Description af the steam generation at power plants. And a basic description of kinds of nowadays nuclear reactors. And physical basis for the calculation of boiling in the energy equipment.

1. MODELING OF
VAPORIZATION PROCESSES
Peter the Great St.Petersburg Polytechnic University
Lecture 1
Institute of Power Energy,
Higher school of nuclear and thermal energy
by
Nataliia Agafonova,
Associate professor

2. Recommended literature:Recommended literature:
IN ENGLISH
1. Boiling, Condensation and Gas–Liquid Flow / Whalley, P. - Oxford:
University Press, 1987.
2. One Dimensional Two-Phase Flow / Wallis, G. B. - New York:
McGraw-Hill, 1969.
3. Boiling heat transfer and two-phase flow / Tong, L. S., Tang, Y. S. –
Taylor & Francis, 1997
IN RUSSIAN
1. Тепломассообмен в ядерных энергетических установках : учебное
пособие для вузов / П. Л. Кириллов, Г. П. Богословская .— Изд. 2-е,
перераб. — М. : ИздАТ, 2008.— 254 с.
2. Гидродинамические расчеты : справочное учебное пособие / П. Л.
Кириллов, Ю. С. Юрьев .— М. : ИздАТ, 2009 .— 213 с.

3. OUTLINE OF THE LECTURE 1
1. Steam generation at power plants
(where and when there is steam in the main equipment of the power plants)
1.1. The principal technological scheme of the power plant
1.2. The principal scheme of the boiler at the thermal power plant.
1.3. The main types of nuclear energy reactors
(Reactors with pressurized water PWR /WWER and boiling water
reactors BWR).
1.4. The main equipment of the nuclear power installations
2. The physical basis for the calculation of boiling
in the energy equipment
2.1. Definitions/Terminology
2.2. The boiling on the wall and in the bulk of fluid
2.3. Mechanism of the bubble formation on the heated wall
2.4. Classification of boiling

4. Steam generation at power plantsSteam generation at power plants
Nuclear power plant NPP differs from the standard thermal power station
in the source of heat required to generate steam, which drives a steam
turbine connected to a generator that produces electricity.
Thermal power plant Nuclear power plant
The heat generated by
the burning of fossil fuels
(coal, natural gas, heating oil)
The heat released in
the chain reaction of
uranium nuclear fission

5. Thermal power plant with fossil fuelThermal power plant with fossil fuel

8. 63% - by the number, 68% - by capacities
● Steam is produced in the steam generator;
● Water is flowing through the reactor vessel without boiling. Since it is an
incompressible fluid at high pressure (more than 15 MPa) and temperatures
(more than 316 oC), pressurizer is to be installed in the coolant circuit.
PWR:
18% - by the number, 20% - by capacities
● Operates in essentially the same way as a fossil-fueled generating plant;
● Steam generation takes place in the reactor core;
● The recirculation pumps and the jet pumps allow to vary coolant flow
through the core and to change reactor power.
BWR:

14. Boiling:Boiling: a) a typical process
-- for boilers with burning of fossil fuels;for boilers with burning of fossil fuels;
-- for the reactor core in BWR andfor the reactor core in BWR and
-- in the steam generators at the NPP normal operationin the steam generators at the NPP normal operation
(second circuit of the two(second circuit of the two--circuit NPP with PWR);circuit NPP with PWR);
b) may occur in emergencies in reactor core in PWR
There are different types of the nuclear steam generators (SG)
for PWR / WWER:
●● steam generator with submerged heat exchange surfacesteam generator with submerged heat exchange surface
((Steam generators with recirculationSteam generators with recirculation)
- horizontalhorizontal designdesign (in Russia) or(in Russia) or
-- vertical designvertical design ((anywhere abroadanywhere abroad););
● directdirect--flow ( orflow ( or onceonce--through)through) steam generatorsteam generator.

15. What is the steam generator for the nuclear power plant?What is the steam generator for the nuclear power plant?
The nuclear steam generatorThe nuclear steam generator is a recuperative type heat exchanger,
which consists from the large amount of the small diameter tubes.
These tubes are fixed in the wall of the distributing and collecting
chambers.
We have the exchange of heat between the coolant and the working
medium through the walls of the tubes.
CoolantCoolant – it is a medium, which removes the heat of the nuclear fission
chain reaction from the active core of the nuclear reactor (water for PWR
and BWR).
Working mediumWorking medium – it is the water, which transforms into the vapor and
makes work in the turbine.

16. Steam generators for PWRSteam generators for PWR

17. Steam generators for PWRSteam generators for PWR
Westinghouse (WH) Steam Generator

18. Babcock & Wilcox Steam Generator

21. The boiling on the wall and in the bulk of fluidThe boiling on the wall and in the bulk of fluid
Boiling is an exothermic process.
The liquid starts to boil only if the heat supply takes place.
Heat normally is supplied through the wall of the vessel (channel) with liquid.
A vapor nucleus (bubbles) may form either at a heated surface or within
the liquid itself if this liquid is sufficiently superheated (a process is called
nucleation), on the nucleation sites (centers):
wall superheat = Tw -Ts
liquid superheat = Tl -Ts
The irregularities of the wall surface of the vessel or channel or additives to the
fluid (i.e. surfactants and/or nanoparticles) may be referred to as the nucleation
sites.
If we have a very smooth surface, such as plastic or polished metal, then under
these conditions a heated liquid may show boiling delay and its temperature
may go somewhat above the boiling point without boiling.
In Energy the boiling usually begins on the walls because in this case the
needed heat supply is lower.

22. Dd – the bubble diameter at the moment
of departure from a heated surface;
qw – heat flux
Mechanism of the bubble formationMechanism of the bubble formation
on the heated wallon the heated wall
1 – water at the saturation
temperature;
2 – superheated liquid;
3 - nucleation site (center) -
it may be jaggies of the surface

23. The heat which is required to vaporize a unit mass of liquid (latent heat
or heat of vaporization):
,
where hvs and hls - enthalpy of the vapor and liquid at the saturation
temperature, respectively (can be found in the steam tables)
h r h hv vs s= = -l l
According to the Laplace and Clapeyron-Clausius equations:
1) the vapor pressure within the bubble must be somewhat higher
than the pressure of the surrounding liquid:
DP=2s/Rb, where Rb – bubble radius, m;
s - surface tension, N/m
2) the temperature in the vapor bubble and in the surrounded liquid
layer must be somewhat higher than the saturation temperature, Ts ,
corresponding to the liquid (or system) pressure:
DT≈ (R – site radius)

24. There are several parameters which may be taken into accountThere are several parameters which may be taken into account
as the linear characteristic at the boiling process description:as the linear characteristic at the boiling process description:
1.
- the critical nucleation site radius corresponding to given DT = Tw-Ts,
defines the minimum bubble size.
The smaller the bubble (i.e. cavities on the wall surface),
the higher is the wall superheat required for nucleation!
2. The bubble diameter at departure:
(may be obtained from the balance of the forces acting on the bubble
at the moment of departure)
- formula by Fritz
Q - contact angle (for water ~ 45o at 0.1 MPa); r‘ – saturated liquid density,
kg/m3; r“ – saturated vapor density, kg/m3; g - acceleration of gravity, m/s2

25. )ρρg(
σ
10K10.25D 5
d
¢¢-¢
××+=
Ar/(Ja/Pr)K 2
=
3/2
2
)ρ-ρg(
σ
ν
g
Ar ÷÷
ø
ö
çç
è
æ
¢¢¢
×=
Here:
ρ
ρ
r
)T(TC
Ja
swp
¢¢
¢
×
-×
=
where:
а – thermal diffusivity, m2/s;
λ – coefficient of thermal conductivity, W/(m∙К);
СР – specific heat, J/kg∙K;
μ – dynamic viscosity, Pa∙s;
ν – kinematic viscosity , m2/s.
and
- dimensionless Jakob number;
- dimensionless Prandtl number;
- dimensionless Archimedes number,

26. 3. Simplified relationships for the determination of the bubble diameter
at departure:
( )
( )ïî
ï
í
ì
×
×
» --
;P/P10
;P/P10
D 0.5
cr
1
cr
2
d
for
for 1.10P/P
;1010P/P
2
cr
24
cr
¸=
¸=
-
--
Here Pcr – the critical pressure for water (Pcr = 22.06 MPa);
)ρρ(g
σ
D
D d
d
¢¢-¢×
=
4. The constant of capillarity:
σ
L
g (ρ ρ )
=
¢ ¢¢× -

30. DimensionlessDimensionless Reynolds numberReynolds number
Osborne Reynolds,
Fellow of Royal Society (FRS),
1842 –1912
(the ratio of inertial forces to viscous forces)
where:
w – mean velocity, m/s;
q – heat flux, W/m2;
r – latent heat of vaporization/condensation, J/kg.
L – characteristic linear dimension (Dd or Rcr), m;
μ – dynamic viscosity of the fluid, Pa∙s;
ν - kinematic viscosity (ν= μ/ρ), m2/s;
ρ – density of the fluid, kg/m3;
; ρ″ - density of the saturated vapor, kg/m3.

31. DimensionlessDimensionless Nusselt numberNusselt number
Wilhelm Nusselt
1882-1957
(the ratio of convective to conductive heat transfer)
where:
L – characteristic linear dimension (Dd or Rcr), , m;
λ – coefficient of thermal conductivity, W/(m∙К);
α – heat transfer coefficient, W/(m2.К);
sw
w
TT
q
α
-
=

32. Max Jakob
1879 – 1955
DimensionlessDimensionless Jakob numberJakob number
ρ
ρ
r
)T(TC
Ja
swp
¢¢
¢
×
-×
=
(the ratio of supplied heat to the latent heat)
where:
Cp – specific heat, J/(kg∙K);
r – latent heat of vaporization/condensation, J/kg;
Tw – wall temperature, K;
Ts – saturation temperature, K;
ρ´ – density of the saturated fluid, kg/m3;
ρ″ - density of the saturated vapor, kg/m3 .
ρ

33. Samson S. Kutateladze
1914-1986
(characterizes the process of changes in the aggregate
state of matter, may be used instead of Jakob number)
where:
r – latent heat of vaporization/condensation, J/kg;
СР – specific heat, J/(kg∙K);
Δt – wall superheat/subcooling as compared with saturation
temperature, К.
DimensionlessDimensionless Kutateladze numberKutateladze number

34. (the ratio of gravitational forces to viscous forces)
DimensionlessDimensionless Archimedes numberArchimedes number
where:
g - gravitational acceleration, 9.81 m/s²;
ρ‫׳‬ – density of the fluid, kg/m3;
ρ″ – density of the vapor, kg/m3;
n ‫׳‬ - kinematic viscosity of the fluid, m2/s;
L – characteristic linear dimension (Dd or Rcr), m.
)ρ/ρ(1
)ν(
Lg
Ar 2
3
¢¢¢-×
¢
×
=
Archimedes
of Syracuse
~287 B.C. - 212 B.C.

35. Ludwig Prandtl
1875-1953
DimensionlessDimensionless PrandtlPrandtl numbernumber
(the ratio of kinematic viscosity to thermal diffusivity)
where:
а – thermal diffusivity, m2/s;
λ – coefficient of thermal conductivity, W/(m∙К);
СР – specific heat, J/kg∙K;
μ – dynamic viscosity, Pa∙s;
ν – kinematic viscosity , m2/s.

36. Franz Grashof
1826-1893
Dimensionless Grashof numberDimensionless Grashof number
(the ratio of the buoyancy to viscous force acting on a fluid )
where:
g – acceleration due to Earth’s gravity, m/s2;
L – the vertical length or another length scale at natural
convection, m;
β – the coefficient of thermal expansion (equal to
approximately 1/T, for ideal gases), 1/К;
ν – kinematic viscosity, m2/s;
Δt – the temperature difference between the wall and the
fluid, К

37. (characterizes the process of heat transfer at natural convection)
John William Strutt,
Lord Rayleigh
1842-1919
where:
g – acceleration due to Earth’s gravity, m/s2;
L – characteristic linear dimension, m;
β – the coefficient of thermal expansion, 1/К;
ν – kinematic viscosity, m2/s;
а – thermal diffusivity, m2/s;
Δt – characteristic temperature difference, К.
DimensionlessDimensionless RayleighRayleigh numbernumber

38. Moritz Weber
1871–1951
(a measure of the relative importance of the
fluid's inertia compared to its surface tension)
where:
w – characteristic velocity, m/s;
L – characteristic linear dimension, m;
ρ – density, kg/m3;
σ – surface tension, N/m.
DimensionlessDimensionless WeberWeber numbernumber

44. Test questionTest questionss
1. Where and when the boiling takes place in power equipment? Give the
examples.
2. What are the necessary conditions for the vaporization beginning?
3. Give the definition of the boiling (evaporation, cavitation).
4. What is the bubble pressure excess over the pressure of the surrounding
liquid?
5. What is the bubble temperature excess over the temperature of the
surrounding liquid?
6. What are the main factors influencing the boiling heat transfer?
7. How may the boiling be classified?
8. Give the definition of the pool boiling.
9. Give the definition of the subcooled boiling.
10.Give the definition of the nucleate boiling.
11.Give the definition of the film boiling.
12.What dimensionless numbers may be used for the processing of
experimental data on boiling?
13.Give the definition of the dimensionless numbers (Re, Nu, Pr, Ar, Ja, Ku,
We).

45. Thank you
for your attention!