation model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060910-060910-15. doi:10.1115/1.4026021.

The nonlinear growth of instabilities of an outward propagating, but decelerating, cylindrical interface separated by fluids of different densities is investigated. Single mode perturbations are introduced around the contact-surface, and their evolution is studied by conducting inviscid 2D and 3D numerical simulations. In the past, a significant amount of work has been carried out to model the development of the perturbations in a planar context where the contact surface is stationary or in a spherical context where a point-source blast wave is initiated at the origin. However, for the finite-source cylindrical blast-wave problem under consideration, there is a need for a framework which includes additional complexities such as compressibility, transition from linear to nonlinear stages of instability, finite thickness of the contact interface (CI), and time-dependent deceleration of the contact surface. Several theoretical potential flow models are presented. The model which is able to capture the above mentioned effects (causing deviation from the classical Rayleigh–Taylor Instability (RTI)) is identified as it compares reasonably well with the DNS results. Only for higher wavenumbers, the early development of secondary instabilities (Kelvin–Helmholtz) complicates the model prediction, especially in the estimation of the high-density fluid moving into low-density ambient.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060911-060911-7. doi:10.1115/1.4026023.

The flow induced by a round turbulent offset jet in a low-aspect ratio cylinder is investigated experimentally, with applications to degassing of U.S. Strategic Petroleum Reserves (SPR). Particle image velocimetry and flow visualization are used for flow diagnostics. The measurements include the jet penetration (mixing) depth l, jet spreading rate, and the mean velocity/vorticity fields for different offset positions Δ. With the introduction of offset, the flow patterns change drastically. For 0 < Δ/D < 0.2 the jet deflects toward the wall while precessing (as in the axisymmetric case), for 0.2 < Δ/D < 0.4 the jet hugs the wall but with an oscillating tail, and for 0.45 < Δ/D the jet appears as a wall jet. In all cases, the jet is destroyed at a certain distance (mixing or penetration depth) from the origin. This mixing depth takes its lowest value for 0 < Δ/D < 0.2, with l ≈ (3.2–3.6)D, becomes maximum at Δ/D = 0.4 with l ≈ 5.2D, and drops to l ≈ 4.5D when the jet is close to the wall. Recommendations are made for suitable Δ/D values for optimal operation of SPR degassing.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060912-060912-5. doi:10.1115/1.4026619.

We analyze a large database generated from recent direct numerical simulations (DNS) of passive scalars sustained by a homogeneous mean gradient and mixed by homogeneous and isotropic turbulence on grid resolutions of up to 40963 and extract the turbulent Schmidt number over large parameter ranges: the Taylor microscale Reynolds number between 8 and 650 and the molecular Schmidt number between 1/2048 and 1024. While the turbulent Schmidt number shows considerable scatter with respect to the Reynolds and molecular Schmidt numbers separately, it exhibits a sensibly unique functional dependence with respect to the molecular Péclet number. The observed functional dependence is motivated by a scaling argument that is standard in the phenomenology of three-dimensional turbulence.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060913-060913-11. doi:10.1115/1.4026416.

The performance of the large eddy simulation (LES) approach in predicting the evolution of a shear layer in the presence of stratification is evaluated. The LES uses a dynamic procedure to compute subgrid model coefficients based on filtered velocity and density fields. Two simulations at different Reynolds numbers are simulated on the same computational grid. The fine LES simulated at a low Reynolds number produces excellent agreement with direct numerical simulations (DNS): the linear evolution of momentum thickness and bulk Richardson number followed by an asymptotic approach to constant values is correctly represented and the evolution of the integrated turbulent kinetic energy budget is well captured. The model coefficients computed from the velocity and the density fields are similar and have a value in range of $0.01-0.02$. The coarse LES simulated at a higher Reynolds number Re = 50,000 shows acceptable results in terms of the bulk characteristics of the shear layer, such as momentum thickness and bulk Richardson number. Analysis of the turbulent budgets shows that, while the subgrid stress is able to remove sufficient energy from the resolved velocity fields, the subgrid scalar flux and thereby the subgrid scalar dissipation are underestimated by the model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(6):060914-060914-3. doi:10.1115/1.4026283.

An elementary closure theory is used to compute the scaling of anisotropic contributions to the correlation function in homogeneous turbulence. These contributions prove to decay with wavenumber more rapidly than the energy spectrum; this property is sometimes called the “recovery of isotropy” at small scales and is a key hypothesis of the Kolmogorov theory. Although comparisons with a more comprehensive theory suggest that the present theory is too crude, its elementary character makes the scaling analysis straightforward. The analysis reveals some characteristic features of anisotropic turbulence, including “angular” energy transfer in wavevector space.

Commentary by Dr. Valentin Fuster

### Research Papers: Fundamental Issues and Canonical Flows

J. Fluids Eng. 2014;136(6):061201-061201-11. doi:10.1115/1.4026662.

Tuned liquid dampers (TLDs) are considered economical and effective dynamic vibration absorbers. They are increasingly being used to mitigate the dynamic resonant response of tall buildings and it is often designed to reduce the structure's acceleration at a serviceability limit state. Slat screens can increase the inherent damping factor of TLDs. They have been used as a common flow damping device in TLDs because of the simplicity of using them and also the ability to control their effects on the performance of a TLD. Two slat screens with the same solidity ratio and different patterns could have different effects on the TLD's performance. Many former numerical researches used the potential and linear theory as a base to describe the fluid flow behavior inside the TLD. The applicability of the linearized flow models was for the condition of the low amplitude of excitations. Under large excitation events such as high return period wind storms or earthquakes, the assumptions of linear theory are no longer valid. Moreover, in the linearized model, screens were modeled as a hydraulic resistance point as a function of the screen solidity ratio without the ability to consider the effect of screen pattern. In the present study, a numerical algorithm has been developed which can handle both the small and large amplitude of excitations. In this algorithm, the fluid flow through the screen is fully resolved and it can take into account the effect of the screen pattern on the TLD's performance. The major focus of this paper is to use this developed algorithm and conduct a numerical investigation to study the effects of the slat screen pattern on the inherent damping and natural frequency of the TLD, as the design parameters of the TLD. In this numerical investigation a selected TLD outfitted by different slat screens and interacted with the structure is exposed by both harmonic and random external excitations. The numerical results have been validated against experimental work. The effect of slat screen pattern on the damping effect and natural frequency of a TLD has been presented. Also in this study, two new parameters termed as slat ratio (SR) and effective solidity ratio (Seff) are presented to imply the physical significance of screen pattern.

Commentary by Dr. Valentin Fuster