NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS

Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.

Panel/full-span free-wake coupled method for unsteady aerodynamics of helicopter rotor blade

A full-span free-wake method is coupled with an unsteady panel method to accurately predict the unsteady aerodynamics of helicopter rotor blades in hover and forward flight. The unsteady potential-based panel method is used to consider aerodynamics of finite thickness multi-bladed rotors, and the full-span free-wake method is applied to simulating dynamics of rotor wake. These methods are tightly coupled through trailing-edge Kutta condition and by converting doublet-wake panels to full-span vortex filaments. A velocity-field integration technique is also adopted to overcome singularity problem during the interaction between the rotor wake and blades. Helicopter rotors including Caradonna–Tung, UH-60A, and AH-1G rotors, are simulated in hover and forward flight to validate the accuracy of this approach. The predicted aerodynamic loads of rotor blades agree well with available measured data and computational fluid dynamics （CFD） results, and the unsteady dynamics of rotor wake is also well simulated. Compared to CFD, the present method obtains accurate results more efficiently and is suitable to rotorcraft aeroelastic analysis.

Trajectory and attitude deviations for internal store separation due to unsteady and quasi-steady test method

The deviations of trajectory and attitude angle for internal store separation are evaluated by two wind tunnel test methods.One is the Freedrop Test(FDT),which is known as unsteady and time-dependent method of scaled model.The other is the Captive Trajectory System(CTS)test,which is usually regarded as a quasi-steady and time-averaged test technology.The result shows that there is a streamwise adverse pressure gradient on the cavity resulting in a nose-up pitching moment coefficient(>0)acting on the store model.When the initial pitch angular velocity is 0,the store exits the shear-layer with a nose-up pitch attitude causing the store to climb back towards and collide with the aircraft.However,the store passes through the shear-layer into the freestream with a nose-down pitch,which causes a successful separation event when the initial pitch angular velocity<0.The pitch angle obtained by unsteady test method is different from that by quasisteady test method.The time-dependent test includes the aerodynamic force induced by pitch angular velocity whereas the time-averaged method(CTS)cannot reflect the effect of unsteady aerodynamic force.The deviation of vertical displacement is not obvious for FDT and CTS test since the store has an initial vertical velocity,which is dominant for the vertical displacement.This means that the highly unsteady flow can create unpredictability in aerodynamic pitching moment of the store,which can lead to the deviation of pitch angle for internal store separation.

FOURIER-LEGENDRE SPECTRAL METHOD FOR THE UNSTEADY NAVIER-STOKES EQUATIONS

Fourier-Legendre spectral approximation for the unsteady Navier-Stokes equations is analyzed. The generalized stability and convergence are proved respectively.

Acceleration of unsteady vortex lattice method via dipole panel fast multipole method

The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).

Experimental and numerical investigation on sound generation from airfoil-flow interaction

Aerodynamic noise due to interaction between incoming turbulence and rotating blades is an important component in the wind turbine noise. The rod-airfoil configuration is used to investigate the interactive phenomenon experimentally and nu- merically. Distribution of unsteady pressure on the airfoil surface is measured for different rod positions and airfoil attack angles. Two National Advisory Committee for Aeronatics （NACA） airfoils, NACA0012 and NACA0018, and two wind turbine airfoils, S809 and S825 are investigated. In addition, for low angles of attack, the flow field around the airfoil＇s leading edge is investigated with the particle image velocimetry （PIV）. The experimental results indicate that unsteady pressure disturbances on the airfoil surface are related to the rod vortex shedding. Meanwhile, the interaction flow field of the rod and NACA0012 airfoil is simulated with the unsteady Reynolds averaged Navier-Stokes method （URANS）, and the obtained pressure spectra are compared with the experimental results.

High-order implicit discontinuous Galerkin schemes for unsteady compressible Navier–Stokes equations

Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.

Transient aeroelastic responses and flutter analysis of a variable-span wing during the morphing process

To investigate the transient aeroelastic responses and flutter characteristics of a variablespan wing during the morphing process,a novel frst-order state-space aeroelastic model is proposed.The time-varying structural model of the morphing wing is established based on the Euler-Bernoulli beam theory with time-dependent boundary conditions.A nondimensionalization method is used to translate the time-dependent boundary conditions to be time-independent.The time-domain aerodynamic forces are calculated by the reduced-order unsteady vortex lattice method.The morphing parameters,i.e.,wing span length and morphing speed,are of particular interest for understanding the fundamental aeroelastic behavior of variable-span wings.A test case is proposed and numerical results indicate that the flutter characteristics are sensitive to both of the two morphing parameters.It could be noticed that the aeroelastic characteristics during the wing extracting process are more serious than those during the extending process at the same morphing speed by transient aeroelastic response analysis.In addition,a faster morphing process can get better aeroelastic performance while the mechanism comlexity will arise.

NUMERICAL SIMULATIONS OF A CENTERED CONDUCTING BODY ON NATURAL CONVECTION AND HEAT TRANSFER IN AN ENCLOSURE

Numerical simulations are performed for laminar natural convection heat transfer from a centered conducting body enclosed in a square cavity. A high accuracy un steady numerical method is used, combining the unique condition of the pressure, the convergent solutions and the streamfunction value of the inside heat conducting body are given simultaneously. Two examples are simulated with this numerical method and compared with the experimental results. The results of the numerical solutions are consistent with the experimental results. It shows that the numerical method is valid and feasible.

On the hydrodynamics of hydraulic machinery and flow control

Hydraulic machinery mainly includes turbine and pump, which is closely related to national economy and people＇s livelihood involving aerospace industry, marine engineering, hydropower engineering, petroleum industry, chemical industry, mining industry, biomedical engineering, environmental engineering, agricultural water-soil engineering, etc.. The internal flow of hydraulic machinery is extremely complex, and its characteristics can be summarized as high Reynolds number, multi-scales, inhomogeneous and vortex-dominant unsteady turbulence which interact with the rotating dynamic boundary（rotor blade）. Based on the analysis of the internal flow characteristics of hydraulic machinery, the author and his research team successively proposed a rotation correction model, a curvature corrected filter-based model, a scalable detached eddy simulation method, and a non-linear hybrid RANS/LES turbulence model to capture unsteady flow structures and then predict hydraulic performance and dynamic characteristics more accurately. According to the analysis on the internal flow, the corresponding flow control measures were put forward. It was verified by experiments that these methods could significantly improve the hydraulic performance, anti-cavitation performance and dynamic characteristics（pressure pulsation and vibration） of hydraulic machinery in a certain range of operating conditions. In addition, the mechanism how flow control measures influence internal flow was analyzed in depth, aiming at finding a feasible and effective way to improve hydraulic performance, anti-cavitation performance and dynamic characteristics of hydraulic machinery.