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Note and discuss the trend in xenon with time. (b) Use the concentrations of I-135 and Xe-135 calculated for long times after startup in part (a) as initial concentrations, and set the flux equal to zero to simulate a sudden shutdown of the reactor. (a) Run the program and study the trends in the concentrations and the reactivity ρ versus time for a startup. The program XETR (Xenon Transient) solves differential equations for the content of iodine-135 and xenon-135. The amount of xenon in a reactor varies with time, especially when large changes in neutron flux occur, as at startup or shutdown. Let all other factors be the same as in (a). Pu has an effective neutron lifetime of only 0.04 s compared with the value for U of 0.083 s. (b) Examine the effect of changing the reactor fuel from uranium to plutonium. (a) Run the program RTF to see how the power, temperature, and reactivity vary with time for the sample problem using uranium. There is a negative temperature coefficient of reactivity, and power is extracted according to a temperature difference. RTF solves simple differential equations that express the rates of change with time of power and temperature. The effect of temperature feedback on the time response of a reactor can be estimated by use of the program RTF (Reactor Transient with Feedback). Try various input reactivity values-positive, negative, and zero small and large with respect to β = 0.0065. Six emitters are used, and feedback is neglected. The program KINETICS solves the time-dependent equations for neutrons and delayed emitters, yielding the neutron population as a function of time. (b) Change the differential equation solver from “ode45” to “ode15s,” and retry the reactivity value of 0.0001. (a) Plot the time responses of neutron population for various reactivity values such as 0.0001, 0.0005, and 0.001. To solve one-group point kinetics equations, the program OGRE (One Group Reactor Kinetics) is used. Show that the burnup is given by the formulas (b) Since most nuclear power plants are base loaded, the power is constant and the product of the flux and fissile atom concentration is likewise. (a) Show that a megawatt per tonne is the same as a watt per gram. What is the final enrichment of the fuel? (b) If instead one-third of the energy came from plutonium, what would the final U-235 enrichment be? 20.14 It operates for a year at 75% of its rated 3000-MWt capacity. (c) Estimate the rod integral worth when the tip is 16 inches up from the bottom. (b) Use simple numerical integration to graph the integral worth versus z. (a) Plot the differential worth against average position z ¯ i = z i + 1 + z i / 2. (a) Taking account of Xe-135 production, absorption, and decay, show that the balance equation is Estimate the contribution of this effect on the power coefficient for the reactor. If the temperature coefficient is –9 × 10 –5/☌, how high will the temperature of the system go above room temperature before the positive reactivity is canceled out? 20.6Ī reactivity of –0.0025 caused by the Doppler effect results when the thermal power goes from 2500 MW to 2800 MW. (Thanks are due Professor Robert Busch for this exercise and its answers.) 20.5ĭuring a critical experiment in which fuel is initially loaded into a reactor, a fuel element of reactivity worth 0.0036 is suddenly dropped into a core that is already critical. Calculate its value in two different ways: (a) with the ratio β/ ℓ, called the Rossi-α, with a value of 1.74 × 10 5/s and β of 0.0068 (b) with a rough formula ℓ = l/( vΣ a) with an average energy of 500 keV neutrons.
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Measurements of the fast neutron cycle time ℓ were made on EBR-I, the first reactor to produce electricity. Noting that this is much less than β, calculate the time required to go to a power of 300 MWe, neglecting any temperature feedback. Control rods are removed to give a reactivity of 0.0005. (c) What is the period for a reactor with prompt neutron lifetime 5 × 10 –6 s if the reactivity is 0.013? (d) What is the reactor period if instead the reactivity is 0.0013? 20.3Ī reactor is operating at a power level of 250 MWe. (a) If the total number of neutrons from fission by thermal neutrons absorbed in U-235 is 2.42, how many are delayed and how many are prompt? (b) A reactor is said to be prompt critical if it has a positive reactivity of β or more. Using Table 20.1, verify that the total delayed neutron fraction β is 0.0065 and that the weighted average half-life is approximately 8.8 s.