Experiments on scale effect and bubble formation in two - phase propulsion

HELSINKI UNIVERSITY OF TECHNOLOGY

SHIP HYDRODYNAMICS LABORATORY

OTANIEMI

FINLAND

Report No. 4

EXPERIMENTS ON SCALE EFFECT AND BUBBLE

FORMATION IN TWO

-

PHASE PROPULSION

by

V. Kostilainen,

1. J. Sukselainen and T. Lindberg

Introduction

Two-phase propulsion offers distinct advantages over other systems for application to some special purpose

vessels and lateral thrust units. This propulsion is not susceptible to damage, and machinery installation is simple, and independent of hull arrangements. The principle and the theoretical aspects of this propulsion

system have been presented earlier [1], together with

the results obtained in some model tests.

Very little information is available on this form of

propulsion. Accordingly, it was decided that the study would be concerned first with the scale-effect, using two geosim models, with a view to providing the necessary basic information for further model tests.

The two-phase flow encountered in this case is very unsteady; this might be harmful in practical applications.

However, this unsteadiness is periodic, and in most

instances its frequency is easily measurable. Measure-ments of this frequency were made with some propulsion arrangements, and a study was made of its relationship to basic parameters.

Extensive literature is concerned with the formation of gas bubbles from orifices submerged in liquids, for

example: [21, [3], [4] and 151. All these studies have

been made either

with liquid at rest, and bubbles

rising freely under gravity, or with gas discharged into liquid which is moving horizontally or vertically. More-over, the quantities of air are generally very small. In this type of two-phase propulsion, large quantities of gas are discharged under the stern of the vessel, and gas bubbles rise along the inclined stern plate. This plate affects the form and the spread of the gas bubbles. Visual observa-tions were made, and analysed to provide an insight into this phenomenon.

Small model experiments

For these tests, a comparatively small model was constructed first. Its main dimensions are:

Length, o.a. 2.3 rn

Breadth 0.5 rn

Draught 0.2 m

Displacement 1270 N

The main features of the model are presented in ref. [1]. Only the air orifice configuration was changed for

TWO - PHASE PROPULSION

by V. Kostiainen, I. J. Sukselainen and T. Lindberg

Abstract

A report is given on an experimental investigation of the two-phase propulsion system, basedupon gravity effects. The scale effect on this particular propulsion has been studied, and the frequency and spread of the bubble formation have been measured and analysed.

these tests. After the modification, it consisted of seven equispaced horizontal tubes with a diameter of 25 mm. Additionally, the model was equipped with a resistance type indicator in the middle of the sloping rear bottom. This indicator made it possible to register the variations in the wetting of the spot concerned on an UV-recorder. The air flow was measured with a nozzle type flowmeter, and the pressures were shown by water manometers.

The tow force was measured with an electrical dynamo-meter, as described in ref. [1].

The model tests were made in the calibration tank of the Hydrological Office of Finland, which has a basin 40 m x 2.3 m x 2.0 m in size. The towing carriage has a maximum speed of 4.1 rn/s. An observation pit allows of underwater observations and photography.

The experiments were performed by application of the British method, viz the model was towed at constant

speed and given air flow the residual force between model and carriage was measured. Tests were made with seven air orifices, and also with only one in operation;

this was effected by closing all but one orifice with streamlined plugs.

Large scale experiments.

In spring 1968, a large model boat (Figs. 1,2 & 3) was designed and built, with an underwater part scaled to a factor of 4.0 in relation to the lines of the small model. The main particulars of the boat are:

The boat is constructed of 4 mm mild steel plate. The bare hull was manufactured by a small firm in Helsinki, and the fitting-out was done at the Helsinki

University of Technology.

The powerplant consists of a Volkswagen 122 air-cooled industrial engine, connected to a single stage radial blower supplied by VALMET Oy, The unit is

capable of delivering about 2.0 m3/s of air at 8000 N/

m2. Electric current is provided by a i kW portable generator. Length, o.a. 10.1 m Length, cwl 7.0 m Breadth 2.0 m Height 1.5 m Displacement 81100 N

2

COtiPRESSOR

AIR COOLED 3L HP ENGINE

CONICAL INLET NOZZLE

AIR ORIFICES

F i g. 3. Air orifices under bottom of large model boat.

REVERSING VALVE

F i g. 1. General arrangement of large model boat.

F i g. 2. Aerial iew of large model boat.

The manoeuvring system of the vessel consists of twin rudders placed abaft the skegs, and a reversing

system. The reversing mode is effected by a flap valve,

which prevents the main air flow, and directs the air

through a pipeline to the bow.

The boat is ballasted with i ton of solid weights, and about 20 water-filled 200-litre barrels. The solid ballast, consisting of concrete slabs, is used only to improve the lateral stability of the vessel. The water

ballast is conveniently handled with a small,

electrically-driven household pump. Thus the need of manpower during the experiments is minimised.

The rotational speed of the blower was monitored by a simple RPM-meter. The rate of the air flow was

measured with a conical inlet nozzle, approved by the British Standards Institution. Initially, an attempt was made to measure the pressure difference of the nozzle

with an inclined tube micromanometer, but it proved rather inaccurate by reason of the movements of the

boat. Subsequently, the monometer was replaced by an

electrical differential pressure transducer, with accompa-nying carrier amplifier and potentiometric recorder. The pressure in the air chamber was measured with a simple water manometer. A spring scale was employed for tow force measurements.

An accurately measured coursc was marked along the shoreline of Otaniemi, in the Laajalahti inlet. The length

of the course was 657.0 m, and the depth of water

about 4 m.

The vessel was towed by a motor-boat for measure-ment of its resistance and for measuremeasure-ments behind the self-propulsion line. The towrope was about 150 m in

length, and made of polypropylene cord 8 mm in

thickness.

In regard to the accuracy of the measurements, it must be mentioned that by reason of the pronounced unsteadiness of the air flow, the rate of flow values arrived at by averaging the pressure difference of the

inflow nozzle is somewhat uncertain. As no information

is available on the performance of such a nozzle in

pulsating flow, no corrections are practicable. Presuma-bly, the indicated value exceeds the actual mean rate of flow by a small percentage.

Scale effect

Results of the scale-effect tests were made dimension-less by means of the coefficients derived in [1]:

CTA F h TA P L g B h2 (1)

-

Bh/

(2) UL (3)

\/gh

The symbols and the definitions of various quantities are listed in the nomenclature.

The apparent thrust coefficient in bollard-pull condi-tions has been plotted as a function of volumetric flow rate coefficient in Fig. 4.

lt is observable that in this case no obvious scale effect exists in particular at the lower values of flow rate coefficient, the point scattering is slight. This figure also contains a plot of the results of some tests made with different numbers and sizes of discharge orifices. The scattering of these points is also small when thegas

flow rate coefficients are below 0.2. At higher flow

rates, different values of apparent thrust coefficient were

obtained, even though the flow rate and the scale were

the same. However, when the gas flow ratesare large,

two-phase flow under the stern of the vessel is very

F i g. 4. Apparent thrust coefficient CTA as a function of

gas flow rate coefficient under bollard-pull

conditions.

unsteady. Thrust variations are large, and the mean values measured are unreliable.

The results of propulsion tests at different speeds

are presented in dimensionless form for both small and large models in Figs. 5 and 6, respectively. Large scale measurements were made only at loadings, which were lighter than or equal to self propulsion loading. Heavier propeller loadings were also studied on a small scale.

Thrust coefficient curves for both model scales are presented in Fig. 7. A reliable comparison can be made, at least

near the

self-propulsion lines

at which a

considerable scale effect is visible. The thrust coefficient values obtained with a large scale model are larger than those with a small scale model. This difference in the thrust coefficient values rises with increasing values of gas flow rate coefficients.

lt is believed that thils scale effect is due to viscous effects. The reference speed applied for calculation of the Froude numbers is the speed of the model. On the small scale, the boundary layer isrelatively thicker than that on the large scale. Nevertheless, the _{sizes of the gas}

bubbles are proportional to the linear scale if the gas

flow rate is _{the same. Thus the amount of the water}

accelerated by the gas bubbles, and consequently the

values of the thrust coefficients attained, are larger_{¡ara e. scale ll1an.on a} on a small one. This assumption further explains why no scale effect was observed under bollard-pull conditions. However, additional research should be made to confirm this hypothesis, and to prepare the necessary data for estimation of the magnitude of this effect.

A peculiar point, clearly visible in Figs. 5 and 7, is

the tendency of curves for the apparent thrust coeffi-cient of the small model to turn upwards beyond the Fflh-value of 0.8. This phenomenon is obviously

attribut-able to the separation of flow under the inclined_stern

0,1*0

4

SMALL SCALE B - 0.5 rn + 49 ORIFICES

A 7 «-10mm

LARGE SCALE 7 ORIF ICES O

7 "-25mmDIA

B-20m h0.680,80m h 017....0.23 ¡ii 5mm DIA 139mm DIA

-DIA I

/

4 01 0.2 0.3 0.4 Q2 0 0.15 CTA 0.10 0.05 o

F i g. 5. Measured values of apparent thrust coefficient

CTA as a function of Froude number Fflh, small

model.

during resistance tests. The separation of flow increases the measured resistance. During the propulsion experi-ment, the flow induced by the rising air bubbles acts in part as a means of propulsion. As a secondary effect, it

prevents the separation under the stern, and thus reduces the resistance of the model. This effect is actually the

dominant one at sufficiently high model speed, as is

observable in Fig. 8, where the cross curves for constant

speed are drawn by use of the data from Fig.5.At low

Ffl h-values, the extrapolated thrust coefficients approach zero as the rate of air flow does. At the highest speed

applied, the apparent thrust remains nearly constant over the whole range of flow rates, and is thus obviously no more than the difference of resistance forces, with

and without separation. According to Fig. 8 only the

thrust values measured at speeds below Fflh = .8 are

meaningful in this particular case.

0 02 04 06 08

F5 10 12

F i g. 6. Measured values of apparent thrust coefficient

CTA as a function of Froude number Fnh, large

model. 1.4 SMALL MODEL B 05m h0,175m 7 ORIFICES 25 mr,, DIA + + + + + o A _{°0.10 Aa015} A 015 ASO.2O 0.20025 a0.2S.cA 030 + 030' c0.40 040 LARGE MODEL B2.0m 5=0.68-0.80 m 7 ORIFICES 139mm DIA (o 0.10 _o#O.15) 0.15 o 0.20 O2toO25 a 0 25' 80.30 * 0 30 A # 8040 0.40 Ø 8= + A

:::

0.40 0.30

SELF PROPULSION LINES

G=0.40 035 0.15

I

0.30

7

0.25 " _F 0 20 0.15 \ SMALL MODEL 8= 05m h0175m 7 ORIFICES 25mm DIA LARGE MODEL 8=2.Cm h=O.68_0 80,,, 7 ORIFICES 139mm DIA I I 0.2 04 06 08 1.0 1.2 11.

Frequency of bubble formation Fnh

From the beginning of the first tests made with this _{F i g.} 7. Apparent thrust coefficient curves for small and

type of propulsion there has been remarked a more or large models.

02 04 06e- 08 10 12 1.4 nh 4 0.22 C 20 0 18 0,16 CTA 0.12 0,10 0.08 0 06 0 04 0.02 o 0.22 0.20 018 0.16 CTA 0.14 0.12 0.10 0.06 0.06 0.04 0 20 018 016 0.14 0.12 CTA 0.10 0.08 0 06 O DL 0.02

F i g. 8. Values of apparent thrust coefficient as a function

of gas flow rate coefficient, small model.

less pronounced unsteadiness of the flow and action of

the propeller. This is induced by the rather regular disintegration of the gas jet into bubbles, and might be harmful in practical application if the frequency is not known at the design stage. Rayleigh [6], inter

alia, has examined the stability of gas jets in liquid and has noted that any small disturbance which reaches the orifice will be communicated to the jet, and that in the

jet this disturbance is either amplified or damped.

Rayleigh has derived the wave length of maximum amplification, this wave length is 6.48 times the mean jet diameter. By use of this value of wave length as an

interval at which the jet will break up, Silberman [3] has

developed two equations for the frequency of bubble

formation. For the case in which the liquid and orifice

are at rest, i.e., the air jet rises under gravity prior to

disintegration, he obtained the frequency: i

f = 0.685 g3 5 (4)

with the liquid moving horizontally with relation to the orifices at speed UL Silberman derived, with the effect of gravity ignored, j-f = 0.137

U3 )2

(5)

it

f 0.685 0315 0020 0.025 o/mys

(gsin)31

VGO

F i g. 9. _{Frequency of bubble formation as a function of}

flow rate, small model, 1 air orifice in operation.

In two-phase propulsion,

the stern of the ship

prevents the free rising of the jet. If the angle of

inclination of the stern plate is , then the acceleration of the jet rising under gravity is g sin ß. If the liquid and orifice are at rest, then the frequency will be

(6)

It should be observed that the gas-flow rate VGO for

use in the previous equations is the rate per jet. For a

single orifice, or for widely spaced orifices, the gas-flow rate per jet corresponds to the rate per orifice. For more closely spaced orifices, several orifices may contribute to each jet.

The results arrived at in the frequency measurements, made with a small model and one air orifice in operation, are presented in Fig. 9, together with the curves corre-sponding to equations (4), (5) and (6). Theoretically, fre-quency values measured at a zero speed of advance (dotted line in Fig. 9), should be the same as the fre-quency values derived from equation (6). However, when the air flow rate is very small, the measured values of frequency are lower. lt is believed that is because when the air flow rate is small, the bubbles are produced one at a time, with the size and frequency being deter-mined primarily by the surface tension, orifice diame-ter and buoyancy. Equation (6) is valid under jet con-ditions only, when the gas emerges in a continuous jet. At higher values of gas flow rate, the measured values of frequency are higher than the values derived from

equa-u0 n,/

U 0.2 Q _L, 0.4 Q U 0.6 O U00.8 O ko 1.0 S 15, 1,2 l.5 14 U1.6 o

k

.

's

:''

* fo0137(.-._) U. .2 vo U,,o0.4 ,,,/ F,4Ù0 Fflh 0,15 F,, 0.31 Ffl OE63 O FnhoO.91 F,5.0.93 A . 23

_

F.I05U

93

V

005 010

5

020 025 030 025 040 02 0.18 016 022 C14 010 008 0.06 004 002 0.005 0010 0.030 0.035 0.040

f Hz 7.0 6.0 50 ¿.0 30 2.0 10 o 6 20 m 10

F i g. 10. Frequency of bubble formation as a function f air

flow rate per orifice, small model, 7 air orifices in operation.

tion (6). This obviously results from the water speed

induced by the bubbles.This induced speed increases the speed of the gas jet, diminishing the jet diameter, and

increasing the frequency.

The speed of advance exerts the same effect as

induced speed: it increases the frequency. However, there seemed to be an upper limit of frequency values, not

exceeded even at the highest speeds tested to date. This

upper limit coincides with the values derived from

equation (4).

Frequency measurements were also made with a small model, with 7 air orifices in operation. The results are presented in Fig. 10. lt should be pointed out that in this case "GO represents the air flow rate per orifice.

UL 0.84m/s

F i g. 11. Typical bubble formation, i air orifice in operation,

UL = ° VJ = 0.0033 m3/s, f = 3.3 1/s.

Spread of bubbles

Extensive literature exists on the formation of gas

bubbles from orifices submerged in liquids; references

[2] to [5] are representative of these publications.

However, these experimental studies have been made either with gas bubbles rising vertically under gravity, or with bubbles dislodged by a passing stream. In two-phase propulsion, both the gravity and the passing stream

affect the bubble formation; in addition to these, above

the bubbles is a fixed boundary, the stern of the ship. For study of the spread of air bubbles in two-phase

propulsion, a small scale model was tested with one air

orifice in operation. Apart from measurement of the usual quantities, jet disintegration and bubble spread were observed by means of photography. A detailed

report on the observations made is presented in [71. Fig.

20 cm 10 20 cm 10 U l.23m/s

F i g. 12. Envelopes of the contact surfaces of the bubbles and stern plate as a plate

as a function of mean bubble volume and speed.

o Q o O G

;;;;rJ

UL= 0.0mm UL=0.2 OUL=0,4 Ui..=06

\<'.:°:.°!

+ + .006 .00 o 001 002 .003 .0O .005 V00 /

11 illustrates typical flow picture taken above the trans-parent stern of the model.

The spread of the bubbles can be described with an

envelope of the contact surfaces of the bubble and

inclined stern plate.

One half of the symmetrical

envelopes, obtained from photography, are presented

O

in Fig. 12 with mean bubble volume VB

_-

as a

parameter.

Both coordinate axes of the system of

reference in Fig. 12 are lying upon the inclined stern

plate, the x-axis on the centreline of the model, y-axis normal to x-axis, origin just above the air orifice.

Ac-cording to these envelopes,at first the bubbles widen sideways at a relatively high speed. Later, widening

becomes slower, and the breadths of the contact surfaces

of the bubbles and the inclined stern plate approach

a maximum value asymptotically. This maximum value decreases with increasing speed, and thus the broadest

air bubbles appear at zero speed of advance. Fig. 13 indicates that this maximum breadth divided by the cubic root of mean bubble volume is nearly constant,

and independent of the mean bubble volume.

50 LO 3O 20 10 VB/dm

i g. 13. Maximum breadth of the contact surface of the

air bubble and stern plate as a function of mean

bubble volume, zero speed of advance.

3

Conclusio ris

The results obtained in the present experimental study enable the following conclusions to be drawn:

In bollard-pull conditions, no scale-effect in propul-sion is apparent. At a non-zero speed of advance, the

values of the apparent thrust coefficient arrived _at with a large

scale model are higher than those

obtained with small scale model.

At small speeds of advance, and low air flow rates, the frequency can be approximated by the equation

i

(gsinß)3

VGO

Increasing speeds and air flow rates raise the

frequen-cy. In general, the maximum values of measured frequency can be described by the same equation by setting sin ß= 1.

Initially, the spread of the bubbles under the stern

plate is relatively rapid; later it becomes slower, and approaches a maximum value. Increasing speed

dimin-ishes the spread of the bubbles. Under bollard-pull

conditions, the maximum breadth of the contact

surface of the gas bubble arid the stern plate, divided

by the cubic root of the mean bubble volume, is

approximately constant, and in the case tested

equal to 3.2.

Acknowledgement

This research work was carried out in the Ship

Hydrodynamics Laboratory of the Helsinki University of Technology. lt has been financially supported by the

Finnish Committee of Technical Sciences, and by the Wihuri Foundation. The authors express their thanks to

all those who contributed to the study.

f = 0.685 j

s-

5 L 3

*8

2

B TA CTA= _{Pi gBh}2

Fnh

-y gh f 8 g h N TA UL Vß = VGO/f VG VGO = VGIN ß PL References

[1} Kostilainen, V., Two-Phase Air-Water Propulsion [5]

System Based on the Gravity Effects. International Shipbuilding Progress, Vol. 15, 1968, No.169

[2j D.W. van Krevelen, P.J. Hoftijzer: Studies of Gas- [6]

Bubble Formation. Chemical Eng. Progress. Vol. 46, 1950,No. 1.

[7] E. Silberman: Production of Bubbles by the Dis-integration of Gas Jets in Liquid. 5th Northwest. Conf. on Fluid Mech. Ann Arbour, 1957.

I. Leibson, E.G.Holcomb, A.G,Cacoso, J.J.Jacmic: Rate of Flow and Mechanics of Bubble Formation from Single Submerged Orifices. A.l.Ch.E.Jourrïal Vol. 2, 1956, No. 3.

VG

Bh \/gh

Nomenclature Breadth of vessel at gas discharge orifices Dimensionless apparent thrust coefficient

Froude number, dimensionless

Gas flow rate coefficient, dimensionless Mass density of liquid

Frequency of bubble formation Acceleration of gravity

Vertical distance between the water surface and orifice centre line Total number of orifices

Apparent thrust = difference between resistance of the vessel with propel

operating, and with propeller in operation Velocity of liquid at orifice

Mean volume of bubble

Volumetric gas flow rate of the propeller at normalised pressure and 15 °C temp Volumetric flow rate pet gas orifice

Angle of inclination of flat bottom plate

PRINT 0V 9E ISI NEI 970

let not

erature

W.B. Hayes, B.W. Hardy, C.D. Holland: Formation of Gas Bubbles at Submerged Orifices. A.l.Ch.E. Journal Vol. 5, 1959, No. 3.

Lord Rayleigh: On the Stability of Cylindrical Fluid Surfaces. Phil. Mag., Vol. 34. 1892. No .207. T. Lindberg: En experimentell undersöknirig av den vid tvâfaspropulsion uppstãende vâgrörelsens frekvens och utbredning. M.Sc. thesis, Ship 1-Jydro-dynamics Laboratory, Helsinki University of Tech-nology. 1969.