Computer simulation of supersonic jet outflow into a prechamber with different values of initial pressure.

 

The objective of this study was in numerical analysis of  M=2 axi-symmetric jet interaction with rigid inclined surface located in a prechamber below a nozzle exit.  The shape of the jet and flow field parameters for different initial pressures in the prechamber (from normal 105 Pa down nearly to a pure vacuum – 0.133 Pa) were analyzed.

The problem was considered in steady state. At the entrance of the nozzle a total pressure of 2 MPa and temperature of 600 K were specified. The exit diameter of the nozzle is equal to 10 mm. The initial temperature in the prechamber and wall temperature was equal to 300 K.

At the initial state 2D axi-symmetryc flow inside the nozzle was calculated.  Fig 1 shows distribution of Mach number and static pressure in convergent-divergent nozzle. A sound line in the throat of the nozzle and consequent acceleration of the flow are clearly seen. Zones of generation and interaction of shock waves and rarefaction waves are recognized in supersonic flow.

 

2D flow in M=2 nozzle

Mach number distribution	Static pressure distribution

Fig. 1

 

A 3D view of supersonic nozzle (M=2), jet and a prechamber

3D simulations of supersonic outflow out of the nozzle were performed in a domain that included the nozzle, the prechamber and the inclined plate. Fig. 2 represents the geometry of half-domain with vertical symmetry plane. A hexa mesh with 800 cells was generated in the domain. Fig. 3 shows a fragment of the mesh in a vertical symmetry plain.

 

Fig. 2. Flow domain	Fig. 3. Mesh fragment in a vertical symmetry plain.

 

A Reynolds averaged Navier-Stokes equations (RANS) together with standard 2 parametric k-epsilon turbulence model, that is typically used for jet flows, are solved numerically. Fig. 4-18 shows in a vertical symmetry plain calculated distributions of velocity field, streamlines, Mach number, static and total pressures, temperatures and energies of turbulent pulsation for 4 different values of initial pressure in the prechamber: 10⁵, 0.5x10⁵ , 10⁴, and 0.133 Pa. The shape of the jet and distribution of flow parameters dramatically changes with decrease of the pressure in the prechamber.

 

Prechamber pressure  105 Pa	Prechamber pressure 0.5x105 Pa
Fig. 4. Velocity distribution in a vertical symmetry plain
Fig. 5. 2D flow field in a vertical symmetry plain
Fig. 6. Mach number distribution in a vertical symmetry plain
Fig. 7. Static pressure distribution in a vertical symmetry plain
Fig. 8. Total pressure distribution in a vertical symmetry plain
Fig. 9. Static temperature distribution in a vertical symmetry plain
Fig. 10. Total temperature distribution in a vertical symmetry plain

 

As one can see from Fig. 4-10 for the prechamber pressures of 10⁵ and 0.5 10⁵ Pa supersonic axi-symmetric jet initially widens and accelerates (Mach number in the first “barrel?” reaches 3.9 and 5.2, correspondingly), and then external pressure starts to narrow the jet forming a structure with  “barrels” resulting in widening and narrowing the jet shape. Up to 3-4 “barrels” can be observed within calculation domain. For prechamber pressure of 10⁵ Pa (left figures) the width of the jet is smaller than in the case of 0.5 10⁵ Pa pressure. At the position where the jet interacts with the plate it curves and attaches to the plate as a result of Coanda effect.

Prechamber pressure  104 Pa	Prechamber pressure 0.133 Pa
Fig. 11. Velocity distribution in a vertical symmetry plain
Fig. 12. 2D flow field in a vertical symmetry plain
Fig. 13. Mach number distribution in a vertical symmetry plain
Fig. 14. Static pressure distribution in a vertical symmetry plain
Fig. 15. Total pressure distribution in a vertical symmetry plain
Fig. 16. Static temperature distribution in a vertical symmetry plain
Fig. 17. Total temperature distribution in a vertical symmetry plain
Fig. 18. Distribution of turbulent pulsation energy in a vertical symmetry plain

 

For lower prechamber pressures (10⁴ and 0.133 Pa, Fig. 11-18) the shape of the jet is strongly different. Tenfold decrease in pressure in the prechamber leads to development of the jet with only one “barrel” (left column of figures). For lower pressure (0.133 Pa) the jet expands rapidly (right column of figures) straight after leaving the nozzle and terminates with inclined compression shock wave, that divides high-velocity supersonic flow inside the jet and much slow sub/supersonic flow in the vicinity of inclined plain.

Conclusions

Computer simulation of supersonic outflow of viscous gas jet into a prechamber with different initial pressure and its interaction with a rigid inclined wall reveals significant changes of the jet shape and flow characteristics depending on the prechamber pressure. The shape changes from a jet with “barrels” for normal atmospheric pressure to a rapid expanding jet after nozzle exit for the case of negligibly small back pressure (0.133 Pa).