In a small-scale experiment, oxygen is added into the oxidising stream of a non-premixed ethylene/air flame to investigate the influence of oxygen concentration (also called oxygen index) on flame length. The non-premixed jet flame issues vertically from a circular tube with a diameter of 10.5 mm, which is surrounded by an air-flow at 298 K. The fuel, ethylene (C2H4), is also at 298K before leaving the fuel tube. Relevant Physical properties are Dynamic viscosity of ethylene: F = 1.0310-5 kg/(ms) at 298 K Density of ethylene: = 1.18 kg/m3 at 298 K Diffusion coefficient of ethylene in air: D = 0.135 cm2/s at 298 K. i. In the ethylene/air flame (the base case), the flow rate of fuel is 0.207 litres/minute. How long would the flame be? (10 marks) Assume the flame temperature is 1750 K. Calculate the exit fuel jet velocity (v), and check fuel jet Reynolds number (Re) to evaluate whether the jet is laminar (Re < 2,000) or turbulent. You can use Re = vD/ F Estimate the flame length using the Ropers model (Lf, thy) and correction (Lf, exp), respectively. (refer to slides 11-14 in Lecture 13: Laminar non-premixed flames) ii. If adding oxygen into the oxidiser flow with volume fractions of 5%, 10% and 20%, respectively, how would the flame length change and how long does the flame become. Estimate flame lengths using Lf, thy and Lf, exp, respectively. (5 marks) Assume the diffusion coefficient does not change when oxygen is added. Assume the flame temperature does not change (because soot is formed in these flames and acts as a temperature buffer) Adding oxygen into the oxidising flow with a volume fraction of 5% means that the oxidising flow composites of 5% O2 and 95% air. iii. If nitrogen was simultaneously diluted into both the fuel and the oxidising streams of the base flame with a volume fraction of 5%, how would the flame length change and how long does the flame become. Estimate flame lengths using Lf, thy and Lf, exp, respectively. (5 marks) The fuel stream becomes 5% N2 + 95% fuel, while the oxidising steam is 5% N2 + 95% air Assume the diffusion coefficient does not change when nitrogen is diluted; Also assume that the flame temperature and the total flow rate of the fuel stream are constant. iv. Discuss your results by comparing them with the flames photos that can be found in Figure 1 of Sun et al., Combustion and Flame, (2020), Vol 211, page 96-111, https://doi.org/10.1016/j.combustflame.2019.09.023 and also to Figure 9.12 of Turns S., (2020), p345. (5 marks)