Variable grid scheme applied to turbulent boundary layers
ABSTRACT A Crank-Nicolson type finite-difference scheme with a nonuniform grid spacing has been interpreted in terms of a coordinate stretching approach to show that it is second-order accurate. The variable grid scheme is applied to a flat plate laminar to turbulent boundary layer flow with a rapidly changing grid interval across the layer. The accuracy of the solution is determined for a different number of intervals and compared to results obtained with the Keller box scheme. The influence of changing the grid spacing on the accuracy of the solutions is determined for one coordinate stretching or grid spacing relation. The use of Richardson extrapolation is also investigated.
- AIAA Journal 01/2008; 46(11):2823-2838. · 1.08 Impact Factor
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ABSTRACT: A computational suite called TRANSMAG has been developed to address corrosion of ferritic/martensitic steels and associated transport of corrosion products in the eutectic alloy PbLi as applied to blankets of a fusion power reactor. The computational approach is based on simultaneous solution of flow, energy and mass transfer equations with or without a magnetic field, assuming mass transfer controlled corrosion and uniform dissolution of iron in the flowing PbLi. First, the new tool is applied to solve an inverse mass transfer problem, where the saturation concentration of iron in PbLi at temperatures up to 550 °C is reconstructed from the experimental data on corrosion in turbulent flows without a magnetic field. As a result, a new correlation for the saturation concentration CS has been obtained in the form CS = e13.604–12975/T, where T is the temperature of PbLi in K and CS is in wppm. Second, the new correlation is used in the computations of corrosion in laminar flows in a rectangular duct in the presence of a strong transverse magnetic field. As shown, the mass loss increases with the magnetic field such that the corrosion rate in the presence of a magnetic field can be a few times higher compared to purely hydrodynamic flows. In addition, the corrosion behavior was found to be different between the side wall of the duct (parallel to the magnetic field) and the Hartmann wall (perpendicular to the magnetic field) due to formation of high-velocity jets at the side walls. The side walls experience a stronger corrosion attack demonstrating a mass loss up to 2–3 times higher compared to the Hartmann walls. Also, computations of the mass loss are performed to characterize the effect of the temperature (400–550 °C) and the flow velocity (0.1–1 m/s) on corrosion in the presence of a strong 5 T magnetic field prototypic to the outboard blanket conditions.Journal of Nuclear Materials 01/2013; 432(s 1–3):294–304. · 2.02 Impact Factor
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ABSTRACT: In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k−ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coeffi-cients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which repro-duces these flows accurately, we perform 13 separate Bayesian calibrations – each at a different pressure gradient – using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the to-tal solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncer-tainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.Journal of Computational Physics 02/2014; 258:73-94. · 2.14 Impact Factor