Thermodynamics, Heat Transfer, And Fluid Flow. V.2. Heat Transfer (776131), страница 10
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Initially a significant temperature difference existsacross the gap to cause heat transfer to take place by convection through the helium gas. As thesize of the gap is reduced, a smaller temperature difference can maintain the same heat flux.When the fuel pellets and clad come in contact, heat transfer by conduction replaces convectionand the temperature difference between the fuel surface and clad decreases even more. Due tothe processes of pellet swell and clad creep, the fuel temperatures of some reactors decreaseslightly over time while the heat flux from the fuel and therefore the power of the reactor remainconstant.Not all changes that occur to the fuel during reactor operation work to enhance heat transfer.If the chemistry of the coolant is not carefully controlled within appropriate limits, chemicalreactions can take place on the surface of the clad, resulting in the formation of a layer ofcorrosion products or crud between the metal of the clad and the coolant.
Typically, this layerwill have a lower thermal conductivity than that of the clad material, so it will act as aninsulating blanket, reducing heat transfer.HT-02Page 50Rev. 0Heat TransferHEAT GENERATIONIf this corrosion layer is allowed to form, a larger temperature difference will be requiredbetween the coolant and fuel to maintain the same heat flux. Therefore, operation at the samepower level will cause higher fuel temperatures after the buildup of corrosion products and crud.SummaryThe important information in this chapter is summarized below:Heat Generation Summary•The power generation process in a nuclear core is directly proportional to thefission rate of the fuel and the thermal neutron flux present.•The thermal power produced by a reactor is directly related to the mass flow rateof the reactor coolant and the temperature difference across the core.•The nuclear enthalpy rise hot channel factor is the ratio of the total kW heatgeneration along a fuel rod with the highest total kW, to the total kW of theaverage fuel rod.•The average linear power density in the core is the total thermal power dividedby the active length of the fuel rods.•The nuclear heat flux hot channel factor is the ratio of the maximum heat fluxexpected at any area to the average heat flux for the core.•The total heat output of a reactor core is called the heat generation rate.•The heat generation rate divided by the volume of fuel will give the averagevolumetric thermal source strength.Rev.
0Page 51HT-02DECAY HEATHeat TransferDECAY HEATDecay heat production is a particular problem associated with nuclearreactors. Even though the reactor is shut down, heat is produced fromthe decay of fission fragments. Limits for each particular reactor areestablished to prevent damage to fuel assemblies due to decay heat.EO 2.7DEFINE the term decay heat.EO 2.8Given the operating conditions of a reactor core and thenecessary formulas, CALCULATE the core decay heatgeneration.EO 2.9DESCRIBE two categories of methods for removingdecay heat from a reactor core.Reactor Decay Heat ProductionA problem peculiar to power generation by nuclear reactors is that of decay heat.
In fossil fuelfacilities, once the combustion process is halted, there is no further heat generation, and only arelatively small amount of thermal energy is stored in the high temperature of plant components.In a nuclear facility, the fission of heavy atoms such as isotopes of uranium and plutonium resultsin the formation of highly radioactive fission products. These fission products radioactivelydecay at a rate determined by the amount and type of radioactive nuclides present. Someradioactive atoms will decay while the reactor is operating and the energy released by their decaywill be removed from the core along with the heat produced by the fission process.
Allradioactive materials that remain in the reactor at the time it is shut down and the fission processhalted will continue to decay and release energy. This release of energy by the decay of fissionproducts is called decay heat.The amount of radioactive materials present in the reactor at the time of shutdown is dependenton the power levels at which the reactor operated and the amount of time spent at those powerlevels.
The amount of decay heat is very significant. Typically, the amount of decay heat thatwill be present in the reactor immediately following shutdown will be roughly 7% of the powerlevel that the reactor operated at prior to shutdown. A reactor operating at 1000 MW willproduce 70 MW of decay heat immediately after a shutdown. The amount of decay heatproduced in the reactor will decrease as more and more of the radioactive material decays tosome stable form. Decay heat may decrease to about 2% of the pre-shutdown power level withinthe first hour after shutdown and to 1% within the first day. Decay heat will continue todecrease after the first day, but it will decrease at a much slower rate. Decay heat will besignificant weeks and even months after the reactor is shutdown.HT-02Page 52Rev.
0Heat TransferDECAY HEATThe design of the reactor must allow for the removal of this decay heat from the core by somemeans. If adequate heat removal is not available, decay heat will increase the temperatures inthe core to the point that fuel melting and core damage will occur.
Fuel that has been removedfrom the reactor will also require some method of removing decay heat if the fuel has beenexposed to a significant neutron flux. Each reactor facility will have its own method of removingdecay heat from both the reactor core and also any irradiated fuel removed from the core.Calculation of Decay HeatThe amount of decay heat being generated in a fuel assembly at any time after shutdown can becalculated in two ways. The first way is to calculate the amount of fission products present atthe time of shutdown.
This is a fairly detailed process and is dependent upon power history.For a given type of fuel, the concentrations, decay energies, and half lives of fission products areknown. By starting from a known value, based on power history at shutdown, the decay heatgeneration rate can be calculated for any time after shutdown.An exact solution must take into account the fact that there are hundreds of differentradionuclides present in the core, each with its own concentration and decay half-life. It ispossible to make a rough approximation by using a single half-life that represents the overalldecay of the core over a certain period of time.
An equation that uses this approximation isEquation 2-16.timelife1Q̇o half2Q̇(2-16)where:Q̇= decay heat generation rate at some time after shutdownQ̇o= initial decay heat immediately after shutdowntimehalf-lifeRev. 0= amount of time since shutdown= overall decay half-life of the corePage 53HT-02DECAY HEATHeat TransferExample:A 250 MW reactor has an unexpected shutdown. From data supplied by the vendor, weknow that decay heat at time of shutdown will be 7% of the effective power at time ofshutdown and will decrease with a 1 hr half life.
Effective power at time of shutdownwas calculated to be 120 MW. How much heat removal capability (in units of Btu/hr)will be required 12 hours after shutdown?Solution:(a)First determine the decay heat immediately following shutdown.(120 MW)(.07) = 8.4 MW decay heat at shutdown(b)Then use Equation 2-15 to determine the decay heat 12 hours later.Q̇timelife1Q̇o half218.4 MW 22.05 x 107000312 hr1 hr 3.413 x 106 Btu/hr MW 1 MWBtuhrThe second method is much simpler to use, but is not useful for forecasting heat loads in thefuture.
To calculate the decay heat load at a given point after shutdown, secure any heat removalcomponents from the primary system or spent fuel pool and plot the heatup rate. If the mass ofthe coolant and the specific heat of the coolant are known, the heat generation rate can beaccurately calculated.Q̇HT-02m cp∆T∆t(2-17)Page 54Rev. 0Heat TransferDECAY HEATwhere:Q̇= decay heat (Btu/hr)m= mass of coolant (lbm)cp= specific heat capacity of coolant (Btu/lbm-oF)∆T = temperature change of coolant (oF)∆t= time over which heatup takes place (hr)Example:Three days after a planned reactor shutdown, it is desired to perform maintenance on oneof two primary heat exchangers. Each heat exchanger is rated at 12,000 Btu/hr.
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