Unsteady flows in turbomachinery

Nonlinear Unsteady Effect on Time-Averaged Flow (‘Deterministic Stress’)


Due to the flow nonlinearity, extra unsteady stress terms will be generated in flow equations  when time-averaging. These stress terms are similar to the Reynolds stress terms generated by turbulence but in the cases of interested, they are generated by periodic unsteadiness with a distinctive frequency (e.g. due to trailing edge vortex shedding), hence they are called ‘Deterministic Stress’.  Our computational analysis (Ning and He 2001) show that a steady-state solution can be obtained by adding the deterministic stress terms to the unsteady flow equations. Without these stress terms the solution will be naturally unsteady, giving a periodic trailing edge vortex shedding. On the other hand, once these stress terms are added, the solution is stabilized, leading to a steady state field which is in agreement with the time-averaged flow field of the unsteady solution.

Instantaneous entropy contours

Instantaneous entropy contours (unsteady solution)

Analysis of Deterministic Stress


     Analysis of Deterministic Stress (trailing edge vortex shedding, VKI turbine cascade)



-    W. Ning and L. He. “Some Modelling Issues on Trailing Edge Vortex Shedding”, AIAA Journal, Vol.39, No.5, pp787-793, May, 2001.

-   T. Chen, P. Vasanthakumar and L. He ,"Analysis of Unsteady Bladerow Interaction using Nonlinear Harmonic Approach",  Journal of Propulsion and Power., Vol.17, No3, pp651-658., May, 2001.



Effects of Circumferential Length Scale and Clocking in Axial-flow Turbomachines

Flow in turbomachinery is inherently unsteady due to the relative motions of adjacent blade rows with circumferential flow non-uniformities.  The effects of the unsteady responses are strongly influenced by the circumferential length scales.  Examples include:

  • stream turbine under partial admission (He 1997), where at the same partial admission flow rate, the axial propagation of the disturbances is shown to be markedly weakened when the circumferential length scale is halved.
  • A periodic unsteady forcing pattern with non equal amplitude and variable inter-blade-phase-angle are induced by the rotor-rotor/stator-stator interactions in high pressure gas turbines (Li and He, 2003).
  • High pressure gas turbine under inlet ‘hot streak’ (temperature non-uniformity from combustors), where both the heat load and unsteady forcing on the turine rotor blades show strong dependency on the length scale/hot stream counts (He, Menshikova and Hall, 2007).

Entropy contours

Entropy contours for two clocking positions of Hot streaks at inlet to a high pressure turbine stage



L. He,  “Computations of Steam Turbine Bladerow with Partial Admission”, IMeche J of Power and Energy, 1997.

H. D. Li and L. He, “Blade Count and Clocking Effects on Three-bladerow Interaction in a Transonic Turbine”, ASME Journal of Turbomachinery, Vol.125, No.4, pp 632-640, Nov, 2003.

L. He, V. Menshikova and B. R. Haller, “Effect of Hot-Streak Counts on Turbine Blade Heat Load and Forcing”, AIAA Journal of Propulsion and Power, Vol.23, No.6, pp1235-1241, Nov, 2007.


Bladerow Interaction in Radial Flow Turbomachinery

The capability in computing radial turbomachinery components, in particular, the interaction between rotor impeller and stator diffuser has been developed.

The validations were firstly carried out for the Krain centrifugal compressor giving good agreement with the experimental data, followed by a study of the diffuser stall characteristics (Sato and He, 2000). For a vanes diffuser, its interaction with the impeller was analysed (Sato and He, 2000).

In order to analyse unsteady flow at very low speed, an incompressible unsteady flow solver was developed combining the techniques of artificial compressibility for preconditioning and the dual time stepping (He and Sato, 2001). The method had been applied to analysis of hydraulic turbine performance (Sato and He, 2001).



K. Sato and L. He, “Effect of Rotor-Stator Interaction on Impeller Performance in Centrifugal Compressors”, International Journal of Rotating Machinery, Vol.5, No.2. pp.135-146, 1999.
L. He and K. Sato, “Numerical Solution of Unsteady Incompressible Flows in Turbomachinery”, Transactions of ASME, Journal of Fluids Engineering, Vol.123. No.3, pp680-685, Sept, 2001.
K. Sato and L He, "Numerical Investigation into Effects of Radial Gap on Hydraulic Turbine  Performance", Proc. IMech.E,  Part-A,  Journal of  Power and Energy, Vol.215, pp.99-107, April, 2001


Blade-Tower Interaction in Wind Turbines (HAWT)

Wind turbine blades are subject to various unsteady flow disturbances which affect both  ‘mean’ (time-averaged) work output and system mechanical integrity. Even at a uniform upstream flow condition without any ‘wind shear’, blades of a horizontal axis wind turbine may interact with downstream supporting tower. The work is attempted to predict unsteady aerodynamic effects of blade-tower interaction using a time-dependent computational fluid dynamics approach. The flow field is governed by the Reynolds averaged unsteady Navier-Stokes equations, discretized in space using a finite volume scheme and integrated in time using an explicit time-marching scheme. The computational domain consists of multiple structured mesh blocks (Fig.1), with body-fitted meshing for both a stationary tower and a moving blade. The moving mesh around the blade and the stationary mesh around the tower are connected by a sliding interface in conjunction with a 2nd order interpolation technique , which produces continuous information exchanges across the interface, as shown in Fig.2 for instantaneous static pressure contours. A computation for  a blade of NACA 63215 profile indicates more than 10% peak-to-peak variation of the circumferential force when the blade passes the tower (period variations of a similar magnitude have been obtained for the axial force). The unsteady behaviour is relevant to time-averaged wind turbine work output performance and blade fatigue life. An issue of interest is how to effectively control/minimise this unsteady loading in WT blade design.

Multi-block moving mesh

Multi-block moving mesh

Instantaneous pressure contours

Instantaneous pressure contours


Wells Turbine Stall Control

A variable stator configuration to enhance aero-thermal efficiency and widen operational range of Wells turbines is examined. At a normal upstream/downstream pressure condition, a major cause of low turbine efficiency is the high exit kinetic energy loss due to strong rotor exit swirling flow. The outlet guide vanes (OGV) can then be set according to the rotor swirling flow angle, to effectively reduce the exit kinetic energy loss. On the other hand, when the turbine upstream/downstream pressures exceed the limit causing the rotor to stall, the stator blades can be adaptively set to throttle to offload a large pressure drop to the OGV, while maintaining a constant un-stalled mass flow rate. Furthermore, the variable stator row can be used to control inlet flow angles in the bi-directional Wells turbine set up.
Another simple method of delaying the Wells- turbine stalling is to make use of vortex generators installed near blade hub. The technique was experimentally investigated, showing positive effects (Williams et al, 2005).

Flow loss (Entropy) contours for Wells turbine

Flow loss (Entropy) contours for Wells turbine


R. Williams, L. He and D.G. Gregory-Smith, “Use of Vortex Generators to Suppress Hub Stall on a Wells Turbine”, Proc. the 6th Euro. Conference on Turbomachinery Fluid-Mechanics and Thermodynamics, Lille, France,  March, 2005