Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Development and experimental validation of a mathematical model for friction between fabrics and a volar forearm phantom.

An analytical mathematical model for friction between a fabric strip and the volar forearm has been developed and validated experimentally. The model generalizes the common assumption of a cylindrical arm to any convex prism, and makes predictions for pressure and tension based on Amontons' law. This includes a relationship between the coefficient of static friction (mu) and forces on either end of a fabric strip in contact with part of the surface of the arm and perpendicular to its axis. Coefficients of friction were determined from experiments between arm phantoms of circular and elliptical cross-section (made from Plaster of Paris covered in Neoprene) and a nonwoven fabric. As predicted by the model, all values of mu calculated from experimental results agreed within +/- 8 per cent, and showed very little systematic variation with the deadweight, geometry, or arc of contact used. With an appropriate choice of coordinates the relationship predicted by this model for forces on either end of a fabric strip reduces to the prediction from the common model for circular arms. This helps to explain the surprisingly accurate values of mu obtained by applying the cylindrical model to experimental data on real arms.

On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.

Linear and nonlinear model large-eddy simulations of a plane jet

The nonlinear Kosovic, and mixed Leray and α subgrid scale models are contrasted with linear Smagorinsky and Yoshizawa Large Eddy Simulations for a Re = 4000 plane jet simulation. Comparisons are made with Direct Numerical Simulation data and measurements. Global properties of the jet such as the spreading and centreline velocity decay rates are investigated. The mean-flow and turbulence parameters in the self-similar region are also studied. All models generally give encouraging agreement with the Direct Numerical Simulation data and reliable measurements. Solution differences for the models are relatively minor, none giving clear improvements for all data comparisons.

Mixed nonlinear LES for DES suitable flows

It is shown that a new mixed nonlinear/eddy viscosity LES model reproduces profiles better than a number of competing nonlinear and mixed models for plane channel flow. The objective is an LES method that produces a fully resolved turbulent boundary layer and could be applied to a variety of aerospace problems that are currently studied with RANS, RANS-LES, or DES methods that lack a true turbulent boundary layer. There are two components to the new model. One an eddy viscosity based upon the advected subgrid scale energy and a relatively small coefficient. Second, filtered nonlinear terms based upon the Leray regularization. Coefficients for the eddy viscosity and nonlinear terms come from LES tests in decaying, isotropic turbulence. Using these coefficients, the velocity profile matches measurements data at Reτ ≈ 1000 exactly. Profiles of the components of kinetic energy have the same shape as in the experiment, but the magnitudes differ by about 25%. None of the competing LES gets the shape correct. This method does not require extra operations at the transition between the boundary layer and the interior flow.

Stabilization of symmetric formations to motion around convex loops

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms. © 2007 Elsevier B.V. All rights reserved.

Minimum maneuver time calculation using convex optimization

The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution. Copyright © 2013 by ASME.

Preliminary laboratory-scale model auger installation and testing of carbonated soil-MgO columns

This paper presents details of the installation and performance of carbonated soil-MgO columns using a laboratory-scale model auger setup. MgO grout was mixed with the soil using the auger and the columns were then carbonated with gaseous CO2 introduced in two different ways: one using auger mixing and the other through a perforated plastic tube system inserted into the treated column. The performance of the columns in terms of unconfined compressive strength (UCS), stiffness, strain at failure and microstructure (using X-ray diffraction and scanning electron microscopy) showed that the soil-MgO columns were carbonated very quickly (in under 1 h) and yielded relatively high strength values, of 2.4-9.4 MPa, which on average were five times that of corresponding 28-day ambient cured uncarbonated columns. This confirmed, together with observations of dense microstructure and hydrated magnesium carbonates, that a good degree of carbonation had taken place. The results also showed that the carbonation method and period have a significant effect on the resulting performance, with the carbonation through the perforated pipe producing the best results. Copyright © 2013 by ASTM International.

Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction. © 2013 IEEE.