MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2 615 INTERNAL COMBUSTION ENGINES Homework Set 8 Due 5 6 2014 Problems 1 The following exercise is for you to get a feel for the magnitude of things for a modern turbo charged truck diesel engine The Hino K13C 4 stroke turbo charged diesel engine has the following specifications No of cylinders Total displacement Bore x Stroke Compression ratio Rated power bsfc rated power Injection common rail max pressure Nozzles Compressor pressure ratio at rated power Intercooler outlet temperature at rated power 6 12882 cc 135 mm x 150 mm 16 5 294 KW 2000 rpm 200 g KW hr 1400 bar 8 per injector 200 m diameter each 2 5 120o C At rated power the volumetric efficiency is approximately 0 8 The fuel pulse width is 40o crank angle We ll assume that the injection rate is constant at the average value for the following analysis The actual needle lift profile has a triangular shape delivery rate Compute the following quantities at rated power You may assume that the cylinder condition at the time of injection to be 50 bar and 800K Diesel fuel at 120o C the fuel operating temperature has s g 0 78 and viscosity 5x10 4 N s m2 a b c d e f g 2 a b What are the air mass flow rate and the average fuel flow rate for the engine What is the A F On a per cylinder per cycle basis what are the air mass the fuel mass and fuel volume injected per cycle You should get a mental picture of these quantities What is the average flow velocity through each nozzle hole If the nozzle hole has a length to diameter ratio of 10 what is the pressure drop Is this drop significant What is the average discharge coefficient for each nozzle If the critical Webber number is 30 what is the average droplet diameter of the diesel spray The surface tension of the diesel fuel at the injection condition is 0 025 N m If all the drops are of the same size as calculated in f how many drops are there If these drops are to be distributed uniformly in the cylinder at TDC what is the average distance between the drops What is the implication of these facts on the air fuel mixing process Neither assumption is a good one but the estimates give a picture of the difficulty of air utilization The compression ratio of a diesel engine must be high enough for fast auto ignition An acceptable ignition delay is 20o crank angle We ll use the ignition delay equations Eq 10 37 38 and 39 to study this Note that there is a typo in Eq 10 37 see errata sheet on the web The inlet pressure and temperatures are 1 bar and 20oC 253K The cranking speed is 200 rpm The fuel has a cetane number of 45 For a truck engine with a 135 mm stroke the polytropic exponent n for compression is 1 2 Plot the ignition delay as a function of compression ratio CR in the range of 12 to 25 Determine the minimum CR required For a small passenger car diesel engine with a stroke of 80 mm because of the higher heat loss n 1 12 Plot the ignition delay on the same graph as in a and determine the minimum CR required 3 The soot burn up rate may be obtained by the Nagle and Strickland Constable formula which is given by Eq 11 41 11 42 and Table 11 10 of the text The value w in the formula is the surface oxidation rate in g cm2 s Since the data for the correlation were obtained from graphite oxidation experiments the rate is the value for carbon We ll assume that the oxidation of soot particle is at the same rate as that of carbon Also the density of the soot is assumed to be 2 g cc Do the calculations for the following conditions a p 100 bar and T 2500 K b p 70 bar and T 2000 K c p 30 bar and T 1400 K The three conditions represent roughly at the peak pressure point at the end of combustion and late in the expansion process i To show that mass transport is not the limiting process for oxidation of small particles calculate the transport time d2 D for particle diameter d of 10 100 and 1000 nm The mass diffusivity D is p T D m 2 s 1 8 x10 5 0 1 81 where p 0 1 bar and T0 300K p T0 ii Calculate the time to oxidize particle of diameter 100 nm for oxygen mole fractions of 0 1 1 and 10 Note that to have fast oxidation sufficient oxygen has to be available at high temperatures