Solutions Manual Internal Combustion Engines: Applied Thermosciences
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1 Solutions Manual Internal Combustion Engines: Applied Thermosciences Professor Allan T. Kirkpatrick Mechanical Engineering Department Colorado State University Fort Collins, CO January 23, 2017
2 2
3 Chapter 1 Introduction to Internal Combustion Engines 1.1 Compute the mean piston speed, bmep (bar, torque (Nm, and the power per piston area for the engines listed in Table 1.2. Bore Stroke Speed Power Engine (mm (mm Cylinders (rpm (kw Marine Truck Airplane Table 1.2 Engine Data for Homework Problems a U p 2Ns U p 2 20 rev min min s 11m /s m /s , m /s b bmep 2Ẇ V d N 12 ( π 4 8 ( π 4 8 ( π 4 2Ẇ ( n π c 4 (b 2 (s(n ( (0.127 ( ( (0.095 ( ( (0.057 ( 10, kpa 23.3bar kpa 12.0bar kpa 22.5bar 3
4 4 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES c d τ Ẇ 2πN (1118(1000 (2π ( Nm (447(1000 (2π ( Nm (522(1000 (2π ( Nm Power Piston Area Ẇ ( n π 2 c 4 (b ( ( π kN /m 2 4 (0.136 (447 ( kN /m 2 8 ( π 4 (522 8 ( π 4 ( ,233kN /m 2
5 5 1.2 A six-cylinder two-stroke engine with a compression ratio r 9 produces a torque of 1100 Nm at a speed of 2100 rpm. It has a bore b of 123 mm and a stroke s of 127 mm. a. What is the displacement volume and the clearance volume of a cylinder? b. What is the engine bmep, brake work, and mean piston speed? a V d ( π ( (b 4 2 π (s ( (0.127 V d m 3 But we know that r V d +V c V c V c V d r 1 Solving for the clearance volume we get V c V d r V c m 3 b bmep 2πτ (2π(1100 n c V d (6 ( Pa 763kPa ( 2100 Ẇ 2πτN (2π( W 242kW ( 2100 U p 2Ns 2 ( m /s
6 6 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.3 A 4 cylinder 2.5 L spark ignited engine is mounted on a dyno and operated at a speed of N 3000 rpm. The engine has a compression ratio of 10:1 and mass air-fuel ratio of 15:1. The inlet air manifold conditions are 80 kpa and 313 K. The engine produces a torque of 1 Nm and has a volumetric efficiency of a. What is the brake power Ẇb (kw? b. What is the brake specific fuel consumption bsfc (g/kwh? a b Ẇ b 2πτN (2π(1 Ẇ b 50.3kw ṁ f ṁa 1 AF 2 (e v(ρ(v d (N ( AF 1 2 ( (0.287(313 ṁ f kg/s ( e4 Nm/s ( 1 2 (e P v R it i (V d (N AF ( ( 3000 AF bsfc ṁf Ẇ b 50.3 bsfc 217 g /kwh kg/kj
7 7 1.4 The volumetric efficiency of the fuel injected marine engine in Table 1.2 is 0.80 and the inlet manifold density is 50% greater than the standard atmospheric density of ρ amb 1.17 kg/m 3. If the engine speed is 20 rpm, what is the air mass flow rate (kg/s? a e v 2(ṁ a +ṁ f ρv d N 2(ṁ a +ṁ f ρ [ n c ( π 4 b2 s ] N We can rearrange the equation to solve for the mass flow rate of air ṁ a 1 2 e vρ i V d N 1 [ ( π ] 2 e vρ i n c b 2 s N 4 ṁ a 1 ( π ] [( ( 0.8(1.5(1.17 ( (0.127 ṁ a kg /s
8 8 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.5 A 380 cc single-cylinder two-stroke motorcycle engine is operating at 5500 rpm. The engine has a bore of 82 mm and a stroke of 72 mm. Performance testing gives a bmep 6.81 bar, bsfc 0.49 kg/kw hr, and delivery ratio of (a What is the fuel to air ratio, FA? (b What is the air mass flow rate (kg/s? a ρ amb 1.17 kg /m 3 Assumed value for density FA ṁf ṁ a bmep Ẇb V d N bsfc ṁf Ẇ Ẇb ṁf ṁ bmep b bsfc D r ṁa ρv d N f (bsfc(v d (N Solving for the fuel mass flow rate: ṁ f (bmep(bsfc(v d (N ( ( 0.49 [(π ] ( ( ( g /s ṁ f kg/s Solving for the air mass flow rate: [( π ] ṁ a (D r (ρ a (V d (N (0.748(1.17 ( ( ( g /s ṁ a kg/s Solving for the fuel to air ratio: FA ṁf 3.23 ṁ a FA b See the calculation above ṁ a kg/s
9 9 1.6 A 3.8Lfour-stroke4 four cylinder fuel-injected automobile engine has a power output of 88 kwat 4000 rpmand volumetricefficiency of0.85. The bsfc is 0.35kg/kWhr. Ifthe fuel has aheat ofcombustionof 42 MJ/kg, what are the bmep, thermal efficiency, and air to fuel ratio? Assume atmospheric conditions of 298 K and 1 bar. a b bmep 2Ẇ V d N 2(88 ( ( bmep 694kPa 1 η bsfc(q 0 1 ( 0.35 η c ( 0.35 ṁ f Ẇ (bsfc ( kg/s 30 ṁ a e v(ρ a (V d (N 2 A ṁa ṁ f A (0.85(1.17( ( kg /s
10 10 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.7 A 4.0 L six cylinder engine is operating at 3000 rpm. The engine has a compression ratio of 10:1, and volumetricefficiency of0.85. Ifthe boreandstrokeareequal, what isthe stroke, the meanpiston speed, cylinder clearance volume, and air mass flow rate into the engine? Assume standard inlet conditions. a b V d n c π 4 b3 b s s m U p 2Ns 2 U p 9.47 m /s [ ] [ 1/3 ( 4Vd ( πn c ( 3000 ( (π(6 ] 1/3 c V c V d r V c m 3 d ṁ a 1 2 e vρ i V d N 1 ( P 2 (e v (V d (N 12 ( RT (0.85 ṁ a kg/s 100 (0.287(298 ( ( 3000
11 1.8 Chose an automotive, marine, or aviation engine of interest, and compute the engine s mean piston speed, bmep, power/volume, mass/volume, and power/mass. Compare your calculated values with those presented in Table
12 12 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.9 Compare the approximate, Equation (1.29, and exact, Equation (1.26, dimensionless cylinder volume versus crank angle profiles for r 8,s 100 mm, and l 150 mm. What is the maximum error and at what crank angle does it occur? Using the program Volume.m, the exact and approximate volume profiles are computed and plotted below. The program output indicates the maximum error is 16.3 % at crank angles of ± 62 degrees. function [ ]Volume( % this program computes and plots the exact % and approximate cylinder volume clear(; r 8; % compression ratio s 100; % stroke (mm len 150; %connecting rod length (mm eps/(2*len; theta-180:1:180; %crankangle theta vector ys1(1-cosd(theta/2; %approx y/s ys2 ys1+ (1-(1- ep^2*sind(theta.^2.^(1/2/(2*ep; %exact y/s vol1 1+(r-1*ys1; %approx volume vol2 1+(r-1*ys2; % exact volume diff abs(vol1-vol2./vol1 * 100; [diffmax, id_max] max(diff; thmaxtheta(id_max; %plot results fprintf( Max Diff (percent %5.2f at theta (deg %5.2f \n, diffmax,thmax; figure; plot(theta,vol1, --,theta,vol2, -, linewidth,2; set(gca, Xlim,[ ], Ylim,[0 r], fontsize,18, linewidth,2; xlabel( Crank Angle (deg, fontsize, 18; ylabel( Dim. Cylinder Volume, fontsize, 18; legend( Approx. Volume, Exact Volume, Location, North ; figure; plot(theta,diff, linewidth,2; set(gca, Xlim,[ ], fontsize,18, linewidth,2; xlabel( Crank Angle (deg, fontsize, 18; ylabel( Dim. Error (%, fontsize, 18; end
13 Approx. Volume Exact Volume Dim. Cylinder Volume Crank Angle (deg Figure 1.1: Problem 1-9 volume plot Dim. Error (% Crank Angle (deg Figure 1.2: Problem 1-9 volume error plot
14 14 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.10 Plot the dimensionless piston velocity for an engine with a stroke s 100 mm and connecting rod length l 150 mm. Using the program Velocity.m, the dimensional and dimensionless velocity profiles are computed and plotted below. The program output indicates the maximum velocity is m/s at an angle of 73 degrees. function [ ]Velocity( % this program computes and plots the % dimensional and dimensionless piston velocity clear(; N2000; %rev/min s 0.10; % stroke (m len 0.150; %connecting rod length (m eps/(2*len; theta0:1:180; %crankangle theta vector term1pi/2*sind(theta; term2 (1+(ep*cosd(theta./(1 - ep^2*sind(theta.^2.^(1/2; %exact y/s Upbarterm1.*term2; %dimensionless velocity UpUpbar*2*N*s/; % m/s [umax, id_max] max(up; %get max velocity thmaxtheta(id_max; % and crank angle %output results fprintf( U max (m/s %5.2f at theta (deg %5.2f \n, umax,thmax; figure; plot(theta,up, linewidth,2; set(gca, Xlim,[0 180], fontsize,18, linewidth,2; xlabel( Crank Angle (deg, fontsize, 18; ylabel( Piston Velocity (m/s, fontsize, 18; figure; plot(theta,upbar, linewidth,2; set(gca, Xlim,[0 180], Ylim,[0 1.8], fontsize,18, linewidth,2; xlabel( Crank Angle (deg, fontsize, 18; ylabel( Dimensionless Piston Velocity, fontsize, 18; end
15 Piston Velocity (m/s Crank Angle (deg Figure 1.3: Problem 1-10 velocity plot Dimensionless Piston Velocity Crank Angle (deg Figure 1.4: Problem 1-10 dimensionless velocity plot
16 16 CHAPTER 1. INTRODUCTION TO INTERNAL COMBUSTION ENGINES 1.11 Assuming that the mean effective pressure, mean piston speed, power per unit piston area, and mass per unit displacement volume are all size independent, how will the power per unit weight of an engine depend upon the number of cylinders if the total displacement is constant? To make the analysis easier, assume that the bore and stroke are equal. a The power/weight can be expanded in terms of the power/area and mass/displacement volume Ẇ Ẇ m A m If b s, then π 4 b2 n c π V d 4 b2 sn c V d π ( 4Vd 4 b3 n c b s πn c Substituting for s 1/3 Ẇ Ẇ m A m V d ( 1/3 πnc 1/3 n c 4V d The power per unit weight scales as the number of cylinders to the 1/3 power.
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