Transcript The Buhl High-Induction Correction for Blade Element Momentum

The Buhl High-Induction Correction
for Blade Element Momentum Theory
Applied to Tidal Stream Turbines
Dr. Ian Masters (Swansea University)
Dr. Michael Togneri* (Swansea University)
Marine Energy Research Group, Swansea University
Singleton 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
2.5
BEMT CFa-a curve
Spera-corrected C Fa-a curve
Glauert-corrected C Fa-a curve
2
Buhl-corrected CFa-a curve
CFa
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a
• Graphs show high-induction corrections with and
without tip/hub loss correction
• Current model uses Buhl-derived formulation
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
0.9
0.8
0.7
0.6
CFa
0.5
0.4
0.3
0.2
Uncorrected curve
HI correction only
Tip/hub loss correction only
Both corrections
0.1
0
0
1
2
3
4
TSR
5
6
7
8
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