diesel engine combustion analysis

1

Compiled by

Ted Diehl, Seaworthy Systems, Inc.

July, 2009

Diesel Engine Combustion Analysis

Thermodynamics vs. Reality Overview

2

General Diesel Engine Terms to Know (Review)

• Top Dead Center = TDC• Bottom Dead Center = BDC• Bore = Diameter of the cylinder• Stroke = Distance from BDC to

TDC (Length of the piston travel)• Displacement Volume = “Swept

Volume” = Bore area x Stroke x number of cylinders

• Clearance Volume = Volume left at top of cylinder, piston at TDC

• Compression Ratio (rc) = Displacement Volume / Clearance Volume

3

General Diesel Engine Parameters to Know (Review)

• Work = force through a distance [lbf-ft or kJ]

• Power = rate of Work [horsepower or kW]

• Mean Effective Pressure (MEP) = Work / Displacement Volume [psig or bar]

• Specific Fuel Consumption (SFC) = mass of fuel consumption rate / Power Output [lbm/hp-hr or g/kW-hr]

• Thermal Efficiency = Work Out / Heat In [%]

• Mechanical Efficiency = Actual Output / Predicted Output [%]

4

Numbers to know• 778 → BTU / ft-lbf• 2,545 → BTU/hr / HP• 33,000 → ft-lbf/min / HP• 550 → ft-lbf/sec / HP• 0.756 → kW / HP

KkgkJ

Rlblbft

R oom

fairdry ⋅

=⋅

⋅= 287.035.53_

KkgkJ

RlbBTUc oo

mp ⋅

=⋅

= 005.124.0

KkgkJ

RlbBTUc oo

mv ⋅

=⋅

= 718.0171.0

4.1==v

p

cc

k

5

2-Stroke vs. 4-Stroke Diesel Comparison

2-Stroke• 1 up-stroke and down-

stroke• Every down-stroke is a

power stroke• Has intake “ports”• Can have exhaust ports or

exhaust valve(s)• Intake and exhaust must

happen faster than 4-stroke

4-Stroke• 2 up-strokes and down-

strokes• Every other down-stroke is a

power stroke• Has intake and exhaust

valves• Uses extra up-stroke to

push out exhaust

Both are “Compression Ignition” engines, relying on the temperature rise of compressed air to ignite the fuel, and with fuel injected into the cylinder rather than the fuel/air mixture used in spark ignition engines

6

2-Stroke Diesel Engine Stages• Up-stroke

1. Intake (“Scavenging” )• Begins early as part of the

downstroke, before BDC, to give gas time to leave cylinder

2. Compression• Injection of fuel happens before

TDC• Down-Stroke

3. Power (Combustion/Expansion)• Ends when port (or exhaust

valve) opens4. Exhaust

• Intake stage helps (somewhat) to push the residual gases out

7

2-Stroke Engine Timing• 1-2 injection (fuel)• 2-3 expansion (power) • 3-5 exhaust• 4-5 scavenging • 4-6 intake• 6-1 compression

8

4-Stroke Diesel Engine Stages• Down-stroke 1

A. Intake• Intake valve opens just before

exhaust valve closes (overlap helps to “clean out” cylinder)

• Piston “sucks” air into cylinder (often assisted by turbocharger pressurizing air)

• Up-stroke 1B. Compression

• Injection of fuel happens before TDC

• Down-stroke 2C. Power (Combustion/Expansion)

• Exhaust valve opens before BDC• Up-stroke 2

D. Exhaust• The piston expels the

combustion byproduct and does some amount of “pumping” work

9

4-Stroke Engine Timing

• 1-2 suction, • 2-3 compression• 3-4 injection (fuel)• 4-5 expansion (power)• 5-6 exhaust

10

Features to Note• There are physical and

practical constraints that effect the timing of the events during the strokes– Ex. The mass of air/gas has inertia

(resistance to motion) so time is required for the gas to enter and leave the cylinder

– Ex. Fuel takes time to ignite and to burn

• These constraints result in necessary overlaps in the events– Valves open at the same time– Fuel injected before

11

Scavenging

12

Types of Power• Indicated

– Theoretical capability of the engine

– As “indicated” from the thermodynamics or measured P-V diagrams

• Brake– As measured directly after the

engine output coupling– Indicated minus friction losses

• Shaft– As measured after all reduction

gear and auxiliary equipment (and associated losses) have been accounted for

– Brake minus transmission friction losses

– Measured using a shaft horsepower meter

13

Thermodynamic Analysis

Describing the engine in terms of theoretical processes and

quantifying them

14

Thermodynamic Approach• Goal is to simplify real world complex behavior into manageable theoretical

model• Treat as a “closed system” even though air passes through as would normally

be described as an “open system”…instead a control volume of one cylinder worth of air mass is considered and the intake/exhaust is treated as a heat exchange process rather than a mass flow through.

• Divide the cycle into stages (not quite same as strokes)– Intake/Exhaust (heat out)– Compression (work in)– Combustion (heat in)– Expansion (work out)

• Characterize each stage as a “Process”– Constant Volume Process ( V = 0, aka Isometric)– Constant Pressure Process ( P = 0, aka Isobaric)– Constant Temperature Process ( T = 0, aka Isothermal)– Constant Entropy Process ( S = 0, aka isentropic & adiabatic)

• Treat the working fluid/media as an ideal gas– Ideal gas law: PV=mRT (m = mass, R = gas constant)– Makes “walking through” process-to-process easier

• Calculate on a “per mass of air” basis

15

Review of Ideal Gas Thermodynamic Processes Properties

All relationships come from:• Constant Volume Process ( V = 0, aka Isometric)

• Constant Pressure Process ( P = 0, aka Isobaric)

• Constant Entropy Process ( S = 0, aka isentropic)

• Constant Temperature Process ( T = 0, aka Isothermal)*

* Not used in these cycles

0=Δw ( )12 TTcq v −⋅=Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

1

212 T

Tvv ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

1

212 v

vTT ( )12 vvpw −⋅=Δ ( )12 TTcq p −⋅=Δ ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

1

2

1

2 lnlnvvc

TTcs pp

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

2

112 v

vpp

12 vv =

12 pp =

12 TT =

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

1

212 T

Tpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

1

212 p

pTT ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

1

2

1

2 lnlnppc

TTcs vv

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

2

112 p

pvv ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⋅=Δ=Δ

2

1

1

2 lnlnppTR

vvTRqw ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

2

1

1

2 lnlnppR

vvRs

k

vvpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

2

112

k

ppvv

1

2

112 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

1

2

112

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

k

vvTT ( )21 TTcw v −⋅=Δ 0=Δq 0=Δs

TRmVp ⋅⋅=⋅ TRvp ⋅=⋅2

22

1

11

TVp

TVp ⋅

=⋅

16

Diagrammatic Representations of the Cycle Parameters

• P-V diagrams – Pressure vs. Volume – describe cycle work– can be compared to

actually measured values of real engines

• T-S diagrams – Temperature vs. Entropy– describe cycle heat– Because entropy cannot be

directly measured are generally better to visualize the theoretical model

17

Historical Theoretical Models• Otto Cycle

– Named for Nikolaus Otto, 1854– Uses constant volume heat addition (combustion)– Assumes that combustion is instantaneous at TDC – Generally associated with four-stroke spark ignition

engines because of rapid explosive combustion of gasoline fuel-air mixture

• Diesel Cycle– Named for Rudolph Diesel, 1897– Diesel fuel and Diesel engine share his name – Uses constant pressure heat addition (combustion)– Assumes that combustion takes some time– Generally associated with two-stroke compression

ignition engines because of slower combustion process of diesel fuel

• Dual Cycle– Aka “Combined Cycle” or “Limited Pressure Cycle” or

“Air Standard Cycle” (all of these cycles are sometimes referred to as “Air Standard Cycles”)

– Hybrid of the Otto and Diesel cycles– Allows for a better characterization of the combustion

process– Limits the peak pressure to avoid material strength

limitations• Other Cycles (not relating to diesel engines)

– Carnot (ideal)– Brayton heating (gas turbine)– Brayton cooling (refrigeration)– Rankine (steam plant cycle)– Stirling (temperature difference engine)– Ericsson (external combustion engine)

18

Otto Cycle P-V Diagram1-2 Isentropic

Compression (Work In)

2-3 Isometric Combustion (Heat In)

3-4 Isentropic Expansion (Work out)

4-1 Isometric Intake/Exhaust (Heat Out)

19

Diesel Cycle P-V Diagram1-2 Isentropic


2-3 Isobaric Combustion (Heat In)

3-4 Isentropic Expansion (Work out)


20

Dual Cycle P-V Diagram1-2 Isentropic


2-3a Isometric Combustion (Heat In 1st Stage)

3a-3b Isobaric Combustion (Heat In 2nd Stage)

3b-4 Isentropic Expansion (Work out)


21

P-V and T-S Diagrams

• The area under P-V diagram relates the cycle in terms of work (use units to verify that psi x in3 to be lbf-in, i.e. force through a distance work units)

• The area under T-S diagram relates the cycle in terms of heat (use units to verify that BUT/lbm-oF x oF to be BTU/lbm, i.e. heat units)

• These two diagrams compare theoretical cycles with the same heat input and compression ratios ∴ the engine with the least amount of heat rejection will be mostefficient = Otto wins!!!

• But maximum pressure creates a practical limit on how must heat can be added into the engine and the Diesel Cycle can operate at higher compression ratios than the Otto Cycle

22

• 1-2 Isentropic Compression (Work In)

• 2-3a Isometric Combustion (Heat In 1st Stage)

• 3a-3b Isobaric Combustion (Heat In 2nd Stage)

• 3b-4 Isentropic Expansion (Work out)

• 4-1 Isometric Intake/Exhaust (Heat Out)

( )kcrpp ⋅= 12crvv 1

2 = ( ) 112

−⋅= kcrTT ( )21 TTcw v −⋅=Δ 0=Δq 0=Δs

“Walk Through” the Dual Cycle

0=Δw ( )23 TTcq av −⋅=Δ23 vv a = ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

2

323 T

Tpp aa ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

2

323 p

pTT aa ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

2

3

2

3 lnlnppc

TTcs a

va

v

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

a

bab T

Tvv3

333

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

a

bab v

vTT3

333

( )ab vvpw 33 −⋅=Δ ( )abp TTcq 33 −⋅=Δ ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

a

bp

a

bp v

vcTTcs

3

3

3

3 lnlnab pp 33 =

k

bb v

vpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

334

kb

b ppvv

1

4

334 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

1

4

314

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

k

b

vvTT ( )43 TTcw bv −⋅=Δ 0=Δq 0=Δs

0=Δw ( )41 TTcq v −⋅=Δ41 vv = ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

141 T

Tpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

141 p

pTT ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

4

1

4

1 lnlnppc

TTcs vv

23

1-2 Isentropic Compression (Work In)

( )kcrpp ⋅= 12cr

vv 12 = ( ) 1

12−⋅= k

crTT

( )21 TTcw v −⋅=Δ

0=Δq 0=Δs

Compression

24

• 2-3a Isometric Combustion – (Heat In 1st Stage)

• 3a-3b Isobaric Combustion – (Heat In 2nd Stage)

Combustion

0=Δw23 vv a =

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

2

323 T

Tpp aa ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

2

323 p

pTT aa ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

2

3

2

3 lnlnppc

TTcs a

va

v

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

a

bab T

Tvv3

333 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

a

bab v

vTT3

333

( )ab vvpw 33 −⋅=Δ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

a

bp

a

bp v

vcTTcs

3

3

3

3 lnln

ab pp 33 =

( )23 TTcq av −⋅=Δ

( )abp TTcq 33 −⋅=Δ

25

• 3a-3b Isobaric Expansion (Work out)

• 3b-4 Isentropic Expansion (Work out)

Expansion

k

bb v

vpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

334

kb

b ppvv

1

4

334 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

1

4

314

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

k

b

vvTT

( )4343 TTcw bvb −⋅=Δ −

0=Δq0=Δs

( )abba vvpw 3333 −⋅=Δ −

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

a

bab T

Tvv3

333 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

a

bab v

vTT3

333 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

a

bp

a

bp v

vcTTcs

3

3

3

3 lnlnab pp 33 = ( )abp TTcq 33 −⋅=Δ

26


Intake/Exhaust

0=Δw

( )41 TTcq v −⋅=Δ

41 vv =

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

141 T

Tpp ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

4

141 p

pTT

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=Δ

4

1

4

1 lnlnppc

TTcs vv

27

Net Work• The actual work that

is delivered to the shaft

• Subtract out the work that is put back into the air to compress it

• The net work is the area within the shape formed by the curves

( ) ( )( )

( ) ( ) ( )214333

2121

43334333

TTcTTcvvpwTTcww

TTcvvpwwwwww

vbvabnet

vin

bvabbbaout

inoutnet

−⋅−−⋅+−⋅=Δ−⋅=Δ=Δ

−⋅+−⋅=Δ+Δ=ΔΔ−Δ=Δ

−

−−

28

Heat In• The heat in due to the

combustion of fuel• Estimated by the higher

heating value (HHV) of the fuel on a per air mass basis (use air to fuel ratio to convert this value)

• The proportion of fuel burned during the isometric vs. isobaric events will affect the net work and thermal efficiency

( ) ( )

FAHHVqor

TTcTTcqqqq

in

abpavin

baain

/

3323

3332

⋅=Δ

−⋅+−⋅=ΔΔ+Δ=Δ −−

29

Thermal Efficiency

( ) ( ) ( )( ) ( )

( ) ( ) ( )

( ) ( )abathermal

vbvabthermal

abpav

vbvabthermal

in

netthermal

TTkTTTT

orFAHHV

TTcTTcvvpor

TTcTTcTTcTTcvvp

qw

3323

14

214333

3323

214333

1

/

−⋅+−−

−=

⋅−⋅−−⋅+−⋅

=

−⋅+−⋅−⋅−−⋅+−⋅

=

ΔΔ

=

η

η

η

η

30

Indicated Mean Effective Pressure (iMEP)

• Sometimes called Mean Indicated Pressure (MIP) to differentiate between Brake Mean Effective Pressure (more commonly associated with land based engines)

• “Averaged” pressure of P-V diagram

• Corresponds to engine torque (work)

• A way to describe the “strength” of the engine and/or how heavily loaded it is

• Also used in the “PLAN”formula to describe power

( )12 vvw

iMEP net

−Δ

=

31

dual cycle

constant volume

combustion

constant pressure

combustionrc = 15.0 15.0 15.0 Compression Ratio

R = 0.287 0.287 0.287 kJ/kgoK Gas Constantcp = 1.0050 1.0050 1.0050 kJ/kgoK Specific Heat Constant Pressure

k = 1.4007 1.4007 1.4007 Specific Heat Ratiocv = 0.7175 0.7175 0.7175 kJ/kgoK Specific Heat Constant VolumeP1 = 1.0 1.0 1.0 bar Inlet PressureT1 = 289.0 289.0 289.0 oKv1 = 0.829 0.829 0.829 m3/kg

P2 = 44.4 44.4 44.4 bar Compression pressureT2 = 855 855 855 oK

v2 = 0.055 0.055 0.055 m3/kgwin = 406.4 406.4 406.4 kJ/kg Work in at process 1 to 2P3a = 114 184 bar maximum pressureT3a = 2,204 3,552 oK

v3a = 0.055 0.055 m3/kgqin,3a-2 = 967.5 1,935 kJ/kg Heat in at process 2 to 3a

P3b = 114 44 bar maximum pressureT3b = 3,166 2,781 oK maximum temperaturev3b = 0.0794 0.1798 m3/kg

wout,3b-3a = 276.3 552.6 kJ/kg Work done during process 3a-3bqin,3b-3a = 967.5 1,935 kJ/kg Heat in at process 3a to 3b

P4 = 4.3 4.2 5.2 bar Exhaust pressureT4 = 1,237 1,200 1,507 oK Exhaust temperaturev4 = 0.829 0.829 0.829 m3/kg

wout = 1,384 1,688 914 kJ/kg Work out from process 3b to 4Q* = qin = 1,935 1,935 1,935 kJ/kgQ*/cvT1= 9.33 9.33 9.33

wnet = 1,254 1,281 1,060 kJ/kg Net WorkPmax = 114.4 184.4 44.4 bar maximum pressure

iMEP = 16.20 16.55 13.70 bar indicated mean effective pressureiMEP/P3 = 0.142 0.090 0.308 ratio of mep to P max

η = 64.8 66.2 54.8 % Thermal Efficiency

Theoretical Cycle P-V Diagram Comparison

0

20

40

60

80

100

120

140

160

180

200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

Volume [m3/kg]

Pres

sure

[bar

]

Compression

Limited Pressure Cycle Constant VolumeHeat AdditionLimited Pressure Cycle Constant PressureHeat AdditionLimited Pressure Cycle Expansion

Exhaust

Constant Pressure Heat Addition

Constant Pressure Heat Addition

Constant Press Cycle Expansion

Constant Vol Cycle Expansion

Represents the theoretical best achievable thermal efficiency

Dependant on compression ratioand heat input (fuel injected)

Cycle Example Values

32

Compare the Dual Cycle Theoretical Model to Reality

• The “Work” portions (1-2 and 3b-4) are not isentropic

– there are losses (friction and heat to cylinder walls)

• Point 3a is rounded off, 3a-3b is not flat

– No part of combustion is truly instantaneous

– The piston is moving while the pressure is rising

• Exhaust/Intake (4-1) is not vertical– By necessity, the exhaust valve(s)

and intake valve(s) (or ports) must open to give time for the gases to exchange in the cylinder (there is not instantaneous drop in pressure)

• Also, the working fluid isn’t, in reality, an ideal gas

Source: Harrington, SNAME, p. 94

33

Source: Pounder, p. 6.

Diesel Engine Heat Balance (aka Sankey Diagram)

34

Old SchoolCurve Based Analysis

“Pull cards” and “Banana Curves”

35

Pressure vs. Crank Angle Diagram“Pull Card”

Source: Harrington, SNAME, p. 94

Old School Diesel Engine Performance Analysis

36

Typical Pull Card Events

Source: Warkman, IME TM, 1983.

37

Typical Pull Card Analysis

Source: Warkman, IME TM, 1983.

38

Pull Card Analysis

Source: RO-CIP Guide.

39

Pull Card Analysis


40

Pull Card Analysis


41

The Pressure vs. Volume Diagram“Banana Curve”


42

Common Issues Identified by the “Toe” of the P-V Diagram


43

Modern Diesel Engine Performance Analysis

(DEPA)

44

Modern DiagramsDoctor

Main EngineTwin Inductive pickups on2-strokes

Junction box

Junction box withMil Spec connector

Fischer connector

CIC-3Connecting cable

AEC-1Connecting cable

DK-2 or DK-2/FVDoctor instrument

For Fuel Pressure measurement, the DK-2/FVhas an extra pressure channel. Fuel valves on the pumps allow connection to eachunit in turn.

45

2-Stroke Diesel Engine Example

46

4-Stroke Diesel Engine Example

diesel engine combustion analysis

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