<<

Heat and

Introduction Definitions

! Internal

! Kinetic and

!

! and specific enthalpy

! H= U + p x V

! Reference to the

! Engineering unit

! ∆H is the done in a process

! J, J/kg More Definitions

! Work

! Standard definition W = f x d

! In a W = p x ∆V

!

! At one time considered a unique form of energy

! Changes in heat are the same as changes in enthalpy Yet more definitions

!

! Measure of the heat in a body

! Heat flows from high to low temperature

! SI unit Kelvin ! and Specific Entropy

! Perhaps the strangest physics concept

! Notes define it as energy loss

! Symbol S

! Units kJ/K, kJ/(kg•k)

! Entropy increases mean less work can be done by the system Sensible and

! Heat transfers change kinetic or potential energy or both ! Temperature is a measure of ! changes kinetic (and maybe potential energy) ! Latent heat changes only the potential energy. Sensible Heat

Q = m⋅c⋅(t f − ti )

! Q is positive for transfers in

! c is the specific

! c has units kJ/(kg•C) Latent Heat

Q = m⋅lv

Q = m⋅lm

! Heat to cause a change of state ( or )

! Temperature is constant Enthalpy Changes

Q = m⋅∆h

! Enthalpy changes take into account both latent and sensible heat changes Thermodynamic Properties of

H2O

Temperature °C

Sensible heat Latent heat

100°C Saturation temp

Saturated Saturated SpecificSuperheated enthalpy Steam Wet steam

Subcooled liquid Effects

! First Law

! Energy is conserved

! Second Law

! It is impossible to convert all of the heat supplied to a into work

! Heat will not naturally flow from to hot

! Disorder increases

Radiation Conduction • • A 4 Q = k ⋅ ⋅∆T QαA⋅T l

A T2 T1 l More Heat Transfer

Convection

Latent heat transfer Flow • from Q = h⋅ A⋅∆T Dalton’s Law

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

Pc = P1 + P2 + P3 +... Condensing

Steam In

P P=Psaturation T=Tsaturation

Coolant In Out T

Water Out Non-Condensables in Heat Exchanger

Steam In

P P=Psaturation+Pg T=Tsaturation

Coolant Coolant In Out T Condenser Appears Subcooled Out For You to do HTS Normal Operation Reactor

QHT Steam to turbine

Feedwater 2nd stage Reheat Preheater drains Boiler blowdown

QP HT pump Bleed cooler

Piping loses

Feed & bleed QL bundle/ HTS

End shield/shield tank

QM Moderator QSC Reactor Power and ∆T

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

• • Q = m⋅c ⋅∆T

! At boiling ∆T stops changing

! In boiling channels total enthalpy increase must be calculated Fuel Safety

! No overpowering

! Adequate Fuel Heat Transfer

Single Nucleate Partial film boiling Full film boiling (dryout) boiling boiling Saturated Subcooled (bulk) boiling D Critical heat F C Log (heat flux)

E

B

A

Tcoolant = Tsat

Log (T – T ) Tsheath = Tsat sheath coolant Two new terms

!

! CHF

! The maximum heat flux can transfer

! Dryout

! When dry patches of vapor exist on the fuel sheath Uniform Heating

sheath surface

T sat T T coolant

Coolant

Fuel element

Single- Subcooled phase nucleate convection boiling Saturated nucleate (bulk) boiling Dryout

Inlet Outlet Factors Affecting CHF

! Coolant Sub-cooling

! Vapour Quality

! Coolant Velocity Actual and Critical Heat Flux

CHF Bundles in dryout

ux fl at

Channel power e l h ua Act

inlet Channel distance outlet Critical Channel Power

! CCP

! The minimum channel power that gives dryout

! Varies with coolant conditions

! Varies with flux shape Boiling and Flow

Boiling mode

10.4 Boiling starts

10.2

Pressure MPa(a) 10.0 Non-boiling mode 9.8

9.6

Inlet Outlet Channel position Temperature Profile

2800 Fuel

2400

2000

1600

1200 Temperature, ° C Fuel Fuel sheath sheath 800 Coolant Coolant

400 Fuel pellet More Temperature Profiles

2800 Fuel melting point Overrating without dryout Possible film of 2400 gaseous fission products (on LOCA) Overrating 2000 and dryout

1600

Nominal rating, Light load 1200 normal cooling and dryout Vapour film Temperature, ° C due to dryout

800

400

Fuel pellet

Fuel Fuel Coolant Coolant sheath sheath Bad things to do to fuel Low HTS Pressure

a) Temperature profile Inlet Outlet

T at normal pressure Coolant temperature at sat normal pressure

Tsat at reduced pressure Coolant temperature at reduced pressure Coolant temperature

Channel position

b) Heat flux profile Inlet Outlet CHF at normal pressure

Heat flux CHF at reduced flux pressure eat al h Actu

Channel position Reduced Flow

a) Temperature profile Outlet Inlet Saturation temperature

Reduced flow

Normal flow Coolant temperature

Channel position

b) Heat flux profile Inlet Outlet CHF at normal flow

Heat flux CHF at reduced flow flux eat al h Actu Dryout zone

Channel position Inlet High Temperature

a) Temperature profile Inlet Outlet

Saturation temperature

High inlet temperature

Normal inlet temperature Coolant temperature

Channel position

b) Heat flux profile Inlet Outlet

CHF at normal inlet temperature

CHF at high inlet Heat flux temperature flux eat al h Actu

Channel position Flux Tilt to Outlet

a) Temperature profile Inlet Outlet

Normal flux Saturation temperature

Skewed flux Coolant temperature

Channel position

b) Heat flux profile Inlet CHF at skewed flux Outlet Dryout zone

CHF at normal flux Heat flux x t flu hea mal Nor lux eat f ed h Skew

Channel position Flux Tilt to Inlet

a) Temperature profile Inlet Outlet

Saturation temperature

Normal flux Coolant temperature Skewed flux

Channel position

b) Heat flux profile Inlet Outlet CHF at skewed flux CHF at normal flux Heat flux x t flu hea mal Nor lux eat f ed h Skew

Channel position Excessive Channel Power

a) Temperature profile Inlet Outlet

Saturation temperature

Excessive channel power Normal channel power Coolant temperature Coolant

Channel position

b) Heat flux profile Inlet Outlet CHF at normal channel power Dryout zone

CHF at excessive channel power Heat flux x t flu hea rmal No Excessive heat flux

Channel position For You to do HTS Components HTS Feed & Bleed Bleed Condenser

! Non-condensable

! Reduce heat transfer

! Steam pressure rises

! Increased reflux cooling

! Vessel appears sub cooled

! Degassing Orifice Pressurizer Control Boiler Shrink and Swell

! are probably more correctly called steam generators Steady State Shrink and Swell

Rise in Level Rise in Level

Zero Load Low Load Full Load 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 Cyclone annulus increases Separators

! Water flow out of

the annulus Downcomer Annulus Expansion decreases Forces

! Instrumentation sees a level increase Boiler Level Control

Swell Margin

Constant Level Full Power Level Swell Margin Shrink Shrink Margin Margin 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 • Q = U ⋅ A⋅∆Tm

! 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

! Limit around 130-150°C due to huge of steam required Ideal Temperature Ramps

! 2.8°C a minute

! This rate minimizes

! Thermal stress

! Probability of delayed cracking

! Feedwater loss For You to do