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A new and efficient time-domain implementation is proposed for the impedance model originally introduced by Tam and Auriauit (Tam, C. K. W., and Auriault, L., 'Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics,' AIAA Journal, Vol. 34, No. 5, May 1996, pp. 917-923). In the frequency domain, the pressure can be calculated from the product of the impedance with the normal velocity. In the time domain, a convolution is needed, which may become a costly operation. Present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency-domain models to time-domain formulations involving time derivatives. The former approach is very costly in terms of memory and CPU time; the latter makes the implementation discretization specific and vulnerable to stability issues. A new formulation, based on recursive convolution, results in an efficient implementation that stores only one accumulator, which can be updated at each time step with minimal addition and multiplication. It allows for the exact representation of the impedance at a given frequency. The formulation is validated by a comparison with the measurement data from the NASA Langley Grazing Flow Impedance Tube. The simulations are performed by introducing a plane wave at a single frequency in the tube, and this is done for six frequencies and five different mean flow speeds.

We demonstrate how real-time holographic interferometry yielding two-dimensional fringes can be recorded and used to determine changes in three-dimensional attitude of a model airplane through digital image processing. A simple bench-top experiment with a model airplane as a test object is conducted to demonstrate interference fringes superposed on the image due to changes in attitudes (pitch, yaw, and roll) as well as distortion. A novel second-generation thermoplastic camera suitable for dynamic multiple reversible registration of thin-phase holograms using thermoplastic and semiconductor film on glass substrate is used for in situ recording and readout during real-time holographic interferometry. Thin-phase holograms also offer the advantage of exact image reconstruction from forward-phase conjugation. OCIS codes: 100.0100, 090.0090, 090.2880.

The response surface method (RSM) has currently become one of the better-known meta-modeling techniques. However, its approximation errors have placed several restrictions on designers as classical RSM uses the least-squares method (LSM) to find the best-fitting approximation models from the given function data. We discuss how to construct RS models efficiently and accurately using the moving least-squares method (MLSM) combined with sensitivity information. The formulations for incorporating the sensitivity using the MLSM are derived. With this method, several parameters should be determined during the construction of response surfaces. The parametric study and optimization for these parameters are performed. However, because of the discontinuity problem of the optimization, a genetic algorithm is adopted. The correlation coefficient is used for the normalized comparison between the function and gradient errors. Also, the reciprocal condition number is applied to avoid ill-conditioned approximations. Several difficulties and their respective solutions during the approximation processes are described, and the numerical examples are then demonstrated to verify the accuracy and the efficiency of this method. If the sensitivity of each sampling point can be calculated efficiently by utilizing a cheap computation, the proposed method is recognized as very efficient and accurate.

The flow over two-dimensional geometries is studied via unsteady numerical simulations that are three dimensional, with periodic conditions applied along the spanwise coordinate. This framework is well accepted for direct numerical simulations (DNS), large-eddy simulations, and detached-eddy simulations (DES), but is here combined with standard Reynolds-averaged Navier-Stokes (RANS) turbulence models. This strategy, which is not new, is referred to as unsteady RANS (URANS). Limited previous evidence suggested that, in URANS, three dimensionality is suppressed by high eddy-viscosity levels. However, three dimensionality proves fairly easy to sustain with adequate initial conditions, in all three cases studied here: stalled airfoil, circular cylinder, and a rounded square, except that for one case three dimensionality failed to last from random-based initial perturbations and was sustained only when using a DES field as initial condition. It is much less fine grained and chaotic than in the classical turbulence-resolving methods (from DNS to DES). Three-dimensional URANS gives clear improvements over two-dimensional URANS. It is less costly than DES, but is not as accurate. URANS also displays a troublesome sensitivity to the spanwise period and to the turbulence model. The approach is interesting and will appear spontaneously in many applications, but remains only partly understood.

Eigenpairs, contextually indicative of the frequencies and oscillatory modes of structural systems, are considered as functions of a single parameter. Undesired permutation of modal designations is noted to arise following events of transitory eigenvalue coalescence with respect to the parameter, resulting in the definition of nonsmooth functions. The tracing of eigenpairs across such events is outlined for the permanently degenerate, general eigenproblem as the general case; the cases of transitorily degenerate and distinct eigenvalues are thus accounted for. The foundation for mode tracing is the assumption of eigenvector consistency across parameter intervals, used as a means of eigenpair reconciliation. The resulting traced modes are smooth and their variations physically pertinent, which is necessary in iterative schemes in which convergence may otherwise be jeopardized. The proposal of an augmented modal assurance routine that potentially augments the assurance of tracing and, therefore, the maximum permissible parameter perturbation, is given; a threefold increase in the insight to consistency entails. The notion of the routine is to forward and backward cast eigenvectors utilizing their derivatives in affine modeling. A numerical example of the modes of a cyclic frame as functions of a cyclic distribution of membrane forces demonstrates the concepts and utility of the proposal.

Based on the analytical solution of Crouch to the problem of a constant discontinuity in displacement over a finite line segment in an infinite elastic solid, in the present paper, the crack-tip displacement discontinuity elements, which can be classified as the left and the right crack-tip elements, are presented to model the singularity of stress near a crack tip. Furthermore, the crack-tip elements together with the constant displacement discontinuity elements presented by Crouch and Startled are used to develop a numerical approach for calculating the stress intensity factors (SIFs) of general plane cracks. In the boundary element implementation, the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called the hybrid displacement discontinuity method (HDDM). Numerical examples are given and compared with the available solutions. It can be found that the numerical approach is simple, yet very. accurate for calculating the SIFs of branched cracks. As a new example, cracks emanating from a rhombus hole in an infinite plate under biaxial loads are taken into consideration. The numerical results indicate the efficiency of the present numerical approach and can reveal the effect of the biaxial load on the SIFs. In addition, the hybrid displacement discontinuity method together with the maximum circumferential stress criterion (Erdogan and Sih) becomes a very effective numerical approach for simulating the fatigue crack propagation process in plane elastic bodies under mixed-mode conditions. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the HDDM. Crack propagation is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. [DOI: 10.1115/1.1796449]

Flight-test and data analysis techniques applied to calibrate the static pressure measured by pitot static systems and the flow angles measured by a five-hole probe mounted on a noseboom are described. Dynamic maneuvers with rapid variations in the aircraft motion are analyzed by application of parameter estimation techniques based on the output error method to calibrate the angle of attack and angle of sideslip. A complementary approach based on the Kalman filter technique is applied to a wind-box maneuver to calibrate the flow variables. The tower flyby maneuvers are analyzed using the classical approach of altitude determination through geometrical evaluation of photographs, and accurate information is derived from redundant sources to calibrate the pitot static system. The investigations showed that the static pressure measured by aircraft-installed pitot static system is accurate, sufficiently whereas that measured by an additional sensor mounted on the noseboom required speed-dependent correction. The flight estimated sensitivity factors for the flow angles measured by the five-hole probe agreed reasonably well with the manufacturer's specifications subject to corrections for biases resulting from misalignment and time delays caused by the recording equipment.

The k-[omega] model is combined with the rapid distortion scheme to develop effective unsteady closures in nonequilibrium wall flows subject to oscillating shear. The phase-averaged eddy viscosity is related to the modulation of the effective strain parameter whose distribution is obtained from the steady turbulent channel flow data. New experimental data on the wall and Reynolds shear stresses are reported. The model predicts the time-mean and phase-averaged flow quantities in a satisfactory way when the imposed frequency is smaller than the median frequency of the near-wall turbulence in the relaxation regime. It is particularly successful at the wall and in the low buffer layer.