A low diffusion E-CUSP (LDE) scheme is applied with 5th order WENO scheme in this paper. The E-CUSP scheme can capture crisp shock profile and exact contact surface. Several numerical cases are presented to demonstrate the accuracy and robustness for the E-CUSP scheme to be used with the WENO strategy.
A novel subsonic airfoil circulation augment technique using co-flow jet(CFJ) to achieve superior aerodynamic performance for subsonic aircraft is proved numerically by CFD simulation. The advantages of co-flow jet airfoil include high lift at high angle of attack, ultra high C l /C d at cruise point, and low penalty to the overall cycle efficiency of the airframe-propulsion system. Unlike the conventional circulation control (CC) airfoil which is only suitable for landing and taking off, the CFJ airfoil can be used for the whole flying mission. No blunt leading and trailing edge is required so that the pressure drag is small. No moving parts are needed and make it easy to be implemented and weight less. The jet to enhance the circulation will be recirculated. Compared with the CC airfoil, the recirculating CFJ airfoil will significantly save fuel consumption because: 1) the power required to energize the jet is less; 2) no penalty to the jet engine thrust and efficiency due to the disposed jet mass flow since the jet mass flow is recirculated. For the NACA2415 airfoil studied, at low AOA with moderate momentum jet coefficient, the coflow jet airfoil will not only significantly enhance the lift, but also dramatically reduce the drag, or even generate the negative drag (thrust). The mechanism is that the coflow jet can control the pressure drag by filling the wake, and could generate negative pressure drag greater than the friction drag. This may allow the aircraft to cruise with very high aerodynamic efficiency. At high AOA, both the lift and the drag are significantly higher than the airfoil with no flow control, which may enhance the performance of taking off and landing within short distance.
Delayed Detached Eddy Simulation of supersonic flutter of a 3D wing is conducted at free stream Mach number of 1.141 using a fully coupled fluid/structure interaction (FSI). Unsteady 3D compressible Navier-Stokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. The low diffusion E-CUSP scheme with a 5th order WENO reconstruction for the inviscid flux and a set of 4th order central differencing for the viscous terms are used to accurately capture the shock wave/turbulent boundary layer interaction of the vibrating wing. The predicted flutter boundary at supersonic Mach number achieves excellent agreement with experiment. It appears to be the first time that a numerical prediction of supersonic flutter boundary matches with experiment accurately.
In this paper, an improved seventh-order WENO (WENO-Z7) scheme is suggested by extending the 5th-order WENO scheme of Borges et al[R. Borges, M. Carmona, B. Costa, W. S. Don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys. 227(2008) 3191-3211]. The sufficient condition for seventh-order accuracy is described for the new smoothness indicator. The role of the parameter ε, which is used to construct the weights of WENO schemes to prevent the denominator from being zero, is discussed, and an optimized value of ε is suggested to improve the convergence and accuracy for practical applications.
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