Viscous Solutions for Transonic Oscillating Cascade Flows Using Dynamic Quadrilateral-Triangular Meshes

A locally implicit scheme with an anisotropic dissipation model is developed on dynamic quadrilateral-triangular meshes. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low-Reynolds-number k − ϵ turbulence model are solved to study turbulent flows over vibrating blades with negative interblade phase angle. A treatment of viscous flux on quadrilateral-triangular mesh is also presented. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, the turbulent flow around an NACA 0012 airfoil is investigated. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which includes the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady flow behaviors for turbulent flows over vibrating blades with negative interblade phase angle are demonstrated.

A time domain numerical approach is carried out to enhance the understanding of three dimensional blade row aeroelastic characteristics under the parallel computation. The vibration energy of unsteady aerodynamic force on the entire blade row is investigated using numerical solution of 3-D Navier-Stokes equations, coupled with structure finite element models for the blades to identify modal shapes and the structural deformations simultaneously. Interactions between fluid and structure are dealt with in a coupled manner, based on the interface information exchange until convergence in each time step. With this approach good agreement between the numerical results and the experimental data is observed. The flutter mechanism is analyzed according to deformation of the blades. The effect of inter-blade phase angle (IBPA) is included in the analysis by releasing the hypothesis of constant phase angle between adjacent blades in the traveling wave model. The results illustrate fully three dimensional unsteady nonlinear behaviors, such as limit-cycle oscillation. It is shown that all blades flutter at the same mode and frequency, but not at the same amplitude and IBPA. The analysis of the influence of different tip clearance gaps on the flutter characteristics of the blade row is also performed.

For the two-dimensional steady and unsteady turbine cascade flows, the Euler/Navier-Stokes equations with Baldwin-Lomax turbulence model are solved in the Cartesian coordinate system. A locally implicit hybrid algorithm on the mixed type of meshes is employed, where the convective dominated part in the flowfield is studied by TVD scheme to obtain high-resolution results on the triangular elements, and the second- and fourth-order dissipative model is introduced on the O-typed quadrilateral grid in the viscous dominated region to minimize the numerical dissipation. When the steady subsonic and transonic turbulent flows are investigated, the distributions of isentropic Mach number on the blade surface, exit flow angle and loss coefficient are obtained. Comparing the present results with the experimental data, the accuracy and reliability of the current approach is confirmed. By giving a moving wake-type total pressure profile at the inlet plane in the rotor-relative frame of reference, the unsteady transonic inviscid and turbulent flows calculations are performed to understand the interaction of the upstream wake with a moving blade row. The Mach number contours, perturbation component of the unsteady velocity vectors, shear stress and pressure distributions on the blade surface are presented. The physical phenomena, which include periodical flow separation on the suction side, bowing, chopping and distortion of incoming wake, negative jet, convection of the vortices and wake segments, and vortex shedding at the trailing edge, are observed. It is concluded that the unsteady aerodynamic behaviors are strongly dependent on the wake/shock/boundary layer interactions.

A preliminary inviscid version of the NASA LeRC/Mississippi State University 3-D aeroelastic computational fluid dynamics code, TURBO-AE, is evaluated using operating conditions from three test cases from an AlliedSignal Engines (AE) advanced technology integrally bladed fan rotor. Two of the cases corresponded to conditions where high op-line flutter vibrations were observed, and the third case was flutter-free during testing. TURBO-AE steady (no blade vibration) computations were performed for each test case and a reasonable match was found with the steady 3-D viscous code DAWES. Following completion of the steady computations, TURBO-AE flutter (blade vibration) analyses were completed by harmonically oscillating the airfoil with mode shapes computed by the structural finite-element code ANSYS. Aerodynamic work per vibration cycle and modal damping was computed by TURBO-AE at 0° and 180° Inter Blade Phase Angles (IBPA). For IBPA = 0°, TURBO-AE predicted aerodynamic damping to be low but positive. Further, for IBPA = 180°, the TURBO-AE predictions indicate a very high level of aerodynamic damping. Flutter was observed on the rotor only for IBPA = 32.7°, and TURBO-AE analyses are in process for this condition. Unsteady pressure perturbation contour plots are presented to aid in the visualization of the TURBOAE flow solution. Results presented in this paper indicate that, although TURBO-AE still requires significant development, it is making the difficult transition from a research code to a flutter and forced-response prediction tool for the U.S. aeropropulsion community.

Effect of oscillation amplitude on velocity distributions in an oscillatory baffled column (OBC)

Experimental investigations of the aerodynamic damping of compressor blades are usually performed by forcing the blades externally to a motion that is similar to a given mode shape and inter-blade phase angle (IBPA) while measuring the motion-induced unsteady pressure distribution. Evaluating this to an aerodynamic work entry from the fluid to the blade, at least a local contribution to the flutter (in-)stability can be determined. Test rigs are usually non-rotating linear or rotating annular cascade wind tunnels. In the latter case, besides measuring in and transmitting data out of the rotating system, the excitation of the blades themselves is still a challenge. In the present case a blisk rotor with realistic fan blade geometries and flow conditions was investigated aeroelastically. For the excitation of the 1st bending (1F) mode shape of the blading a sector of five blades was chosen. In this sector the natural vibration of the blading, represented by constant vibration amplitudes and a given IBPA should be simulated. Therefore the blades were equipped with Macro Fiber Composites (MFC). These foils of piezoelectric material expand and contract due to the applied high voltage. A control system was developed to adjust the amplitude and the IBPA of the blade vibration. For the transmission of the high voltage, a separate data transmission system on the base of liquid metals was chosen. The blade vibration was measured by strain gauges and additionally monitored by a specific rig system. The aeroelastic investigations were carried out in the compressor test facility M2VP of the DLR Institute of Propulsion Technology in Cologne. During the measurement, the MFCs were able to excite the blades to a certain extent. The paper will present the technique to excite the blades of a compressor blisk by means of MFCs as well as achieved vibration amplitudes and limitations under engine-like operating conditions.

Results of computing the aerodynamic stability limit for basic modes on supersonic turbines for LOX and LH2 turbo pumps in open cycles are presented and discussed. It is shown that it will be virtually impossible to design blades for supersonic turbines that satisfy the criterion that all modes be aerodynamically stable. An engineering approach based on total damping is subsequently suggested using a characteristic aerodynamic damping that can be used for modes that are aerodynamically unstable. Nomenclature c – chord Cw- aerodynamic work coefficient f – frequency IBPA- Inter blade phase angle k – reduced frequency L – blade span m – modal mass n- number of blades of the blade row ND- Nodal diameter P0 – inlet total pressure Uaero – aerodynamic work Ustruct Vrel - inlet relative flow velocity δ - vibration amplitude ω - circular frequency

In this study, laser oscillation welding was utilized to offer an effective solution for the joint welding of heat-treatment-free die-cast aluminum alloys, which expands the practical applications of automotive structural parts and heat sinks for electronic devices. The effects of oscillation amplitude on the macro-morphology, microstructure, and properties of the alloy weld were examined, and a molten pool flow model was developed to compare the behavior of the molten pool with and without oscillation. The results show that increasing the oscillation amplitude eliminates the coarse Al15(Fe,Mn)3Si2 phase, resulting in a finer and more uniform distribution of the eutectic Si and Mg2Si phases. At an oscillation amplitude of 7 mm, the maximum tensile shear load and displacement were 2761 N and 1.17 mm, respectively. Laser oscillation was found to enhance the fluidity of the molten pool, reduce porosity, improve weld quality, and effectively decrease cracks and inhomogeneous grain distribution. These findings provide a research basis for optimizing the laser oscillation welding process and for the practical welding of fabricated devices.

This paper describes the development of the source-doublet-based potential paneling method for oscillating cascade unsteady aerodynamic load predictions. By using the integral influence coefficient method and by using the interblade phase angles, the unsteady loads on an oscillating cascade can be accurately predicted at a minimum cost. As the grids are placed only on the blade surfaces, the blades are allowed to vibrate without grid deformation problems. Four notable subsonic oscillating cascade test cases that cover most important parameters, e.g., blade geometry, interblade phase angle, flow coefficient, flow speed, frequency, etc., are studied in this paper. The agreement between the present solutions and other numerical/experimental results demonstrates the robustness of the present model. Applicability of the method for realistic compressible flow cascades is also discussed.

A spectral-Tchebychev solution for three-dimensional dynamics of curved beams under mixed boundary conditions

Effects of oscillation amplitude on aerodynamic derivatives

Sleep regularity is associated with sleep-wake and circadian timing, and mediates daytime function in Delayed Sleep-Wake Phase Disorder

ABSTRACTA mathematical model was used to examine the effect of Pliocene and Quaternary changes in sea level on the development of tectonically active and inactive rock coasts. The model calculated rates of mechanical wave erosion according to such factors as the deep water wave regime, bottom topography and surface roughness, and the resistance of the rocks. Subaerial terraces were truncated or eliminated by subsequent terrace formation at lower elevations, especially on steeply sloping landmasses experiencing slow rates of uplift. Submarine terraces formed during glacial stillstands were best preserved when rapid subsidence quickly carried them below the level of wave action. On slowly subsiding landmasses, submarine terraces formed during interglacials and glacial periods experienced repeated erosional modification during subsequent periods of rising and falling sea level and were generally less distinctive. On rapidly rising or subsiding (>5 mm yr‐1) landmasses, terraces that formed during interglacial stages alternated, above and below present sea level, with terraces formed during glacial stages. Despite some differences in terrace occurrence and elevational distribution, it may be difficult to distinguish profiles cut during accelerating or decelerating uplift. The amount of erosion during sea level oscillations increases with oscillation amplitude and the larger oscillations in the middle to late Quaternary were therefore more conducive to erosion than the smaller oscillations of the Pliocene and early Quaternary. The effect of oscillation amplitude may have been countered during the earlier stages of profile development, however, by steeper submarine gradients and reduced rates of wave attenuation. Copyright © 2014 John Wiley & Sons, Ltd.

Thermomechanical fatigue behavior and lifetime modeling of powder metallurgy superalloy considering phase angle effect

Unstarted supersonic flutter in a cascade is characterized by the existence of a detached bow shock wave ahead of each airfoil. To study the influence of the bow shock wave on this flutter, analysis is performed on the corresponding flow field, with use of the semiactuator disk theory. We investigate oscillation in the bending mode with the interblade phase angle, considering the effect of reflection of the pressure wave and production of a vorticity wave and an entropy wave by the bow shock wave. The results show that the existence of detached bow shock waves greatly destabilizes bending oscillation, and the flutter boundary drastically extends to a high-frequency region.