WIND POWER AND ITS METROLOGIES (20 points)

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Norman Manning
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1 page 1 of 11 WIND POWER AND ITS ETROLOGIES (0 points) A. Theoretical Background (1.0 points) A.1 (0.4 pts) A. 1 P w = v dm 0 dt 1 3 Pw = ρ Av 0 0 n = v0 ρ Av0 3 PR = ρ A (1 + λ) 1 λ = (1 + λ λ λ ) 4 dp R = 0 1 λ 3λ = 0 dλ 1 λ = 3 Betz efficiency: PR 16 C 7 ~ 59.6% P = = (0.4 pts) ( ) A.3 (0. pts) PW λ B. The Wind Tunnel (3. points) B.1 (0.8 pts) We move the motor generator blade manually, and the voltage at the opto-sensor signal will increase every time the sensor hits the reflective sticker in the blade. This signal provides frequency signal to the meter. V(V) B. (.4 pts) n n PW ρaav 0 0 ρaav 0 0 η = = P = P P η Wind tunnel diameter: D T = 13.5 cm. A0 = π R T = m. ρ AA0 ln P = ln + nln v y = a+ bx η From the plot and linear regression below we obtain the power factor: n = 3.0, in good agreement with the theory thus showing that the wind

2 page of 11 power P W ~ v 3. ρ AA0 η = =.8% a e Results for full score / grading scheme (sampling from several setups): η = (3± )%, to anticipate wide variability in motor quality. Connection diagram: Note that for best results the voltmeter has to be placed right across the motor to avoid extra voltage drop across the amperemeter. f v V I P ln v ln P (Hz) (m/s) (V) (A) (W)

3 page 3 of 11 C. Ping Pong Ball Anemometer (3.5 points) C.1 (0.7 pts) Force diagram at static equilibrium: FD CD ρα ABv tanθ = = W m g v = m B mbg tn a θ C ρ A D A B m C. CDρ AAB (.8 pts) ln tanθ = ln + mln v y = a+ bx m B g The deflection can be calculated from: tan θ =Δ x/ h, where Δx is the displacement and h is the height from the ruler. The cross section of the ball is: A B B = π d /4 where d B = m. In the tunnel the wind velocity is given as (Eq. 4) in the tunnel v= c1 f where c 1 = m. In this example we have: m= b=.

4 page 4 of 11 C D mbg = e ρ A A B a = 0.40 Results for full score / grading scheme (sampling from several setups): m =.0 ± 0.3 C = 0.4 ± 0.05 D f tan θ V ln v ln tan θ (Hz) (m/s) NOTE: These values are in very good agreement with the theoretical and established value of n =, i.e. the drag force is proportional to the square of the velocity. The drag coefficient C D is in close to the ideal known value: C D = 0.47 for smooth ball with particle Reynold number Re ~ as shown below. In this experiment the maximum Reynold number is:

5 page 5 of 11 ραvdb ReB = = = µ Α Discrepancy in our C D values could be due to finite boundary of our wind tunnel. (1) Figure 1. Drag coefficient as a function of the particle Reynold number D. Hotwire Anemometer (HWA) (6.7 points) [D.1] Constant Temperature (3. points) D.1.1 (0.4 pts) In the Wheatstone bridge we have: RW VW = VINP = c1vinp R + R W V R W W W B INP W W RW B c R c = ( a + bv ) A ( T T ) V = A ( T T )( a+ bv ) W w w 0 INP W W 0 c1 ( R + R ) c V = A ( T T )( a+ bv ) = c ( a+ bv ) c 0 Where ( R + R ) c = A ( T T ) is a constant. W B W W 0 RW A = ca B = cb D.1. (0.3 pts) D.1.3 (.5 pts) V INP y = 1 V0 wind. c = 0.7 ± 0. with V0 = A is the input potential when there is no

6 page 6 of 11 b a = ± f V INPUT v ln v ln((v/v 0 ) -1) (Hz) (V) (m/s) y = x R² = 0.99 log (V/(V0)^- 1) CTA log v [D.] Constant Current (3.5 points) First we need to determine k and R 0. D..1 (0. pts) D.. (1. pts) aa k = w α R 0 = (7.0 ± 1.5) Ω V W I W P W R W (V) (ma) (W) (Ω)

7 page 7 of y = 8.04x R² = V/I D..3 (0. pts) D..4 (1.9 pts) y V I R W W 0 = VW k R0 I W b a = ± 1 c = 0.77 ± 0.07 V W f v y ln(v) ln(y) (V) (Hz) (m/s)

8 page 8 of ln(y) y = x R² = CCA ln(v) E. Wind Turbine (5.6 points) E.1 (0.4 pts) We use D in ohmmeter mode, we first measure the lead resistance of the ohmmeter cables by shorting them to get the lead resistance. R D,0 ~ 0. Ω Then we measure the resistance of the motor directly with D several times, looking for its minimum values and subtract it with the lead resistance R D,0. We get : R = (0.8 ± 0.) Ω E. (1. pts) To eliminate the contact or lead resistance we can perform: (1) Two point resistance measurement at several lengths. () Four point resistance measurement with current source (using CCA box) ampmeter and voltmeter as shown below. This yields: λ = (0.1 ± 0.0) Ω/ cm R

9 page 9 of 11 (a) Two-wire method (b) Four-wire method ethod #1: Using two-wire measurement ethod #: Using four-wire method at l = 50 mm. V (mv) I (ma) Nichrom length = 5 cm y = 5.614x R² = 1 V (mv) I (ma) E.3 (.4 pts) We vary the nichrom wire length and calculate the power output, we obtain peak at: R L = 1.0Ω

10 page 10 of 11 Results for full score / grading scheme (sampling from several setups): R L = (1.0 ± 0.4) Ω R L,theor = R V (mv) l (cm) R (ohm) P (mw) P (mw) λr=0.1 Ω/cm l (cm) E.4 (1.6 pts) We use the optimum load by setting R L = 1.05 Ω or setting the length of nichrom wire at l = 5 cm. The wind turbine efficiency : η WT where PT VT / RL 1 3 PW ρ Α AWT v AWT π R = = = is the wind turbine cross section area with R = 55 mm, and v= c1 f (Eq. 4) with c 1 = m and f is the frequency of motor generator. TSR = π T f R c f 1

11 page 11 of 11 f f T V T TSR P T P W η WT (Hz) (Hz) (mv) (mw) (mw) (%) Our turbine has range of efficiency <.5% and tends to increase with higher TSR as the turbine spin faster. Note that at some point this efficiency will drop, unfortunately this is beyond the capability of our wind generator fan.

WIND POWER AND ITS METROLOGIES

Problem Wind Power and Its Metrologies Experimental Question 1 page 1 of 14 WIND POWER AND ITS METROLOGIES I. APPARATUS Figure 1. Overall setup 1. Wind tunnel with nichrom (nickel-chromium) wire 2. Computer