Unformatted text preview: ENU 4134 – Nuclear Heat Generation
D. Schubring Fall 2011 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
... with respect to peak centerline temperatures in fuel?
... with respect to temperature (or radiation damage) in
... 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: q (r , z ) = qmax cos πz
Le J0 2.4048 r
Re (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 f (r )
Rpin (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
R q = 2π
2 q (r , z ) dzrdr (4) −L
2 Linear heat rating:
R q (z ) = 2 π q (r , z ) rdr (5) 0 Many models for gap conductance require that parameter; it is also
frequently used in industry.
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 ﬁssions occuring 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. Decay heat from post-shutdown ﬁssions negligible for
most accidents. (Why – what property of the reactor core allows
Decay heat from ﬁssion products:
= 0.066 ts 0.2 − (ts + τS )−0.2 ts : time since shutdown. τS : time of operation. (8) ...
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