Journal of Applied Mathematics and Physics, 2013, 1, 62-64
Published Online November 2013 (
Open Access JAMP
Stress Analysis for Reactor Coolant Pump Nozzle of
Nuclear Reactor Pressure Vessel
Lijing Wen, Chao Guo*, Tieping Li, Chunming Zhang
Nuclear and Radiation Safety Center, MEP, Beijing, China
Email:, *
Received September 2013
Integrated reactor structura l design makes the pressure vesse l itself and loads more complicated, so stress concentration
makes strength failure easier at reactor coolant pump nozzle. The general purpose finite element program ANSYS/
WORKBENCH was used for 3D stress and fatigue analysis and the results of the evaluation are based on RCC-M crite-
ria. The integrated reactor structural design is evaluated to demonstrate with applicable criteria and ANSYS/WORK-
BENCH has better operability than ANSYS APDL on stress analysis of reactor pressure vessel.
Keywords: Numerical Simulation; Reactor Pressure Vessel; Stress Analysis
1. Introduction
Integrated reactor is new generation pressurized water
reactor developed by China [1]. Reactor structure is
highly integrated, for example, once through steam ge-
nerator placed in a pressure vessel; reactor coolant pump
is placed on the pressure vessel nozzles; press ure vessel
fixed and supported the main pump, control rod drive
mechanism and the top of the h eap struc ture. This struc-
tural design can simplify a loop system and eliminate
LBLOCA, but makes the pressure vessel itself and load s
more complicated. So the stress analysis is necessary to
ensure the effectiveness and safety of the design and the
integrity of th e reactor pressure vessel.
Most domestic researchers [2-5] using traditional
ANSYS APDL for stress analysis and evaluation of reac-
tor pressure vessel calculation. With the development of
computing software, ANSYS, Inc. has developed AN-
SYS/WORKBENCH software and pre-processing, cal-
culation and post-processing become more convenient
[6]. ANSYS/WORKBENCH is used in this paper.
2. Calculation Model
According to the structure features of the reactor pressure
vessel, the reactor pressure vessel cylinder and outlet
nozzle is are simplified:
1) According to RCC-M, surfacing layer is not exposed
to any structural strength in criteria O, criteria C and cri-
teria D. So surfacing layer is ignored in numerical model.
2) Bolt holes on reactor coolant pump nozzle and the
effect of in-line casing and annular flow distribution
plate are ignored.
3) To reduce edge effects influence on the reactor
coolant pump nozzle, pressure vessel cylinder must be
long enough in calculation model. According to RCC-M,
the length in pressure vessel cylinder axial direction from
the center line of the reactor coolant pump nozzle is at a
length of
2.5 Rt
at least, whe r e R = (R1 + R2)/2. R1
and R2 are the inside and outside radius of the pressure
vessel cylinder, and t is the thickness of the pressure
vessel cylinder.
Three-dimensional finite element model of pressure
vessel cylinder and outlet nozzle is built by ANSYS/
WORKBENCH program as shown in the Figure 1. 1 /4
model of pressure vessel cylinder and complete model of
pressure vessel nozzle are built by hexahedral meshes
with the size of 40 mm.
Reactor pressure vessel design temperature is 343˚C.
Pressure vessels and outlet nozzle materials are 16MND5
forgings. According to RCC-M Parameter Manual, 16
MND5 material parameters at 350˚C are shown in Table 1.
3. Evaluation Conditions, Loads and
Boundary Conditions
According to RCC-M, stress strength must conform to
criteria O in the first operating condition when pressure
vessel nozzle is analyzed. Self-weight, internal pressure
and earthquake load are considered and each load is
composed of six components. Force and moment are
*Corresponding a uthor.
Open Access JAMP
Figure 1. Reac tor pressure vessel simulation mode.
Table 1. Material parameters of 16MND5.
kg·m3 E
GPa k
W·m1·K1 α
˚C 1 Sm
MPa Sy
MPa Su
7800 180 38.7 1.34 × 105 184 345 552
transmitted to the cylinder and nozzle ends through ex-
tension of pressure vessel cylinder.
Fixed boundary condition A is set in the bottom of the
vessel; symmetry boundary condition B is set on the sec-
tion of symmet r i c a l structur e of the reactor pressure ves-
sel; hydrostatic pressure C and F are set on the upper
section of reactor pressure vessel and reactor coolant
pump nozzle; the mechanical loads D and E caused by
self-weight and e ar thquake loa d are set on the upper sec-
tion of the reactor coolant pump nozzle; the internal
pressure G is set on the inner surface of all parts as
shown in the Figure 2.
4. Results and Evaluation
The calculated stress intensity contours shown in Figure
3. The maximum stress is in the junction of the cylinder
nozzle. According to RCC-M, stress is divided into pri-
mary membrane stress, secondary membrane stress and
bending stress to be evaluated.
A typical evaluation section usually is the structural
discontinuous section where stress intensity is high due
to mechanical loads. Stress is analyzed by stress lineari-
zation in ANSYS/WORKBENCH. Firstly, the high stress
intensity area is searched on the stress intensity contours,
Figure 2. Load s an d bou ndary condi t i on s .
Figure 3. Stress intensity contours.
and then the two nodes which can run through the thick-
ness of pressure vessel cylinder and nozzle are selected
in the structure discontinuous area. Result data can be
mapped to the path formed by connecting two nodes, and
then the numerical calculation results can be analyzed by
the selected path. Based on the above principles, twelve
paths are set in the structure continuous areas, and stress
concentration areas and structural discontinuous areas are
shown in Figur e 4.
Table 2 sho ws the results of stress analysis on evalua-
tion section. The bending stress of the whole disconti-
nuous area on the path 2, 3, 5, 8, 10 and 11 are secondary
stress, and they are not evaluated in criteria O.
According to RCC-M, primary stress must conform to
criteria O in the first operating condition. The criteria O
requires that Pm Sm, PL 1.5Sm, and Pm (PL) + Pb
1.5Sm. Pm is general primary membrane stress, PL is pri-
mary local membrane stress, Pb is primary bending stress
Open Access JAMP
Figure 4. Evaluation section and paths.
Table 2. Stress linearization results.
Path Pm PL Pm + Pb
1 149.5 - 167.0
2 - 168.5 *
3 - 199.5 *
4 34.3 - 47.6
5 - 33.3 *
6 40.3 - 49.8
7 38.6 - 49.5
8 - 8.1 *
9 20.7 - 38.3
10 - 199.7 *
11 - 167.2 *
12 127.4 - 137.3
and Sm is Allowable Stress.
Path 1, 4, 6, 7, 9 and 12 are in the structure continuous
areas. The membrane stre ss there is general primary
membrane stress and the maximum “Pm(149.5 MPa)is
lower than “Sm(184 MPa)”. The bending stres s there is
primary bending stress and the maximum “Pm + Pb
(167.0 MP a)is lowe r than1.5Sm (276 MPa)”.
Path 2, 3, 5, 8, 10 and 11 are in the structural discon-
tinuous areas. The membrane stress th ere is primary local
membrane stress and the maximum “PL(199.7 MPa)is
lower than1.5Sm (276 MPa) ”. The bending stress there
is secondary stress and it is not evaluated in criteria O.
As can be seen from the above, the stru ctu re designed
can satisfy the intensity requirement in the criteria O of
6. Conclusions
1) The str ess of reactor coolant pump nozzle of nuclear
reactor pressure vessel is analyzed and evaluated by
ANSYS/WORKBENCH. The results show that the
structure designed c an satisfy the intensity requirement in
2) ANSYS/WORKBENCH is more convenient than
the traditional ANSYS APDL, whi ch can be widely used
in the geometry modeling, loading and post processing.
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