Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Wall Shear Fluctuations in a Turbulent Boundary Layer

IN the last two decades, the instantaneous structure of a turbulent boundary layer has been examined by many in an effort to understand the dynamics of the flow. Distinct and well-defined flow patterns that seem to have great relevance to the turbulence production mechanism have been observed in the wall region.1'2 The flow near the wall is intermittent with periodic eruptions of the fluid, a phenomenon generally termed "bursting process." Earlier investigations in this field were limited to liquid flows at low speeds and the entire flowpattern was observed using flow visualization techniques.Study was later extended to boundary-layer flows in windtunnels at higher speeds and Reynolds numbers using hot-wiresignals for the analysis of the bursting phenomenon.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.

Microstructural evolution and grain boundary sliding in a superplastic magnesium AZ31 alloy

Tensile experiments on a fine-grained single-phase Mg–Zn–Al alloy (AZ31) at 673 K revealed superplastic behavior with an elongation to failure of 475% at 1 × 10−4 s−1 and non-superplastic behavior with an elongation to failure of 160% at 1 × 10−2 s−1; the corresponding strain rate sensitivities under these conditions were 0.5 and 0.2, respectively. Measurements indicated that the grain boundary sliding (GBS) contribution to strain ξ was 30% under non-superplastic conditions; there was also a significant sharpening in texture during such deformation. Under superplastic conditions, ξ was 50% at both low and high elongations of 20% and 120%; the initial texture became more random under such conditions. In non-superplastic conditions, deformation occurred under steady-state conditions without grain growth before significant flow localization whereas, under superplastic conditions, there was grain growth during the early stages of deformation, leading to strain hardening. The grains retained equiaxed shapes under all experimental conditions. Superplastic deformation is attributed to GBS, while non-superplastic deformation is attributed to intragranular dislocation creep with some contribution from GBS. The retention of equiaxed grain shapes during dislocation creep is consistent with a model based on local recovery related to the disturbance of triple junctions.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Unsteady Self-similar Stagnation Point Boundary Layers for Micropolar Fluids

The self-similar solution of the unsteady laminar incompressible two-dimensional and axisymmetric stagnation point boundary layers for micropolar fluids governing the flow and heat transfer problem has been obtained when the free stream velocity and the square of the mass transfer vary inversely as a linear function of time. The nonlinear ordinary differential equations governing the flow have been solved numerically using a quasilinear finite-Difference scheme. The results indicate that the coupling parameter, mass transfer and unsteadiness in the free stream velocity strongly affect the skin friction, microrotation gradient and heat transfer whereas the effect of microrotation parameter is strong only on the microrotation gradient. The heat transfer is strongly dependent on the prandtl number whereas the skin friction gradient are unaffected by it.

Boundary layer transition observations on a body of revolution with surface heating and cooling in water

Boundary layer flow visualization in water with surface heat transfer was carried out on a body of revolution which had the predicted possibility of laminar separation under isothermal conditions. Flow visualization was by in-line holographic technique. Boundary layer stabilization, including elimination of laminar separation, was observed to take place on surface heating. Conversely, boundary layer destabilization was observed on surface cooling. These findings are consistent with the theoretical predictions of Wazzan et al. in The stability and transition of heated and cooled incompressible laminar boundary layers, in Proceedings of the Fourth International Heat Transfer Conference, Vol. 2, FCI 4. Elsevier, Amsterdam (1970).

Unsteady nonsimilar compressible laminar two-dimensional and axisymmetric boundary-layer flows

Unsteady nonsimilar laminar compressibletwo-dimensional and axisymmetric boundarylayer flows have been studied when external velocity varies arbitrarily with time and the flow is nonhomentropic. The governing nonlinear partial differential equations with three independent variables have been solved using an implicit finite difference scheme with quasilinearization technique from the origin to the point of zero skin-friction. The results have been obtained for (i) an accelerating stream and (ii) a fluctuating stream. The skin friction responds to the fluctuations in the free stream more compared to the heat transfer. It is observed that Mach number and hot wall cause the point of zero skin friction to occur earlier whereas cold wall delays it.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

EPR studies on donor doped BaTiO3 grain boundary layer ceramic dielectrics

Donor doped BaTiO3 ceramics become insulating5 under controlled conditions with effective dielectric constants >10. The changes in EPR signals indicate that a certain fraction of the donor doped BaTiO3 is cubic even at room temperature and that the cubic fraction increases with the donor content. X-ray powder diffraction data support the EPR results. The coexistence of both the phases over a range of temperature is characteristic of diffused phase transition. The effect of grain size variation on EPR signal intensities indicate that the boundary layers surrounding the grains may constitute the cubic phase as a result of higher Ba-vacancies and donor contents at the grain boundary layer than in the bulk. Since the acceptor states arising from the Ba-vacancies and the impurities are activated in the cubic phase, they capture electrons from the conduction band, rendering the cubic phase electrically more insulating than the semiconductive tetragonal grain interiors. Thus, the cubic grain boundary layers act as effective dielectric media where the field tends to concentrate.

Structural phase transition study of the morphotropic phase boundary compositions of Na0.5Bi0.5TiO3-PbTiO3

Neutron, synchrotron x-ray powder diffraction and dielectric studies have been performed for morphotropic phase boundary (MPB) compositions of the (1 - x )Na1/2Bi1/2TiO3-xPbTiO(3) system. At room temperature, the MPB compositions (0.10 < x <= 0.15) consist of a mixture of rhombohedral (space group R3c) and tetragonal ( space group P4mm) structures with the fraction of tetragonal phase increasing with increasing PbTiO3 content. On heating, while the rhombohedral phase just outside the MPB region, i.e. x = 0.10, transforms directly to a cubic phase, the rhombohedral phase of the MPB compositions transforms gradually to a tetragonal phase, until interrupted by a rhombohedral-cubic phase transition. The correspondence of the dielectric anomalies with the structural transitions of the different compositions has been examined and compared with earlier reports.

Solutions of Boundary Layer Equations Governing Free Convective and Magnetohydrodynamic Flows through Parametric Differentiation

In der vorliegenden Arbeit wird die Methode der parametrischen Differentiation angewendet, um ein System nichtlinearer Gleichungen zu lösen, das zwei- und dreidimensionale freie, konvektive Grenzschichströmungen bzw. eine zweidimensionale magnetohydrodynamische Grenzschichtströmung beherrscht. Der Hauptvorteil dieser Methode besteht darin, daß die nichlinearen Gleichungen auf lineare reduziert werden und die Nichtlinearität auf ein System von Gleichungen erster Ordnung beschränkt wird, das, verglichen mit den ursprünglichen Nichtlinearen Gleichungen, viel leichter gelöst werden kann. Ein anderer Vorzug der Methode ist, daß sie es ermöglicht, die Lösung von einer bekannten, zu einem bestimmten Parameterwert gehörigen Lösung aus durch schrittweises Vorgehen die Lösung für den gesamten Parameterbereich zu erhalten. Die mit dieser Methode gewonnenen Ergebnisse stimmen gut mit den entsprechenden, mit anderen numerischen Verfahren erzielten überein.

A parametric differentiation version with finite-difference scheme applicable to a class of problems in boundary layer flow with massive blowing

A numerical procedure, based on the parametric differentiation and implicit finite difference scheme, has been developed for a class of problems in the boundary-layer theory for saddle-point regions. Here, the results are presented for the case of a three-dimensional stagnation-point flow with massive blowing. The method compares very well with other methods for particular cases (zero or small mass blowing). Results emphasize that the present numerical procedure is well suited for the solution of saddle-point flows with massive blowing, which could not be solved by other methods.

Boundary-layer flows with swirl and large suction

An analytical solution is presented for the laminar swirling flow in a tube. Attention is given to a particular type of swirling flow corresponding to a zero longitudinal acceleration parameter, with large suction at the surface. The investigation shows that in the case of very large rates of suction the velocity overshoot can be almost eliminated. This is even possible in flows with swirls which are characterized by a velocity overshoot in the longitudinal direction.