# This Week > POWER CYCLES

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This Week > POWER CYCLES
Definition of a thermodynamic cycle? Carnot Cycle (Max Efficiency Cycle) Otto Cycle (Spark Ignition Engine) Diesel Cycle (Compression Engine) Brayton Cycle (Gas-Turbine Engine)

Analysis of Power Cycles
Energy balance of a thermodynamic cycle Because system returns to initial state - no net change in energy Power Cycle - Net work to surrounding from net heat transfer to system

Power Cycles Energy conversion from heat to work - thermal efficiency
Commonly employed assumptions and idealizations: Cycle is frictionless - no pressure drops in flow Expansion and compression quasi-equilibrium (meaning what is in equilibrium?) 3) Heat transfer through connecting pipes is negligible

Carnot Cycle Devised by Nicolas Leonard Sadi Carnot (1796 - 1832)
Research was concerned with determining the motive power of heat (relation between heat and mechanical energy) First to show that even under ideal conditions an engine cannot convert all of the heat energy supplied to it His work was a prelude to Joule and Kelvin

Carnot Cycle as a Heat Engine
Most efficient cycle for converting a given amount of thermal energy to work Two isothermal and two isentropic steps Work in or out? What if you reverse?

Carnot Engine 1) Reversible isothermal expansion of the gas at the "hot" temperature, TH (isothermal heat addition). During this step (A to B on diagram) the expanding gas causes the piston to do work on the surroundings (move down). The gas expansion is propelled by absorption of heat from the high temperature reservoir. 2) Reversible adiabatic expansion of the gas. For this step (B to C on diagram) we assume the piston and cylinder are thermally insulated (or the heat source is removed), so that no heat is gained or lost. The gas continues to expand while cooling (until TC is reached), doing work on the surroundings.

Carnot Engine 3) Reversible isothermal compression of the gas at the "cold" temperature, TC. (isothermal heat rejection) (C to D on diagram) Now the surroundings do work on the gas, causing heat to flow out of the gas to the low temperature reservoir and the gas to recompress. 4) Reversible adiabatic compression of the gas. (D to A on diagram) Once again we assume the piston and cylinder are thermally insulated. During this step, the surroundings continue do work on the gas, compressing it further and causing the temperature to rise to TH. At this point the gas is in the same state as at the start of step 1. Play movie!!!!!!!!!!!

Carnot Efficiency Combine with cycle efficiency to get:
Starts from the cycle efficiency and a form of the second law Engine returns to original state and all processes are reversible, so change in entropy of engine is zero Hot reservoir delivers entropy to the engine and is rejected to the cold reservoir in equal amounts, so: Combine with cycle efficiency to get:

Internal Combustion Engine - Otto Cycle
Conceptualized by Nikolaus August Otto (June 14, January 28, 1891) Four stroke is more fuel efficient and clean burning than a two stroke cycle Otto cycle consist of strokes: Intake stroke Compression stroke Power stroke Exhaust stroke

Reciprocating Internal Combustion Engine
It is important to realize that an internal combustion engine operates on a mechanical cycle because the piston system goes to the same initial points. However from the thermodynamics stand point this does not occur because new air and fuel enters the engine in order to initiate the combustion process. Thus internal combustion engines operate in Internal cycles. Compression Ratio - Defined as volume at bottom dead center divided by volume at top dead center

Actual and Ideal Cycles in Spark-Ignition Engines and Their P-v Diagram

Air Standard Otto Cycle
In summary the Otto Cycle is internally reversible, so the area Underneath the P-v diagram represents work and the T-s Represents heat. Also the cycle has: 2 Isentropic Processes when work is produced or input 2 processes at constant v, when heat is added or removed. Air Standard Otto Cycle Otto, Diesel, and Brayton cycles are gas power cycles - working fluid remains a gas throughout the cycle Actual gas power are very complex - to simplify we approximate > air standard assumptions Working fluid is air (neglect combustion products) Air circulates in a closed loop acting as an ideal gas (constant specific heats) All processes are internally reversible Combustion is replaced by a heat addition process from an external source Exhaust is replaced by a heat rejection process that return working fluid to initial state

Air Standard Otto Cycle
The air standard Otto Cycle is an ideal cycle that approximates a spark-ignition internal combustion engine. It assumes that the heat addition occurs instantaneously while the piston is at TDC. Process (1-2) Isentropic Compression Compression from ν1 => v2 ↓ ↓ BDC(β=180º ) TDC (θ=0º) (2-3) Constant Volume heat input: QH While at TDC: umin Ignition of fuel (chemical reaction takes place) (3-4) Isentropic Expansion Power is delivered while s = const. (4-1) Isentropic Expansion QL at umax=constant (BDC, θ =180º) To the board for Otto cycle efficiency

Parameters affecting thermal efficiency
Octane rating - measure of the resistance to autoignition of the fuel Unleaded vs. leaded Leaded fuel resistant to autoignition - unleaded restricts engines to a compression ratio of around 9 Specific heat ratio Thermal efficiency degrades as the molecules in the fluid get larger Efficiencies of actual engines range from around 25 to 30 Now - sample problem Thur. - compression ignition cycle - no knocking problems