Diesel Cycle

11 Key excerpts on "Diesel Cycle"

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  Thermal Power Plant

  Design and Operation

  • Dipak Sarkar(Author)
  • 2015(Publication Date)
  • Elsevier

    (Publisher)

  v is the specific volume. The ideal Diesel Cycle follows four distinct processes: compression, combustion, expansion, and cooling. The cycle follows the numbers 1–4 in the clockwise direction.

  • Process 1 to 2 is a isentropic compression process. The air is compressed isentropically through a volume ratio v 1 /v 2 . During this process work (W in ) is done by the piston compressing the working fluid.

  • Process 2 to 3 is a reversible constant-pressure heat addition process. Heat (Q in ) is supplied by combustion of the fuel while the air expands at constant pressure to volume v 3 during this process.

  • Process 3 to 4 is an isentropic expansion process to the original volume v 1 . Work (W out ) is done by the working fluid expanding on to the piston, which produces usable torque.

  • Process 4 to 1 is a reversible constant volume heat rejection (cooling) process. During this process heat (Q out ) is rejected by exhausting air until the cycle is completed.

  Figure 8.2 P-v Diagram of ideal Diesel Cycle.

  Figure 8.3 T-s Diagram of ideal Diesel Cycle.

  The stages of these four processes are discussed in the following. Note that theoretically each of the strokes of the cycle complete at either top dead center (TDC) or bottom dead center (BDC). However, due to delay in the opening and closing of the inlet and exhaust valves, the inertia of inlet air and exhaust gas, each of the strokes invariably begin and end beyond the TDC and BDC.

  8.2.1.1 Compression

  The cycle is started by drawing air at ambient conditions into the engine (Figure 8.4 ). This air is then compressed adiabatically by moving the piston upward in the cylinder from BDC to TDC (Figure 8.5 ). This compression raises the temperature of the air to a level where the fuel mixture, which is formed by injecting fuel once the air is compressed, spontaneously ignites. It is in this part of the cycle that work is applied to

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  Pounder's Marine Diesel Engines

  • C. T. Wilbur, D. A. Wight, Marine Propulsion(Authors)
  • 2016(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  1 Theory and general principles THEORETICAL HEAT CYCLE In the original patent by Rudolf Diesel, the diesel engine operated on the Diesel Cycle in which the heat was added at constant pressure. This was achieved by the blast injection principle. Nowadays the term is universally used to describe any reciprocating engine in which the heat induced by compressing air in the cylinders ignites a finely atomised spray of fuel. This means that the theoretical cycle on which the modern diesel engine works is better represented by the dual or mixed cycle, diagram-matically illustrated in Figure 1.1. The area of the diagram, to a suit-able scale, represents the work done on the piston during one cycle. Ρ Ε -• Volume Figure 1.1 Theoretical heat cycle of true Diesel engine 1 2 THEORY AND GENERAL PRINCIPLES Starting from point C, the air is compressed adiabatically to a point D. Fuel injection begins at D, and heat is added to the cycle partly at constant volume as shown by vertical line DP, and partly at constant pressure, as shown by horizontal line PE. At the point Ε expansion begins. This proceeds adiabatically to point F when the heat is rejected to exhaust at constant volume as shown by vertical line FC. The ideal efficiency of this cycle (i.e. of the hypothetical indicator diagram) is about 55-60%: that is to say, about 40-45% of the heat supplied is lost to the exhaust. Since the compression and expansion strokes are assumed to be adiabatic, and friction is disregarded, there is no loss to coolant or ambient. For a four-stroke engine the exhaust and suction strokes are shown by the horizontal line at C, and this has no effect on the cycle. PRACTICAL CYCLES While the theoretical cycle facilitates simple calculation, it does not exactly represent the true state of affairs.

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  Rules of Thumb for Mechanical Engineers

  • J. Edward Pope(Author)
  • 1996(Publication Date)
  • Gulf Professional Publishing

    (Publisher)

  = 1- T4/T3 = 1- T~/T 2 R=Compression ratio =v 1/v 2 3 Q ~=constant 'n S=c0nstant ~ -00ut 1 v 2 v 1 3 Win ~ 4 1 Qout Figure 8. Otto cycle (ideal closed system). Wou t Diesel Cycle: Another Power Cycle In a diesel engine, only air is compressed; fuel is intro- duced only at the end of the compression stroke. That is why it is often referred to as a compression-ignition engine. This cycle (Figure 9) uses the heat of the compression process to start the combustion process. The four process- es involved are 1-2 Adiabatic compression 2-3 Heat addition at constant pressure 3-4 Adiabatic expansion (power stroke) 4-1 Heat rejection at constant volume The heat flow in and out of the system and the work input and work output terms are: qin = Cp (T 3 - T2), qout = Cv (T4- T l) Win = c, (I2 - Tl), Wout = Cv (T3 - T4) + (Cp - Cv) (T 3 - T2) The thermal efficiency of the cycle is: q in - qout % - TI rlthermal = = 1- qin k (T 3 - T 2) 64 Rules of Thumb for Mechanical Engineers , Gout 1 V 1 Gout Figure 9. Diesel Cycle. Gas Power Cycles with Regeneration Use of regeneration is an effective way of increasing the thermal efficiency of the cycle, particularly at low com- pressor pressure ratios. The Stirling and Ericsson cycles are such attempts to get efficiencies close to that of the ideal Carnot cycle. Stirling Cycle This cycle (Figure 10) can come to attain the thermal ef- ficiency very close to that of a Carnot cycle. The isother- mal processes can be attained by reheating and intercool- ing. This cycle is suitable for application in reciprocating machinery. The four processes involved are: 1-2 Heat addition at constant volume (compression) 2-3 Isothermal expansion with heat addition (energy input and power stroke) 3-4 Heat rejection at constant volume 4-1 Isothermal compression with heat rejection In an ideal regenerator, the quantity of heat rejected during 3-4 is stored in the regenerator and then is restored to the working fluid during the process 1-2.

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  Thermodynamics

  A Smart Approach

  • Ibrahim Dinçer(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  There have been many power generators that have used the Diesel Cycle. Therefore, the engines are enlisted as compression ignition internal combustion engines. The combustion process occurs when the air is compressed to the autoignition temperature; pressurized fuel is then sprayed and instantaneously combusts. For the combustion process to occur the air temperature has to be over 800 K ; the volume ratio, also known as the compression ratio for the Diesel Cycle, is in the range r v = 12 – 24. With such a compression ratio and high temperatures a spark is no longer required to initiate the combustion process in a compres-sion ignition engine. The rate of the reaction due to no spark plug causes the combustion to be relatively slow compared to that of the spark ignition engine. The pressure within the cylinder can be kept relatively steady contingent that the injection process of the fuel occurs at the top dead center of the cylinder. Although the Diesel Cycle looks similar to the Otto cycle due to the three common processes, there is heat addition taking place during an isobaric process. The volume during the combustion process increases and the temperature of the gas will also increase. The four processes that make up the Diesel Cycle are shown in Figure 6.7 along with P-v (in Figure 6.7a) and T-s (in Figure 6.7b) diagrams. It is also equally important to explain each of these processes briefly. Isobaric heat addition Isobaric heat addition Isentropic expansion Isentropic expansion Isentropic compression Isentropic compression Isochoric heat rejection Isochoric heat rejection (a) (b) q in q in q out q out W out W ou t v W in W in P T 2 2 2 s 4 s s 4 4 1 1 1–2 1–2 3–4 4–1 4–1 3–4 2–3 2–3 3 3 Figure 6.7 A basic, ideal Diesel Cycle processes along with (a) P-v diagram and (b) T-s diagram. 320 6 Power Cycles • Process 1-2: This process includes an isentropic compression of the working gas (air) as external work is being applied.

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  Thermodynamic Cycles

  Computer-Aided Design and Optimization

  • Chih Wu(Author)
  • 2003(Publication Date)
  • CRC Press

    (Publisher)

  Combustion in the Otto cycle is based on a constant-volume process; in the Diesel Cycle, it is based on a constant-pressure process. However, combustion in actual spark-ignition engine requires a finite amount of time if the process is to be complete. For this reason, combustion in the Otto cycle does not actually occur under the constant-volume condition. Similarly, in compression-ignition engines, combustion in the Diesel Cycle does not actually occur under the constant-pressure condition, because of the rapid and uncontrolled combustion process.

  The operation of the reciprocating internal combustion engines represents a compromise between the Otto and the Diesel Cycles, and can be described as a dual combustion cycle. Heat transfer to the system may be considered to occur first at constant volume and then at constant pressure. Such a cycle is called a dual cycle.

  The Dual cycle as shown in Fig. 3.20 is composed of the following five processes:

  Figure 3.20

  Dual cycle.

  1-2 Isentropic compression 2-3 Constant-volume heat addition 3-4 Constant-pressure heat addition 4-5 Isentropic expansion 5-1 Constant-volume heat removal

  Figure 3.21 shows the dual cycle on p–v and T–s diagrams.

  Figure 3.21

  Dual cycle on p–v and T–s diagrams.

  Applying the first and second laws of thermodynamics of the closed system to each of the five processes of the cycle yields: and

  The net work (Wnet ), which is also equal to net heat (Qnet ), is

  The thermal efficiency of the cycle is This expression for the thermal efficiency of an ideal Otto cycle can be simplified if air is assumed to be the working fluid with constant specific heat. Equation (3.48) is reduced to:

  Example 3.11

  Pressure and temperature at the start of compression in a dual cycle are 14.7 psia and 540°R. The compression ratio is 15. Heat addition at constant volume is 300 Btu/lbm of air, while heat addition at constant pressure is 500 Btu/lbm of air. The mass of air contained in the cylinder is 0.03 lbm. Determine (1) the maximum cycle pressure and maximum cycle temperature, (2) the efficiency and work output per kilogram of air, and (3) the MEP. Show the cycle on T–s

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  Thermodynamics and Heat Power, Ninth Edition

  • Irving Granet, Jorge Alvarado, Maurice Bluestein(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  Fuel is distributed through a distribution valve, which directs the metered fuel to the individual injection valves. The injection valves have mechanically operated plungers to raise the oil pressure to the required injection pressure. In this system, the injection valve pressurizes the fuel and also times the fuel injection. However, it does not meter the fuel. Because of the exacting requirements for fuel injection in a Diesel engine, these engines run in a narrow range of speeds. Thus, Diesel engines used for transportation require more transmission gearing than comparable Otto cycle engines. 9.4 Air-Standard Analysis of the Diesel Cycle All the assumptions made for the air-standard analysis of the Otto cycle regarding the working fluid and its properties apply to the present analysis of the idealized Diesel Cycle. The idealized air-standard Diesel Cycle consists of four processes. The first is an isentropic compression of the air after it has been inducted into the cylinder. At the end of the compression process, fuel is injected, and combustion is assumed to occur at constant pressure. Subsequent to the heat release by combustion, the gas is expanded isentropically to produce work, and finally, heat is rejected at constant volume. The gas is assumed to be recycled rather than rejected. Figure 9.11 shows the ideal Diesel Cycle on both p–v and T–s coordinates. FIGURE 9.11 Diesel Cycle. Heat is received (reversibly) during the nonflow, constant-pressure process, © to ®. The energy equation for a constant-pressure (flow or nonflow) yields q in = c p (T 4 − T 3) Btu/lb m, kJ/kg (9.12) The energy rejected during the constant-volume process is q r = c v (T 5 − T 2) Btu/lb m, kJ/kg (9.13) The net work available from the cycle is W = q in − q r = c p (T 4 − T 3) − c v (T 5 − T 2) Btu/lb m, kJ/kg (9.14) The efficiency thus. becomes η Diesel = c p (T 4 − T 3) − c v (T 5 − T 2) c p (T 4 − T 3) = 1 − 1 k T 5 − T 2 T 4 − T 3 (9.15) Where k = c p / c v

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  Fundamentals of Heat Engines

  Reciprocating and Gas Turbine Internal Combustion Engines

  • Jamil Ghojel(Author)
  • 2020(Publication Date)
  • Wiley-ASME Press Series

    (Publisher)

  In this comparison, the Diesel Cycle is the most efficient and the Otto cycle the least efficient. Problems 3.1 Consider the following data for the ideal piston-engine cycle with constant-volume heat addition (Otto cycle): p 1 = 0.1 MPa , T 1 = 293 K , 𝜀 = 4.5, 𝛼 = 3.5, 𝛾 = 1.4. Assuming constant specific heat, determine Problems 117 (a) Properties at the characteristic points of the cycle (b) Amounts of heat supplied and rejected (c) Thermal efficiency (d) Net cycle work 3.2 The following information provided is for an ideal piston-engine cycle with constant-pressure heat addition (Diesel Cycle): p 1 = 0.1 MPa , T 1 = 293 K , 𝜀 = 12.7, 𝛾 = 1.4, c pa = 1.0117 kJ / kg . K . Determine (a) Properties at the characteristic points of the cycle (b) Amounts of heat supplied and rejected (c) Thermal efficiency (d) Net cycle work 3.3 The hypothetical cycle 1 − 2 − 3 − 4 has two constant-pressure and two constant-volume processes. If the specific heats at constant pressure and constant volume are assumed constant, and 𝛼 = p 2 / p 1 , 𝜌 = v 3 / v 2 , show that the thermal efficiency is given by the following equation: 𝜂 t = 1 − 𝛽 ( 𝛼 − 1 + 𝛾 ) − 𝛾 𝛼 − 1 + 𝛾𝛼 ( 𝛽 − 1 ) p V 4 1 3 2 3.4 The initial pressure and temperature in an air-standard cycle with dual combustion process are 90 kPa and 340 K , respectively. The total heat input into the cycle is Q in = 1090 kJ / kg , and the compression ratio 𝜀 = 10. If the maximum cycle pressure is not to exceed 6.5 MPa , calculate the percentage of the total heat that must be provided at constant volume. Assume constant heat capacity throughout. 3.5 A small truck has a four-cylinder, four-litre compression ignition (CI) engine operating on the air-standard dual cycle shown. The heat q in provided externally per cycle to each cylinder is from the combustion of 0.05 g of light diesel fuel with lower heating value of 42 500 kJ/kg . The compression ratio of the engine is 15:1, and the cylinder bore is 100 mm.

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  Advanced Thermodynamics

  Fundamentals, Mathematics, Applications

  • Mehrzad Tabatabaian, R. K. Rajput(Authors)
  • 2017(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  This cycle comprises the following operations: (i) 1–2......Adiabatic compression. (ii) 2–3......Addition of heat at a constant pressure. (iii) 3–4......Adiabatic expansion. FIGURE 11.15. Diesel Cycle on p-v (left) and T-s (right) diagrams. GAS POWER CYCLES • 545 (iv) 4–1......Rejection of heat at a constant volume. Point 1 represents that the cylinder is full of air. Let p 1 , V 1 , and T 1 be the corresponding pressure, volume, and absolute temperature. The piston then compresses the air adiabatically (i.e., pVγ = constant) till the values become p 2 , V 2 , and T 2 , respectively (at the end of the stroke) at point 2. Heat is then added from a hot body at a constant pressure. During this addition of heat let volume increase from V 2 to V 3 and temperature T 2 to T 3 , corresponding to point 3. This point (3) is called the point of cut-off. The air then expands adiabatically to the conditions p 4 , V 4 , and T 4 , correspond- ing to point 4. Finally, the air rejects the heat to the cold body at a constant volume till point 1 where it returns to its original state. Consider 1 kg of air. ( ) 3 2 Heat supplied at constant pressure p c T T = − ( ) 4 1 Heat rejected at constant volume v c T T = − Work done Heat supplied heat rejected = − ( ) ( ) 3 2 4 1 p v c T T c T T = − − − diesel Work done η Heat supplied ∴ = ( ) ( ) ( ) 3 2 4 1 3 2 p v p c T T c T T c T T − − − = − ( ) ( ) ( ) 4 1 3 2 1 ... γ γ p v c T T i T T c −   = − =   −    Let compression ratio, 3 1 2 2 Volume at cut-off , and cut-off ratio, ρ . ., Clearance volume v v r i e v v = = Now, during adiabatic compression 1–2, ( ) ( ) γ 1 γ 1 γ 1 2 1 2 1 1 2 or . T v r T T r T v − − −   = = =     During constant pressure process 2–3, ( ) γ 1 3 3 3 2 1 2 2 ρ or ρ. ρ. . T v T T T r T v − = = = = 546 • ADVANCED THERMODYNAMICS During adiabatic expansion 3–4 γ 1 3 4 4 3 T v T v −   =     γ 1 ρ r −   =     4 1 1 2 3 3 2 3 ρ v v v v r v v v v   = = × =      ( ) γ 1 1 γ 3 4 1 γ 1 γ 1 ρ.

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  Thermodynamics and Heat Power

  • Irving Granet, Maurice Bluestein(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  At the end of the com-pression process, fuel is injected, and combustion is assumed to occur at constant pressure. Subsequent to the heat release by combustion, the gas is expanded isentropically to produce work, and finally, heat is rejected at constant volume. The gas is assumed to be recycled rather than rejected. Figure 9.11 shows the ideal Diesel Cycle on both p – v and T – s coordinates. Heat is received (reversibly) during the nonflow, constant-pressure process, ③ to ④ . The energy equation for a constant-pressure (flow or nonflow) yields q in = c p ( T 4 − T 3 ) Btu/lb m , kJ/kg (9.12) The energy rejected during the constant-volume process is q r = c v ( T 5 − T 2 ) Btu/lb m , kJ/kg (9.13) The net work available from the cycle is W = q in − q r = c p ( T 4 − T 3 ) − c v ( T 5 − T 2 ) Btu/lb m , kJ/kg (9.14) 447 Gas Power Cycles The efficiency thus becomes η Diesel = ----= --c T T c T T c T T k T T T v p p ( ) ( ) ( ) 4 3 5 2 4 3 5 2 1 1 4 4 3 -T (9.15) At this point, it becomes conventional to introduce two terms and to define them as follows: compression ratio r v v c = 2 3 (9.16) and expansion ratio r v v e = 5 4 (9.17) Based on the nonflow processes discussed in Chapter 6, we can write T T r T T r k k 3 2 1 5 4 1 1 = = --( ) ( ) c e and (9.18) Because heat is received at constant pressure, T T v v 4 3 4 3 = (9.19) The ratio of r r v v v v v v v v v v v v c e = = = = 2 3 5 4 4 2 3 5 2 5 4 3 / / and because ( ) (9.20) p T v s 3 1 5 4 2 3 2 4 5 Work out Work Work out in Work in Q in Q r Q r Q in FIGURE 9.11 Diesel Cycle. 448 Thermodynamics and Heat Power This ratio v 4 / v 3 is called the cutoff ratio . Therefore, T T r r r 4 3 = = c e c.o. (9.21) By substituting Equations 9.16 through 9.21 into Equation 9.15 and rearranging, we obtain η Diesel / / = ---( ) = -1 1 1 1 1 k r r r r r k k ( ) ( ) c e c e c 1 1 1 1 1 ----r r k r k k c ( ) ( ) .

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  Thermodynamics and Energy Systems Analysis

  • Lucien Borel, Daniel Favrat, Dinh Lan Nguyen, Magdi Batato(Authors)
  • 2012(Publication Date)
  • EPFL PRESS

    (Publisher)

  394 Brayton cycle Process 3-4 The integration of the general relations gives, for an isentropic process, according to Table 8.6 (Vol. I): 4 3 a - = 4 Z 3 P dv = c v T 3 1 - P 4 P 3 Γ ! = c v T 1 χ c (χ γ-1 - χ γ-1 c ) 4 3 q + = 0 Process 4-1 The integration of the general relations gives, for an isochoric process, ac- cording to Table 8.1 (Vol. I): 1 4 a - = 0 1 4 q - = - 1 Z 4 T ds = c v (T 4 - T 1 ) = c v T 1 (χ γ c - 1) Power effectiveness of the cycle The power effectiveness of the cycle is, according to Definition (13.43) and according to (13.44): m = 3 2 a - + 4 3 a - - 2 1 a + 3 2 q + = 1 - 1 4 q - 3 2 q + = 1 - χ γ c - 1 γχ γ-1 (χ c - 1) The diagram of Figure 13.9 shows the power effectiveness of the Diesel Cycle as a function of the compression ratio χ c , with the compression ratio χ as a parameter. 13.F Brayton cycle Description A Brayton cycle is a bithermal power cycle, with internal heat transfer, made of two isentropic processes and of two isobaric processes (Fig. 13.10). It is theoretically possible to realize a Brayton cycle by means of the closed system, with fluid transfer and in steady-state operation, shown in Figure 13.11. We consider a system operated with air. The air flowing through the cycle undergoes the following processes: 1-2: adiabatic compression without dissipation; 2-3: isobaric heating by reversible internal heat transfer ˙ Q R ; Thermodynamic cycles 395 Figure 13.9 3-4: isobaric heating by external heat transfer ˙ Q + E with a hot source at tem- perature T h ; 4-5: adiabatic expansion without dissipation; 5-6: isobaric cooling by internal heat transfer ˙ Q R , reversible; 6-1: isobaric cooling by external heat transfer ˙ Q - a with a cold source at tem- perature T a (atmosphere). Hypotheses • The changes of kinetic and potential energies are negligible.

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  Engineering Principles in Everyday Life for Non-Engineers

  • Saeed Benjamin Niku, Saeed Benjamin(Authors)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  Consequently, the air feels better because it is cooler and also drier. However, like refrigerators, the condensed water has to be drained. You may have noticed that in many air-conditioning systems, it appears that the unit is leaking. That is in fact condensed water and not a leak. The same is true in automobile air- conditioners. Other than these differences, an air-conditioning system and a refrigeration system are thermodynamically very similar. 4.3 SPARK-IGNITION POWER CYCLE A spark-ignition cycle approximates the cycle of power development by an internal combustion engine with spark plugs. This is also similar to what is referred to in thermodynamics as an Otto Cycle which is an ideal cycle (an ideal cycle is approximate. Real cycles differ somewhat from ideal cycles. But to learn the principles, we always start with an ideal cycle, then modify the cycle to a more realistic model). Conversely, a compression ignition cycle approximates a diesel engine, where the air is compressed much more and consequently, it becomes much hotter to the point that when the fuel is injected into it, it explodes and burns without the need for a spark plug. We will discuss the differences between these two engines later. An internal combustion engine in general refers to any type of engine in which the com- bustion of the fuel and air within a closed environment produces the gases that generate the mechanical work, and includes regular gasoline engines, diesel engines, rotary engines, and jet engines. Conversely, steam engines are not internally combusting engines; in steam engines, the fire is outside of the engine and instead, combustion products boil water into steam in a boiler and the steam is used to power the engine. Common gasoline and diesel engines are called recip- rocating IC engines because the piston reciprocates (moves up and down) in a cylinder, rotating a crankshaft that is connected to it via a crank and a connecting rod.

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