Quasisteady Aerodynamics for Flutter Analysis Using Steady Computational Fluid Dynamics Calculations. Scott, R., C. & Pototzkyt, A., S. Journal of Aircraft, 1996. ![Quasisteady Aerodynamics for Flutter Analysis Using Steady Computational Fluid Dynamics Calculations [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
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Website doi abstract bibtex A quasisteady method is presented where the results of steady computational fluid dynamics (CFD) calculations are used to obtain generalized aerodynamic forces for flutter analysis. For high-speed flows, the method provides a bridge between the computational efficiency, but relative, inaccuracies of piston theory and the greater accuracy, but high, computational cost of CFD flutter calculations. The method uses the structure's vibratory modes to modify the boundary conditions in the steady CFD calculations. Two steady CFD solutions are required per vibratory mode: one for the static part and one for the harmonic part of the pressure distribution. The pressure distributions of these solutions can be used to compute generalized aerodynamic forces necessary for flutter analysis. Sample two-and three-dimensional aerodynamic force calculations are provided demonstrating the method, and a flutter analysis of a National Aerospace Plane type wing is also discussed. Nomenclature A () = matrix of coefficients related to the static part of the generalized aerodynamic forces A, = matrix of coefficients related to the harmonic part of generalized aerodynamic forces b = wing semichord C p = pressure coefficient, (p-p x)/q d = arbitrary scale factor, q^lV^ k = reduced frequency, a)b/V x p = pressure q = dynamic pressure, ip^VJ qj = yth generalized coordinate qj = arbitrary scale factor used in calculation of static pressures for yth mode 4y = arbitrary scale factor used in calculation of harmonic pressures for yth mode Sj = surface grid contour deformed into yth mode shape S = surface grid contour t = time V = velocity W s = steady-state mass flux vector w = downwash x = x coordinate, origin at leading-edge root, positive aft y = y coordinate, origin at leading-edge root, positive spanwise Z = vertical deformation of surface Z () j = complex amplitude of yth mode Presented as Paper 93-1364 at the AIAA 34th Structures, Struc-z = z coordinate, origin at leading-edge root, positive up a = angle of attack p = density a = real part of eigenvalue j = yth mode shape function j = yth integrated mode shape function for calculating harmonic pressures (0-circular frequency Subscripts le = value of quantity at leading edge of wing or vehicle lower = value of quantity on lower surface of wing or vehicle ss = steady state or static aeroelastic value of quantity te = value of quantity at trailing edge of wing or vehicle upper = value of quantity on upper surface of wing or vehicle 3° = freestream value of quantity Superscripts I = harmonic part of quantity R = static part of quantity
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title = {Quasisteady Aerodynamics for Flutter Analysis Using Steady Computational Fluid Dynamics Calculations},
type = {article},
year = {1996},
volume = {33},
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abstract = {A quasisteady method is presented where the results of steady computational fluid dynamics (CFD) calculations are used to obtain generalized aerodynamic forces for flutter analysis. For high-speed flows, the method provides a bridge between the computational efficiency, but relative, inaccuracies of piston theory and the greater accuracy, but high, computational cost of CFD flutter calculations. The method uses the structure's vibratory modes to modify the boundary conditions in the steady CFD calculations. Two steady CFD solutions are required per vibratory mode: one for the static part and one for the harmonic part of the pressure distribution. The pressure distributions of these solutions can be used to compute generalized aerodynamic forces necessary for flutter analysis. Sample two-and three-dimensional aerodynamic force calculations are provided demonstrating the method, and a flutter analysis of a National Aerospace Plane type wing is also discussed. Nomenclature A () = matrix of coefficients related to the static part of the generalized aerodynamic forces A, = matrix of coefficients related to the harmonic part of generalized aerodynamic forces b = wing semichord C p = pressure coefficient, (p-p x)/q d = arbitrary scale factor, q^lV^ k = reduced frequency, a)b/V x p = pressure q = dynamic pressure, ip^VJ qj = yth generalized coordinate qj = arbitrary scale factor used in calculation of static pressures for yth mode 4y = arbitrary scale factor used in calculation of harmonic pressures for yth mode Sj = surface grid contour deformed into yth mode shape S = surface grid contour t = time V = velocity W s = steady-state mass flux vector w = downwash x = x coordinate, origin at leading-edge root, positive aft y = y coordinate, origin at leading-edge root, positive spanwise Z = vertical deformation of surface Z () j = complex amplitude of yth mode Presented as Paper 93-1364 at the AIAA 34th Structures, Struc-z = z coordinate, origin at leading-edge root, positive up a = angle of attack p = density a = real part of eigenvalue </>j = yth mode shape function <l>j = yth integrated mode shape function for calculating harmonic pressures (0-circular frequency Subscripts le = value of quantity at leading edge of wing or vehicle lower = value of quantity on lower surface of wing or vehicle ss = steady state or static aeroelastic value of quantity te = value of quantity at trailing edge of wing or vehicle upper = value of quantity on upper surface of wing or vehicle 3° = freestream value of quantity Superscripts I = harmonic part of quantity R = static part of quantity},
bibtype = {article},
author = {Scott, Robert C and Pototzkyt, Anthony S},
doi = {10.2514/3.46921},
journal = {Journal of Aircraft},
number = {1}
}
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For high-speed flows, the method provides a bridge between the computational efficiency, but relative, inaccuracies of piston theory and the greater accuracy, but high, computational cost of CFD flutter calculations. The method uses the structure's vibratory modes to modify the boundary conditions in the steady CFD calculations. Two steady CFD solutions are required per vibratory mode: one for the static part and one for the harmonic part of the pressure distribution. The pressure distributions of these solutions can be used to compute generalized aerodynamic forces necessary for flutter analysis. Sample two-and three-dimensional aerodynamic force calculations are provided demonstrating the method, and a flutter analysis of a National Aerospace Plane type wing is also discussed. Nomenclature A () = matrix of coefficients related to the static part of the generalized aerodynamic forces A, = matrix of coefficients related to the harmonic part of generalized aerodynamic forces b = wing semichord C p = pressure coefficient, (p-p x)/q d = arbitrary scale factor, q^lV^ k = reduced frequency, a)b/V x p = pressure q = dynamic pressure, ip^VJ qj = yth generalized coordinate qj = arbitrary scale factor used in calculation of static pressures for yth mode 4y = arbitrary scale factor used in calculation of harmonic pressures for yth mode Sj = surface grid contour deformed into yth mode shape S = surface grid contour t = time V = velocity W s = steady-state mass flux vector w = downwash x = x coordinate, origin at leading-edge root, positive aft y = y coordinate, origin at leading-edge root, positive spanwise Z = vertical deformation of surface Z () j = complex amplitude of yth mode Presented as Paper 93-1364 at the AIAA 34th Structures, Struc-z = z coordinate, origin at leading-edge root, positive up a = angle of attack p = density a = real part of eigenvalue </>j = yth mode shape function <l>j = yth integrated mode shape function for calculating harmonic pressures (0-circular frequency Subscripts le = value of quantity at leading edge of wing or vehicle lower = value of quantity on lower surface of wing or vehicle ss = steady state or static aeroelastic value of quantity te = value of quantity at trailing edge of wing or vehicle upper = value of quantity on upper surface of wing or vehicle 3° = freestream value of quantity Superscripts I = harmonic part of quantity R = static part of quantity","bibtype":"article","author":"Scott, Robert C and Pototzkyt, Anthony S","doi":"10.2514/3.46921","journal":"Journal of Aircraft","number":"1","bibtex":"@article{\n title = {Quasisteady Aerodynamics for Flutter Analysis Using Steady Computational Fluid Dynamics Calculations},\n type = {article},\n year = {1996},\n volume = {33},\n websites = {http://arc.aiaa.org},\n id = {308866d5-1697-3a2e-a0ba-4c1ca628868a},\n created = {2021-10-26T17:51:19.601Z},\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 = {2021-10-26T17:51:20.191Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n citation_key = {scott:ja:1996},\n private_publication = {false},\n abstract = {A quasisteady method is presented where the results of steady computational fluid dynamics (CFD) calculations are used to obtain generalized aerodynamic forces for flutter analysis. 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Nomenclature A () = matrix of coefficients related to the static part of the generalized aerodynamic forces A, = matrix of coefficients related to the harmonic part of generalized aerodynamic forces b = wing semichord C p = pressure coefficient, (p-p x)/q d = arbitrary scale factor, q^lV^ k = reduced frequency, a)b/V x p = pressure q = dynamic pressure, ip^VJ qj = yth generalized coordinate qj = arbitrary scale factor used in calculation of static pressures for yth mode 4y = arbitrary scale factor used in calculation of harmonic pressures for yth mode Sj = surface grid contour deformed into yth mode shape S = surface grid contour t = time V = velocity W s = steady-state mass flux vector w = downwash x = x coordinate, origin at leading-edge root, positive aft y = y coordinate, origin at leading-edge root, positive spanwise Z = vertical deformation of surface Z () j = complex amplitude of yth mode Presented as Paper 93-1364 at the AIAA 34th Structures, Struc-z = z coordinate, origin at leading-edge root, positive up a = angle of attack p = density a = real part of eigenvalue </>j = yth mode shape function <l>j = yth integrated mode shape function for calculating harmonic pressures (0-circular frequency Subscripts le = value of quantity at leading edge of wing or vehicle lower = value of quantity on lower surface of wing or vehicle ss = steady state or static aeroelastic value of quantity te = value of quantity at trailing edge of wing or vehicle upper = value of quantity on upper surface of wing or vehicle 3° = freestream value of quantity Superscripts I = harmonic part of quantity R = static part of quantity},\n bibtype = {article},\n author = {Scott, Robert C and Pototzkyt, Anthony S},\n doi = {10.2514/3.46921},\n journal = {Journal of Aircraft},\n number = {1}\n}","author_short":["Scott, R., C.","Pototzkyt, A., S."],"urls":{"Paper":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0/file/21824254-9086-cdaf-682d-a74531dad850/full_text.pdf.pdf","Website":"http://arc.aiaa.org"},"biburl":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0","bibbaseid":"scott-pototzkyt-quasisteadyaerodynamicsforflutteranalysisusingsteadycomputationalfluiddynamicscalculations-1996","role":"author","metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0","dataSources":["qwkM8ZucCwtxbnXfc","ya2CyA73rpZseyrZ8","2252seNhipfTmjEBQ"],"keywords":[],"search_terms":["quasisteady","aerodynamics","flutter","analysis","using","steady","computational","fluid","dynamics","calculations","scott","pototzkyt"],"title":"Quasisteady Aerodynamics for Flutter Analysis Using Steady Computational Fluid Dynamics Calculations","year":1996}