Adjoint-based sensitivity analysis of flames

Abstract

Simulation of chemically reacting flows using detailed chemistry introduces a large number of chemistry model parameters. While not all significantly affect the target outcomes of a simulation, the parameters that do are not always known a priori. In order to improve simulations for specified target outcomes, termed quantities of interest (QoIs), the sensitivity of these QoIs to the model parameters are needed. However, evaluating the sensitivities is computationally expensive, especially for complex fuels that may involve many parameters. For these simulations, the forward sensitivity method requires the solution of an additional number of governing equations proportional to the number of parameters. Here, an adjoint sensitivity approach is formulated where the computational cost scales as the number of QoIs and not the number of parameters. Specifically, adjoint equations are derived for laminar, incompressible, variable density reacting flow and applied to hydrogen flame simulations. From the solution of the corresponding adjoint equations, sensitivity of the QoIs to chemistry model parameters is calculated. The one-dimensional simulation results show that the adjoint sensitivity results closely match those of forward sensitivity methods, thus providing validation of the adjoint method. The two-dimensional simulation results indicate the most sensitive parameters for two QoIs, flame tip temperature and NOx emission. For these tests, the adjoint method reduces computational expense compared to forward sensitivity methods by a factor proportional to the number of QoIs over the number of parameters, here 2/172. Such savings can be more drastic for cases that involve complex fuels, such as combustion of jet fuel, requiring thousands of chemistry model parameters. Further, this sensitivity information can be used in development of experiments by pointing out which are the critical chemistry model parameters.

Adjoint Methods as Design Tools in Thermoacoustics

“…In Reynolds-averaged Navier-Stokes (RANS) simulations, Wang et al [141] accelerated Monte-Carlo assessment for uncertainty quantification of the scramjet unstart by adjoint methods. The sensitivity of the flame tip temperature and NOx emissions in hydrogen flames to chemistry model parameters was investigated in [142]. Other implementations of adjoint methods in steady reacting flow solvers can be found in [143][144][145].…”

Adjoint-based sensitivity analysis of quantities of interest of complex combustion models

“…For example, in fluid mechanics, the influence of the geometry on lift and drag of an aerofoil, as a QoI, is commonly analysed by the adjoint approach [20]. The adjoint method was applied to several reactive systems for different applications such as optimisation [21], uncertainty quantification [22,23], data assimilation [24], and sensitivity analysis [25].…”

“…In the present study, the goal is to develop an appropriate adjoint-based framework for sensitivity analyses of complex QoIs like ignition delay time in spatially homogeneous, unsteady systems considering dependencies on the system state and on model parameters without simplifications. In contrast to the work of Braman et al [25] and the KPP-package, an adjoint method is applied, which makes use of a numerical operator reconstruction. This strongly simplifies the methodological application efforts by avoiding the analytical formulation of adjoint equations and allows the treatment of user-defined reaction laws.…”

Modeling of Fine-Particle Formation in Turbulent Flames

“…In complex configurations that have a large number of parameters, forward sensitivity approaches are not tractable. Instead, adjoint-based techniques are better suited (see, e.g., Braman et al 2015). Extension of such tools to LES and chaotic flow solvers will be of tremendous utility (see, e.g., Wang 2013).…”