10
1 The Experimental Approach in Aerodynamic Design
layers and wakes, on the other the shock layers when the Reynolds number tends to
infinity.
At very high Reynolds number further difficulty arises due to the unstable nature
of the flow. As the Reynolds number increases, the flow over a surface can undergo
transition from a laminar regime, where the flow is stationary and almost twodimensional, to a chaotic turbulent regime characterised by unsteady and threedimensional vortex structures. Turbulence is characterised as an energy cascade
between large and smaller eddies, where energy is extracted from large structures
and transferred to the smallest structures where it is dissipated into heat. We thus pass
from a scale L, associated with a very high Reynolds number Re, to the smallest scale
known as Kolmogoroff scale, characterised by a Reynolds number of about unity.
The numerical simulation of vortex structures in turbulent flows is of increasing
complexity with increasing Reynolds number as these structures are even smaller. It
is however fundamental to account for their effect on the characteristics of the flow,
even if some simplifications or approximations are made while modelling turbulence.
For the very high values of Reynolds number, of the order of one million or more,
the Reynolds Averaged Navier-Stokes (RANS) statistical approach is by far the most
used method for most practical aerodynamic studies. When the Reynolds number is
smaller, of the order of one hundred thousand, the scale of the turbulent structures
increases, we can describe quite precisely the largest of them thanks to the methods
called LES (Large Eddy Simulation). This approach is based on a separation between
large scales, described by numerical simulation, and small unresolved scales to be
modelled. The LES methods require a great refinement of the mesh to describe the
attached boundary layers. An intermediate approach called Detached Eddy Simulation (DES) has been developed in the LES method which is activated only when the
flow separates. The very rapid progress of the computing resources (Moore’s law!)
has led to these tools to be used on full aircraft configuration in the aerodynamic
design offices and will probably be in common use in less than a decade.
Direct Numerical Simulation (DNS) does not pose a problem of modelling since
it solves the full instantaneous Navier-Stokes equations, assuming that they represent
the turbulent motion down to the smallest scales. In practice, this constraint leads to
meshes of very high density and consequently to very long computation times which
increases rapidly with the Reynolds number. Their applications are currently limited
to the simulation of fundamental aerodynamic problems. Despite the advances in
computational power it is still not a viable tool for applied industrial problems.
Another approach, currently limited to incompressible flows, is the Lattice
Boltzmann Method (LBM), introduced in the mid-1980s. This technique involves
modelling the fluid as a set of particles while expressing all the physical quantities characterising their trajectories, these quantities are length, speed and time. The
particles are free to move on a lattice or regular network of points called nodes, displacements being inferred from a two-step protocol. The first associates with each
node a distribution function for the velocities; the second step is to model the collisions between particles. Currently, this approach is mostly used in the automotive
industry.
1 The Experimental Approach in Aerodynamic Design
layers and wakes, on the other the shock layers when the Reynolds number tends to
infinity.
At very high Reynolds number further difficulty arises due to the unstable nature
of the flow. As the Reynolds number increases, the flow over a surface can undergo
transition from a laminar regime, where the flow is stationary and almost twodimensional, to a chaotic turbulent regime characterised by unsteady and threedimensional vortex structures. Turbulence is characterised as an energy cascade
between large and smaller eddies, where energy is extracted from large structures
and transferred to the smallest structures where it is dissipated into heat. We thus pass
from a scale L, associated with a very high Reynolds number Re, to the smallest scale
known as Kolmogoroff scale, characterised by a Reynolds number of about unity.
The numerical simulation of vortex structures in turbulent flows is of increasing
complexity with increasing Reynolds number as these structures are even smaller. It
is however fundamental to account for their effect on the characteristics of the flow,
even if some simplifications or approximations are made while modelling turbulence.
For the very high values of Reynolds number, of the order of one million or more,
the Reynolds Averaged Navier-Stokes (RANS) statistical approach is by far the most
used method for most practical aerodynamic studies. When the Reynolds number is
smaller, of the order of one hundred thousand, the scale of the turbulent structures
increases, we can describe quite precisely the largest of them thanks to the methods
called LES (Large Eddy Simulation). This approach is based on a separation between
large scales, described by numerical simulation, and small unresolved scales to be
modelled. The LES methods require a great refinement of the mesh to describe the
attached boundary layers. An intermediate approach called Detached Eddy Simulation (DES) has been developed in the LES method which is activated only when the
flow separates. The very rapid progress of the computing resources (Moore’s law!)
has led to these tools to be used on full aircraft configuration in the aerodynamic
design offices and will probably be in common use in less than a decade.
Direct Numerical Simulation (DNS) does not pose a problem of modelling since
it solves the full instantaneous Navier-Stokes equations, assuming that they represent
the turbulent motion down to the smallest scales. In practice, this constraint leads to
meshes of very high density and consequently to very long computation times which
increases rapidly with the Reynolds number. Their applications are currently limited
to the simulation of fundamental aerodynamic problems. Despite the advances in
computational power it is still not a viable tool for applied industrial problems.
Another approach, currently limited to incompressible flows, is the Lattice
Boltzmann Method (LBM), introduced in the mid-1980s. This technique involves
modelling the fluid as a set of particles while expressing all the physical quantities characterising their trajectories, these quantities are length, speed and time. The
particles are free to move on a lattice or regular network of points called nodes, displacements being inferred from a two-step protocol. The first associates with each
node a distribution function for the velocities; the second step is to model the collisions between particles. Currently, this approach is mostly used in the automotive
industry.