baham g j.stack design technol.1977.trans

SNAME Transactions, Vol. 85, 1977, pp. 324-349

Stack Design Technology for Naval and Merchant Ships

Gary J. Baham, 1 Member, and Donald McCallum, 2 Associate Member

This paper discusses design techniques for surface ship stack casings and exhaust duct terminals. The discussion treats both naval combatant and auxiliary vessel stack designs, as well as commer- cial stack configurations. The traditional engineering problems unique to stack design are described. These include naval architectural problems associated with topside arrangements and superstructure design as well as safety and esthetic considerations associated with entrainment of the smoke plume in downwash passing over ship's decks. The experimental data base for the design practices used by the U. S. Navy is presented and discussed. Examples of unique contributions to the state-of-the-art are presented. Analytical theory and procedures are described in detail. These include design guidance for selecting the height, shape, location of the stack, and techniques for estimating the downwind plume gas temperatures and trajectories.

Introduction STACK DESIGN TECHNOLOGY for ships has received little

attention in the United States during recent decades. More or less standard solutions have been applied to naval and merchant vessel designs for steam and diesel propulsion plants. The most notable exceptions have been in the design of certain classes of naval destroyer escorts and fossil fuel-powered aircraft carriers where hot exhaust gases tend to become trapped in the downwash of the stack casing or superstructure and expose various topside operational areas, ventilation openings, electronics, and weapon systems to high temperatures and contamination. The' avoidance of these problems of U. S. naval vessels has resulted in continuing development of design and testing techniques.

This paper presents a brief compilation of the significant theory and design practices which are used as well as the results of recent full-scale trials conducted on a new class of gas turbine-powered destroyers. The Naval Ship Engineering Center has been collecting model and full-scale data for the past 10 to 15 years, and has developed formulas for the prediction of plume shape, trajectory, and temperature. This paper represents the latest update, based upon the most recent trials data.

Plume flow theory for exhaust gases ejected into a uniform, stable crosswind has been the subject of study by NACA (prior to NASA), by the Massachusetts Institute of Technology, by the University of Minnesota at St. Anthony Falls for power plants in this country, and by the Cranfield Institute of Technology in Great Britain for the Royal Navy.

This paper presents design guidance for stack height and shape in the form of a step-by-step procedure. Also, guidelines for selection of stack gas design velocity are given and a worked example of a complete stack design for an auxiliary oiler. Test data collected on board USS Foster are presented in the Ap- pendix. The paper presents guidelines which should be used in stack design, such as the importance of having the stack gases

l The BAHAM Corporation, Columbia, Maryland. Naval Ship Engineering Center, Washington, D. C.

Presented at the Annual Meeting, New York, N. Y., November 10-12, 1977, of THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS.

clear the ship's boundary layer. It is concluded that ship stacks can be optimally designed to perform well at a variety of wind and engine power settings.

Background Since ships changed from sail to steam plants, smoke nuisance

problems have existed. The first steamers, with thick black smoke belching out, often made traveling a nuisance, since, in certain unpredictable wind conditions, the black smoke would be directed by the wind over the deck. The passengers had the choice of staying below or going forward. The era of the two-, three- and four-stack passenger liners brought relief from smoke nuisance problems. The thirties produced the Queens, both powered by oil-fired boilers, whose classical funnels did much to enhance the age of the passenger liner.

The problem which concerned the passenger liner designer was principally one of keeping the effluents off the passenger decks and recreation areas. Why would passengers want to spend a large sum on a Mediterranean cruise, and be troubled by inhaling smoke from the boilers? Also, soot which was precipitated over the decks caused maintenance problems and was another passenger annoyance. Designing the stack high enough to penetrate the ship's aerodynamic boundary layer was obviously the most straightforward solution, but other inno- vations such as the wings on United States and the air eductor system on Queen Elizabeth II have also been used.

With the advent of motor ships, the classical high, narrow smokestack gave way to the squat and streamlined stack with which we are very familiar. Often included within the stack casing are ventilation intakes, engine air supply intakes, emergency generator room, and other small spaces such as wet gear lockers. The exhaust gas temperatures are in the range of 450 to 550 F (282 to 288 C) for these reciprocating engines. Sherlock [1] 3 and Nolan [2] wrote papers describing good practice in stack design in the forties. Then, because of the occurrence of smoke nuisance problems, Acker [8] wrote his classic guidelines on how to avoid such problems.

With the development and implementation of gas turbines

Numbers in brackets designate References at end of paper.

324

Fig. 1 Ideal flow around a circular cylinder

Fig. 2 Real gas flow around a circular cylinder

ACCELERATED FLOW SEPARAT~

DECELERATED FLOW SEPERATED FLOW IN CORNER

Fig. 3 Flow around a bluff body

during the 60's and 70's, other problems due to vastly increased mass flow and higher temperatures presented themselves, particularly in the case of warship designs, with their prepon- derance of topside electronics being threatened by degradation due to heat. In 1972, the Royal Navy performed full-scale temperature measurements of the smoke plume on board two County Class cruisers [41.

These tests provided a source of data which was used in the prediction of plume temperatures in new designs. Recent (1976) testing by the U. S. Navy on board a DD 963 Class destroyer, the USS Foster [5] amplifies this body of data. The Foster (DD 964) has gas turbine engines, but a novel eductor design mixes the hot gases down to temperatures in the range of diesel exhausts.

On ships such as aircraft carriers and helicopter carriers, extra care must be taken during the design to ensure that the exhaust gas will not interfere with normal aircraft operations; indeed the stacks should be designed such that the range of allowable wind conditions for aircraft operations is maximized.

The. critical impact of these hot gases has resulted in recurring problems with topside gear such as antennas, electronics for communications; radar, and weapons systems. Naval ships have tended to favor very short stack casing heights due to competition for topside space, weight, and electronic inter- ferenee. The need for the capability to predict the local temperature of gases which impinge on topside areas of the superstructure has prompted developing a theory for predicting gas plume height and temperature decay after the gases leave the exhaust pipe.

Plume f low and temperature theory

Gas flow around bodies To visualize flow in an airstream around a stack, consider the

stack as a long circular cylinder in a crossflow of ambient fluid. If the gas in this flow were perfect (that is, no losses due to viscosity), it would regain its original flow pattern after passing the cylinder as shown in Fig. 1.

As an ideal gas passes the cylinder, the velocity of the flow increases. This results in a corresponding increase in kinetic energy with a corresponding decrease in pressure. At the point where the flow passes the maximum width of the cylinder, kinetic energy is at a maximum and is sufficient to cause the flow to return to the original streamlines. However, air is not a perfect gas. As a real gas it possesses frictional viscosity which causes kinetic energy losses when traveling past the cylinder. Because of this reduction in "kinetic energy the flow cannot return to the original streamlines and is forced to separate as shown in Fig. 2.

Separation forms a region where the static pressure is lower than free stream but higher than the fast-moving layers immediately around it. These fast moving layers support a pressure difference due to their momentum. Eventually they turn in upon themselves-and roll up into vortices, with axes parallel to the axis o f the cylinder. These vortices flow downstream and slowly disintegrate as the low-pressure central region entrains free-flowing gases. This causes the vortices to increase in mass and decrease in rotational momentum. Eventually rotation breaks down completely and flow no longer follows any particular pattern. It has been shown that vortices must be staggered to be dynamically stable and form what is known as a "Karman Trail" [5].

The flow over a bluff body separates from the boundary ahead of the body to form an eddy region on the windward surface. A second separation occurs on the leading edge of the upper surface and spreads to fill the area behind the body. Regions above the separation are smooth. The flow has generated a streamline flow over an abrupt obstacle and a turbulent. region immediately in contact with the obstacle. Mixing of the free stream with the turbulent area occurs at the interface and tends to continue the disturbance downstream. Vortices are generated as shown in Fig. 8.

The flow around the ship stack is a combination of the circular cylinder flow and the bluff body flow. To complicate matters this body ejects gases vertically and the entire turbulent flow pattern-is subject to abrupt changes as the yaw angle changes.

1. Deformation of the plume as it is bent. Usually, the stack plume is emitted perpendicular to a laminar crossflow. In a region of laminar flow a gas jet has distinct boundaries. At its source the jet has a reasonably uniform velocity profile and relatively low turbulence. As the jet rises it is deflectedby the crossflow and the plume bends until its flow is principally horizontal. A pressure field forms around the jet as it is deflected, causing it to form a kidney shape. The jet will remain distinct as long as the crossflow is laminar but in a region of turbulent flow the jet will quickly spread out and no longer be distinct. This is what hapl~ens if the plume enters the turbulence of the ship's superstructure.

2. Local effect. The stack usually can be represented as a short cylinder. Gas flowing around this cylinder experiences an increase in pressure on the windward face and a corresponding decrease of pressure on the sides and back. Air flows over the top and down the back of the stack as shown in Fig. 4. If the gas emitted from Point A of Fig. 4 has sufficient velocity, Vs, it will be carried along Path C. But, if gas is emitted at A with a very low Vs, then the influence of Vw will cause it to

Stack Design Technology for Naval and Merchant Ships 325

follow a path to B. This second flow is called a "downwash" and if sufficiently strong will cause gas to come down to the deck as it mixes in with the vortices behind the stack. For typical merchant ships the "downwash" does not extend more than one-half to one stack diameter below the stack outlet. The velocity ratio, V.~/Vw, is the determining factor for downwash being a problem. The amount of downwash is also influenced

• by the shape of the stack and yaw angle. A streamlined stack at small yaw angles will not generate the vortex trail that a circular stack generates. The strength of these trailing .vortices is a major contributor to downwash.

3. Ships turbulent zone effect. The superstructure of a ship is composed of a number of bluff bodies each of which con- tributes its own turbulent wake. Each obstacle acts as a turbulence generator that sheds vortices which gradually mix with the region of laminar flow as they travel downstream. To- gether these generators combine to form a general turbulent region which encompasses the entire ship superstructure and is known as the turbulent zone. Model tests have confirmed the existence of a turbulent zone of varying depth. These tests have also shown that the turbulent zone is a function of ship superstructure and yaw angle. In the previous section it was noted that when a plume enters a turbulent region it will mix throughout that region. Therefore, if the stack plume enters the turbulent zone via stack downwash, the smoke will be brought down to the deck. Traditionally the top of the stack was well above the turbulent zone and downwash did not cause a problem. But this is not now the case. The transition from laminar to fully turbulent flow is a gradual one that takes place through a region of significant depth. A stack ejecting gas into this transitional region will perform satisfactorily only if downwash is properly controlled. The Navy FFG-7 Class is an example of a ship class that ejects the stack gases directly into the turbulent zone. This was possible after increasing the stack gas velocity to 260 fps (85 m/s).

4. Yaw angle. Yaw angle is the angle of the wind relative to the ship's heading. Yaw angle affects both the turbulent zone and the downwash around tile stack. Usually ship stacks are longer than they are wide and will therefore have different flow patterns as the yaw changes. Generally, the performance of an individual stack in a laminar crosswind degenerates as yaw increases from 15 to 60 deg and improves from 60 to 90 deg [3]. This improvement is caused by a change in the direction of flow over the stack. For small yaw angles the flow over the stack is largely horizontal and continues to be horizontal until the flow approaches 60 deg of yaw. From this point on, the vertical sides of the ship become dominant flow directors, the direction of the flow becomes vertical, and the vertical flow carries the stack gases higher. The result is improved stack performance.

Plume momentum and buoyancy

The exhaust flow plume from a stack is a mass of heated gas that is buoyant and this buoyancy affects the plume trajectory. Buoyant forces become increasingly important at higher velocity ratios. Normally, the higher velocity ratios are not critical design conditions because the plume tends to travel straight up at nearly 90 deg to the crossflow and is not significantly deflected. Thus for low velocity ratios, the stack gas and ambient wind momentum--and not stack gas buoyancy--will determine the plume trajectory.

Houit, Fay, and Forney have formulated a theory for a buoyant plume in a laminar crosswind [6]. They were able to show that the equations governingthe fluid motion indicate three nondimensional parameters which must be duplicated in order to establish complete correspondence belfween laboratory experiments and full-scale plumes. These are:

• 326 Stack Design Technology

- - - - v w

I=Jg. 4 Resultant path of stack gases in wind

Vs _ plume exit velocity Vw crosswind velocity (1)

Fr = Froude number - Vs ,/~g~Rs (2/ P,~-- P s T s - T ~

- ( 3 ) p~ Ts

Previous investigators have generally neglected ¢~ because for most plumes it is a small value (6 << 1). The rate of entrainment of ambient fluid is assumed to be the product of a velocity difference, plume perimeter or mixing area, and two nondimensional constants for the tangential and normal velocity differences, a =/3. Two flow regimes are defined. First, the momentum length scale Lm is defined as

where Lm is defined as being the horizontal length from the gas exit up to the point where the plume is deflected 45 deg by the crosswind. Momentum flow dominates when

Beyond that, the buoyancy length scale is

Fs L~ = ~ (5)

where

Fs = Vs Rs26g g = acceleration due to gravity

and Lb measures the rate of rise of a buoyant plume far downstream of the stack.

In the near field, or momentum-dominated flow region, the form of the equation for plume rise derived by Hoult, Fay, and Forney is

(6)

They have concluded that c~ is a universal constant with a value of 0.15. /3 does not have a universal value but depends upon VJVw and Ft. /3 has been chosen from experiments to obtain the best agreement between theoretical and observed plume trajectories. The following range of values has been observed in field tests:

0 . 8 < / 3 < 1 . 2

A value of 1.2 for/3 has been chosen from model testing con-

for Naval and Merchant Ships

REFERENCE

Table 1

EQUATIONS

[6]

dp = If Vw is constant and ~yy 0, then for x < xc

y _ (V,s/Vw) (xlRs) 1/2 R.~ (/3 + (~ V.JVw) 1/2

where x~ is given by:

x< = ' , ~ - I ',l~ 4 ~ ~,Jvw/

For x > Xc the trajectory is given by:

y = (~---~)1/3Lbl/3x2/3

Stack exit Froude No.

Fr =

[11}

Plume radius is given by:

= - y

in the near field V.~

- - 2

L g ~ "'j

[91

y _ (V , /Vw) (x /R, ) 1/2 R~ (~ + , V , /V , , ) ~/2

y _ ( V J V w ) (x lRD °'37

R, (1.2 + 0.15 V~IV~) 112

Temperature equations:

Tm - - To _ ~,(x/R~) °.63 T.~ - T= 1 + "¥(x/Rs) °.s3

Plume behavior lheories

NOTES AND ASSUMPTIONS Trajectory equations are presented for two regions of flow.

' The work herein is derived from the case of a high stack so that atmospheri c turbulence is minimum. In addition, if the momentum of the exhaust gas is sufficiently high, the effect 111' turbulence can be neglected. However, the final equations are derived assuming a constant crosswind.

Lab work has shown that velocity profiles are locally similar within 10 orifice diameters. Hence it is likely that the shapes of the velocities and density profiles do not change except for a scaling factor as the plume moves downstream. Jordinson showed that the main factor in determining the

(6) trajectory of a plume is the rate at which it entrains mass from the ambient atmosphere. Thus plume trajectory can be determined from conservation of mass, momentum and energy by using the entrainment assumption to determine the rate of mass, momentum and energy addition to the

(12) ~ plume.

The length scales: (pure, jet length scale) Lm = momentum length scale Lm = Rs Vs/Vw Lm 2 is proportional to the initial momentum of the jet

(13) Lb = buoyancy length scale, measures the length of a pure plume

From equation (12) we note that L m a/Lb 2 is proportional to ( V J V , , ) :~, The results indicate that although y is a

(2) function o f x n, n is not a universal constant.

Geometric similarity can exist i fLm/Rs and Lb/Rs are the same for two flows. However, usually the velocity ratio and stack Froude no., Fr, are used to judge similarity.

From these scaling factors come values of c~ and fl which are: (~ = 0.15 (universal constant), ~ varies with Vs/Vw and F~. f:~ generally lies between 0.6 and 1.2 with a mean of 0.9 for the Tennessee Valley Authority Data. Charwat selected fl = 1.2

(10)

(2)

Model Test Series 1. Stack Reynold's number varied from 28 to 2800. V J V w

= 4 and (p= - ps)/p~ = 0.4 2. Tests were conducted in a water tank. 3. Results:

A. Values of optimum fl for equations by Hoult, Fay and Forney [6] 1. fl = 0.9 for field cases 2. fl = 0.56 for laboratory experiments

B. Transition from laminar flow in the stack to full turbulent flow occurs when the local Reynold's number is of the order 1000.

C. Plume behavior does not depend on stack Reynold's number.

(6)

(14)

(15)

This equation is the Hoult equation. Charwat modified it by using ~ = 0.15 and ~ = 1.2 and adjusting the exponents until the equation fit his data.

Charwat proposed that the difference between his data and theory is due to wind tunnel effects. Hoult states that although x" is a controlling factor of plume rise, n cannot be a universal constant:

= mass averaged local plume temperature

v = (fl + ¢o V / V , , , W 2

(continued)

ducted by Charwat [9] for the DD 963, Beyond the momentum-domina ted flow region, where

L m R < x < Lb

the p lume trajectory cannot be de te rmined f rom any simple formula. Several investigators have published empir ica l solutions for p lume trajectory based on model and full-scale data. Several of these theories are summar ized in Table 1.

The British have conducted extensive study and full-scale trials of stack plume flow with gas turbine prime movers [4] and they have conf i rmed that the m a x i m u m temperature , Tm, along the center axis is a funct ion of the nondimensional path length along the plume. McCal lum der ived a modif ied relationship for t empera tu re 'decay based on data collected by the U. S. Navy [8]. The resulting equat ion f rom the U. S. Navy studies is


REFERENCE

]41

[8]

[71

EQUATIONS

Vs 2 1.3 ] (},) K

¢ - S/D.~

Plume trajectory

( - ~ s ) 3 = [ ~ s (~--sw)2]l'3(x/ns)

TemPerature prediction (V , /Vw) o-25

,h = s/Ds

Table 1 (continued) NOTES AND ASSUMPTIONS

Trajectory equa t ion- - th i s is a modification of "Ivanov's

I cubic." T m - T~

Plume tempera ture = ~b - Ts - T=

1. Effective diameter, D.~, based on stack exit area.

(16) 2 This subst i tut ion is valid T---2~ ~ pi • T i - - p - ~

(17) ~ 3. Values of K (shown to be independent of velocity ratio between the values of 2 and 5). a. Free-s tanding funnel discharging into free stream, K

=1.1 b. Flush orifice, with jet at 90 deg to flow, K = 1.9 c. Flush orifice, 20 deg to vertical upwind and downwind

is, respectively, K = 1.2 and K = 2.1

Equation (17) was used to make predict ions under the (18) following conditions:

Relative winds from ~t V J V w < 3 ahead

Relative winds from @ V J V w < 4 astern

Plume trajectory becomes Y _ N (Vs/Vw) ( X / R J O4s [(T~/Ts) 5"7 + 0.063)] D [2.4 + 0.3 (VffVw)] °5

where

N = 8.6 for a single stack N = 6.6 fnr multiple stacks

Tempera ture prediction

~h = 5 .86(VJVw)°25[ (Ds /S) 1"44

+ O.O17][(T~/T,) 4,5 + 0.20]

(7)

(8)

(9)

Equations were derived based on GE LM2500 gas turbine data, Brit ish DD data, SCS model tests, DD 963 model test data, PF design data and Cranfield model test data.

Equat ions based upon full-scale testing of DD 964 (USS Foster) at a wide range of V J V w ratios• The data were meshed with British full-scale results and allow for buoyancy effects.

A s

D~=

B =

Fr =

H = L b =

L m "=

M = Res ---

nez =

a s -~

L s -~

R e =

S =

• T,r ~

T,=

T m =

T= = W a =

W s ~-

exhaust pipe area (total for one or several pipes)

equivalent exhaust pipe diameter = (4A,/Tr)~/2

stack casing width at the base stack exit Eroude number Vs/(gR~

(T, -- T = ) T / . ) 1/2 height of stack exit above flatum/B buoyancy length scale momentum length scale = Rs(V~/Vw) mass flow ratio = rh=/rh~ stack Reynold's number = D~Vw/u=

local flow Reynold's number = xV, /v~

equivalent exhaust pipe radius = Ds/2

characteristic length of ship model ship Reynold's number = VwL~/v= plume length measured along

plume plume temperature, T, at radius,

r, at a point, S, along plume average stack gas exhaust

temperature plume centerline temperature

(along plume) ambient wind temperature ship speed velocity of stack gas exhaust

averaged over exhaust area

Nomenclature

Fig. 5 Plume definitions

y(VERTICAL)

Vw J

Ps' Ts" VS_~

x (DOWNWIND) D s

~ " STACK

Vs/Vw - velocity ratio VT = true wind speed Vw = average horizontal crosswind

velocity (relative) b = beam of ship e = uptake duct extension/B g = gravitationalconstant h = turbulent zone height above

datum/b ht = turbulent zone height above

datum/B h' = interpenetration/B

°F = temperature, deg F °R = temperature, deg R (°F + 459.67 °) r0 = maximum plume radius at a point,

S, along plume

x = horizontal distance downwind from stack exit centerline

y = vertical distance above stack exit Tm - T=

~D = temperature ratio = - - T s - T =

0 = yaw angle of relative wind ~,® = kinematic viscosity of wind p~ = density of wind p~ = density of stack gas at stack exit p = interpenetration fraction ~ = mass flow of mixing air

rhs = mass flow of stack gas P ~ - - Ps

t3 = buoyancy ratio = • Ps

T , - T ~

T=

328 Stack Design Technology for Naval and Merchant Ships

dJ

11 -e-

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.i 1

\\X,. N N

k \ N

\

BRITISH DD • p= 2 ENGINES D S = 7.5"

I I ~"= 4 ENGINES DS = i0"6" TEST ---------X~\' . !

DATA .. Xk"~ \ ~ 8] - CHARWAT'S DATA [1.8<VV--~ 2.2] ~ N ~ N \ (MODEL TEST) k ~ ¢ Vs/V w = 17.4

,, ,, m-LM2 oo I \- ~,<s/V~ = 2 V/Vw = ~7+

><"%,I "' Vs/V w = 2 .b " . ~NF "NN

N," \ \

• , \ X

X \ \ 2 3 4 5 6 7 8 9 i0 20

S/D s

Fig. 6 Plume temperature data from British DO, LM 2500, and Charwat's model test

30

¢b - Tm -- T..........__~ _ (Vs /Vw) 0"25 (7) T+ - W~ S/D+

The equation is plotted in Fig. 6 along with full-scale trials data from British [4], Charwat [9], and U. S. Navy tests of the LM2500 gas turbine engine [10].

The recent full-scale tests conducted on board USS Foster (see the Appendix) have modified equation (7); also, the equation for plume trajectory has been further refined to satisfy this extensive body of data in addition to the British [4[ testing. Using curve-fitting techniques, we have

Y N ( V s / V w ) (X /R) °48 [(T=/T,) 5,7 + 0.063] = [2.4 + 0.3 (Vs/Vw)] °.5 (8)

where

N == 8.6 for single stack N --= 6.6 for multiple stacks

and

Tm - T~ - T+ - T= = 5"86(VJVw)°25 [(Ds/S)144 + 0.017]

X [(T=/Ts) 4.5 + 0.201 (9)

" - ' + '

~ - 9 - i ' (11)

Table 1 contains a summary of the essential sources for plume behavior theory.

Plume radius

Equation (10) presents the radius, r0, of the plume as a function of plume centerline height. The equation was re- ported by Well [11], who had based his theoretical work on Hoult, Fay, and Forney [6]:

r0 = as -k [2 (0.15 -]- 1 . 2 / ( V s / V w ) ) - 1/(2Fr2)]Y (10)

Equation (11) can be used to predict the temperature within the plume, T, at a given radius, r, given the maximum radius from ~uation (10) and thetemperature at the plume centerline Tm.


Design procedures

The design procedure for a ship's stack falls into three cate- gories.

• Selection of stack, height based upon boundary-layer considerations.

• Selection of velocity ratio and stack shape. • Check on plume temperature and trajectory. A fourth step, that of model testing the above-water line, may

be taken to verify the performance of the stack. This should be done for most warships and for certain unusual auxiliary and merchant ship stack designs. However, if the procedures outlined herein are followed, no model testing should normally be necessary for conventional stacks. The following subsections take each step in its logical order.

Selection of stack height based upon boundary zone height (h)

The following method is based upon work performed by Ower and Third [12] utilizing full-scale ~ind model test data. Figure 7 shows the critical dimensions used in the calculation of boundary-layer height h.

Effec ts o f forecastle, bulwark and sheer. The first step in estimating the zone height from the drawirigs of the ship is to determine the level above which the height, a', is to be measured (see Fig. 8). If there is no sheer of the deck forward of the superstructure and no forecastle deck, a' is measured above deck level, but if there is sheer or a forecastle, a ' must be mea- surod from some level above deck level, since the superstructure front is then partly shielded.

329

~._ . . . . ~ . . . . - - ' ~ n o t e : a l l d i m e n s i o n s a r e i n t e r m s o f b e a m b(= 1.0)

Fig. 7 Critical superstructure dimensions

For forecastle

v-z-a l-mq±__ [

(a) •

Fig. 8

For sheer

a 2 (b)

Dimensions for forecastle, bulwark and sheer

If it is assumed that the shielding due to sheer or forecastle raises the effective base of the superstructure to a height as above the deck level (see Figl 8), a3 can be calculated from the following formulas:

When cz is less than 1.25b

a3 = a2 (19)

When cz is greater than 1.25b

1 a3 = ~ a~ (20)

When the forecastle is sheered, az should be taken as the average height of the forecastle deck.

Effect of deckhouse. The tests made by Ower and Third indicate that the structure can be represented with sufficient accuracy by taking an effective height

a' = a + a, bl (21)

where a I is the height of the deckhouse above the superstructure of full width, and then finding the zone height h from the curves for a full-width superstructure of height a' and a similar form in other respects. It is important to note that the datum from which h is measured when using this formula is the top of an imaginary superstructure of height a'.

Determination of h, boundary zone height~beam. The preceding secHon shows how the effective height a' of the superstructure is obtained when the real height has to be corrected for fronts not of constant width (bridges, deckhouses, etc.) and the level above which it should be measured to allow for the effect of forecastle and sheer. Frequently these corrections will not be necessary, and a' can be taken as the height of the superstructure itself measured from deck level. The value of h can now be obtained from Fig. 9. This value is further modified, as necessary, for five additional variables: rounding-in plan, rounding-in elevation, angle of slope or step-back, length

9

% <

%

0.8

0.7

0.6

0.5

i .4

~ 0.3

~ 0 . 2

0.I

/ /

/ o/

0 0.2

Fig. 9

j ~

/ /

0.4 0.6 0.8

Superstructure height a"

Basic boundary-layer height

1 . 0

fr I

0.8

0.6

0.4

0.2

0

0.5 1.0 1.5 2.0

1 / r

1

Correction for rounding-in plan Fig. 10

a = 0 . 2

a 0.4

a 0.5 a = 0.6

1.0

0.8

0.6

fr 2

0.4

0.2

0

Fig. 11

I

0 0.2 0.4 0.6 0.8 1.0

r 2

a

Correction for rounding-in elevation

of superstructure, and intermediate step-down. Correction for front rounded-in plan. Considering the

effect of a bridge front of radius rl in the plan view, by using Fig. 10, we can obtain the correction factor, frl. Thus the corrected value becomes h × frl.

Correction to h for rounded-in elevation. Figure 11 shows the approximate relationship between the ratio rz/a and the correction factor frz. It should be noted that a marked low- ering of the value of h can be obtained by having a fairly small radius. For a superstructure of reasonable length, rounded beth in plan ( r j and elevation ( r j , and the value of h can be ob-


fo

Fig. 12

1.0 r /

0.8 /

0.6 /

0.2 t

1 ° I 0 0 15 30 45 60 75 90

8, degrees

Deckhouse slope correction

1.2

1.0

0.8

f3 0.6-

0.4

0.2

Fig. 14

--Flat front

~ l . 33

r 2 - - = 0 . 5 /

Y, 0 I !

0.25 0.50 0.75 1.00 a 1 a

Intermediate step-down correction

1.5

1.0

fc

0.5

0 0

Fig. 13

r 2 m = 0

a

r~ ~ . . . . . . . 2 . 2 -... . . . .o.3

0.5 1.0 1.5 2 C

Superstructure length correction

tained by multiplying the basic h in turn by factors fri and fr~ as obtained from Figs. 10 and 11.

C~rrection to h for stepped-back or sloping superstructure. The results of the model tests [12] show that the h value for a That is, sloping-back front does not differ much from that for a stepped-back front of the same angle of slope (0), which is defined as the angle to the horizontal of the line joining the ex- and treme edge of the steps in side view. A faCtor fo has been derived from the data and is applied in the same way as the factors frl and fr~. This is given in Fig. 12.

Correction to h for superstructure length. Figure 13 shows value,,; of a length factor fc for superstructures of various lengths c and degrees of rounding r2/a. It should be noted tliat this factor fc includes the allowance for rounding in elevation. Therefore, when it is necessary to use this factor, no separate allowance (factor fr2) should be made for rounding in elevation.

Correction to h for intermediate step-down. This effect has not been sufficiently defined, but Fig. 14 can be used as a guide. This figure relates to a superstructure height of 0.4b. The effect is significant only for superstructures rounded in elevation. For such superstructures, and probably also for well-sloped or stepped-back fronts, it is clear that an appreciable intermediate step-down will destroy much of the improvement due to rounding or slope.

Typical example of boundary-layer calculation. We refer back to Fig. 7, which represents a ship design with the following Hence particulars:

a = height of superstructure of full width = 0.54b a] = 0.108b az = 0.14b bl = 0.48b cl -'= 0.1b c2 = 0.7b b = beam (= unity)

Determination of effective height a' of superstructure: (i) Allowance for forecastle and sheer. Since c2 is less than

1.25:

a3 = az = 0.14

(ii) Allowance for wheelhouse, which is flush with front of superstructure:

a' = a - a3 + albl

= 0.54 - 0.14 + 0.108 × 0.43

= 0.44

(iii) Allowance for rounding-in plan:

ri (measured on drawing) -- 1.1

1/rl = 0.9

fri = 0.8 from Fig. 10

(iv) Allowance for rounding-in elevation: None. (v) Allowance for stepped-back front: The angle 0 mea-

sured from the drawing is about 60 deg:

fo = 0.92 from Fig. 12

(vi) Allowance for length of superstructure: The length of the superstructure is somewhat uncertain because of variations of height, but it is at least 1.8:

fc = 1.0 from Fig. 13

(vii) Determination of h

h(corrected) = h(basic) X frl × fo X fc

From Fig. 9 it is found that for a ' = 0.44:

h(basic) = 0.6

h = 0.6 x 0.8 × 0.92 × 1.0

= 0.44

This is measured from the top of the imaginary superstructure, lower than the actual superstructure (which is assumed to extend to the wheelhouse top) by the amount al - aibi; that is, 0.06. "


Hence h measured above the wheelhouse top is

= 0.44 - 0.06

= 0.38

Thus the stack height for a normal design should extend to a height of 0.38b above the wheelhouse top. From full-scale validation tests, this prediction is accurate to within about three feet.

Select ion of veloci ty ra t io and s tack shape

The next step in stack design is to estimate the exit velocity of the stack gas (Vs). With that velocity, the velocity ratio (ratio of stack to wind velocity) can be calculated.

Stack area is calculated using the minimum acceptable back pressure at maximum power. Back pressure is spevified by the engine manufacturer or, in the case of steam plants, taken from boiler back pressure criteria. If no other data are available, the following procedure can be used to approximate exhaust velocity at full power.

Calculate the exhaust stack exit flow area (As) and equivalent diameter (Ds = 4As/Tr) with the following data, assuming no major obstructions in the duct flow path; use the exhaust volume flow (ft3/s) from engine characteristics, and the maximum exhaust velocities (fps) from Table 2. For the purpose of this discussion, 40 knots is taken as the worst absolute wind speed. This velocity corresponds to the wind velocity in the North Atlantic that is annually exceeded about 2 percent of the time. Winds of higher speedwill cool the plume faster and can be expected to contain more turbulence.

When the stack exit velocity V, has been selected for the full-power condition, then the velocity ratio V~/Vw must be checked at other power settings.

A design table should be prepared which examines the predicted velocity ratios in various conditions of wind and engine setting. This should be similar to Table 3, which is a summary of some recent U. S. Navy designs. Generally speaking, the stack velocity ratio should not fall much below the value of 1.0 at the lowest underway power setting, say 25 percent of full power.

Stack shape and height. See Fig. 15 for a definition of terms. The design procedure follows:

(a) Determine the height of the turbulent zone (h) with procedure described above.

(b) Determine the casing shape and the projection of the exhaust smoke pipe above the top of the casing. Figure 16 presents offsets for various stack shapes. Figures 17 and 18 give the interpenetration (h') of the plume as a function of velocity ratio for a number of model stacks. The largest (absolute) value of interpenetration (h') possible is most desirable. These stacks were tested individually in a region of laminar flow. Referring to Figs. 17 and 18 the Streamlined uptake (No. 2) consistently shows good performance. Special tops were included in the model series to preserve the benefits of a projecting uptake and improve overall appearance of the stack. All the stacks in these plots have projecting uptakes that extend above the casing top 0.475 times the casing width at the base. Successful designs with projections as small as 1/4 to ]/z of this extension have been achieved. Extension'values of 2 to 4 ft (0.6 to 1.2 m) or about l/4 to l/3 of the base width have consistently given good results in more recent model tests conducted by the U. S. Navy. The plots can be used for stack designs that can be approximated by the stacks included in the model series. The choice of casing shape depends on the selected critical yaw angles that are likely to present problems; see Fig. 19. A 4- 30 deg yaw angle (wind angle off-the-bow) is a standard operating condition for air operations on U. S. naval vessels.

(c) Two basic rules were formulated b y O w e r and Third [5] for stack casing design: Rule 1--The lower boundary of the smoke plume may be allowed to penetrate the zone of turbulence created by the ship's structure to a vertical depth in ac: cordance with Table 4. Rule 2 - -The lower boundary of the smoke plume must not descend below the stack top by an interpenetration distance (h') greater than two stack widths (2B). For stack heights of less than 2B, the allowable interpenetration distance is reduced accordingly. This rule is applicable to all angles of yaw between 4-30 deg.

(d) If no criteria exist for determining the maximum yaw angle for design, determine the value as illustrated in Fig. 19.

Table 2 Stack exit velocity assumptions

Ship Stack Stack Exit Velocity, fps (m/s) Class Height Steam Gas Turbine

All--stack height above turbulent 130 {42.6) 180 (59) zone

All--low-profile stack 180-200 (59-66) 250 (82)

332

Table 3 U. S. Navy stack designs

Ship VJV,, V JV,, Power Speed, Tg Vs, Head- Tail-

Ship Type Level knots °R fps (m/s) wind wind

Combatant max 30 1257 236 (72) 2.00 14.60 Destroyer cruise 20 1090 152 (46) 1.50 4.45 (2 DG/AEGIS) a.c idle 10 953 54 (16) 0.64 1.06

Combatant max 28 1240 264 (80) 2.30 13.20 Frigate cruise 20 1110 186 (57) 1.85 5.46 (FFG 7) a idle 5 1060 56 (17) 0.56 0.95

Auxiliary max 21-23 1320 130 (40) 1.24 4.28 tanker cruise 20 1275 105 (32) 1.04 3.11 (AO 177) 5 15 knots ahead 15 i250 63 (19) 0.68 1.47

10 knots astern -10 1260 88 (27) 1.70 1.04

Helo- sustained 25 1310 234 (71) 2.13 9.24 carrier max, 1 engine 22 1317 251 (77) 2.40 8.26 (Sea Control half throttle 17 1182 161 (49) 1~70 3.97 Ship) a," slow ahead 9 1127 131 (40) 1.58 2.50

a Low-profile stack design. b Stack height penetrates boundary layer. c This ship is an engineering design only; construction was not authorized.


] ~ ~ TU~ULENCE A " / BOUNDARY

h t

B I

I

b -WIDTH OF' STACK CASING AT BASE e -UPTA~] DUCT EXTENSION. 2 "H -HEIGHT OF' STACK EXIT ABO~ DATUM. 2 h'-INTE~ENET~TION 2 ht-TU~ULENT ZONE HEIGHT ABOVE DATUM. 2 AC p -INTE~ENET~TION F~CTION OF PLUME AND TU~ULENT ZONE A~

NOTES: (i) h' IS A NEGATIVE VALUE IN THE EX~PLE ABO~. (2) EXP~SSED IN TE~S OF STACK WIDTH B. (3) SOURCE; ~FE~NCE [5]

Fig. 15 Interpenetration of plume

Construct a line aft of the stack centerline with a downlook 'angle of 20 deg. Extend the intersection radially to the beam of the ship. This angle may be between 10 and 20 deg. At yaw angles greater than 20 deg, the smoke plume passes off most ships' decks before penetrating the turbulent zone. Rule 1 can be ignored if the 20-deg downlook angle does not intersect the centerline of the ship. If the maximum yaw angle is greater than 2,0 deg, use 20 deg in the next calculation.

(e) Calculates velocity ratios at full power for a true wind of 40 knots and the maximum yaw angle for Rule 1 by using the following:

Vw = sin[180 - {0 + arc sin [(sin0) (Vo/VT)]}] (22) sin(O)/VT

The velocity ratio is, then, VJVw. 0 c) Pick values of h ' from Figs. 1'7 and 18 for the velocity

ratio and type of stack selected. Then pick appropriate values of p from Table 4.

(g) Use equation (23) to determine the minimum stack height based on Rule 1 for zero yaw and maximum yaw:

n = ht (1 - p) + h' (23)

(h) Use equation (22) to determine the Vw for 30-deg yaw and a true wind of 40 knots. Check compliance of the velocity ratio under these conditions with Table 5 to satisfy Rule 2.

Conventional and special s tack shapes

Ower and Third [5] have written an exhaustive paper On stack shape which includes design guidelines for standard designs. For unconventional stack design, special studies to determine the required characteristics are necessary. The general guidelines are as follows:

1. Since the main cause of downwash is the bulk of the stack casing;, casings should be reduced to a minimum.

2. Within the range of normal practice in design, the shape and length/breadth ratio of the casing profile in plan have no great influence on the performance of the funnel. An increase in fineness of the profile gives good results in head wind conditions, but can cause severe eddying at critical yaw angles.

3. Some improvement can be effected in yaw only by placing the uptake discharge as far aft as possible in the casing.

4. A tapering casing is beneficial under most circumstances,

Stack Design Technology

particularly if it results in an appreciable reduction in breadth at the top.

5. A substantial improvement results from a simple extension to the uptake beyond the stack top. A streamlined section rather than cylindrical gives improved results.

6. Specially shaped tops can be designed to take full ad- vantage of the benefits of a projecting uptake. All have as their main object the reduction of the disturbing effect of the casing. Even at the higher angles of yaw, their'performance is much better than that of a casing with only a projecting cylindrical uptake. Minor modifications to the shapes of these tops do not seem to have a vital bearing on performance, but with dome- shaped tops it is recommended that the uptake discharge be angled at 20-25 deg to the vertical. Rounding the stack top eliminates tendency for smoke to creep forward over the top [3].

7. Slope of the stack top. The horizontal top is best but a downward rake aft of 1 in. (2.54 cm) per foot does not affect performance. Greater rake deflects the flow downward into the stagnated region. It also forms a large eddy at the forward edge which will cause the smoke to drift forward [31.

These results were based on a study of a typical variety of stack shapes. The authors noted that the stack casing is more detrimental to stack flow than any other individual characteristic. This is due to the downwash caused by the casing. But casings are now generallyused to house machinery and are necessary despite their detrimental effect on gas flow.

The following stack configurations have one design goal and that is to surround the plume with smooth-flowing air at all yaw angles. Most of these shapes work well under some conditions and exhibit little or no improvement for other conditions. They are presented to familiarize the designer with several alternative types of stacks.

• Streamlined stacks. Most conventional stack designs have streamlined,body sections. Streamlined sections are chosen in preference to cylindrical sections due to architectural and flow considerations (in a head wind). Streamlined stacks with long, slender sections fore and aft cause considerably more suction in a sidewind than an equivalent cylinder. However, aesthetic considerations and fore-and-aft design 6onditions dictate selection of streamlined designs.

Although there are numerous variations of streamlined stack types, a good example of this type of simck casing is the Clyde- bank funnel design. The design was introduced by John Brown

for Naval and Merchant Ships 333

TOP SHAPES

WIND DIRECTION (HEADWIND)

OPEN TOP

CASING TOP I\ 0 . 4 7 5

0.28I. D.

CAGEDTOP TOP SHAPES

22 1/2 ° 0.56 22 1/2 ° 0.292

0:or CAS__2 .G T___oy _] .0 .50 CASING

0 . 6 6 2 . 1 6 H A D 0 . 4 7 5

e--215 1

1.12

DOMED TOP SHAPED TOP

UPTAKE SHAPES

0.875 I.D. ~ ' ~

1.25 05 RAD

0.64

CASING SHAPES CIRCULAR STREAMLINED

~22J2~SSS

CASING A

CASING C

10.45 C)¢nO~o~O~O

CASING E ~

NOTES:

FIGURE

(a) ALL DIMENSIONS IN INCHES

(b) SOURCE; REFERENCE [5]

cc ~2 ~ ~ '~ ~o cqco r - - o ~ o'~ r,.. ue c~

CASING AND UPTAKE SHAPES TESTED BY OWER AND THIRD

Fig. 16 Casing, top and uptake shapes

CASING B (BASE ORDINATES AS FOR CASING A)

CASING D

CASING F

& Co. in the early 1950's. Figure 20 shows some elevation and sectional views of the casing. The upper one-third has a section similar to Casing A in Fig. 16. This upper section tapers into the base, which has a section shape similar to Casing E in Fig. 16. An additional feature of the Clydebank design is the addition of a domed top, which the designers felt greatly improved the flow characteristics and aesthetics of the funnel.

• Fins. Fins are usually horizontally arranged although best performance is observed when they are parallel to the flow.

The fin is located near or at the top of the stack and should extend aft to the trailing edge and out to the full width of the stack. Fins provide improved performance over conventional stacks for head winds and up to 20 deg of yaw. Beyond 20 deg their performance degenerates. They can be useful for vessels where the headwind condition is most critical.

• T h o r n y c r o f t s tack . This stack has vanes surrounding a streamlined casing (see Fig. 21). It was patented by John I. Thornycroft, Ltd. and H. J. Watson. It has been installed with


0

Z

- 2

- 3

L

V

4//8

2 ii

9

5

7

UPTAKE TOP

FUNNEL CASING TOP

l) CYLINDRICAL UPTAKE ALONE 2) STREAMLINED UPTAKE ALONE

• 3) CASING A, CYLINDRICAL UPTAKE FORWARD 4) CASING B, CYLINDRICAL UPTAKE FORWARD

5) CASING C, CYLINDRICAL UPTAKE FORWARD 6) CASING A, STREAMLINED UPTAKE FORWARD

7) CAGED TOP, CYLINDRICAL UPTAKE 8) CAGED TOP, STREAMLINED UPTAKE

9) DOMED TOP, CYLINDRICAL UPTAKE ANGLED 22 1/2 DEG. i0) DOMED TOP, RECTANGULAR UPTAKE ANGLED 22 1/2 DEG. ii) SHAPED TOP, RECTANGULAR UPTAKE ANGLED 22 1/2 DEG.

-4 1 2 3 4

VELOCITY RATIO (Vs/Vw)

Flg. 17 Influence of stack design on interpenetration h': e = 0.475 (approx.), 0-deg yaw

2

2

i / i - -

4 6

o

~ - 2

0 i 2 3 4

VELOCITY RATIO (Vs/Vw)

Fig. 18

UPTAKE TOP FUNNEL

FUNNEL CASING TOP

i) CYLINDRICAL UPTAKE ALONE 2) STREAMLINED UPTAKE ALONE 3) CASING A, CYLINDRICAL UPTAKE FORWARD 4) CASING B, CYLINDRICAL UPTAKE FORWARD 5) CASING C, CYLINDRICAL UPTAKE FORWARD 6) CASING A, STREAMLINED UPTAKE FORWARD, 7) CAGED TOP, CYLINDRICAL UPTAKE 8) CAGED TOP, STREAMLINED UPTAKE 9) DOMED TOP, CYLINDRICAL UPTAKE ANGLED 22 1/2 DEG. i0) DOMED TOP, RECTANGULAR UPTAKE ANGLED 22 1/2 DEG. ii) SHAPED TOP, RECTANGULAR UPTAKE ANGLED 22 1/2 DEG.

Influence of stack design on interpenetration h': e = 0.475 (approx.), 20-deg yaw

good results aboard various ships [3]. • FCM/Valensi (Strombos) funnel. This stack casing has

such a low length-breadth ratio in cross section (,-~ 0.2) that i t is similar to a vertical air[oil. The tip of this {o!1 generates a trailing vortex in which the smoke is entrained. This stack is most effective at small yaw angles [8]. A diagram o{ a model tested by Nolan [2] to demonstrate the Strombos principle is shown in Fig. 22.


• Added air or dampers. Dampers have been used suc- cessfully on many designs to increase the stack gas velocity at low powers. Figure 23 shows a typical arrangement o{ dampers in the uptake. This setup requires alarms in the engine room that would sound when the dampers are closed to the point that the exhaust back pressure increases beyond acceptable limits. Acker [3] makes reference to another technique which would improve plume performance at low powers by

335

jjjjjj jjj I

J ]~* <MAX IFMUMRYAW ANGLE

Fig. 19 Maximum yaw angle for Rule ,1

BLR P,}4 EXHAUST FAN UPTAKE

STEAM WH I S T ~ ~ AFTER BOILER EXHAUST

"b.. UPTA~ ~

PORT BOILER UPTAKE

BOILER ROOM EXHAU

STBO BOILER UPTAKE

ELEVATION AND CROSS-SECTIONS THROUGH THE CLYDEBANK FUNNEL

Fig. 20 Clydebank funnel

blowing air into the uptakes beyond the boilers. This technique would be perhaps more effective than an annulus flow of the same volume and would require a degree of sophistication on a par with the annulus. No reference was found of a ship on which this technique of adding air has been employed.

• A thwar t sh ip s t e rmina l ex tent ions . The SS France stack configuration is a vertical casing with two faired fins extending horizontally athwartships. The smoke is ejected from the ends of these fins and thereby removed from the stagnation region in the lee of the vertical casing. Often in operation the downwind fin is sealed as an extra precaution in keeping stack gas out of the stagnation region. This design has been successful in eliminating the downwash effect behind the stack even though the stack gases are given no vertical thrust. The FF

1052 stack terminal uses a similar technique to direct exhaust gases clear of the ship's superstructure. Exhaust gas is directed into two separate port and starboard terminal pipes, angled aft and slightly above horizontal. Figure 24 illustrates this design 113].

• A n n u l u s . An air annulus surrounding the exhaust flow can improve plume structure and compactness but does not

Table 4 Interpenetration Fraction

Interpenetration, h' Allowed, p

Above -0.5 0.35 -0.5 to - 1.5 0.50 Below -1.5 0.70

t Casing A (parallel) h' cylindrical uptake

forward

-2.0 ~e =0e =0.25e =0.475 ! 2.42 1.86 1.48

For definitions ofe and h' see Fig. 15.

Table 5 Minimum Vs/Vw values to comply with Rule 2

Casing A, Casing B (tapered) Streamlined streamlined cylindrical uptake uptake uptake forward

e = 0.475 e = 0 e = 0.25 e = 0.476 e = 0.475 0.86 1.59 1.41 1.02 1.06

• Rectangular uptake (22 deg)

e =0.5 1.39

Shaped top rectangular uptake (22 deg) e =0.475 1.13


STREAMLINED TOP

SECTION

AT TOP

r/////////V/////X/////~ F////////X//////I"////A

I I I I I I I I I I i I I I I

Fig. 21

HORIZONTAL VANES

Thornycroft funnel

l\ \ l l l l

, , \ \ \

k

,s-- L J

Fig. 22 Strombos-type funnel model

BKT

I.~'~ i~ ~ DAMPER 6.1 \ ..J,-

DAMPER OPEN

/ J ~ z ~ , ~ .

Fig. 23 Damper arrangement of the Independence (Acker [3])


- - ~7'~/- n -

MAST

\i

f Fig. 24

UPTAKE

FF 1052 stack--sect ion looking aft

\ STACK/MAST

COOLING AIR

STACK-----------~

MIXING TUBE 3 PER ENG~

EXHAUST NOZZLE 12 PER [

INSULATION. ~l

Fig. 25

SHELL

SHROUD

COOLED EXHAUST

TUrbINE EXHAUST

i ~ UPTAKE DUCT

Eductors on the DD 963

EDUCTOR PLENUM

increase the trajectory height. To be effective the annulus should have a velocity not less than one to two times the free- stream velocity and at a volume at least equal to the exhaust at full power. Schultz and Matthews [14] tested three annuli with widths 8.8, 16.0 and 24.4 percent of the stack diameter and found the smallest annulus to be best. Acker [:3] suggests keeping the annulus width less than 10 percent of the stack diameter.

• Eductors. Eductors were utilized in the DD 965 Class destroyers to cool the exhaust gases being emitted from the stack. In this design the exhaust temperature into the eductor is 900 F (482 C) and the temperature out of the eductor is 400 to 600 F (204 to 315 C). The cooling eductor airflow is 0.8 to 1.0 times the turbine exhaust flow. Figure 25 shows a typical eductor. This design was guided by model tests by Charwat I9] at UCLA, where many configurations of eductors were tested. At this time any eductor design must be accompanied by detailed model tests to verify the eductor mixing ratio, that is, secondary to primary airflow.

Plume trajectories and isotherms

Plume trajectories and isotherms are to be drawn directly on the ship's profile. To predict plume trajectory and temperature, equations (8) and (9) should be applied. A step-by-step method for determining the expected peak temperature at a given topside location due to gas turbine exhaust gases is illustrated in the following.

Determine from equation (8) the velocity ratio (Vs/Vw) which has a trajectory through the X and Y coordinates of the

EQUIPMENT ]~

i . . . . . . IZ t - : r

m .I DATUM -- ~

I

I STACK

Fig. 26 Plume trajectory definition

k selected topside location. See Fig. 26 criteria for the critical velocity ratio and operating conditions just presented. Here, X is the true length in plan view between the stack center (or equivalent center in the case of several exhaust pipes) and the center of the equipment.

Draw in the plume centerline, based upon equation (8) and the calculatedVs/Vw ratio.

Measure along the plume centerline, the distance S by means of a tick-strip.

Using this value of S and equation (9), calculate the value of 4~ and hence Tin. (Note, use absolute values for T=, Tm and

This value of Tm is the maximum predicted temperature " which, the equipment would experience. This temperature includes the effects of ambient wind gustiness, and resulting temperature fluctuations. It is the predicted maximum tem-

338 Stack Design Techno logy for Naval and Merchant Ships

• . 9 b ~ . 5b

. J

Fig. 27 AO 177 deckhouse

Y

perature which would be sustained over a period of 5 to 10 min, if the center core of the plume coincided with the equipment.

Plume radius. Finally, the radius of the lowest trajectory should be plotted to show the lowest extent of the plume boundary by using equation (10).

The profile drawing with plume trajectories, isotherms and radii allows the designer to estimate typical temperatures in heat~sensitive antennas, weapon systems and other components. It also allows him to check for reingestion of exhaust gases, exhaust gas in crew areas and the possibility of plume interference in air operations. At this point, adjustments can be made in topside arrangements. This would necessitate an interaction with other design groups. A reevaluation of stack height, location, exhaust pipe rake and stack exit velocity may be necessary after this interaction.

Stack design of Auxiliary Oiler AO-177

The FY75 Auxiliary Oiler AO-177 stack configuration was selected as a design example. Reference [ 13] summarizes the design efforts of NAVSEC 6136 during preliminary and con- tract design of the AO-177.

The reference drawing used was the general arrangements (inboard profile). Critical areas identified during the drawing review were possible impingement of the exhaust plume on:

(a) The ship's superstructure adjacent (forward) of the stack exit terminal.

(b) The ship's antenna mast and mast-mounted electronic components 40 ft (12 m) forward of the stack.

(c) The helicopter operations (hovering) area above VER- TREP, 40 ft (12 m) aft of the stack discharge.

1. Boundary-layer height. The AO-177 deckhouse is Shown in Fig. 27. The boundary-layer height was calculated in acc, ordance with the previous guidance given. Thus h(corn~ted) = 0.42 and height of boundary layer above 07 level = 0.42, x 80 = 33.7 ft (10.3 m).

2. 'Velocity •ratio. The design velocity ratio is determined using the method of Ower and Third. The ship profile is illustrated in Fig. 28. The procedure for applying Rule 1 is as follows:

(a) Find the maximum yaw angle for which.Rule 1 should

Fig. 28 Rule 1 for AO 177 -"

be applied. This will vary between 10 and 20 deg. At yaw angles greater than 20 degl the smoke plume passes off most ships' decks before penetrating the turbulent zone.

(b) Draw a line from the stack casing top at a down angle of 20 deg below the horizontal. The downward sloping line should be rotated to form a cone whose apex is at the stack terminal. The maximum yaw angle in plan view is where the cone intersects the beam of the ship.

(c) Since the cone clears the ship's decks (see Fig. 28), Rule 1 does not apply.

Therefore, the next step is to apply Rule 2. Assuming a maximum ship speed of 23 knots (VA), and true wind speed of 40 knots (VT), and a yaw (/9) of 30 deg, determine the relative wind speed (Vw) from equation (22):

sin{180 ° - [30 ° + arc sin(30 °) (23/40)}} vw= sin(30°)/40

Vw = 58.2 knots (107.8 kin/h) = 80.8 fps (26.25 m/s)

Selecting a 130 fps (42 m/s) stack exit velocity (Vs) from Table 6, the design velocity ratio becomes:

130 Vs/Vw - - 1.32

80.8

A nominal design velocity ratio of 1.3 was selected. The exhaust characteristics at the full-power sustained speed condition are given in Table 6.

3. Stack configuration. The final AO-177 stack configuration is shown in Fig. 29. The configuration most closely approximates Case 9 from Ower and Third (see Figs. 17 and 18), a dome-top cylindrical uptake with a 221/2-deg slope. From Fig. 18 at a velocity ratio of 1.6, the interpenetration (h') allowed is:

h' = -1.2

Taking the interpenetration factor (p) from Table 4, p = 0.5. From Fig. 15, the relationship is:

(H - h') p = l ht

Solving for h':

and

h' = ht (p - 1 ) + H

34 +3_3 _ 16 h' = ~ - ( 0 . 5 - 1) 'B B

16 16 B h' 1.2 13.3 ft (4.1m)

A nominal value of 14 ft (4.3 m) base width was chosen at the center line of the stack as shown in Fig. 29. The domed top was simplified to a 45-deg Slope to simplify construction. Theory

Ship Type Ship Class Auxiliary AO 177

Table 6 AO-177 exhaust characteristics at full power

Stack Exhaust Velocity at Sustained Full Power Stack Area Stack Diameter

130 fps (39 ra/s) 9.62 ft 2 (0.89 m 2) 3.5 ft (1.06 m)

Stack Design Techno logy for Naval and Merchant Ships

Exhaust Temperature at Sustained Full Power

4O0 F (204 C)

339

Fig. 29 AO 177 stack configuration

INCINERATOR EXHAUST 6" DIA. APP

26'9"

6 .II.

3 ' 3" R A D ~

6'3" R A D ~

5'9" PAD /

4'

MAIN BOILERS EXHAUST 3' 6" INSIDE DIAMETER AT OUTLET

45 ° 2'6"

SLOPE / I

Ji ! ! •

i/'l , /

o I I 77.5 °

22 ' 0"

33 ' 0"

07 LEVEL

10'4" APPROX. ~ 3'4-1/2" PAD

- " 5'10'1/2" PAD

07LEVEL

/

would call for a pipe extension (e) of 0.475 × 14 ft (4.8 m) -~ 6 ft (1.8 m). However, previous model test experience [8] had shown a 8 ft (0.9 m) pipe extension with this shape to be sufficient.

4. Plume trajectories and isotherms. Predictions of plume trajectory and centerline temperature in headwind and tailwind conditions are shown in Figs. 80 and 81, respectively. Table 7 presents the respective ship operating conditions and power plant parameters used to calculate the plume conditions.

S u m m a r y This paper has presented a summary of stack design proce-

dures based upon U. S. Navy experience. Both the classical methods of Ower and Third [12], Acker 18], Sherlock and Stalker [1], Nolan [2], and others, as well as recently applied exhaust gas plume flow theory have been outlined. The theory and design procedures by model and full-scale trails taken on the USS Foster (DD 964) confirm the ability of empirical mathematical expressions to predict plume rise and temperature decay with reasonable accuracy. The step-by-step method outlined in the paper has been tested in practice on several design programs of the U. S. Navy. The papei" has attempted to provide practical guidance for properly selecting the stack casing location, shape, height, and exit velocity early in the design process.-

340

Vs/V w 2.O

^ - - ~ F I N A L STACK CONFIGURATION

Vs/V w 1.5 Vs/V w 1.0 Vs/V w .75

07 LEVEL - 113'-0" ABL 1.-----

06 LEVEL - ]05'-0" ABL

Fig. 30 AO 177 aft plume displacement

A c k n o w l e d g m e n t s

The authors gratefully acknowledge the help of the Naval Ship Engineering Center, and in particular Mr. Ralph Lacey, Mr. Jack Abbott, Mr. William Bauman and Mr. Robert Keane. In addition, the contributions of Mr. John Kloetzli of Hydro- nautics Inc. and Mr. David Little of John J. McMullen Inc. have added significantly to the value of this paper.


YARDARM WITH ANTENNAS

FINAL STACK

CONFIGURATION

160 ° 150 ° 140 °

130 ° 120 °

Vs/V w = 4

Vs/V w = 3

Vs/V w : 1.5

Vs/V w = i.

SPS - 55

(140 ° F)

SIGNAL

SHELTER

07 LEVEL

Fig. 31 AO 177 fwd plume displacement (following wind)

Table 7 Power plant performance parameters a,b

Combined Propulsion Boiler

Full Power Exhaust Airflow Gas temperature, stack 400 F Velocity (~, stack exit 130 fps Exhaust weight flow 61 lb/sec Ship speed 21-23 knots

Cruise Power (max) Gas temperature, stack 355 F Velocity (q stack exit 105 fps Exhaust weight flow 49 lb/sec Ship speed 20 knots

15 Knots (?,as temperature, stack 330 F Velocity at stack exit 63 fps Exhaust weight flow 30 lb/sec

10 Knots (Astern) Gas temperature, stack 340 F Velocity at stack exit 88 fps Exhaust weight flow 42 lb/sec

a Ambient temperature (T~) = 100 F. b Stack diameter = 3.5 ft.

Stack Gas Dispersion Prediction," Naval Ship Engineering Center, Hyattsville, Maryland, Code 6136, Jan. 1973.

9 Charwat, Andrew, "DD 968 Exhaust Stack Studies," University of California at Los Angeles, July 10, 1971.

10 "'Exhaust Plume Temperature Survey, DD 968 Propulsion Gas Turbine Module," General Electric Company Test Report, Aircraft Engine Group Document No. PF-I-100, Cincinnati, Ohio, Sept. 1972.

11 Weil, J. C., "Model Experiments of High Stack Plumes," Massachusetts Institute of Technology, Mechanical Engineering De- partment Thesis, Aug. 1968.

12 Ower, E. and Third, A. D., "Superstructure Design in Relation to the Descent of Funnel Smoke, Trans. Institute of Marine Engineers (London), Vol. 1, 1959.

13 "Technical Practices Manual for Surface Ship Stack Design,'" Naval Engineering Center Report 6136-76-18, July 1976.

14 Schultz, M P. and Matthews, J. T., "Wind Tunnel Investigation of Smokestack Annulus Parameters,' NSRDC Aero Report 1137, Aug. 1967.

References 1. Sherlock, R. H. and Stalker, E. A., "A Study of Flow Phenomena

in the Wake of Smokestack," Engineering Research Bulletin No. 29, Department of Engineering Research, University of Michigan, Ann Arbor, March 1941.

2 Nolan, Robert W., "Design of Stacks to Minimize Smoke Nui- sance." TRANS. SNAME, Voi. 54, 1946.

3 Acker, H. C., "Stack Design to Avoid Smoke Nuisance," TaANS. SNAME, Vol. 60, 1952.

4 Unpublished British report, Sept. 1972 (restricted). 5 Third, A. D. and Ower, E., "Funnel Design and the Smoke

Plume," Trans. Institute of Marine Engineers (London), Vol. 72, 1962.

6 Houh, D. P., Fay, J. A., and Forney, L. J., "A Theory of Plume Rise Compared with FieldObservations," Fluid Mechanics Laboratory Publication No. 68-2, Mechanical Engineering Department, Massa- chusett:~ Institute of Technology, March 1968.

7 Little, David, "Full Scale Stack Gas Testing on DD 964 (USS Foster)/" J. J. McMullen Associates, NAVSEC Report No. 6136-77-12, 19 July 1976.

8 Pollitt, G. and McCallum, D., "'Sea Control Ship, Airflow and


Appendix

Stack gas trials on the USS Foster (DD 964) Full-scale trials to determine the exhaust plume distribution

after it exits the eductor pipes were conducted on board USS Paul F. Foster (DD 964), on 21 September 1976, by the U. S. Navy. The test patterns were made on a run out of the U. S. Naval Base, San Diego, California. Details of these tests and analysis of the results are contained in reference [7]. A pho- tograph of the ship is shown in Fig. 32. The general arrangement of the ship propulsion system for the DD 963 Class is shown on Fig. 33.

The approach taken is to first translate the raw data into a format usable for profile and centerline temperature evalua- tions. This was done by locating plume centerlines by the drawing of isotherm plots at each of the grid locations. These plots will also indicate the maximum gas temperatures at the given point in space. The next step was to relate the data to existing mathematical models. To do this, all modeling parameters must be known. Most of these parameters can be easily defined. However, the velocity ratio, Vs/Vw, and stack temperature, Ts, must be estimated by interpretation of test data. The model was modified by changing already existing

341

Fig. 32 USS Paul F. Foster (DD 964)

PROPULSION" LOCAL CONTROL~ CONSOLE tJL.

INLET' PLENUM

3AS TURBINE

~GAS TURBINE !ENGINE IA I

A~TER I " ~.,~UEL SYSTEM OIL i CL[TCH

NOISE ISOLATING FLEXIBLE COUPLING

EXHAUST DUCT

ENGINE R

~IN THRUST

BEARING IAUX AUX M ~ M C H R Y MCHRY

ROOM ROOM NO. 2 NO. 1

NOISE ISOLATING FLEXIBLE COUPLING'

3AS TURBINE

DUCT

'CRP SERVO PUMP

.MAIN THRUST BEARING

INLET PLENUM

FROM

I i CONSOLE i

FORWARD ENGINE ROOM

L .i

Fig. 33 DD 963 plant schematic


Ic 40'

68

I m m

I

~-8,~

1-1/2" STEEL PIPE

/

\

/

.I

3"

/

79'

64'

(ALL CROSSMEMBERS) 1-1/2" STEEL

49'

34'

ALUMINUM (ALL COLUMNS

2 0 '

5" STEEL (ALL COLUMNS)

/ 03 LEVEL

Fig. 34 USS Foster (DD 964) stack gas trials aft gridwork assembly

Fig. 35 Gridwork installation aboard Foster


Table 8

f

Run Number Time Engine 2A (shp) RPM (Propeller) Engine 2B (shp) Engine 1A (shp) RPM (Propeller) Engine 1B (shp) Relative Wind Velocity (knots) Relative Wind Direction Ambient Temperature

1A1 10:44

0 55

65O 1100

58 1100

14.85 11 ° 68

(

Run Number Time Engine 2A (shp) RPM (Propeller) Engine 2B (shp) Engine 2A (shp) RPM (Propeller) Engine 1B (shp) Relative Wind Velocity (knots) Relative Wind Direction Ambient Temperature

USS Foster (DD 964) slack gas trials--run sequence

Single Engine Testing: 1A2 1A3 1A5 1B1 1B2 1B4

10:55 11:08 11:19 1 1 : 5 1 11:39 11:28 0 0 0 0 0 0

62 83 94 87 107 117 850 700 500 9150 8900 7300

2750 7200 16000 500 5000 17400 79 108 150 55 108 158

2800 7400 16900 500 5100 17900 17.60 22.00 29.85 20.15 28.05 33.25

7 ° 5* 2 ° 354 ° 0 ° 1 ° 69 70 70 70 70 70

Two Engine Testing: 2A1 2A4 2B1 2B2 2B3 14:24 14:29 13:49 13:40 13:19

500 500 9600 9500 8300 55 55 115 137 144

200 200 10500 10700 9500 4000 12000 500 5400 1600

83 120 57 120 161 4000 12200 500 5400 17700 23.00 27.75 28.10 41.00 47.00 357 ° 0 ° 2* 0* 354 °

71 71 71 71 71

1C1 1C3 1D2 1D3 12:01 12:14 12:33 12:24

0 0 0 0 104 129 135 141

15200 12500 20000 18400 500 16800 5400 15900

55 158 121 158 500 17400 5600 16600

22.40 38.50 37.65 40.06 355 ° 355* 351 ° 355 °

70 70 70 70

2C1 2C2 2D2 13:58 13:04 12:55 13800 14400 15800

129 163 168 15200 15200 20100

500 18300 117800 57 168 168

500 19800 19500 29.00 45.75 44.75 354 ° 354 ° 350 °

71 71 71

Engine

2B(a~

2B/2A

NOTES:

Table 9 USS Foster stack gas trials, plume center average temperature and path length

Vertical Y, ft Temperature TM, °F Path Lengths, ft

Run V,JVw TA/T~, FWD (c) AFT (c) FWD AFT FWD AFT

1A1 1.75 0.689 25.0 33.0 175. 125. 48.4 73.7 1A2 1.57 0.691 24.0 29.0 172. 125. 50.5 72.6 1A3 1.30 0.677 20.0 25.0 175. 122. 43.1 67.4 1A5 0.86 0.678 12.5 16.5 170. 125. 35.8 60.0 1B1 3.18 0.626 25.5 30.0 160. 140. 50.5 74.7 1 B2 2.16 0.635 20.0 27.0 175. 135. 42.1 67.3 1B4 1.64 0.642 18.0 21.0 175. 145. 41.0 64.2 1C1 3.52 0.593 24.5 27.0 170. 145. 50.5 74.7 1C3 1.78 0.614 13.5 16.5 193. 145. 37.9 55.8 1D2 2.26 0.582 13.5 19.5 225. 155. 34.7 60.0

1D3 2.02 0.589 14.0 20.0 213. 151. 35.8 60.0 2A1 0.90 0.722 13.0 18.0 220. 160. 34.7 59.5 2A4 0.75 0.722 10.0 15.0 220. 150. 32.6 56.8 2B1 2.24 0.631 23.0 29.0 245. 190. 46.3 71.0 2B2 1.52 0.625 14.5 21.0 245. 175. 36.8 62.1 2B3 1.29 0.625 12.0 18.5 274. 170. 33.7 58.9 2C1 2.54 0.607 24.0 29.0 254. 200. 47.4 71.6 2C2 1.63 0.596 14.0 21.0 255. 190. 35.7 61.0 2D2 1.81 0.582 13.0 20.0 300, 200. 34.7 58.9

(a) 2A denotes port-outboard gas turbine. 2B denotes port-inboard gas turbine. (b) The equivalent diameter (D,) is based upon the equivalent area of a single stack of the total

ENG 2B: Ds -- 7.79 ft

ENG 2B/2A: D, = 11.02 ft

(c) FWD refers to grid ~ x = 20 ft from stack centerline. AFT refers to grid at X = 36 ft from stack centerline.

factors in the equations, by in t roducing new terms to be used as correct ion factors, by delet ing terms, or a combina t ion of these methods. The data from these trials were then compared with empir ica l relationships previously developed. These expressions were der ived f rom previous model tests conducted by Ingalls on the D D 968, full-scale tests of the LM 2500, and f rom full-scale trials per formed by the Royal Navy on a British DD, the latter being the most significant source of data. However , to use the British data correctly a significant amount of extrapolation is required. It was found that the p lume height relationship did not correlate well when compared with pre- vioulsy deve loped formulas. O n e basic d i f fe rence in the two sets of data was that the D D 968 velocity or m o m e n t u m ratios and exhaust gas tempera tures were lower than those experi- enced on the British D D [4]. The following relationships were previously used.

Trajectory was def ined as

- - - - ( 2 4 )

Ds .(2"4 + 0.3 (~ww))Vs 0.5

and for p lume eenter l ine t empera tu re

Ds(Vs ) °'z~ = T (7)

where

N = 1.15 for single-pipe stacks

N = 0.86 for double-pipe stacks

After the p lume exits the exhaust pipe, the flow is initially


y

8O

f --"

NOTE :

i. TEMPERATURE IN °F.

Fig. 36

, " - L

J "k '

DD 964 typical Isotherm contours, fwd grid location

l /

dominated by gas momentum. That is, the ratio of exhaust gases to the ratio of a unit volume of crosswind air is the primary driving force which causes the plume to bend over.

The objective of the tests was to verify the existing equations which were being used to predict plume temperature distri-. bution and trajectory, or to use the data to modify these equations.

The equations derived from the tests are (8) and (9), for plume trajectory and temperature, respectively. These are explai~ed more fully in the "Plume flow" and:"Temperature theory" sections in the body of the paper.

Design of apparatus and testing procedure This section describes the overall testing approach. The

testing equipment was similar to that used for the full-scale testing previously performed on the British DD 14], although the data recorded and the variation in engine performance were more extensive. Testing details revised included:

• Data for a given plume cross section was taken during a

Stack Design Technology for

shorter time interval to minimize the effect of shifting relative winds. (British DD data reflected a 48-sec interval to record all points on a single grid.)

• More data points were taken to give a more detailed pic- ture of the plume cross-sectional temperatures at each grid.

• Engine power was to be varied as much as possible to record data for a large range of stack temperatures and velocity ratios.

The task of building the test grids, transporting the prefab- ricated structures and recording apparatus to San Diego, erecting the test rig, and data collection and reporting was performed by NAVSEC Philadelphia in a very efficient and workmanlike manner.

The measuring of the plume temperatures was to be ac- complished utilizing two thermocouple gridwork assemblies as described in Section 3.3 of reference [7]. The overall dimensions of these assemblies were determined by estimating the plume centerline heights for the range of testing to be performed. Two thermocouple grids were erected at downwind locations aft of the forward stack casing. The grids were

Naval and Merchant Ships 345

FF.

6O

50

PROFILE:

TEMP: ¢

240

50

40

Y _ 6.6(Vs/Vw) (X/R)

Run No. = IAI

Vs/Vw = i. 75

Ts = 306°F

0.48 5.7

[ (Too/Ts) + 0.063] D [2.4 + 0.3(Vs/Vw)]0.5

0.25 Tc - T~

- 5.86 (Vs/Vw) [ (D/S) Ts - T~

1.44 4.5

+ 0.017] [ (Too/Ts)

F~:. 224 50

Y PROFILE : D

0.25 0.86(Vs/Vw)(X/R)

[ 2 . 4 + 0.3(Vs/Vw)] 0~

TEMP: @ _ Tc - T~ _ TS - To

(D/s) (vs/vw) .025

50

t NEW ~ PREDICTION

+ 0 . 2 0 ~ _ ~ _ ~

PRELCTION

MEASURED PLUME¢

40 ~ 40

~ F

3%.

I 169°F

40

175°F

Ft. 204

20 20

2 0 . 0 '

9. '

i0!"

"0

<

10 '

16'

0-

0

I 1 (2) Main A : 95.4 ft 2 Engines DE= ]1.02 ft

1 (i) Main A = 47.7 ft2 Engines DE= . 7.79 ft

04 Level

03 Level

Fig. 37 Profile and temperature comparisons

secured to the 03 and 04 levels of the ship and supported by extensive guywire networks. A sketch of the aft gridwork assembly is shown in Fig. 34 and photos of the actual installation on the Foster in Fig. 35. Structural materials available included 31~-in. aluminum conduit, lllz-in, steel tubing, and 5-in. steel pipe. The quantities of these materials were limited and the structure had to be designed with the material at hand, due to the time constraint on the testing.

Types of recording equipment that could be used for the tests included multipoint digital scanners for sequential data re-

cording or "data loggers" for simultaneous recording. Of the equipment available, the muhipoint scanners were most abundant and would definitely be available for the proposed test date. The availability of the data logger equipment was questionable. The use of the sequential scanners was discussed, and considered acceptable if this scan interval was 10 to 15 sec, this time interval being considered small enough to avoid detrimental effects of shifting winds. Twenl~y-four recorders were used for all thermocouple recording, resulting in a 12-sec scan.


Profile and temperature comparisons The ship was oriented with approximately a zero-degree

relative head wind so that the plumes would pass through the center of the grid section. A total of 19 runs was made. Table 8 summarizes the test conditions.

Results from a typical isotherm pl0t are shown in Fig. 36. The hollow dots indicate the thermocouple locations where temperature readings were available. A set of isotherm (constant temperature) curves is plotted over the drawing of the gridwork to allow better visualization of the plume temperature profile. Isotherm plots for all runs are given in reference [7]. As can be seen, the average temperatures at all the thermocouple locations were indicated on the gridwork assembly drawing. Isothermal lines, generally at 20 F (11 C) intervals, were then estimated and drawn to indicate maximum- temperature zones and the approximate shape of the plume. These plots for the forward and aft grids of a given run describe the overall plume profile and temperature decay, both axially and radially from the plume centerline. From each grid plot, a centerline height and temperature value were obtained. These values are summarized in Table 9.

These data were used to develop corrections to the equations presented earlier in this Appendix. The final mathematical expression developed for prediction of plume centerline 'trajectory is as follows:

~g = N (V f fVw)(X/Rs) °'4s [(T=/Ts) ~.7 + 0.063] (8) 19

where

[2.4 + 0.3 (Vs/Vw] °.5

N = 8.6 for a single exhaust pipe

N = 6.6 for multiple exhaust pipes

This equation assumes minimal blockage ahead of the stack, producing a nonstratified uniform flow field.

The final model for plume centerline temperature is as follows:

~h - TM - T_.________~ _ 5.86 (Vs/Vw) °.25 [(D/S) T M T s - T ~

+ O.O17][(T~/Ts) 4.5 + 0.20] (9)

A typical comparison of actual versus predicted trajectory using the modified equation is shown in Fig. 87. Data comparisons revealed that the temperature expression shown in equation (7) required only minor modification based upon the data taken in this test.

Conclusion The full-scale testing performed on the DD 964 is the most

comprehensive stack gas testing performed to date. The quantity of data obtained and the method of recording yield the most useful information for accurate mathematical model development. Merits of the testing include:

• Data for a large range of velocity ratios (0.75 to 3.53 ) were recorded.

• Data for a large range of stack exit temperatures (275 to 452 F) (135 to 238 C) were obtained.

• A large and consistent data base was formed for plume trajectory and temperature analysis, involving future shipboard eductor designs.

• Used in conjunction with other full-scale testing, the data provided a basis for the development of an applicable mathematical model for the full range of expected exhaust gas temperatures (250 to 1000 F) (121 to 588 C).

• The successful testing on the DD 964 forms a baseline for future testing apparatus designs and testing procedures.

Discussion- Robert G. Keane, Jr., Member

[The views expressed herein are the opinions of the discusser and not necessarily those of the Department of Defense or the Department of the Navy. ]

As one intimately involved in naval ship design, I wish to compliment the authors on their excellent technical presentation o~ a subject gaining the interest of an ever-increasing segment of the ship design community. I admire the authors' success in treating such a large, complex subject and condensing its many facets into a single paper which presents guidelines to be used in stack design. There are, however, a few additional areas that should be discussed by the authors to complement their fine technical 'paper.

First, the prediction of the ship's boundary-layer height and- the exhaust plume centerline trajectory by "conventional" model tests in the circulating water channel should be compared with both full-scale results and the authors' empirical relationships in Fig. 9 and equation (8), respectively. Hopefully, -this comparison would provide more definitive guidance in the use of these model tests in connection with the fourth step of the "Design procedures" section outlined by the authors.

Second, it would be appreciated if the authors would specify some examples of fore-and-aft design conditions, as noted in the subsection "Conventional and special stack shapes," that dictate selection of streamlined stack shapes.

Third, an additional discussion on the authors' statement, later in the same subsection, concerning the use of detailed model tests to verify the eductor mixing ratio would also be appreciated. A brief summary of the authors' outstanding

Stack Design Technology for

' work in redesigning the eductor system in the DDG 47 in order to significantly reduce topside weight would be a good example of the importance of such model tests.

Fourth, Fig. 37 should be clarified in order to more clearly compare the exhaust gas temperatures measured on the DD 964 with those predicted by equations (7) and (9).

Finally, I again express to the authors my appreciation for their significant contribution to this important area of ship design.

David E. Little, Member

I would like to congratulate the authors on the presentation of a very useful tool for the ship design industry. The paper presents a compreher/sive method for feasible stack design based on a significant amount of full-scale and model test data. My comments do not concern the technical applicability of the procedure as presented, but are a discussion of some of the basic assumptions presented and recommendations for future de- velopments.

In the authors' discussion of general plume trajectory analysis, they state that "Buoyant forces become increasingly .important at higher velocity ratios" and " . . . for low velocity ratios, the stack gas and ambient wind momentum--and not stack gas buoyancy--will determine the plume trajectory." Due to a lack of supportive data regarding the relative contributions of buoyancy and momentum in defining a plume trajectory, such a generalization could be premature. Stack gas momentum is basically a function of stack gas mass velocity, which is directly related to velocity ratio. Buoyancy is a function of stack gas density, related to temperature, pressure, and chemical

Naval and Merchant Ships 347

composition, and is essentially independent of the resultant stack gas velocity and velocity ratio. Assuming a superposition of buoyancy and momentum contributions to the trajectory, it becomes possible to have significantly more buoyancy in a high-temperature, low-velocity-ratio exhaust (gas turbine at low power) than in a low-temperature, high-velocity-ratio exhaust (steam plant at high power). In considering a single ship design, such as a gas turbine plant, it can be seen that for a reduction in power, the stack gas momentum will decrease at a faster rate than the density of the gas. Assuming a similar relative wind, it is possible that the relative contribution of buoyancy may, in fact, increase with a decrease of velocity ratio. However, perhaps through future model and full-scale testing, the actual contributions of buoyancy and momentum can be more accurately defined.

I would also like to include a recommendation for the development of the boundary zone height trajectory prediction as a function of distance aft of the top of the deckhouse. The estimation of boundary zone height given in the procedure is assumed to be a reasonable maximum. However, as in the case of the aft deckhouse of large tankers, with stacks located in the immediate vicinity of the deckhouse front, this maximum value could place an excessive stack height requirement for pene- tration of the boundary layer by the plume.

Again, I would like to congratulate the authors on presenting such a useful and comprehensive study.

John McCallum, Member

This additional written contribution to the discussion has been made because the writer heard Mr. Donald McCallum, one of the co-authors, remark in his oral reply that he had very little information on the QE2 stack. This discusser was in charge of technical matters during the design and construction of the ship at John Brown's and will try to fill in some background.

In a combined operation such as the design and building of a large passenger ship, the ultimate marketing aspect is important. The ship has not only to perform well, but to look good, too, and preferably distinctive, both inside and out, and . the funnel has a big contribution to make. So a team of in- dustrial and decorative designer consultants were engaged, and the leader of that team, after considering the profile of the ship, determined that she required a tall, slim funnel. With the benefit of hindsight, I think he was right, but confess I was not so sure then.

This aesthetic constraint was the first technical design boundary, but the first real technical move was to construct another boundary, namely, a set of streamlines around the upper silhouette, and then to project the funnel design upward from there.

All the model experiments were effected in the open jet tunnel at the National Physical Laboratory at Feltham in Middlesex, England.

Some five models of a tall, slim, tapering stack (some with a knuckle near the top) were tested on a model ship mock-up. Each model had a slightly different rake and aspect ratio, and each was tested in ahead, beam and astern air flow conditions at various wind speeds. Further intermediate tests were effected at about 20 or 30 deg off the bow, and these generally gave poorest results. In fact, none of these tests was entirely satisfactory, as the smoke plume tended to be eventually drawn into the lower turbulent regions.

Two further models were then constructed having a step some 45 ft (13.7 m) (on full scale) above the deck. The total flue height was 90 ft (27.4 m). Exhaust air from the engine and boiler spaces was ejected from the top of the step, and this satisfactorily carried the plume away from the ship at all angles of attack.

Again for aesthetic reasons, the step was raised to about 60

348

ft (18.2 m) in an eighth model, also with satisfactory results. Residual drifting smoke at very low relative wind speeds was

dealt with by fitting "armchairs" or scoops at the lower end of the funnel and these also worked'well.

In all, some 89 test series were, to the best of my recollection, effected.

I would add to the other contributors' remarks my own congratulations on a most informative paper.

Authors' Closure

We wish to thank the discussers for their kind and valuable contributions. The volume of response from the membership at large indicates the concern of the marit ime community for well-designed and functional stacks. We especially thank Mr. John McCallum of Lloyd's Register of Shipping for his written contribution concerning the extensive testing performed in support of the Queen Elizabeth II stack design.

Mr. Keane's comments regarding the correlation of model to full-scale test results are germane. To address this question, a scale model of the DD 963 was tested in the Circulating Water Channel at DTNSRDC, Carderock, Maryland. The full-scale test conditions, described in the Appendix of the paper, were simulated in the Carderock model tests. The data, which are shown in Fig. 38, compare the plume height of the model test to the full-scale results. It is apparent that the model plume does not rise as fast as the full-scale plume at equivalent velocity ratios. It was concluded that the results of the model studies could be used to simulate full-scale location of the plume if they were corrected by using a momentum correction, factor. From ideal gas theory, the following relationships can be used to express this correction:

(p~Vs~ pwVw ; (25)

or

where

30

model \ p w V w ,I ship

( wVq =(TwVq T ~ - ~ w / m o d e I \T~s~w zt shi p (26)

25

2O

[ ]

15

[ ]

10 •

[ ]

5

[ ] [ ]

• FULL SCALE TESTS DD 964 [ ] M O D E L TESTS IN WATER CHANNEL

[ ] CORRECTED M O D E L TEST D A T A a

[ ]

[ ]

[ ] [ ] [ ]

a A DENSITY CORRECTION FACTOR EQUAL TO ]HE RATIO OF STACK GAS DENSITY TO WIND DENSITY WAS USED TO CORRECT THE MODEL DATA

0 I I I I 0.5 1.0 1.5 2.0 2.5

VELOCITY RATIO (Vs /Vw)

Fig. 3 8 P l u m e h e i g h t c o r r e l a t i o n


I I

3.0 3.5

Vs, Vw = stack and relative wind exit velocity T~,Tw = stack and relative wind exit temperature Pw,pw = stack and.relative wind density

The absolute temperature correction factor given in equation (26) can thus be used to approximate the momentum or density effects of full-scale conditions. Figure 38 illustrates the ap- plication of this correction [actor. ;~ ,~

Regarding Mr. Keane's second comment on streamlined stack shapes, we would refer him to Figs. 17 and 18 of the paper. These figures indicate, both for headwind and 20-deg yaw. angles, that the streamlined uptake is consistently one of the best performers.

The following comments are offered in response to Mr. Keane's request for additional discussion on eductor mixing tests. Figure 25 illustrates the DD 963 eductor design. During the design of the DDG 47 Class, which is a derivation of the DD 983 Class, extensive redesign of the stacks and uptakes was undertaken 4 to reduce topside weight while maintaining acceptable stack performance. M6del tests were conducted at the Naval Postgraduate School (NPGS) in Monterey, California. One of the primary objectives was to measure the eduetor mixing ratio, that is, the ratio of induced secondary airflow to prima:ry engine exhaust mass flow. The results indicated that over a wide range of operating conditions the mixing ratio is about 1:1. This was confirmed by full-scale results on the USS Foster.

We als0 thank Mr. Keane for his final comment regarding

4 Baham, Gary and McCallum, Donald, "DDG 47 Class Stack Re- design Study," Naval Ship Engineering Center Report 6136-77-14, March 1977.

the typographical errors in Fig. 37 of the prepfint; they have been appropriately corrected.

Mr. Little's comments concerning the momentum and buoyancy dominated plume regions, and their scaling, are only partly addressed in the paper. Equations (4), (5), and (6) are based upon work performed by Hoult, Fay, and Forney [6]: However, these eq.uati0ns are only approximations of the two flow regions, andsh0flld be used only for general guidance. Obviously,. under high-velocity-ratio conditions, when the plume is only deflected slightly by ambient winds, the 45-deg approximation for the transition region between momentum and buoyancy dominated regions is not precise. In this transition region where Lm < x < Lb, no simple formula for plume rise exists. For most practical cases, a fairly accurate approximation for plume rise can be derived from equation (6). This is borne out by the full-scale test results where the plume flow is principally momentum dominated; that is, plume rise is proportional to x n. The authors agree that more work should be done in this important area.

The comment made by Mr. Little regarding the development of a boundary zone height trajectory prediction method is valid. The authors understand that the boundary zone height, h, does decrease from the maximum value, going forward toward the point of flow separation. For the majority of ship designs, however, the maximum h value, as determined in this paper, is a very close approximation. This is because the stack is not normally positioned in close proximity to the forward edge of the bridge. We refer those interested in this variation to Ower and Third's work [12]. Also, for any significant stack design, model test experiments should be conducted, and small variations in boundary layer height would then become apparent.


baham g j.stack design technol.1977.trans

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