SUMMARYThe stability of flow in a lid-driven cavity is investigated using an accurate numerical technique based on a hybrid scheme with spectral collocation and high-order finite differences. A global stability analysis is carried out and critical parameters are identified for various aspect ratios. It is found that while there is reasonable agreement with the literature for the critical parameters leading to loss of stability for the square cavity, there are significant discrepancies for cavities of aspect ratios 1.5 and 2. Simulations of the linearized unsteady equations confirm the results from the global stability analysis for aspect ratios A = 1, 1.5 and A = 2.
Towards meeting the objective of simulating heat transfer processes in urban areas, the study of dispersion from a scalar (ground) surface area source has been addressed as a first step, as dispersion from such a source is in some ways analogous to heat transfer from the surface. Two different urban-like geometries are considered in this study: an array with uniform height cubes and an array with random height cuboids. Some point measurement dispersion experiments in a wind tunnel have previously been carried out in identical arrays using a naphthalene sublimation technique. Large-eddy simulations (LES) of these experiments have been performed as a validation study and the details, presented here, demonstrate the influence of the roughness morphology on the dispersion processes and the power of LES for obtaining physically important scalar turbulent flux information.
field studies included several vegetation (e.g. Gao et al., 1989) and urban (e.g. Chris-35 ten et al., 2007) areas to understand the similarities and differences in the transport 36 of momentum and heat over the two kinds of canopies. One of the similarities that 37 was observed is that sweep events contribute most to the momentum flux below and 38 immediately above the canopy height and ejection events dominate further above the 39 canopy; these events are considered to be the signatures of the large coherent struc- computational studies can therefore be particularly useful. 46The simplest geometry, yet challenging if thermal stratification is included, is tional studies (e.g. Cai, 2012;Kim and Baik, 1999;Park et al., 2012). In the case of 65It is necessary to quantify the effects of such thermal stratification on street and/or 66 neighborhood scale flows in order to provide required parameters for city or regional 67 scale modelling. For this purpose, we first performed computations to simulate pas-68 sive scalar dispersion from a surface area source in an array of uniform and random 69 height blocks (Boppana et al., 2010), followed by simulation of heat transfer from 70 the strongly heated leeward surface of a large building (Boppana et al., 2013). These investigations led naturally to the current LES study where, instead of heating a sin-75 gle surface of an isolated obstacle, the entire ground surface (i.e. all streets, in direct 76 contact with the atmosphere) is uniformly heated (see Fig. 1) or cooled and the re-77 sulting buoyancy effects are included to model the flow over an array of staggered 78 cubes. It is to be noted that, in this study, thermal stratification in a fully-developed 79 boundary layer is a result of surface heating or cooling within the bottom canopy, 80 which is rather different to the case of a thermally stratified approach flow over an 81 unheated region (e.g. Xie et al., 2013). 82The overall goal of the present paper is to obtain insights on the effects of uniform 83 ground heating or cooling on the flow over an array of uniform height staggered 84 buildings. To address this, the following objectives were formulated: (1) Numerical Details and Settings 92The filtered continuity and Navier-Stokes equations governing unsteady incompress-and,The resolved-scale velocity and pressure are respectively given by u i and p with u, 96v and w the streamwise, lateral and vertical velocity components respectively. The 97 flow was driven by a constant mean streamwise pressure gradient ∂ P /∂ x and δ i1 is 98 the Kronecker-delta. f δ i3 is the body force due to thermal buoyancy and is estimated 99 using the Boussinesq approximation. ρ and ν are the density and kinematic viscosity 100 of the fluid. τ i j is the subgrid-scale (SGS) Reynolds stress and was handled using 101 the Smagorinsky model in conjunction with a Lilly damping function near the walls. 102We set Smagorinsky's constant C s = 0.1 since this was found to provide satisfactory 103 results in our earlier computations (Boppana et...
Large-eddy simulations of the dispersion from scalar line sources at various locations within a fully developed turbulent channel flow at Re = uh/ν = 10400 are presented. Both mean and fluctuating scalar quantities are compared with those from the single available set of experimental data (Lavertu and Mydlarski, 2005) and differences are highlighted and discussed. The results are also discussed in the context of scalar dispersion in other kinds of turbulent flows, e.g. homogeneous shear-flow. Initial computations at a much lower Reynolds number are also reported and compared with the two available direct numerical simulation data sets.
The local thermal effects in the wake of a single cube with a strong heated 6 rear face, representing a large building in an urban area, are studied using large-eddy ter. Quadrant analysis along the shear layer behind the cube showed that the strength 19 of sweeps that contribute to momentum flux is considerably enhanced by heating. 20The contribution of different quadrants to the heat flux is found to be very different 21 to that of the momentum flux for lower Ri. (Sini et al., 1996;Kim and Baik, 1999; Li et al., 2010; Cheng and Liu, 35 2011;Cai, 2012; Park et al., 2012). In these studies, it was observed that buoyancy 36 forces due to ground or leeward wall heating strengthen the intensity of the circula-37 tion within the canyon, resulting in increases in the vertical exchange rates of passive (Nottrott et al., 2011). This implies that grid resolution in the computations has to be 52 very fine, or that sophisticated near-wall models need to be developed. 53Therefore, with the broader aim of simulating canopy stability effects in urban 54 areas and obtaining accurate estimates of the heat flux from building walls by resolv-55 ing the thermal boundary layer, we first simulated dispersion from a passive scalar 56 area source in an array of roughness elements using LES (Boppana et al., 2010). This 57 is analogous to dispersion from surface heat sources when the resulting temperature 58 differences are sufficiently small that they do not influence the flow dynamics. These -and this paper presents the results. A wind-tunnel study by Richards et al. (2006), 63 in which the leeward face of a cube was heated, was considered to be appropriate 64 for validation of our numerical methodology. Hereafter, 'experiments' refer to this 65 wind-tunnel study unless specified otherwise. 66The numerical details of the computational study are outlined in Sect. 2. In Sect. 3, The filtered continuity and Navier-Stokes equations governing unsteady incompressible flow areandThe resolved-scale velocity and pressure are respectively given by u i and p with u, The filtered governing equation for temperature iswhere θ is the resolved-scale temperature. k s is the subgrid turbulent diffusivity and 89 is given by ν s /Pr s , where ν s is the subgrid viscosity and Pr s is the subgrid Prandtl 90 number whose value was set to 0.9. k m is the molecular diffusivity and is defined as 91 ν/Pr m . The gradient (normal to the boundary) of the temperature was set to zero at 92 the top of the domain and at the outlet. 93A finite volume approach was followed to discretize the flow and temperature 94 equations. The monotone advection and reconstruction scheme (?) with a blending 95 factor of 0.9 was used for the spatial convective terms and the central difference 96 scheme is used for spatial diffusive terms of (1) is the distance from the wall to the centre of the first grid). 146In order to understand the local thermal effects on the flow, experiments were 147 conducted for various Ri, defined asHere β is the coefficient of the...
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