Model-Based Control of Particulate Processes.
Panagiotis D. The interest in control of particulate processes has been triggered by the need to achieve tight distributed control of size distributions that greatly influence particulate product properties and quality. Drawing from recent advances in dynamics of infinite-dimensional systems and nonlinear control theory, control of particulate processes using population balances has evolved into a very active research area within the field of process control.
This book - the first of its kind - presents general methods for the synthesis of nonlinear, robust and constrained feedback controllers for broad classes of particulate process models and illustrates their applications to industrially-important crystallization, aerosol and thermal spray processes. The controllers use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output tracking, attenuation of the effect of model uncertainty and handling of actuator saturation. Finally, a section on the use of on-board virtual soot sensors i.
Where appropriate, experimental results are cited to reinforce the points brought forward by the simulation approach. For larger engines maybe two such lines will be required, doubling the number of required hardware components 2 Taxonomy of DPF simulation tools Performance assessment, reliability improvement and cost optimisation are some of the needs that pose specific requirements on DPF simulation tools.
Performance assessment requires tools that allow the estimation of various integral quantities of interest under fresh and aged conditions, as functions of the soot and ash mass quantity and spatial distribution in the DPF such as: filtration efficiency mass, number and size specific based , pressure drop, regeneration efficiency, regeneration limits, safety limits and secondary emissions e. Cost optimisation is connected to the capability to simulate capital costs including those associated with system integration and optimisation , operating costs including fuel penalty and maintenance costs e.
The core elements of any DPF simulation tool are user inputs e. There are many classification schemes that can be used to differentiate DPF simulation tools e. At the present state of development, and from a purely scientific point of view, we find it instructive to present recent advances in DPF simulation according to a spatial scale classification scheme.
Vlachos The basic simulation module employed most frequently is the single channel model originally developed by Bissett and further extended in Konstandopoulos and Kostoglou , and Konstandopoulos et al. In general there are three coexisting length scales that need to be taken into account for the modelling of DPFs. The first scale refers to the phenomena occurring across the soot layer and the porous filter walls, the second scale to the phenomena occurring along the filter channels and the third scale is the macroscopic scale of the entire DPF.
In the following sections we discuss selected recent developments from our work at each scale. In the literature it has been common practice to assume that the soot layer grown on the filter wall could be described by a uniform density equivalently porosity , surface area and permeability, which were parameters that had to be tuned according to experiments, leading to widely varying values among different publications, that for the sake of brevity will not be reviewed here.
Konstandopoulos et al. The data of Konstandopoulos et al. Figure 3 demonstrates the influence that flow conditions and substrate have on diesel soot cake structure. The multiscale nature of diesel particulate filter simulation Figure 3 Experimental measurements of soot cake permeability as a function of Peclet number Notes: Measurements have been performed with cordierite filters of various sizes Konstandopoulos et al. The solid lines are theoretical predictions based on a primary particle size of 32 nm Konstandopoulos et al. The CAST is a quenched diffusion flame gas propane burner that allows the stable and controlled generation of soot aggregates over a much larger size range than that found in diesel exhaust.
As flow in porous media represents a challenging area of fluid mechanics, initial approaches Konstandopoulos and Johnson, ; Konstandopoulos et al. By employing filtration theory and a local re-computation of the evolving unit-cell geometry due to deposition of particles Figure 6 , a transient filtration model has been derived and tested with very good success against experimental data with ceramic, metallic and fibrous filters Vlachos et al. In addition to unit-cell models, it is possible to employ flow simulation in geometrically faithful representations of porous media. This is especially important for the development of new filter materials, the optimisation of catalyst deposition inside the porous wall and for the design of gradient-functional filter microstructures where multiple functionalities, in terms of particle separation and catalyst distribution for combined gas and particle emission control , can be exploited.
Figure 6 Unit-cell filtration model Notes: The collector size dc and the empty envelope b are matched to the macroscopic porosity of the filter. The unit-cell blocks when the size of the collector becomes a fraction of b Konstandopoulos et al. In addition Figure 7 depicts flow visualisation examples for two of the most popular filtration media: extruded ceramic filters and sintered metal media. Depending on the way the catalyst is applied e. Vlachos the catalyst coating degree of uniformity Figure 8 is expected to lead to different flow resistance behaviour of the DPF. At first, SEM images of the filter wall are taken at different magnifications to identify the range of homogeneity of the material.
Then a number of polished cross sections of the material embedded in a special resin are prepared and additional images in the SEM backscattered image mode are obtained, e.
Figure 9 c. The SEM image is converted into a binary image with appropriate thresholding algorithms as shown in Figure 9 d. The binary image is then analysed with respect to different statistical descriptors e. Vlachos Figure 9 a , b SEM images of prototype SiC filter walls, made from coarse grains; c backscattered SEM image of a filter wall; d binary thresholded image pore space is denoted in black ; e computer reconstruction of filter shown in d ; f comparison of autocorrelation function of reconstructed medium to that of the real filter The flow resistance behaviour of the reconstructed medium is examined by performing 3D flow simulations with the Lattice Boltzmann method Chen and Doolen, , and obtaining the permeability of the material Konstandopoulos, Using the reconstructed porous material and the computed flow field the computation of soot deposition in the filter can be carried out.
On the experimental front, the flow resistance properties of soot cakes under reactive conditions are studied by performing permeability experiments on partially reacted soot cakes. The data are interpreted with the aid of the mathematical model of Konstandopoulos and Kostoglou for an isothermal soot deposit as shown in Bissett this is a very good assumption.web.difccourts.ae/procedimiento-de-gestin-de-los-tributos-uf1816.php
Model-Based Control of Particulate Processes
Presently such a description is based on a simple phenomenological approach, as embodied in the so-called two-layer model Konstandopoulos and Kostoglou, Above this catalyst-influenced layer a normal soot deposit exists that can only react predominantly through a thermal oxidation mechanism. Vlachos The influence of NO2-assisted soot oxidation in conjunction with highly selective NO to NO2 oxidation promoting catalytic coatings was, for the first time, studied experimentally and theoretically in Konstandopoulos et al.
If the inlet conditions to the DPF can be assumed to be spatially radially uniform, formulating the DPF simulation model for two representative channels inlet and outlet is equivalent to solving it for the entire DPF assumed radially homogeneous. It is not therefore surprising that this scale claims most of the published works in the literature, starting with Bissett who formulated the first comprehensive model which takes into account the detailed flow distribution in the channel.
As the transient behaviour of the monolith is slow with respect to the residence time of the exhaust gas as it travels across the filter, the quasi-steady-state approximation for the exhaust flow in the channels simplifies considerably the computational burden. Although the flow in the filter channels is actually 3D, it can be accurately approximated by a perimeter averaged 1D configuration. This has been confirmed by Konstandopoulos et al.
Most of the new developments in the filter channel scale phenomena simulation pertain to the mechanistic modelling of ash transport and deposition dynamics originally introduced in Konstandopoulos et al. The same formalism can be applied to account for shear-induced soot particle re-entrainment and further downstream deposition Peters, Experimental studies of ash deposition and transport in filters require extensive and costly engine runs and are scarce in the literature.
Ash particles result from the oxidation of metal fuel additives, like Ce and Fe, doped in the fuel to promote low temperature combustion of the soot collected in the filter, as well as from engine oil-derived inorganic compounds of Ca, Zn, P and S. The time scale of the ash accumulation process is much larger than that of the soot loading and regeneration so the direct simulation of the DPF operation is impractical from the computational point of view.
An alternative way is to decompose the problem in fast loading, regeneration and slow ash accumulation modes and to define the appropriate two-way coupling between them. When the local ash layer deposit thickness reaches the half-width of the channel, the channel is blocked and its active filtration length is reduced. The ash simulation model consists of ash transport and ash layer evolution equations describing the interaction between ash deposition and re-entrainment in the channels along with the gas mass balance and momentum balance equations in the inlet and outlet channels of the DPF.
Model-Based Control of Particulate Processes
Ash re-entrainment is initiated by flow shear stresses along the channel whenever the shear stress in the channel exceeds locally a critical shear stress characteristic of the ash type as e. The kinetics of ash re-entrainment are determined by the ash stickiness that for a given type of ash depends on the previous filter temperature history currently accounted by the maximum temperature that the filter wall has experienced , as obtained by a separate filter regeneration simulation Konstandopoulos et al.
Ash stickiness is described by a critical ash sticking temperature by analogy to the ash fusion temperature employed in studies of ash fouling in heat transfer equipment. Despite its apparent simplicity, the dynamic ash transport and deposition model can exhibit a rich behaviour, depending on the ash quality, and prevailing flow conditions leading to different ash deposition profiles inside DPFs: sticky ash leads to deposition along the walls while non-sticky ash can be transported towards the end of the filter.
A comparison to the experimental data of Bardasz et al. As a realistic size filter consists of several thousand channels, its direct simulation via the numerical solution of a coupled discrete multi-channel problem is an intractable task with the currently available computational resources. An alternative way to deal with the scale-up problem is to employ a continuum model of the filter honeycomb structure. Rigorous scale homogenisation procedures lead to continuum models for the entire DPF Konstandopoulos et al. This continuum multi-channel description of the DPF can accommodate various regeneration methods thermal, catalytic and NO2-assisted and can provide spatio-temporal information of several quantities of interest e.
Vlachos Figure 13 Comparison of simulated ash profile thickness, wash , along the filter length against the experimental data of Bardasz et al. In this case while the filter centre is regenerated, the periphery of the filter remains blocked with soot, leading to a strong radially non-uniform soot profile in the DPF.
Control of Particulate Processes
This has as a result the non-uniqueness of the pressure drop versus the collected soot mass relationship, as shown in Figure Such simulation tools are currently extensively employed by the automotive industry to guide DPF system selection and design. As we proceed to the entire exhaust system scale, we face the task of interfacing the DPF behaviour to that of other emission control devices in the exhaust e.
We observe how a hydrocarbon pulse injection upstream of the DOC raises the exhaust temperature and causes regeneration of the DPF. Such simulation tools are very useful for the development and optimisation of post-injection strategies for DPF regeneration. Vlachos Figure 15 Temporal evolution of temperature probes inserted in a regenerating SiC diameter mm, length mm DPF bottom along with the spatial distribution of filter temperature at s, i.
A uniform loading would be depicted as a uniform shade. The soot is partially oxidised e.
Current research at this scale focuses on the rigorous integration into the continuum multi-channel framework of segmented filter designs, computationally efficient discretisations of non-axisymmetric filter geometries e. An interesting example is the coupled simulation of the 3D distribution of soot in a DPF during loading shown in Figure While the interested reader is encouraged to consult the cited relevant references for more detailed information on the underlying assumptions regarding the treatment of the various physicochemical phenomena including soot particle transport, deposition and oxidation , in the present paragraph we provide an overview of the mode of use of the different models in practice.
The models at each spatial scale are classified according to their complexity and detail in the representation of the actual situation. Three sub-models corresponding to the three size scales wall, channel, entire filter must be combined to give an overall model of the filter. Ideally we would like to employ the most detailed treatment from each scale. Such an approach thus would entail a MicroFlowS description of the wall, along with a 3D CFD simulation of each channel, coupled through a conjugate heat transfer 3D code to the other numerous on the order of a few thousands channels of the DPF.
As this is for obvious reasons impossible even with computing resources of the foreseeable future, the employed strategy is to use the most detailed models at each spatial scale in order to validate and extract parameters for simpler lower-degrees-of-freedom models. These relatively simple, lower order models are then connected with the models in their hierarchically superior spatial scale, and the procedure is repeated for the next scale as shown in Figure The models at this scale therefore are of highest interest to the manufacturers of filter media. In this case the majority of the experimental development evolves around small scale filter samples, frequently in disk form that are quite convenient to use in laboratory scale experiments Konstandopoulos et al.
Model-Based Control of Particulate Processes - Panagiotis D. Christofides - Google книги
Depending on the outcome of this development interesting filter structures can be scaled-up into monolithic honeycomb samples. The use of a unit-cell structural description of the filter wall can be very advantageous at this stage, since with a minimal number of physically relevant parameters and well-characterised experiments, a description of the filtration and pressure drop behaviour of the DPF can be achieved in a very computationally efficient manner.
Vlachos state variables needed for this is an order of magnitude higher.