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Actively controlled trailing-edge flaps (ACFs) have been extensively studied for vibration and noise control in rotorcraft using various approximate aerodynamic models. In this study, two-dimensional unsteady airloads due to oscillating flap motion obtained from computational fluid dynamics (CFD) are compared with approximate unsteady loads. The ap...
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... simulate unsteady flap deflection, an overset mesh option is employed where a separate body- fitted mesh for the trailing-edge flap is generated in addition to the airfoil mesh, as illustrated in Fig. 2. An overset grid approach is convenient for mod- eling arbitrarily large grid motions; however, non- conservation of flow variables at the grid zonal in- terfaces may affect the solution accuracy [29]. Sinu- soidal flap motions about the hinge axis can be pre- scribed in the CFD++ code. The relative motion of the two grids requires re-computation of over- set boundary zonal connections at each time step, which is executed automatically by the ...
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... domain for the CFD computations is de- picted in Fig. 5, and the far field boundary extends to 50 chord lengths. The details of the grid near the airfoil and the flap are given in Figs. 2 and 3. The grids for the airfoil and the flap are structured grids with quadrilateral elements, generated using the ICEM-CFD software and converted into the na- tive format in CFD++. The grids are refined at the solid wall boundaries so that the equations are directly solved to the walls and wall functions are not used. Two grids representing different levels of mesh resolution are generated for grid conver- gence studies. A medium resolution grid contains 90,000 grid points, as shown in Figs. 2, 3 and 5; while the finer grid has 244,000 points. The flow is first allowed to reach steady state, before the time- dependent results due to flap deflections are gener- ated using the overset mesh approach that was de- scribed earlier. The time-accurate simulations uti- lize time steps such that at least 250 points are used per cycle. The computational cost of the CFD sim- ulations was approximately 1 hour for each cycle on the medium grid and over 2 hours on the finer grid, using four CPUs on a Linux cluster of Opteron processors with speeds of 1.8-2.4GHz. The results presented are organized in the follow- ing manner. First, a grid sensitivity study is con- ducted on the medium and fine grids. Next, un- steady values of the lift coefficient C l , moment coef- ficient C m , and hinge moment coefficient C hm due to oscillatory flap motion are presented, comparing the RFA and the CFD results. Note that the mo- ment coefficient C m is defined about the quarter chord point, and the hinge moment C hm is mea- sured about the hinge axis. The effects of freestream Mach number on predicted unsteady airloads are also discussed by comparing the RFA and CFD re- sults. Subsequently, the drag coefficient C d is com- pared for the CFD and approximate drag ...
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... domain for the CFD computations is de- picted in Fig. 5, and the far field boundary extends to 50 chord lengths. The details of the grid near the airfoil and the flap are given in Figs. 2 and 3. The grids for the airfoil and the flap are structured grids with quadrilateral elements, generated using the ICEM-CFD software and converted into the na- tive format in CFD++. The grids are refined at the solid wall boundaries so that the equations are directly solved to the walls and wall functions are not used. Two grids representing different levels of mesh resolution are generated for grid conver- gence studies. A medium resolution grid contains 90,000 grid points, as shown in Figs. 2, 3 and 5; while the finer grid has 244,000 points. The flow is first allowed to reach steady state, before the time- dependent results due to flap deflections are gener- ated using the overset mesh approach that was de- scribed earlier. The time-accurate simulations uti- lize time steps such that at least 250 points are used per cycle. The computational cost of the CFD sim- ulations was approximately 1 hour for each cycle on the medium grid and over 2 hours on the finer grid, using four CPUs on a Linux cluster of Opteron processors with speeds of 1.8-2.4GHz. The results presented are organized in the follow- ing manner. First, a grid sensitivity study is con- ducted on the medium and fine grids. Next, un- steady values of the lift coefficient C l , moment coef- ficient C m , and hinge moment coefficient C hm due to oscillatory flap motion are presented, comparing the RFA and the CFD results. Note that the mo- ment coefficient C m is defined about the quarter chord point, and the hinge moment C hm is mea- sured about the hinge axis. The effects of freestream Mach number on predicted unsteady airloads are also discussed by comparing the RFA and CFD re- sults. Subsequently, the drag coefficient C d is com- pared for the CFD and approximate drag ...
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... oscillatory portion of C l , denoted by ∆C l , due to flap deflection amplitudes of A = 2 • and 4 • , is compared in Fig. 12. Figure 12 indicates that the difference in ∆C l between the RFA and CFD predic- tions increase as the flap deflection angle increases. This behavior is reasonable since the nonlinear flow effects are enhanced as the flap deflections increase. Similar to the 2 • case, the RFA model overestimates ∆C l at 4 • as compared to the results generated from the CFD code. Generally, the amplitudes of ∆C l di- minish as the flap oscillation frequency ν increases, reflecting the unsteady effect of the flap. This trend is captured by both the RFA model and CFD re- sults. However, ∆C l predicted by the CFD code starts to increase slightly at frequencies above 80Hz. The maximum error in ∆C l is 45% and the mini- mum error is 21%, for the cases considered ...
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... oscillatory portion of C l , denoted by ∆C l , due to flap deflection amplitudes of A = 2 • and 4 • , is compared in Fig. 12. Figure 12 indicates that the difference in ∆C l between the RFA and CFD predic- tions increase as the flap deflection angle increases. This behavior is reasonable since the nonlinear flow effects are enhanced as the flap deflections increase. Similar to the 2 • case, the RFA model overestimates ∆C l at 4 • as compared to the results generated from the CFD code. Generally, the amplitudes of ∆C l di- minish as the flap oscillation frequency ν increases, reflecting the unsteady effect of the flap. This trend is captured by both the RFA model and CFD re- sults. However, ∆C l predicted by the CFD code starts to increase slightly at frequencies above 80Hz. The maximum error in ∆C l is 45% and the mini- mum error is 21%, for the cases considered ...
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... amplitude of the oscillatory portion of C m , denoted by ∆C m , is shown in Fig. 17 ¢C m CFD A = 2.0° RFA A = 2.0° CFD A = 4.0° RFA A = 4.0° exists between the average value of C hm that is ob- tained from CFD and the RFA model. Figures 20 and 21 show the hinge moment coefficient C hm plot- ted versus time and flap deflection at zero incidence α = 0 • . In this case, there is no offset between the average C hm values. The amplitude of the oscilla- tory component of C hm , denoted by ∆C hm is shown in Fig. 22 for flap deflections of 2 • and 4 • . These fig- ures indicate that the RFA model significantly over- predicts the hinge moment. This behavior is not surprising because the flap is immersed in relatively thick boundary layers where linear aerodynamic as- sumptions may not be valid. These findings are also consistent with the conclusions presented in Ref. ...
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... amplitude of the oscillatory portion of C m , denoted by ∆C m , is shown in Fig. 17 ¢C m CFD A = 2.0° RFA A = 2.0° CFD A = 4.0° RFA A = 4.0° exists between the average value of C hm that is ob- tained from CFD and the RFA model. Figures 20 and 21 show the hinge moment coefficient C hm plot- ted versus time and flap deflection at zero incidence α = 0 • . In this case, there is no offset between the average C hm values. The amplitude of the oscilla- tory component of C hm , denoted by ∆C hm is shown in Fig. 22 for flap deflections of 2 • and 4 • . These fig- ures indicate that the RFA model significantly over- predicts the hinge moment. This behavior is not surprising because the flap is immersed in relatively thick boundary layers where linear aerodynamic as- sumptions may not be valid. These findings are also consistent with the conclusions presented in Ref. ...
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... effect of free stream Mach number on the accuracy of the predicted unsteady airloads is con- sidered next. Four different values of the free stream Mach number are chosen, namely, M = 0.3, 0.6, 0.7, and 0.85. Time history of the lift coefficient C l is shown in Fig. 23 for 2 • flap deflection at reduced frequency k = 0.031. At this airfoil incidence an- gle, α = 5 • , the agreement in C l between the two models is reasonable until M=0.7, after which the discrepancy between the two approaches becomes quite large. At M=0.85 the RFA model predicts a C l value that is three times larger than the CFD ...
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... of Mach contours of the flow over a NACA0012 airfoil at the instant when δ e = 0 • are shown in Fig. 24 for M = 0.7 and 0.85. A strong shock on the airfoil ahead of the flap is evident for the M = 0.85 case and it produces massive shock- induced boundary layer separation as can be seen in Fig. 24. The RFA model is not suitable for pre- dicting airloads at such flow ...
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... of Mach contours of the flow over a NACA0012 airfoil at the instant when δ e = 0 • are shown in Fig. 24 for M = 0.7 and 0.85. A strong shock on the airfoil ahead of the flap is evident for the M = 0.85 case and it produces massive shock- induced boundary layer separation as can be seen in Fig. 24. The RFA model is not suitable for pre- dicting airloads at such flow ...
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... simulate unsteady flap deflection, an overset mesh option is employed where a separate body- fitted mesh for the trailing-edge flap is generated in addition to the airfoil mesh, as illustrated in Fig. 2. An overset grid approach is convenient for mod- eling arbitrarily large grid motions; however, non- conservation of flow variables at the grid zonal in- terfaces may affect the solution accuracy [29]. Sinu- soidal flap motions about the hinge axis can be pre- scribed in the CFD++ code. The relative motion of the two grids requires ...
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... domain for the CFD computations is de- picted in Fig. 5, and the far field boundary extends to 50 chord lengths. The details of the grid near the airfoil and the flap are given in Figs. 2 and 3. The grids for the airfoil and the flap are structured grids with quadrilateral elements, generated using the ICEM-CFD software and converted into the na- tive format in CFD++. The grids are refined at the solid wall boundaries so that the equations are directly solved to the walls and wall functions are not used. Two grids ...
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... into the na- tive format in CFD++. The grids are refined at the solid wall boundaries so that the equations are directly solved to the walls and wall functions are not used. Two grids representing different levels of mesh resolution are generated for grid conver- gence studies. A medium resolution grid contains 90,000 grid points, as shown in Figs. 2, 3 and 5; while the finer grid has 244,000 points. The flow is first allowed to reach steady state, before the time- dependent results due to flap deflections are gener- ated using the overset mesh approach that was de- scribed earlier. The time-accurate simulations uti- lize time steps such that at least 250 points are used per cycle. The ...
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... oscillatory portion of C l , denoted by ∆C l , due to flap deflection amplitudes of A = 2 • and 4 • , is compared in Fig. 12. Figure 12 indicates that the difference in ∆C l between the RFA and CFD predic- tions increase as the flap deflection angle increases. This behavior is reasonable since the nonlinear flow effects are enhanced as the flap deflections increase. Similar to the 2 • case, the RFA model overestimates ∆C l at 4 • as compared to the results ...
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... oscillatory portion of C l , denoted by ∆C l , due to flap deflection amplitudes of A = 2 • and 4 • , is compared in Fig. 12. Figure 12 indicates that the difference in ∆C l between the RFA and CFD predic- tions increase as the flap deflection angle increases. This behavior is reasonable since the nonlinear flow effects are enhanced as the flap deflections increase. ...
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... amplitude of the oscillatory portion of C m , denoted by ∆C m , is shown in Fig. 17 ¢C m CFD A = 2.0° RFA A = 2.0° CFD A = 4.0° RFA A = 4.0° exists between the average value of C hm that is ob- tained from CFD and the RFA model. Figures 20 and 21 show the hinge moment coefficient C hm plot- ted versus time and flap deflection at zero incidence α = 0 • . In this case, there is no offset between the average C hm values. ...
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... average value of C hm that is ob- tained from CFD and the RFA model. Figures 20 and 21 show the hinge moment coefficient C hm plot- ted versus time and flap deflection at zero incidence α = 0 • . In this case, there is no offset between the average C hm values. The amplitude of the oscilla- tory component of C hm , denoted by ∆C hm is shown in Fig. 22 for flap deflections of 2 • and 4 • . These fig- ures indicate that the RFA model significantly over- predicts the hinge moment. This behavior is not surprising because the flap is immersed in relatively thick boundary layers where linear aerodynamic as- sumptions may not be valid. These findings are also consistent with the ...
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... effect of free stream Mach number on the accuracy of the predicted unsteady airloads is con- sidered next. Four different values of the free stream Mach number are chosen, namely, M = 0.3, 0.6, 0.7, and 0.85. Time history of the lift coefficient C l is shown in Fig. 23 for 2 • flap deflection at reduced frequency k = 0.031. At this airfoil incidence an- gle, α = 5 • , the agreement in C l between the two models is reasonable until M=0.7, after which the discrepancy between the two approaches becomes quite large. At M=0.85 the RFA model predicts a C l value that is three times larger than the CFD ...
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... of Mach contours of the flow over a NACA0012 airfoil at the instant when δ e = 0 • are shown in Fig. 24 for M = 0.7 and 0.85. A strong shock on the airfoil ahead of the flap is evident for the M = 0.85 case and it produces massive shock- induced boundary layer separation as can be seen in Fig. 24. The RFA model is not suitable for pre- dicting airloads at such flow ...
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... of Mach contours of the flow over a NACA0012 airfoil at the instant when δ e = 0 • are shown in Fig. 24 for M = 0.7 and 0.85. A strong shock on the airfoil ahead of the flap is evident for the M = 0.85 case and it produces massive shock- induced boundary layer separation as can be seen in Fig. 24. The RFA model is not suitable for pre- dicting airloads at such flow ...
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Citations
... In the context of rotorcraft engineering and design, approaches that use information from an available set of CFD solutions have been studied in the last decade. In the recent literature, these are referred to as surrogate methods and have been primarily adopted to get integral quantities like aerodynamic coefficients and loads [24] [25] [26]. These approaches are essentially based on response surface methods (RSM) and neural networks (NN). ...
A reduced order methodology, based on Proper Orthogonal Decomposition (POD) and multidimensional interpolation, is proposed for the parametric study of rotor flows under hovering conditions. The POD-based methodology makes no simplification of the complexity of the three-dimensional, viscous turbulent flow generated by the rotor but still yields accurate solutions at a fraction of the time required by standard CFD. The use of interpolation techniques other than projection operators allows dealing in a unified manner with experimental data, CFD computations or a combination of both. The method provides fast and accurate solutions for local flow details and integral quantities like aerodynamic coefficients. The POD-based methodology is demonstrated to have a multiplier effect on wind tunnel and CFD simulations of rotorcraft aerodynamics and as a potential powerful methodology to construct a new generation of rotorcraft simulators.
... In addition to developing computationally efficient aerodynamic models based on simplifying assumptions, reduced-order modeling approaches that seek to approximate CFD results by extracting information from a limited number of full-order simulations have been proposed. Examples of such approaches include proper orthogonal decomposition (POD) [4][5][6][7], Volterra series [4,8], and surrogate-based approaches [9][10][11][12][13]. A major advantage of reducedorder modeling of full-order CFD compared to approaches based on simplifying assumptions is that the reduced-order models can be easily upgraded as the CFD solvers from which they are generated continue to improve. ...
A reduced-order nonlinear unsteady aerodynamic modeling approach suitable for analyzing pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described. The reduced-order model uses kriging surrogates to account for flow nonlinearities and recurrence solutions to account for time-history effects associated with unsteadiness. The resulting surrogate-based recurrence framework generates time-domain predictions of unsteady lift, moment, and drag that accurately approximate computational fluid dynamics solutions, but at a fraction of the computational cost. Results corresponding to transonic conditions demonstrate that the surrogate-based recurrence framework can mimic computational fluid dynamics predictions of unsteady aerodynamic responses when flow nonlinearities are present. For an unsteady aerodynamic modeling problem considered in this study, an accurate reduced-order model was generated by the surrogate-based recurrence framework approach with significantly fewer computational fluid dynamics evaluations compared to results reported in the literature for a similar problem in which a proper-orthogonal-decomposition-based approach was applied. Furthermore, the results show that the surrogate-based approach can accurately model time-varying freestream Mach number effects and is therefore applicable to rotary-wing applications in addition to fixed-wing applications.
A comprehensive study on unsteady effects of oscillating Gurney flaps, or microflaps, has been conducted. Two-dimensional unsteady airloads for lift, moment, and drag due to an oscillating microflap were computed using a compressible Reynolds-averaged Navier-Stokes flow solver. The computational fluid dynamics results were generated with an overset-mesh approach that captures oscillatory microflap motion. Three microflap configurations were examined to determine the type most suitable in terms of actuation efficiency and practical implementation. Furthermore, a reduced-order model for the unsteady microflaps was developed based on computational fluid dynamics simulations, using the rational function approximation approach. The resulting rational function approximation model is a state-space time-domain aerodynamic model that accounts for unsteadiness, compressibility, and time-varying freestream effect. The agreement between the reduced-order model and direct computational fluid dynamics calculations was found to be excellent for a wide range of flow conditions examined. The approximate model is suitable for incorporation in a comprehensive code, from which the potential of microflaps for active control of vibrations in rotors can be determined. Open-loop control studies indicated that the microflap produces substantial vibration reduction (80% reduction in vertical shear), whereas closed-loop control using combined harmonic inputs consisting of a sum of four harmonics (2-5/rev) reduced the vibration objective by 92%, on a hingeless rotor configuration resembling the Messerschmitt-Bolkow-Blohm BO-105. These results confirmed the control authority and effectiveness of the microflap for vibration reduction in rotorcraft.
