Multi-Body Dynamic Analysis Computer Program - PowerPoint Presentation

Slide1

Multi-Body Dynamic Analysis Computer Program

For the Prismatic Core of a HTGR

2015/8/11

Ji-Ho Kang

Korea Atomic Energy Research Institute

SMiRT-23 2015

1

Introduction

Korean NuH2 (Nuclear Hydrogen) project Development of an efficient hydrogen production systemDevelopment of

a HTGR (High Temperature Gas-Cooled Reactor) as a high temperature source for the hydrogen production systemPrismatic core of HTGRKorean HTGR design uses a prismatic-type core with hexagonal graphite blocks.In the active ring, graphite blocks contain fuels.In the inner and outer ring of the core, graphite blocks are used as neutron reflectors.-2-

Array of Graphite Blocks

composing Reactor CoreKorean HTGR

Multi-body Dynamic Analysis of Prismatic CoreGraphite blocks are stacked inside of a core barrel without mechanical joints.

Upper and lower blocks are connected with dowel pin/socket joints resulting in rigid-body motions of blocks.Small gaps exist between adjacent block columns for the replacement of the blocks and the lateral displacements of block columns can accumulate at the side boundaries of the core.The rigid-body motions and accumulation of lateral displacements may cause large impact forces.

To assess structural integrity of the prismatic core, a precise multi-body dynamic analysis of the graphite blocks is needed.In this study, a computer program is being developed to solve the equations of motion of 2-D block models.-3-

Governing Equations of MotionThe original form of governing equations, which is based on Kelvin-Voigt impact model, was introduced by Iyouku et al. (1992).

Improvement in the force diagram and the equationsCorrection of force terms of horizontally misaligned blocksCorrection of dowel force directionCorrection of friction acting pointsPenalty friction

model with allowable viscous slipThe System of ODEs for all blocks is solved by ODEPACK library (FORTRAN library for initial value problems of ODE systems) or Runge-Kutta Method.-4-

Computer ProgrammingA shell program was developed using Python 2.7.

SciPy Module was included to implement ODEPACK (FORTRAN library for initial value problems of ordinary equation systems).User can select a solver from ODEPACK or in-house code of Runge-Kutta Fehlberg method.

-5-Python Shell Program using

SciPy Module(including ODEPACK)

Schematic Flowchart

Modularization of Force TermsEach force term is programmed as one module.Exception: Friction terms (can be calculated only after the vertical reaction forces are determined)

The program is not completed yet, but the each module can be tested and verified independently due to modularization.Currently, the lateral, vertical and dowel modules with relevant frictions were completed and verified.-

6-

Lateral Impact Modes7

Lateral Forces – Formulation(only upper left corner is shown)

8

Lateral Forces - Verifications-9

-Case 3

Hand calculationComputer calculation

Case 1b

Hand calculation

Computer calculation

Vertical Forces - Formulation-10

-

Vertical Forces - Verifications-11

-Case 5

Case 4aHand calculation

Computer calculation

Hand calculation

Computer calculation

Dowel Forces - Formulation-12

-

Dowel Forces - Verifications-13

-Case 4

Case 1cHand calculation

Computer calculationHand calculation

Computer calculation

Friction Forces – Penalty Friction ModelPenalty Friction Model was proposedIdeal Coulomb friction model which uses the slip/stick criticality condition is difficult to be implemented in numerical simulations.

Especially in the integration-based ODE solvers, the force equilibrium is not checked and the traction force cannot be determined at the current state which means the friction force also cannot be determined in the stick condition.To avoid this difficulties, a small viscous slip is allowed at very small relative velocity of the contact points.

Also, a continuous friction coefficient was used to eliminate the discontinuity problem.

Penalty Friction Model – Formulation (only left corner is shown)

Calculation of relative velocity

Calculation of friction force on bottom of upper block

w

here,

Friction force of lower block and moments of both blocks

Friction Forces - Verifications-16

-

Case 1

Case 2

Case 3

Ex #1 – Free Vibration of a Block17

Displacement (m)

Time (sec)

M = 0.5 kgK = 1.0 kg/s2C = 0.5 kg/s

v0 = 1 m/s

Analytic Solution

where,

Ex #2 – Free Fall and Restitution18

M = 0.1 kg

K = 5e6 kg/s2C = 100 kg/sx0 = 1 m

Displacement (m)

Time (sec)Analytic Solution (i-th rebound)

, 0≤t

i

<2v

i

2

/g

,

2v

i

2

/

g

≤t

i

and

F

impact

>0

Ex #3 – Spring-Damper Restrained Blocks in a Vessel(Code-to-Code Verification)

19

Block in a Spring-DamperConstrained VesselDisplacement (m)

Time (sec)

FEM Model using Abaqus

SummaryA computer program was developed to simulate the dynamic responses of graphite blocks in the prismatic core of a HTGR.

The program is not completed yet, but the program was well ready for the module-wise verifications for the lateral, vertical, dowel forces with relevant frictions.Three examples were performed and verified with theoretical solutions and a code-to-code benchmark result showing very good agreements.In the near future, the program will be completed and the whole core model of real Korean HTGR will be simulated.

AcknowledgementThis study was funded by Korean government as the Nuclear Hydrogen Development and Demonstration project (NRF-2012M2A8A2025679).-20-