3Mechanical engineering 20/2/2008Mechanical engineeringConservation of MassFor a certain control volume conservation of mass (continuity equation) is:
4Mechanical engineering 20/2/2008Mechanical engineeringAnd the mass flow rate is given by Where : V : velocity (m/s) A : cross sectional area (m2) v : specific volume (m3/Kg)
5Mechanical engineering 20/2/2008Mechanical engineeringExample:Air is flowing in a 0.2-m-diameter pipe at a uniform velocity of 0.1 m/s. The temperature is 25 ºC and the pressure 150 kPa. Determine the mass flow rate.
7Mechanical engineering 20/2/2008Mechanical engineeringNozzle: A nozzle is a steady-state device whose purpose is tocreate a high velocity fluid stream at the expense of the fluid’s pressure. It is contoured in an appropriate manner to expand a flowing fluid smoothly to a lower pressure, thereby, increasing its velocity. There is no means to do any work – there are no moving parts. There is little or no change in PE and usually little or no heat transfer
8Mechanical engineering 20/2/2008Mechanical engineeringDiffuser: A steady-state diffuser is a device constructed todecelerate a high velocity fluid in a manner that results in an increase in pressure of the fluid. In essence, it is the exact opposite of a nozzle, and it may be thought of as fluid flowing in the opposite direction through a nozzle, with the opposite effects.
9Mechanical engineering 20/2/2008Mechanical engineeringExample:Air at 0.6 MPa and 200 ºC enters an insulated nozzle with a velocity of 50 m/s. It leaves at a pressure of 0.15 MPa and a velocity of 600 m/s. Determine the final temperature of the air.
10Mechanical engineering 20/2/2008Mechanical engineeringTurbine: A turbine is a rotary steady-state machine whose purposeis to produce shaft work at the expense of the pressure of the working fluid. Two general classes of turbinesSteam turbines, in which the steam exiting the turbine passes to a condenser, where it is condensed to a liquid.Gas turbines, in which the gas usually exhausts to the atmosphere from the turbine.
11Mechanical engineering 20/2/2008Mechanical engineeringIn either type, the turbine exit pressure is fixed by the environment into which the working fluid exhausts, and the turbine inlet pressure has been reached by different ways (boiler, combustion).
12Mechanical engineering 20/2/2008Mechanical engineeringCompressor and Pump: The purpose of a steady-state compressor (gas) or pump (liquid) is the same: to increase the pressure of a fluid by putting in shaft work. The internal processes are essentially the opposite of the two processes occurring inside a turbine.
13Mechanical engineering 20/2/2008Mechanical engineeringThe working fluid enters the compressor at low pressure, moving into a set of rotation blades, from which it exits at high velocity, a result of the shaft work input to the fluid
14Mechanical engineering 20/2/2008Mechanical engineering2nd law of thermodynamics
16Mechanical engineering 20/2/2008Mechanical engineeringThe second law acknowledges that processes proceed in a certain direction but not in the opposite direction Examples: A hot cup of coffee cools by virtue of heat transfer to the surroundings, but heat will not flow from the cooler surroundings to the hotter cup of coffee.
17Mechanical engineering 20/2/2008Mechanical engineeringGasoline is used as a car drives up a hill, but the fuel level in the gasoline tank cannot be restored to its original level when the car go down the hill.
18Mechanical engineering 20/2/2008Mechanical engineeringConsider the cycle shown, known from our experience to be impossible actually to complete.
19Mechanical engineering 20/2/2008Mechanical engineeringThese two examples lead us to a consideration of the heat engine and the refrigerator, which is also referred to as a heat pump. With the heat engine we can have a system that operates in a cycle and performs a net positive work and a net positive heat transfer. With the heat pump we can have a system that operates in a cycle and has heat transferred to it from a low-temperature body and heat transferred from it to a high-temp body though work is required to do this.
20Mechanical engineering 20/2/2008Mechanical engineeringA simple steam power plant as a whole may be considered a heat engine. It has a working fluid (steam) to which and from which heat is transferred, and which does a certain amount of work as it undergoes a cycle.
21Mechanical engineering 20/2/2008Mechanical engineeringIn general, we say that efficiency is the ratio of output, the energy sought (work), to input, the energy that costs (cost of the fuel). Thermal efficiency is defined asTypical values for the thermal efficiency of real engines are about 35 – 50 % for large power plants, 30 – 35 % for gasoline engines, and 35 – 40 % for diesel engine.
22Mechanical engineering 20/2/2008Mechanical engineeringThe “efficiency” of a refrigerator is expressed in terms of the coefficient of performanceA household refrigerator may have a coefficient of performance (COP) of about 2.5, whereas a deep freeze unit will be closer to 1.0
23Mechanical engineering 20/2/2008Mechanical engineeringThe Kelvin-Planck Statement: It is impossible to construct a device that will operate in a cycle and produce no effect other than the raising of a weight and the exchange of heat with a single reservoir.
24Mechanical engineering 20/2/2008Mechanical engineeringThe Clausius Statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a cooler body to a hotter body. This statement is related to the refrigerator or heat pump. In effect, it states that it is impossible to construct a refrigerator that operates without an input of work. This also implies that the COP is always less than infinity.
25The two statements of the second law are equivalent The two statements of the second law are equivalent. The truth (violation) of each statement implies the truth (violation) of the other.
26Carnot CycleFor an engine working between two reservoirs at different temperatures. It consists of two reversible isothermal and two reversible adiabatic processes. For a cycle :Undergoes isothermal expansion in 1-2 while absorbing heat from high temperature reservoirUndergoes adiabatic expansion in 2-3Undergoes isothermal compression in 3-4Undergoes adiabatic compression in 4-1.Heat is transferred to the working materialduring 1-2 (Q1) and heat is rejected during 3-4 (Q2). The thermal efficiency is thus ηth = W/Q1. Applying first law, we have, W = Q1 − Q2, so that ηth = 1 − Q2/Q1.
27Carnot's principle states that 1. No heat engine working between two thermal reservoirs is more efficient than the Carnot engine, and2. All Carnot engines working between reservoirs of the same temperature have the same efficiency.The proof by contradiction of the above statements come from the second law, by considering cases where they are violated.Since T and S are properties, you can use a T-S graph instead of a p-V graph to describe the change in the system undergoing a reversible cycle. We have, from the first law, dQ + dW = 0. Thus the area under the T-S graph is the work done by the system. Further, the reversible adiabatic processes appear as vertical lines in the graph, while the reversible isothermal processes appear as horizontal lines.
28Rankine CycleIn the Rankine cycle, also called the standard vapor power cycle, the working fluid follows a closed cycle. We will consider water as a working substance. In the Rankine cycle, water is pumped from a low pressure to a high pressure using a liquid pump. This water is then heated in the boiler at constant pressure where its temperature increases and it is converted to superheated vapor. This vapor is then expanded in an expander to generate work. This expander can be a turbine or a reciprocating (i.e. piston) machine such as those used in older steam locomotive or ship. The output of the expander is then cooled in a condenser to the liquid state and fed to the pump. The Rankine cycle differs from the Carnot cycle in that the input to the pump is a liquid (it is cooled more in the condenser). This allows the use of a small, low power pump due to the lower specific volume of liquid compared to steam. Also, the heat transfer in the boiler takes place mainly as a result of a phase change, compared to the isothermal heating of the ideal gas in the Carnot cycle, so that the efficiency is quite good (even though it is still lower than the Carnot efficiency). The amount of heat transferred as the liquid is heated to its boiling point is very small compared to the heat transfer during phase change. The steam is superheated so that no liquid state exists inside the turbine. Condensation in the turbine can be devastating as it can cause corrosion and erosion of the blades.
31Refrigeration CyclesThe ideal refrigeration cycle is reverse of Carnot cycle, working as a heat pump instead of as a heat engine.COP (efficiency) = Ql / W = Tl / (Th – Tl) (for Carnot)However, there are practical difficulties in making such a system work. The gas refrigeration cycle is used in aircraft to cool cabin air. The ambient air is compressed and then cooled using work from a turbine. The turbine itself uses work from the compressed air, further cooling it. The output of the turbine as well as the air which is used to cool the output of the compressor is mixed and sent to the cabin.The Rankine vapor-compression cycle is a common alternative to the ideal Carnot cycle
45Closed Cycle Open Cycle Power and Refrigeration Cycle
469.2 Rankine Cycle Rankine Cycle (Two-phase Power Cycle) Simple steam power plant whichoperates on the Rankine cycleRankine Cycle
471-2: Reversible adiabatic pumping (pump) 2-3: Constant pressure heat addition (boiler) 3-4: Reversible adiabatic expansion (turbine) 4-1: Constant pressure heat rejection (condenser) Heat and work may be represented by various areas in the T-s diagram. PE and KE negligible. Carnot Cycle; Pumping of two-phase mixture – difficult !! Superheating at dropping pressure – difficult !! -> Rankine cycle is the ideal cycle that can be approximated in practiceRankine Cycle
489.3 Reheat and Regeneration Ideal reheat cycleReheat and Regeneration
49Ideal regenerative cycle (Rankine) = (Carnot) w/ reversible heat transfer -> Impractical heat transfer from turbine Moisture content from turbineReheat and Regeneration
50Regenerative cycle with an open feedwater heater Open Feedwater: Less expensive Requires a pump between each heaterReheat and Regeneration
51Arrangement of regenerative feedwater heaters in an actual power plant Reheat and Regeneration
57Single-Phase Power Cycle (Air-Standard Power Cycle) Brayton cycle – Shaft work, gas turbine Otto cycle – PdV work, gasoline engine Diesel cycle – PdV work, Diesel engine IC engine with an open cycle -> Approximation by a closed cycle Combustion replaced by heat transfer Fixed mass of air as the working fluidReheat and Regeneration