Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling

The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momentum transfer in the wall-parallel direction. However, the effect of Reynolds stresses cannot be neglected for the thickness of the kinetic boundary layer. Using a conceptual wind model, we find that the friction factor C_f should scale proportional to the thermal boundary layer thickness as C_f ~ lambda_Theta, while the kinetic boundary layer thickness lambda_u scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number lambda_u ~ lambda_Theta^{-1} Re^{-1}. The predicted trends for C_f and \lambda_u are in agreement with DNS results

The turbulence boundary of a temporal jet

We examine the structure of the turbulence boundary of a temporal plane jet at $\mathit{Re}= 5000$ using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity ${v}_{n}$ based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate of entrainment so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude $2{v}_{n}$ and $- {v}_{n}$ , respectively. We further identify a turbulent core region (TC) and a buffer region (BR) connecting the VSL and the TC. The BR grows in time and inviscid enstrophy production is important in this region. The BR shows many similarities with the turbulent-non-turbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e.the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximit

Impact of Air-to-Air Heat Pumps on Energy and Climate in a Mid-Latitude City

Exploring the potential effects of transitioning entirely to air-to-air heat pumps (AAHPs), we use an integrated weather and heat pump model to understand their performance across several building and weather conditions in Toulouse, France. In central Toulouse, where electric and gas heating are similarly adopted, a shift to AAHPs cuts annual electric consumption. Yet, during colder periods, a drop in their efficiency can cause a spike in electricity use. In regions predominantly relying on non-electric heaters, such as gas boilers, introducing AAHPs is expected to increase electricity demand as the heating system transitions to all-electric, though to a lesser extent and with much greater efficiency than traditional systems such as electric resistive heaters. In a separate analysis to evaluate the impact of AAHPs on local climate conditions, we find that AAHPs have a small influence of about 0.5 {\deg}C on the outdoor air temperature. This change is thus unlikely to meaningfully alter AAHPs' performance through feedback.Comment: Submitted manuscrip

Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling

The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momentum transfer in the wall-parallel direction. However, the effect of Reynolds stresses cannot be neglected for the thickness of the kinetic boundary layer. Using a conceptual wind model, we find that the friction factor C_f should scale proportional to the thermal boundary layer thickness as C_f ~ lambda_Theta, while the kinetic boundary layer thickness lambda_u scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number lambda_u ~ lambda_Theta^{-1} Re^{-1}. The predicted trends for C_f and \lambda_u are in agreement with DNS results

Urban air quality: What is the optimal place to reduce transport emissions?

We develop a linear model based on a complex network approach that predicts the effect of emission changes on air pollution exposure in urban street networks including NO–NO2–O3-chemisty. The operational air quality model SIRANE is used to create a weighted adjacency matrix A describing the relation between emissions of a passive scalar inside streets and the resulting concentrations in the street network. A case study in South Kensington (London) is used, and the ad- jacency matrix A0 is determined for one wind speed and eight different wind directions. The physics of the underlying problem is used to infer A for different wind speeds. Good agreement between SIRANE predictions and the model is observed for all but the lowest wind speed, despite non-linearities in SIRANE’s model formulation. An indicator for exposure in the street is developed, and it is shown that the out-degree of the exposure matrix E represents the effect of a change in emissions on the exposure reduction in all streets in the network. The approach is then extended to NO–NO2–O3-chemisty, which introduces a non-linearity. It is shown that a linearised model agrees well with the fully nonlinear SIRANE predictions. The model shows that roads with large height-to-width ratios are the first in which emissions should be reduced in order to maximise exposure reduction

Improving the worthiness of the Elder problem as a benchmark for buoyancy driven convection models

An important trapping mechanism associated with the geosequestration of CO~2~ is that of dissolution into the formation water. Although supercritical CO~2~ is significantly less dense than water, experimental data reported in the literature show that the density of an aqueous solution of CO~2~ could be slightly greater. Under normal situations, the transfer of gas to solution is largely controlled by the relatively slow process of molecular diffusion. However, the presence of variable densities can trigger off gravity instabilities leading to much larger-scale convection processes. Such processes can potentially enhance rates of dissolution by an order of magnitude. Consequently there is a need for future performance assessment models to incorporate buoyancy driven convection (BDC). A major issue associated with BDC models is that of grid convergence when benchmarking to the Elder problem. The Elder problem originates from a heat convection experiment whereby a rectangular Hele-Shaw cell was heated over the central half of its base. A quarter of the way through the experiment, Elder (1967) observed six plumes, with four narrow plumes in the center and two larger plumes at the edges. As the experiment progressed, only four plumes remained. The issue is that depending on the grid resolution used when seeking to model this problem, modelers have found that different schemes yield steady states with either one, two or three plumes. The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem using a pseudospectral method