1. Diesel / Brayton Cycles
ASEN 3113

2. Diesel Cycle Invented by Rudolf Christian Karl Diesel in 1893
First engine was powered by powdered coal
Achieved a compression ratio of almost 80
Exploded, almost killed Diesel
First working engine completed generated 13 hp

3. Diesel Engine Also known as Compression Ignition Engine (CI)
Can this engine “knock”?
Difference from Otto Cycle?

4. Thermodynamic Cycles for CI engines
In early CI engines the fuel was injected when the piston reached TDC
and thus combustion lasted well into the expansion stroke.
In modern engines the fuel is injected before TDC (about 15o)
Fuel injection starts
Fuel injection starts
Early CI engine
Modern CI engine
The combustion process in the early CI engines is best approximated by
a constant pressure heat addition process  Diesel Cycle
The combustion process in the modern CI engines is best approximated
by a combination of constant volume and constant pressure  Dual Cycle

5. Early CI Engine Cycle and the Thermodynamic Diesel Cycle
Fuel injected
at TC A I R
Air
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Qin
Qout
Air
Diesel
Cycle BC
Compression
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process

6. Air-Standard Diesel cycle Process a b Isentropic compression
Cut-off ratio:
Process a b Isentropic compression
Process b  c Constant pressure heat addition
Process c  d Isentropic expansion
Process d  a Constant volume heat rejection
- a=1,b=2,etc…for book

7. First Law Analysis of Diesel Cycle
Equations for processes 12, 41 are the same as those presented
for the Otto cycle
23 Constant Pressure Heat Addition
now involves heat and work
AIR
Qin

8. 3  4 Isentropic Expansion
AIR
note v4=v1 so

9. Thermal Efficiency
For cold air-standard the above reduces to:
recall,
Note the term in the square bracket is always larger than one so for the
same compression ratio, r, the Diesel cycle has a lower thermal efficiency
than the Otto cycle
So why is a Diesel engine usually more efficient?

10. When rc (= v3/v2)1 the Diesel cycle efficiency approaches the
Thermal Efficiency
Typical CI Engines
15 < r < 20
When rc (= v3/v2)1 the Diesel cycle efficiency approaches the
efficiency of the Otto cycle
Higher efficiency is obtained by adding less heat per cycle, Qin,
 run engine at higher speed to get the same power.

11. The cut-off ratio is not a natural choice for the independent variable
a more suitable parameter is the heat input, the two are related by:
as Qin 0, rc1
k = 1.3
k = 1.3
- compares performance of engines of the same size

12. Modern CI Engine Cycle and the Thermodynamic Dual Cycle
Fuel injected
at 15o before TDC A I R
Air
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Qin
Qin
Qout
Air
Dual
Cycle TC BC
Compression
Process
Const volume
heat addition
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process

13. Process 1  2 Isentropic compression
Dual Cycle
Process 1  2 Isentropic compression
Process 2  2.5 Constant volume heat addition
Process 2.5  3 Constant pressure heat addition
Process 3  4 Isentropic expansion
Process 4  1 Constant volume heat rejection 3
Qin
2.5 3 2
Qin
2.5 4 2 4 1 1
Qout

14. Thermal Efficiency
Note, the Otto cycle (rc=1) and the Diesel cycle (a=1) are special cases:

15. The use of the Dual cycle requires information about either:
the fractions of constant volume and constant pressure heat addition
(common assumption is to equally split the heat addition), or
ii) maximum pressure P3.
Transformation of rc and a into more natural variables yields
For the same initial conditions P1, V1 and the same compression ratio:
For the same initial conditions P1, V1 and the same peak pressure P3
(actual design limitation in engines):

17. Brayton Cycle Introduced by George Brayton (an American) in 1872
Used separate expansion and compression cylinder
Constant Combustion process

18. Brayton Cycle

19. Other applications of Brayton cycle
Power generation - use gas turbines to generate electricity…very efficient
Marine applications in large ships
Automobile racing - late 1960s Indy 500 STP sponsored cars

20. Schematic of simple cycle

21. Idealized Brayton Cycle

22. Brayton Cycle 1 to 2--isentropic compression
2 to 3--constant pressure heat addition (replaces combustion process)
3 to 4--isentropic expansion in the turbine
4 to 1--constant pressure heat rejection to return air to original state

23. Brayton cycle analysis
Because the Brayton cycle operates between two constant pressure lines, or isobars, the pressure ratio is important.
The pressure ratio is not a compression ratio.
Efficiency:
Net work:

24. Brayton cycle analysis
1 to 2 (isentropic compression in compressor), apply first law
**When analyzing the cycle, we know that the compressor work is in (negative). It is standard convention to just drop the negative sign and deal with it later:

25. Brayton cycle analysis
2 to 3 (constant pressure heat addition - treated as a heat exchanger)
3 to 4 (isentropic expansion in turbine)

26. Brayton cycle analysis
4 to 1 (constant pressure heat rejection)
We know this is heat transfer out of the system and therefore negative. In book, they’ll give it a positive sign and then subtract it when necessary.

27. Brayton cycle analysis
net work:
Substituting:

28. Brayton cycle analysis
Thermal efficiency:

29. Brayton cycle analysis
assume cold air conditions and manipulate the efficiency expression:

30. Brayton cycle analysis
Using the isentropic relationships,
Define:

31. Brayton cycle analysis
Then we can relate the temperature ratios to the pressure ratio:
Plug back into the efficiency expression and simplify:

32. Brayton cycle analysis

33. Brayton cycle analysis
An important quantity for Brayton cycles is the Back Work Ratio (BWR).

34. The Back-Work Ratio is the Fraction of Turbine Work Used to Drive the Compressor

35. EXAMPLE PROBLEM
The pressure ratio of an air standard Brayton cycle is 4.5 and the inlet conditions to the compressor are 100 kPa and 27C. The turbine is limited to a temperature of 827C and mass flow is 5 kg/s. Determine
a) the thermal efficiency
b) the net power output in kW
c) the BWR
Assume constant specific heats.

36. Draw diagram

37. Start analysis Let’s get the efficiency:
From problem statement, we know rp = 4.5

38. Net power output: Net Power: Substituting for work terms:
Applying constant specific heats:

39. Need to get T2 and T4 Use isentropic relationships:
T1 and T3 are known along with the pressure ratios:
T2:
T4:
Net power is then:

40. Back Work Ratio
Applying constant specific heats:

41. Brayton Cycle
In theory, as the pressure ratio goes up, the efficiency rises. The limiting factor is frequently the turbine inlet temperature.
The turbine inlet temp is restricted to about 1,700 K or 2,600 F.
Consider a fixed turbine inlet temp., T3

42. Brayton Cycle Irreversibilities
Compressor and turbine frictional effects - cause increase in entropy
Also friction causes pressure drops through heat exchangers
Stray heat transfers in components
Increase in entropy has most significance
wc = h2 – h1 for the ideal cycle, which was isentropic
wt = h3 – h4 for the ideal isentropic cycle

43. Brayton Cycle
In order to deal with irreversibilities, we need to write the values of h2 and h4 as h2,s and h4,s.
Then