PSI - Issue 42

A. Sulamanidze et al. / Procedia Structural Integrity 42 (2022) 412–419 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

414

3

3. Algorithm for TMF IP and OOP multi-physics computations In order to determination a local thermo-mechanical stress-strain rate and displacement fields a new algorithm for the multi-physics numerical calculations developed and implemented incorporates Maxwell 3D, Fluent and Transient Structural modules of ANSYS 2021R1. The algorithm builds upon a coupled heat loss from eddy currents of magnetic induction and force convective cooling accounting for by k-omega SST turbulence model response, which cause gradients of mechanical elastic-plastic deformations (Fig. 2a).

Fig. 2. (a) Algorithm and (b) FE model for TMF multi-physics computations.

The Maxwell 3D solver computes the values by Maxwell's curl equation (Eq. 1) to solve for the magnetic field H (ANSYS, 2021):

1

 

  

(1)

H j  = −     

H



k j +   

 

where j - current density A/m2;  - magnetic permeability;  - imaginary component of permittivity;  - is the angular frequency of the wave rad/s ; k – bulk conductivity S/m. At the stage of computational fluid dynamics (CFD) analysis, a two-equation eddy-viscosity Shear-stress transport (SST) k- ω turbulence model was used to close unsteady Reynolds averaged Navier – Stokes (URANS) equations. The pressure-based coupled algorithm was used to solve a coupled system of equations comprising the momentum equations and the pressure-based continuity equation. The total strain as a result of thermomechanical loading is equal to:

el pl th     = + +

(2)

where el th ref t t   =  − thermal expansion; th  - linear thermal expansion; ref t - reference temperature. The elastic-plastic material behavior is set by Power law nonlinear isotropic hardening model E   = elastic strain according to Hooke's law; ( ) th

N

3      

  

G  = +  

(3)



pl



0

0

0

where N = 1/n is strain hardening exponent. The main electromagnetic, fluid dynamics and mechanical properties used in the numerical study for SENT specimen configuration produced from a high-temperature nickel-based alloy ХН73М are listed in Tables 1 and 2. In our computations, a sequence of thermomechanical loading was simulated, which was implemented in experiments using an inductor coil and nozzles, as shown in Fig.2b.