Download - What is BEMT?
The Buhl High-Induction Correction for Blade Element Momentum Theory
Applied to Tidal Stream TurbinesDr. Ian Masters (Swansea University)
Dr. Michael Togneri* (Swansea University)
Marine Energy Research Group, Swansea UniversitySingleton Park, Swansea, SA2 8PP, United Kingdom
What is BEMT?• Synthesis of two simple turbine models:
– Stream tube & enclosed actuator disc– Hydrodynamic forces on 2D foils
Rotor disc enclosed in streamtube, with velocity and pressure variation. Image from Hansen, M “Aerodynamics of Wind Turbines”, Earthscan Flow velocities for blade segment at radius r. Image from Burton, T
et al, “Wind Energy Handbook”, John Wiley & Sons
Characteristics of BEMT
• Simpler problem than full CFD– Turbine effects on fluid ignored– Requires less computational power– Can obtain results much faster– Allows rapid investigation of wide range of cases
• Simplifying assumptions:– Inflow/wake can be regarded as an enclosed streamtube– No wake mixing– Momentum change described by two parameters:
• Axial induction factor (AIF, a), tangential induction factor (TIF, b)
High induction state• AIF values in excess of
0.5 non-physical in classical BEMT
Uwake = (1 – 2a)U∞
• Semi-empirical correction necessary
• Must be validated against experiment
High induction correction schemes
• Graphs show high-induction corrections with and without tip/hub loss correction
• Current model uses Buhl-derived formulation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
a
CFa
BEMT CFa-a curve
Spera-corrected CFa-a curve
Glauert-corrected CFa-a curve
Buhl-corrected CFa
-a curve
High induction correction schemes
• Mathematical formulation straightforward• Momentum flux through annular element equated with
hydrodynamic forces on corresponding portion of rotor blade:– f1: axial momentum flux; f2: axial blade forces; g1: tangential momentum
flux; g2: tangential blade forces
• Each term a function of AIF and TIF• Minimise (f1 – f2)2 + (g1 – g2)2 across (a,b)-space to determine
solution• High induction correction simply modifies f1 for high values of
AIF (e.g., a > 0.4)
High induction correction schemes
• Classical Buhl formulation of axial force for a > ac:
• Assumes perfect reversal of flow (i.e., CFa = 2) for a = 1• Other values are plausible - e.g., 3D drag coefficient for a
flat plate gives CFa(a = 1) = 1.3
• In general, denoting CFa(a = 1) by CFa1 :
Validation against experiment
• Experimental data from work by Tedds et al., Mason-Jones et al.
Effects of HI correction on thrust
• Uncorrected solution has higher thrust• More pronounced nearer the tip
Effects of HI correction on thrust
• Uncorrected solution has near-tip region of relatively high annular thrust
• Coincides with the region where uncorrected AIF reaches physically meaningful limit
HI correction for an existing rotor
• 5o increase in rotor pitch moves rotor into HI regime
HI correction for an existing rotor
• 10o increase in pitch has more pronounced effect• Difficulties finding solution without HI correction
Combining HI correction with tip/hub losses
• HI correction has greater effect in conjunction with tip/hub losses
• Losses lead to greater AIF values
0 1 2 3 4 5 6 7 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
TSR
CFa
Uncorrected curveHI correction onlyTip/hub loss correction onlyBoth corrections
Summary• Classical BEMT does not deal with high induction,
semi-empirical correction needed• Modified Buhl correction validated against
experiment– Good agreement for power, less good for thrust
• Correction works in conjunction with tip/hub losses
• BEMT results for a high-induction rotor without HI correction not physically meaningful