Iterative optimization based on an objective functional in frequency-space with application to jet-noise cancellation

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

“…5). The anti-sound case was chosen since it has become a common test-case for code validation (Wei and Freund, 2006;Kim et al, 2010;Schulze et al, 2011). Fig.6 shows the cost-functional for some random perturbations along with estimations from a Taylor series expansion to first order…”

“…Recently, there have been several successful attempts using the adjoint equations in shape optimization (Kuruvila et al, 1994;Anderson and Venkatakrishnan, 1999;Giles and Pierce, 2000;Jameson, 2001;Brezillon and Gauger, 2004;Giering et al, 2005;Carpentieri et al, 2007;Zymaris et al, 2009;Peter and Dwight, 2010;Srinath and Mittal, 2010;Zymaris et al, 2010;Jameson and Ou, 2011), optimal boundary control (Bewley et al, 2001;Collis et al, 2000;Collis et al, 2004) and optimal noise control (Cerviño and Bewley, 2002;Joslin et al, 2005;Wei and Freund, 2006;Spagnoli and Airiau, 2008;Babucke et al, 2009;Kim et al, 2010;Rumpfkeil and Zingg, 2010;Schulze et al, 2011). However, because of the expensive iterative optimization procedure, which involves solving the adjoint equations backward in time and which necessitates the storage of the flow fields obtained during the solution of the Navier-Stokes equations, calculations for the purpose of noise reduction have been carried out almost exclusively for 2D-DNS only and recently for 3D-LES in Kim et al (2010).…”

Nonlinear optimal control of bypass transition in a boundary layer flow

“…For instance, Mao et al 37 applied this framework to suppress vortex shedding from a circular cylinder using wall normal transpiration. Schulze et al 38 performed iterative optimization on both 1D Burgers equation and the 2D compressible Navier-Stokes equations to remove specified frequency bands in the acoustic spectrum.…”

Optimal control of a transitional jet using a continuous adjoint method

“…Early efforts using the adjoint method in combination with DNS or LES suffered due to this excessive storage requirement, and focused on simple canonical flows such as periodic channel flow [6], and spatially developing [7], or convective mixing layers [8]. More recently, optimal control using the adjoint method was applied to reduce jet-noise emisssions using the compressible Navier-Stokes equations, e.g., Marinc and Foysi [9], Schulze et al [10] and Kim et al [11].…”