Supersonic Flutter Analysis Based on a Local Piston Theory. Zhang, W., Ye, Z., Zhang, C., & Liu, F. AIAA Journal, 2009. ![Supersonic Flutter Analysis Based on a Local Piston Theory [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
Paper doi abstract bibtex A highly efficient local-piston theory is presented for the prediction of inviscid unsteady pressure loads at supersonic and hypersonic speeds. A steady mean flow solution is first obtained by an Euler method. The classical piston theory is modified to apply locally at each point on the airfoil surface on top of the local mean flow to obtain the unsteady pressure perturbations caused by the deviation of the airfoil surface from its mean location without the need of performing unsteady Euler computations. Results of two-and three-dimensional unsteady air loads and flutter predictions are compared with those obtained by the classical piston theory and an unsteady Euler method to assess the accuracy and validity range in airfoil thickness, flight Mach number, and angle of attack and with the presence of blunt leading edges. The local-piston theory is found to offer superior accuracy and much wider validity range compared with the classical piston theory, with the cost of only a fraction of the computational time needed by an unsteady Euler method. Nomenclature A = aerodynamic stiffness matrix a = speed of sound B = aerodynamic damping matrix b = airfoil semichord C l = lift coefficient C m = moment coefficient C p = pressure coefficient h = plunge displacement at the elastic axis, positive down I = cross-sectional mass moment of inertia about its elastic axis K h , K = airfoil plunge stiffness, airfoil pitch stiffness k = reduced frequency, ! b=V 1 M = Mach number m = airfoil mass per unit span p = pressure r = dimensionless radius of gyration about elastic axis S = static moment per unit span t = physical time x = dimensionless static imbalance of the airfoil about its elastic axis V f = reduced flutter speed V 1 = freestream speed = angle of attack, torsion deflection 0 = airfoil steady (mean) background flow angle of attack = amplitude of the pitch motion = mass ratio, m=b 2 = air density = dimensionless time, ! t ! = circular frequency, rad=s ! , ! h = uncoupled frequency of plunging and pitching
@article{
title = {Supersonic Flutter Analysis Based on a Local Piston Theory},
type = {article},
year = {2009},
volume = {47},
id = {2e072120-985c-36a3-ade2-67a331b87564},
created = {2021-10-26T17:56:02.347Z},
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last_modified = {2021-10-26T17:56:03.043Z},
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abstract = {A highly efficient local-piston theory is presented for the prediction of inviscid unsteady pressure loads at supersonic and hypersonic speeds. A steady mean flow solution is first obtained by an Euler method. The classical piston theory is modified to apply locally at each point on the airfoil surface on top of the local mean flow to obtain the unsteady pressure perturbations caused by the deviation of the airfoil surface from its mean location without the need of performing unsteady Euler computations. Results of two-and three-dimensional unsteady air loads and flutter predictions are compared with those obtained by the classical piston theory and an unsteady Euler method to assess the accuracy and validity range in airfoil thickness, flight Mach number, and angle of attack and with the presence of blunt leading edges. The local-piston theory is found to offer superior accuracy and much wider validity range compared with the classical piston theory, with the cost of only a fraction of the computational time needed by an unsteady Euler method. Nomenclature A = aerodynamic stiffness matrix a = speed of sound B = aerodynamic damping matrix b = airfoil semichord C l = lift coefficient C m = moment coefficient C p = pressure coefficient h = plunge displacement at the elastic axis, positive down I = cross-sectional mass moment of inertia about its elastic axis K h , K = airfoil plunge stiffness, airfoil pitch stiffness k = reduced frequency, ! b=V 1 M = Mach number m = airfoil mass per unit span p = pressure r = dimensionless radius of gyration about elastic axis S = static moment per unit span t = physical time x = dimensionless static imbalance of the airfoil about its elastic axis V f = reduced flutter speed V 1 = freestream speed = angle of attack, torsion deflection 0 = airfoil steady (mean) background flow angle of attack = amplitude of the pitch motion = mass ratio, m=b 2 = air density = dimensionless time, ! t ! = circular frequency, rad=s ! , ! h = uncoupled frequency of plunging and pitching},
bibtype = {article},
author = {Zhang, Wei-Wei and Ye, Zheng-Yin and Zhang, Chen-An and Liu, Feng},
doi = {10.2514/1.37750},
journal = {AIAA Journal},
number = {10}
}
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Nomenclature A = aerodynamic stiffness matrix a = speed of sound B = aerodynamic damping matrix b = airfoil semichord C l = lift coefficient C m = moment coefficient C p = pressure coefficient h = plunge displacement at the elastic axis, positive down I = cross-sectional mass moment of inertia about its elastic axis K h , K = airfoil plunge stiffness, airfoil pitch stiffness k = reduced frequency, ! b=V 1 M = Mach number m = airfoil mass per unit span p = pressure r = dimensionless radius of gyration about elastic axis S = static moment per unit span t = physical time x = dimensionless static imbalance of the airfoil about its elastic axis V f = reduced flutter speed V 1 = freestream speed = angle of attack, torsion deflection 0 = airfoil steady (mean) background flow angle of attack = amplitude of the pitch motion = mass ratio, m=b 2 = air density = dimensionless time, ! t ! = circular frequency, rad=s ! , ! h = uncoupled frequency of plunging and pitching","bibtype":"article","author":"Zhang, Wei-Wei and Ye, Zheng-Yin and Zhang, Chen-An and Liu, Feng","doi":"10.2514/1.37750","journal":"AIAA Journal","number":"10","bibtex":"@article{\n title = {Supersonic Flutter Analysis Based on a Local Piston Theory},\n type = {article},\n year = {2009},\n volume = {47},\n id = {2e072120-985c-36a3-ade2-67a331b87564},\n created = {2021-10-26T17:56:02.347Z},\n accessed = {2021-10-26},\n file_attached = {true},\n profile_id = {6476e386-2170-33cc-8f65-4c12ee0052f0},\n group_id = {5a9f751c-3662-3c8e-b55d-a8b85890ce20},\n last_modified = {2021-10-26T17:56:03.043Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n citation_key = {zhang:aj:2009},\n private_publication = {false},\n abstract = {A highly efficient local-piston theory is presented for the prediction of inviscid unsteady pressure loads at supersonic and hypersonic speeds. 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