Computing Profiles of Porosity and Surface/Volume Ratio in a Packed Bed Using Monte Carlo Method

2013 ◽  
Author(s):  
Genong Li
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Particle Diameter ◽  
Volume Ratio ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Accuracy Requirement ◽  
Radial Profiles ◽  
Novel Method ◽  
Rigorous Error

Porosity and surface/volume ratio are two important parameters for a packed bed. In cylindrical packed beds at low tube-to-particle diameter ratio, they vary greatly in the radial direction. In the existing literature, radial profiles of porosity and surface/volume ratio have been computed using some analytical equations which involve elliptic integrals. In this paper, a Monte Carlo method is used to compute those profiles. To the authors’ knowledge, the method has never been employed in this context. The procedure of using this novel method is explained in detail. Through a rigorous error analysis based on statistics, the accuracy of the simulation result can be controlled. Before any simulation, the number of sampling points needed in the Monte Carlo simulation can be determined given an accuracy requirement. The method is completely general and can be used to compute profiles of porosity and surface/volume ratio in any packed bed with any shape of packing elements.

Monte Carlo Optimization of Two-Stage Cascade R134A Refrigeration System With Flash Chamber

2008 ◽  
Author(s):  
Yousef M. Abdel-Rahim
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Pressure Ratio ◽  
Volume Ratio ◽  
Heat Rate ◽  
Cycle Performance ◽  
Specific Work ◽  
Refrigeration System ◽  
Two Stage ◽  
Monte Carlo Optimization

Present paper studies the optimal characteristics of the two-stage cascade R134A refrigeration system with flash and mixing chambers over its operating ranges of all cycle controlling parameters. The COP, total heat rate in Qin, total work rate in Win and second law efficiency ηII are used as cycle performance parameters. Compared to the practically-limited other rate-based optimization methods and to other experimentally-optimized specific cases of cycle parameters, the application of Monte Carlo method has proved to be very effective for optimizing the cycle performance in its global sense over all cycle controlling parameters. Correlations relating performance and cycle controlling parameters are presented and discussed. Study shows that COP of the cycle can reach a value of 8 at intermediate pressure P2 of about 200 kPa, and a maximum value of 9.92 at about 370 kPa and 720 kPa, beyond which COP goes as low as 4.2. P2 alone has no significant effect on Qin, Win and ηII unless values of other controlling parameters are specified. Values of Qin, Win and ηII can reach as high as 94 kW, 23 kW and 0.85 and as low as 6.8 kW, 1.1 kW and 0.57 respectively depending on other cycle parameters. Neither pressure ratio nor volume ratio of the HP compressor has any effect on Qin, Win or ηII. However, the ratio of inlet to exit temperatures of the condenser has the greatest effect on both ηII and the volumetric specific work of the HP compressor, which is about double the value of the volumetric specific work of the LP compressor. Study shows an almost linear relationship between the two mass flow rates in the upper and lower loops of the cycle, where its value in the lower LP loop is about 75% that in the upper HP loop. Findings of the present work as well as the elaborate application of Monte Carlo method to real cycles can greatly open the way for reducing the trade-off design methods currently used in developing such systems as well as direct the useful experimentations and assessment of such designed systems.

The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio

2018 ◽  
Vol 16 (11) ◽  
Author(s):  
F. I. Molina-Herrera ◽  
C. O. Castillo-Araiza ◽  
H. Jiménez-Islas ◽  
F. López-Isunza
Keyword(s):  
Thermal Conductivity ◽  
Heat Transport ◽  
Mass Flux ◽  
Flow Model ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Measured Temperature ◽  
Orthogonal Collocation

Abstract This is a theoretical study about the influence of turbulence on momentum and heat transport in a packed-bed with low tube to particle diameter ratio. The hydrodynamics is given here by the time-averaged Navier-Stokes equations including Darcy and Forchheimer terms, plus a κ-ε two-equation model to describe a 2D pseudo-homogeneous medium. For comparison, an equivalent conventional flow model has also been tested. Both models are coupled to a heat transport equation and they are solved using spatial discretization with orthogonal collocation, while the time derivative is discretized by an implicit Euler scheme. We compared the prediction of radial and axial temperature observations from a packed-bed at particle Reynolds numbers (Rep) of 630, 767, and 1000. The conventional flow model uses effective heat transport parameters: wall heat transfer coefficient (hw) and thermal conductivity (keff), whereas the turbulent flow model includes a turbulent thermal conductivity (kt), estimating hw via least-squares with Levenberg-Marquardt method. Although predictions of axial and radial measured temperature profiles with both models show small differences, the calculated radial profiles of the axial velocity component are very different. We demonstrate that the model that includes turbulence compares well with mass flux measurements at the packed-bed inlet, yielding an error of 0.77 % in mass flux balance at Rep = 630. We suggest that this approach can be used efficiently for the hydrodynamics characterization and design and scale-up of packed beds with low tube to particle diameter ratio in several industrial applications.

Hydrodynamic Models for Packed Beds with Low Tube-to-Particle Diameter Ratio

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Carlos O. Castillo-Araiza ◽  
Felipe Lopez-Isunza
Keyword(s):  
Experimental Data ◽  
Effective Viscosity ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Hydrodynamic Models ◽  
Viscous Term ◽  
Measured Velocity ◽  
Viscosity Parameter

In the last decade it has been a special interest to incorporate the hydrodynamics in packed bed reactor models. This seems to be important in the case of highly exothermic partial oxidation reactions normally performed in packed beds with low tube/particle diameter ratio (dt/dp< 5) because of the large void distributions in the radial and axial directions, which have a direct impact on the magnitude of radial, angular and axial profiles of the velocity field, and consequently on both, the temperature and concentration profiles in the catalytic reactor. A successful reactor model needs an adequate hydrodynamic description of the packed bed, and for this reason several models additionally incorporate empirical expressions to describe radial voidage profiles, and use viscous (Darcy) and inertial (Forchheimer) terms to account for gas-solid interactions, via Ergun's pressure drop equation. In several cases an effective viscosity parameter has also been used with the Brinkman's viscous term. The use of these various approaches introduce some uncertainty in the predicted results, as to which extent the use of a particular radial voidage expression, or the use of an effective viscosity parameter, yield reliable predictions of measured velocity profiles.In this work the predictions of radial velocity profiles in a packed bed with low tube to particle diameter ratio from six hydrodynamic models, derived from a general one, are compared. The calculations show that the use of an effective viscosity parameter to predict experimental data can be avoided, if the magnitude of the two parameters in Ergun's equation, related to viscous and inertial energy losses, are re-estimated from velocity measurements, for this particular packed bed. The predictions using both approaches adequately fit the experimental data, although the results are analyzed and discussed.

Wireless Sensor Networks Deployment Based on Monte Carlo Method

2014 ◽  
Vol 568-570 ◽  
pp. 573-576
Author(s):  
Qiang Wei Xin ◽  
Ding Yi Fang
Keyword(s):  
Wireless Sensor Networks ◽  
Monte Carlo ◽  
Sensor Networks ◽  
Monte Carlo Method ◽  
Sensor Node ◽  
Wireless Sensor ◽  
Node Deployment ◽  
Monitoring Task ◽  
Accuracy Requirement ◽  
Algorithm Base

How to use the least nodes to complete the monitoring task is an important problem about deploying in wireless sensor networks (WSN). We present MBT algorithm, base on Monte Carlo method combines the edge betweenness and signal transition distance, in order to study sensor node deployment problem. The proposed algorithm of sensor node deployment can meet the demand or the monitoring accuracy requirement of the premise, and reduce the number of nodes. Simulation experiments show that MBT algorithm can reduce the required nodes of deploying.

Heat-Transfer Studies in Packed-Bed Catalytic Reactors of Low Tube/Particle Diameter Ratio

2007 ◽  
Vol 46 (23) ◽  
pp. 7426-7435 ◽  
Author(s):  
C. O. Castillo-Araiza ◽  
H. Jiménez-Islas ◽  
F. López-Isunza
Keyword(s):  
Heat Transfer ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Catalytic Reactors
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