493
13.4 Compressor Blade Profiles
by the fluctuations in the main flow. This means that the transition is not caused by
instability of the boundary layer flow with forming of Tolmien-Schlichting waves
(see fluid mechanics). Transition caused by instability, called natural transition, is
typical for aircraft wings in a very low turbulence level flow (typically about 0.01 %
turbulence level in cruise conditions). The directly induced transition is called bypass transition, meaning that the instability mechanism is bypassed. A consequence
for practise is that the boundary layer thickness for transition, normally expressed
with a Reynolds number based on momentum thickness, lowers considerably with
increasing free stream turbulence level. Further, this critical Reynolds number becomes independent of the pressure gradient for high free stream turbulence. This is
in contrast with natural transition where the critical Reynolds number increases in
accelerating flow. So, it becomes harder to keep a boundary layer in laminar state
in the presence of a high free stream turbulence level. So, the acceleration of the
boundary layer in the leading edge zone has to be sufficiently strong in order to
keep the momentum thickness Reynolds number below the critical value. Clearly,
the optimisation of the accelerated zone strongly depends on the turbulence level of
the incoming flow.
A major difference between a laminar boundary layer and a turbulent one is that
a turbulent boundary layer can withstand a much higher adverse pressure gradient
before entering into separated state. The reason is turbulent exchange of momentum
from the outer region of the boundary layer to the near-wall region. So, to avoid
separation, it is advantageous to let the boundary layer transition from laminar state
into turbulent state at the position where the boundary layer edge flow changes from
accelerating flow to decelerating flow. At the other hand, by the turbulent momentum exchange, the shear stress in a turbulent boundary layer is higher for the same
edge velocity. So, optimisation includes making a balance between the extent of the
laminar part of the boundary layers, with lower shear stress level, and the turbulent
part with higher resistance to separation. The optimum strongly depends on the free
stream turbulence level, but also on the chord Reynolds number. The lower is the
chord Reynolds number, the weaker is a laminar boundary layer against separation
under an adverse pressure gradient.
A compressor cascade is called subsonic when the Mach number of the oncoming flow is low enough such that the entire flow over the profile is subsonic. For
higher Mach number of the oncoming flow, a supersonic zone may form at the
suction side, ending with a normal shock. The flow is then called supercritical
(subsonic upstream flow, subsonic downstream flow, but a supersonic zone on the
profile). The shock at the suction side creates a sudden pressure rise which may
lead to boundary layer separation. In order to avoid shock-induced separation, the
Mach number just upstream of the shock should not be too high (a typical limit is
1.25) and the boundary layer state should be turbulent at the shock position (better
resistance against separation). The consequence is that the optimum profile shape
becomes dependent on the Mach number of the oncoming flow.
The optimisation strategy for supercritical rotor cascades remains as with stator
vanes, but with rotor cascades the Mach number is higher and the flow turning is
lower (typically under 20° compared to 40°). The resulting blade shape depends
13.4 Compressor Blade Profiles
by the fluctuations in the main flow. This means that the transition is not caused by
instability of the boundary layer flow with forming of Tolmien-Schlichting waves
(see fluid mechanics). Transition caused by instability, called natural transition, is
typical for aircraft wings in a very low turbulence level flow (typically about 0.01 %
turbulence level in cruise conditions). The directly induced transition is called bypass transition, meaning that the instability mechanism is bypassed. A consequence
for practise is that the boundary layer thickness for transition, normally expressed
with a Reynolds number based on momentum thickness, lowers considerably with
increasing free stream turbulence level. Further, this critical Reynolds number becomes independent of the pressure gradient for high free stream turbulence. This is
in contrast with natural transition where the critical Reynolds number increases in
accelerating flow. So, it becomes harder to keep a boundary layer in laminar state
in the presence of a high free stream turbulence level. So, the acceleration of the
boundary layer in the leading edge zone has to be sufficiently strong in order to
keep the momentum thickness Reynolds number below the critical value. Clearly,
the optimisation of the accelerated zone strongly depends on the turbulence level of
the incoming flow.
A major difference between a laminar boundary layer and a turbulent one is that
a turbulent boundary layer can withstand a much higher adverse pressure gradient
before entering into separated state. The reason is turbulent exchange of momentum
from the outer region of the boundary layer to the near-wall region. So, to avoid
separation, it is advantageous to let the boundary layer transition from laminar state
into turbulent state at the position where the boundary layer edge flow changes from
accelerating flow to decelerating flow. At the other hand, by the turbulent momentum exchange, the shear stress in a turbulent boundary layer is higher for the same
edge velocity. So, optimisation includes making a balance between the extent of the
laminar part of the boundary layers, with lower shear stress level, and the turbulent
part with higher resistance to separation. The optimum strongly depends on the free
stream turbulence level, but also on the chord Reynolds number. The lower is the
chord Reynolds number, the weaker is a laminar boundary layer against separation
under an adverse pressure gradient.
A compressor cascade is called subsonic when the Mach number of the oncoming flow is low enough such that the entire flow over the profile is subsonic. For
higher Mach number of the oncoming flow, a supersonic zone may form at the
suction side, ending with a normal shock. The flow is then called supercritical
(subsonic upstream flow, subsonic downstream flow, but a supersonic zone on the
profile). The shock at the suction side creates a sudden pressure rise which may
lead to boundary layer separation. In order to avoid shock-induced separation, the
Mach number just upstream of the shock should not be too high (a typical limit is
1.25) and the boundary layer state should be turbulent at the shock position (better
resistance against separation). The consequence is that the optimum profile shape
becomes dependent on the Mach number of the oncoming flow.
The optimisation strategy for supercritical rotor cascades remains as with stator
vanes, but with rotor cascades the Mach number is higher and the flow turning is
lower (typically under 20° compared to 40°). The resulting blade shape depends