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/(kg•k) ! 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 = m⋅c ⋅(t f − ti ) ! Q is positive for transfers in ! c is the specific heat capacity ! c has units kJ/(kg•C) Latent Heat Q = m⋅lv Q = m⋅lm ! Heat to cause a change of state (melting or vaporization) ! 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 Saturation temp 100°C Saturated Saturated liquid steam Superheated Steam Wet steam Subcooled liquid Specific enthalpy 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 Conduction • • A 4 Q = k ⋅ ⋅∆T QαA⋅T l A T2 T1 l More Heat Transfer Convection Condensation Latent heat transfer Mass Flow • from vapor Q = h⋅ A⋅∆T Dalton’s Law If we have more than one gas in a container the pressure is the sum of the pressures associated with an individual gas. Pc = P1 + P2 + P3 +... Condensing Heat Exchanger Steam In P P=Psaturation T=Tsaturation Coolant 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 Water Out For You to do HTS Normal Operation Reactor Thermal Power QHT Steam to turbine Feedwater Boiler 2nd stage Reheat Preheater drains Boiler blowdown QP HT pump Bleed cooler Piping loses Feed & bleed Fuel QL bundle/ HTS End shield/shield tank QM Moderator QSC Reactor Power and ∆T ! ∆T is an indicator of reactor power if boiling 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 cooling Fuel Heat Transfer Single Nucleate phase Partial film boiling Full film boiling (dryout) boiling convection boiling Saturated Subcooled (bulk) boiling D F Critical heat flux C Log (heat flux) E B A Tcoolant = Tsat Log (T – T ) Tsheath = Tsat sheath coolant 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 T sheath surface T sat 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 C HF Channel power Bundles in dryout inlet Actual heat flux 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 10.2 Boiling starts 10.0 Pressure MPa(a) 9.8 Non-boiling mode 9.6 Inlet Outlet Channel position Temperature Profile 2800 Fuel melting point 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 Inlet a) Temperature profile Saturation temperature Outlet Coolant temperature Skewed flux Normal flux Inlet Channel position b) Heat flux profile CHF at skewed flux Heat flux CHF at normal flux Outlet Normal heat flux Skewed heat flux 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 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 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 temperatures ! Limit around 130-150°C due to huge volume of steam required Ideal Temperature Ramps ! 2.8°C a minute ! This rate minimizes ! Thermal stress ! Probability of delayed hydride cracking ! Feedwater loss For You to do.