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HUVINETT 2012/1 Thermal hydraulics of nuclear reactors General considerations Prof Dr Attila ASZÓDI Director Budapest University of Technology and Economics Institute of Nuclear Techniques (BME NTI) Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Basic considerations of nuclear safety – Safety objective is ranked higher than electricity production! • Specialties of nuclear fuel and NPPs: – – – – No real environmental risk of fresh (non-irradiated) fuel High risk of irradiated fuel High thermal density Reactor power possible in a very wide range (even over nominal power, in a short pulse hundreds of nominal power – see Chernobyl) – Cooling of irradiated fuel needed after shut-down (removal of remanent (decay) heat in the first ~5 years in water feasible, later in gas atmosphere over hundreds of years possible) Prof Dr Attila Aszódi, BME NTI Prof Dr Attila Aszódi, BME NTI Design of NPPs • Nuclear Power Plant in normal operation: very low emission, practically only thermal load to the environment • But high risk: Large amount of highly dangerous radioactive material generated and accumulated in the reactor core • Safety objective: protect the environment from this highly dangerous radioactive material Thermal hydraulics Thermal hydraulics Design necessary not only for normal operation, but also for anticipated operational transients and for wide range of so called Design Basis Accidents – Beside operational systems separated safety systems required – Due to single failure criteria multiple independent safety systems needed for the same function Construction of an NPP is much more expensive than of a fossil power plant, where safety is not that critical Electricity generated in NPPs will be competitive only if high annual load factor is ensured fuel cost has to be much lower than by fossil power plants Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Example: Bulgaria, Kozloduy NPP, VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Example: Bulgaria, Kozloduy NPP, VVER-1000 Example: Bulgaria, Kozloduy NPP, VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Example: Bulgaria, Kozloduy NPP, VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Example: Bulgaria, Kozloduy NPP, VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Example: Bulgaria, Kozloduy NPP, VVER-1000 Example: Bulgaria, Kozloduy NPP, VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 10 Basic safety functions – Efficient control of the chain reaction and hence the power produced – Fuel cooling assured under thermal hydraulic conditions designed to maintain fuel clad integrity, thus constituting an initial containment system – Containment of radioactive products in the fuel but also in the primary coolant, in the reactor building constituting the containment or in other parts of the plant unit Independent and redundant water source to avoid loss of ultimate heat sink Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 11 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 12 Fuel design Fuel design • Possible objectives of thermal hydraulical design of fuel • Limits in design: thermal hydraulics (cooling) is more limiting than reactor physics – Maximizing power density to decrease Reactor Pressure Vessel (RPV) size – Maximizing power density to decrease number of fuel assemblies in the core – Maximizing power density to increase reactor power (by given RPV size) – Maximizing coolant outlet temperature to increase NPP efficiency – Maximizing fuel burnup to enhance fuel economy – Choice of coolant material (H2O, CO2, He, Na, Pb), pressure, temperature – Choice of flow velocity and other flow parameters (turbulence, mixing, boiling) • Many parameters have to be optimized: – – – – – – – Enrichment Burn-up Power, power density Fuel and cladding temperature Cladding integrity and durability Coolant parameters Etc Thermal hydraulics Prof Dr Attila Aszódi, BME NTI • Limits in thermal hydraulics design: – Maximal fuel temperature (to avoid fuel melting), – Maximal cladding temperature (to avoid cladding oxidation, decrease in strength) – Maximal coolant temperature (to avoid boiling or boiling crisis) – Other thermal limits (to keep reactivity feedbacks between reactor physical limits) 13 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 14 Fundamentals of heat transport • Heat: energy transport due to temperature difference • Conduction: In heat transfer, conduction (or heat conduction) is the transfer of thermal energy between neighboring molecules in a substance due to a temperature gradient It always takes place from a region of higher temperature to a region of lower temperature, and acts to equalize temperature differences Conduction needs matter and does not require any bulk motion of matter • Convection in the most general terms refers to the movement of molecules within fluids (i.e liquids, gases) Convection is one of the major modes of heat transfer and mass transfer In fluids, convective heat and mass transfer take place through both diffusion – the random Brownian motion of individual particles in the fluid – and by advection, in which matter or heat is transported by the larger-scale motion of currents in the fluid In the context of heat and mass transfer, the term "convection" is used to refer to the sum of advective and diffusive transfer • Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the light emitted by a glowing incandescent light bulb Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation Fundamentals of heat transport Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 15 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 16 The definition of heat transfer Energy production and heat transfer • Heat transfer: across the surfaces of two different materials it is a complex physical process which combines the three fundamental heat transport methods (conduction, convection, radiation) • In the technical practise: investigation of the heat transfer process between solid wall and liquid, solid wall and steam/gas, for example: – Cooling the fuel rods; – Heat transfer through a surface between the primary and secondary side of a steam generator • • • • • • Volumetric heat power rate: Heat flux: Linear heat power rate : Pin power: Core power: Core volumetric power density: r q& ′′′(r ) r q& ′′( A) q& ′(z ) q& Q& Q& / V ≡ Q′′′ • Thermal hydraulics: coupled thermal- and hydrodynamics analysis of the reactors Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 17 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Energy production in fuel Energy production and heat transfer • Energy release in fission: 200 MeV/fission • Thermal hydraulical design of the fuel: – 92-94% discharged in fuel – 2,5% discharged in moderator r r A V • Metallurgical design: r ∫ q&′( z )dz = ∫∫∫ q&′′′(r )dV L i r Φ th ( r ) Thermal neutron flux [1/cm2s] Type of fissionable material (e.g 235U, 239Pu, 241Pu) [-] i Energy release in one fission of an „i” type atom [J/fission] ci r r r [atoms/cm3] N i ( r ) Number of „i” type atoms in cm3 around σ fi Fission cross section of „i” type fissionable material [cm2] r Space coordinate r Prof Dr Attila Aszódi, BME NTI r ∫∫ q& ′′( A) ⋅ ndA = ∫∫∫ q&′′′(r )dV • Calculation of volumetric heat power generation from the thermal neutron flux r r r q& ′′′ ( r ) = Φ th ( r )∑ c i ⋅ N i ( r ) ⋅ σ fi Thermal hydraulics 18 19 V • Pin power: r q& = ∫∫∫ q& ′′′(r )dV V • Core power: N Q& = ∑ q&n where N: number of fuel pins inside the core n =1 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 20 Newton's law of cooling Newton's law of cooling • A related principle, Newton's law of cooling, states that the rate of heat loss of a body is proportional to the temperature difference between the body and its • In the technical practise the average heat transfer coefficient is often used In this case (Tw − T ∞ ) temperature difference is an averaged value along the F surface • In some cases the heat transfer coefficient strongly alters along the surface due to the changing influential properties This is the local heat transfer coefficient: at the x place on the dF surface the thermal surroundings, or environment The law is Q& = α ⋅ F ⋅ (Tw − T ∞ ) where: Q& the thermal power from the solid surface to the fluid, W; F Surface area of the heat being transferred, m2; Tw Temperature of the object's surface, °C or K; T∞ average Temperature of the environment , °C or K; α average Heat Transfer coefficient, W/(m2·K) power is the following: dQ& x = α x ⋅ (Tw ,x − T ∞ ) ⋅ dF where: Tw,x T∞ αx (instead of α „h” is also used) Thermal hydraulics The aim of investigation on thermal processes is to describe the heat transfer coefficient Prof Dr Attila Aszódi, BME NTI 21 50,000 α CFX = Prof Dr Attila Aszódi, BME NTI q& w ' ' Tw − Tnw 40,000 Spacer Grid 35,000 ∫ w ⋅ ρ ⋅ h(T ) ⋅ dF = m& ⋅ h(T 30,000 α GEN 25,000 22 • The T∞ temperature is equal to that temperature which can be measured far from the heated surface in case of flow in half unlimited space • In closed channel flow, if the mass flow rate is m& , the density is ρ, the velocity is w and the enthalpy is h = h(T) : The distribution of the average heat transfer coefficient 45,000 Thermal hydraulics Newton's law of cooling Local heat transfer coefficient – example: Avera erage Heat Transfer Coefficient [W/(m [W K)] local Temperature of the object's surface, °C or K; average Temperature of the environment , °C or K; local Heat Transfer coefficient, W/(m2·K) q& w ' ' = Tw − Tave ∞ ) F 20,000 If the specific enthalpy is h = cp·T and cp= constant, than SST Model - CFX Definition SST Model - General Definition Dittus-Boelter Correlation Dittus-Boelter Correlation + 25% Dittus-Boelter Correlation - 25% 15,000 10,000 5,000 ∫w ⋅ ρ ⋅c ⋅ T ⋅ dF = m & ⋅ c p ⋅ T∞ where: F 0 0.5 1.5 2.5 Height [m] • The average heat transfer coefficient calculated according to the general definition agrees well with the value calculated by Dittus-Boelter correlation Stockholm, 10.10.2006 Thermal hydraulics p S Tóth, A Aszódi, BME NTI Prof Dr Attila Aszódi, BME NTI T∞ = 18 23 Thermal hydraulics ∫ w ⋅ ρ ⋅ T ⋅ dF F m & Prof Dr Attila Aszódi, BME NTI 24 The equilibrium equations - Boussinesq-approach • The flow velocity field: w = w(r ) , in Descartes coordinate system: w x = w x (x , y, z ) w y = w y (x , y, z ) w z = w z (x , y, z ) • The temperature field: T = T (r ) = T (x , y, z ) • The pressure field: p = p(r ) = p(x , y, z ) • Continuity (if the density is constant): div(w ) = • The general differential equation of heat conduction (no heat source, the fluid heat conductivity (λ), isobaric heat capacity (cp), density (ρ) are constant, steady-state condition): w∇T = a ⋅ ∇ 2T Thermal hydraulics , where: a = λ ρ ⋅ cp (thermal diffusivity) Prof Dr Attila Aszódi, BME NTI 25 The hydraulic boundary layer The equilibrium equations - Boussinesq-approach Navier-Stokes equations (steady-state, kinematic viscosity is const.): (w ⋅ ∇ ) ⋅ w = ν ⋅ ∇ w − ∇p + g − β ⋅ ∆T ⋅ g ρ Conditions for the above equations: – The gravity has only a component in z direction, whereas g = −g ⋅ k , where: k is the unit vector in z direction; – The density dependency on the temperature is only considered at the gravity term of the above equation to consider the temperature difference (∆T) which causes a buoyancy force due to the density difference (β is the volumetric heat expansion or compressibility) – ∆T is the temperature difference, T is the temperature and T∞ is the average temperature difference Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 26 The hydraulic boundary layer in the flow near a solid plane • Ludwig Prandtl’s recognition (1904) – the flow can be divided into two regions at the vicinity of solid wall: – first: inside the boundary layer, where viscosity is dominant and the majority of the drag experienced by a body immersed in a fluid is created, – second: outside the boundary layer where viscosity can be neglected without significant effects on the solution Experiment: This experiment has been performed in water where very small hydrogen bubbles have been generated by hydrolysis • The thickness of the hydraulic boundary layer (δ): if the velocity deviate from the main flow velocity The bubbles have very slow lifting movement so they are suitable to visualize the flow (w∞) more than 1% then it is inside the hydraulic boundary layer Reference: Lajos Tamás: Az áramlástan alapjai (Fundamentals of fluid mechanics – in Hungarian, CD), Műegyetemi Kiadó, Budapest, 2004 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 27 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 28 The hydraulic boundary layer in the flow near a solid plane The hydraulic boundary layer in pipe flow Experiment: This experiment has been performed in water where very small hydrogen bubbles have been generated by hydrolysis Physical model: δx = 5⋅ ν ⋅x The bubbles have very slow lifting movement so they are suitable to visualize the flow w∞ ( x < x kr ) x kr = 3,2 ⋅ 10 ⋅ ν Reference: Lajos Tamás: Az áramlástan alapjai (Fundamentals of fluid mechanics – in Hungarian, CD), Műegyetemi Kiadó, Budapest, 2004 w∞ Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 29 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI The hydraulic boundary layer in pipe flow The hydraulic boundary layer in pipe flow Physical model: Physical model: • The boundary layer on the pipe wall abuts after a certain distance from the entrance of the pipe • The constant velocity field before the entrance modify and a characteristic velocity profile builds up after the suitable distance from the entrance After this certain length this is the so called fully developed flow Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 31 30 & , the density is ρ The flow area is A, the mass flow rate is m m w ⋅D & < Re kr = 2300 , where w = The flow is laminar, if Re = ρ⋅A ν The flow can be laminar along the whole pipe length, if the diameter: D < 2300 ⋅ Thermal hydraulics ν w Prof Dr Attila Aszódi, BME NTI 32 The thermal boundary layer The heat transfer NUSSELT’s equation: • The thermal boundary layer: this is analogue with the hydraulic boundary layer If the wall temperature (Tw) is not equal to the bulk temperature (T∞), than: – the fluid temperature is equal to the wall temperature on the solid wall; – approaching to the bulk from the wall the temperature approximate the bulk temperature • The mechanism of heat transfer: if the heat radiation is negligible, then the energy from the wall (which has Tw temperature) to the fluid (which has T∞ temperature) transported by heat conduction through the boundary layer at x position where the thickness of boundary layer is δx The δx alters along the heated length but the viscose sub layer exists everywhere near the solid wall • At a certain place (x) the surface heat flux can be defined by two ways, if the local heat transfer coefficient is αx: q& W′′ (x ) = −λ ⋅ gradT (x ) W • ′′ (x ) = α x ⋅ (TW − T∞ ) q& W The heat transfer NUSSELT’s equation: − λ ⋅ gradT (x ) W = α x ⋅ (TW − T∞ ) • The thermal boundary layer (δt): if the temperature deviate from the main flow temperature (T∞ ) more than 1% then it is inside • λ is the heat conductivity of the fluid, The heat transfer NUSSELT’s equation is not equal to the 3rd kind boundary condition the thermal boundary layer Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 33 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Methods to calculate the heat transfer coef Similarity of heat transfer processes • Solving the steady state equations by using certain boundary conditions the velocity and temperature field can be determined Using the temperature field and the NUSSELT equation the heat transfer coefficient can be calculated • Two physical processes are similar, if • Measuring the heat transfer coefficient and the generalization of the experimental data, using them for similar flows (Similarity theory) is possible Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 35 34 – The differential equations are the same; – The geometries are similar; – The initial and boundary conditions of the differential equations can be transformed in the same values using proper ratios • The similarity theory enables to investigate an unmeasured heat transfer process using a geometrically similar and previously measured example • To characterize the similarity many similarity number are used in practice • In the followings the practically important similarity numbers are defined Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 36 Similarity of heat transfer processes Similarity of heat transfer processes • To define the similarity numbers let’s use the Boussinesqapproach of the steady state equations: • The z component of Navier-Stokes equation: • Let’s transform the steady state equations into dimensionless form using normalization The base value of the normalization must be well measurable L is the characteristic geometrical parameter, w∞ is the characteristic velocity, Tw is the surface temperature, T∞ is the flow characteristic temperature! • The dimensionless parameters: wx ⋅ ∂wz ∂wz ∂w z + wy ⋅ + wz ⋅ =ν ∂x ∂y ∂z  ∂ 2wz ∂ 2wz ∂ 2wz ⋅  + + ∂y ∂z  ∂x  ∂p  − ⋅ − g − g ⋅ β ⋅ ∆T  ρ ∂z • The energy equation: wx ⋅  ∂ 2T ∂ 2T ∂ 2T ∂T ∂T ∂T = a ⋅  + + + wz ⋅ + wy ⋅ ∂z ∂y ∂z ∂y ∂x  ∂x    – Velocity: • The continuity equation: ∂w x ∂w y ∂w z + + =0 ∂x ∂y ∂z – Pressure: • The Nusselt-equation: − λ ⋅ gradT (x ) W = α x ⋅ (TW − T∞ ) Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 37 ωx = wx w∞ ωy = ωz = w∞ wz w∞ p π = ρ ⋅ w ∞2 – Temperature: ϑ= T − T∞ TW − T∞ – Space: ξ = x L Thermal hydraulics wy η= y L ζ = z L Prof Dr Attila Aszódi, BME NTI 38 Similarity of heat transfer processes Similarity of heat transfer processes • Replacing the dimensionless parameters into the Navier-Stokes equations and reassembling: • The dimensionless similarity parameters in the above mentioned equations are the following: – The Péclet number (this number shows a relationship between the w ⋅L velocity field and temperature field): Pe = ∞ ωx ⋅ ∂ω z ∂ω ∂ω ν + ω y ⋅ z + wz ⋅ z = ∂ξ L ⋅ w∞ ∂η ∂ζ  ∂ 2ω z ∂ 2ωz ∂ 2ωz + + ⋅  ∂ζ ∂η  ∂ξ  ∂π L ⋅ g L ⋅ g  − − − ⋅ β ⋅ (TW − T∞ ) ⋅ ϑ w∞ w∞  ∂ζ • Replacing the dimensionless parameters into the energy equation and reassembling : ∂ϑ   ∂ 2ϑ ∂ 2ϑ ∂ 2ϑ  ∂ϑ ∂ϑ w∞ ⋅ L   + ωz ⋅ + + ωy ⋅ + ⋅  ωx ⋅ = ∂ζ   ∂ξ ∂η ∂ζ  ∂η ∂ξ a  – The Nusselt number (the criteria of the similarity of the heat α ⋅L transfer): Nu = ∂ωx ∂ω y ∂ωz + + =0 ∂ξ ∂η ∂ζ λ – The Froude number (this number shows the relationship between w∞ Fr = the gravity and inertia forces): • The Nusselt-equation: Thermal hydraulics – The Reynolds number (this number shows the relationship between w ⋅L the inertia and drag forces): Re = ∞ ν • The continuity equation: gradϑ W = − a L⋅g α ⋅L ⋅ϑ W λ – The Archimedes number (this number shows the relationship between the buoyancy and inertia force): Ar = L ⋅ g ⋅ β ⋅ (TW − T∞ ) Prof Dr Attila Aszódi, BME NTI 39 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI w∞2 40 CANDU Thermal hydraulics Prof Dr Attila Aszódi, BME NTI VVER-440 105 Thermal hydraulics VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Prof Dr Attila Aszódi, BME NTI 106 VVER-1000 107 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 108 VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI VVER-1000 109 VVER-1000 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 110 Fuel properties of VVER-440 and VVER-1000 111 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 112 THTR-300 Boiling heat transfer Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 113 Thermal hydraulics Multiphase flows • Definitions – For example two phase, air-water flow in horizontal pipe: • The total mass flow rate: m& = m& f + m& g • In the following slides water-steam systems are going to examined: Prof Dr Attila Aszódi, BME NTI 114 Multiphase flows • The most often is the boiling and condensation, here water and its steam are the two phases, • The air-water flow is very often in pipes • Practical examples: steam generator, compensator, BWR, chemical reactors, etc Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 115 • Volume flow rate: Q = Q f + Qg = m& f • Volumetric ratio (αi): < α i < 1; α i = Vi ; ∑αi = ∑Vi • Mass ratio: Xi = Thermal hydraulics ρf + m& g ρg m& i ∑ m& i Prof Dr Attila Aszódi, BME NTI 116 Multiphase flows Multiphase flows • The most of the flow systems are transition between the stratified and disperse flows; • They can be identified by the characteristic shape of the flow, for example annular flow, bubbly flow, droplet flow, film boiling • Flow systems: Stratified and disperse flows Stratified flow: Thermal hydraulics Disperse flow: Prof Dr Attila Aszódi, BME NTI 117 Thermal hydraulics Multiphase flows • Bubble generation: – The bottom layer reaches the saturation temperature first in a bottom heated vessel, – The generated bubble comes up and collapses, – Homogenised bubble generation: the bubbles generates in saturated water (this is not existed because the water can boil at 220 °C at bar) – Heterogenic bubble generation (subcooled boiling): the steam bubbles generate at the irregular parts of the heated surface (bubble generator sites) p f R Π + RΠ σ = p g R Π 2σ ∆p = p g − p f = R 2R pg pf – This amount of pressure is needed between the bubble and water for the existence of the bubble • Condensation: in an analogous way Prof Dr Attila Aszódi, BME NTI 118 Multiphase flows • Boiling (bubble generation): homogenised or heterogenic Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 119 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 120 Multiphase flows Multiphase flows • q& ′′= α (∆T ) = α (Tw − Tsat ) • if q&′′ increases, then • Bubble formation – R ≈ 0: ∆p → ∞ – on plane surface unlimited pressure is needed to form a bubble – Steam generator centrums are necessary: errors on the surface where the bubbles can be formatted – Lower over heating is necessary for the bigger bubble generator centrums Thermal hydraulics Prof Dr Attila Aszódi, BME NTI →If the pressure is higher then the typical dimension of the bubbles are lower, the bubble departure frequency decreases 121 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 122 Heat transfer with boiling • The transferred heat from the heated surface to the fluid: • The Heat transfer with boiling depends on: –It occurs in steady or moving fluid? q′s′ = α (Tw − Tsat ) = α∆Te • Turbulence by flow • The bubble leave the surface earlier Where Tw is the wall temperature of the heated surface, Tsat is the saturation temperature of the fluid, α is the heat transfer coefficient –The pressure and the thermo physical features of the fluid: • If the pressure increases then it causes lower dimensions of bubbles, the number of bubble generator centrums and the frequency of bubble leaving are higher • The heat transfer coefficient consist of two parts: the heat transfer due to boiling (removed heat of generated bubbles) and the convective heat transfer Prof Dr Attila Aszódi, BME NTI is also increases →Then little and little steam generator centrums start to operate →The intensity of the boiling increases, which enhance the heat transfer coefficient Heat transfer with boiling Thermal hydraulics (Tw − Tsat ) 123 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 124 Heat transfer with boiling Boiling in vessel • The fluid staies in the vessel, the natural convection is the main flow process which leads the movement of the fluid particles • If the fluid temperature is much higher than Tsat then volumetric boiling occurs • The Heat transfer with boiling depends on: –The degree of sub cooling and the temperature of the heated surface: higher surface overheat and lower α↑ fluid sub cooling –The roughness of heated surface: the higher roughness the higher α↑ number of steam generator centrums Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 125 Thermal hydraulics Boiling in vessel Prof Dr Attila Aszódi, BME NTI Prof Dr Attila Aszódi, BME NTI 126 The boiling curve • In the reality if the temperature exceed Tsat then the boiling starts • subcooled (surface) boiling • Starts at the steam generator centrums Thermal hydraulics Volumetric boiling in vessel Single phase flow, heat transfer process is only by convection 127 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 128 The boiling curve The boiling curve Surface (bubbly) boiling Surface (tubular) boiling – The departure of bubbles generates turbulence on the surface – The efficiency of the heat transfer increases fast Thermal hydraulics – The steam bubbles joins to each other and forms bigger tubular – The efficiency of the heat transfer increases fast Prof Dr Attila Aszódi, BME NTI 129 Thermal hydraulics The boiling curve Prof Dr Attila Aszódi, BME NTI 130 The boiling curve Transitional boiling – Increasing Tw the steam generation enhances and a steam film forms next to the solid surface – If q”max (critical heat flux) is reached then the heat transfer suddenly goes down Thermal hydraulics Film boiling – Steam film covers the whole heated surface – Tw increases and the heat radiation becomes an important method of heat transport, so above q”min (Leidenfrost-point) the heat transfer is enhanced Prof Dr Attila Aszódi, BME NTI 131 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 132 The boiling curve The boiling curve • For example: Nukiyama experiment – In steady fluid (at atm pressure, saturated FC-72) an electrically heated platinum wire with a diameter of 75 mm is emerged into the fluid (Tsat=56°C) – The video films were recorded with a high speed video camera (600 frame/s) The play has frame/s as velocity, except for the "H" point, which has 10 frame/s Boiling crises –If Tw is not increased smoothly and constant heat source assumed (this is more likely in the practice), when q”max is reached then suddenly film boiling occurs which leads to fast temperature rise Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 133 Thermal hydraulics The boiling curve Prof Dr Attila Aszódi, BME NTI 134 The boiling curve • „A”: The start of the boiling – Boiling starts at: W/cm heat flux – Listen to the initial shape of the bubbles in the vicinity of the wire! This can lead to film boiling instead of bubbly boiling under certain circumstances Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 135 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 136 The boiling curve The boiling curve • „B”: Volumetric boiling / with low heat flux – Bubbly boiling with a heat flux of 12 W/cm Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 137 Thermal hydraulics The boiling curve Prof Dr Attila Aszódi, BME NTI 138 The boiling curve • „C”: Volumetric boiling / with high heat flux – Bubbly boiling with a heat flux of 18 W/cm Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 139 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 140 The boiling curve The boiling curve • "D": Critical heat flux (CHF) – This record shows the transition from bubbly boiling to the film boiling so the critical heat flux (CHF) can be seen The critical heat flux is 25 W/cm at this experiment Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 141 Thermal hydraulics The boiling curve Prof Dr Attila Aszódi, BME NTI 142 The boiling curve • "E": Film boiling / at low heat flux – Film boiling can be seen on this record at 76 W/cm heat flux The regular bubble generation can be recognized! Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 143 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 144 The boiling curve The boiling curve • „F": Film boiling / at high heat flux – Film boiling can be seen on this record at 293 W/cm heat flux The irregular (chaotic) bubble generation can be recognized! Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 145 Thermal hydraulics The boiling curve Prof Dr Attila Aszódi, BME NTI 146 The boiling curve • "G": dry out and burn up – This record shows the dry out of the wire The heat flux is about 500 W/cm The wire melts at the beginning of the length („burnout”) Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 147 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 148 The boiling curve The boiling curve • "H": Secondary critical heat flux (MHF) – The transition from film boiling to bubbly boiling can be seen on this record which occurs at the secondary critical heat flux This MHF is 15 W/cm for this experiment Film Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 149 • Boiling under forced flow 150 B: the fluid temperature exceed Tsat, and sub – The fluid is not in steady state – The heat transfer consists of the forced convective part and another part due to boiling cooled bubbly boiling starts here The bulk temperature is below to Tsat The turbulence due to boiling enhances the heat transfer so the wall temperature increases moderately • Example: upward flow in vertical pipe with constant heat flux (external heating) Prof Dr Attila Aszódi, BME NTI Prof Dr Attila Aszódi, BME NTI A: the fluid comes in to the tube with a temperature less than Tsat Multiphase flow in pipes Thermal hydraulics Thermal hydraulics 151 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 152 C: the bulk temperature exceed Tsat, the saturated volumetric boiling starts G: „dry out” - The steam phase wrests the liquid drops from the wall - The fluid is steam with dispersed liquid drops - The convective heat transfer stops here and the wall temperature increases on a fast way The heat radiation plays here important role D: the bubbles form slugs The wall temperature does not increases due to phase change even decreases due to the generated turbulence E: the bubbles form a big slug in the middle of the pipe and there is a fluid film on the wall H: single phase, saturated steam flow F: little water props goes into the inner steam slug Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 153 If the heat flux high enough, after „C” steam film appears on the wall, which separates the liquid phase from the heated surface Prof Dr Attila Aszódi, BME NTI 154 Boiling crises • Boiling crises: such a phenomenon which causes a dramatic change in the heat transfer mechanism and intensity • This phenomena have to be avoided in technical systems because it can lead to lose of functionality • Boiling crises can be first or second order Then boiling crises can occur Thermal hydraulics Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 155 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 156 Boiling crises Boiling crises • First order boiling crises: • Second order boiling crises: „dryout” – First kind: from bubbly boiling to film boiling kind (DNB: Departure from Nucleate Boiling) kind – Second kind: from film boiling kind to bubbly boiling – Third kind: direct transition to single phase film boiling Thermal hydraulics Prof Dr Attila Aszódi, BME NTI – Transition from annular flow with entrainment to drop flow – The heated surface dries out 157 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI Boiling crises Boiling crises • First order boiling crises ′′ = q& ′DNB ′ = CHF (Critical Heat Flux) • q& krit • Dimensionless parameter: DNBR (Departure from Nucleate Boiling Rating ′ • DNBR (r, t) q& ′DNB DNBR = 158 • Design and operational requirement: everywhere and every time: ′ q& ′′ < q& ′DNB DNBR = + δ > • The reserve up to the critical heat flux: δ= q& ′′ ′ − q& ′′ q& ′DNB q& ′′ • The minimal reserve δm>0 • Time dependency: operational state, xenon oscillation, position of control rod, burn up DNBRmin ≥ DNBRm = + δ m • The incidental minimal reserve δm=0,05-0,1 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 159 Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 160 Heat transfer with boiling Heat transfer with boiling • In the region of bubbly boiling: •The pressure dependency of the critical heat flux α = Aq"0,7 = B∆T 2,33 q" p ,kr • The ‘A’ and ‘B’ tag depend on the fluid material properties and the pressure q"1,kr • The characteristic value of water for bubbly boiling at atmospheric pressure: = 3,5 q" p ,kr q"1,kr ∆T=5 25 [K] lg q” For water α=f(q”,p) q”=5,8·103 1,2 · 10 [W/m2] Water in boiling(0,2≤p≤100 bar) Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 161 Topics of the whole semester TH lectures • • • • • • • • • • • • • • • • • • • • • • • • Technical solutions of the heat removal in different type of nuclear reactors Process and spatial distribution of heat generation in a reactor General differential equation of heat conduction and the solutions for different initial and boundary conditions Numerical solution of steady state and transient heat conduction problems Material properties of UO2 Temperature distribution in fuel pins Equations of hydraulic systems, calculation of pressure losses Calculation of convective heat transfer Thermal instabilities Heat transfer in natural convection Characteristics of boiling heat transfer Boiling curve Boiling crisis DNBR Condensation Two phase flow patterns in vertical and horizontal pipes Flow maps Steady-state thermal hydraulics of the coolant subchannels Temperature distribution in the fuel, the cladding and the coolant Computer codes in thermohydraulics Numerical algorithms in TH codes Containment thermal hydraulics Fundamentals of reactor safety Design Basis Accidents Courses of different size break LOCA incidents The role of human factor Design limits for nuclear fuel Beyond Design Basis Accidents Physics of severe accidents Preliminaries, conditions, causes, course, thermal hydraulical processes and consequences of TMI-2, Chernobyl and Fukushima accidents Analysis of other relevant incidents and accidents References • - N E Todreas, M S Kazimi: Nuclear Systems I; Thermal hydraulic fundamentals, 1990 • - L S Tong, J Weisman: Thermal Analysis of Pressurized Water Reactors, ANS, 1996 • - Manuscript of the lectures Thermal hydraulics Prof Dr Attila Aszódi, BME NTI 163 Thermal hydraulics p = 0,35 0,4 pkr • The relation is identical for different fluids between p/ pkr and q”p,kr/ q”1,kr: p: given pressure pkr: the critical pressure q”p,kr: the surface critical heat load next to the p pressure q”1,kr: the surface critical heat load next to the p pressure •The maximal value for water: q”p,kr=3,5 4·106 W/m2 this is valid between p =80-90 bar Prof Dr Attila Aszódi, BME NTI 162