Chapter 39. A GUIDE TO THE DESIGN OP AIR BUBBLERS FOR MELTING ICE Simon Ince Hydraulics Section, National Research Council Ottawa, Canada

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1 Chapter 39 A GUIDE T THE DESIGN P AIR BUBBLERS FR MELTING ICE Simn Ince Hydraulics Sectin, Natinal Research Cuncil ttawa, Canada INTRDUCTIN The use f air bubblers fr maintaining ice-free areas in lakes and in the sea has been reprted abundantly in the technical literature. This authr (1962) reprted his bservatins n tw air bubbler installatins in the Canadian Arctic t the Eighth Internatinal Cnference n Castal Engineering. The results f these investigatins were, at that time, still incnclusive. Tday, sme f the mystery is reslved and it is the authr's pinin that the existence f a heat reserve is the answer t the prblem. Based n this premise, an attempt is made here t develp sme guide lines fr the prper utilizatin f this thermal reserve. AIR BUBBLER SYSTEMS A review f the literature and evaluatin f experiments and bservatins bring ut the fllwing salient pints. 1. PREVENTIN P ICE-CVER FRMATIN T prevent ice frmatin the peratin f the air bubbler must begin befre freeze-up. If a large thermal reserve due t stratificatin exists, then the upward transprt and mixing f the warmer strata supplies t the surface layers water abve its freezing pint and cmpensates fr the heat lsses t the atmsphere. The size f the ice-free area depends - aside frm atmspheric cnditins - upn the temperature structure f the water, the quantity f water transprted t the surface, the mixing in the vertical plume and the temperature and velcity decay f the surface current. If there is insufficient thermal reserve t cmpensate fr heat lsses, the system may still wrk t a limited extent, prvided there is enugh turbulence created n the surface t prevent the frmatin f a slid ice cver. The heat lsses in this case are cmpensated by the frmatin f frazil ice, each gram f which liberates upn freezing its latent heat f fusin. The frazil particles are carried away by the currents and depsited n the underside f the adjacent ice sheets. The principles invlved in this prcess are the same in fresh r sea water. 600

2 A GUIDE T THE DESIGN F AIR BUBBLERS FR MELTING ICE MELTING P AN EISTING ICE CVER The melting f an ice cver when a large thermal reserve exists is a functin f the flw factrs utlined in the previus sectin. If there is insufficient thermal reserve within the range f influence f the air bubblers, nly a limited amunt f ice can be remved frm the underside f the cver. There are reprts, hwever, that by using underwater purips, under certain cnditins it is pssible t "erde" the sea ice by the mechanical actin f abrasin rather than melt it by thermal energy. The disturbing part f these claims is that the efficiency f the system is reprted t be much greater than 100 percent, i.e. the energy input is smaller than that required t melt the vlume f ice. This is undubtedly an area which will require mre research. Based n reprts f the peratin f this pump, it is the pinin f this authr that tw factrs might have cntributed t the success f the peratin. ( a) There must have been in the regin a small thermal reserve nt detected by cnventinal ceangraphic instruments. With the very large amunts f water circulated by the pump this may have been sufficient t hneycmb the ice cver and cause its disintegratin. (b) The experiments were cnducted in relatively mild weather ( abut 0 C) at which time the strength f sea ice had decreased cnsiderably, thus cntributing t the rapid decay. SME APPRIMATE RULES FR THE DESIGN P AIR-BUBBLER SYSTEMS n the premise that ice remval is due t thermal effects, an attempt will be made t give simple wrking rules fr the practicing engineer, t guide him in the efficient design f air bubbler installatins. The hydrdynamics f bubble curtains in hmgeneus water has been studied quite extensively. Fr the practicing engineer the results f Bulsn (1961) and Abraham and Burgh (196ij.) are mst useful. In summary and referring t Figure 1, the fllwing relatinships are fund t be valid within reasnable limits. (a) The maximum hrizntal velcity V 0 ccurs apprximately at a distance x = d/2 (1) (b) V 0 = 1.2 (g.q a ) l/3 (2) (c) b = da (3) where

3 602 CASTAL ENGINEERING UJ DC Q. >- h; _l Ui > z < DC UJ H- I- < Z 3 QC

4 A GUIDE T THE DESIGN F AIR BUBBLERS FR MELTING ICE 603 d = depth f water q = rate f air flw per unit length f manifld measured at atmspheric pressure g = acceleratin f gravity b = thickness f hrizntal jet at x = p The authr has pltted the decay f the surface velcity, given by Bulsn and Abraham, in dimensinless frm in Figure 2, and has btained the relatinship 0.50 = 1.5 1$) U) («)" In view f the scatter f the experimental pints and because in stratified fluids the surface jet tends t plunge and be effective nly up t a limited distance, this simple relatinship seems fr the present sufficiently accurate. The hrizntal jet under an ice cver has, f curse, the velcity distributin shwn in Figure 3, but it can be reasnably assumed that the decay f the maximum velcity fllws the same law. The effect f the bubbler's rifice size n the maximum velcity has als been investigated and fund t have n significant influence. Prus pipes d increase V p by abut 10 percent but are impracticable because f the higher air pressures required. Fr practical purpses simple squareedged rifices f l/8" t l/l6" diameter are recmmended. The effect f rifice spacing has nt been studied extensively but it was bserved that fr the same air flw a large number f smaller rifices spaced clsely tgether were mre effective than larger rifices spaced widely apart. HEAT TRANSFER THRUGH THE ICE The transfer f heat frm the hrizntal jet t the ice cver is at best a mst cmplicated prblem. By making sme very rugh assumptins, hwever, it may be pssible t arrive at cnclusins which may be f help in designing air bubbler installatins. As a first apprximatin, It is pssible t cnsider the hrizntal flw induced by the air bubbler as a frm f tw-dimensinal wall-jet, where the jet velcity Vj is replaced by V 0, and jet thickness a by b.

5 604 CASTAL ENGINEERING 1 8)1 r^a TT ' >^ -%-f ^_ F <> N D \>HW"" ^ N 8 10 x b a d = 85 ft d = 17 ft d = 25 ft d = 34 ft q» Icfs/ft (? ) BULSN a q 0 = 1-5 l/sec/m a = 6-8 l/sec/m q * 8 l/sec/m } d=2-85m (ABRAHAM ft BURGH) q 3-7 -f l/sec/m i/sec/m I \* 141 l/sec/m d = IIm (ABRAHAM a BURGH) I = 27 l/sec/m i FIG-2 DIMENSINLESS PLT F DECAY F MAIMUM HRIZNTAL VELCITY

6 A GUIDE T THE DESIGN F AIR BUBBLERS FR MELTING ICE 605 V \ i k (VI ^ - II : L ar Ul > Ul a: UJ. > z \l 3 i, /VJL >- / 1 V. ^ I / 1 t 6 li-. / -1 < 1 K ^\ \ / > c Z \; 1 \ / \ 1 A i ^"^*-J' * i^j^-~~ +J ^ ^^ ^ i ' ^ ^\. 1 ' -" ^ * ^^... -» _J Ul > N u. Ul u. a.

7 606 CASTAL ENGINEERING Cmparing the hrizntal velcity decay functin f air bubblers with that f wall-jets, * ->(*) given by Sigalla (1958), it is seen that the analgy des nt appear far-fetched. In the absence f further experimental data n air bubblers, it seems reasnable fr a first apprximatin t use fr ur applicatin temperature variatin and shear distributin functins btained experimentally fr wall-jets. Sigalla (1959 reprts 9 «3 (f) (6) Here 9 =(T ± - T 0 )/(Tj - T Q ) where T-^ = maximum temperature at any psitin alng the wall, T Q = ambient temperature, T* = temperature at nzzle exit. In the case f air bubblers, It wuld crrespnd t the temperature f the hrizntal current at x = d/2. ship Fr the skin frictin, Sigalla reprts the relatin- 0 f = V^V 2 = /(TT) ' fr f > 30. (7) Assuming fr ur case, 0.2 C 'f = ~ " 0.1/(^) J -'\vj L "" fr Vi ~ b > 2, (8) we can make use f the relatinship derived by Sidrv (1957) fr heat transfer by the turbulent hrizntal jet t the lwer surface f the ice, Here, where N = C f R P r l/3 N = Nusselt number = q x/k (T^ - T g ) R = Reynlds number = *» P = Prandtl number = C! ^/k r p (9)

8 A GUIDE T THE DESIGN F AIR BUBBLERS FR MELTING ICE 607 q = lcal rate f heat transfer k = thermal cnductivity f water evaluated at a temperature f ( T-^ + T g ) T g = temperature f wall surface v = kinematic viscsity f water f- = dynamic viscsity f water C = specific heat f water V = maximum velcity at pint x. The Prandtl number fr water at 32 F is It is cnvenient t assume it cnstant fr all applicatins where the temperatures are clse t this value. Substituting int equatin (9) the value f C f frm ( 8) and that f V frm (If), we get * (. and hence, N-.9i*Hr) (I) u), v rffe - -* (-H (!) <»> With the help f the relatinships (1), (2), (3), (6} and (11), a mre ratinal design f air bubblers can be accmplished than has been pssible up t nw. A very simple example may illustrate the new apprach. Cnsider the water-temperature structure in a lake, shwn in Figure 1}.. It is desired t melt the ice at x = 20 m. within 2i(. hurs after installatin f the air bubbler. This requires, n the average, a heat supply q^ = 0.05 cal/cm /sec. Assuming the heat lsses t the atmsphere t be, q 2 = cal/cm 2 /sec. (3600 BTU/ft?/day) the ttal heat t be supplied is, q = q^ + q 2 = cal/cravsec.

9 . 608 CASTAL ENGINEERING x E CM * II " ILE PERATURE PRF >» S > A ~ % ^ a) 3 s E EAMPLE UJ h- t- < 6 u_ a * h 2 < 3 fe's en -J e-2 </) -J v ^ e. UJ ~" 0 z a: - E" c ^ * S ^ f,, > r ' < % UJ «> ^ tt> ^i t «* K

10 A GUIDE T THE DESIGN F AIR BUBBLERS FR MELTING ICE 609 If the bubbler is t be installed at the bttm (d - 20 m.), it seems reasnable t assume that the temperature f the hrizntal jet at x = d/2 will be ppprximately T± = 1 C. Cnveniently, T s = 0 With q = cal/cm 2 /sec. = 2000 cm. k s cal/sec.cm/ C T l " T s = 1 C. V = " 2 cm 2 /sec. h - = 500 cm. equatin (11) yields V Q = 32 cm/sec. Prm equatin (2), q = 1920 cm-'/sec/m. The energy per secnd available in the air leaving the manifld, assuming isthermal cnditins and an air pressure just sufficient t vercme the static head, is given by where = specific weight f water Y w H Q = atmspheric pressure in cm. f water. Substitutin f values yields, E A = 207 watts/m. Fr the same cnditins, if the manifld is suspended at a depth f 10 m, d b = -r = 250 cm, and we get cm 3 V 0 = b$ cm/sec, q a = j^/m, and E. = 373 watts/m. CNCLUSINS The paper is an attempt t put n a mre ratinal basis the design f air bubblers fr melting the ice cver and maintaining ice-free areas in lakes and in the sea. Since there is nt sufficient experimental data t supprt the validity f sme f the relatinships used frm the wall-jet analgy, cautin shuld be exercised in putting t much

11 610 CASTAL ENGINEERING faith in exact numerical results. Nevertheless, it is believed that the prcedure utlined abve might be useful in estimating the rder f magnitude f the air supply and pwer requirements, nce infrmatin is available abut the atmspheric and ceanic r limnlgic envirnment. REFERENCES Ince, S. (1962). Winter regime f a tidal inlet in the Arctic and the use f air bubblers fr the prtectin f wharf structures: Eighth Internatinal Cnference n Castal Engineering, Mexic, pp Bulsn, P. S. (1961). Currents prduced by an air curtain in deep water: The Dck and Harbur Authrity, May, pp Abraham, G. and Burgh, P.v.d. (I96I].). Pneumatic reductin f salt intrusin thrugh lcks: Prc. Am. Sc. Civil Engrs., vl. 90, N. HY1, January 1961;, part 1, pp Sigalla, A. (1958) Experimental data n turbulent wall jets: Aircraft Engineering, vl. 30, pp Sidrv, A. (1957)* The relatin f surface frictin and heat transfer: Sviet Physics, vl. 2, N. 3, pp. lj.99-5>lj..