Transonic Code Research Articles

Transonic separated solutions for an augmentor wing

The viscous transonic flow about a multielement airfoil (augmentor-wing) is simulated by coupling full-potential and direct/inverse differential boundary-layer algorithms. Solutions have been obtained for a variety of conditions and are in fair agreement with available experimental data. Typical results from this transonic augmentor-wing code (TAUG-V) require approximately three minutes of CRAY-XMP CPU time. Since this viscous transonic code accounts for most of the important flow physics, yet is still economical, it is a practical tool for the design aerodynamicist.

Transonic time responses of the MBB A-3 supercritical airfoil including active controls

Aeroelastic time-response analyses are performed for the MBB A-3 supercritical airfoil in small-disturbance transonic flow based on the use of transonic code LTRAN2-NLR. Three degrees of freedom are considered: plunge, pitch, and aileron pitch. The main objective was to investigate the applicability and accuracy of statespace aeroelastic modeling for two-dimensional airfoils with active controls in transonic flow. A state-space aeroelastic model was formulated using a Fade aerodynamic approximation. The resulting equations are explicitly solved in the time domain yielding the aeroelastic displacement responses. Parallel time-marching response histories were determined numerically through a coupled integration of the structural equations of motion with the unsteady aerodynamic forces of LTRAN2-NLR. The Fade and time-integration responses are in good agreement. The Fade eigenvalues compare well with the time-marching damping and frequency estimates. A simple feedback control loop was included in the aeroelastic system to study the effects of active control on the aeroelastic response. A variety of control laws utilizing displacement, velocity, and acceleration sensing were considered. Transonic time-response behavior of the MBB A-3 airfoil is discussed and comparisons are made. b,c ce CQ ^ Cp,C*p [C] { G } h KA,KD,KV [K] m M [M] p {p }

Application of transonic codes to aeroelastic modeling of airfoils including active controls

A study is performed using aeroelastic modeling to investigate the stability behavior of airfoils in small-disturbance transonic flow. Two conventional airfoils, NACA 64.A006 and NACA 64A010, and a supercritical airfoil, MBB A-3, are considered. Three sets of unsteady aerodynamic data are computed using three different transonic codes (LTRAN2-NLR, LTRAN2-HI, and USTS) for comparison purposes. Stability results obtained using a constant matrix, state-space, aeroelastic model are presented in a root-locus format. Use of the state-space model is demonstrated through application to flutter suppression using active controls. Aeroelastic effects due to simple, constant gain, partial feedback, control laws that utilize displacement, velocity, and acceleration sensing are studied using a variety of control gains. Calculations are also performed using linear subsonic aerodynamic theory to reveal the differences between including and not including transonic effects in the aeroelastic model. Aeroelastic stability behavior of these airfoils is physically interpreted and discussed in detail.

A Fast Viscous Correction Method for Unsteady Transonic Flow About Airfoils

This study modified the inviscid, small-disturbances, unsteady, transonic code, LTRAN2, so that the viscous effect could be considered for the purpose of improving the code's accuracy without substantially increasing the computational time. By using a conventional integral boundary layer method to determine the displacement thickness and an empirical model of viscous wedge to simulate the suddenly thickened boundary layer behind a shock, it resulted in better agreement with experimental data for both the shock position and the pressure coefficient. Aerodynamic performances were calculated for two supercritical airfoils. When the unsteady procedure was used to obtain steady state results as the initial condition, the unsteady viscous solution for the RAE 2822 airfoil required 100.5% of the computational time of the inviscid solution. When an iterative scheme was used to obtain the steady state results as the initial condition, the unsteady viscous solution for the NLR 7301 airfoil required 88% of the computational time of the inviscid solution.

Transonic time-response analysis of 3-degree-of-freedom conventionaland supercritical airfoils

Aeroelastic time-response analyses are performed for two conventional airfoils, NACA 64A006 and NACA 64A010, and one supercritical airfoil, MBB A-3, in small-disturbance transonic flow. Response results for forces and displacements were obtained by simultaneousl y integrating the structural equations of motion with the unsteady aerodynamic forces computed using two transonic codes: LTRAN2-NLR and USTS. Three-degreesof-freedom—plunge, pitch, and aileron pitch—are considered. Flutter analyses are first performed, with the results used as a guideline for time-response parameter selection. Time-response results are presented showing that for each case the flight speed used to obtain neutrally stable responses is either exactly or nearly the same as the flutter speed determined in the separate flutter analysis. Effect of response amplitudes is investigated. Applicability and limitations of the two transonic codes are evaluated, compared, and discussed. Transonic time-response behavior of these airfoils is physically interpreted and discussed, and comparisons are made.

Transonic flutter and response analyses of two 3-degree-of-freedom airfoils

Flutter and time-response analyses are performed for a NACA 64A006 conventional and a MBB A-3 supercritical airfoil, both oscillating with plunge, pitch, and aileron pitch degrees-of-freedom (DOF's) in smalldisturbance transonic flow. The aerodynamic coefficients are calculated using the transonic code LTRAN2NLR. The effects of various kinds of aeroelastic parameters on flutter speeds for the bending-torsion, bendingaileron, and torsion-aileron branches are studied. The flutter speeds associated with the bending-torsion branch are plotted against Mach number for different parameter values and the transonic dip phenomenon is demonstrated. To study the flutter modes, the flutter speed, amplitude ratio, and phase difference at different Mach numbers are plotted against the mass ratio for both a 2DOF and a 3DOF case. Time-response results are obtained for the NACA 64A006 and the MBB A-3 airfoils at M=Q.85 and 0.765, respectively. Based on the same sets of parameter values, the flight speeds used to obtain all the neutrally stable responses are very close to the flutter speeds obtained in the flutter analysis. The principle of linear superposition of airloads is used in the flutter analysis, but not in the response analysis.

Application of Transonic Codes to Flutter Analysis of Conventional and Supercritical Airfoils

Transonic flutter analyses are performed for two conventional airfoils, NACA 64A006 and NACA 64A010, and three supercritical airfoils, MBB A-3, CAST 7, and the NASA TF-8A wing section at 65.3% semispan. Two degrees of freedom, plunging and pitching about the quarter-chord axis, are considered. The aerodynamic data are obtained by using the two transonic aerodynamics codes LTRAN2 (indicial and time integration methods) and STRANS2/UTRANS2 (harmonic analysis method). The unsteady aerodynamic data are computed within the low reduced frequency range. For all airfoils, the effect of Mach number on flutter speed is studied for several values of four different aeroelastic parameters. For the MBB A-3 supercritical airfoil, the effect of angle of attack on flutter speed is studied. For the cases of a flat plate and a NACA 64A006 airfoil, time response results are obtained by LTRAN2. Applicability and limitations of the two transonic codes are evaluated. Results for the transonic flutter characteristics of these airfoils are discussed and some comparisons are made. ah b,c

Alternating-Direction Implicit Algorithm for Unsteady Potential Flow

Art implicit finite-difference scheme is presented for the efficient computation of unsteady potential flow about airfoils. The formulation uses density and the velocity potential as dependent variables and is cast in conservation form to assure the theoretically correct determination of shockwave location and speed. To enable boundary conditions to be imposed directly on the airfoil surface, a time-varying sheared-rectilinear coordinate transformation is employed. Calculated time-history solutions on a pulsating airfoil are compared with the results of other unsteady transonic codes, including a previous method of the authors. The present method is demonstrated to be unconditionally stable and to give accurate solutions with sharply resolved shocks.

Aeroelastic time response analysis of thin airfoils by transonic code LTRAN2

A computer based numerical procedure is used to perform aeroelastic time response analysis of thin airfoils oscillating with single and two d.o.f.'s in two-dimensional, unsteady, low-frequency, small-disturbance, transonic potential flow. A computational transonic code LTRAN2 based on fully implicit time integration scheme is employed to obtain the aerodynamic forces. Structural equations of motion and the aerodynamic equations are integrated simultaneously by a numerical method. Results are first obtained for a time response example for a flat plate oscillating at M ∞ = 0.7 with (1) a single pitching d.o.f.; (2) a single plunging d.o.f.; and (3) two d.o.f.s—plunging and pitching. A parallel set of results are also obtained based on subsonic aerodynamic theory for comparison. The agreement is good. Results are then obtained for a time response example for a NACA 64A006 airfoil pitching and plunging at M ∞ = 0.85 which was found to give the lowest flutter speed for the case considered. The parameters that result in neutrally stable response agree with those found in a separate flutter analysis. It was found through comparison between flutter results and response analysis that the principle of superposition of airloads is valid for the present example cases. The results also include the effect of altitude on aeroelastic response.

Evaluation of Three-Dimensional Transonic Codes Using New Correlation-Tailored Test Data

A comprehensive research program was conducted for the specific purpose of acquiring benchmark test data suitable for evaluations of three-dimensional transonic codes. High-quality data were obtained for three advanced technology wings by using a unique test apparatus and by devoting careful attention to details of the experiment. The test apparatus included provisions for removal of the wind tunnel boundary layer and measurements of far-field pressures. The test data were used in preliminary evaluations of three selected transonic computational methods. For these limited evaluations, nonconservative formulations more closely predicted measured pressures than conservative formulations. In addition, full potential solutions were found to be uniformly in better agreement with experiment than small disturbance results.

Flutter analysis of a NACA 64A006 airfoil in small disturbance transonic flow

Flutter analyses are performed for a NACA 64A006 airfoil pitching and plunging in small-disturbance, unsteady transonic flow. Aerodynamic coefficients are obtained for M^ = 0.7, 0.8, 0.85, 0.8625, and 0.87, and for various values of low reduced frequencies. Two computer codes are used: 1) STRANS2 and UTRANS2 based upon the relaxation method and 2) LTRAN2 based upon the time-integration (indicial) method. Flutter results are presented as plots of flutter speed and corresponding reduced frequency vs one of the four parameters: airfoil/air mass density ratio, position of mass center, position of elastic axis, and freestream Mach number. In each figure, several sets of curves for different values of plunge/pitch frequency ratios are shown. The two sets of results based upon the two separate computer codes are, in general, in good agreement. For a special flutter analysis of a flat plate at M^ =0.7, the present methods agree well with the linear flat plate theory. The effect of each parameter on the trend of each curve of flutter speed is discussed in detail. The examples demonstrate the dip phenomenon of the curves for flutter speed in the transonic regime. Flutter results of transonic codes are compared with those obtained by linear flat plate theory.