Nozzle Numerical Simulations New approach of CFD simulations

Nozzle Numerical Simulations New approach of CFD simulations BGC Meeting 15 -09 -2017 6/9/2021 Przemysław Smakulski

Basic difference between the models Reynolds-averaged Navier–Stokes Previous simulations Large eddy simulation Present simulation 6/9/2021 Przemysław Smakulski

Boundary conditions – Paolo’s simulation p_chamber = 0. 1 bar p_in =10 bar 6/9/2021 Przemysław Smakulski Nozzle φ30 mm

CFD simulation. Chamber pressure �� =0. 1 [������ ] RANS model Steady State 6/9/2021 Przemysław Smakulski

CFD simulation. Chamber pressure �� =0. 1 [������ ] RANS model Steady State ? ? ? 6/9/2021 Przemysław Smakulski

Theoretical Mach disc dimension – present simulation comparison Nozzle Barrel Nozzle Tank chamber Mach disc shock diameter pressure position diameter d_n [mm] p_t [bar] p_nc [bar] x_M [mm] d_Bs [mm] 3. 00 E-02 10 1. 0 E-01 0. 20 0. 15 1. 0 E-02 0. 64 0. 32 0. 48 1. 0 E-03 2. 01 1. 51 1. 0 E-04 6. 36 3. 18 4. 77 1. 0 E-05 20. 10 10. 05 15. 08 8. 80 E-06 21. 43 10. 71 16. 07 6/9/2021 Przemysław Smakulski

Convergence criteria (RMS) in model with LES RMS <10 -6 6/9/2021 Przemysław Smakulski

6/9/2021 Przemysław Smakulski

Statistics Outlet pressure 0. 1 bar No. of procesor cores used 16 No. of iterations 155 861 Total simulation time 5· 10 -4 s Calculation hours ~68 h Number of elements (numerical mesh) 91 828 Model of turbulence LES Symultaion type 6/9/2021 Transient Przemysław Smakulski

T-s diagram for nitrogen p = 10 bar Gas N 2 p = 1 mbar Isentropic expansion Gas/Liquid N 2 Solid N 2 6/9/2021 Przemysław Smakulski Real process

Temperature profile Nozzle chamber diameter Tank pressure d_n [mm] p_t [bar] p_nc [bar] 3. 00 E-02 10 1. 0 E-01 1. 0 E-02 1. 0 E-03 1. 0 E-04 1. 0 E-05 8. 80 E-06 6/9/2021 Mach disc position x_M [mm] 0. 20 0. 64 2. 01 6. 36 20. 10 21. 43 Mach disc diameter d_M [mm] 0. 10 0. 32 1. 01 3. 18 10. 05 10. 71 Barrel shock diameter d_Bs [mm] 0. 15 0. 48 1. 51 4. 77 15. 08 16. 07 Przemysław Smakulski

De Laval micro nozzle [1] - K. Chen, M. Winter, R. F. Huang, Supersonic flow in miniature nozzles of planar configuration, J. Micromechanics Microengineering. 15 (2005) 1736– 1744. 6/9/2021 Przemysław Smakulski

Simulation of de Laval nozzle Residiual RMS for Steady State calculations Throat dimension 60 µm Inlet pressure 2 bar Outlet pressure 1 mbar 6/9/2021 Przemysław Smakulski