Efficient Thermo-Chemistry Tabulation for Non-Premixed Combustion at High-Pressure Conditions

Abstract

Propellant injection and turbulent combustion in high-pressure engines is often dominated by real-gas effects. However, previous studies suggested that the departure of the fluid properties from an ideal gas behavior has only a limited effect on the laminar flame structure. This is due to the fact that chemical reactions take place in the flame zone where the temperature is sufficiently high and molecular interactions are negligible, i.e., the ideal gas assumption is valid. On the other hand, various experimental and numerical studies of injection processes at high-pressure conditions demonstrated that real-gas effects can have a strong impact on the turbulent flow. Mixing is influenced by the rapid change of fluid properties. In this work, we exploit the gap in the fidelity of the thermodynamics model needed to describe the laminar flame structure and that needed to describe the turbulent flow field. We then propose a new real-gas flamelet model with increased numerical performance. The computational cost of the new formulation is not significantly higher than that of an ideal gas simulation. The performance of the method is analyzed and the error that is introduced by our assumptions is assessed by comparison to more complete modeling. Finally, the method is used to simulate a turbulent jet flame emanating from a coaxial injector at supercritical pressure and cryogenic oxidizer temperature. The results are compared with experimental OH^∗ images giving evidence of the suitability of the present method.

Appendices

Appendix A: Effects of Strain

Figure 18a shows the maximum temperature T_max of the resulting flamelets over a range of scalar dissipation rates. The maximum temperature does not experience significant changes up to χ_st ≈ 2 ⋅ 10⁴ 1/s. A further increase of the scalar dissipation rate rate leads to a monotonic decrease of T_max until extinction occurs at χ_ext ≈ 7 ⋅ 10⁵ 1/s. Figure 18b demonstrates the effect of strain on the temperature profile. Comparing the flamelet solutions at χ_st = 1, 1 ⋅ 10², 1 ⋅ 10⁴ and 1 ⋅ 10⁵ 1/s shows that higher strain rates lead to increasing temperatures in the diffusion dominated region of the flame on the fuel side.

Fig. 18

Effects of strain. Left: Maximum flamelet temperature as function of the scalar dissipation rate. The circles denote the flamelet solutions shown on the right. Right: Flamelet temperature for various scalar dissipation rates

Appendix B: Effects of Pressure

Two additional flamelet solutions at χ_st = 1000 1/s with varying pressure are evaluated to assess the influence of pressure variations on the flame structure in the turbulent flow. The pressure boundaries are chosen to be 50.1 bar and 61.7 bar which represents a deviation of approximately 10% to the operating pressure of 56.1 bar in both directions. These boundaries lie well above the pressure fluctuations observed in the LES results.

Figure 19 reveals that a deviation in this range has only a minor effect on the flame structure. The density at the oxygen boundary varies as $\rho _{O_{2},50.5\text {bar}} = 1176.36~\text {kg/m}^{3}$ and $\rho _{O_{2},61.7\text {bar}} = 1178.06~\text {kg/m}^{3}$ compared to the reference value $\rho _{O_{2},56.1\text {bar}} = 1177.21~\text {kg/m}^{3}$. The differences for the temperature and species mass fraction profiles are also negligible. However, note that the insensitivity of the results observed in mixture fraction space can not directly be transferred to physical space. In particular, Ribert et al. [37] showed for high pressure LOx/H₂ flames that the flame thickness decreases with $\delta (x) \propto 1/\sqrt {p}$ and the species profiles shift toward the fuel side.

Fig. 19

Effects of pressure: Temperature and product mass fraction profiles for three different pressures