OPTIMAL LOCATION OF SUCTION OR BLOWING JETS USING THE CONTINUOUS ADJOINT APPROACH

This paper presents the use of the continuous adjoint method as a low-cost tool to derive useful information regarding the optimal location and type of steady suc- tion/blowing jets, used to control flow separation. An objective function that expresses the total pressure losses between the inlet and outlet of the flow domain is devised. The derivatives of this objective function with respect to hypothetical jet velocities at the wall boundaries are then computed using the continuous adjoint method. Emphasis is laid on the computation of the exact sensitivity derivatives and, for this reason, the adjoint to the turbulence (Spalart-Allmaras) model is also used, as proposed in a recent publication by the same authors. The proposed method is demonstrated by controlling the separated flow in a S-shaped duct.

[1]  Liang Huang,et al.  Numerical study of blowing and suction control mechanism on NACA0012 airfoil , 2004 .

[2]  Gianluca Iaccarino,et al.  RANS Simulation of the Separated Flow over a Bump with Active Control , 2003 .

[3]  Paolo Luchini,et al.  Algebraic growth in boundary layers: optimal control by blowing and suction at the wall , 2000 .

[4]  Oh-Hyun Rho,et al.  Feasibility Study of Constant Eddy-Viscosity Assumption in Gradient-Based Design Optimization , 2003 .

[5]  A. Cain,et al.  NUMERICAL SIMULATION OF SYNTHETIC JET ACTUATORS , 1997 .

[6]  B. Stratford The prediction of separation of the turbulent boundary layer , 1959, Journal of Fluid Mechanics.

[7]  R. Dwight,et al.  Effect of Approximations of the Discrete Adjoint on Gradient-Based Optimization , 2006 .

[8]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[9]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[10]  D. Darmofal,et al.  An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids , 2004 .

[11]  Klaus Gersten,et al.  Boundary Layer and Flow Control. Vols. 1 and 2 , 1963 .

[12]  Marian Nemec,et al.  Improvements to a Newton-Krylov Adjoint Algorithm for Aerodynamic Optimization , 2005 .

[13]  W. K. Anderson,et al.  Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation , 1997 .

[14]  Gustav Victor Lachmann,et al.  Boundary layer and flow control: its principles and application , 1961 .

[15]  Farrukh S. Alvi,et al.  Use of High-Speed Microjets for Active Separation Control in Diffusers , 2006 .

[16]  Byung Joon Lee,et al.  Automated design methodology of turbulent internal flow using discrete adjoint formulation , 2007 .

[17]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[18]  A. Jameson,et al.  A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION , 2000 .

[19]  Eli Turkel,et al.  Simulation of Synthetic Jets Using Unsteady Reynolds-Averaged Navier-Stokes Equations , 2006 .

[20]  D. Mavriplis Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2007 .

[21]  Kyriakos C. Giannakoglou,et al.  A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows , 2007 .

[22]  Albert L. Braslow,et al.  A History of Suction-Type Laminar - Flow Control with Emphasis on Flight Research , 2012 .

[23]  W. Tollmien,et al.  Über Flüssigkeitsbewegung bei sehr kleiner Reibung , 1961 .

[24]  Ionel M. Navon,et al.  Optimal control of cylinder wakes via suction and blowing , 2003, Computers & Fluids.

[25]  Kyriakos C. Giannakoglou,et al.  Continuous adjoint approach to the Spalart–Allmaras turbulence model for incompressible flows , 2009 .

[26]  W. K. Anderson,et al.  Airfoil Design on Unstructured Grids for Turbulent Flows , 1999 .

[27]  A. D. Gosman,et al.  Two calculation procedures for steady, three-dimensional flows with recirculation , 1973 .

[28]  A. Jameson,et al.  Optimum Aerodynamic Design Using the Navier–Stokes Equations , 1997 .