Three-dimension losses and correlation in turbomachinery refers to the measurement of flow-fields in three dimensions, where measuring the loss of smoothness of flow, and resulting inefficiencies, becomes difficult, unlike two-dimensional losses where mathematical complexity is substantially less.
Three-dimensionality takes into account large pressure gradients in every direction, design/curvature of blades, shock waves, heat transfer, cavitation, and viscous effects, which generate secondary flow, vortices, tip leakage vortices, and other effects that interrupt smooth flow and cause loss of efficiency. Viscous effects in turbomachinery block flow by the formation of viscous layers around blade profiles, which affects pressure rise and fall and reduces the effective area of a flow field. Interaction between these effects increases rotor instability and decreases the efficiency of turbomachinery.
In calculating three-dimensional losses, every element affecting a flow path is taken into account—such as axial spacing between vane and blade rows, end-wall curvature, radial distribution of pressure gradient, hup/tip ratio, dihedral, lean, tip clearance, flare, aspect ratio, skew, sweep, platform cooling holes, surface roughness, and off-take bleeds. Associated with blade profiles are parameters such as camber distribution, stagger angle, blade spacing, blade camber, chord, surface roughness, leading- and trailing-edge radii, and maximum thickness.
Two-dimensional losses are easily evaluated using Navier-Stokes equations, but three-dimensional losses are difficult to evaluate; so, correlation is used, which is difficult with so many parameters. So, correlation based on geometric similarity has been developed in many industries, in the form of charts, graphs, data statistics, and performance data.
Types of losses
Three-dimensional losses are generally classified as: Three-dimensional profile losses Three-dimensional shock losses Secondary flow Endwall losses in axial turbomachinery Tip leakage flow losses Blade boundary layer losses
Three-dimensional profile losses
The main points to consider are: Profile losses that occur due to the curvature of blades, which includes span-wise mixing of flow field, in addition to two-dimensional mixing losses (which can be predicted using Navier-Stokes equations). Major losses in rotors that are caused by radial pressure gradient from midspan to tip (flow ascending to tip). Reduction in high losses between annulus wall and tip clearance region, which includes the trailing edge of a blade profile. This is due to flow mixing and flow redistribution at the inner radius as flow proceeds downstream. Between the hub and annulus wall, losses are prominent due to three-dimensionality. In single-stage turbomachinery, large radial pressure gradient losses at exit of flow from rotor. Platform cooling increases the endwall flow loss and coolant air increases profile loss. Navier-Stokes identifies many of the losses when some assumptions are made, such as unseparated flow. Here correlation is no longer justified.
Three-dimensional shock losses
The main points to consider are: Shock losses continuously increase from the hub to tip of the blade in both supersonic and transonic rotors. Shock losses are accompanied by shock-boundary-layer interaction losses, boundary-layer losses in profile secondary flow, and tip clearance effects. From the Mach number prospective, fluid inside rotor is in supersonic phase except at initial hub entry. The Mach number increases gradually from midspan to tip. At the tip, the effect is less than secondary flow, tip clearance effect, and annulus wall boundary-layer effect. In a turbofan, shock losses increase overall efficiency by 2% because of the absence of tip clearance effect and secondary flow being present. Correlation depends on many parameters and is difficult to calculate. Correlation based on geometric similarity is used.