Engineering Applications of Control Volume-2

P M V SubbaraoProfessor

Mechanical Engineering Department

More Innovations for Extrasomatism…..

Steam Power Plant: A series of CVs in SSSF

outlet

inlet

inoutinpump dpvmhhmW

inoutinoutin ppvmpvupvum

inoutinininoutoutoutin ppvmvpvpmuum

Pumping of Incompressible Fluids

0

outin uum

outin uu

outin TT

Adiabatic pumping of a liquid is almost an Isothermal process!!

2 – 3 : Steam Generation : Isobaric Heating

No work transfer, change in kinetic and potential energies are negligible

QCV

CVout

outin

inCV WgzVhmgzVhmQ

22

outoutininCV hmhmQ

inoutSG hhmQ

Oil Fired Steam Boiler

inoutSG hhmQ

Turbine : Adiabatic Process

No heat transfer. Change in kinetic and potential energies are negligible

3

4

T

outin mmCMSSSF

::

CVout

outin

inCV WgzVhmgzVhmQ

22

CVoutoutinin Whmhm

ssuming a single fluid entering and leaving…

43 hhmhhmW outinturbine

Diagram of Large Power Plant Turbine

HP Turbine Rotor

LP Turbine Rotor

Highly compressible flow through Turbine

outinturbine hhmW

outlet

inlet

outin vdpmhhm

inout vv

ininoutoutininoutoutoutin vpvpn

nmvpvpmuum

1

!!! 0 outin uu

Steam Power Plant: A series of CVs in SSSF

4 – 1 : Condenser : Isobaric Cooling : p4 = p1

No work transfer, change in kinetic and potential energies are negligible

QCV

CVout

outin

inCV WgzVhmgzVhmQ

22

outoutininCV hmhmQ

ssuming a single fluid entering and leaving…

inoutCondenser hhmQ

Schematic for PC Power Plant with cooling Water from A River

Windcatcher (Bagdir)

Schematic for PC Power Plant with cooling tower

Air Cooled Condenser System

Net Heat and work Actions

• First law for a cycle:

WQ

11 i

i

i

i

wmqm

11 iii WmQm

Turbojet Engine: A Heat Engine with Single Phase –Non Pure Substance

Qin

Qout

Wout

Structure of A Domestic Refrigerator

1: Evaporator/Freezer 2: Condenser3: Compressor4 : Throttling Device

Thermodynamic Cycle of A Refrigerator

                                                                                                                                          

Simplified Diagram of A Refrigerator

Throttling Valve

Compressor

All the parts are CVs working in USUF processes.

Condenser : Transient Constant Pressure Cooling.

Compressor : Transient adiabatic Compression.

Throttling Device: Homogeneous and Transient Isoenthalpic process.

Evaporator: Transient Constant Pressure Cooling.

Analysis of Uniform State Uniform Flow Devices

First Law for CV:Uniform State Uniform Flow

• Conservation of mass:

outinCV

inoutCV mm

dt

dmmm

dt

dm 0

• Conservation of energy:

Wdt

dEQ out

CVin

Properties of CV are variant:

Continuous Accumulation or/and depletion of mass of a CV.

Continual Addition or removal of energy for a CV.

Salient Features of CV @USUF Process

• Rate of mass inflow Rate mass outflow.

• The states of inflows and outflows are invariant although the mass flow rates may be time varying.

• Rate of Work done is variant.

• Rate of Heat transfer is variant.

• Change of state or process is both for the CV and Flows!

• The incoming fluid changes its state from inlet(at one time t0) to exit (at time t0+t) condition.

• A CV with USUF process is approximates as a homogeneous but variant device.

• The importance of time is very high!

CV following A USUF Process for time t

• A change of state occurs in a CV with USUF due to change in time.

• A total change in a CV over time t can be calculated using:

tt

t

outin

tt

t

CV dtmmdtdt

dm 0

0

0

0

tt

t

outinCVCV dtmmtmttm0

0

)( 00

Total change in mass of A CV during a time interval t

Total change in energy of A CV during a time interval t

dtWdtdtdt

dEdtdtQ

tt

t

tt

t

out

tt

t

CV

tt

t

in

tt

t

0

0

0

0

0

0

0

0

0

0

in

inin gzV

hm

2

2

out

outout gzV

hm

2

2

gz

VumE CVCV 2

2

All parameters mentioned above are homogeneous and variant.

Let us now integrate this equation over time t, during which time we have

dtQQtt

t

CV

0

0

dtWWtt

t

CV

0

0

dttt

t

inin

0

0

dttt

t

outout

0

0

1

21

112

22

22 22

0

0

gZV

umgZV

umdtdt

dEtt

t

CV

First Law for A CV executing USUF for finite time

Throttling Devices

• Throttling devices are any kind of flow restricting devices.

• They cause large pressure drop in the fluid.

• The pressure drop in fluid is often accompanied by a large drop in temperature and rarely a raise in temperature.

• The magnitude of temperature drop or rise during a throttling process is governed by a property called Joule-Thomson Coefficient.

Throttling Valves• Throttling: Reduces Pressure• Common Assumptions:

– SSSF– No work or heat transfer– Neglect changes in PE and KE

• Energy Balance:Throttling Valve

CV

out

out

in

inCV WgzV

hmgzV

hmQ

22

220 0

outin

gzV

gzV

22

22

outoutininoutin pvupvuhh

• Isenthalpic (h = constant) Process

Internal energy + Flow energy = Constant

The fluids whose pv increases during throttling generate cooling effect.The fluids whose pv decreases during throttling generate cooling effect

The Joule-Thomson Experiment

constant

H

p

T