1.Reactor Criticality(a)Starting from the ‘reactor equation’, ,but otherwise deriving all results that you use, show that, if the core and reflector diffusion coefficients are equal, the reduction in the critical radius of a spherical reactor when an infinite reflector is added is approximately one diffusion length.
(b)Determine the critical core radius for such a reflected reactorof the composition and other characteristics in the table below.SpeciesNumber density / m^3C8.00E+28Fe7.50E+27O2.67E+28U-2356.10E+25U-2386.59E+27Diffusion coefficient0.08mResonance escape probability0.94Fast fission factor1.012.Reactor Kinetics
(a)Derive equations describing the time dependent behaviour of a reactor in the presence of multiple groups of delayed neutrons
(b)Show how the various initial values needed are determined.
(c)Sucha reactor, when critical,is subject to a step reactivity increase of about $1. Sketch and explain the subsequent variation of reactor power.
3.Fluid flow and heat transfer
(a)Explain,with reference to aPWR fuel geometry how flowin reactor core flow passages can be analysed using correlations obtained from measurements in circular pipes.(50 words maximum.)
(b)Explain the meaning and physical significance of the Reynolds number. (50 words maximum.)(c)What is meant by ‘heat transfer coefficient’, and how might you obtain a value to use in analysing a PWR core under normal conditions?(50 words maximum.)∇2+B2()φ=0
(d)Explain the meaning and physical significance of the Nusselt number.(50 words maximum.)(e)Discuss from a thermal point of view the issues associated with ‘gap’ heat transfer, between the outside of a fuel pellet and the inside of the cladding. (100 words maximum.)
4.Core Thermal Hydraulics Data for a novel PWR-type Small Modular Reactor (SMR) are listed below. Neglect control rodsand take coolant physical properties at 300C saturated. Assume the flux distribution corresponding to a simple bare cylindrical core. As required, useappropriate empirical correlations from the module.
(a)Determine the Reynolds number of the flow in the core.
(b)Determine the Darcy-Weisbach (Moody-chart) friction factor for the flow in the core.
(c)Calculate the wall shear stress, and the pressure drop between core inlet and outletof the core.
(d)Determine the pumping power required for the core.
(e)What fraction of the electricity the plant generates is required to pump the coolant through the core?
(f)What will be the heat transfer coefficient between the fuel rods and the coolant?
(g)Determine the cladding external temperature at the axial mid-planefor an average rod. Will this be the highest external cladding temperaturefor that rod? Explain your answer.Fuel rod outside diametermm8.5Rod pitch (square lattice)mm13.0Core coolant mass flow ratekg/s12,000Number of fuel rods-26,000Fuel rod lengthm3.4Axial peak linear rating (average over all rods)kW/m25.5Pump efficiency-0.88Plant cycle efficiency-0.36