- Email: [email protected]
Wave power potential off the south-west Indian coast
0360-5442/87 $3.00 +O.OO Pergamon Journals Ltd
Energy Vol. 12, No. 6, pp. 501-507, 1987 Printed in Great Britain
WAVE POWER POTENTIAL OFF THE SOUTH-WEST INDIAN COAST M. BARA Centre for Earth Science Studies, Regional Centre, Co&in 682 018, India (Received 12 June 1986)
Abstract-The wave power potential off the south-west Indian coast is examined using wave data recorded at four locations for one year. Salter’s method is used but modified for intermediate waters. The annual average wave power ranges between 0.7 and 10.9 kW/m, with Trivandrum recording the highest and Tellicherry the lowest. At Trivandrum, the average power varies from 2.2 to 30.9 kW/m through the different months, the peak occurring in June. Here, the monsoonal average is 17.4 kW/m and the highest recorded value is 68.9 kW/m.
1. INTRODUCTION
Ocean wave energy is a possible source of renewable energy. Considerable laboratory work has been done on the utilization of waves for the generation of electrical energy. However, few prototype stations have been established for commercial production. Some models for India have been developed’ and require field tests. The wave-power potential along the Indian coasts has been reportedzm3 and is mainly based on ship-reported deep-water wave data. Studies based on one month’s recorded data are also available.4 All these works point towards the high potential of the Kerala coast. The ship data have accuracy limitations and hence recorded wave information at a given coastal site may give a realistic assessment of the power potential. Coastal sites are found to be commercially viable for wave power generation. ’ Here, an analysis of wave power availability off the Kerala coast is examined with one year of recorded wave information.
2. WAVE DATA
The wave data were recorded at 3-hr intervals for Trivandrum, Alleppey, Calicut, and Tellicherry along the Kerala coast (Fig. 1). The wave records were subjected to TuckerDraper analysis5 and corrected for pressure attenuation.6 The monthly average significant wave heights, monthly maximum significant heights, monthly average zero up-crossing periods, etc. for a period of one year (1981) for all the four stations are given in Fig. 2 and reported in detail in Baba et aL7 Recording at Calicut was started in May.
3. WAVE POWER
IN INTERMEDIATE
WATERS
The wave power per unit wave crest width transmitted across a plane perpendicular to the wave advance is P=EC,
(1)
where E is the wave energy per unit area and C, the group velocity. In deep water,
c, = +c, where the phase velocity is C = gTf2rr, 501
(3)
502
M.
BABA
12
[(Contours beyond IOOOm m atdud+
Fig. 1. Kerala
\
coast and the wave recording
sites.
g = acceleration due to gravity, and T = wave period. The power in deep water is then P = +CE = +dpgH;(gTfh)
= pg=H;Tf32n,
(4)
where p = sea water density and H, = deep water wave height. For a significant wave height H, and zero up-crossing period T,, Salter* obtained P = pg2H,2z j&h.
(5)
For the range of wave periods (5-15 set) and corresponding wave lengths (L = 30100 m) at depths d = 3 and 5.5 m, the present wave data belong to the intermediate water regime (A < d/L < +) according to the Airy wave theory.g For intermediate water, C, = i{ 1 + [(4lcd/L)/sinh(4rrd/L )]}(gT/2n)tanh(2nd/L).
(6)
The wave power in intermediate water is then obtained by using Eqs. (1) and (6), viz. P = (pg2H:T, /64x){ 1 + [(4nd/L)/sinh(4nd/L
or P = (pg2H,2T,/64n)f(d/L).
)]} tanh(2nd/L )
(7)
Wave power potential
503
5
15 Trlvondrum
14
4
13 ave max
ave
12
3
11 IO
2
9 6
1
7 6
-0
5
z
14
;
13 i F2
r-" c
12
0 .o
2
11
$
g' 3
IO 9
!? '5
6
;
14
9
13
g
12
N
Eo
::
: E3 E 0) U-J 2
1
11 1
10 9
0
6 nTell~chery
1 I3
2
12
1
IO
11
9 0
51 J
F
Fig. 2. Distribution
If p = 1030kg/m3,
M
of average
A
M
J
and maximum
g = 9.81 m’/sec,
f (d/L) depends
significant periods.
A
S
0
N
D
"
wave heights and average zero-up-crossing
and H,, d, L are in m and T, in set, Eq. (7) reduces
P = 0.4938: The function
J
T,f(d/L) kW/m.
on T, and d and is given in Fig. 3 for depths
4. RESULTS
AND
to (8)
of 3 and 5.5 m.
DISCUSSION
The monthly average significant wave heights varied from 0 to 2.76 m, while the monthly maximum was O-4.12 m (Fig. 2). The zero height values are due to the occasional calms associated with the occurrence of a phenomenon called mudbank at Calicut and Alleppey. The monthly average zero crossing periods ranged between 8.3 and 13 set, the lowest occurring during the monsoon period. A systematic reduction in wave heights is observed towards the north, with Tellicherry recording the lowest in the range of 0.12-0.67m. Trivandrum recorded the highest in the range 0.75-2.76m and for nearly the entire year the monthly mean significant wave height exceeded 1 m. The waves are highest from May
M. BABA
504
0.6
0.4[ 5
1" 6
Zero
7
8
0 9
upcrossing
” 10
11
period
“1 12
,Tz
13
14
15
(set)
Fig. 3. Variation in f(d/L) as a function of zero crossing period, T, for the two wave recording depths.
to October. At all stations, the peak occurs in June. The maximum significant wave heights recorded at Trivandrum, Alleppey, Calicut, and Tellicherry are 4.12, 2.66, 2.37, and 1.11 m, respectively. The wave power per unit frontage for one year along the Kerala coast is presented in Fig. 4. The monthly mean wave power (Fig. 4) shows both spatial and temporal variations. When the power varies between 0.1 and 1.4kW/m at Tellicherry, it is between 2.3 and 30.9 kW/m at Trivandrum. The higher values occur during the monsoon season. There is a systematic decrease in power potential towards the northern coasts of Kerala, corresponding to a similar decrease in wave height. At Trivandrum, the wave power is near or above 10 kW/m for more than six months (May to October). The monthly mean wave power increases to 30.9 kW/m for June. The one-year average wave power P at different stations are given in Table 1. The earlier study3 of the wave power potential along the Indian coast using 5-yr, shipreported data revealed that the deep water monthly average wave power varies between 5 and 50 kW/m along the stretch of the present study. The maximum of 30-50 kW/m occurred from June to July and the minimum from November to April. The present recorded values fall within those given in this earlier study. The values are lower since recording was done in intermediate waters, where the deep-water waves are subject to refraction, shoaling, bottom frictional effects, etc. The wave power P corresponding to the maximum significant wave heights for each month are given in Fig. 5. Wave-power values as large as 68.9 kW/m are obtained in individual cases at Trivandrum during the peak of the monsoon. Here, a secondary peak is seen at 63.3 kW/m during September. Similar patterns with lower values occurred also at other locations. Trivandrum shows the highest values throughout the year. With wave data for one month (September-October), from deeper waters around the southern coasts of India between Visakhapatnam and Murmugoa, Gopinathan et al4 reached similar conclusions. They obtained values ranging between 2.4 and 6.7 kW/m for the Kerala coast, with Trivandrum recording the maximum. We conclude that the Trivandrum coast has relatively greater potential for the establishment of a wave energy development programme. Mansard” stated that the use of spectral analysis techniques gives values 18% higher than those derived from our equations. Hence, the present values may be under-estimates. The wave climate of the Kerala coast is dominated by swell waves for most of the year” and hence most of the available power appears to be associated with these. These waves approach mainly from the W to SW direction.’ Division of individual spectra into sea and swell components for a station off south Uist l2 led to the conclusion that more than 60% of the annual power was due to swell. The directional properties of the waves determine
Wave power potential 3*r
ALLEPPEY
w > a 3
6
6
CALICUT
0 4
0
TELLICHERY
A
JFMAMJJ
S
0
N
D
Fig. 4. Monthly mean wave power for one year for the four locations along the Kerala coast.
Table
Stations Trivandrum
1. Average
wave power
Annual 10.9
in kW/m
off the Kerala
coast
Monsoon
Non-monsoon
17.4
4.3
Alleppey
4.5
7.5
1.4
calicut
2.8
3.5
0.6
Tellicherry
0.7
0.9
0.4
M.
BABA
TRIVANDfWM
ALLEPPEY
20 CALlCUT IO
‘JFMAMJJASOND
Fig. 5. Monthly maximum wave power for one year for the four locations along the Kerala coast.
optimum system response. I2 In order to assess this aspect, the directional properties of wave power may have to be studied. Another important consideration is the year-to-year variation in wave power potential at a given site, corresponding to similar variations in wave height. l3 It is important to understand long-term wave climatology with direction, as was suggested by Baird and Gludowskii4 in choosing a site suitable for a wave-energy utilization. Acknowledgements-The author thanks the Director, Centre for Earth Science Studies, for the facilities and permission to publish this paper. N. P. Kurian, K. V. Thomas, T. S. Shahul Hameed, C. M. Harish and M. Prasannakumar helped to organize the wave-data collection programme. They were ably assisted by M. Rameshkumar, K. K. Varghese and others.
REFERENCES 1. V. S. Raju, M. Ravindran and U. A. Korde, Proc. 2nd Indian Conf: Ocean Engng Pune, II, 1215 (1983). 2. V. Kesavadas, B. A. Ramesh and M. J. Varkey, Estimation of Wave Power Potential Along the Indian Coastline, paper presented at the National Workshop on Energy from the Sea, NIO, Goa (1980). 3. T. V. S. N. Rao and V. Sundar, Energy 9, 839 (1982). 4. C. K. Gopinathan, P. V. Sathe and D. V. Ramaraju, Mahasagar 12, 135 (1979). 5. Draper, Proc. Int. Conf Coastal Engng I, 1. ASCE, New York (1966). 6. M. Baba and C. M. Harish, Ind. J. Mar. Sci. 14, 1 (1985). 7. M. Baba, P. S. Joseph, N. P. Kurian, K. V. Thomas, T. S. S. Hameed and C. M. Harish, Wave ProjectInterim Report (1981), Centre for Earth Science Studies, Technical Report No. 31-83 (1983), Trivandrum 695010, India. 8. S. H. Salter, Nature 249, 720 (1974). 9. U. S. Army, Coastal Engineering Research Centre, Shore Protection Manual, Vol. I. U.S. Government Printing Office, Washington, DC. (1977). 10. E. P. D. Mansard, Different Methods of Evaluating Wave Power in a Random Sea State: A Comparative
Wave power potential
11. 12. 13. 14.
507
Study, National Research Council of Canada, Hydraulics Laboratory memorandum HY-97, Dartmouth, N. S., Canada B2Y 4A2 (1978). M. Baba and C. M. Harish, Ind. J. Mar. Sci. 15, 144(1986). J. A. Crabb, Synthesis of a Directional Wave Climate. In Power from Sea Waves (Edited by B. Count). Academic Press, London (1980). M. Baba, Proc. 1st Natn. Conf: Dock Harbour Engng I, E 49. Bombay, India (1985). W. F. Baird and C. W. Glodowski, Proc. ht. Symp. Waoe Tidal Energy II, F.3, 39. Canterbury, England (1978).
Energy Vol. 12, No. 6, pp. 501-507, 1987 Printed in Great Britain
WAVE POWER POTENTIAL OFF THE SOUTH-WEST INDIAN COAST M. BARA Centre for Earth Science Studies, Regional Centre, Co&in 682 018, India (Received 12 June 1986)
Abstract-The wave power potential off the south-west Indian coast is examined using wave data recorded at four locations for one year. Salter’s method is used but modified for intermediate waters. The annual average wave power ranges between 0.7 and 10.9 kW/m, with Trivandrum recording the highest and Tellicherry the lowest. At Trivandrum, the average power varies from 2.2 to 30.9 kW/m through the different months, the peak occurring in June. Here, the monsoonal average is 17.4 kW/m and the highest recorded value is 68.9 kW/m.
1. INTRODUCTION
Ocean wave energy is a possible source of renewable energy. Considerable laboratory work has been done on the utilization of waves for the generation of electrical energy. However, few prototype stations have been established for commercial production. Some models for India have been developed’ and require field tests. The wave-power potential along the Indian coasts has been reportedzm3 and is mainly based on ship-reported deep-water wave data. Studies based on one month’s recorded data are also available.4 All these works point towards the high potential of the Kerala coast. The ship data have accuracy limitations and hence recorded wave information at a given coastal site may give a realistic assessment of the power potential. Coastal sites are found to be commercially viable for wave power generation. ’ Here, an analysis of wave power availability off the Kerala coast is examined with one year of recorded wave information.
2. WAVE DATA
The wave data were recorded at 3-hr intervals for Trivandrum, Alleppey, Calicut, and Tellicherry along the Kerala coast (Fig. 1). The wave records were subjected to TuckerDraper analysis5 and corrected for pressure attenuation.6 The monthly average significant wave heights, monthly maximum significant heights, monthly average zero up-crossing periods, etc. for a period of one year (1981) for all the four stations are given in Fig. 2 and reported in detail in Baba et aL7 Recording at Calicut was started in May.
3. WAVE POWER
IN INTERMEDIATE
WATERS
The wave power per unit wave crest width transmitted across a plane perpendicular to the wave advance is P=EC,
(1)
where E is the wave energy per unit area and C, the group velocity. In deep water,
c, = +c, where the phase velocity is C = gTf2rr, 501
(3)
502
M.
BABA
12
[(Contours beyond IOOOm m atdud+
Fig. 1. Kerala
\
coast and the wave recording
sites.
g = acceleration due to gravity, and T = wave period. The power in deep water is then P = +CE = +dpgH;(gTfh)
= pg=H;Tf32n,
(4)
where p = sea water density and H, = deep water wave height. For a significant wave height H, and zero up-crossing period T,, Salter* obtained P = pg2H,2z j&h.
(5)
For the range of wave periods (5-15 set) and corresponding wave lengths (L = 30100 m) at depths d = 3 and 5.5 m, the present wave data belong to the intermediate water regime (A < d/L < +) according to the Airy wave theory.g For intermediate water, C, = i{ 1 + [(4lcd/L)/sinh(4rrd/L )]}(gT/2n)tanh(2nd/L).
(6)
The wave power in intermediate water is then obtained by using Eqs. (1) and (6), viz. P = (pg2H:T, /64x){ 1 + [(4nd/L)/sinh(4nd/L
or P = (pg2H,2T,/64n)f(d/L).
)]} tanh(2nd/L )
(7)
Wave power potential
503
5
15 Trlvondrum
14
4
13 ave max
ave
12
3
11 IO
2
9 6
1
7 6
-0
5
z
14
;
13 i F2
r-" c
12
0 .o
2
11
$
g' 3
IO 9
!? '5
6
;
14
9
13
g
12
N
Eo
::
: E3 E 0) U-J 2
1
11 1
10 9
0
6 nTell~chery
1 I3
2
12
1
IO
11
9 0
51 J
F
Fig. 2. Distribution
If p = 1030kg/m3,
M
of average
A
M
J
and maximum
g = 9.81 m’/sec,
f (d/L) depends
significant periods.
A
S
0
N
D
"
wave heights and average zero-up-crossing
and H,, d, L are in m and T, in set, Eq. (7) reduces
P = 0.4938: The function
J
T,f(d/L) kW/m.
on T, and d and is given in Fig. 3 for depths
4. RESULTS
AND
to (8)
of 3 and 5.5 m.
DISCUSSION
The monthly average significant wave heights varied from 0 to 2.76 m, while the monthly maximum was O-4.12 m (Fig. 2). The zero height values are due to the occasional calms associated with the occurrence of a phenomenon called mudbank at Calicut and Alleppey. The monthly average zero crossing periods ranged between 8.3 and 13 set, the lowest occurring during the monsoon period. A systematic reduction in wave heights is observed towards the north, with Tellicherry recording the lowest in the range of 0.12-0.67m. Trivandrum recorded the highest in the range 0.75-2.76m and for nearly the entire year the monthly mean significant wave height exceeded 1 m. The waves are highest from May
M. BABA
504
0.6
0.4[ 5
1" 6
Zero
7
8
0 9
upcrossing
” 10
11
period
“1 12
,Tz
13
14
15
(set)
Fig. 3. Variation in f(d/L) as a function of zero crossing period, T, for the two wave recording depths.
to October. At all stations, the peak occurs in June. The maximum significant wave heights recorded at Trivandrum, Alleppey, Calicut, and Tellicherry are 4.12, 2.66, 2.37, and 1.11 m, respectively. The wave power per unit frontage for one year along the Kerala coast is presented in Fig. 4. The monthly mean wave power (Fig. 4) shows both spatial and temporal variations. When the power varies between 0.1 and 1.4kW/m at Tellicherry, it is between 2.3 and 30.9 kW/m at Trivandrum. The higher values occur during the monsoon season. There is a systematic decrease in power potential towards the northern coasts of Kerala, corresponding to a similar decrease in wave height. At Trivandrum, the wave power is near or above 10 kW/m for more than six months (May to October). The monthly mean wave power increases to 30.9 kW/m for June. The one-year average wave power P at different stations are given in Table 1. The earlier study3 of the wave power potential along the Indian coast using 5-yr, shipreported data revealed that the deep water monthly average wave power varies between 5 and 50 kW/m along the stretch of the present study. The maximum of 30-50 kW/m occurred from June to July and the minimum from November to April. The present recorded values fall within those given in this earlier study. The values are lower since recording was done in intermediate waters, where the deep-water waves are subject to refraction, shoaling, bottom frictional effects, etc. The wave power P corresponding to the maximum significant wave heights for each month are given in Fig. 5. Wave-power values as large as 68.9 kW/m are obtained in individual cases at Trivandrum during the peak of the monsoon. Here, a secondary peak is seen at 63.3 kW/m during September. Similar patterns with lower values occurred also at other locations. Trivandrum shows the highest values throughout the year. With wave data for one month (September-October), from deeper waters around the southern coasts of India between Visakhapatnam and Murmugoa, Gopinathan et al4 reached similar conclusions. They obtained values ranging between 2.4 and 6.7 kW/m for the Kerala coast, with Trivandrum recording the maximum. We conclude that the Trivandrum coast has relatively greater potential for the establishment of a wave energy development programme. Mansard” stated that the use of spectral analysis techniques gives values 18% higher than those derived from our equations. Hence, the present values may be under-estimates. The wave climate of the Kerala coast is dominated by swell waves for most of the year” and hence most of the available power appears to be associated with these. These waves approach mainly from the W to SW direction.’ Division of individual spectra into sea and swell components for a station off south Uist l2 led to the conclusion that more than 60% of the annual power was due to swell. The directional properties of the waves determine
Wave power potential 3*r
ALLEPPEY
w > a 3
6
6
CALICUT
0 4
0
TELLICHERY
A
JFMAMJJ
S
0
N
D
Fig. 4. Monthly mean wave power for one year for the four locations along the Kerala coast.
Table
Stations Trivandrum
1. Average
wave power
Annual 10.9
in kW/m
off the Kerala
coast
Monsoon
Non-monsoon
17.4
4.3
Alleppey
4.5
7.5
1.4
calicut
2.8
3.5
0.6
Tellicherry
0.7
0.9
0.4
M.
BABA
TRIVANDfWM
ALLEPPEY
20 CALlCUT IO
‘JFMAMJJASOND
Fig. 5. Monthly maximum wave power for one year for the four locations along the Kerala coast.
optimum system response. I2 In order to assess this aspect, the directional properties of wave power may have to be studied. Another important consideration is the year-to-year variation in wave power potential at a given site, corresponding to similar variations in wave height. l3 It is important to understand long-term wave climatology with direction, as was suggested by Baird and Gludowskii4 in choosing a site suitable for a wave-energy utilization. Acknowledgements-The author thanks the Director, Centre for Earth Science Studies, for the facilities and permission to publish this paper. N. P. Kurian, K. V. Thomas, T. S. Shahul Hameed, C. M. Harish and M. Prasannakumar helped to organize the wave-data collection programme. They were ably assisted by M. Rameshkumar, K. K. Varghese and others.
REFERENCES 1. V. S. Raju, M. Ravindran and U. A. Korde, Proc. 2nd Indian Conf: Ocean Engng Pune, II, 1215 (1983). 2. V. Kesavadas, B. A. Ramesh and M. J. Varkey, Estimation of Wave Power Potential Along the Indian Coastline, paper presented at the National Workshop on Energy from the Sea, NIO, Goa (1980). 3. T. V. S. N. Rao and V. Sundar, Energy 9, 839 (1982). 4. C. K. Gopinathan, P. V. Sathe and D. V. Ramaraju, Mahasagar 12, 135 (1979). 5. Draper, Proc. Int. Conf Coastal Engng I, 1. ASCE, New York (1966). 6. M. Baba and C. M. Harish, Ind. J. Mar. Sci. 14, 1 (1985). 7. M. Baba, P. S. Joseph, N. P. Kurian, K. V. Thomas, T. S. S. Hameed and C. M. Harish, Wave ProjectInterim Report (1981), Centre for Earth Science Studies, Technical Report No. 31-83 (1983), Trivandrum 695010, India. 8. S. H. Salter, Nature 249, 720 (1974). 9. U. S. Army, Coastal Engineering Research Centre, Shore Protection Manual, Vol. I. U.S. Government Printing Office, Washington, DC. (1977). 10. E. P. D. Mansard, Different Methods of Evaluating Wave Power in a Random Sea State: A Comparative
Wave power potential
11. 12. 13. 14.
507
Study, National Research Council of Canada, Hydraulics Laboratory memorandum HY-97, Dartmouth, N. S., Canada B2Y 4A2 (1978). M. Baba and C. M. Harish, Ind. J. Mar. Sci. 15, 144(1986). J. A. Crabb, Synthesis of a Directional Wave Climate. In Power from Sea Waves (Edited by B. Count). Academic Press, London (1980). M. Baba, Proc. 1st Natn. Conf: Dock Harbour Engng I, E 49. Bombay, India (1985). W. F. Baird and C. W. Glodowski, Proc. ht. Symp. Waoe Tidal Energy II, F.3, 39. Canterbury, England (1978).