20030902

Heat and Thermodynamics

Introduction

Definitions! Internal energy

! Kinetic and potential energy! Joules

! Enthalpy and specific enthalpy! H= U + p x V! Reference to the triple point! Engineering unit ! H is the work done in a process! J, J/kg

More Definitions

! Work! Standard definition W = f x d! In a gas W = p x V

! Heat! At one time considered a unique form of

energy! Changes in heat are the same as changes

in enthalpy

Yet more definitions! Temperature

! Measure of the heat in a body! Heat flows from high to low temperature! SI unit Kelvin

! Entropy and Specific Entropy! Perhaps the strangest physics concept! Notes define it as energy loss! Symbol S! Units kJ/K, kJ/(kgk)! Entropy increases mean less work can be done by

the system

Sensible and Latent Heat! Heat transfers change kinetic or

potential energy or both! Temperature is a measure of kinetic

energy! Sensible heat changes kinetic (and

maybe potential energy)! Latent heat changes only the potential

energy.

Sensible Heat

! Q is positive for transfers in! c is the specific heat capacity ! c has units kJ/(kgC)

)( if ttcmQ =

Latent Heat

! Heat to cause a change of state (melting or vaporization)

! Temperature is constant

m

v

lmQlmQ==

Enthalpy Changes

! Enthalpy changes take into account both latent and sensible heat changes

hmQ =

Thermodynamic Properties of H2O

TemperatureC

Specific enthalpy

100C

SuperheatedSteam

Latent heat

Wet steam

Sensible heat

Subcooledliquid

Saturatedsteam

Saturatedliquid

Saturation temp

Pressure Effects

Laws of Thermodynamics

! First Law! Energy is conserved

! Second Law! It is impossible to convert all of the heat

supplied to a heat engine into work! Heat will not naturally flow from cold to hot! Disorder increases

Heat Transfer

Radiation

4TAQ

Conduction

TlAkQ =

l

AT1T2

More Heat Transfer

Convection

Mass Flow

TAhQ =

Condensation

Latent heat transfer from vapor

Daltons Law

If we have more than one gas in a container the pressure is the sum of the pressures associated with an individual gas.

...321 +++= PPPPc

Condensing Heat Exchanger

CoolantIn

CoolantOut

SteamIn

WaterOut

P

T

P=PsaturationT=Tsaturation

Non-Condensables in Heat Exchanger

CoolantIn

CoolantOut

SteamIn

WaterOut

P

T

P=Psaturation+PgT=Tsaturation

Condenser AppearsSubcooled

For You to do

HTS Normal Operation

Reactor Thermal Power

Fuelbundle/

HTS

Moderator

End shield/shield tank

QSCQM

Bleed cooler

Boiler

PreheaterBoiler

blowdown

Feedwater

HT pump

2nd stage Reheatdrains

Steam toturbine

Feed & bleedQL

Pipingloses

QP

QHT

Reactor Power and T

! T is an indicator of reactor power if boiling is not taking place

TcmQ =

! At boiling T stops changing! In boiling channels total enthalpy

increase must be calculated

Fuel Safety

! No overpowering! Adequate cooling

Fuel Heat Transfer

D

A

Critical heat flux

Singlephase

convection

Nucleateboiling Partial film boiling Full film boiling (dryout)

S

u

b

c

o

o

l

e

d

b

o

i

l

i

n

g

S

a

t

u

r

a

t

e

d

(

b

u

l

k

)

b

o

i

l

i

n

g

Tsheath = Tsat

L

o

g

(

h

e

a

t

f

l

u

x

)

CF

Log (Tsheath Tcoolant)

B

Tcoolant = Tsat

E

Two new terms

! Critical Heat Flux! CHF! The maximum heat flux nucleate boiling

can transfer

! Dryout! When dry patches of vapor exist on the

fuel sheath

Uniform Heating

Inlet Outlet

Tcoolant

Single-phase

convection

Subcoolednucleateboiling Saturated nucleate (bulk) boiling Dryout

Tsheath surface

Tsat

Fuel element

Coolant

Factors Affecting CHF

! Coolant Sub-cooling! Vapour Quality! Coolant Velocity

Actual and Critical Heat Flux

Channel distance

C

h

a

n

n

e

l

p

o

w

e

r

inlet outlet

CHF

Actual h

eat flux

Bundles in dryout

Critical Channel Power

! CCP! The minimum channel power that gives

dryout! Varies with coolant conditions! Varies with flux shape

Boiling and Flow

Inlet OutletChannel position

9.6

9.8

10.0

10.4

10.2Boiling starts

Non-boiling mode

Boiling mode

P

r

e

s

s

u

r

e

M

P

a

(

a

)

Temperature Profile2800

2400

2000

1600

1200

800

400

T

e

m

p

e

r

a

t

u

r

e

,

C

Fuel melting point

Fuelsheath

Coolant

Fuelsheath

Coolant

Fuel pellet

More Temperature Profiles

Overratingand dryout

2400

2000

1600

1200

800

400

T

e

m

p

e

r

a

t

u

r

e

,

C

FuelsheathCoolant

Fuelsheath Coolant

Fuel pellet

Fuel meltingpoint

Nominal rating,normal cooling

Overratingwithout dryout

Light loadand dryout

2800

Possible film ofgaseous fission

products (on LOCA)

Vapour filmdue to dryout

Bad things to do to fuel

Low HTS Pressure

Tsat at reduced pressure

Tsat at normal pressure

Coolanttemperature at

reducedpressure

Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

CHF at reducedpressure

CHF at normal pressure

Channel position

H

e

a

t

f

l

u

x

Inlet Outlet

a) Temperature profile

b) Heat flux profile

Actual hea

t flux

Coolant temperature atnormal pressure

Reduced FlowSaturation temperature

Reduced flow

Normal flow


Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

Outlet

CHF at reducedflow

CHF at normal flow

Channel position

H

e

a

t

f

l

u

x

Inletb) Heat flux profile

Actual hea

t flux

Dryout zone

Inlet High Temperature

Saturation temperature

High inlettemperature

Normal inlettemperature

Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

CHF at high inlettemperature

CHF at normal inlet temperature

Channel position

H

e

a

t

f

l

u

x

Inlet Outlet



Actual hea

t flux

Flux Tilt to Outlet


Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

CHF at skewed flux

CHF at normal flux

Channel position

H

e

a

t

f

l

u

x

Inlet Outlet



Normal he

at flux

Normal flux

Skewed heat

flux

Skewed flux

Dryoutzone

Flux Tilt to Inlet


Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

CHF at skewed fluxCHF at normal flux

Channel position

H

e

a

t

f

l

u

x

Inlet Outlet



Normal he

at flux

Normal flux

Skewed heat

flux

Skewed flux

Excessive Channel Power


Channel position

C

o

o

l

a

n

t

t

e

m

p

e

r

a

t

u

r

e

Inlet Outlet

CHF at excessivechannel power

CHF at normal channel power

Channel position

H

e

a

t

f

l

u

x

Inlet Outlet



Normal he

at flux

Normal channelpower

Excessivechannel power

Dryout zone

Excessiveheat flux

For You to do

HTS Components

HTS Feed & Bleed

BleedCondenser

! Non-condensable gases! Reduce heat transfer! Steam pressure rises! Increased reflux

cooling! Vessel appears sub

cooled

! Degassing Orifice

Pressurizer Control

Boiler Shrink and Swell

! Boilers are probably more correctly called steam generators

Steady State Shrink and Swell

Zero Load Low Load Full Load

Rise inLevel

Rise inLevel

Transient Shrink and Swell

! Shrink and swell from short term effects! Reactor power boiler level

! Boiling increases

! Boiler Pressure boiler level ! Water flashes to steam! Steam expands

Effects on the Downcomer! Water flow into the

annulus increases! Water flow out of

the annulus decreases

! Instrumentation sees a level increase

ExpansionForces

CycloneSeparators

DowncomerAnnulus

Boiler Level Control

SwellMargin

ShrinkMargin

SwellMargin

ShrinkMargin

Constant Level Full Power Level

Zero Power Level

Fixed Level Control Ramped Level Control

Improper Level! Low

! If tubes are uncovered! Reduce heat transfer! Time in loss of feedwater events is reduced! Reactor power automatically reduced

! Setback or stepback and finally a trip

! High! High vapor content in steam! Slugs of water to turbine! Turbine trip

Boiler Pressure

! Boiler pressure is the key parameter in matching heat source to sink

! Reactor Leading! Reactor Lagging

Warm-up and Cool-down

! Heat transfer in the boiler

mTAUQ =

! A low power levels the HTS is about the same temperature as the boiler

Rx for Warm-up

! Put some energy into HTS from pumps and reactor power

! Increase boiler pressure! Boiler temperature follows (saturated

vessel)! HTS temperature follows that

Rx for Cool-down

! Heat sources are pumps and decay heat! Boiler pressure is ramped down ! Steam energy released is greater that

energy input! Down go temperatures! Limit around 130-150C due to huge

volume of steam required

Ideal Temperature Ramps

! 2.8C a minute! This rate minimizes

! Thermal stress! Probability of delayed hydride cracking! Feedwater loss

For You to do

Heat and Thermodynamics COURSEHeat and Thermodynamics Presentation

20030902

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