ENVE3150 Environmental Systems, Dynamics and Modelling Project 1 Combustion of a liquid fuel The burning process of a combustible liquid fuel stored in a pool is a heat and mass transfer governed process. For this project, you will be required to develop a model, which simulates the combustion of a liquid fuel using energy and mass. You are required to create a conceptual model using systems thinking, which is to be verified using the mechanistic model created on STELLA (derived from mathematical principles). Then, you will calibrate your model using laboratory data. Calibration of the model will be done by fine tuning of relevant parameters to fit the real system. Your task is to provide an analysis of the real system against the calibrated simulation model. Finally, in order to check if the model is an accurate representation of the real system, model validation must be completed using different data used for model calibration. Figure 1. Visual representation of the real system to be modelled. System details Fuel liquids burn under appropriate conditions, reacting with oxygen from the air, generating combustion products and releasing heat. The ignition process of a combustible liquid is governed by the rate of vaporisation of the fuel. Ignition of the liquid occurs once the fraction of vapours in the air-fuel mixture at the surface of the liquid reach the lower flammability limit and the flame provides sufficient heat to maintain the rate of vaporisation (firepoint). Once ignited, the liquid fuel will continue to burn (lose mass) based on an energy balance defined at the surface of the liquid. This is defined by the energy provided by the flame to the liquid surface in the form of convection and radiation and the energy required to vaporise the liquid (enthalpy of vaporisation). Heat balance analysis in the fuel layer The energy to vaporise the fuel comes from the chemical energy released as convective and radiative heat when the fuel burns. Usually, the heat feedback from the flame to the fuel ENVE3150 Environmental Systems, Dynamics and Modelling surface dominates the burning of the pool fire. The following equation describes the heat balance in the liquid fuel: ?"#$% + ?'() - ?"#$) - ?+%(, = ??012 ?? where Qconv, Qcond and Qrad are the heat from convection due to combustion gas, conduction from the tank wall, and radiation from the flame, respectively. Eliq represents the energy contained in the liquid fuel. The conduction term refers to heat transfer through the rim of the container, thus ?"#$) = ?"#$) ?8(?; - ?() where TL and Ta are the liquid and ambient temperatures, respectively, and kcond is a constant which incorporates additional heat transfer terms and A1 is the area that is in contact with the liquid. The radiation term is given by: ?'() = ?=?8 ?(?? @ - ?; @) where s is the StefanBoltzmann constant (5.67 10-8 W/m2 K4 ) and k1 is a measure of the efficiency of the surface as a radiator, known as the emissivity. For convection direct to the fuel surface: ?"#$% = ?= ?=(?? - ?;) where k2 is the convective heat transfer coefficient and A2 is the exposed surface area of liquid. The heat loss due to evaporation (Qevap) is equal to the energy needed to vaporise the fuel and this is obtained after the energy of the fuel has surpassed the energy needed to increase the liquid fuel temperature from its initial temperature to the boiling point (Tb): Q+%(, = ??????? Where mevap is the evaporated mass, Hv is the heat required to produce the volatiles (kJ/g) which, for a liquid, is simply the latent heat of evaporation (Table 1). Qevap controls the rate that the fuel is burnt. However, even if the whole fuel liquid has not reached the boiling point temperature, evaporation of the fuel still occurs at the boundary layer between fuel and flame. Therefore, for combustible liquids, the rate that the fuel vaporises in the surface of the liquid pool is controlled by the rate of heat transfer through convection and radiation from the flame to the fuel. As such, mevap can be also expressed quite generally as: ?+%(,(H#I$)('J 0(J+') = ?(?"#$% + ?'() - ?"#$)) ?,(?H - ?#) + ?% where ? is the efficiency of the heat transfer process. ENVE3150 Environmental Systems, Dynamics and Modelling Note: Two steady burning phases will be considered in this fuel pool fire. In the initial steady phase, only the fuel surface temperature reaches the boiling point. Heat transferred from the flame to the fuel surface is absorbed by the fuel beneath. During this phase, the fuel beneath the surface layer is preheated. As the temperature of the bulk fuel rises and approaches the boiling point, the rate of vaporisation increases because of agitation of the bulk liquid caused by boiling. The rate of vaporisation therefore enters a second higher plateau, which is called the bulk boiling phase. In addition to this agitation, a greater amount of fuel is at the vaporizing temperature during this phase, and the steady burning rate is thus enhanced. Table 1. Latent heats of vaporisation of some liquids. Liquid Boiling point (C) Hv (kJ/g) Water 100 2.258 Methanol 64.6 1.100 Ethanol 78.3 0.838 Benzene 80.09 0.394 Hexane 66.73 0.335 Heptane 98.5 0.318 Decane 174.15 0.273 Kerosene 200 0.251 Gasoline 200 0.350 to 0.400 1. Model Development a) Develop a conceptual model using systems thinking (CL and SFD). The following assumptions can be made when developing the model: The vaporisation process occurs at the surface of the liquid pool, where temperature of the liquid fuel reaches the boiling point, therefore the rate of vaporisation can be considered as a flux that is independent of the energy required to preheat the liquid below the surface. The vaporisation process occurs right after the fuel has been ignited and it occurs at the surface of the liquid pool. Heat loss from the liquid fuel to the surroundings only occurs through conduction. The temperature of the flame is constant. Note that in reality, the energy generated in the combustion process is used to heat up the combustion products (flame) up to a flame temperature (TF). b) Develop a mechanistic model on Stella that describes a) the fuel consumption due to combustion process and the change of energy in the fuel liquid. For this, use the necessary equations, which include the energy and mass balances. To complete these equations, use the following information: Energy balance will be carried out in the liquid fuel, which is affected by the heat transfer from the flame through radiation and convection, the heat of conduction and the heat of vaporisation. ENVE3150 Environmental Systems, Dynamics and Modelling The vaporised fuel mixes with air to combust and produce heat called heat of combustion. This process determines the temperature of the flame, however, the energy balance on the vaporised fuel is outside the boundary of the system to be modelled. Enter the values for the parameters, initial conditions and constants in your problem. Table 2 can be used to help build your model. When presenting this section in the report, include plots of the energy, temperature and mass loss of the liquid fuel from the predicted model. Table 2. Parameters, initial conditions and constants used for constructing the model. Parameters ?;= Temperature of the liquid fuel (Initial value 25 C) ??= Temperature of the flame (assumed constant) 1000 C Ta=Temperature air (Initial value 25 C) T0= Reference temperature ?"#$)=Heat transfer coefficient due to conduction from the liquid to the pool walls ?"#$) [100 - 200]~ [? ?= / ?] ?8= Emissivity of the flame ?8 [0 - 1] ?== Convective Heat Transfer Coefficient from the flame to the liquid fuel ?= [4 - 20] ~ [? ?= / ?] ?= Efficiency ? [0.6 - 0.9] Initial conditions ? = Pan diameter 0.3 m M= Mass of the liquid fuel (Initial value 1000 g) A1= Area in contact with the liquid (Initial value to be calculated) A2= Surface area of the liquid To be calculated ?012I1) =Energy of the liquid fuel ??,(?; - ?]) Constants ?%= Enthalpy of vaporisation from the liquid fuel See Table 1 ?= Stefan-Boltzmann constant ? = 5.67 x 10ab [? ?= ?@ / ] cp= Heat capacity of the fuel Kerosene 2.01 [??/?? ?] Gasoline 2.22 [??/?? ?] ?;= Density of the fuel 800 ?? ?f / ] 2. Model Verification a. Develop a simplified analytical solution for TL and ? with assumptions that allow the simplification of the analytical equations. b. Compare your numerically predicted trend from Stella under the same initial conditions with the analytical solution and the original numerically predicted case by plotting these on the same axes. Does your numerical model agree with the analytical solution? Provide an analysis of this. ENVE3150 Environmental Systems, Dynamics and Modelling 3. Model Calibration Calibrate your model by tuning the fitting parameters such that the SSQ between experimental data (see section 5. Experimental data collection) and your model predictions of either TL or ? are minimised. For example, for M that is ??? ??? = ??? ? k?(?)1 - ?l(?)1m $ 1n8 = where ? STELLA model prediction and ?l = the experimental values at ti and n = number of time points ti. A similar equation is used for TL. Two parameters can be tunned (k1 and k2), but you need to find the best strategy to fit each parameter. a. Demonstrate you have bounded the optimum value of the fitting parameter by presenting a plot of SSQ versus the fitting parameter. A spread-sheet is clearly advantageous in calculating SSQ. The plot should include approximately 5 values for each fitting parameter, with a trend towards a minimum SSQ in the middle of the plot. It is not a requirement to find the absolute minimum value of SSQ, but to rather demonstrate that the minimum is somewhere within the range of your points. b. Plot your optimised model against the experimental values. 4. Model Validation Validate your model for its use in different conditions (see 5. Experimental data collection). For this, first plot the experimental values at a different condition of your calibrated values and the predicted values of the mass and water temperature, from your calibrated model (using the optimised value of the fitting parameters determined during model calibration). Then, determine whether there is a lack of fit by using a goodness of fit test discussed in class. 5. Experimental data collection* Experimental data of the change of temperature of the liquid, temperature of the pan and mass of the liquid fuel during the burning process is required for model calibration. This data will be compared with your numerical model (STELLA model). The experiment will be carried out in the Fire laboratory (AEB 6th floor) and will be done in teams of 7 students (details on blackboard). Note that only experimental data collection is in teams, while the project work and report is done and submitted individually). For model validation, you will use the experiment of another team that used a different fuel or a different mass of fuel. Methodology ENVE3150 Environmental Systems Dynamics & Modelling 2021 1. Carry out the necessary inductions before starting the experiment. Know what you are going to do in the laboratory by reading this section before entering the laboratory. Keep in mind you only have a 1.5 hr session to complete the experiments. 2. Measure and obtain any initial conditions (e.g. ambient temperature, pan diameter, etc.) you may need. What initial information will require you to model the system appropriately? What is the burning rate dependent on? Record results. 3. Locate the type-K thermocouple(s) below the surface of the flammable liquid to measure the temperature of the liquid fuel and the temperature of the pan. Be careful to not locate the thermocouples too close to the flame. Ensure the thermocouple is connected to the computer. 4. Ensure that the scale is connected to the computer. 5. Place a protective non-flammable insulating material over the scale to avoid overheating of the equipment. 6. Tare the pan. 7. Fill the pan with the liquid fuel of testing, record the mass of the fuel. 8. Turn on the exhaust system. 9. Start the data logger. 10. Ignite the fuel with the blowtorch. 11. Extinguish the flame once measurements have been taken. Record the time between ignition and extinction. 12. Measure the mass of remaining fuel inside the pan. 13. Extract your results from the computer. 14. Repeat the experiment 3 times. For each experiment, use the same initial conditions and record the temperature at the same time points so that direct comparisons can be made. 15. Clean up and pack away the equipment you have used. *Depending on the university restrictions in place at the moment of this project, the experimental data will be collected by the students by doing the experiment at the Fire Laboratory, or will be provided. 6. Report requirements Aside from the diagrams, plots and information requested in the previous section, the report must contain the following information: ENVE3150 Environmental Systems Dynamics & Modelling 2021 a. The report must describe the problem that you modelled, the system boundaries and the model goals. Use the modelling process diagram from Lecture 1 to explain the steps that you followed in order to develop your model. b. The report must contain a short discussion from the diagrams, plots and information requested in the previous section and at the end of the report, a short conclusion on the project. c. The report must contain if not all, at least some representative examples of how the data was processed during model calibration and validation. Marking Item Description Marks available A Presentation and formatting Quality of the report including well-presented figures and images and text 1 B Project tasks 1 Q1 Model development, causal loop diagram, stock flow diagram, model equations and parameters Model goals, boundaries and assumptions CLD and SFD Equations of heat and mass flows Model plots Mass and T vs time along the three stages Discussion 4 2 Q2 Model verification Development of the analytical solutions for T and for M Comparison of the analytical solution and the numerical solution Analysis and discussion 4 3 Q3 Model calibration Demonstration that you found the most optimum value fitting parameter values by presenting the plot(s) of SSQ versus the fitting parameter with at least 5 values, which show trend towards a minimum SSQ. Plot of your optimised model against the experimental values Analysis and discussion that includes the parameters sensitivity 4 4 Q4 Model validation Plot of the experimental values used for model validation and the predicted values Goodness of fit test and analysis of the type of error. Discussion 4 5 General conclusions Appropriate contextualisation of conclusions derived from the results of each task 1 ENVE3150 Environmental Systems Dynamics & Modelling 2021 6 Examples of experimental data processing for items 3 and 4 2 TOTAL MARKS 20 References: Gregory E. Gorbett, James L. Pharr, Scott Rockwell. Chapter 5. Steady Burning of Liquids and Solids. In: An Introduction to Fire Dynamics. LI, Y., XU, D., HUANG, H., ZHAO, J. & SHUAI, J. 2020. An experimental study on the burning rate of a continuously released n-heptane spill fire on an open water surface. Journal of Loss Prevention in the Process Industries, 63, 104033.

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