Performance of a wind-turbine-driven compressor for lifting water

Pergamon

PH: S0360-5442(96)00089-8

PERFORMANCE

Energy Vol. 22, No. 1, pp. 21-26, 1997 Copyright© 1996ElsevierScienceLtd Printed in Great Britain. All rights reserved 0360-5442/97 $17.00+0.00

OF A WIND-TURBINE-DRIVEN FOR LIFTING

COMPRESSOR

WATER

K. A. ABED Mechanical Engineering Department, National Research Centre, Dokki, Giza 12311, Egypt (Received 27 November 1995)

Abstract--Energy storage is important for renewable energy systems. Compressed air storage is an attractive alternative to pumped water storage. It is suitable for use with wind-energy systems. We have studied a system consisting of a wind turbine, compressor, storage tank, and air-lift pump. The output power and capacity factor were accurately determined. Characteristics of the air-lift pump were investigated by using a numerical model. Wind turbines with compressed air storage and capacity factors greater than 40% are feasible with air-lift pumps. With air-lift pumps, increases of air-flow rates were accompanied by corresponding increases in water-flow rates, up to maximum outputs. The efficiency of the system reaches 22% when the ratio of water to air flow rate equals 2.15 and decreases thereafter. Copyright © 1996 Elsevier Science Ltd.

1. INTRODUCTION Wind-powered pumping systems may be positive displacement or air-lift pumps. Air-lift pumps are easy to install in a well. The location of the wind power unit is critical. A wind turbine and compressor may be placed at a suitable site, with the pump installed near a water source and at some distance from the energy source. Compressed air may be conveyed over considerable distances without serious pressure losses (see Fig. 1 ). It may be stored in underground reservoirs for later release to the combustor

A. ~

--- Driveshaft

7

N'~

\\

Wellcasin'g ~ -=-,-,~

Water

dischg___.. Deliverypipe

Air pipe. - ~

IL FOOT-PW_,CE- ~ - Fig. 1. Assembly of the proposed system. 21

22

K.A. Abed

of a gas turbine generating plant or an air-lift pump.l.2 The latter has a vertical riser tube that is partially immersed in the fluid to be pumped; air is injected at the base of the fluid to produce upward flow. The two-phase air-fluid mixture rises to the surface because it is lighter than the surrounding well water. 3 2. WIND CHARACTERISTICS The power generated by a wind turbine is determined by the design characteristics of the turbine and the wind-speed probability density as a function of wind velocity F(V). The wind frequency may be described 4 by the Weibull probability distribution

F(V)=(klC)x(VIC) k-1 exp[-(VIC)k],

(1)

where k = shape factor, C = scale factor (m/s), and V= wind speed (m/s). The scale factor has the dimensions of velocity and its maximum value is 1.1 times the average velocity. The shape of F(V) is largely determined by k. A k value close to 1 indicates a highly variable wind regime, while k > 3 indicates more regular, steadier winds. Since detailed information on the wind-speed frequency is often lacking, a k factor of 2 is often assumed for simplicity in evaluating a wind resource, which may lead to a significant understimate of power output. The power output as a function of V is P=O,

V< V~,

P = P(V),

V~ ~< V ~< V,,

P=P,,

V~V~Vo,

(2)

where p = output power (W), Vi = cut-in speed (m/s), Vr = rated speed (m/s), Pr = rated output power (W), Vo = cut-out speed (m/s), and V= average wind speed (m/s). The average power output is

Pay8 =

fF(v x P(v x dV.

(3)

This is the power output of the wind turbine at a given velocity times the frequency at which that velocity occurs, summed over all possible velocities. The quantity Pavg/P, is defined as the capacity factor of the wind turbine. Our system has a small wind turbine, a compressor, storage tank, and an air-lift pump. 3. NUMERICALCALCULATIONS 3.1.

Wind turbine

According to blade-element theory, the output power from a wind turbine is

P=4~rxpxVx~f~(1-a) xa, xr~xdr,

(4)

where p = air density (kg/m3), O = angular velocity of the wind-turbine rotor (sec -I ), r = blade radius at the hub (m), R = blade radius at the tip (m), a = axial induction factor, and at = angular induction factor. A mathematical model and a computer program which simulate the operation of a small-scale wind turbine has been constructed by Abed et al.5 The computer program was loaded with the following data for a horizontal-axis wind turbine: number of blades = 12, blade chord = 0.42 m, rotor diameter = 6 m, blade length = 1.8 m, blade angle at the tip = 14 ° and at the hub = 35 °, rated wind speed = 6 m/s,

Wind-turbine-driven compressor

23

V, m/$ 10

/

o

0

8

f

~ 7 ~ 6 5

I

0

I

0.5

0

I

1

I

1.5

I

2

2.5

3

Tip Speed Ratio

Fig. 2. Wind-turbine output vs tip-speed ratio.

and tip-speed ratio = 2. Figure 2 shows the output power vs the tip-speed ratio for wind speeds of 5, 6, 7, 8, 9, and 10 m/s. The capacity factor was estimated with proper account of machine characteristics using the method established by E1-Mallah and Abed. 6 The capacity factor is

Cz={exp[-(V/C)k]-exp[-(V/C)k]}/[(V/C)*-(V/C)k]•

(5)

Figure 3 shows the capacity" factor of a wind turbine as a function of k for rated speeds of 4, 8, and 12 m/s and average speeds of 6 or 8 m/s. If k = 3, the capacity factor is 5 - 1 0 % greater than that for k = 2, implying correspondingly larger output per machine and lower costs per unit of output.

1.0

Vr , m/s = 8 m/s

0.8

..... V

6

~

............................

4

m

o t~

~

0.6

0.4

U

0.2 ..... 0.0 0.5

I

I

I

I

t

1.0

1.5

2.0

2.5

3.0

K-factor

Fig. 3. Wind-turbine capacity factor vs Weibull k parameter. EGY

22-1-6

-.

3.5

12 4.0

24

K.A. Abed

3.2. Compressor The indicated compressor power is

(6)

where n = index of compression, ih = mass flow rate (kg/s), Ra = gas constant for air, T~ = inlet compressor temperature (K), and E = compressor pressure ratio. 3.3. Air-lift pump The method described by Clark and Dabolt7 allows explicit calculation of the lifted water. The calculation program of Stone s was modified for the present analysis. The relation between water and air-flow rates according to the model of Stenning and Martin is

(7) where S = actual submergence depth (m), L = length of the riser (m), Vw= water velocity (m/s), V~ = air velocity (m/s), Qa = air flow rate (l/rain), Qw = water flow rate (1/min), g = acceleration of gravity (m/s2), A = cross-sectional area of the pump (m), f = pipe roughness, and ID = inner diameter of the riser (mm). The solution is obtained by iteration. The procedure used is to assume a liquid velocity, calculate the lift for this velocity, and then correct the estimated liquid velocity to bring the lift closer to the actual lift. Reasonably fast convergence is obtained by setting the liquid velocity initially equal to one half of the air velocity and then correcting the liquid velocity by using the fourth power of the ratio of actual to calculated lift after each iteration. Iteration is continued until two consecutive lift values agree within 0.1%. The pump operates in slug flow and below the maximum on the air vs liquid-flow curve, which means that the calculation will be stopped when an increase of the air flow is not accompanied by a corresponding increase of water flow, which agrees with assumptions made in Ref. 9.

600

2 500 ¢I

";

4oo

,~

300

25 3 3.5

0

4 200

I O0

I

I

I

I

I

I

I

I

100

200

300

400

500

600

700

800

Wind-Turblne Power, W

Fig. 4. Wind-turbinepowervscomp~ssor ~ r - f l o w

~.

900

Wind-turbine-driven compressor

L=5 m,

0.16

/

0.12

C~

0.08

25

ID=30 mm

S/L-0,8

S/L=0.7 S/L=0.6

0.04

0.00 0.50

I

1

I

1

I

I

0.75

1.00

1.25

1.50

1.75

2.00

2.25

Qa / Qw

Fig. 5. Dimensionless plot of pump performance.

0.22

® 0.20

u

4J

o.18

0.16

0.14

1.5

I

I

I

I

I

I

1.6

1.7

1.8

1.9

2

2.1

2.2

QW / Qa

Fig. 6. Efficiencyof the system. 3.4. System efficiency The system efficiency is defined as ~sys " ~ hydraulic power/wind-turbine output power = Qw x pw x g x (L-S)/Po,,,

(8)

where Qw = water-flow rate (l/min), pw = water density (kg/m3), L - S = static head (m), and Pou, = output power (W). 4. RESULTS AND DISCUSSION The output power of the wind turbine is plotted against the air-flow rate of the compressor for different compression ratios, as shown in Fig. 4. We assumed an overall compressor efficiency of 0.65. Two air-lift pumps, each with a 5 m riser length, were analyzed. The results obtained are conveniently

26

K.A. Abed

presented by using the dimensionless parameters Qa/Q~ on the horizontal axis and QJA2~-gL on the vertical axis, as shown in Fig. 5. This dimensionless plot leads to the result that the air-flow rate increases when the submergence ratio SIL decreases. Figure 6 shows the system efficiency vs QJQo when the inner diameter of the pump equals 40 mm, the static head is 2 m and the compressor pressure ratio is 3.5. It is clear from Fig. 6 that the system efficiency increases when the water flow increases until no further change in water flow occurs when the air flow increases. 5. CONCLUSIONS A wind-turbine-compressor combination with a capacity factor greater than 40% is feasible with airlift pumps. The capacity factor of the wind turbine is increased by choosing turbines with lower rated speeds for sites with higher average wind speeds. At the same time, the maximum of the capacity factor occurs at sites with higher k values as the rated speed decreases. In air-lift pumps, an increase of airflow rates was accompanied by a corresponding increase of water-flow rate, up to the condition of maximum water flow. The efficiency of the system reaches 22% when Qw/Qo --- 2.15; beyond this value for the ratio, the efficiency decreases. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Glendenning, I., Storing the Energy of Compressed Air. CEGB Report: R/M/N783, Bonn, 1975. Daehee, L., Mechanical Engineering, 1991, 1, 67. Parker, G. J., International Journal of Heat and Fluid Flow, 1980, 2, 245. Cavallo, A., Wind Energy, 1994, 15, 87. Abed, K. A., Badr, M. A. and E1-Mallah, A. A., Journal of the Egyptian Society of Engineers, 1995, 34(1), 31. El-Mallah, A. A. and Abed, K. A., Journal of the Egyptian Society of Engineers, 1994, 33(4), 22. Clark, N. N. and Dabolt, R. J., American Institute of Chemical Engineering, 1986, 32(1), 56. Stone, J. N., J. Microsoftwarefor Engineers, 1987, 3(3), 114. Stenning, A. H. and Martin, C. B., Journal of Engineering for Power, Transactions of ASME, Series A, 1968, 90(2), 106.