CHAPTER5MEC 451ThermodynamicsAir Standard CycleLecture Notes:MOHD HAFIZ MOHD NOHHAZRAN HUSAIN & MOHD SUHAIRIL Faculty of Mechanical EngineeringUniversiti Teknologi MARA, 40450 Shah Alam, SelangorFor students EM 220 and EM 221 only

Upon derivation the performance of the real cycle is often measured in terms of its thermal efficiencyThe Carnot cycle was introduced as the most efficient heat engine that operate between two fixed temperatures TH and TL. The thermal efficiency of Carnot cycle is given byReview Carnot Cycle*

The ideal gas equation is defined aswhereP = pressure in kPav = specific volume in m3/kg (or V = volume in m3)R = ideal gas constant in kJ/kg.Km = mass in kgT = temperature in KReview Ideal Gas Law**

The u and h of ideal gases can be expressed asu - constant volume processh - constant pressure process*

According to a law of Review Thermodynamics Processes*

ProcessDescriptionResult of IGLisochoricconstant volume (V1 = V2)isobaricconstant pressure (P1 = P2)isothermalconstant temperature(T1 = T2)polytropic-none-isentropicconstant entropy (S1 = S2)

R = 0.2871 kJ/kg.KCp = 1.005 kJ/kg.KCv = 0.718 kJ/kg.Kk = 1.4whereR = ideal gas constantCp = specific heat at constant pressureCv = specific heat at constant volume k = specific heat ratioReview Properties of Air*

IC Engine combustion of fuel takes place inside an engines cylinder.Introduction*

Air continuously circulates in a closed loop. Always behaves as an ideal gas. All the processes that make up the cycle are internally reversible. The combustion process is replaced by a heat-addition process from an external source.Air-Standard Assumptions*

A heat rejection process that restores the working fluid to its initial state replaces the exhaust process.The cold-air-standard assumptions apply when the working fluid is air and has constant specific heat evaluated at room temperature (25oC or 77oF).No chemical reaction takes place in the engine.Air-Standard Assumptions*

Top dead center (TDC), bottom dead center (BDC), stroke, bore, intake valve, exhaust valve, clearance volume, displacement volume, compression ratio, and mean effective pressureTerminology for Reciprocating Devices*

The compression ratio r of an engine is defined as The mean effective pressure (MEP) is a fictitious pressure that, if it operated on the piston during the entire power stroke, would produce the same amount of net work as that produced during the actual cycle.*

Otto CycleThe Ideal Cycle for Spark-Ignition Engines*

The processes in the Otto cycle are as per following:*

Process Description1-2 Isentropic compression2-3 Constant volume heat addition3-4 Isentropic expansion4-1 Constant volume heat rejection

1

2

3

4

Qout

Qin

Pvg=Constant

v1

v2

v

P

Qout

Qin

1

2

3

4

(a) P-v diagram

(b) T-s diagram

s

T

Related formula based on basic thermodynamics:*

Thermal efficiency of the Otto cycle:Apply first law closed system to process 2-3, V = constant.Thus, for constant specific heats*

Apply first law closed system to process 4-1, V = constant.Thus, for constant specific heats,The thermal efficiency becomes *

Recall processes 1-2 and 3-4 are isentropic, soSince V3 = V2 and V4 = V1,*

The Otto cycle efficiency becomes Since process 1-2 is isentropic,where the compression ratio is r = V1/V2 and *

An Otto cycle having a compression ratio of 9:1 uses air as the working fluid. Initially P1 = 95 kPa, T1 = 17C, and V1 = 3.8 liters. During the heat addition process, 7.5 kJ of heat are added. Determine all T's, P's, th, the back work ratio and the mean effective pressure.Example 5.1Solution:Data given:*

Example 5.1*

Example 5.1*

Example 5.1Then:*

Example 5.1What else?*

Supplementary Problems 5.1An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kPa and 27C, and 750 kJ/kg of heat is transferred to air during the constant-volume heat-addition process. Taking into account the variation of specific heats with temperature, determine (a) the pressure and temperature at the end of the heat addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. [(a) 3898 kPa, 1539 K, (b) 392.4 kJ/kg, (c) 52.3 percent,(d ) 495 kPa]The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at 100 kPa, 35C, and 600 cm3. The temperature at the end of the isentropic expansion process is 800 K. Using specific heat values at room temperature, determine (a) the highest temperature and pressure in the cycle; (b) the amount of heat transferred in, in kJ; (c) the thermal efficiency; and (d) the mean effective pressure. [(a) 1969 K, 6072 kPa,(b) 0.59 kJ, (c) 59.4 percent, (d) 652 kPa]*

The processes in the Diesel cycle are as per following:Diesel Cycle*

Diesel Cycle*

Related formula based on basic thermodynamics:*

Thermal efficiency of the Diesel cycle Apply the first law closed system to process 2-3, P = constant. Thus, for constant specific heats*

Apply the first law closed system to process 4-1, V = constantThus, for constant specific heatsThe thermal efficiency becomes*

Recall processes 1-2 and 3-4 are isentropic, soSince V4 = V1 and P3 = P2, we divide the second equation by the first equation and obtainTherefore,*

An air-standard Diesel cycle has a compression ratio of 18 and a cut-off ratio of 2.5. The state at the beginning of compression is fixed by P = 0.9 bar ant T = 300K. Calculate:the thermal efficiency of the cycle,the maximum pressure, Pmax, andThe mean effective pressure.Example 5.2Solution:Data given:*

Example 5.2*

Example 5.2What we need?*

Supplementary Problems 5.2An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the thermal efficiency and (b) the mean effective pressure. Assume constant specific heats for air at room temperature. [ (a) 63.5 percent, (b) 933 kPa]An ideal diesel cycle has a compression ratio of 16 to 1. The maximum cycle temperature is 1700C and the minimum cycle temperature is 15C. Calculate:the specific heat transfer to the cycle the specific work of the cycle the thermal efficiency of the cycle*

Dual cycle gives a better approximation to a real engine. The heat addition process is partly done at a constant volume and partly at constant pressure. From the P-v diagram, it looks like the heat addition process is a combination of both Otto and Diesel cycles. Dual Cycle*

The same procedure as to Otto and Diesel cycles can be applied to Dual cycle. Upon substitutions, the thermal efficiency of Dual cycle becomes Dual Cycle*

At the beginning of the compression process of an air-standard dual cycle with a compression ratio of 18, the temperature is 300 K and the pressure is 1 bar. The pressure ratio for the constant volume part of the heating process is 1.5 to 1. The volume ratio for the constant pressure part of the heating process is 1.2 to 1. Determine (a) the thermal efficiency and (b) the mean effective pressure. (WRONG SOLUTION!!)Example 5.3Solution:Data given:*

*

Information needed?*

Answer the questions ?*

Indicated power (IP)Brake power (bp)Friction power (fp) and mechanical efficiency, mBrake mean effective pressure (bmep), thermal efficiency and fuel consumptionVolumetric efficiency, vCriteria of Performance*

Defined as the rate of work done by the gas on the piston as evaluated from an indicator diagram obtained from the engine using the electronic engine indicator.For four-stroke engine,And for two-stroke engine,Indicated Power*ip = work done per cycle cycle per minuten is the number of cylinders.

Indicated Power*Indicated mean effective pressure, pi given by:,For one engine cylinder Work done per cycle = pi A L Where A = area of piston L = length of stroke

Power output = (work done per cycle) x (cycle per minute)

For four-stoke engines, the number of cycles per unit time is N/2 and for two-stroke engines the number of cycles per unit time is N, where N is the engine speed.

Brake power is a way to measure the engine power output.The engine is connected to a brake (or dynamometer) which can be loaded so that the torque exerted by the engine can be measured.The torque is obtained by reading off a net load, w at known radius, r.Brake Power*

ThereforeBrake power is also can be expressed asThen the brake mean effective pressure (Pb) is*

Friction Power*The difference between the Ip and bp is the friction power (fp). It is the power that overcome the frictional resistance of the engine parts.

Power input to the shaft is usually bigger than the indicated power due to frictional losses or the mechanical efficiency.Mechanical Efficiency*

Brake Mean Effective Pressure*From the definition of Brake power Since for 4 stroke engine andSince and Pi are difficult to obtain, they may be combined and replaced by a brake mean effective pressure, PbEquating this equation to another definition of bp: So: Its observed that bmep is proportional to torque.

Brake Thermal Efficiency*The power output of the engine is obtained from the chemical energy of the fuel supplied. The overall engine efficiency is given by the brake thermal efficiency, mf = mass flow fuel , Qnet,v = net calarofic value of the fuel.

sfc is the mass flow rate of fuel consumed per unit power output and is a criterion of economical power production.Specific Fuel Consumption*

Volumetric efficiency is only used with four-stroke cycle engine, which have a distinct induction process. The parameter used to measure the effectiveness of an engines induction process is the volumetric efficiency.Volumetric Efficiency*

An engine operating at 2400 rpm consumes 12 ml of fuel (s.g. 0.85) in 60 second. The engine indicates a load of 30 N on the pony brake system and the brakes torque arm is 20 cm. Determine (a) the brake power, (b) the mass flow rate of fuel, and (c) the specific fuel consumption.Example 5.4Solution:*

A four-cylinder petrol engine has a bore of 57 mm and a stroke of 90 mm. Its rated speed is 2800 rpm and it is tested at this speed against a brake which has a torque arm of 0.356 m. The net brake load is 155 N and the fuel consumption is 6.741 l/h. The specific gravity of the petrol used is 0.735 and it has a net calorific value of 44,200 kJ/kg. The engine is tested in an atmospheric condition at 101.325 kPa and 15 oC at air-fuel ratio of 14.5/1. Calculate for this speed, the engine torque, the bmep, the brake thermal efficiency, the specific fuel consumption and the volumetric efficiency of the engine.Example 5.4Solution:*

Real Case*

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