Unformatted text preview: ENU 4134 – Nuclear Heat Generation
D. Schubring October 29, 2010 Learning Objectives 3a Identify locations where heat from nuclear ﬁssion is deposited in a reactor 3b Compute decay heat and discuss signiﬁcance of this energy for postaccident/incident safety analysis Chapter 3 Topics The following topics are included in the scope of the course: Sections 31 and 32 (introductory material), with particular attention to Table 31 Section 33B: volumetric heat generation, pin power, (heat ﬂux), and core power Section 38 (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 31 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 singlechannel analysis, but not necessarily for all physics analyses. Reactor Heat Flux Proﬁles For the entire reactor, assuming a cylindrical 1zone 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 zerothorder 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 claddingtocoolant 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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 Spring '11
 Schubring
 Thermodynamics, Electron, Nuclear Fission, Heat, Nuclear technology

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