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UBC MECH327 A6.tex
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\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \usepackage{cancel} \begin{document} {\large UBC MECH327 Assignment 6} \begin{align*} &\text{One method of increasing the output of an internal combustion engine is turbo-compounding, in which the exhaust gases are}\\ &\text{expanded in an isentropic turbine to produce useful work as shown below. The engine can be modeled using an ideal Otto air}\\ &\text{standard cycle, with a compression ratio of 8:1. The engine is operating such that the maximum in-cylinder pressure is 8 MPa}\\ &\text{and the initial mixture temperature and pressure are 320 K and 90 kPa, respectively. Assume constant specific heat capacities}\\ &\text{of the working fluid at 300 K.}\\ \\ &\text{1. On the supplied $Ts$ diagram, draw the corresponding air standard cycle for the turbo-compounded system (system (ii)).}\\ &\text{The isobars and isochores are intentionally not labelled on the diagram and correspond to:}\\ \\ &\quad p=10\text{ kPa},\quad v=8\text{ m$^3$/kg},\quad T=278.7\text{ K}.\\ &\quad p=90\text{ kPa},\quad v=1\text{ m$^3$/kg},\quad T=313.6\text{ K}.\\ &\quad p=1\text{ MPa},\quad v=0.125\text{ m$^3$/kg},\quad T=435.5\text{ K}.\\ &\quad p=8\text{ MPa},\quad v=0.0313\text{ m$^3$/kg},\quad T=872.5\text{ K}.\\ \\ &\text{Identify the proper isoline for each process.}\\ \\ &\text{2. Find the 1st law efficiency of the engine (system (i))}\\ \\ &\text{3. Find the 1st law efficiency of the turbo-compounded engine (system (ii))}\\ \\ &\text{4. Find the additional work per unit mass of air provided by the turbine in system (ii)}\\ \\ &\text{5. Compare the total exergy destruction of the heat rejection process for each of the air standard cycles.}\\ \\ \end{align*} \end{document}