The two-phase filtered mass density function (FMDF) method is employed for large eddy simulation (LES) of high speed evaporating and combusting nheptane sprays using simple (global) and complex (skeletal) chemical kinetic mechanisms. The resolved fluid velocity and pressure fields are obtained by solving the filtered compressible Navier-Stokes equations with high-order Eulerian finite difference methods. The liquid spray and gas scalar (temperature and species mass fractions) fields are both obtained by Lagrangian stochastic models. The chemistry calculation is accelerated by incorporating the parallel in situ adaptive tabulation (ISAT) method. There are two-way interactions among Eulerian and Lagrangian fields. Simulations of evaporating sprays with and without combustion indicate that the two-phase LES/FMDF results are consistent and compare well with the available experimental data at different gas temperatures and oxygen concentrations. The spray controlled flame tends to move away from a diffusion flame structure toward a premixed one as the oxygen concentration decreases and/or the ambient gas temperature increases because of changes in spray-induced turbulence and mixing. The LES/FMDF results for ignition delay show more sensitivity to the chemical kinetic model at lower gas temperatures due to slower reaction and stronger turbulence-chemistry interactions. The liftoff length is less sensitive to the kinetics.
Large eddy simulations of high speed evaporating sprays are conducted to study spray interactions with the gas flow and turbulence generated by the spray. The spray is simulated with a Lagrangian droplet method and a stochastic breakup model together with non-equilibrium, finite-rate heat and mass transfer models. The Lagrangian spray/droplet field is fully coupled with the Eulerian gas flow through mass, momentum and energy coupling terms. The interaction of spray induced gas flow and turbulence with the droplets is studied for different gas chamber densities and temperatures as well as different nozzle sizes and injection pressures. Our results indicate that although the droplet transport and evaporation are both important to the generated gas flow and its interactions with the spray, the major source of momentum transfer to the gas is the high speed vapor generated by evaporation. It is shown that sprays injected from larger nozzles generate more perturbations in the gas due to increase in evaporation rate by higher entrained gas. However, the liquid spray penetration remains unchanged with the variation in injection pressure due to competing effects of evaporation and vapor convection. While the liquid penetration is not significantly affected by the injection pressure, the evaporated vapor penetrates more and mixes better at higher injection pressures due to higher induced gas velocity and turbulence.
A gradient based optimization using the continuous adjoint method for inverse design of a turbine blade cascade is presented. The advantage of the adjoint method is that the objective function gradients can be evaluated by solving the adjoint equations with coefficients depending on the flow variables. This method is particularly suitable for aerodynamic design optimization for which the number of design variables is large. Bezier polynomials are used to parameterize suction side of the turbine blade. The numerical convective fluxes of both flow and adjoint equations are computed by using a Roe-type approximate Riemann solver. An approximate linearization is applied to simplify the calculation of the numerical flux of adjoint variables on the faces of computational cell. The problem examined is that of the inverse design of NASA C3X blade that reproduces a given pressure distributions over its surfaces. Adjoint results show a good agreement with those obtained by finite-difference method.
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