1. INTRODUCCIÓN
2.3 TÉCNICAS, MÉTODOS Y ESTÁNDARES PARA EL DIAGNÓSTICO DE UN TRANSFORMADOR . 19
2.3.2 Diagnóstico de un transformador en operación con aceite mineral
The specification of the catalyst ( ) comprises data of its geometry, its fluid and
thermodynamic behavior and the conversion reactions taking place. This input data is discussed in the following sub-sections:
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5.1.3.1. General
In order to simulate the chemical processes in the catalyst - either heterogeneous or homogeneous reactions - the switch Chemical Reactions needs to be activated. As a
consequence the input pages to define the required input for the single-channel converter model are activated as well.
If deactivated, no chemical reactions can be modeled and default values will be considered for the numerical and physical properties for the single-channel converter model.
Furthermore the basic geometry has to be defined by the following data:
Typical Values
and Ranges Monolith Volume Determines the volume of the monolith,
comprising both, the volume of the gas phase and the solid substrate.
1-10 (dm3)
Length of Monolith Determines the length of the monolith. 0.1-0.5 (m) Inlet Collector
Volume
Determines the volume of the inlet cone.
This information is only required for the Cycle Simulation task.
1 (dm3)
Outlet Collector Volume
Determines the volume of the inlet cone.
This information is only required for the Cycle Simulation task.
1 (dm3)
Couple to upstream element
Select to thermally couple the catalyst to an upstream element via wall heat conduction (see Thermal Coupling page [75] for details).
-Consider Air Gap between the Substrates
When deselected, thermal coupling to an upstream element's substrate (e.g. another catalyst or a particulate filter) is active. Select to suppress this thermal coupling (see Thermal Coupling (Substrates) page [76] for details).
Note: Relevant only when Couple to upstream element is active.
-5.1.3.2. Initialization
The monolith (solid phase) initial temperature can be defined by the user:
Typical Values
and Ranges Initial Solid
Temperature
Determines the initial temperature of the solid substrate as constant or as a function of the catalyst length.
273-1000 (K)
5.1.3.3. Type Specification
The cell structure of the monolith can either be defined assuming Squared Cell Catalysts in a simplified way or within any geometrical assumptions for General Catalysts.
If Square Cell Catalyst is selected, the following input data has to be defined:
Typical Values
and Ranges
Cell density (CPSI) Determines the type of monolith using the number of channels per in2 .
100-900 (1/in2)
Wall Thickness Determines the thickness of the monolith's walls.
0.006-0.015 (in)
If General Catalyst is selected, the following input data has to be defined:
Typical Values
and Ranges Open Frontal Area
(OFA)
Determines the open frontal area (= fluid volume fraction) of monolith.
0.50-0.75 (-)
Hydraulic Diameter
(Hydraulic Area)
Determines the hydraulic unit (diameter or area) of the monolith channels.
0.001-0.005 (m)
5.1.3.4. Friction
The friction of the catalytic converter model can either be specified by Target Pressure Drop or by a friction Coefficient. If the catalyst is simulated in the aftertreatment analysis mode, only the specification of a friction coefficient can be used. For a standard BOOST cycle simulation both input variants can be used.
If Target Pressure Drop is selected, the following data is required:
Typical Values
and Ranges Inlet Mass Flow Determines the inlet mass flow, as reference value
for the evaluation of a friction coefficient.
0 (kg/s)
depends on the catalyst size Inlet Temperature Determines the inlet temperature, as reference
value for the evaluation of a friction coefficient.
300 (K)
Inlet Pressure Determines the inlet pressure, as reference value for the evaluation of a friction coefficient.
1 (bar)
Target Pressure Drop
Determines the pressure drop of the element as basis for the evaluation of a friction coefficient.
0.003 (bar)
For more detailed information about the input variant Pressure Drop refer to the BOOST Users Guide.
If Coefficient is selected, the following input data is required:
Typical Values
and Ranges Laminar
Coefficient a
Determines a laminar friction coefficient according to Eq.29 page [14].
64 (-)
Laminar Coefficient b
Determines a laminar friction coefficient according to Eq.29 page [14].
-1 (-)
Turbulent (Friction Coefficient)
Determines a turbulent friction coefficient. The friction coefficient can be specified as constant or table value (see typical values below). The
0.01-0.04 (-)
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Friction Multiplier Channel Shape
Determines a dimensionless factor that considers the influence of the channel shape in the case of laminar flow. The multiplier either can be chosen for different channel geometries (see section BOOST Balance Equations, Single Channel Model
page [13]
) or setup completely freely.
0.04-1 (-)
5.1.3.5. Discretization
The required input of the discretization does not concern the physical situation of the catalyst, but is required in order to setup and 'tune' its numerical model.
Typical Values
and Ranges Model Dimension Determines the dimension of the catalyst model.
Here either 1D or 2D can be set. Note that for adiabatic radial heat loss conditions 2D models are reduced to 1D (refer to section Heat Loss page [191]
).
1D/2D
Axial Direction Number of Grid Point:
Determines the number of calculation cells in axial direction.
Grid Shape Factor:
Determines the allocation of the axial grid points.
Values below 1 produce a grid which gets more dense toward the boundaries (according to a geometrical series), whereas values greater than 1 increase the grid density toward the middle of the catalyst.
10-100 (-) 0.8 (-)
If a 2D simulation is chosen, the following data should be set in addition to the radial direction:
Typical Values
and Ranges Radial Direction Number of Channels:
Determines the number of channels located in radial direction
Grid Shape Factor:
Determines the allocation of the radial channels.
Values below 1 produce a grid along the radius which is more dense toward the center and the shell of the catalyst (according to a geometrical series), whereas values greater than 1 yield a grid which is more dense in the middle of the radius.
2-7(-) 0.5 (-)
5.1.3.6. Catalyst Physical Properties
Physical properties of the catalyst's solid phase are required in order to model the thermal behavior of the converter.
Typical Values
and Ranges Density Determines the bulk density of the monolith material
considering the volume in the pores.
400-2000 (kg/m3)
Thermal Conductivity
Determines the thermal conductivity of the monolith material (= bulk solid material considering the volume in the pores). This property can specified as constant value or as a function of temperature.
0.1-50 (W/(m·K))
Specific Heat Determines the specific heat of the monolith material (= bulk solid material considering the volume in the pores). This property can specified as constant value or as a function of temperature.
500-2000 (J/
(kg·K))
Anisotropic
Conduction Factor
Corrects the diffusion coefficients of the solid temperature equation normal to axial direction. A value of 1.0 simulates an isotropic conductivity. A value of 0.5 would be a good choice for monoliths.
This value is only needed for 2D simulations.
0-10 (-)
Heat Transfer Model
Determines different approaches for calculating the heat transfer through the boundary layer (see Section Transfer Coefficients page [28]). If 'Constant' is chosen, a heat transfer coefficient needs to be specified.
Sieder-Tate (default)
Heat Transfer Coefficient
Determines a constant heat transfer coefficient through the boundary layer.
5-500 (W/m2)
Heat Transfer Multiplier
Specify a factor by which the heat transfer is scaled. 0.1-10 (-) Mass Transfer
Model
Determines different approaches for calculating the mass transfer through the boundary layer (see Section Transfer Coefficients page [28]). If 'Constant' is chosen, a mass transfer coefficient needs to be specified.
Sieder-Tate (default)
Mass Transfer Coefficient
Determines a constant mass transfer coefficient through the boundary layer.
0.01-0.1 (kg/
(m2s)) Mass Transfer
Multiplier
Specify a factor by which the mass transfer is scaled. Possible input is 'Constant' (mass transfer of every species is scaled in the same way) or 'Table' (mass transfer of selected species is scaled).
0.01-10 (-)
Catalysts whose substrates are axially structured in a way that there is heat- and mass-transfer between channels, can be modeled using the options from the Catalyst Segmentation section:
Typical Values
and Ranges Repeat Turbulent
Inlet Region
Enable this option in order to consider recurrent turbulent inlet regions along the catalyst's axial direction.
-Repeating Length Specify a length at which the turbulent inlet region is repeated.
0.001-0.1 (m)
5.1.3.7. Heat Loss
In the current model, Adiabatic Simulation can be chosen, or the radial heat transfer to
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in the following figure. More detailed information on how the radial heat transfer is modeled can be found in Section Boundary Conditions page [19]. In the second case, where the canning and insulation can be modeled in detail by specifying individual wall layers, Variable Wall Temperature needs to be enabled and the required input data can be provided on the related sub-page. Detailed information on the multi-layered wall model can be found in sectionMulti-Layered Wall Model page [65].
Figure 56. Heat Loss - Specification of Radial Heat Transfer Conditions
The following input data has to be specified:
Typical Values
and Ranges Variable Wall
Temperature
Enables the specification of a multi-layer wall model around the monolith and disables the input for the simplified heat-loss-to-ambient model below.
External Heat
Transfer Coefficient
Determines the heat transfer between the shell and the environment. This property can be defined as constant or as function of the simulation time.
10-100 (W/(m2·K))
Thickness, Shell Determines the thickness of the shell. 0-5 (mm) Thickness,
Insulation
Determines the thickness of the insulation mat. 0-30 (mm)
Thermal
Conductivity, Shell
Determines the thermal conductivity of the shell. 10-100 (W/(m·K))
Thermal Conductivity, Insulation
Determines the thermal conductivity of the insulation mat.
0.01-0.1 (W/(m·K))
Environment Temperature
Determines the temperature of the environment.
This property can be defined as constant or as function of the simulation time.
This (i.e. the temperature of the medium surrounding the catalyst) may be specified as a function of time. The temperature profile is considered to be periodic if not the entire integration time is covered by the input data.
298-350 (K)
5.1.3.7.1. Variable Wall Temperature
Typical Values
and Ranges Solid Material
Table
Add a solid wall layer by clicking on Insert.
Solid Material Determines a solid material for a given wall layer.
Click in the input field and select a material from the selection field.
The properties of the solid material can be specified in the pull-down menu <Model | Solid Materials>.
The first line in the table represents the innermost wall layer and the last line the outermost wall layer.
Layer Thickness Determines the thickness of each individual wall layer.
0.1-30 (mm)
No. of Grid Points Determines the numerical discretization of each wall layer in radial direction.
3-10 (-)
Ambient Temperature
Determines the temperature of the ambient. This value is a constant or a function of simulation time.
273-1000 (K)
Radiation Sink Temperature
Determines the temperature used for the evaluation of radiative heat transfer. This value is a constant or a function of simulation time.
273-1000 (K)
Convection Model Enables the application of a convection model for the external heat transfer from the outer wall layer surface to the ambient.
Convection Coefficient
Enables the application of a convection coefficient for the external heat transfer from the outer wall layer surface to the ambient.
Coolant Determines a fluid which is assumed to flow around the outer wall layer. Fluid properties of air and water are available.
Characteristic Velocity of Coolant
Determines the velocity of the coolant flowing around the outer wall layer. A cross-flow regime is assumed.
0.1-30 (m/s)
Convection Coefficient
Determines a convective heat transfer coefficient for the external heat transfer. This value is constant or a function of simulation time.
7-100 (W/(m2·K))
5.1.3.8. Washcoat
At "Washcoat" the physical properties of the washcoat material, as well as the reaction mechanism and mass transfer models are specified.
Two different approaches are available to model heterogeneous reactions in the catalyst's washcoat:
In the Surface Reaction Model approach, the mass transfer, i.e. pore diffusion, through the washcoat layer(s) is neglected. In the Washcoat Layer (WCL) Model approach, pore diffusion is taken into account. Therefore, every washcoat layer is discretized in the direction perpendicular to the catalyst solid surface, resulting in a 1D+1D simulation model. The Surface Reaction
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A single Catalyst can consider either the Surface Reaction Model or the WCL Model; they cannot be mixed.
Surface Reaction Model
The necessary input for the Surface Reaction Model is the thickness of the washcoat, as well as the reaction mechanism describing the chemical behavior of the converter. The set-up of the Conversion Reactions is located in the first reaction branch My_Reaction page [197]
.
The input of Washcoat Layer Thickness can be done directly in the Catalyst component mask, by selecting "Washcoat Layer Thickness" or it can be taken from an AUCI Catalytic Reaction Mechanism. Details on making use of washcoat properties from custom models can be found in the related section Washcoat Properties from AUCI Custom Models page [221]
.
Specify the thickness of the washcoat. >0-0.003 (m)
From AUCI Catalytic Reaction Mechanism
Indicate that the thickness of the washcoat shall be taken from an AUCI custom kinetic model loaded at subnode My_Reaction page [197]
. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table.
Extruded Catalyst The entire converter is modeled as an extruded catalyst. The washcoat thickness is calculated out of the input from subnode Type Specification page
[188]
.
Tip: An example for extruded catalyst modeling can be found in the related section in the BOOST Aftertreatment Application Examples Guide.
The washcoat thickness is used in the calculation of the hydraulic diameter in case of a "Square Cell Catalyst" and the fraction of solid substrate in the overall converter volume in case of a
"General Catalyst" (cf. Type Specification page [188]
).
Washcoat Layer (WCL) Model
In the WCL Model an arbitrary number of washcoat layers can be defined. This is done in the related table of washcoat layers that is editable as soon as the WCL model has been selected.
For each washcoat layer a separate row is added to the table. The required input for the simulation is done on related subnodes: For each washcoat layer the following subnodes are created:
1. My_Layer page [195]
: Specify the physical properties of the washcoat material and input required for the numerical simulation model.
2. My_Reaction page [197]
: Specify the reaction mechanism taking place in the related washcoat layer.
3. My_Transport page [219]
: Specify the pore diffusion model that describes the mass transfer within the washcoat layer.
Tip: The labels of these subnodes may be changed within the table listing all washcoat layers; for example "My_Layer" at washcoat layer #1 could be renamed to "Top_Layer":
Simply double-click the related input field and enter a new label.
5.1.3.8.1. Washcoat Layer Specification
At "My_Layer" physical properties of the washcoat layer as well as numerical simulation model input is given.
Below, the required input for single washcoat layer (WCL) is described. Some of the WCL properties may either be typed-in directly at this input pages or an AUCI custom model may be indicated as source. Details on this treatment are given in the related section Washcoat Properties from AUCI Custom Models page [221]
. Dimension
For each washcoat layer its thickness needs to be indicated. Note that the washcoat layer thickness needs to be greater than zero. The following input possibilities are available:
Typical Values and Ranges Washcoat Layer Thickness
Washcoat Layer Thickness
(direct GUI input)
Specify the thickness of the washcoat layer. >0-0.003 (m)
From AUCI Catalytic Reaction Mechanism
Indicate that the thickness of the washcoat layer shall be taken from an AUCI custom kinetic model loaded at the related My_Reaction page [197]
subnode for this WCL. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table.
From AUCI Transfer Model
Indicate that the thickness of the washcoat layer shall be taken from an AUCI custom pore diffusion model loaded at the related My_Transport page [219]
subnode for this WCL.
Extruded Catalyst The entire converter is modeled as an extruded catalyst. The washcoat thickness is calculated out of the input from subnode Type Specification page
[188]
.
Note: In order to use this option in the Washcoat Layer Model there is only a single washcoat layer allowed in the catalyst.
Tip: An example for extruded catalyst modeling can be found in the related section in the BOOST Aftertreatment Application Examples Guide.
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Reference for Chemistry Data
Optionally, reference data can be provided to specify the ratio of washcoat layer volume to converter volume of the particular catalyst for which the kinetic parameters have been calibrated.
More details on this topic can be found in the related section Reference for Chemistry Data page [23]. Typical Values and Ranges Specify a Reference
WCL Volume
Select this option to type-in the reference washcoat layer volume.
>0-0.01 (-)
Discretization
The following input is required for the computational model.
Typical Values and Ranges Number of Grid
Points
Specify the number of computational cells of each washcoat layer.
1-10 (-)
Washcoat Physical Properties
The following physical properties of the washcoat layer material can be specified.
Typical Values and Ranges Washcoat Bulk Density
WCL Bulk Density (direct GUI input)
Specify the density of the washcoat layer material.
400-2000 (kg/m3) From AUCI Catalytic
Reaction Mechanism
Indicate that the bulk density of the washcoat layer material shall be taken from an AUCI custom kinetic model loaded at the related My_Reaction page [197]
subnode for this WCL.
Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table.
Washcoat Porosity WCL Porosity (direct GUI input)
Specify the porosity of the washcoat layer material.
0-1 (-) From AUCI Catalytic
Reaction Mechanism
Indicate that the porosity of the washcoat layer material shall be taken from an AUCI custom kinetic model loaded at the related My_Reaction
page [197]
subnode for this WCL. Additionally specify from which custom model it shall be taken by typing its row index in the User Defined Reactions table.
From AUCI Transfer Model
Indicate that the porosity of the washcoat layer material shall be taken from an AUCI custom pore diffusion model loaded at the related My_Transport page [219]
subnode for this WCL.
5.1.3.8.2. Reaction Model (Conversion Reactions)
At "My_Reaction" several different reaction models are available. Either no reactions are taken into account, pre-defined or custom kinetic models are chosen or the application of map based conversion is possible.
Pre-Defined Kinetic Models
The pre-defined reaction models use global kinetic approaches given by Langmuir Hinshelwood equations and also transient mechanisms where adsorption and desorption steps are explicitly taken into account. All reaction models are supplied with default values for the individual kinetic parameters. The user can use the kinetic model and adjust all kinetic parameters.
Note: The suggested reaction parameters have been successfully applied to several validation simulations, but they may have to be adjusted for use in other types of
catalysts. In this case it is recommended to apply the pre-defined reaction model and to supply it with adequate reaction parameters.
The following pre-defined reaction models are available:
• Diesel Oxidation Catalyst (DOC)
This model is dedicated for DOCs comprising the three major oxidation reactions of CO, HC and NO.
• Three Way Catalyst (TWC)
This model is a dedicated TWC model comprising seven conversion reactions and surface storage reactions on cerium, rhodium and barium. By selecting specific reactions and adapting the related kinetic parameters, this model also can be applied to other catalysts such as DOCs.
• Selective Catalytic Reduction (SCR), Steady Kinetics
This model comprises seven reaction rates which can be enabled/disabled individually for three different reaction sections in the catalyst. The SCR rates use Eley-Rideal
mechanisms, thus it assumes steady-state conditions for the reaction steps of adsorption, catalytic reaction and desorption.
mechanisms, thus it assumes steady-state conditions for the reaction steps of adsorption, catalytic reaction and desorption.