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Unformatted text preview: ENU 4134 – Nuclear Heat Generation D. Schubring October 29, 2010 Learning Objectives 3-a Identify locations where heat from nuclear fission is deposited in a reactor 3-b Compute decay heat and discuss significance of this energy for post-accident/incident safety analysis Chapter 3 Topics The following topics are included in the scope of the course: Sections 3-1 and 3-2 (introductory material), with particular attention to Table 3-1 Section 3-3-B: volumetric heat generation, pin power, (heat flux), and core power Section 3-8 (Shutdown Heat Generation – decay heat) Material from other sections is included only if specifically in these notes. Heat Source in a Reactor Heat generation from each fission: 3.2 × 10−11 J (200 MeV). Approximately 190 MeV of this is deposited in the reactor, primarily in the fuel, with the rest escaping as neutrinos. (n, γ ) reactions also generate some energy; approximately 7 MeV for each fission in an LWR. Much of this energy is also deposited in the fuel. Table 3-1 T&K Typical TH Model It is typically assumed that all of the heat is deposited in the fuel and that there is about 200 MeV net (heat) energy per fission. Is this a conservative estimate (compare to actual situation from previous slide)... ... with respect to peak centerline temperatures in fuel? ... with respect to temperature (or radiation damage) in structures? ... with respect to CHF? Result: This assumption is made primarily for TH calculations such as single-channel analysis, but not necessarily for all physics analyses. Reactor Heat Flux Profiles For the entire reactor, assuming a cylindrical 1-zone core, the neutron flux (and therefore heat generation profile, assuming homogeneous pin cells) looks a lot like: πz Le r Re q (r , z ) = qmax cos J0 2.4048 (1) Le and Re are extrapolated dimensions, typically only slightly larger than L or R . J0 is the zeroth-order Bessel function of the first kind. Note that the center of the reactor is taken as (0, 0): the location where z = 0 is not at the bottom of the core. Reactor Heat Flux Profiles (2) Within each fuel pin (fuel only, not gap or cladding), the power profile will look like: q (r , z ) = q0 cos q (r , z ) ≈ q0 cos πz Le πz Le f (r ) 1+A r Rpin (2) (3) ... where A is a factor that indicates how much the heat generation varies within a pin. Is A positive or negative? When is modeling A = 0 conservative? Pin Power, Linear Heat Generation, and Heat Flux Pin power: R L 2 q = 2π 0 q (r , z ) dzrdr (4) −L 2 Linear heat rating: R q (z ) = 2 π 0 q (r , z ) rdr (5) Many models for gap conductance require that parameter; it is also frequently used in industry. Heat flux: q (r > Rfuel ) = q 2π r (6) This is the parameter that affects cladding-to-coolant heat transfer. Shutdown Heat Generation – Decay Heat Decay heat from fission after shutdown: q (t ) = q (tshutdown ) 0.0625e −0.0124t + 0.9375e −960t (7) Second term: negligible after t > 0.01 s. First term: period of 80 seconds. Fission decay heat negligible for most accidents. (Why – what property of the reactor core allows for this?) Decay heat from fission product (and other radioactive) decay: P P0 − = 0.066 ts 0.2 − (ts + τS )−0.2 (8) ts : time since shutdown. τS : time of operation. ...
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