Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier-Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton's method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

No abstract

No abstract

No abstract

Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are omnipresent in nature and engineering applications, and their accurate simulation is essential for providing insights into these processes. While PDEs are typically solved with numerical methods, the recent success of machine learning (ML) has shown that ML methods can provide novel avenues of finding solutions to PDEs. ML is becoming more and more present in computational fluid dynamics (CFD). However, up to this date, there does not exist a generalpurpose ML-CFD package which provides 1) powerful state-of-the-art numerical methods, 2) seamless hybridization of ML with CFD, and 3) automatic differentiation (AD) capabilities. AD in particular is essential to ML-CFD research as it provides gradient information and enables optimization of preexisting and novel CFD models. In this work, we propose JAX-FLUIDS: a comprehensive fullydifferentiable CFD Python solver for compressible two-phase flows. JAX-FLUIDS allows the simulation of complex fluid dynamics with phenomena like three-dimensional turbulence, compressibility effects, and two-phase flows. Written entirely in JAX, it is straightforward to include existing ML models into the proposed framework. Furthermore, JAX-FLUIDS enables end-to-end optimization. I.e., ML models can be optimized with gradients that are backpropagated through the entire CFD algorithm, and therefore contain not only information of the underlying PDE but also of the applied numerical methods. We believe that a Python package like JAX-FLUIDS is crucial to facilitate research at the intersection of ML and CFD and may pave the way for an era of differentiable fluid dynamics.