MECE541_homework1_solultion

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Apr 3, 2024

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DEPARTME N T OF MECHA N ICAL E N GI N EERI N G I N TER N AL COMBUSTIO N E N GI N ES MECE 541 M. Shahbakhti HOMEWORK #1 SOLUTION

MECE 541: Assignment 1 2 M. Shahbakhti THE UNIVERSITY OF ALBERTA INTERNAL COMBUSTION ENGINES - MEC E 541 1. Early Internal Combustion Engines [12 marks] a. Otto and Langen developed a free piston internal combustion engine and then a reciprocating piston internal combustion engine. What was important about their engines that allowed them to compete with the already-established Lenoir engines? Solution: Otto and Langen's engines used compression of the unburnt mixture prior to combustion and thus gave higher power for a given cylinder size and higher efficiency than the Lenoir engine. b. Rudolph Diesel created a compression-ignition engine with considerably higher efficiency than the Otto cycle engine. What advantage gave his engine such high efficiency? Solution: Diesel's objective was to use a very high compression ratio to give high efficiency. Even though the Diesel cycle is less efficient than the Otto cycle for the same compression ratio, Diesel was able to use compression ratios more than three times as the contemporary Otto engines. 2. Engine Performance and Dimensions [28 marks] WardsAuto ™ had awarded "Ten Best Engines of 2021" status to the Ford F-150 Hybrid PowerBoost™ twin-turbocharged 3.5-liter V-6 engine. This six-cylinder turbocharged port fuel injection & direct-injection SI engine has the peak brake torque of 570.0 lbf.ft @ 3000.0 rpm and the peak brake power of 430.0 hp @ 6000.0 rpm. The engine compression ratio is 10.5:1; the bore is 3.64 inches and the stroke is 3.41 inches. [Interesting video to watch: https://www.youtube.com/watch?v=KMVZ2eHUiUk&t=33s ] Image: wardsauto.com a. What is the engine power band? Solution: Power Band is commonly defined as the range from peak torque to peak power which, in this case is only 3000 rpm to 6000 rpm so: “The engine has a 3000 -rpm power band from 3000 to 5000 rpm.”

MECE 541: Assignment 1 3 M. Shahbakhti b. Is the displacement precisely 3.5 liters? Solution: Bore is 3.64 inches = 0.092 m and the stroke is 3.41 inches = 0.087 m ࠵? ࠵? = 6 (࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?) × ࠵?࠵? 2 4 ࠵? = 6 × ࠵?×0.092 2 4 × 0.087 = 3.45 × 10 − 3 ࠵? 3 = 3.5 liter The ideal displacement is 3.5 liters and it matches the calculation. c. What is the engine bmep at peak torque? at peak power? Solution: At peak torque (570.0 lbf.ft = 773 N .m): ࠵?࠵?࠵?࠵? = 2࠵? ࠵? ࠵? ࠵? ࠵?࠵?࠵?࠵? ࠵? ࠵? = 2×࠵?×2×773. 3.5 ×10 −3 = 2775372.7 ࠵?࠵? = 27.8 bar At peak power ( 430.0 hp ): ࠵?࠵?࠵?࠵?࠵? = 430. (hp) 1.341 ( hp kW ) = 320.7 kW ࠵?࠵?࠵?࠵? = ࠵? ࠵?࠵?࠵?࠵? ࠵? ࠵? ࠵? ࠵? ࠵? = 320.7 × 1000 × 2 3.5 × 10 −3 × 100 = 1832571.4 Pa = 18.33 bar d. What is the mean piston speed at peak torque? at peak power? Solution: ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? (࠵? ࠵? ) = 2࠵?࠵? At peak torque (773 N.m ): ࠵? ࠵? = 2 × 0.087 × 3000.0 rev min × 1min 60 sec = 8.70 m/s At peak power (430 hp): ࠵? ࠵? = 2 × 0.087 × 6000.0 rev min × 1min 60 sec = 17.4 m/s e. If you were selecting transmission gears to give an economical cruise speed, what engine speed would you select as a base? Solution: As a rule of thumb, we assume 5.0 m/s piston speed ( V p ) for an economical cruise state (this idea comes from the course note on the page 1.12) ࠵? = ࠵? ࠵? ( m s ) × 60 ( sec min ) ࠵? ࠵? ( stroke rev ) × ࠵? ( m stroke ) = 5.0 × 60 2 × 0.087 = 1724 rpm Hence, I would plan on having the engine speed around 1720 rpm for cruise.

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MECE 541: Assignment 1 4 M. Shahbakhti 3. Engine Specific Power [21 marks] The power per unit piston area P/A p (often called the specific power) is a measure of the designer's success in using the available piston area regardless of size. a. Derive an expression for P/A p , in terms of mean effective pressure and mean piston speed for two- stroke and four-stroke engine cycles. Solution: ࠵?࠵?࠵? = ࠵? ࠵? ࠵? ࠵? ࠵? ࠵? Recall that: ࠵? ࠵? = ࠵? ࠵? ࠵? Therefore: ࠵?࠵?࠵? = ࠵? ࠵? ࠵? ࠵? ࠵? ࠵? ࠵? Rearranging the previous expression, we get: ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵?࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵?࠵? × 2 ࠵? ࠵? × 2 = (࠵?࠵?࠵?) 2࠵?࠵? 2࠵? ࠵? Recall that: ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? (࠵? ࠵? ) = 2࠵?࠵? Therefore: ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵? ࠵? 2࠵? ࠵? For 2-stroke engine, ࠵? ࠵? = 1, and for 4-stroke engine, ࠵? ࠵? = 2. Thus: ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵? ࠵? 2 (2 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?) ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵? ࠵? 4 (4 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?)

MECE 541: Assignment 1 5 M. Shahbakhti b. Compute typical maximum values of P/A p for the following two engines. State your assumptions clearly. 2021 Cummins X15 Performance 14.9-liter inline 6-cylinder compression ignition engine; Application: Long-haul trucks; Bore 137 mm, stroke 169 mm, compression ratio 18.9:1, maximum power 421 kW at 1900 rev/min [Cummins.com] Solution: Convert Bore and stroke to meters, convert power to Watt and Rotational speed to rev/sec. Cummins Engine: ࠵?࠵?࠵? = ࠵? ࠵? ࠵? ࠵? ࠵? ࠵? = 421000 × 2 14.9 × 10 −3 × 31.7 rev/sec = 1782652 Pa= 1782.6 kPa= 17.8 bar ࠵? ࠵? = 2LN = 2 × 0.169 × 31.7 = 10.7 m S ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵? ࠵? 4 = 1782.6 × 10.7 4 = 4768.5 kW/m 2 = 4.77 MW/m 2

MECE 541: Assignment 1 6 M. Shahbakhti Large Wärtsilä- Sulzer RTA96-C two-stroke turbocharged 14-cylinder marine diesel engine. Bore 960.0 mm, stroke 2500.0 mm, rated power 80.080 MW at 102.00 rev/min [wartsila.com; topspeed.com] Solution: Large Marine Engine: ࠵? ࠵? = 14 × ࠵?࠵? 2 4 × ࠵? = 14 × ࠵?(0.96) 2 4 × 2.5 = 25.3 m 3 ࠵?࠵?࠵? = ࠵? ࠵? ࠵? ࠵? ࠵? ࠵? = 80.080 × 10 6 × 1 25.3 × 1.7 rev/sec = 1,861,892 Pa = 1862 kPa= 18.6 bar ࠵? ࠵? = 2 × ࠵? × ࠵? = 2 × 2.5 × 1.7 = 8.5 m/s ࠵? ࠵? ࠵? = (࠵?࠵?࠵?) ࠵? ࠵? 2 = 1862 × 8.5 2 = 7913 kW/m 2 = 7.9 MW/m 2

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MECE 541: Assignment 1 7 M. Shahbakhti 4. Engine BSFC and Fuel Conversion Efficiency [10 marks] The brake fuel conversion efficiency of a compression-ignition engine is 0.360, and varies little with fuel type. Calculate the brake specific fuel consumption for diesel, and methane in g/(kW.h). The lower heating value for diesel and methane fuels are 43.20 MJ/kg and 50.01 MJ/kg, respectively . Solution: Brake fuel conversion efficiency is given by: ࠵? ࠵?,࠵? = 1 ࠵?࠵?࠵?࠵? × ࠵? ℎ࠵? = 0.36 Where bsfc = break specific fuel consumption, Q hv = lower heating value For diesel: Q hv = 43.2 MJ/kg ࠵?࠵?࠵?࠵? = 1 0.36 × ࠵? ℎ࠵? = 1 0.36 × 43.2 = 0.0643 g kJ × kJ. sec kW × 3600 sec 1 h = 231.5 g kWh For methane: Q hv = 50.01 MJ/k g ࠵?࠵?࠵?࠵? = 1 0.36 × ࠵? ℎ࠵? = 1 0.36 × 50.01 = 0.0555 g kJ × kJ. sec kW × 3600 sec 1 h = 200. g kWh

MECE 541: Assignment 1 8 M. Shahbakhti 5. Engine Multiple-choice Questions [21 marks] Four marks for correct answer, three marks for brief justification for each question 5.1 Your friend is working in an oil and gas Company where they recently installed a newly developed Cummins turbocharged, 12-cylinder 45-Liter direct injection 4-stroke diesel engine for a stationary application. Which of the following can be the specifications of the new engine? Why? a) Compression ratio: 10 Bore/Stroke ratio: 1.8 Ratio of rod length to crank throw: 4.4 c) Compression ratio: 16 Bore/Stroke ratio: 1.2 Ratio of rod length to crank throw: 8.2 b) Compression ratio: 14 Bore/Stroke ratio: 0.5 Ratio of rod length to crank throw: 6.4 d) Compression ratio: 8.0 Bore/Stroke ratio: 0.4 Ratio of rod length to crank throw: 7.4 Solution: Option b is correct because the engine is an industrial diesel engine, so i. the compression ratios of 10 and 8 seem too low (see the eClass handout on the page 1.11). Selections a and d are wrong. ii. the Bore/Stroke ratio of 1.2 seems too high (see the eClass handout on the page 1.12). Selection c is wrong. iii. Selection b is correct as all the specifications can match a typical diesel industrial engine. 5.2 2009 Ferrari F430 runs with a 4.3 Liter V8 engine with a compression ratio of 11.3. The engine is rated as having the peak IMEP 11 bar @5000 rpm. Peak brake power of the engine is 490 bhp @8500 rpm. What do you expect to be the engine speed at peak BMEP? Why? a) 8500 rpm c) 5500 rpm b) 5000 rpm d) 4500 rpm Solution: Option d is correct because BMEP = IMEP - FMEP and FMEP increases linearly with the engine speed, so peak of BEMP is expected to occur at an engine speed below the engine speed for the peak IMEP. Thus the answer should be an engine speed below 5000 rpm. 5.3 2021 Toyota Prius 1.8 Liter in-line, 16-valve, 4-cylinder DOHC gasoline engine is rated as having peak torque of 142N.m at 3600 rpm and peak power of 96 hp at 5200 rpm. How much do you expect for the mechanical efficiency of this engine at idling condition (e.g., 700 rpm)? Why? a) 0% c) 30% b) 40-50% d) 90% Solution: Option a is correct because at idling condition with closed throttle, the engine output power is zero. Thus, the mechanical efficiency would be zero.

MECE 541: Assignment 1 9 M. Shahbakhti 6. Alternative Propulsion Systems [8 marks] Purely electric vehicles are becoming more common. What are the major advantages and disadvantages of electric vehicles compared to vehicles using internal combustion engines? Solution: Electric vehicles alone do not produce combustion-related emissions (although the methods used to produce electricity often do have emissions). Emissions from ICEs are a major problem in urban areas, that is why Canada and France will ban ICE-only vehicles by 2040 (plug-in hybrids using ICEs will still be allowed). In addition, electric motors have maximum torque at low motor speed which means electric vehicles can accelerate very quickly. Energy conversion efficiency of electric motors are typically between 70 to 95% that is substantially higher than ICEs with typical peak brake fuel conversion efficiencies up to 55%. The major problem with electric vehicles is that the energy density of the batteries is still very low compared to gasoline or diesel fuel, resulting in a low vehicle range. Vehicle cost, charging time, and availability of charging stations are other limiting factors. See the image below from the most recent report by the United States Energy Information Administration (EIA) for forecasting new vehicles sale in the US up to year 2050.

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