Numerical Simulation Of Fan Noise Propagation In A Turbofan Engine Inlet By DRP Methods

Computational aeroacoustics (CAA), which is essentially different from computational fluid dynamics (CFD), is a subject to study noise radiated from an aeroacoustic source or the propagation of sound waves in a flow field. CAA has already been used extensively to study the fundamental aspects of noise generation and propagation in a number of practical problems like jets, cavities, fans, airframes and ducts and to study the properties of sound absorbing structures. Aircraft noise is usually divided into two categories:one is airframe noise and the other is noise radiated from the power plant. Since the high-bypass-ration turbofan engine came into service, noise radiated from the fan has become the major noise source. Due to the variety and complexity of the mechanisms involved in fan noise, the problem is often tackled by dividing it into a noise generation problem and a propagation problem. The propagation of noise at a jet engine inlet is studied by high-accuracy dispersion-relation-preserving (DRP) schemes in this dissertation.The complex geometries of the casing and spinner in the physical plane are mapped into parallel lines in the computational plane by a conformal mapping method. Cartesian grids are meshed in computational plane and then transformed into the physical plane inversely by Newton's iteration method. During the meshing, apart from taking the efficiency and parallel computing into consideration, many state-of-the-art technologies such as multi-block and overset grids are used. The time step is evaluated by a frozen analysis. Numerical damping is needed to suppress the spurious waves of the computation, and the metod to add numberical damping in the computation in curvilinear coordinates is presented.During the computation, interpolation is inevitably needed and the 2-N point interpolation is formulated. The interpolation formulas should have the characteristics of DRP when DRP schemes are used to discretize the partial differential equation (PDE) and they can be optimized by minimizing the global error in the low wave number range. Furthermore, there should be no interpolation error if the function to be interpolated is a constant. So the optimization is reduced to the problem of finding the minimum with one constraint, and it is readily solved by theLagrange multiplier method. The optimized interpolation formulas are more accurate than the Lagrange ones in the range of low wave numbers.The methods to optimize DRP compact finite difference schemes and filtering schemes are presented. Through Fourier analyzing, the optimization object is reduced to a problem of finding the minimum of a nonlinear multi-variable function with multi-constraint. The advanced sequential quadratic programming (SQP) method is employed to find the minimum. In order to obtain high accuracy and resolution, three strategies are applied. The asymptotical stability of the optimized DRP compact finite-difference-scheme is proved through the theoretical analysis. A modified Gaussian function is introduced to obtain the sharp cutoff spectrum of the pentadiagonal filters. The accuracy, stability and efficiency of computation are improved in the optimized filters. The impoved performances of the optimized are demonstrated by two one-dimensional examples.The transform coefficient of the perfectly matched layer (PML) is deduced from the characteristics of the wave equation, and the PML for the full Euler equation in both Cartesian and cylindrical coordinates are presented. It is also proved that PML of linearized Euler equation is just a special case of that of the full Euler equation.The dispersion relation of acoustics in an annular duct with uniform mean flow is derived from the linearized Euler equation, and the methods, including narrow gap approximation and bisection method, to solve this relation equation are presented. It is shown that only the sound wave with a frequency greater than the cut off frequency can propagate in the duct. The sound energy relation in the duct is deduced from the equation of sound intensity in an inhomogeneous mean flow.The propagation mchanisim of a single Fourier component at the inlet of the jet engine is studyed by solving the linearized Euler equation. The meanflow field is computed before the simulation of acoustics propagation by solving the Euler equation. The multi-mesh-size and multi-time-step DRP method is empolyed in both meanflow computation and acoustics simulation. During meanflow computation, radiation boundary conditions are imposed at the open boundary; non-slip boundary conditions are used at hard walls due to artificial selective damping; outflow boundary conditions are imposed at the fan face, and axis symmetric boundary conditions are imposed at theχaxis. However, boundary conditions for the acoustics simulation are totally different from those for the mean flow computation:radiation boundary conditions are imposed at open boundaries to allow sound waves exit without any reflection; slip boundary conditions are used at hard walls by the ghost point method; a PML boundary layer is added at the fan face to prescribe the incident sound wave and to absorb waves reflected from the inner domain; more complicated axial boundary conditions are imposed at theχaxis. The numerical methods are validated by simulating plane wave propagation at the inlet without mean flow, and then the impact on sound wave propagation from factors such as the Mach number at the fan face, the cut-on cut-off ratio of the incident wave, and the radial mode number is investigated.