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This study presents a new model to predict the additional pressure drop for series-arranged misaligned monoliths, relevant for high-flow industrial applications. Long reactor tubes often contain multiple short monoliths, leading to extra pressure drops as the flow enters and leaves multiple monoliths. Existing models address aligned monoliths, but this research considers misalignment, where extra pressure drop is higher. Channel Reynolds from 50 to 320, spacings from 0.1 to 20 channel diameters, and several void fractions are investigated using a discrete channel model. Results indicate a significant impact of misalignment on extra pressure drops in closely spaced monoliths due to flow collisions. A correction factor model that adapts to misalignment is proposed, starting from large values for closely spaced channels and decreasing as spacing increases. The proposed model aligns with discrete channel data and phenomenological behavior of aligned channels both in trend and magnitude, showing an R2 above 0.93. • Innovative model for pressure drop correction in misaligned monoliths. • Accounts for a wide range of Reynolds numbers and gap lengths. • Demonstrates a significant impact of misalignment on pressure drop. • Validated against discrete channel CFD data and real-world behavior. [ABSTRACT FROM AUTHOR]

[Display omitted] • Lewis number deviates from one in the entrance length. • The catalyst activity do not modify the initial Nu and Sh inside of the channels. • Re modifies the thermal entrance length because of the reduction of the flow area. This paper is devoted to the multi-scale model of the heat and mass transfer inside of a honeycomb monolith substrate. Due to computational limitations, monoliths are modelled as a continuum in full-scale catalytic reactors models. That makes it necessary to use correlations or sub-models derived from channel scale results to account for a physically consistent heat and mass transfer inside of the substrate. In this paper detailed computational models at a channel and reactor scales are analyzed. Catalytic oxidation of CO is used as a reaction and the fluid properties are considered to be temperature-dependent. First, a channel scale model is used to analyze Nusselt, Sherwood, Lewis, and Damköhler numbers inside of the monolith channels. Secondly, sub-models obtained at a channel level are implemented in a full-scale reactor model using the continuum approach, to evaluate the impact of using detailed vs. highly simplified correlations for heat and mass transfer. The reactor scale model accounts for the transitions of the flow regime, entrance length effects, an-isotropic substrate thermal conductivity and temperature-dependent fluid properties. According to the results, the Lewis number can deviate significantly from one in the entrance length, however, it approaches asymptotically to unity as the flow develops. Regarding Nusselt and Sherwood, current interpolating methodologies are not able to predict the correct value in the entrance region when Damköhler is low, nonetheless, are reasonably accurate for the asymptotic one. [ABSTRACT FROM AUTHOR]

The honeycomb type monolith reactor dominates the field of catalytic automotive exhaust gas after treatment systems and is increasingly being used in other applications. Advanced computational modelling of such systems can provide valuable insight into their operating characteristics and be used as a design tool. This reactor provides an excellent example of a multi-scale modelling challenge with many complexities. This paper provides a perspective on the development and use of computational modelling tools in this context over the last 30 years, with an emphasis on the work published by the researchers at the University of Alberta. This paper covers all aspects of model development, including single channel and full-scale reactor models and inter and intra mass and heat transfer effects, with the latter including radiation. [ABSTRACT FROM AUTHOR]

• The flow through a wall-flow filter has been described using a 3D CFD model. • New statistically validated models for the pressure drop are developed. • The friction factor inside the filter channels is not constant. • The friction factor is different from that for pipes with non-porous walls. • Kinetic energy and momentum flux correction factors are presented. This paper presents a detailed study of the fluid dynamics inside a wall-flow filter and proposes a new pressure drop model. A 3D channel scale computational model of a filter validated with experiments is used. A detailed description of the pressure drop for flow entering, passing through and leaving the filter is provided. The computational grid is extensively analyzed, and it is found that wall-flow is very insensitive to the grid quality, opposite to the local pressure, which is very sensitive. Several flow rates and wall permeability are analyzed. The most critical assumptions commonly found in current models are discussed based on the results. It is found that the friction factor of the channels is non-constant, it is different for the inlet and the outlet channels, and both differ from that for pipes with non-porous walls. A new criterion to determine the flow inside the filter as fully developed is also presented. The wall-flow along the perimeter of a cross-section is observed to be variable, consistently for many flow rates and wall permeability. The results are also used to develop a comprehensive, physically based, pressure drop model that shows very good agreement with experimental data. It is found that the propagation error when using the model to back-calculate physical parameters is strongly sensitive to the experimental conditions; hence, guidelines to minimize it in further experiments are provided. [ABSTRACT FROM AUTHOR]

This paper reports a study of turbulence generation after a monolith honeycomb. Large eddy simulation is used to analyze the turbulence generated when steady, turbulent, or pulsating flow leaves a monolith channel. Substrates with different cell densities, wall thicknesses, and channel cross‐sectional shapes are investigated. The results show that the magnitude of the turbulence generated depends on the wall thickness and monolith void fraction, though not much on the cell density. For pulsating flow, different frequency of the pulsations produced only slightly different results, however, the amplitude of the pulsations is proportional to the magnitude of the turbulence generated. The outflow of the channels can act as a jet and trigger turbulence along a distance from 10 to 30 channel diameters, significantly affecting the total pressure drop and the inlet conditions for elements in series downstream, such as particulate filters or other substrates. [ABSTRACT FROM AUTHOR]

• Improved pressure drop model for a honeycomb monolith system. • Multi-zone permeability accounts for all observed effects in single channel model. • Includes all entrance and exit effects and developing flow pattern. • Model extended to continuum porous medium mode for entire converter. • Velocity profile in converter closer to experiment than single permeability model. This paper presents an improved model for pressure drop in a honeycomb monolith reactor, which configuration is widely used in automotive exhaust gas after treatment systems. The model is based on pressure drop simulations for single channel models complemented with large eddy simulation. The model has multiple zones, and accounts for the pressure losses for flow entering, passing through, and leaving the substrate. The new multi-zone model is theoretically more consistent than those that use a single permeability for the whole the monolith, and it gives a superior result for pressure drop and hence flow distribution. [ABSTRACT FROM AUTHOR]

Abstract In a typical practical monolith reactor implementation, turbulent flow in a large pipe or inlet header enters small monolith channels. After some distance the flow becomes fully developed laminar flow. It has been shown that the distance over which the turbulence transitions to laminar flow is significant. This paper reports results of investigation into the value of the Nusselt number in the entry region of a circular tube under conditions of decaying turbulence. Large Eddy Simulations (LES) are used to model the flow. LES simulations show that the Nusselt number is significantly larger in the entry region compared to the classical case of developing laminar flow. The entry length Nu number depends not only on the inverse Graetz number, but also independently on the Reynolds number, turbulence length scale and upstream turbulence intensity. A general correlation is developed that relates the Nu number in the entry region to the inverse Graetz number, Reynolds number, inlet turbulence intensity and turbulence length scale. Highlights • Entry length Nusselt numbers for a monolith channel are analyzed with decaying turbulence. • Nusselt numbers are higher than for developing laminar flow. • Nusselt number depends on Reynolds number and turbulence levels. • A general correlation for developing flow Nusselt numbers is developed. [ABSTRACT FROM AUTHOR]

Highlights • New approach to predict turbulent flows inside of a catalytic converter. • Decay and ignition of turbulence at the entrance and exit zone of the monolith. • Model simplicity in terms of implementation in any commercial or open-source CFD software. Abstract This work presents a new approach to predict turbulent flows inside of a catalytic converter taking into account a decay and ignition of turbulence at the entrance and exit zone of the monolith, respectively. The core part of the converter is a monolith substrate, which is commonly represented as a homogeneous porous medium due to computational limitations. Such simplification eliminates any interaction with the solid when the flow is entering and leaving the substrate. This work extends the previously addressed decay of the turbulence entering the monolith, with the turbulence generation exiting it. This is achieved using an immersed boundary condition immediately after the porous medium, whose values are estimated using a local Reynolds, based on observations made in a discrete channel geometry. The results are compared with commonly used converter models, finding substantial differences in the effective viscosity and kinetic energy inside and after the monolith. The proposed model agrees with the one obtained in discrete geometry, and it also prevents unrealistic changes in the flow observed in existing models. The distinguishing feature of the proposed model is its simplicity in terms of implementation in any commercial or open-source CFD software. Model performance using models based on Reynolds-averaged Navier–Stokes equations (RANS) and Large eddy simulations (LES) of the whole automotive converter is illustrated. [ABSTRACT FROM AUTHOR]

This paper is concerned with the modeling of the pressure drop through monolith honeycombs. Monolith substrates are promising for the intensification of catalytic processes, especially because of their low back-pressure. There have been several improvements in the modeling of monolith reactors during the last decade, most of them focused on a single substrate configuration, while research in multiple substrates in a single reactor is still sparse. One example is the so-called "minor losses", such as those because of the flow entering and leaving a substrate. Both phenomena interact when two monoliths are placed close in series, and the extra losses produced by them may become relevant when relatively short monoliths are used. In this paper, a spatially resolved computational model of monolith channels arranged in series is used to compute the extra pressure drop because of the flow leaving one substrate and entering the next one downstream. Several Reynolds numbers and spacing lengths for the channels between substrates are investigated. According to the results, for close-coupled monoliths, the inlet and outlet effects produce a negligible pressure drop compared to that in a single monolith configuration. This phenomenon can be accounted for by introducing a correction factor. The magnitude of the correction factor depends on the channel's Reynolds number, diameter, and spacing length. A model for such a factor is proposed. The model accurately predicts the trend and magnitude of the correction factor. [ABSTRACT FROM AUTHOR]

Monolith-type substrates are extensively used in automotive catalytic converters and have gained popularity in several other industrial processes. Despite their advantages over traditional unstructured catalysts, such as large surface area and low pressure drop, novel monolith configurations have not been investigated in depth. In this paper, we use a detailed computational model at the reactor scale, which considers entrance length, turbulence dissipation and internal diffusion limitations, to investigate the impact of using a dual cell substrate on conversion efficiency, pressure drop, and flow distribution. The substrate is divided into two concentric regions, one at its core and one at its periphery, and a different cell density is given to each part. According to the results, a difference of 40% in apparent permeability is sufficient to lead to a large flow maldistribution, which impacts conversion efficiency and pressure drop. The two mentioned variables show a positive or negative correlation depending on what part of the substrate—core or ring—has the highest permeability. This and other results contribute relevant evidence for further monolith optimization. [ABSTRACT FROM AUTHOR]

Structured catalytic reactors are enjoying an increasingly important role in the reaction engineering world. At the same time, there are large and growing efforts to use advanced computational models to describe such reactors. The structured reactor represents a multi-scale problem that is typically modelled at the largest scale only, with sub-models being used to improve the model granularity. Rather than a literature review, this paper provides an overview of the key factors that must be considered when choosing these sub-models (or scale bridges). The example structured reactor selected for illustration purposes is the washcoated honeycomb monolith design. The sub-models reviewed include those for pressure drop, inter- and intra-phase mass and heat transfer, and effective thermal conductivity. [ABSTRACT FROM AUTHOR]

This paper reports an investigation of heat and mass transfer coupled with fluid flow inside monolith honeycomb substrates. Many important aspects of multiscale models of a monolith are investigated. Three common geometrical representations of monolith channels are tested, and their advantages and disadvantages are analysed. A detailed computational model and a large set of computational experiments, covering a broad range of substrate void fractions, channel Reynolds numbers and heating rates is used. Results assuming constant and temperature-dependent fluid properties are reported and compared. At a high heating rate, assuming constant fluid properties leads to a significant error in the estimation of Nusselt and Sherwood numbers in the entry region. At a constant wall temperature and a high heating rate, there is a minimum in the Nusselt curve that classical models are not able to describe. Hence, a novel correlation that shows excellent agreement with channel data is presented together with a methodology to fit it. Additionally, empirical models to estimate the placement and value of the minimum Nusselt are proposed. These results contribute significantly to the improvement of lumped parameter multiscale models of monolith catalytic reactors. • Entry Nusselt numbers for a monolith channel are analysed with realistic conditions. • Nusselt number depends on Reynolds number, inlet geometry and variable properties. • Improved correlations for developing flow Nusselt numbers is developed. [ABSTRACT FROM AUTHOR]

• A fully predictive multiscale pressure drop model for monolith substrates is presented. • Excellent agreement with experimental velocity profiles was observed. • The model works for several channel shapes and substrate void fractions. • The methodology has general applicability to substrates with other channel shapes. This paper presents a detailed physics based model for the pressure drop through a honeycomb substrate for several channel shapes and void fractions. A CFD-based computational model of a single channel is used to study the pressure drop when flow is entering, passing through and leaving the substrate. An extensive set of 3D computational experiments covering square, hexagonal and triangular channel cross-sections, void fractions from 0.39 to 0.84 and channel Re from 95 to 1284 is used. It is shown that altering the void fraction changes the pressure drop at the inlet and outlet of the substrate, however, its effect on the friction factor inside the substrate is minor. The resulting model can be used either as a semi-empirical lumped model for pressure drop and in 3D full-scale simulations with a porous medium representing the substrate. A validation for the velocity profile in a full scale monolith with experimental data available in the literature is carried out and an excellent agreement is observed. The proposed model significantly improves the prediction of the flow distribution across the substrate, which has remained unaddressed historically by existing models and is the most important effect required to make accurate predictions of heat distribution, conversion efficiency and others in full-scale simulations. [ABSTRACT FROM AUTHOR]

• RANS and LES models used for turbulent flow modelling in a monolith. • The resulting pressure drop, power spectrum and flow regime are analysed. • RANS predicts a small fraction of the turbulence entering the channels to decay rapidly. • LES predicts a total dissipation of the turbulence before the flow enters the channels. • RANS predicts steady flow and LES predicts pulsating flow after turbulence decay. This paper reports the pressure drop through a monolith for turbulent and laminar flow. A computational model of a monolith channel together with the open sections before and after it is used. Simulations at several channel Reynolds numbers, and assuming laminar and turbulent flow approaching the substrate are considered. Reynolds average Navier Stokes (RANS) and large eddy simulation (LES) are used as flow models in the cases with turbulence. The resulting pressure drop, power spectrum and flow regime are analysed. RANS predicts a decay of the turbulence as the flow approaches the substrate, a small fraction of the turbulence effectively entering the channels to decay rapidly, then steady flow from that point. On the other hand, LES predicts a total dissipation of the turbulence before the flow enters the channels; however, the flow remains unsteady along the entire substrate, in a sort of pulsating regime. Despite the significant differences in the flow regime, both models predict a marginal influence of the upstream turbulence on the total pressure drop. The dominating frequencies of the pulsating flow inside the channels were found to be comparable to the ratio of the channel velocity over the channel diameter, therefore, to the channel Reynolds number. [ABSTRACT FROM AUTHOR]