Gas Power Cycles

Thermodynamics

Professor Lee Carkner

Lecture 17

PAL # 16 Exergy Balance Cooling chickens with a water stream Mass flow of chickens

m’c = (500 c/hr)(2.2 kg/c) / (3600 s/hr) =

Heat removed from chickens can be found from specific heat Q’c = m’ccpT = (0.3056)(3.54)(15-3) =

Heat gained by water is Q’w = Q’c + Q’environ = 13.0 + (200 kJ/h) / (3600

s/hr) = Absorbing heat raises water temp by 2 C

m’w = Q’w/cpT = 13.056 / (4.18)(2) =

PAL # 16 Exergy Balance Find Sgen from equation of flow systems

S’gen =

But s = c ln (T2/T1) for an incompressible substance S’gen = (0.3056)(3.54) ln(276/288) + (1.56)

(4.18) ln(275.5/273.5) – 0.0556/298 =

X’destroyed = T0S’gen = (298)(0.00128) =

Modeling Power Cycles

We often generate power by performing a series of processes in a cycle

We use instead an ideal cycle

We will often be looking for the thermal efficiency th = Wnet/Qin = wnet/qin

Diagrams

Pv diagram

Ts diagram

But, net heat = net work

Ideal Diagrams

Carnot

The Carnot cycle is the most efficient

It is very hard to build even an approximation

th,Carnot = 1 – (TL/TH) In general want high input and low output

temperatures

Carnot Diagrams

Air Standard For most internal combustion engines the working

substance is a gas and is a mixture of air and fuel Can assume:

All processes are internally reversible

Can think of exhaust as heat rejection to an external sink

Cold-air standard

Reciprocating Engine Top dead center

Bottom dead center

Stroke

Bore

Intake Valve

Exhaust value Allows combustion products to

leave

Volumes of a Cylinder

Compression Clearance volume

Displacement volume

Compression ratio

r = Vmax/Vmin = VBDC/VTDC

Mean Effective Pressure (MEP) is the equivalent pressure that would produce the same amount of work as the actual cycle

MEP = Wnet / (Vmax – Vmin)

MEP Illustrated

Otto Cycle The ideal cycle for reciprocating

engines ignited by a spark was developed in 1876 by Nikolaus Otto

Basic cycle:

Can also combine the exhaust and intake into the power stroke to make a two-stroke engine

Ideal Otto Cycle

We can approximate the cycle with

An isochoric (no V) heat addition

An isochoric heat

rejection

Otto Analysis

We can write the heats as cvT qin =

qout =

th = 1 – qout/qin =

But we also know that for the isentropic process (T1/T2) = (v2/v1)k-1 and r = v1/v2

th,Otto =

Otto Compression Ratios

Efficient Otto Engines

As we increase r the efficiency gain levels off at

about 8 Also, high r can mean the fuel is compressed so

much it ignites without the spark

Can’t really increase k since we are using air Typical values for th,Otto ~

Otto Engine Exercise

Diesel Cycle

We can approximate the cycle with

An isobaric heat addition An isochoric heat rejection

Only the second process is different from the Otto

Diesel Efficiency The heat in is the change of internal energy plus

the isobaric work qin = u + Pv = h3-h2 =

The heat out is just the change in internal energy qout = u4-u1 =

So then the efficiency isth,diesel = 1 – qout/qin = 1 – (T4-T1) / k(T3-T2)

We can rewrite as:th,diesel = 1 – (1/rk-1)[(rk

c-1)/k(rc-1)]

rc = v3/v2

Diesel Compression Ratios

Making Diesels Efficient

Want large r and small rc

Diesels can operate at higher compression ratios and are usually more efficient th,diesel ~

Diesels also have lower fuel costs because they don’t have to worry about autoignition and engine knock

Next Time

Read: 9.8-9.12 Homework: Ch 9, P: 22, 37, 47, 75