 # Design Analysis of Spherical Pressure Vessel

## Overview

The aim of this test case is to validate the following functions:

• Transient thermostructural analysis

The simulation results of SimScale were compared to the analytical results presented in [Amir14].

Import validation project into workspace

## Geometry

A B C D E F
x [m] 0 0.19 0 0.2 0 0
y [m] 0.19 0 0.2 0 0 0
z [m] 0 0 0 0 0.19 0.2

## Analysis type and Domain

Tool Type : Calculix, Code_Aster

Analysis Type : Transient Thermostructural

Mesh and Element types :

Case Mesh type Number of nodes Element type Value of Kappa Tool type
(A) linear tetrahedrals 164344 3D isoparametric 20 Calculix
(B) linear tetrahedrals 164344 3D isoparametric 20 Code_Aster
(C) linear tetrahedrals 164344 3D isoparametric 22 Calculix
(D) linear tetrahedrals 164344 3D isoparametric 22 Code_Aster

## Simulation Setup

Material:

• isotropic: E = 190 GPa, ν
$\nu$

= 0.305, ρ

$\rho$

= 7750 kg/m³, Kappa = 20 W/(m.K) & 22 W/(m.K), Expansion coefficient = 9.7e-6 1/K, Reference temperature = 300 K, Specific heat = 486 J/K

Initial conditions:

• Temperature = 300 K

Constraints:

• Face AECF zero x-displacement
• Face BEDF zero y-displacement
• Face ABCD zero z-displacement

• Face ABE linear increasing pressure from 0 MPa to 1 MPa according to formula P = (0.2e6).t, where ‘t’ is time from 0 to 5 sec

Temperature:

• Face ABE linear increasing temperature from 300 K to 500 K according to formula T = 40t + 300, where ‘t’ is time from 0 to 5 sec

Heat flux:

• Face CDF convective heat flux of h = 90 W/(m².K) with reference temperature of 300 K

## Results

Since no value of conductivity (kappa) was provided, the values of 20 W/(m.K) and 22 W/(m.K) were used. Comparison of vonMises stress (MPa) and temperature (K) computed over the edge EF with [Amir14] at final timestep are given below.