Instability of Combined Forced and Free Flow in an Inclined Porous Channel

2016 ◽  
Vol 13 (02) ◽  
pp. 1640001 ◽  
Author(s):  
Antonio Barletta ◽  
Michele Celli
Keyword(s):  
Shooting Method ◽  
Numerical Technique ◽  
Heat Fluxes ◽  
Basic Flow ◽  
Porous Channel ◽  
Neutral Stability ◽  
Weighted Residuals ◽  
Method Of Weighted Residuals ◽  
Thermoconvective Instability ◽  
Downslope Flow

The aim of this paper is to analyze the onset of convective instability in a plane porous channel inclined to the horizontal. A net upslope or downslope flow is considered, so that mixed convection takes place as caused by the uniform and symmetric heat fluxes prescribed on the impermeable bounding walls. The thermoconvective instability of the basic flow is studied versus small-amplitude wavelike perturbations. The hybrid analytical–numerical technique adopted in this paper, in order to track and illustrate the parametric changes of neutral stability curves, is Galerkin’s method of weighted residuals. Numerical values at significant points on the neutral stability curves are obtained by employing an accurate Runge–Kutta solver combined with the shooting method.

On Hadley flow in a porous layer with vertical heterogeneity

2012 ◽  
Vol 710 ◽  
pp. 304-323 ◽  
Author(s):  
A. Barletta ◽  
D. A. Nield
Keyword(s):  
Thermal Conductivity ◽  
Temperature Gradient ◽  
Porous Layer ◽  
Plane Waves ◽  
Neutral Stability ◽  
Horizontal Temperature Gradient ◽  
Weighted Residuals ◽  
Thermal Boundary Conditions ◽  
Vertical Heterogeneity ◽  
Thermoconvective Instability

AbstractThe onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability.

Inverse Heat Conduction Applied to the Measurement of Heat Fluxes on a Rotating Cylinder: Comparison Between an Analytical and a Numerical Technique

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Fabien Volle ◽  
Michel Gradeck ◽  
Denis Maillet ◽  
Arsène Kouachi ◽  
Michel Lebouché
Keyword(s):  
Heat Flux ◽  
Numerical Technique ◽  
Rotating Cylinder ◽  
Local Heat ◽  
Heat Fluxes ◽  
Inverse Heat Conduction ◽  
Analytical Technique ◽  
Inner Radius ◽  
Direct Model ◽  
Stable Estimation

A method using either a one-dimensional analytical or a two-dimensional numerical inverse technique is developed for measurement of local heat fluxes at the surface of a hot rotating cylinder submitted to the impingement of a subcooled water jet. The direct model calculates the temperature field inside the cylinder that is submitted to a given nonuniform and time dependent heat flux on its outer surface and to a uniform surface heat source on an inner radius. In order to validate the algorithms, simulated temperature measurements inside the cylinder are processed and used by the two inverse techniques to estimate the wall heat flux. As the problem is improperly posed, regularization methods have been introduced into the analytical and numerical inverse algorithms. The numerical results obtained using the analytical technique compare well with the results obtained using the numerical algorithm, showing a good stable estimation of the available test solutions. Furthermore, real experimental data are used for the estimation, and local boiling curves are plotted and discussed.

Modeling of a Urea SCR Catalyst With Automotive Applications

2002 ◽  
Author(s):  
Devesh Upadhyay ◽  
Michiel Van Nieuwstadt
Keyword(s):  
Catalytic Reduction ◽  
Chemical Properties ◽  
Lumped Parameter Model ◽  
Scr Catalyst ◽  
Weighted Residuals ◽  
Method Of Weighted Residuals ◽  
Lumped Parameter ◽  
1D Model ◽  
Continuously Stirred Tank Reactor ◽  
Three State Model

A zero order lumped parameter control oriented model of a Selective Catalytic Reduction (SCR) catalyst is presented. The lumped parameter model is developed using two approaches. in the first approach it was assumed that the catalyst behaves as an Isothermal Continuously Stirred Tank Reactor (ICSTR). The second approach involved deriving the lumped parameter model from a 1D model using the method of weighted residuals. Both approaches led to a three state model, with the gas phase concentrations of NOx and NH3 and the surface coverage fraction as the states. The model depends on chemical properties specific to the SCR catalyst; consequently model validation requires knowledge of these parameters, either via laboratory-based experiments or as supplied by the catalyst supplier. We present an alternate approach that allows estimation of the essential parameters through a minimization of the l2 errors between measured and simulated results.

scholarly journals Surface Stress and Atmospheric Boundary Layer Response to Mesoscale SST Structure in Coupled Simulations of the Northern California Current System

2019 ◽  
Vol 148 (1) ◽  
pp. 259-287
Author(s):  
R. M. Samelson ◽  
L. W. O’Neill ◽  
D. B. Chelton ◽  
E. D. Skyllingstad ◽  
P. L. Barbour ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Current System ◽  
California Current ◽  
Heat Fluxes ◽  
Neutral Stability ◽  
Northern California ◽  
Coupling Coefficients ◽  
California Current System ◽  
Northern California Current

Abstract The influence of mesoscale sea surface temperature (SST) variations on wind stress and boundary layer winds is examined from coupled ocean–atmosphere numerical simulations and satellite observations of the northern California Current System. Model coupling coefficients relating the divergence and curl of wind stress and wind to downwind and crosswind SST gradients are generally smaller than observed values and vary by a factor of 2 depending on planetary boundary layer (PBL) scheme, with values larger for smoothed fields on the 0.25° observational grid than for unsmoothed fields on the 12-km model grid. Divergence coefficients are larger than curl coefficients on the 0.25° grid but not on the model grid, consistent with stronger scale dependence for the divergence response than for curl in a spatial cross-spectral analysis. Coupling coefficients for 10-m equivalent neutral stability winds are 30%–50% larger than those for 10-m wind, implying a correlated effect of surface-layer stability variations. Crosswind surface air temperature and SST gradients are more strongly coupled than downwind gradients, while the opposite is true for downwind and crosswind heat flux and SST gradients. Midlevel boundary layer wind coupling coefficients show a reversed response relative to the surface that is predicted by an analytical model; a predicted second reversal with height is not seen in the simulations. The relative values of coupling coefficients are consistent with previous results for the same PBL schemes in the Agulhas Return Current region, but their magnitudes are smaller, likely because of the effect of mean wind on perturbation heat fluxes.

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