About the Direct reduction model

This model is built during the master thesis project "Dynamic modeling and simulation of Direct reduction furnace" in 
the spring of 2024 (Thesis can be found here: https://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-107922). 
The model is centered on the 1D mass- and energy balances inside the furnace and the Unreacted 
shrinking core model for describing the pellet reduction, it also contains tables and expressions for how material 
constants, equation coefficients etc. changes with temperature and concentration. For full details of the model, see 
the thesis report.

The folder contains several MATLAB scripts and Simulink files that can be used to find steady state, generate 
datasets, simulate the dynamic behavior, or regulate the model. Some Steady-state solutions are within the files, 
called start.mat and start49.mat, and are solutions based on reactor data from the Siderca Plant in Argentina.

All different files will be described below (created with the MATLAB and Simulink release R2023b):

MATLAB Script: calc_lambda_cp_my.m

	This script generates datasets and tables that are necessary for the simulation models. The script uses
	expressions and tabulated values to create datasets that is stored in structs for each element and then 
	saved in the file lambda_cp_my.mat so that the script doesn't need to be run every time.

	Example: All necessary data for hydrogen gas can be found in the struct H2. All properties can be found in 
	the different fields of the struct and are tabulated against the temperature, which can be found in H2.T.  

MATLAB Script: Const.mlx

	This script is used as an initialization script for the SS_solve script. In the file, there are multiple 
	coefficients, constants, and reactor-specific parameters that can be modified to change the process. All 
	parameters regarding material properties are added to each material struct, while the rest of the 
	constants are added to the struct named Var. In some cases, there exists an option to choose between two 
	ways of entering the constant (like choosing between the number of pellets or the the porosity of the 
	reactor)

	Example: The iron-ore mass flow is a property that can be changed. By changing the ms value in the script, 
	the new value will be stored in the struct. However, the emass flow is not used directly in the model, and 
	therefore the mass flow is calculated into velocity instead. If the velocity is known, then there exists an 
	option to enter the velocity instead.

MATLAB Script: coeff.m

	This script calculates the necessary coefficient inside the reactor given values of temperatures and 
	concentrations for the different materials. coeff interpolates material properties from the material structs 
	and uses the expressions to find values of the gas mix conductivity, the reaction rate, metallization grade,
	etc. 

	The script is used together with derivativecalcc in the SS_solve.m script to find the steady-state solutions.

MATLAB Script: derivativecalcc.m

	derivativecalcc calculates the state time derivatives in the DR model based on the known PDEs and the upwind 
	discretization of the equations using an input vector X containing the temperatures and concentrations in an 
	N-by-5 vector. The full derivation of these matrices can be found in the thesis report. The output gives a 
	value of the time derivative of each inner point of the reactor, stored in an analogous N-by-5 vector.

	The script uses coeff.m to calculate all coefficients and is used in the SS_solve.m script to find steady-
	state solutions.

MATLAB Script: SS_solve.m

	SS_solve implements the "lsqnonlin" function to find the zero solution to the derivative functions (in other 
	words, the steady-state solution). The script uses the Const.mlx script to initialize all constants, and the 
	lsqnonlin tries to minimize the derivativecalcc script. The solver is initialized by setting the minimum and 
	maximum values for all states as the inlet and oputlet temperatures of the materials. 
	There also exist options to change the wanted tolerance, maximum function evaluations, and the maximum number 
	of iterations. When the zero solution is found, the script prints a table showing the outlet conditions as 
	well as giving the option for the user to print figures for temperature, concentration, and metallization 
	profiles by choosing a number between 0 and 3.

MATLAB Script: Initialization.mlx

	The Initialization script is very similar to the Const.mlx script. This script is linked to the Model.slx 
	file and differs from the Const.mlx by clearing the workspace before running and also loading initial 
	values of all states - which is used in the Simulink simulation. By choosing between 49 and 100 inner 
	points, the script loads the MAT-files start49.mat or start.mat respectively - which is the steady-state 
	solution to the Siderca-plant specifications found by running the SS_solve script.

Simulink file: Model.slx

	This Simulink file is the main implementation of the dynamic model. The model is implemented in implicit 
	form, where the block "Temperature- and concentrations dependent coefficients" calculate all necessary 
	coefficients in the model by implementing the same code as in  the coeff.m script in a "MATLAB-function" 
	block. The block "ODE time derivatives" calculates the derivatives for all node-states in a  
	"MATLAB-function block", which is the same code as in the derivativecalcc.m script.  After the "ODE time 
	derivatives" -block, the states are integrated and fed to the blocks again - completing the implicit loop. 
	Also, scopes for temperatures, concentration, and Metallization are present.

	The function blocks are having multiple inputs defined as "Parameter data" - meaning that the values are  
	taken from the MATLAB workspace.

	By clicking the button "Initialize", the script Initialization.mlx is run. Making all material parameters, 
	constants and the initial state available in the workspace.

Simulink file: Model_regulator.slx

	A modification of the Model.slx file where two types of regulators is implemented to control the 
	metallization grade by changing the solid mass flow. One is a continuous PI-controller, that can be used 
	to show how the regulation could work. The other is a discrete PI-controller since metallization can't be 
	measured continuously. The controller is therefore fed a signal with a certain interval (standard is 5 
	minutes) that mimics the speed at which the measurements are done.