2

THE HEAT TRANSPORT What is heat transfer ? Heat transfer (or heat) is energy in transit (motion) due to a

temperature difference (anology current flow, mass flow) Modes :Conduction, Convection and Radiation How is heat transferred ? When a temperature gradient exists in a stationary

medium, which may be a solid or a fluid, we use the term conduction to refer to the heat transfer that will occur across the medium

In contrast, the term convection refers to heat transfer that will occur between a surface and a moving fluid when they are at different temperatures.

The third mode of heat transfer is termed thermal radiation. All surfaces of finite temperature emit energy in the form of electromagnetic waves. Hence, in the absence of an intervening medium, there is net heat transfer by radiation between two surfaces at different temperatures

Why is it important to study it ?All the three kinds of heat transfer modes prevail in a nuclear reactor core, however the dominant ones are conduction and convection.

3

THE HEAT TRANSPORT(continued)Physical Origins OF Conduction

Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions between the particles. We may speak of the net transfer of energy by random molecular motion as a Diffusion of energy

Examples :  The exposed end of a metal spoon suddenly immersed in a cup of hot tea

will eventually be warmed due to the conduction of energy through the spoon.On a winter day there is significant energy loss from a heated room to the outside air. This loss is principally due to conduction heat transfer through the wall that separates the room air from the outside air.

Rate Equation for ConductionIt is possible to quantify heat transfer processes in terms of appropriate rate equations.These equations may be used to compute the amount of energy being transferred per unit time. For heat conduction, the rate equation is known as Fourier’s Law.For the one dimensional plane wall shown in Figure 2, having a temperature distribution T(x), the rate equation is expressed as

  qx’’ = - k dxdT

4

THE HEAT TRANSPORT(contd)

• The heat flux qx’’ (W/m2) is the heat transfer in the x

direction per unit area perpendicular to the direction of transfer, and it is proportional to the temperature gradient, dT/dx, in this direction.

• The proportionality constant k is a transport property known as the thermal conductivity (W/m.K) and is characteristic of the wall material. The minus sign is a consequence of the fact that heat is transferred in the direction of decreasing temperature. Under the steady state conditions shown in Figure 3, where the temperature distribution is linear, the temperature gradient may be expressed as

and the heat flux is then

qx’’ =

L

TT

dx

dT 12

L

TTk

12

5

THE HEAT TRANSPORT(contd) ConvectionThe convection heat transfer mode is comprised of two mechanisms. In Energy transfer due to random molecular motion (diffusion), there is also energy being transferred by the bulk, or macroscopic, motion of the fluid. This fluid motion is associated with the fact that, at any instant, large numbers of molecules are moving collectively or as aggregates. Such motion, in the presence of a temperature gradient, will give rise to heat transfer. Because the molecules in the aggregate retain their random motion, the total heat transfer is then due to a superposition of energy transport by the random motion of the molecules and by the bulk motion of the fluid. It is customary to use the term convection when referring to this cumulative transport and the term advection when referring to transport due to bulk fluid motion

Types of Convection Forced Convection Natural Convection

6

THE HEAT TRANSPORT(contd)Forced Convection

Convection heat transfer may be classified according to the nature of the flow. We speak of forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.As an example, consider the use of a fan to provide forced convection air cooling of hot electrical components on a stack of printed circuits boards.

Natural ConvectionIn contrast, for free (or natural) convection the flow is induced by buoyancy forces that arise from density differences caused by temperature variations in the fluid.

Rate Equation for Convection  For convection heat transfer process, the Newton’s Law of Cooling

expresses the rate equation as:q’’ = h(Ts – Tf)where q’’ is the convective heat flux (W/m2) that is proportional to the difference between the surface and fluid temperatures, Ts and Tf, respectively.The proportionality constant h (W/m2 C) is referred to as the convection heat transfer coefficient. It encompasses all the parameters that influence convection heat transfer. It particular it depends on the surface geometry, the nature of fluid motion, and an assortment of fluid thermodynamic and transport properties.

7

HEAT GENERATION IN REACTORS In nuclear reactors, the main source of energy is the nuclear reaction namely, Fission. A second important class, but one that produces much less energy (relative to fission) is radioactivity. In nuclear reactors fission, of a heavy nucleus of Uranium, Plutonium or Thorium splits into two or more lighter nuclei resulting in a net decrease of mass that ultimately converts into exothermic energy.

The average total energy is about 200 MeV per fission in case of 235U.

The complete fission of 1 g of 235Unuclei in a fuel element thus produces a quantity of energy equal to

 (Avogadro No. x 200 Mev)/U235 isotope mass

= (6.0225 x 1023 x200)/235.0439 = 0.513 x 1024 Mev=2.276 x 104 kW-hr=948 kW-Day=0.948 MW-Day

8

HEAT GENERATION IN REACTORS(Contd)Figures to remember

200 Mev per fission 1 g of fissionable material per day generates nearly 1 MW of energy approximate energy consumed by normal human during daily business

is 100 Watt when we wink eye, the energy consumed is less than 1eV.

Heat Generation Rate in Fuel‘In a nuclear reactor the role of neutrons is analogous to that of oxygen in case of a coal fired plant.’The rate of nuclear heat generation is equal to the rate of reaction producing energy times the energy per reaction. In general, the rate of any reaction between mono-energetic neutrons and the nuclei of material is given byR = . (1)Where is the macroscopic cross section, cm—1, of the reactor and the neutron flux, neutrons/s-cm2. R therefore has the units ‘reactions/s-cm3’ The energy generated in a reaction per unit time and volume is called volumetric thermal source strength, q’’’, given byq’’’ = G.R=G.. (2)

    

9

HEAT GENERATION IN REACTORS(Contd)Where G is the energy per reaction, MeV. In case of energy by fission by neutrons of a given distribution [In nuclear reactors neutrons are available with energies ranges form 17 MeV (Fast) down to 0.4 eV (Thermal)]

The is the macroscopic cross section given by = N

q’’’ = G N (3)

where N is the density of fissionable fuel in nuclei/cm3. The value is the microscopic cross section cm2 for the fissionable fuel used and the energy distribution of the neutrons in the reactor. q’’’ has the units of Mev/s cm3

Significance

For heat transfer calculations of a nuclear reactor, it is important to evaluate the volumetric thermal source strength at different positions in a reactor core before evaluating the core temperature distributions, and core heat generation and heat removal. The neutron flux is obtained from neutronic analysis/considerations

10

HEAT GENERATION IN REACTORS(Contd) Example

Calculate the volumetric thermal source strength at a position in a reactor core in which the neutron flux is 1013. The core is loaded with a fuel having fissionable fuel density of 8.5 x 1020 nuclei/cm3. The moderator temperature at the same core position is 60 oC corresponding to which the effective microscopic cross section is 400 barns.Solution N = 8.5 x 1020 =400 b = 400 x 10-24 cm2

G = 180 Mev/fissionTherefore volumetric source strength, q’’’q’’’ = G. .N.

= 180 x 8.5 x 1020 x 400 x 10-24 x 1013

= 6.12 x 1014 Mev/s-cm3

= 6.12 x 1014 Mev/s-cm3 x 1.602 x 10-13 w/cm3 per Mev/s-cm3

= 98.04 w/cm3

A fuel rod, having diameter and active fuel length of 3.454 and 306 cm, respectively, when placed at this location will have an average power out put of.=98.04 x x 1.7272 x 306/1000 281 kW

11

CORE THERMAL DESIGN• The amount of reactor power generation in a given

reactor is limited by thermal rather than by nuclear considerations. The reactor core must be operated at such a power level, that with the best available heat removal system, the temperatures of the fuel and cladding anywhere in the core must not exceed safe limits. Otherwise fuel element damage might result in release of large quantities of radioactive material into the coolant, or in core fuel meltdown.

• Reactor cores are usually limited by those parameters that cause the temperatures to exceed safe limits. (For KCP Reactors, Fuel Centerline and Clad Temperatures).

12

Peaking Factors• Radial peaking factor of a fuel rod is ratio of its power generation to

the average power generated by a rod. (maximum 1.483)• In axial direction flux also varies like a ‘Cosine Shape’. Power

generated from central region of fuel rod (moderated portion) is greater than its upper & lower parts.

• Axial peaking factor of a fuel rod at its any location/ portion is ratio of its power or power density or flux at that location to the average power or power density or flux of same fuel rod. (maximum 1.525) Fuel centerline, fuel surface & clad surface Temperatures are maximum near central portion of fuel rod and least at ends (top/ bottom) of fuel rod.

• Radial peaking factor of a fuel rod depends upon its location in core & is independent of power level or power density. Radial peaking factor of each rod in a circle (25 in KCP-3/ 4) is approximately same.

• Axial peaking factor of a fuel rod does not depend upon its location in core & depends upon power level or power density. Axial peaking factors of all fuel rods in the core is approximately same.

15

CORE THERMAL DESIGN

From now onwards procedures will be discussed for obtaining maximum temperatures (fuel, clad and coolant) in a nuclear reactor with particular emphasis to the PR100.

Coolant Outlet, Maximum Clad and Fuel Centre Line Temperatures

The applicable equations and correlations used for the estimation of various temperatures of interest are found below. Detailed derivation of these follow from the basic principles of heat balance.

Axial Variation of Thermal Source Strength

In a reactor core, the axial variation of neutron flux along the fuel element is given by

(1)

and so is the variation of volumetric source strength for a fuel element/rod having uniform x-section and enrichment.

(2)

where q’’’ and qc’’’ are the volumetric thermal source strengths at

any point along the height and centre of the fuel rod, respectively.

H

zc

cos

H

zqqc

cos

16

Power Distribution (kW) in Core with All Shutoff Rods Out Reference Core at 40 MW

A B C D E F G H J K L M N P Q R S29 150.5 159.6 149.6 2928 155.1 173.5 173.0 153.8 2827 156.1 184.2 194.8 183.6 154.9 2726 151.3 190.1 212.0 212.2 189.4 150.4 2625 142.8 188.6 222.8 237.8 229.0 193.2 141.6 2524 179.3 232.5 250.8 255.1 233.5 182.6 2423 164.8 225.2 260.7 EXP SOR ASOR 164.1 2322 180.2 207.2 SOR 287.1 282.9 262.3 210.4 179.3 2221 187.0 253.9 290.7 297.6 285.9 253.7 186.1 2120 162.1 231.5 284.1 ASOR 296.4 276.9 231.2 161.1 2019 136.2 210.2 EXP 302.6 308.6 296.0 EXP 204.1 135.9 1918 178.1 249.5 290.4 313.3 305.0 290.0 252.0 173.2 1817 142.2 ASOR 276.5 304.9 301.3 304.4 280.6 220.0 141.6 1716 184.8 260.9 295.4 303.6 303.2 295.7 SOR 180.7 1615 144.4 229.7 281.7 306.5 CT 306.4 281.6 229.5 144.3 1514 180.8 SOR 295.8 303.2 303.5 295.3 260.8 184.6 1413 141.7 220.2 280.7 304.4 301.3 304.9 276.4 ASOR 142.0 1312 173.3 252.1 290.1 305.1 313.3 290.3 249.4 178.0 1211 136.0 204.3 EXP 296.1 308.6 302.5 EXP 210.1 136.1 1110 161.2 231.3 277.0 296.4 ASOR 284.0 231.4 161.9 109 186.2 253.8 285.9 297.6 290.7 253.8 186.8 98 179.6 210.5 262.4 282.9 287.0 SOR 207.0 179.8 87 164.3 ASOR SOR EXP 260.6 225.0 164.5 76 182.8 233.6 255.1 250.8 232.4 179.1 65 141.9 193.3 229.1 237.8 222.8 188.5 142.5 54 150.7 189.5 212.2 212.0 190.0 151.0 43 155.1 183.6 194.8 184.1 155.9 32 153.9 173.0 173.5 155.0 21 149.6 159.6 150.4 1

A B C D E F G H J K L M N P Q R S

17

INDIVIDUAL FUEL CHANNELS FLOW AT KCP-II A B C D E F G H J K L M N P Q R S

29 22.8 20.5 22.7 2928 24.6 23.6 20.1 22.4 2827 21.8 22.5 24.9 21.5 23.5 2726 22.8 23.4 23.5 24.3 21.9 23.2 2625 22.4 23.4 23.2 22.7 23.9 22.9 24.9 2524 22.3 23.6 24.7 24.5 24.3 22.7 2423 22.6 22.0 24.7 EXP SOR ASOR 21.9 2322 22.9 24.5 SOR 26.3 26.6 24.2 23.8 21.7 2221 23.0 24.9 26.1 27.2 25.8 24.3 24.6 2120 23.5 25.4 25.9 ASOR 28.7 25.1 26.1 21.4 2019 23.3 24.9 EXP 27.8 30.4 25.5 EXP 23.5 20.4 1918 22.4 24.3 28.4 31.5 31.9 26.1 23.8 22.3 1817 20.0 ASOR 26.4 30.3 29.6 30.7 24.9 23.0 21.7 1716 23.0 25.5 27.4 31.7 29.4 28.0 SOR 21.8 1615 23.4 25.4 26.8 31.0 CT 28.8 25.6 23.5 22.3 1514 22.1 SOR 28.2 31.2 29.4 27.2 24.6 24.0 1413 21.9 26.3 26.4 31.3 31.2 30.7 26.2 ASOR 23.3 1312 22.7 25.1 27.7 31.9 31.5 27.6 23.5 19.9 1211 22.5 25.7 EXP 26.3 29.5 26.3 EXP 25.1 23.4 1110 21.7 24.2 26.0 27.5 ASOR 25.4 21.5 21.7 109 21.0 23.6 26.3 28.4 26.8 24.3 23.9 98 22.0 25.2 24.4 27.0 26.0 SOR 25.4 24.7 87 22.8 ASOR SOR EXP 25.1 24.7 22.6 76 22.0 22.0 23.1 24.0 22.4 21.4 65 21.4 24.2 24.4 24.8 24.0 21.6 22.3 54 23.5 21.1 24.2 23.5 22.5 22.3 43 22.5 20.5 23.7 21.7 19.8 32 22.4 21.5 20.6 23.0 21 20.7 21.5 25.7 1

A B C D E F G H J K L M N P Q R S

18

COOLANT EXIT TEMPERATURESCoolant inlet Temperature 46 oC

Moderator Height 290 cm

A B C D E F G H J K L M N P Q R S29 66.1 69.7 66.1 2928 65.2 68.4 72.3 66.9 2827 67.8 70.9 69.9 72.0 66.1 2726 66.2 70.7 73.5 72.7 72.3 65.7 2625 65.4 70.6 75.3 77.9 75.3 71.7 63.3 2524 70.5 76.0 77.0 77.7 75.3 70.5 2423 68.2 77.2 78.2 EXP SOR ASOR 68.9 2322 70.0 71.8 SOR 79.3 78.4 79.1 72.9 71.1 2221 70.8 77.2 80.0 79.4 79.8 77.8 69.1 2120 67.0 73.8 79.5 ASOR 77.5 79.7 73.0 69.0 2019 63.8 71.8 EXP 79.2 77.0 81.4 EXP 72.5 66.2 1918 70.3 77.3 77.2 76.3 75.2 80.0 78.3 69.7 1817 67.6 ASOR 77.9 76.7 77.0 76.2 80.4 75.1 65.8 1716 70.5 77.3 78.9 75.2 77.5 78.2 SOR 71.2 1615 64.8 73.6 78.1 76.1 CT 78.5 79.5 75.8 65.7 1514 70.9 SOR 78.0 75.6 77.5 79.1 78.3 69.5 1413 65.7 71.5 78.4 75.7 75.4 76.3 78.2 ASOR 64.6 1312 69.2 76.6 77.9 75.1 76.3 78.1 78.4 73.3 1211 64.4 70.2 EXP 80.4 77.9 81.0 EXP 71.5 63.7 1110 68.6 75.1 78.5 78.9 ASOR 80.1 78.9 68.7 109 73.0 78.8 79.2 78.0 79.1 77.8 69.8 98 70.9 71.4 78.8 78.0 79.7 SOR 70.8 68.1 87 68.0 ASOR SOR EXP 77.7 73.8 68.2 76 71.3 78.4 79.7 77.9 77.7 71.5 65 66.2 70.4 74.6 75.2 74.3 72.6 65.4 54 65.5 73.4 72.8 73.5 71.8 66.7 43 67.0 73.3 71.0 71.8 70.0 32 66.9 70.5 71.7 66.5 21 68.0 68.6 63.8 1

A B C D E F G H J K L M N P Q R S

19

CLAD SURFACE TEMPERATURESA B C D E F G H J K L M N P Q R S

29 81.1 86.5 81.1 2928 80.0 85.2 90.5 82.4 2827 83.8 89.0 87.8 90.5 81.2 2726 81.3 88.9 93.4 92.2 91.1 80.6 2625 79.9 88.7 96.2 100.1 96.3 90.3 76.8 2524 88.2 97.4 99.3 100.3 96.5 88.3 2423 84.6 98.8 101.1 EXP SOR ASOR 85.5 2322 87.6 90.9 SOR 103.3 102.0 102.4 92.5 89.1 2221 88.8 99.5 104.3 103.8 104.0 100.4 86.4 2120 82.8 94.4 103.5 ASOR 101.0 103.6 93.2 85.5 2019 77.4 90.9 EXP 103.6 100.7 106.4 EXP 91.7 80.9 1918 87.9 99.6 100.6 99.8 98.0 104.3 101.0 86.9 1817 83.1 ASOR 101.1 100.2 100.5 99.5 104.6 95.9 80.5 1716 88.4 99.9 103.0 98.0 101.2 102.1 SOR 89.3 1615 79.1 94.0 101.5 99.4 CT 102.7 103.5 97.0 80.3 1514 88.9 SOR 101.8 98.6 101.2 103.2 101.3 86.9 1413 80.4 90.8 102.0 98.7 98.3 99.6 101.6 ASOR 78.7 1312 86.3 98.8 101.5 98.0 99.8 101.8 101.2 92.1 1211 78.2 88.5 EXP 105.0 101.9 106.1 EXP 90.6 77.2 1110 85.1 96.2 102.0 103.0 ASOR 104.4 101.2 85.2 109 91.9 101.8 103.1 101.8 103.1 100.4 87.5 98 80.8 90.5 102.0 101.4 103.8 SOR 89.5 84.9 87 84.3 ASOR SOR EXP 100.4 94.1 84.5 76 89.5 100.6 103.0 100.4 99.6 89.6 65 81.0 88.5 95.4 96.5 94.8 91.5 80.0 54 80.3 92.5 92.4 93.4 90.3 82.0 43 82.5 92.2 89.4 90.3 86.8 32 82.4 88.1 89.7 81.9 21 83.8 85.0 77.8 1

A B C D E F G H J K L M N P Q R S

20

FUEL SURFACE TEMPERATURESA B C D E F G H J K L M N P Q R S

29 84.1 89.7 84.1 2928 83.1 88.6 94.0 85.5 2827 86.9 92.6 91.7 94.2 84.3 2726 84.3 92.7 97.6 96.5 94.9 83.6 2625 82.8 92.4 100.7 104.9 100.9 94.2 79.6 2524 91.8 102.1 104.3 105.4 101.1 92.0 2423 87.9 103.3 106.4 EXP SOR ASOR 88.8 2322 91.2 95.0 SOR 109.1 107.7 107.6 96.7 92.7 2221 92.6 104.6 110.2 109.7 109.7 105.5 90.1 2120 86.0 99.0 109.2 ASOR 107.0 109.1 97.8 88.7 2019 80.1 95.1 EXP 109.6 106.9 112.3 EXP 95.8 83.6 1918 91.4 104.6 106.4 106.1 104.1 110.1 106.0 90.4 1817 85.9 ASOR 106.7 106.3 106.5 105.6 110.2 100.3 83.3 1716 92.1 105.1 108.9 104.7 107.3 108.0 SOR 92.9 1615 81.9 98.6 107.1 105.6 CT 108.8 109.1 101.6 83.2 1514 92.5 SOR 107.7 104.7 107.3 109.1 106.5 90.6 1413 83.2 95.2 107.6 104.8 104.3 105.5 107.1 ASOR 81.5 1312 89.8 103.8 107.3 104.1 106.1 107.6 106.2 95.6 1211 81.0 92.6 EXP 110.9 108.1 112.1 EXP 94.8 79.9 1110 88.3 100.8 107.5 108.9 ASOR 110.0 105.8 88.4 109 95.7 106.9 108.8 107.7 108.9 105.5 91.2 98 92.4 94.7 107.3 107.0 109.6 SOR 93.6 88.5 87 87.5 ASOR SOR EXP 105.6 98.6 87.8 76 93.1 105.3 108.1 105.5 104.3 93.2 65 83.8 92.3 100.0 101.2 99.2 95.2 82.8 54 83.3 96.3 96.6 97.6 94.1 85.0 43 85.6 95.9 93.3 93.9 89.9 32 85.5 91.5 93.1 85.0 21 86.8 88.2 80.8 1

A B C D E F G H J K L M N P Q R S

21

FUEL CENTER LINE TEMPERATURESA B C D E F G H J K L M N P Q R S

29 311.2 328.5 309.9 2928 316.8 346.8 350.4 317.0 2827 321.3 364.6 378.2 365.0 317.5 2726 312.4 372.7 405.7 405.1 373.4 310.6 2625 299.2 370.4 422.0 444.9 430.5 378.0 294.9 2524 357.3 435.9 461.0 467.3 436.5 361.9 2423 334.2 427.4 475.0 EXP SOR ASOR 333.9 2322 358.0 397.4 SOR 509.7 503.5 477.9 402.9 358.0 2221 368.4 465.2 514.8 522.9 508.6 465.6 365.2 2120 329.0 432.3 506.1 ASOR 519.5 497.2 431.0 329.8 2019 287.5 401.4 EXP 528.9 534.1 522.8 EXP 393.9 290.1 1918 355.4 459.6 511.8 539.2 527.9 513.9 463.8 347.8 1817 300.9 ASOR 494.9 529.3 525.5 528.2 502.5 418.3 298.0 1716 365.0 474.3 519.6 526.2 527.9 519.4 SOR 360.1 1615 300.8 429.7 501.6 530.7 CT 532.8 502.9 431.7 301.7 1514 359.9 SOR 519.2 526.1 528.3 519.7 475.2 363.6 1413 298.0 414.8 500.8 527.6 523.5 528.9 495.1 ASOR 297.1 1312 347.5 462.3 512.1 528.0 539.2 512.5 460.6 358.6 1211 288.0 391.7 EXP 521.9 535.0 530.5 EXP 401.0 287.3 1110 329.5 433.4 496.1 520.9 ASOR 506.6 437.3 330.6 109 369.7 466.7 508.0 521.5 514.0 465.7 367.0 98 358.1 401.5 477.8 503.1 509.9 SOR 396.0 355.4 87 333.2 ASOR SOR EXP 474.3 423.5 333.7 76 363.1 439.8 469.3 461.9 437.4 358.1 65 298.8 379.7 429.9 442.1 421.1 372.5 298.8 54 310.8 374.7 405.2 405.7 373.7 312.6 43 318.9 366.4 379.5 365.5 323.4 32 317.1 348.4 350.4 318.2 21 312.1 327.2 308.4 1

A B C D E F G H J K L M N P Q R S

22

Axial Temperature Distribution in the Hottest Channel at 40 MW

Critical Moderator Height :290 cm Coolant Flow Rate: 30 Igpm

Active Peak Temperatures, (oC) Saturation

Temperature

Local Fuel Height Fuel Fuel Clad Coolant Of Water Pressure

(cm) Centreline Surface Surface Exit ( oC) (kPa) 0 150.50 87.24 86.43 82.34 137.5 335.86

20.7 239.77 93.43 91.48 81.62 139.1 352.13

34.5 320.12 99.24 96.19 80.75 140.2 362.78

48.3 391.15 104.36 100.28 79.51 141.2 373.22 62.1 452.54 108.72 103.70 77.92 142.2 383.48

75.9 504.31 112.26 106.40 76.03 143.1 393.55

89.7 546.43 114.92 108.35 73.86 144.0 403.45

103.5 578.95 116.64 109.49 71.47 144.9 413.20 117.3 602.01 117.39 109.81 68.91 145.7 422.82

131.1 615.67 117.13 109.28 66.22 146.3 432.33

144.9 620.00 115.84 107.90 63.47 147.1 441.77

158.8 615.01 113.48 105.61 60.71 147.8 451.14 172.6 600.52 110.04 102.41 58.00 148.6 460.49

186.4 576.58 105.56 98.32 55.40 149.3 469.82

200.2 542.96 100.08 93.39 52.96 150.1 479.16

214.0 499.56 93.65 87.65 50.73 150.8 488.55 227.8 446.30 86.40 81.21 48.77 151.5 497.99

241.6 383.02 78.43 74.16 47.11 152.2 507.51

255.4 309.85 69.90 66.66 45.79 152.9 517.13

269.2 226.89 61.01 58.85 44.83 153.6 526.86 290.0 132.92 51.59 50.58 44.00 154.6 541.63

23

Axial Temperature Distribution in the Hottest Channel at 48 MW

  Peak Temperatures, ( ºC)

Active Fuel Height (cm) Fuel Center Fuel Surface Clad Surface Coolant Exit

Saturation Temperature of

Water ( ºC)

292 127.8 53.8 52.9 47 148.9

271 221.1 63 60.9 47.8 147.7

257 304.6 71.8 68.6 48.7 146.9

243 378.4 80.3 76.1 50 146.2

229 442.2 88.3 83.1 51.7 145.6 216 496.2 94.9 89 53.7 144.8 202 540.4 101.4 94.7 55.9 144.0 188 574.8 107 99.7 58.4 143.2 174 599.3 111.6 103.9 61 142.3 160 614.4 115.1 107.2 63.7 141.4 146 619.8 117.5 109.5 66.5 140.5 132 615.9 119 111 69.3 139.6 118 602.4 119.3 111.7 72 138.7 104 579.5 118.6 111.4 74.6 137.7 90 546.8 116.9 110.3 77.1 136.8 76 504.6 114.3 108.4 79.3 135.7 63 452.5 110.8 105.7 81.2 134.6 47 391.1 106.4 102.3 82.8 133.4 35 319.6 101.3 98.2 84.1 132.2 21 239 95.5 93.5 84.9 131.0 0 148.8 89.2 88.4 85.6 129.0

24

Axial Temperature Distribution (Hottest and Average Channel of KCP-III)

0

50

100

150

200

250

300

40 50 60 70 80 90 100 110 120 130 140

Temperature ( ²C)

Fuel Surface (hot) Fuel Surface (avg) Clad Surface (hot)

Clad Surface (avg) Coolant Exit(hot) Coolant Exit (avg)

25

Criteria for Safe Operating Power LevelThe safe operating power level as a function of moderator height has been assessed based on the following criteria which is to be satisfied under all operating conditions i.e. overpower limiting set point of 110% and low flow set point of 90%.

• The maximum temperatures at fuel centerline, fuel‑clad and clad‑coolant interfaces should remain within the following prescribed limits:

1. The fuel center line temperature should not exceed 668 oC in order to avoid the phase change;

2. The fuel surface temperature should not exceed 200 oC to prevent formation of uranium‑aluminium alloy;

3. The clad surface temperature should not exceed 130 oC to preclude corrosion of aluminium by coolant water.

4. Nucleate boiling should not commence at any point in the core

5. The core should have sufficient safety margins against onset of nucleate boiling and departure from nucleate boiling.

27

Boiling,Sub cooled,Bulk boiling,Saturation Temp.

Boiling:Process in which the vapours formed with in the liquid when vapour pressure is equal to the atmospheric pressure.When temperature of fluid approached saturation temp. boiling starts.

Saturation Temp:The temp. at which boiling starts.

Sub cooled Nucleate Boiling:When heating surface temp. is greater that Tsat. But bulk liquid temperature is below Tsat.(small bubbles form and collapse before reaching surface temperature.

Bulk Boiling:When all the liquid is at Tsat(100 oC).During phase change no increase in Temperature.

Latent Heat of Vaporization:Heat supplied (at Tsat) to change the phase is called “latent heat of vaporization.

28

Boiling Regimes

aa

c

b

ed

f

Tc – Tf (Clad Surface – Coolant) 0C

Su

rfac

e h

eat

flu

x (w

/cm

2 )

o

29

Boiling Regimes (Contd)• (0 to a) Natural / Forced convection heat transfer b/w

clad and coolant.• (a to b) Via Natural/Forced Convection,agitation(bubble

formation),subcooled nucleate boiling at ‘b’(ONB starts) bubble forms and collapse at clad surface before reaching bulk liquid.(local/sub cooled boiling)

• (b to c) number of bubble formation increases,turbulent increases and surface heat flux increases. (bulk/volume boiling)

• At point “C” DNB starts.• (c to d) film boiling reduces the heat transfer(partial

film boiling).• (d to e) full film formation which insulate heating

surface.• (e to f) heat transfer is mainly via radiation,super

heated steam. Back

30

MARGIN to ONB and DNB

BACK

Moderator Height (cm)

Power Level (MW)

Peak Temperatures in Hot Channel, ( oC ) (Average Channel)

Power, (MW) (Safety Margin)

Fuel Center Fuel Surface Clad Surface Coolant Exit ONB DNB

217 30.05 619.5 (415.0)

113.5 (91.8)

105.6 (87.2)

72.8 (64.3)

61.00 (2.03)

94.66 (3.15)

220 30.41 618.8 (409.9)

113.5 (85.8)

105.6 (81.2)

73.2 (60.9)

61.79 (2.03)

95.80 (3.15)

230 31.84 619.8 (410.6)

114.1 (86.2)

106.3 (81.7)

74.6 (61.8)

64.63 (2.03)

98.95 (3.11)

240 33.20 619.8 (410.6)

114.6 (86.5)

106.8 (81.9)

75.9 (62.5)

67.40 (2.03)

104.5 (3.15)

250 34.55 619.6 (410.5)

115.1 (86.8)

107.4 (82.4)

77.1 (63.3)

70.14 (2.03)

105.2 (3.05)

260 35.90 619.6 (410.5)

115.6 (87.2)

170.8 (82.8)

78.4 (64.0)

72.63 (2.02)

107.4 (3.00)

270 37.27 619.8 (410.7)

116.2 (87.6)

108.6 (83.2)

79.7 (64.8)

75.16 (2.02)

111.8 (3.00)

280 38.63 619.7 (410.7)

116.7 (87.9)

109.2 (83.6)

81.1 (65.6)

77.40 (2.00)

116.0 (3.00)

290 39.97 619.6 (410.7)

117.1 (88.4)

109.8 (83.9)

82.3 (66.3)

79.90 (2.00)

120.0 (3.00)

300 41.31* 619.5 (410.6)

117.6 (88.7)

110.4 (84.3)

83.6 (67.1)

83.03 (2.01)

123.0 (3.00)

31

Accident and Transient Analysis• Accident/ Transient Analysis using Computer

Code “PARET” for different PIEs: Uncontrolled Moderator Pump upWithdrawal of a Shutoff rod Removal of an In Pile ExperimentAccident Drop of an Enriched Fuel RodsRamp Reactivity InsertionStep Reactivity Insertions