Numerical analysis of transient pressure variation in the condenser of a nuclear power station

Journal of Mechanical Science and Technology 30 2 2016 953~962 www.springerlink.com/content/1738-494xPrint/1976-3824Online DOI 10.1007/s12206-016-0149-y Numerical analysis of transient

Journal of Mechanical Science and Technology 30 (2) (2016) 953~962 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online)

DOI 10.1007/s12206-016-0149-y

Numerical analysis of transient pressure variation in the condenser of

Xinjun Wang1, *, Zijie Zhou1, Zhao Song1, Qiankui Lu2 and Jiafu Li2

1 Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an, 710049, China

2

Dong Fang Turbine Co., Ltd, Deyang, 618000 , China (Manuscript Received June 2, 2015; Revised September 5, 2015; Accepted September 24, 2015) -

Abstract

To research the characteristics of the transient variation of pressure in a nuclear power station condenser under accident condition, a

mathematical model was established which simulated the cycling cooling water, heat transfer and pressure in the condenser The

calcula-tion program of transient variacalcula-tion characteristics was established in Fortran language The pump’s parameter, cooling line’s organizacalcula-tion,

check valve’s feature and the parameter of siphonic water-collecting well are involved in the cooling water flow’s mathematical model

The initial conditions of control volume are determined by the steady state of the condenser The transient characteristics of a 1000 MW

nuclear power station’s condenser and cooling water system were examined The results show that at the condition of

plant-power-suspension of pump, the cooling water flow rate decreases rapidly and refluxes, then fluctuates to 0 The variation of heat transfer

coeffi-cient in the condenser has three stages: at start it decreases sharply, then increases and decreases, and keeps constant in the end Under

three conditions (design, water and summer), the condenser pressure goes up in fluctuation The time intervals between condenser’s

pres-sure signals under three conditions are about 26.4 s, which can fulfill the requirement for safe operation of nuclear power station

Keywords: Condenser of nuclear power station; Power supply halt of pump; Flow rate of cooling water; Transient heat transfer; Pressure of condenser

-

1 Introduction

As an important equipment in condensing turbine set, the

condenser can keep stated backpressure and coagulate steam

into clean water The condenser is a kind of heat exchanger

which plays the role of cold source in the turbine’s

thermody-namic system

For security thought, three signals are settled in a

con-denser: signal of emergent halt of turbine, signal of emergent

halt of reactor and signal of emergent halt of condenser When

there is a forced outage accident in a nuclear power station,

the recycle water pump shuts down As a result, the flow rate

of cooling water decreases to zero gradually due to siphonage

In consequence, the heat transfer coefficient and capacity of

heat transmission in condenser decline and the condenser

pressure goes up dramatically Ultimately, the rising of

pres-sure in condenser triggers signals of emergent halt of the

tur-bine and emergent halt of the reactor, which causes the

shut-down of both the reactor and main valve of the turbine But

there is still live steam production after the shutdown of the

reactor To avoid overpressure of the second circuit, live

steam should be discharged through the bypass system into the condenser, which means the pressure in the condenser will boost further Consequently, if the signal of emergent halt of the condenser is triggered because of the high pressure, the bypass valve will close so the main steam cannot flow into the condenser, which means the emergency condition in nuclear power station will turn worse Therefore, the condenser in a nuclear power station must fulfill both the requirements under normal condition and emergency condition In emergency condition, a condenser is required to take in and condense the steam of high temperature and high pressure timely

To determine the pressure of emergent halt of condenser signal, the reliability, safety and economy of the system should be taken in consideration If the pressure of emergent halt of reactor or emergent halt of turbine is set at a low level, the frequent fluctuation of condenser’s pressure will cause the continual halt of turbine and reactor, which will shorten the lifetime of the turbine set and the reactor If the pressure is set too high, the condenser pressure will trigger an emergent halt

of the condenser signal in no time when live steam flows into the condenser through the bypass system In this situation, the requirement of a nuclear power station’s secure operation cannot be fulfilled Considering the time needed for the halt and the main steam flow, the interval between emergent halt

* Corresponding author Tel.: +86 29 82660313, Fax.: +86 29 82660313

E-mail address: xjwang@mail.xjtu.edu.cn

† Recommended by Associate Editor Kwang-Hyun Bang

© KSME & Springer 2016

of turbine and emergent halt of condenser should be 12 s or

longer The sudden absence of the house power is the worst

situation in a nuclear power station The interval between

these two signals directly and dominantly influences the

sta-tion's security and is an important index parameter of

con-denser and cooling water system design

Much research has been conducted on flow rate and the

transient pressure variation at the condition of

plant-power-suspension of pump in a power station [1, 2] But research on

condensers has mainly focused on some aspects like flow and

heat transfer on steady condition, variable working condition

and dynamic performance In the 1970s, Spalding and

Patankar [3] proposed the idea of a porous media model In

that case, the flow in steam side of the condenser is simplified

to the flow of mixture of steam and air in porous media with

distributed resistance and distributed mass Hu and Zhang [4]

investigated the condensate tubes that were submerged by

condensing water, and proposed a new relation to calculate the

heat transfer and flow characteristics in the condenser Hou et

al [5] did numerical research on flow field and heat transfer

characteristics in the vapor side of a condenser using the

po-rous media model Yang et al [6] numerically simulated the

flow in the vapor side in condenser of a 300MW power station

using PHONEICS software Oh and Revankar [7] did some

research on the surface condenser with elevation arranged

tubes by experiment, and observed some characteristics of

heat transfer and variable working conditions Using the

over-all heat transfer coefficient equation of condenser proposed by

the Heat Transfer Institute (HEI), Raj [8] gave some

predic-tion and advice on different condipredic-tions of condenser Zhu et al

[9] did some experimental study and indicated the cooling

water flow's influence on condenser’s heat transfer coefficient,

temperature difference and pressure Electric Power Research

Institute (EPRI) [10] developed a real-time simulation

soft-ware (MMS) which can simulate the dynamic performance of

different facilities in the unit Furthermore, this software can

also evaluate the influence of difference disturbances on the

operation of the unit Carcasci and Facchini [11] at the

Insti-tute of Automation and Computing of Italy developed a highly

flexible computerized method which can do real-time

simula-tion on the power stasimula-tion Using the method of artificial neural

network, Prieto et al [12] made predictions of the heat transfer

coefficient and cleanness factor in the condenser of a power

station cooled by sea water And the result of the prediction

seems to be accurate with error less than 5%

In the condition of plant-power-suspension of pump in

power station, the transient heat transfer process in condenser

is of changeable pressure, changeable steam flow and

change-able cooling water flow Little attention has been devoted to

this situation expect for Jiang and Ding [13], who studied the

transient pressure variation in designed and summer

condi-tions when cooling water lost In Ref [13], the HEI formula

was used in the calculation of the heat transfer rate And the

study in Ref [13] takes no account of the change of the heat

transfer area caused by the reflux of the cooling water

We analyzed the characteristics of cooling water flow and the transient variation of pressure in a 1000 MW nuclear power station condenser when lost house power consumption The flow of cooling water is under the effect of siphonage Different from the literature study [13], the formula by partial

is used in the calculation of the heat transfer rate And the change of the heat transfer area caused by the reflux of the cooling water is taken into consideration The results of this paper may provide a new theoretical foundation for the secure operation of a nuclear power station

2 Transient computation of cooling water flow When cycling water pump lost its power, the cooling water flow in the once-through siphonic cooling system changes The water flow can be affected by the pump, arrangement of cooling line, check valve’s specialty and the parameter of the siphonic water-collecting well

2.1 Model and governing equation of water hammer Fig 1 shows the once-through siphonic cooling system of a

1000 MW nuclear power station The cooling water comes out from the condenser and discharges into the front pool of the siphonic water-collecting well When the water level of the front pool climbs higher than the siphon wall (as shown in the shaded part), the cooling water overflows into the back pool of the siphonic well and comes into the natural water source Water hammer, manifested as the violent changes of fluid flow rate and pressure, is a transient process which occurs when s pump starts, pump suspends or check valve closes In calculation, the siphonic well is assumed to be a pool with constant water level All the cooling lines in the condenser are equivalent to one pipe whose flux is equal to the total flux of the cooling water The sectional area of this equivalent pipe is equal to the total sectional area of all cooling lines The water hammer wave’s propagation speed and friction coefficient in Fig 1 Schematic of the once-through siphonic cooling system

this pipe are the same as in one cooling line In this way, the

whole system can be simplified to a system of “pump - inlet

pipe - equivalent cooling line - outlet pipe - water well”

Darcy-Weisbach’s friction expression is introduced in and

the kinematic equation of the water hammer is deduced as

follows:

1

where the inertial force of unit volume is expressed on the left

The three parts on the right mean the pressure of unit volume

of fluid, the friction resistance head of unit length and the

velocity head

The continuity equation of water hammer has the form:

2

= −

∂ ∂ (2)

Coefficient γ is introduced in the linear combination of

Eqs (1) and (2):

2

We assume that Ve x t( ,)and Hp x t( ,) are the solutions of

Eq (3) Comparing the total derivative of Ve x t( ,)and

,

Hp x t( ), we obtain:

2

Ve

Ve

dt

γ

λ









(4)

The solution of Eq (4) is

g

a

γ= ± (5)

Substituting γ into Eqs (3) and (4), then we have:

Along C+：

0 2

Ve Ve

dx

dt







(6)

Along C―：

0 2

Ve Ve

dx

dt







(7)

Eqs (6) and (7) are the characteristic line equation sets and

/

dx dt is the expression of characteristic line Ve x t( ,)and

,

Hp x t( ) satisfy the differential relations on their own charac-teristic lines

Fig 2 shows the computational grid of water hammer basis

on the characteristic line equation set (Eqs (6) and (7)) In this grid, the x axis is along the length of the pipe and y axis de-notes time In view of friction resistance, the whole pipe is sectioned into n parts and the time step is∆ = ∆t x a/ Gener-ally speaking, when ∆x and ∆tminish, the result of compu-tation will approach the real transient flow situation In this figure, AP and BP (marked as C+ and C-) whose slope are 1/a and -1/a, are characteristic lines in x-t plane

Discretize the water hammer’s characteristic line equation

by time, and then we have the general expression of discrete equations:





where the subscripts ( i-1, i+1 and Pi ) stand for the position A,

B and P in Fig 2 Hi+1, Hi−1, Qpi+1 and Qpi−1 respec-tively stands for the mass flow and pressure head of different nods a moment before Their units are m and m3.s-1 Hpi(m) and Qpi( m3.s-1) are the transient pressure and mass flow

x

∆ (m) is the step length of the pipe

a TB Ag

2

f x FP DgA

∆

= are the calculation factors For a certain cooling line system, the values of TB and FP

do not change over t and x Once the flow state before ∆tis known, they can be easily worked out by Eq (8)

2.2 Numerical condition

In the computation process of water hammer using the char-acteristic line equations, the initial conditions and the bound-ary conditions of cooling water are needed Initial conditions are parameters of steady state of the cooling water Boundary conditions consist of (1) the suspension condition of pump, (2) the condition of cascaded pipeline of cooling water, and (3) the constant pressure of the pool For detailed expressions, refer to Ref [2]

2.3 Verification of the program The self-written program is checked by the example "water hammer caused by suspension of pump in a valveless pipe" in

t

P

C-X

x Fig 2 Computational grid of water hammer

Ref [1] The calculation condition is briefly listed in Table 1

For more details, see Ref [1] Fig 3 shows the comparison

calculation in Ref [1] and the results of this paper The curves

in Fig 3 express the pressure head, non-dimensional mass

flow and non-dimensional torque From this comparison we

see that the maximal pressure head in this paper is 97 m, while

that in Ref [1] is 96.7 m The max reflux in this paper is 0.98

m3/s, while that in Ref [1] is 1 m3/s After comparing these

two results, a conclusion is drawn that the self-written

calcula-tion program is reliable enough to get a precise result

3 Transient pressure calculation of condenser

In a power station’s surface condenser, the cooling water is

insulated from the steam by the wall of cooling lines The

space in the condenser can be divided into two sides: the

steam side and the water side The space of steam side in

con-denser is invariant and can be divided into three parts: gaseous

phase part, air part and hot well part Though there is no

obvi-ous bound between gaseobvi-ous phase part and air part, the

inter-faces between the hot well part and the gaseous part and the

interface between the hot well part and the air part are vivid

The water side in the condenser is of two parts: cooling lines and cooling water Cooling lines can be divided into two parts: exposed part and nonexposed part (nonexposed part is located

in the condensed water) The exposed part and the nonexposed part convert with the change of quantity of condensed water

3.1 Calculation model and governing equation It’s a complex procedure of flow and heat transfer when there is a plant-power-suspension of pump in a power station The steam discharged into the condenser cannot be condensed completely so that the temperature and pressure in the con-denser will rise up The steam then fills in the steam side and a heat transfer and condensation procedure with changeable pressure and mass happens The pressure and mass flow of the cooling water decrease to zero gradually With the rise of cooling water’s level, the cooling water lines become sub-merged To calculate the transient change of pressure in the condenser, we set the gaseous side of condenser and ex-hausted casing of turbine (except for the condensed water) as control volume Assume that:

(1) The gaseous phase of the condenser is in thermody-namic equilibrium;

(2) The steam discharged into condenser from bypass sys-tem is of high pressure, so that the mass flow of discharged steam cannot be influenced by the pressure fluctuation of con-denser;

(3) The mass flow and flow rate of cooling water in con-denser are homogeneous in calculation;

(4) Take no account of chemical filling water and flash of condensation;

(5) In every time node, the heat transfer is steady and the changes between neighboring time nodes are step changes The continuity equation of control volume open system can

be written as:

,

v

v in con

dG

dt

∑ ɺ ɺ , (9)

where ∑Gɺv in, denotes the mass flow of total steam

(includ-ing steam from the bypass system and the turbine’s exhaust steam) into the control volume Gɺcon is the total condensa-tion rate Gvis the steam mass in the control volume And t denotes time

The energy equation of the control volume's vapor filling procedure becomes (ignore the kinetic energy and poten-tial energy of the steam ):

OPS

v in v in con l s

dU

dt

− +ɺ ∑（ɺ ）− ɺ = , (10)

where Qɺdenotes the capacity of heat transmission between the control volume and outside When the control volume

Table 1 Condition of the check calculation

Rotating inertia moment of pump 636.5 N·m 2

Rated flow of pump 0.912 m 3 /s

Rated torque of pump 1283.9 N·m

Water hammer wave velocity 860 m/s

0

20

40

60

80

100

120

140

time/s

h(result of literature[1]) h(result of check calculation)

-3 -2 -1 0 1 2 3

4 β(result of literature[1])

β(result of check

calculation)

v(result of literature[1])

v(result of check

calculation)

Fig 3 Comparison of check calculation result and the result of Ref [1]

releases heat to the outside, Qɺ is positive Otherwise, Qɺis

negative ∑（Gɺv in v in, h, ）denotes the energy which is brought

along with the steam into the control volume hv in, is the

specific enthalpy of the steam in control volume Gɺcon l sh, is

the energy which is brought away by the condensed water

,

l s

h is the specific enthalpy of saturated water under the

pres-sure of condenser UOPS is the total energy of the control

volume

The rate of internal energy’s change in control volume can

be written in the form:

dt = dt ⋅ + dt ⋅ (11)

The capacity of heat transmission Qɺ has two different

sources: One, the capacity of the heat transmission between

steam and water; two, from the heat transmission between

steam , cooling line, condenser casing, and the heat

transmis-sion between casing and outside

We then write the relation between the capacity of heat

transmission and the condensation rate:

,

con v l s

Qɺ=Gɺ h −h (12)

Discretize Eqs (9)-(12) by time, and we have the governing

equations of the transient pressure change of condenser:

,

t t v

,

t t t

v in con

t t t ops ops

v in v in con l s

t t t t t t t t

con v l s

t

t

+∆

+∆







∑

∑









(13) 3.2 Calculation of heat transfer coefficient

When the flow rate of cooling water is higher than 0.9 m/s,

HEI [8] standard can be used to calculate the overall heat

transfer coefficient of condenser:

0 c t m

where K0 is the basic heat transfer coefficient β is the c

correction factor of cooling lines' cleanliness β is the cor-t

rection factor of temperature β is the correction factor of m

cooling lines' material and wall thickness The specific value

of each factor can be found in Ref [15]

When the flow rate of cooling water is less than 0.9 m/s, the

overall heat transfer coefficient can be calculated using

ex-perimental correlations For forced heat convection in tube, we

use the formula recommended by Gnielinski:

w 1/ 2 2/3

w

w

w i

Re

Re d

λ α

λ

−



= 



(15)

where awis the forced convection heat transfer coefficient in tube λ is the heat conductivity coefficient of the cooling w water di denotes the inner diameter of the cooling line

w

Re denotes the Reynolds number of the cooling water flow and Prw is the Prandtl number of the cooling water

For the outside surface of the cooling line, we use the cor-rection heat transfer coefficient of film condensation in Ref

[16]:

(16) where α is the condensation heat transfer coefficient in the v steam side Π expresses the influence of air flow’s shear stress on the water film outside the tube α is the film con-n densation heat transfer coefficient of the horizontal tube

Nuis the Nusselt number corresponding to α n Z is the number of passes Sis the correction factor of cooling lines organization ε is the correction factor of air content The 0 specific expression of each coefficient can be found in Refs

[14, 16]

When the flow rate of cooling water is less than 0.9 m/s, the overall heat transfer coefficient of condenser can be expressed as:

o w

1

1 ln 2

K

=

, (17)

where λ ( W/m.K )is the heat conductivity of cooling line m o

d (m) denotes the outside diameter of the cooling line pipe

3.3 Calculation of the temperature of the cooling water and the capacity of heat transmission

Fig 4 shows the calculation grid of cooling water’s flow and heat transfer The cooling line’s wall is shown as the shaded portions The grid is of four sections: inlet Sec (I), heat transfer Sec (W) and outlet Sec (O), and grid M The first three sections of grid trace the position and temperature

of cooling water so that the whole pipe’s capacity of heat transfer can be calculated no matter if backflow happens Grid

M is used for comparison General calculation steps are:

(1) Calculate the cooling water node’s position at t and

t+ ∆t separately according to the known change regularity of cooling water’s flow rate;

(2) Confirm the grid nodes that are in the cooling line at ∆t

period by their position coordinates Only these nodes

partici-pate in the heat transfer process

(3) Calculate cooling water’s temperature and heat transfer

capacity by HEI formula or the formula by partial The I, W,

O grid of cooling water should be taken into consideration

(4) Acquire every node’s temperature at the moment of

t+ ∆t Use linear interpolation strategy to calculate M grid’s

temperature at the moment of t+ ∆t Prepare for next

calcu-lation

The logarithmic mean temperature difference is mainly

adopted in the calculation of steady calculation of heat transfer

in condenser In this study, the length of pipe of each grid is

small enough and the temperature variation is not remarkable

In the calculation of cooling water’s temperature, the

tempera-ture difference between cooling water and steam is used for

the heat transfer temperature difference

Adopting implicit format time discretization on grid node

WN we have the equation of heat balance:

n

t t t

t

+∆

−

∆

where cdenotes specific heat at constant pressure; mis the

mass of cooling water; T is the temperature; ∆t denotes

the time step length; A is the area of heat transfer In the

subscript, Wn is the number of segment and v means steam

From Eq (18), we have the temperature calculation

equa-tion of cooling water at the moment of t+ ∆t:

n

t t

T

+∆

+∆

+

=

+ (19)

Calculating all the nodes in grid W according to Eqs (18)

and (19), then we have the cooling water’s temperature of grid

W and the heat transfer rate

n

W

Qɺ of each segment of cooling water We have to use iteration in the calculation of

tempera-ture and heat transfer rate because of using implicit format

After we know the temperature rise and heat transfer rate of

all the nodes, the overall heat transfer rate of cooling water

and condenser can be calculated:

Qɺ =∑Qɺ (20)

Strictly speaking, the heat transfer rate calculated from HEI

equations and the formula by partial is aimed at the whole

condenser Here, the result calculated from the formula by

partial should be corrected When corrected, the heat transfer rate, pressure and temperature of condenser should be the same as the steady state of calculation The correction factor is equal to the heat transfer rate which was calculated from the formula by partial dividing the heat transfer rate calculated from overall:

,1 ,1

HEI HEI SEP SET

fac



= 

<



where QɺHEI,1 is section’s heat transfer rate calculated from HEI equations QɺSEP,1 is section’s heat transfer rate calcu-lated from the formula by partial QɺHEI is the overall heat transfer rate calculated from HEI equations QɺSEP is the overall heat transfer rate calculated from the formula by partial

fac denotes the correction factor

The corrected overall heat transfer rate of cooling water and condenser becomes:

1 0/

Qɺ =Qɺ fac (22)

The heat storage rate of the metal wall of cooling water line pipe is:

dT

dt

=

ɺ , (23)

where mmexpresses the mass of the wall of cooling water line pipe cm is the specific heat of metal wall of tube and m

T is the mean temperature of the cooling water line pipe The heat absorptivity of the condenser’s shell can be repre-sented as:

3

shell shell shell

dT

dt

=

ɺ , (24)

where mshell is the mass of condenser’s shell cshell is the specific heat of metal shell Tshell is the temperature of the shell

Assume that the temperature of the condenser shell is al-ways equal to the average temperature of the two sides of wall The shell’s radiation heat transfer rate to outside is:

4 4

273.15

100

shell

shell

T

Qɺ =εσ + ⋅A , (25)

where ε is the blackness or emissivity which is set to 0.8

σ is the radiation coefficient of black body, set to 5.67 shell

A is the radiation area of the condenser

In the control volume, the total heat transfer rate between steam and outside is:

Qɺ=Qɺ +Qɺ +Qɺ +Qɺ (26)

Fig 4 Calculation grid of cooling water's flow and heat transfer

3.4 Initial conditions

The initial conditions of vapor side in the condenser are the

same as three working conditions: designed, winter and

sum-mer working condition The initial condition of water side in

condenser is the steady status of cooling water In steady

working status, the temperature of all nodes of inlet Sec I is

equal to the water source’s temperature The temperature of all

nodes of outlet Sec O is equal to the cooling water’s

ture at the outlet of condenser The cooling water’s

tempera-ture of grid M accords exponential distribution The

calcula-tion expression of initial temperature of grid W is [15]:

x x

w w

K A

q c

v w x v w in

−

∆ = ∆ , (27)

where x is the distance from the inlet opening of the cooling

water ∆Tv w x, , is the temperature difference between steam

and cooling water at x ∆Tv w in, , denotes the temperature

difference between steam and cooling water at the inlet

open-ing Ax is the heat transfer area from inlet opening to x

x

K is the general heat transfer from inlet opening to x

w

q is he mass flow of cooling water and cw is the specific

heat of the cooling water

4 Results and analysis

The study is based on a 1000 MW nuclear power station

set’s cycle cooling water system When 85% of the main

steam is discharged into the condenser through bypass system

and both the cycle cooling water and the attemperation water

are lost, the transient variation of temperature in condenser is

focused on The study was conducted in three working

condi-tions: designed, winter and summer

4.1 The Program and process of calculation

The self-written program based on FORTRAN language is

applied to calculate the transient variation of cooling water

and condenser’s pressure The basic calculation process is

shown in Fig 5

4.2 Characteristics of cooling water flow

In the 1000 MW power station set, there is a check valve at

the outlet of cycle cooling water pump which is controlled by

an electric actuator When there is plant-power-suspension of

pump, the check valve is closed due to elastic force and

grav-ity In that way, the cooling water can flow backwards in a

while When the electric controlled check valve is closed

line-arly, the change of cooling water’s flow rate is shown in Fig 6

The close duration time of the check valve is 45 s The

varia-tion of flow rate is of 3 stages: at 0-18.1 s, the flow rate

de-creases to zero almost linearly; at 18.1-45.0 s, the cooling

water flows backwards; the flow rate decreases to zero again

at 45.0 s and then fluctuates; in the end, the cooling water

stops flowing

4.3 The transient characteristics of pressure variation in condenser

Fig 7 is a schematic of the cycle water system in a nuclear

Fig 5 Calculation process

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Time/s Fig 6 Cooling water’s flow rate variation

Fig 7 Schematic of the cycle water system in a nuclear power station: (a) reactor; (b) steam generator; (c) bypass valve; (d) live steam valve; (e) steam turbine; (f) electric generator; (g) condenser; (h) pump of cycling water; (i) check valve; (j) pump of nuclear loop.

power plant Table 2 shows the calculation condition of the

condenser The turbine exhaust steam mass flow is the mass

flow that is designed in normal working condition The

at-tenuation rate of exhaust steam means the decrease rate of

turbine's exhaust steam mass flow when power is lost

sud-denly The steam mass flow of bypass is the steam mass flow

through the bypass system to the condenser when power lost

The bypass valve opens or closes linearly

The variation characteristics of steam mass flow, heat

trans-fer coefficient, heat transtrans-fer capacity, and pressure in

con-denser are shown in Fig 8

Fig 8(a) shows the variation curve of steam mass flow

From this we can see that the change of steam mass flow in

designed, winter and summer conditions are almost the same

When there is plant-power-suspension of the pump, the

tur-bine works as usual and the exhaust steam mass flow is the

same as usual When the condenser pressure reaches 20 kPa and triggers an emergent halt of the turbine signal, the live steam valve closes so that the mass flow of steam that is

dis-Table 2 Condition of the condenser’s calculation

Working condition Designed Summer Winter

Live steam pressure (MPa) 6.5 6.5 6.55

Live steam specific

enthalpy(kJ/kg) 2771.2 2771.2 2770.6

Turbine exhaust steam mass

Exhaust steam specific enthalpy

Condenser pressure (designed)

Attenuation rate of exhaust

steam mass flow (kg/s) 4000 4000 4000

Steam mass flow of bypass

Heat transfer area of condenser

Material of cooling line Ti Ti Ti

External diameter of cooling

Temperature of cooling water

Flow rate of cooling water

Volume of vapor phrase in

condenser (m 3 ) 5800 5800 5800

Volume of exhaust casing (m 3 ) 600×2 600×2 600×2

Live steam valve close duration

Bypass steam valve open

Bypass steam close duration (s) 5 5 5

Emergent halt of turbine (kPa) 20 20 20

Emergent halt of reactor (kPa) 20 20 20

Emergent halt of condenser

0 200 400 600 800 1000

Summer Designed Winter

Time/s (a) Steam mass flow variation

0 5 10 15 20 25 30 35 40 45 50 0

1000 2000 3000

4000

Summer Designed Winter

-2 ·℃

Time/s

(b) Heat transfer coefficient variation

0.0 0.5 1.0 1.5 2.0 2.5

3.0

Summer Designed Winter

(c) Heat transfer capacity variation

0 5 10 15 20 25 30 35 40 45 50 0.00

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Time/s

Summer Designed Winter

(d) Variation of condenser's pressure Fig 8 Variation of condenser's parameter

charged into the condenser decreases sharply When the

by-pass valve opens, the steam entering into the condenser

through bypass system increases The emergent halt of

con-denser signal and emergent halt of reactor signal are triggered

when the condenser’s pressure reaches 50 kPa Then the steam

mass sharply decreases to zero again

Fig 8(b) shows the variation heat transfer coefficient The

changes of heat transfer coefficient in three working

condi-tions are same too The variation is of three stages: first, the

pipe’s convection heat transfer coefficient and the overall heat

transfer coefficient decrease sharply and touch bottom when

the cooling water’s flow rate is zero and the steam mass flow

is minimum Second, the cooling water flows back The pipe’s

convection heat transfer coefficient and the overall heat

trans-fer coefficient increase first and then decrease Third, the heat

transfer coefficient touches bottom and keeps constant while

the cooling water fluctuates at 0 and the steam mass flow is 0

The capacity of heat transfer of the condenser is related to

the heat transfer coefficient, steam mass flow and the

tempera-ture difference (the heat transfer area is fixed) Based on the

change characteristics of these three parameters, the change of

heat transfer capacity can be calculated and Fig 8(c) shows

this change

The pressure variation of the condenser, which is affected

by cooling water flow rate, heat transfer coefficient, heat

transfer capacity, steam mass flow and temperature difference,

is shown in Fig 8(d) In three working conditions, the

con-denser pressure increases in fluctuation At the start of

plant-power-suspension of the pump, the steam mass flow keeps

invariant while the condenser pressure increases gradually and

reaches the peak value in about 17 s Soon afterwards, the

main steam valve closes and the bypass valve opens The

steam flow rate increases and decreases sharply At the same

time, the cooling water is refluxing As a result, the condenser

pressure decreases a little and then increases quickly At 20 s,

it peaks for the second time From 20 s to 45 s, the bypass

steam mass flow is constant and the cooling water refluxes

while the heat transfer coefficient and capacity increase and

then decrease As a consequence, the condenser pressure

de-creases and then inde-creases At about 45 s, the condenser

pres-sure reaches the third peak value At the end, the steam mass

flow that enters into condenser decreases to zero rapidly and

the condenser pressure starts to decrease because of the

emer-gent halt of the condenser signal The time when condenser

pressure reaches the third peak value is later than the emergent

halt of the condenser signal-50 kPa because the reactor still

generates live steam while stopping

From Fig 8(d), we can conclude that when there is

plant-power-suspension of pump, the condenser pressure increases

to 20 kPa and triggers an emergent halt of the turbine signal in

some time In summer, designed and winter condition, it needs

15.7 s, 16.7 s and 17.0 s severally The pressure of the

con-denser increases to 50 kPa and triggers an emergent halt of the

condenser signal in some time In summer, designed and

win-ter condition, it needs 42.1 s, 43.1 s and 43.4 s severally In

these three conditions, the time interval between these two signals is 26.4 s, 26.4 s and 26.3 s In conclusion, the time intervals can fulfill the operation requirements of the nuclear power station

5 Conclusions The calculation model of cooling water flow and transient pressure variation of condenser has been established using the self–written calculation program of water hammer in once-through siphonage cooling water system We focused on the change of cooling water flow, heat transfer and pressure in a 1000MW nuclear power station in designed, winter and sum-mer working conditions Based on the analytical and mathe-matical investigation, the following conclusions may be drawn: (1) When there is plant-power-suspension of pump, the cooling water flow rate decreases sharply and refluxes, and then it fluctuates to zero

(2) Corresponding to the change of cooling water flow rate and steam mass flow, the variation of the condenser’s heat transfer factor can be divided into three stages: decreases sharply, increases and then decreases, keeps constant

(3) In a 1000 MW power station, if the electric controlled valve closes linearly in 45 s, the time interval between con-denser-pressure-signal of emergent halt of turbines and that of condensers is more than 12 s, which can fulfill the operation requirements of the nuclear power station no matter if the work condition is designed, winter or summer

(4) The calculation model of cooling water flow and tran-sient pressure variation of condenser in once-through sipho-nage cooling water system can be used in the accident sce-nario in a nuclear power plant The self-written program may provide an analysis method and tool for the design of a nu-clear power plant's condensation system

Nomenclature -

a : Spread rate of water hammer, m/s

A : Heat transfer area, m2

c : Constant pressure specific heat, kJ/(kg.K)

i

d : Inner diameter of cooling line, m

o

d : External diameter of cooling pipe, m

D : Diameter of pipe, m

f : Resistance coefficient of pipe fac : Correct factor of heat transfer rate

g : Gravitational acceleration, m/s2

Gɺ : Steam mass flow, kg/s

h : Specific enthalpy, kJ/kg

H : Pressure head of cooling water, m

p

K :Overall heat transfer coefficient of condenser, W/(m2.K)

0

K : Basic heat transfer coefficient of HEI, W/(m2.K)

m : Mass of cooling water, kg

Nu : Nusselt number corresponding to

w

Pr : Prandtl number of cooling water

Qp : Volume flow rate of cooling water, m3/s

Qɺ : Heat transfer capacity between control volume and

outside, kW

w

Re : Reynolds number of cooling water

S : Correct number factor of cooling line’s organization

t

∆ : Time step length , s

T : Temperature , K

u : Internal energy, kJ/kg

U : Total energy of control volume, kJ

Ve : Flow rate of cooling water, m/s

x : Flow direction of cooling water

x

∆ : Step length of calculation pipe

n

α : Film condensation heat transfer coefficient on horizontal

circular tube, W/(m2.K)

v

α : Condensation heat transfer coefficient of vapor phase,

W/(m2.K)

w

α : Forced convection heat transfer coefficient inside tube,

W/(m2.K)

c

β : : Correction factor of cleanness of tube

m

β : Correction factor of wall thick and material of tube

t

β : Correction factor of cleanness of tube

0

ε : Correction factor of air content

Π : Influence factor of air flow’s sheer stress on the water

film outside the cooling piping

λ : Heat conductivity coefficient, W/(m2.K)

Subscripts

0 : Heat transfer coefficient between condenser and cooling

water (calculated)

1 : Heat transfer coefficient between condenser and cooling

water (corrected)

2 : Heat transfer rate between condenser and cooling

pip-ing’s wall

3 : Heat absorptivity of condenser’s shell

4 : Radiation heat transfer rate between condenser’s shell

and outside

con : Steam condensation in control volume

ops : Control volume

shell : Condenser shell

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Xinjun Wang, Ph.D., is an Assistant professor, Institute of Turbomachinery, School of Energy and Power Engineer-ing, Xi’an Jiaotong University He has been mainly engaged in the research of aerodynamics and two-phases flow in turbomachinery