Six patents were secured by E. H. Lanier from 1930 to 1933 for aeroplane designs that were intended to be exceptionally stable. A feature of five of these was a flow-induced “vacuum chamber” which was thought to provide superior stability and increased lift compared to typical wing designs. Initially, this chamber was in the fuselage, but later designs placed it in the wing by replacing a section of the upper skin of the wing with a series of angled slats. We report upon an investigation of the Lanier wing design using inviscid aerodynamic theory and viscous numerical simulations. This took place at the 2005 Australia–New Zealand Mathematics-in-Industry Study Group. The evidence from this investigation does not support the claims but, rather, suggests that any improvement in lift and/or stability seen in the few prototypes that were built was, most probably, due to thicker airfoils than were typical at the time.

To compute the maximum speed threshold for helicopters, we model the lift produced by the rotor blades. Using this model, we derive limits for each method traditionally used to alleviate dissymmetry of lift. Additionally, we find the minimum rotor angular velocity required to produce a prescribed lift at a given forward velocity. We derive conditions on the coefficient of lift for helicopter airfoils that maintain altitude. Further considerations are also made with regard to the properties of the air and its effect on helicopter dynamics.

With lower turbulence and less rigorous restrictions on noise levels, offshore wind farms provide favourable conditions for the development of high-tip-speed wind turbines. In this study, the multi-objective optimization is presented for a 5MW wind turbine design and the effects of high tip speed on power output, cost and noise are analysed. In order to improve the convergence and efficiency of optimization, a novel type of gradient-based multi-objective evolutionary algorithm is proposed based on uniform decomposition and differential evolution. Optimization examples of the wind turbines indicate that the new algorithm can obtain uniformly distributed optimal solutions and this algorithm outperforms the conventional evolutionary algorithms in convergence and optimization efficiency. For the 5MW wind turbines designed, increasing the tip speed can greatly reduce the cost of energy (COE). When the tip speed increases from 80m/s to 100m/s, under the same annual energy production, the COE decreases by 3.2% in a class I wind farm and by 5.1% in a class III one, respectively, while the sound pressure level increases by a maximum of 4.4dB with the class III wind farm case.

The lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

Determining the drag of a flowover a rough surface is a guiding example for the need to take geometric micro-scale effects into account when computing a macroscale quantity. A well-known strategy to avoid a prohibitively expensive numerical resolution of micro-scale structures is to capture the micro-scale effects through some effective boundary conditions posed for a problem on a (virtually) smooth domain. The central objective of this paper is to develop a numerical scheme for accurately capturing the micro-scale effects at essentially the cost of twice solving a problem on a (piecewise) smooth domain at affordable resolution. Here and throughout the paper “smooth” means the absence of any micro-scale roughness. Our derivation is based on a “conceptual recipe” formulated first in a simplified setting of boundary value problems under the assumption of sufficient local regularity to permit asymptotic expansions in terms of the micro-scale parameter.

The proposed multiscale model relies then on an upscaling strategy similar in spirit to previous works by Achdou et al. [1], Jäger and Mikelic [29, 31], Friedmann et al. [24, 25], for incompressible fluids. Extensions to compressible fluids, although with several noteworthy distinctions regarding e.g. the “micro-scale size” relative to boundary layer thickness or the systematic treatment of different boundary conditions, are discussed in Deolmi et al. [16,17]. For proof of concept the general strategy is applied to the compressible Navier-Stokes equations to investigate steady, laminar, subsonic flow over a flat plate with partially embedded isotropic and anisotropic periodic roughness imposing adiabatic and isothermal wall conditions, respectively. The results are compared with high resolution direct simulations on a fully resolved rough domain.

The paper addresses the construction of a non spurious mixed spectral finite element (FE) method to problems in the field of computational aeroacoustics. Based on a computational scheme for the conservation equations of linear acoustics, the extension towards convected wave propagation is investigated. In aeroacoustic applications, the mean flow effects can have a significant impact on the generated sound field even for smaller Mach numbers. For those convective terms, the initial spectral FE discretization leads to non-physical, spurious solutions. Therefore, a regularization procedure is proposed and qualitatively investigated by means of discrete eigenvalues analysis of the discrete operator in space. A study of convergence and an application of the proposed scheme to simulate the flow induced sound generation in the process of human phonation underlines stability and validity.

High-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

The unsteady flow separation of airfoil with a local flexible structure (LFS) is studied numerically in Lagrangian frames in detail, in order to investigate the nature of its high aerodynamic performance. For such aeroelastic system, the characteristic-based split (CBS) scheme combined with arbitrary Lagrangian-Eulerian (ALE) framework is developed firstly for the numerical analysis of unsteady flow, and Galerkin method is used to approach the flexible structure. The local flexible skin of airfoil, which can lead to self-induced oscillations, is considered as unsteady perturbation to the flow. Then, the ensuing high aerodynamic performances and complex unsteady flow separation at low Reynolds number are studied by Lagrangian coherent structures (LCSs). The results show that the LFS has a significant influence on the unsteady flow separation, which is the key point for the lift enhancement. Specifically, the oscillations of the LFS can induce the generations of moving separation and vortex, which can enhance the kinetic energy transport from main flow to the boundary layer. The results could give a deep understand of the dynamics in unsteady flow separation and flow control for the flow over airfoil.

Compressible flow past a circular cylinder at an inflow Reynolds number of 2 x 105 is numerically investigated by using a constrained large-eddy simulation (CLES) technique. Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows. Some typical and characteristic physical quantities, such as the drag coefficient, the root-mean-square lift fluctuations, the Strouhal number, the pressure and skin friction distributions around the cylinder, etc. are calculated and compared with previously reported experimental data, finer-grid large-eddy simulation (LES) data and those obtained in the present LES and detached-eddy simulation (DES) on coarse grids. It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well. Then, the effects of Mach number on the flow patterns and parameters such as the pressure, skin friction and drag coefficients, and the cylinder surface temperature are studied, with Mach number varying from 0.1 to 0.95. Non-monotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5. Additionally, the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures. It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature. Moreover, the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point. Moreover, the influences of different thermal wall boundary conditions on the flow field are graduallymagnified from the front stagnation point to the rear stagnation point. It is inferred that the CLES approach in its current version is a useful and effective tool for simulating wall-bounded compressible turbulent flows with massive separations.

A 3D lattice Boltzmann (LB) model with twenty-seven discrete velocities is presented and used for the simulation of three-dimensional porous media flows. Its accuracy in combination with the half-way bounce back boundary condition is assessed. Characteristic properties of the gas diffusion layers that are used in polymer electrolyte fuel cells can be determined with this model. Simulation in samples that have been obtained via X-ray tomographic microscopy, allows to estimate the values of permeability and relative effective diffusivity. Furthermore, the computational LB results are compared with the results of other numerical tools, as well as with experimental values.

A concept of “static reconstruction” and “dynamic reconstruction” was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a “hybrid reconstruction” approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piece-wise polynomial are computed locally in a cell by the traditional DG method (called as “dynamic reconstruction”), while the higher-order derivatives are re-constructed by the “static reconstruction” of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.

A localized flexible airfoil at low Reynolds numbers is modeled and the aerodynamic performance is analyzed numerically. With characteristic based split scheme, a fluid solver for two dimensional incompressible Navier-Stokes equations is developed under the ALE framework, coupled with the theory of shallow arch, which is approximated by Galerkin method. Further, the interactions between the unsteady flow and the shallow arch are studied in detail. In particular, the effect of the self-excited vibration of the structure on aerodynamic performance of the airfoil is investigated deeply at various angles of attack. The results show that the lift-to-drag ratio has been increased greatly compared with the rigid airfoil. Finally, the relationship between the self-excited vibration and the evolution of the flow is analyzed using FFT tools.

A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., 1(2008), pp. 92-112] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan limiter. To fix the problems, in this paper the WENO type reconstruction is employed to gain both the accurate approximations in smooth region and non-oscillatory sharp profiles near the shock discontinuity. The numerical experiments will demonstrate the efficiency and robustness of the proposed numerical strategy.