This can occur in pumps, fans and valves, resulting in reduced performance, vibration and noise. It should not be confused with the hump on a pump head curve, which indicates where the pump operates with maximum efficiency.
Hump instability is a particular problem in compressible and supersonic flows. While air is always compressible, under many aerodynamic interactions it doesn’t compress significantly. Many situations can therefore be considered as incompressible flows, where air behaves in fundamentally the same way as a liquid. Such a flow regime can be characterised by a parameter known as the Reynolds number and given by
where ρ is the density of the fluid, u is the flow speed, L is a characteristic length, and μ is the dynamic viscosity of the fluid. At low Reynolds numbers, laminar flow is seen, with layers of fluid sliding past each other, a flow regime dominated by viscous forces. The ‘no-slip’ boundary condition means that the flow at the surface will always have zero velocity relative to the surface. The flow velocity increases with distance from the surface, until it reaches the bulk flow velocity.
In a laminar flow, this change in velocity is smooth, with each layer travelling past each other, and aerodynamic drag a result of the shear forces between the layers. As the Reynolds number increases, the boundary layer separates and flow becomes turbulent. The boundary layer is the thin layer of fluid close to the surface of the solid object with the fluid flowing over it. The turbulent movement increases the exchange of kinetic energy between layers travelling at different speeds, and therefore increases the aerodynamic drag significantly.
Flow around a particular shape depends primarily on the Reynolds number. This means that a very small object will see the same flow patterns as a much larger object of the same shape, if the density of the fluid or the flow speed is increased.
The speed of sound in a fluid is related to the average speed at which molecules are moving around (the temperature). At flow rates approaching the speed of sound, molecules are being impacted faster than the resulting pressure waves can propagate away. This means that a very high-pressure shock wave will form, and it is extremely difficult for a blunt object to travel faster than the speed of sound. At Mach numbers over 0.3, fluids can normally be considered compressible.
Hump instability arises from the interaction between the boundary layer and the freestream flow. Under certain conditions – such as high flow speeds or adverse pressure gradients – disturbances can develop within the boundary layer and grow into humps or waves along the surface. This instability can have significant effects on the aerodynamic performance of the object. It can lead to increased drag, altered pressure distribution and changes in flow separation patterns. These effects can be particularly detrimental in high-speed or high-lift situations, where maintaining smooth and attached flow is crucial for optimal performance and stability.
Methods of avoiding hump instability include altering surface geometries, adding turbulence control devices or adjusting the aerodynamic design to minimise the occurrence or effects of hump instability.
Pump head curves
A pump head curve, also known as a performance curve or characteristic curve, is a chart illustrating the relationship between the pressure (head) and flow rate (capacity) generated by the pump. Typically the pressure is on the vertical axis and flow rate is on the horizontal axis. The maximum pressure is generated at zero flow, known as
‘shut-off’ head. As the flow rate increases, the pressure decreases gradually. Often, efficiency is shown on the same chart, with a hump indicating where the best efficiency point (BEP) occurs. Pumps typically work best close to the BEP. For example, most centrifugal pumps have a preferred operating range of 70% to 110% of BEP.
Specific speed is a dimensionless number used to characterise turbomachinery speed, independent of the actual size and flow rate of the impeller. It is therefore in some ways equivalent to the Reynolds number and can be used to determine the correct shape for an impeller. As specific speeds increase, the point on the head curve where hump instability will occur moves closer to the BEP. If hump instability occurs very close to the BEP, then this seriously compromises the flexibility and operating range of a pump.
The NPSHR (net positive suction head required) may also be plotted: this is the minimum pressure at the suction port of the pump to keep the pump from cavitating. Cavitation should always be avoided as it will lead to greatly accelerated wear from cavitation erosion and secondary damage due to vibration, as well as excessive noise.
Another industry impacted by this problem is hydroelectric power. While the cost of generating renewable power is now lower than any other form of energy, intermittency remains a significant issue for wider adoption. Although batteries can buffer supply and demand over 24-hour cycles, for longer term energy storage, pumped-storage hydroelectricity (PSH) remains the dominant technology. This stores energy by pumping water up to an elevated reservoir. When the energy is required, the water is allowed to flow back down through a turbine to generate electricity. The principal power component of such systems is a reversable pump-turbine. These devices must change direction quickly and frequently to meet the fluctuations of load in the electrical grid.
Hump instability is a major issue in pump mode for pump-turbines. When hump instability occurs, the head curve will reverse, with a positive slope indicating that additional energy being transferred to the fluid does not increase the head but is instead being dissipated by vortices and rotating stall. This can prevent startup and operation under high head conditions. The strong vibrations produced also cause noise and damage.
The formation of hump instability is closely associated with guide vane geometry, especially rotational stall of guide vanes. This is a situation in which one blade stalls, leading to flow separation that impacts the flow over downstream blades and a subsequent domino affect causing all blades to stall.
Flow instabilities such as hump instability and rotating stall not only affect performance, they can also result in significant damage to equipment. This highlights the complexity of how issues can arise with turbomachinery and the importance of ensuring plant is operated within recommended limits.