The noise made by helicopters is clearly a problem, adding to the already high levels of noise pollution in urban areas, and increasing the chances of military helicopters being detected in places where stealth is a requirement. But before being able to solve these problems it is important to recognize what is causing the noise.

As the blades on a helicopter rotate, they disturb the air they pass through, causing a wake that spirals off the trailing edge of each blade. It is this wake (particularly the vortex from the blade tip) being hit by the following blade that produces the loud vibrating sound. In order to minimise the sound caused by these collisions, an accurate understanding of the blade–vortex interaction is essential.

It is a question of aerodynamics, for which there are three possible approaches: experimentation (sometimes including real flight testing), theoretical analysis and computational or simulation methods. Experimentation is currently difficult and expensive – not to mention dangerous – since it is very hard to measure or visualise flow on the spinning blade of a rotor. Theoretical analysis has its limitations because the set of equations that govern fluid flow (air is a compressible fluid) are so complex that they can only be solved for very simple cases. Unfortunately, rotor flows are so complicated that such simple analytical methods are next to useless. The only viable alternative is computer simulation. With rapidly increasing computer power and memory now available, it has become feasible to perform full simulations of the air flow around a rotor blade. This is one of the specialisations of the Aeroelastic Simulation Group at Bristol, led by Chris Allen. The goal is to predict and improve the dynamic response of the blade in flight, which is of direct and obvious interest to the rotorcraft industry.

The aerodynamics of helicopter rotor blades is one of the most interesting and challenging problems facing aerodynamicists. The speed of the blade varies from very low at the root to very high at the tip, and in forward flight the effective velocity the blade ‘sees’ is different at every point around the axis of rotation. Hence, the flow around the rotor blade is highly three-dimensional and unsteady. Furthermore, and most significantly, each blade moves into air that has already been disturbed by the previous blade.

To compute and then visualise the air flow, the physical domain of interest is divided into a computational grid – a large number of cells, each with local values of flow variables such as density, pressure and velocity stored in them. With applied techniques from mathematics and physics, this local solution is ‘marched forward’ in time as each cell interacts with its neighbours.

## The ‘chopping’ noise is due to the wake that spirals off the trailing edge of each blade being hit by the following blade

After a sufficient number of such marching steps, a solution on the overall grid emerges. The numerical error between the grid solution and the real flow is a function of the grid spacing, thus the finer the computational grid, the more accurate the solution. On the other hand, the finer the grid, the longer the computation time and the more memory required to store the solution. This is the major trade-off in this field.

Simulating air flow over a rotor blade requires an extremely fine grid to resolve the wakes from each blade that are then hit by the next blade. Furthermore, capturing the wake over many turns, particularly for hovering rotors where a helical wake develops beneath the blades, requires a large number of time-steps. Rotor flow simulation therefore requires many timesteps on a very fine grid, and this leads to huge run times. Forward flight simulation is an additional challenge, as the complete air space around the rotor needs to be resolved with a fully time-accurate method. Dr Allen has written a computer code for this task from scratch, which exploits all possible acceleration and efficiency techniques. His code is also ‘parallelised’, so it can be run on many processors simultaneously. The simulations shown here were run on 32 processors of the 160- processor Linux machine at the University’s Laboratory for Advanced Computation in the Mathematical Sciences. Even so, the computations required three days of running time!

The first stage of the simulation is to fill the flow domain – the area of interest – with computational cells. To this end, the domain is first split into many different grid blocks, the boundaries of which are shown by thick lines in the figure on page 12. Once computed, the results of the simulation show where the air behind the blades is most disturbed. As each blade rotates, a vortex is shed from its tip. In forward flight, when the blade is advancing the tip vortex is swept away, out of the rotor disk, but when the blade is retreating the vortex is swept into the rotor. It is this periodic interaction of the vortex with the following blade that leads to the ‘chopping’ noise we hear. The frequency of the noise depends on the ratio between forward flight and rotor tip speeds, and the number of blades.

## The computations required three days of running time

These simulations allow accurate analysis of the effects of blade–vortex interaction, in terms of both noise and unsteady forces, and hence stresses, on the structure. This information is vital for both aerodynamic and structural optimisation of the rotor blades. Furthermore, vibrations of the blades feed into the fuselage, and accurate modelling of these vibrations allows detailed analysis of the structural dynamics aspects of the helicopter. Hence, high resolution aerodynamic simulation is also essential to source the structural and dynamics research on helicopters being performed in the Engineering Faculty. In short, multidisciplinary research at Bristol will help understand the dynamics nightmare that is a helicopter.