Application of a lattice Boltzmann method to some challenges related to micro-air vehicles

Abstract

The demand for micro-air vehicles is increasing as well as their potential missions. Whether for discretion in military operations or noise pollution in civilian use, the improvement of aerodynamic and acoustic performance of micro-air vehicles propeller is a goal to achieve. Micro-and nano-air vehicles operate at Reynolds numbers ranging from 10 3 to 10 5. In these conditions, the aerodynamic performance of conventional fixed and rotary wings concepts drastically decreases due to the increased importance of flow viscous forces that tend to increase drag and promote flow separation, which leads to reduced efficiency and reduced maximum achievable lift. Reduced efficiency and lift result in low endurance and limited payloads. The numerical simulation is a potential solution to better understand such low Reynolds number flows and to increase the micro-air vehicles' performance. In this paper, it is proposed to review some challenges related to micro-air vehicles by using a Lattice-Boltzmann method. The method is first briefly presented, to point out its strengths and weaknesses. Lattice-Boltzmann method is then applied to three different applications: a DNS of a single blade rotor, a large eddy simulation of a rotor operating in-ground effect and a large eddy simulation of a rotor optimised for acoustic performance. A comparison with reference data (Reynolds Averaged Navier-Stokes, DNS or experimental data) is systematically done to assess the accuracy of lattice-Boltzmann method-based predictions. The analysis of results demonstrates that lattice-Boltzmann method has a good potential to predict the mean aerodynamic performance (torque and thrust) if the grid resolution is chosen adequately (which is not always possible due to limited computational resources). A study of the turbulent flow is conducted for each application in order to highlight some of the physical flow phenomena that take place in such rotors. Different designs are also investigated, showing that potential improvements are still possible in terms of aerodynamic and aero-acoustic performance of low-Reynolds rotors.

Prediction of Noise from Low Reynolds Number Rotors with Different Number of Blades using a Non-Linear Vortex Lattice Method

“…Overall, it is shown that NVLM predicts thrust within 6% of experimental values. This level of accuracy is in line with previous works on low Reynolds number rotors [14][15][16]. Note that results obtained from NVLM depend on aerodynamic polars used as input for the look-up table procedure.…”

Fluid–Structure Interactions and Unsteady Kinematics of a Low-Reynolds-Number Rotor

“…The [25]. Previous works [26] have shown that the convergence of thrust and torque requires us to achieve a grid resolution corresponding to Δx∕C 0.01-0.015. The dimension of the first cell in the direction normal to the wall is thus set to Δx∕C 0.015, corresponding to y ≈ 50.…”

Towards silent micro-air vehicles: optimization of a low Reynolds number rotor in hover

“…In addition, it was verified that the results are converged with respect to the typical cell size. 33 Analysing the characteristics of the optimized geometry with such a numerical method is justified by its capacity to accurately estimate correlation lengths 33 and by the possibility to investigate unsteady aerodynamic behaviour, calibrate the broadband noise models in the optimization tool and eventually give insight for low noise design solutions (such as vortex generators or edge treatments). An unsteady behaviour occurs around 75% of the blade radius, where the twist angle increases again ( Figure 2) suggesting that having an inflection point on the twist distribution law should probably be avoided.…”

“…Several length scales can be used to quantify turbulence: the integral scale L, the Taylor microscale k g and the Kolmogorov scale g. These length scales are illustrated in Figure 9 on a turbulent boundary layer. The Taylor microscale appears relevant to describe turbulence impinging a leading edge with a wake characterized by a sub-critical Rossby number, 33 identifying a region where vortex breakdown is likely to occur and inducing strong rotational effects. The Taylor microscale is representative of the actual length the leading edge will see when hit by turbulent structures 34,35 (Figure 9).…”

“…Additionally to its computational performance, the main advantage of LES–LBM is that the method is stable without artificial dissipation, which makes it equivalent to solve the Navier–Stokes equations with a high-order numerical scheme. 32 In a recent study, 33 such a strategy has been identified as a good candidate to estimate turbulence length scales and is used now for the same reason. The present discretization of the equations ensures that the method is second-order accurate both in time and space.…”