Dong-Kyun Im

Periodic Unsteady Flow Analysis Using a Diagonally Implicit Harmonic Balance Method

An implicit harmonic balance method is applied to periodic unsteady flow problems. Diagonal terms of the harmonic source vector are treated implicitly and easily implemented on a diagonalized implicit solver that is very similar to a flow solver. The multi-grid performance and solution convergence of the present implicit harmonic balance method are investigated with a 2-D oscillating airfoil and a 3-D wing with pitching motion. Computational results are compared with results from explicit trials and a dual timestepping method in the time-domain. The present harmonic balance method provides fast and stable convergence characteristics regardless of the number of harmonics. Results show that the present method can largely reduce the computing time for unsteady flow problems, compared to that necessary in the dual time-stepping and explicit harmonic balance methods.

A Preliminary Study of Open Rotor Design Using a Harmonic Balance Method

An open rotor is one of the next generation aero-engines as it has 30% higher efficiency compared to the conventional turbofan engines. However, a high level of noise loudness has been a major drawback of the open rotor for its commercial use in aviation market. Although there have been a number of efforts to reduce its noise level, an accurate prediction of unsteady and complex flow field of the open rotor makes it difficult for the design methodologies to be applied. This paper introduces one of the state-of-the-art design methodologies to handle the unsteady problem of low-noise open rotor design. A harmonic balance method which is an order of magnitude more efficient than the conventional timeaccurate CFD method is used to analyze open rotor flows. To demonstrate the accuracy of the harmonic balance method, a wind-tunnel experiment of the scaled model of the open rotor is carried out and aerodynamic performances are compared with the harmonic balance predictions. With the steady formulation of the flow governing equations through the harmonic balance method, a design method using a surrogate model is employed to find an optimum configuration that minimizes the noise level and total power at a constant thrust level. A noise prediction is computed using the Farassat formula, derived from the FfowcsWillimas Hawkings equation. Design variables of the blade radii, rotor spacing, and the pitch angle variation of the aft rotor are chosen. A parameter study to investigate the sensitivities of the design parameters to thrust and torque/power levels as well as to the noise loudness is carried out. A genetic algorithm to handle multi-objectives is used in combination with the surrogate model of Kriging response surface. An optimum configuration is obtained from the pareto front of the optimization results and shows the reduction of noise level by 7dB and power level by 4% from the baseline values.

Design of a Low-Noise Open Rotor Using an Implicit Harmonic Balance Method

A coaxial contra-rotating open rotor belongs to the next generation of aero-engines. It has an efficiency that is about 30% higher than that of a conventional turbojet engine. However, because of the high noise level, the open rotor has not been introduced into the commercial aviation market. Although there have been numerous efforts to reduce its noise level, the need to accurately predict the unsteady and complex flow field around the open rotor makes it difficult to apply the conventional design methodologies. In this paper, we introduce a state-of-the-art design methodology for solving the unsteady flow field problem of the lownoise open rotor design. A harmonic balance method that is an order of magnitude more efficient than the conventional time accurate CFD method is used to predict the aerodynamic performance of the open rotor. With the accurate formulation of the governing equations through the harmonic balance method, a design method that uses a surrogate model is employed to find optimum configuration that minimizes the noise level and total power at a constant thrust level. A noise prediction is made using the Farassat formula, derived from the Ffowcs-Williams-Hawking’s equation. To efficiently search for the optimum configuration, the design optimization is divided into the rotor topology design level and blade planform design level. In a previous study, we investigated the optimum rotor topology parameters such as the blade radii, rotor spacing, and pitch angle of the aft rotor. In this paper, an investigation is conducted to determine the optimum planform variables such as the twist angle, chord length for several design sections, and tip shape control parameters for the aft rotor. A genetic algorithm is used as a multi-objective optimization algorithm in combination with the Kriging surrogate model. Through the planform design for the aft rotor, the noise level and power consumption of the optimum rotor are reduced by 0.6 dB and 6.8% respectively.

2-D Periodic Unsteady Flow Analysis Using a Partially Implicit Harmonic Balance Method

An efficient solution method for harmonic balance techniques with Fourier transform is presented for periodic unsteady flow problems. The present partially-implicit harmonic balance treats the flux terms implicitly and the harmonic source term is solved explicitly. The convergence of the partially Implicit method is much faster than the explicit Runge-Kutta harmonic balance method. The method does not need to compute the additional flux Jacobian matrix from the implicit harmonic source term. Compared with fully implicit harmonic balance method, this partial approach turns out to have good convergence property. Oscillating flows over NACA0012 airfoil are considered to verify the method and to compare with results of explicit R-K(Runge-Kutta) and dual time stepping methods.

Efficient Aerodynamic Computation of a Wing Model Considering Body Effect for the Aeroelastic Application

The typical aeroelastic analysis for a complex configuration such as a complete aircraft was done using the aerodynamic results of the wing and the structural modes of a complete aircraft; that is, the aerodynamics of a wing of a complete aircraft is assumed to be not much influenced by the body shape. Nevertheless, the body shape can cause a distortion of aerodynamic pressure on the wing surface and it is necessary to investigate the body effect in flutter analysis. In this reseasrch, MGM inverse design method is applied to include the body effect of a wing-body model which disturbs the pressure distribution on the wing surface.

Gradient Based Optimization using Spectral Formulation-Based FSI and Coupled Sensitivity Analysis

In this study, gradient based optimization using efficient computational methods for fluid-structure interaction and corresponding coupled sensitivity analysis. Considering that many dynamic aeroelatic problems are periodic in nature, a spectral based formulation has been used to solve them. A harmonic balance method (HBM) is used for computational fluid dynamics and modal analysis based reduced order model is employed for computational structural dynamics. One of the advantages of the spectral based formulation is the computational efficiency obtained by eliminating transient flow solutions to reach a periodic steady state, through the solution approximation of a discrete Fourier series. Hence, dynamic aeroelastic problems are solved by the solution methods for the static aeroelastic problems. The spectral form of the governing equation also facilitate the application of the steady form of adjoint sensitivity analysis for the dynamically coupled system. Hence, the high memory and computational time required for unsteady adjoint sensitivity analysis are avoided in the current study by directly using the steady adjoint formulation. Using the adjoint sensitivity analysis formulation, the shape sensitivity of the AGARD 445.6 wing has been computed and has been validated by comparing with FDM based results. The wing surface has been parameterized using the amplitude of Hicks-Henne functions on the wing surface as the design parameters.

Aerodynamic Analysis of Rotor Blades using Overset Grid with Parallel Computation

The helicopter aerodynamics is simulated in hovering and forwarding flight using the unsteady Euler equations. As the steady condition, flight test of DLR-F6 and hovering flight test data of Caradonna & Tung’s rotor blades were used, and as the unsteady condition, non-lift forwarding flight test data of the rotor blades were used. The parallelized numerical solver was validated with the two of data above. By using this solver, AH-1G rotor blades to forwarding flight numerical test were conducted. In the test of forwarding flight, the numerical trim was applied to decide cyclic pitching angles using the Newton-Raphson method, and the results were good well match to the experimental data, Especially, the BVI effects were well simulated in advancing side in comparison with other numerical results. To consider the blade motion and moving effects, an overset grid technique is applied and for the boundary, Riemann invariants condition is used for inflow and outflow.

Unsteady Aerodynamic Analysis for Helicopter Rotor in Hovering and Forward Flight Using Overlapped Grid

In this paper, the helicopter aerodynamics is simulated in hovering and forward flight. Also, an overlapped grid technique is applied in this simulation to consider the blade motion and moving effects. The Caradonna & Tung`s rotor blade was selected to analyze the unsteady aerodynamics in hovering and non-lift forward flight. Also, the AH-1G rotor blade was selected in forward flight. In forward flight case, the numerical trim was applied to determine the cyclic pitching angles using Newton-Raphson method, and the numerical results were in good agreement with experimental data, especially, the BVI effects were well simulated in advancing side in comparison other numerical results. The governing equation is a three dimensional unsteady Euler equation, and the Riemann invariants condition is used for inflow and outflow at the boundary.

Spectral Formulation-Based FSI and Coupled Sensitivity Analysis for Dyanmic Aeroelastic Problems

Efficient computational methods for fluid-structure interaction and corresponding coupled sensitivity analysis based on spectral formulation are introduced to solve dynamic aeroelastic problems. A time-spectral method is used for computational fluid dynamics and a modal analysis based finite element method is employed for computational structural dynamics. One of the advantages is computational efficiency by eliminating transient flow solutions to reach a periodic steady state, through the solution approximation of a discrete Fourier series. Through the spectral formulation of the FSI problems, dynamic aeroelastic problems are solved by the solution methods for the static aeroelastic problems. The biggest advantage is the availability of the steady form of the adjoint sensitivity analysis for the dynamically coupled system. Computational time and memory requirement for the unsteady adjoint sensitivity analysis are avoided in the current study by directly using the steady adjoint formulation in the spectral form of the governing equations of both fluids and structures. In this study, a practical threedimensional problem of wing flutter is be solved to show the validity of the proposed coupled-sensitivity analysis method in terms of solution accuracy and computational efficiency as well as optimality achieved for the design cases.

THE WING-BODY AEROELASTIC ANALYSES USING THE INVERSE DESIGN METHOD

Flutter phenomenon is one of the most dangerous problems in aeroelasticity. When it occurs, the aircraft structure can fail in a few second. In recent aeroelastic research, computational fluid dynamics (CFD) techniques become important means to predict the aeroelastic unstable responses accurately. Among various flow equations like Navier-Stokes, Euler, full potential and so forth, the transonic small disturbance (TSD) theory is widely recognized as one of the most efficient theories. However, the small disturbance assumption limits the applicable range of the TSD theory to the thin wings. For a missile which usually has small aspect ratio wings, the influence of body aerodynamics on the wing surface may be significant. Thus, the flutter stability including the body effect should be verified. In this research an inverse design method is used to complement the aerodynamic deficiency derived from the fuselage. MGM (modified Garabedian-McFadden) inverse design method is used to optimize the aerodynamic field of a full aircraft model. Furthermore, the present TSD aeroelastic analyses do not require the grid regeneration process. The MGM inverse design method converges faster than other conventional aerodynamic theories. Consequently, the inverse designed aeroelastic analyses show that the flutter stability has been lowered by the body effect.