THE EFFECT OF IRREGULAR SURFACE
ROUGHNESS
ON THE FRICTIONAL RESiSTANCE OF SHIPS
R. L KARLSSON
Chàlmers University of Technology, Department of Applied Thermo S-402 20 GOTEBORG, Sweden
dw vo
Mekefwag 2, 28
DeiftTEL. 015..
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-It is shown that the effect of irregular ship hull roughness on the frictional resistance of full-scale ships can be investigated by experiments made in a
flat-plate turbulent boundary layer in a wind tunnel with moderately large subsonic free-stream velocities. Measurements of local skin friction with the floating element method were carried out in a wind tunnel on smooth walls and on replicas of four different ship hull surfaces. Roughness functions for these four surfáces are reported. It was found that the roughness function varies linearly with the roughness Reynolds number Rk for small values of Rk. Measüre-ments of the surface structure did not yield any conclusive results regarding which roughness parameters are of hydrodynamical relevance.
Predictions of the effect of surface roughness on the frictional resistance of full-scale ships were made with a simple method. Charts, presenting the rela-tiv,e increase in total skin friction on full-scale ships as a function of ship length and with the ship speed as parameter, are. given for each rough surface tested in the experiments. The results indicate, that it is possible to make large savings by improving the surface finish of both new and old ships, since not even new ships seem to have sufficiently smooth surfaces to assure hydro dynamically smooth flow conditions.
NOTATION
A Area of floáting element surface
b Width of floating element
C Constant iti asymptotic form of roughness function
Cf Local skin friction coefficient (
2/pU)
Cf Increment in Cf due to roughness
CF Total skin friction coefficient
CF Increment in CF due to roughness
CLA Centre-line average height (
F Shea± force on floating element surface; also flatness factor
g Roughness function
h Height of edge of floating element
k Characteristic roughness height; here taken as cr
L Length of ship (; flat plate)
Rx Reynolds number (= Ux/v)
Reynolds number (
R.k Roughness Reynolds number ( uk/v)
r(X)
Normalized auto-correlation function of the roughness amplitudeS Skewness factor
U Mean velocity
U0 Free-stream velocity
U Dimensionless velocity (
U/u)
u Friction velocity
u' RMS value of longitudinal velocity fluctuations
Downward shift of the logarithmic velocity ditribution Coördinate in streamwise direction
y Distance from wall; also roughness amplitude
y Dimensionless wall distance (= uxylu)
e Momentum thickness
von Kármán's constant
A Longitudinal separation in auto-correlation function
y Kinematic viscosity
p Density of fluid
a RMS value of roughness amplitude or slope
T Wall shear stress
Slope of surface roughness (degrees, O)
Subscripts
r Rough-wall conditions
s Smooth-wall conditions
y Refers to roughness amplitude
Ç Refers to roughness slope
1. INTRODUCTION
The drag due to skin friction is of great importance in màny technical appli-cations, for example in naval architecture. The frictional resistance of large slow-going ships may amount to 80 - 90 % of the total resistance of such ships (Lackenby [li). Roughness on a ship's hull yields a further increase in the frictional resistance. Considerable increases in the frictional resistance of ships have been observed after the ships have been in service for some time. The increased resistance is caused by gradual deterioration of the surface by corrosion and organic fouling. Although the quality of marine paints is
stead-uy improving, the effect of surface roughness on the frictional resistance of
ships is still a major problem. Attempts to reduce the operational costs for ships by taking appropriate measures to control or reduce ship hull roughness are complicated by the fact that there does not exist any general relationship between the roughness magnitude of irregular ship hull roughness and the cor-responding effect on the frictional resistance of full-scale ships. The experi-mental literature on this particular problem is also limited. Therefore, ex-perimental data on skin friction and surface structure on irregularly rough ship hulls, as well as predictions for full-scale ships, are highly needed.
The difficulties mentioned above depend on several factors.
i The problem of obtaining a hydrodynamically relevant description of
irregularly rough surfaces;
ii The problem of making accurate skin-friction experiments on rough walls
under conditions which satisfy the aPpropriate similarity laws.
The irregular character of ship hull roughness makes it necessary to use
statistical methods to describe the surface structure, and it is reasonable to assume that not only the average height but also the spatial distribution and possible periodicity of the roughness will affect the hydrodynarnical behaviour of the surface. In order to obtain consistent descriptions of the roughness one must therefore find out which roughness parameters are relevant from a hydro-dynamical point of view, that is, the soecific characteristics of the surface which by interaction with the flow cause the increased frictional resistance. There seems to be a need for further research in this area.
Since it is almost impossible to increase the scale of an irregularly rough surface without violating the condition of geometrical similarity of the sur-faces, one is forced to use the rough surface in a 1:1 scale in laboratory experiments. If positive copies (replicas) of real ship hull surfaces are used in the laboratory experiments, the characteristic roughness length k will be the same in the test situation and in the full-scale flow. The problem is then to simulate in the laboratory the essential features of the turbulent boundary layer at such high Reynolds numbers as those developed by full-scale shios. Karisson et al. [2] studied this question and showed that it is necessary to have equal viscous length scales v/u* for the test flow in the laboratory and the full-scale flow. This necessary condition is a direct consequence of the
dynamical similarity of the flow Close to the wall in turbulent boundary layers (Preston [3]). If the experimental conditions can be chosen so that this criterion is satisfied and a replica of the real ship hull surface is used, the roughness Reynolds number .Rk.u*k/v will be the sáme in the labOra-tory test and in full scale. Fama [4] has shown that the increase in local skin friction is uniquely related to the roughness Reynolds number. If suffi-ciently high values of Rk can be achieved in the laboratory test, it will be possible to determine the effect of roughness on the frictional resistance.
How can one achieve sufficiently small values of the viscous length scale v/u* in laboratory flows? It is import-ant to stress that it is not necessary to achieve the high Reynolds numbers of ships (RlO9) for this purpose, since the viscous length scale is not a unique function of R. It will be shown in this paper (section 2) that a thin flat-plate turbulent boundary layer with, high (subonic) free-stream velocity in a wind tunnél yields viscous length scales that are small enough to make skin-friction experiménts on real ship hull surfaces meaningful. This type of wall-layer simulation has already been used successfully by Musker et al. [5], who used fully developed turbulent pipe flow to obtain small viscous length scales.
According to the theory given by Hama [4], it is necessary tô knowthe local skin friction in order to determine the roughness function. Towing-tank tests, in which the total drag is determined, are therefore not as suitable as expé-rimental methods which give the local skin friction. However, it is difficult to make accurate measurements of local skin friction on rough walls. Wall-similarity techniques can not be used with any higher degree of accuracy. The momentum technique is an excellent tool in fully developed pipe añd channel flow, where the skin friction can be determined directly from meauremen-ts of the pressure drop. This technique was used by Musker et al.[5]. Application of the momentum integral equation on the flat-plate boundary layer by substituting measured quantities into the equation will involve the derivative of the
momen-tum thickness and may thus give low accuracy. in the determination of the local skin friction coefficient.
The only remaining direct method for measurement of local skin friction is the floating element method. This technique was first used by Kémpf [6] in his classical investigations on local skin friction. For measurements with the
floating element method, a part oft-he surface is cút out and is made to move by the shear force that is exerted on the surface element by the flow. The force acting on the element is detected and measured, and the local skin
friction coefficieñt is determined from this force. The.floating element method has now become a standard technique for accurate measurements of local skin friction on smooth walls (Smith and Walker [7], Winter and Gàudet [8]), and has also been used by the author (Karisson [9]) for measurements on smooth walls. In the present investigation, the use of the floating elément method has been extended to measurements of local skin friction on rough surfaces. The work to be presented here is part of a fundamental investigation on skin friction and turbulence structure in flat-plate turbulent boundary layers on smooth and rough walls, currently in progress at the Department of Applied Thermo and Fluid Dynamics. The Objective of this work is to study experiment-ally the effect of typical irregular ship hull roughness on the local skin friction and thereby determine the increase in skin friction that is caused by the roughness. The experiments were performed in a flat-plate turbulent boundary layer on a wind tunnel wall, and the local skin friction was measured with the floating element method. Four different rough surfaces (replicas of real ship hull surfaces) were tested.
The effect of roughness on the local skin friction is described in terms of Hama's roughness function, which is suitable for incorporation in many existing boundary-layer predictioì methods. Predictions of the increase in local and total skin friction on full-scale ships are made with the measured roughness functions as input. The full-scale ship is thereby apnroximated by a flat plate with corresponding length and speed.
94
2. MEASUREMENTS OF LOCAL SKIN FRICTION
2.1 Theoretical Background
It is assumed that the rough surface of the full-scale ship and the rough sur-face to be tested in the laboratory have identical roughness charaCteristics. This assumptioñ will be satisfied in the experiment, since the test surface is a replica of the original ship hull surfàce. The criterion to be satisfied in the experiment in order to obtain the same roughness Reynolds number
Rk u*k/v (1)
in the test situation and in the full-sCale flow is then
test ship (2)
that is, identical viscous length scales u/u* (Karlsson et al.[2]). Hama [LI] has shown that the Increase in local skih friction due to roughness is uniquely related to the roughness Reynolds number Rk by an equation of the form
g(uk/v)
, (3)
where the function g is dependent on the roughness geometry of the surface and must be determined from experiments for
each Darticular surface.. The asymp-totic form of Eq. (3) for large values of Rk is
ln(u'k/v) + C
as shown by Flama. The quantity AU1u* is the downward shift of the
logarithmic velocity distribution as shown in Fig. 1 and is related to the local skin fric-tion coefficients for the smooth and rough surface by the equafric-tion
(/r)
(/L)
Cr
By use of the definition Cf2(u*/U0)2, Eq. (5) can be written
_Uo
U0u*
-s r
Combination of Eq. (6) and Eq. (3) yields
U U o o -s r = g(ukIv) (7)
Equation
(7)
can be used to evaluate the roughness functiong from measurements of local skin friction on smooth and rouSh walls in a given experimental set-up. After a local skin-friction line has been established for smooth-wall flow in
the particular experimental configuration the wall is covered by the
rough-wall replica for a sufficiently long distance, and the measuremeñts are
repeat-ed over the saine range of the indeDenden-t variàble. A skin-frictiOn
line for
the rough surface is thus established Typical results are shown schematically
in Fig. 2, where the local skin friction coefficients for the
smooth arid the rough wall are given as functions of the unit Reynolds number U0/v. The
left-hand side of Eq. (7) is known, as well as the roughness Reynolds number
Rk
for each value of U0/v that is covered by the exoeriment. The
function g can
then be determined by plotting U0/u - U0/u
(:U/u*) as à function of u k/v.
As mentioned earlier, the viscous length scale \)/u* is not
a unique function of
the Reynolds number R. A given value of R
for a flat-plate flow can be
velocity and a long plate, and the viscous length scale for the same value of will become quite different. The viscous length scale can be expréssed in free-stream velocity and local skin friction coefficient by the relation
(8)
Since the effect of R on Cf is small, the main variation of /ú* must be
accomplished by a variation of the free-stream velocity. In order to simulaté the small viscous length scales on full-scale ships by using a flat-plate boun-dary layer,one should therefore, according to Eq. (8), have a short development length (high Cf) and high free-stream velocity.
An estimate of the variation of v/u which is encountered on full-scale ships
(:: flat plate) yields /u*c 3 20 um for free-stream velocities lower than
10 m/s, if the values of the first few meters on ti-e ship are excluded. The present experiments will be performed in a low-speed wind tunnel with air as fluid. The minimum value of v/u* that can be obtained is 6 - 7 um. This limit is determined by the maximum wind-tunnel speed, 65 m/s. Thus it is possible to satisfy the criterion Eq. (2) except for the extremely small length scales
3 - 6 um. This is probably no serious disadvantage. For really rough surfaces
(high values of k), the roughness function may already have taken its asymptotic form for such small length scales. If the roughness height is not too small, it will be possible to study the departure of the rough-wall skin-friction line from the smooth-wall line, that is, the region between fully rough flow
condi-tions (Eq. (Li)) and hydraulically smooth flow conditions. This region is
prob-ably of oarticular interest in naval atchitecture.
2.2. Wind Tunnel and Flow Quality
The large low-speed wind tunnel L2 at the Department was used for the experi-ments. The tunnel is of the closed type and has a working section of the follow-ing dimensions: length 2.8 m, width 1.8 rn, and height 1.25 m. The working
section is provided with fillets in the corners to minimize possible corner
flows. The areä of the fillets is diminishing in the flow direction to compensate
for the boundary-layer growth. The naturally grown boundary layer on one of the smooth side walls was used as the test boundary layer, because the floating ment had to be mounted on a vertical wall. This positioning of the floating
ele-ment thade an extensive investigation of the flow quality necessary.
Measuremexfts of boundary-layer development and static pressure distribution
along the smooth side-wall were therefore made by Karlsson [10]. He found that the turbulent boundary layer at the downstream end of the working section, where the floating element was mounted, corresponded to an equilibrium flat-plate turbulent boundary layer within the experimental accuracy for velocities
higher than 18 rn/s. For free-stream velocities lower than 18 m/s, the flow was
similar to a developing flat-plate boundary layer, since the velocity defect profiles were not independent of the Reynolds number. Â small spanwise varia-tion of local skin fricvaria-tion with an amplitude of ±2 % of Cf was detected at velocities lower than 15 m/s. However, the flow quality was considered to be good enough for the purposes of the present investigation. The free-stream
tur-bulenàe intensity u'/'Jowas about 0.2 %. Fig. 3 shows the geometry of the wind
tunnel wall, the coordinate system, the static pressure distribution along the smooth wall, and the position of the rough wall and the floating element. The flow development length in zero pressure gradient down to station 7, where the floating element is situated, was aboüt 2.0 m.
2.3 Copies of Rough Surfaces
Four positive copies of rough ship hull surfaces were tested in the wind tunnel. Surfaces no i - 3 were manufactured by TNO, Deift, the Netherlands. Surface
no Li was manufactured at the University of Liverpool and is a replica of a
part of the surface on the ship !0rtegafl. A description of the roughness struc-ture of the surfaces is given in section 3.
Fig. Li shows in more detail how the rough surfaces were mounted
on the wind tunnel wall. The front edge of the rough surface was positioned at x=685 mm
the rough surface. Double-adhesive tape was used to fix the rough surface to the under-lying aluminium wall. Since the width of the rough-wall replicas was only 600 mm, masonite with the rough side turned outwards was mounted on the sides of the replica in order to cover the whole wall in the spanwise direction. The floating element was located on the centreli-ne of the wall at xl735 mm. The flow development length on the rough will down to the floating element was- 1050 mm. Hot-wire measurements showed that this leng-thwas sufficient to establish equilibrium conditions in the rough-wall turbulent boundary layer at the measuring station. Due.to the small thiòkness of the rough-wail repli-cas- (2 - 5 mm) compared with the width of the tunnel (1800 mm), the static pressure distribution along the wall was very little affected by the insertion of the rough wall. Thus, zero pressure gradient conditions were approximately retained along the wall for the rough-wall flow.
2.. Measurement Techniques
The floating element used in this investigation is of the centred type, that is,the floating surface is brought back to its initial, unloaded position, be-fore the readings are taken. The floating surface is a square with the side bl00.0 mm. This instrument was also used by Karlsson [9] for measurements of the local skin friction in the same position (xl735 mm) on the smooth wall. His results will be used in this paper as the local skin-friction line for the smooth wall. A detailed description of the instrument is given by Karlsson [9]. The principle of the floating element is shown in Fig. 5. The flow exerts a force F:T.A on the element surface, and the element is displaced in the flow direction. A micrometer screw is used to restore the element to its unloaded position, which is indicated by a differential transformer. If there is -no
pressure difference between the gaps, the restoring force Fr F. Pressure
differences over the element will give a parasitic pressure force tp.A'(A'b.h), which can not be completely avoided. When this force is taken into account, the
equation for force equilibrium of t-he floating element
becomes-F Fr + ¿pA' . (9)
The local s-kin friction coefficient Cf is obtained from the equation
Cf
pUA
2F(10)
The pressure force was measured and corrected for, bût it did not exceed 3 %
of F in the smooth-wall measurements. For the rough-wall measurements, however, the pressure forces became more important.
Fig. 6 shows the arrangement of the rough surface on the floating element. Double-adhesive was also here used to fIx the rough surface to the floating element surfäce. The part of the surface to be mounted on the floating element was cut out from the rough-wall replica by means of milling.wi-th a thin disk as tool.- The width of the gaps could be kept to about 0.3 mm. Five pressure tappings were drilled directly into the rough surface at the fore and aft edges of the element to permit measurements of the pressure i-n the gaps. Fig.6 also shows that the average height h on which the pressure force acts, could not be kept as small as in the smooth-wall measurements. The parasitic pressure
force therefore amounted to between O and 10 % of F for the rough-wall measure-ments.
The height of the floating element relative to the surrounding rough surface was measured with a dial indicator. The adjustments were made so as to mini-mize the "jump" when the dial indicator was traversed over the gap. Measure-ments of gap pressures verified that proper adjustment of the height also gave very small pressure differences over the element. The correction itself was also verified by making measurements of local skin friction with different settings of the height of the element. The procedure described here was used for the surfaces no 1, 3, and . For surface no 2, which was tested first, this technique was not fully developed. The scatter in experimental results
is therefore larger for urface 2 than for the other surfaces.
A reference velocity U0 was recorded for all measurements by means of a
pitot-static tube of Prandtl's design and an accurate single-limb micromano-meter. The same pitot-static tube was used during the whole experimental
period (several years) in a fixed position (x = 1735 mm, y = 300 mm, z 0),
that is, far outside the boundary layer at the same spanwise and streamwise position as the floating element. Static calibrations of the floating element were made in situ before and after each test period. The calibration was ex-tremely stable. Readings taken from the floating element together with the velocity U0 and appropriate values of barometric pressure, wind tunnel tempera-ture etc., were used for the evaluation of local skin friction coefficient according to the Eqs. (9) and (10) as a function of unit Reynolds number U0/v. For further details, see Karlsson [li].
Hot-wire measurements of the streamwise velocity were made at three positions (station 5, 6, and 7, according to Fig. 3) along the wall on three surfaces. Digital linearization of the hot-wire signal was used in order to minimize the errors caused by the nonlinear response of the anemometer (}(arlsson [12]). A full report on the results will appear as soon as the data are fully evalu-ated. Here, only the mean velocity distributions on the floating element for one surface will be given.
2.5. Experimental Results on Local Skin Friction Along Rough Walls
Fig. 7 shows the experimental results on local skin-friction coefficients for
the rough surfaòes no i - and for the smooth-wall flow (Karlsson [9]), as
functions of the unit Reynolds number. The roughness functions were evaluated from the data by means of Eq. (7), with the roughness height k taken as the
rms value y of the roughness amplitude (see section 3). In Fig 8, the
measured roughness functions and their analytical approximations are shown as functions of the roughness Reynolds number Rk. Full lines describe the exp-erimental results, and broken lines show the suggested extrapolations to the measured roughness functions.
One interesting observation can be made from the data in Fig. 8: the roughness
functiun is linearly dependent on Rk for small values of Rk, which is a
parallel totlie law of the wall for small values of y+ Only surface no 3 can
be followed from the onset of the effect of surface roughness on local skin friction and to the region where the asymptotic form of the roughness function (Eq.(4)) is approximately reached.
The extrapolations to large values of Rk of the roughness functions for the surfaces 1, 2, and 4, were based on the following òbservations. The position of the asymptotic logarithmic roughness line depends on the extent and shape of the roughness function in the transitional region between smooth-wall flow and fully rough-wall flow. Colebrook and White [13] showed that the extent of the transitional region is strongly dependent on the roughness structure, with nonuniform roughness height giving a larger transitional region. Surface no 3 has a highly irregular roughness structure with relatively few very large pro-. tuberances compared with the other surfaces with more regular roughness
character (see Fig,.
10).
One can therefore assume that the transitional regionshould have a larger extent for surface no 3 than for the other surfaces. Moreover, there seems to exist a break-point in the linear relationship of
U/u* versus Rk at tU/u*1.6 for surface no 3. The roughness function varies linearly with Rk in the range of experimental data for the surfaces 1, 2, and 4. In lack of further information, it is therefore assumed that the asymptotic form of the roughness function is valid in the range tU/u* 1.6 for the
surfaces i and 4. Surface no 2 has a more irregular character than the surfaces 1 and 4, and the roughness function also seems to have a larger linear region. In this case, the logarithmic roughness function is chosen to join the linear
roughness function at U/u* 2.2. However, lower accuracy in the experiments
on surface no 2 than on the other surfaces may have caused larger experimental scatter and a different constant of proportionality in the linear form of the roughness function for this particular surface. Table 1 gives the analytical approximations and extrapolations of the measured data.
Table 1. Analytical description and extrapola-tionof measured roughness functions for rough surfaces no i - 4.
9:8
Fig. 9 shows méan velocity distributions measured on the floating element
on surface no 3. Appropriate values on friction velocity u* were taken from
the skin-friction meäsurernents, and reasonable estimates on the starting
position y0 close to the wall were made with knowledge of the surface charac-ter and the position of the hot-wire relative to the surfäce. The increasing downward shift of the logarithmic velocity distributions with increasing fre.-stream velocity (increasing values of Rk) is clearly demònstrated.
The profile for U0 = 8.6 m/s is falling above the standard logarithmic law
(Coles [14])
2.44 in y + 5.0
due to the fact (Karisson [9]) that the additive constant in Eq. (ii)
seems
to be depèndent on Reynolds number R® for R0 6000.
3. MEASUREMENTS OF STRUCTURE OF SURFACE ROU(HNESS
Surface profiles, 52.5 mm in length, were measured ori the iough surfaces previously positioned on the floating element. The measurements were made
by means of a Talysurf 4 -instrument, equiDed with a Talyrnin 4 gauge had.
A conical stylus (angle 600) with a nose radius of 10 pm was used in order to dbtain a detailed description of the surface. The surface profiles
were recorded on paper and digitized ianualiy with a sampling interval of 0.05
mm-in the longitudmm-inal Cx) direction and with a resolution of 2 pm (4 pm for surface no 3) in the vertical (y) direction. Thus, 1051 samples of the roughness height were taken on each surface.
3.1. Evaluatioñ and Results
A computer program was written for statistical evaluation of the data. The method of least squares tas used to determine the position of the centre line, which served as datum for the y-coordinate in subsequent calculations. The condition Ey:O for the deviations from the centre line was therefore satisfied identically. Measured surface profiles for 'ough surfaces no 1 - 4 are showñ in Fig. 10. A definition of the slope P of the surface relative
Surface 1:
0,
= 31 pm Surface 2: 0 65 pm 0;ORk3.05,
0.6(Rk_3.05); 3.05<Rk5.7, AU = 2.44 in Rk_2.SS; Rk>S.7. 0;0Rk3.8,
= O.35(Rk-3..8); 3.8<Rk10, = 2.44 in Rk-3.49; Rk>iO.Surface 3: O = 183 pm Surface 4;Oy 29 pm
= 0;
0Rk6.6,
-=
O.6(Rk-6.6); 6.6<Rk9.0, = 3.8 in Rk-S.9; 9.0<Rk l7, = 2.44 in Rk_3.QS;, Rk> 17. 0; = O.G(Rk_3,3); 3.3<Rk6.O, 2.44 in Rk_2.76; Rk>B.O.to the centre line is also given in the figure.
-Variance, -rms value, cènter-line-average value, maximum range, skewness and flatness factor, probability dènsity distribution, and the normalized auto-correlatIon functioíi ±'(À) (p denotes amplitude or slope) were calculated for the amplitude y and the slope 'P. The results, based on 1051 samples taken over the length 52.5 mm,are presentedin Table 2. Fig. llshows the probability density distributions of the roughness amplitude and slope fòr surfaces no l_4. Gaussian distributions based on the same rms values are also shown for comparison. Normalized auto-correlation functions of the roughness amplitude are presented in Fig. 12.
Table 2. Statistical characteristics of roughness amplitude and slope for surfaces no 1 - 4.
Remarks: * Manufacturer of the ship hull replica..
** Correlation length is here taken as the separation at which the value of the normalized auto-correlation function has decreased to 0.5.
3.2. Discussion of Roughness Measurements
The results on roughness structure presented in Tàble 2 and Figs. 10 - 12 must be considered as only indicative. It is obvious (see Fig. 10) that several surface profiles taken over longer sampling length are necessary In order to obtain an accurate statistical representation of large, long-wave surface ir-regularities. Further, more extensive, roughness measurements are therefore planned.
The term "irregularity" in the description of ship hull surfaces has one obvious imolicàtion. Measurements at different positions on the same surface may give quite different roughness characteristics. Surface no '4 is a copy of
a urface which has also been investigated at the University of Liverpool. A
comparison of the measured surface profile parameters is given in Table 3. The sampling interval was 0.05 mm in both investigations.
Amplitude (y)
Surface no Statistical moments Peak-to
Correla-tion CLA y s y valley height length** (:j) (um) (pm) (pm) 1 (TNO)* 25 31 0.5 2.4 132 2050 2 (TNO) 55 65 0.0 2.5 344 4400 3 (TNO) 148 183 0.1 2.7 825 3700 '4 (Liver-pool) 23 29 0.3 3.3 154 2200 Slope ()degrees (°)
Surface no Statistical moments.
-'0max Correla-tion length : Prn±n 1 1.2 1.6 -0.05 3.7 12 240 2 2.7 3.6 0.0 3.8 25 145 3 7.6 12.3 0.5 9.2 115 75 4 1.2 2.3 -3.5 46 40 110
Table 3.Acomparison of surfàce profile parameters for rough surface no 4.
9:10
Differences in roughness height of 30 % are noted. For the average slope, the differences are extremely large.
The auto-correlation function (Fig. 12) of the roughness amplitude contains information on the amplitude/wavelength distribution (Pekienik [15]). The extremely long correlation length for surfaces no 2 and 3 indicate the long-wave periodicity of these surface profiles. The probability density distribu-tions presented in Fig. 11 differ appreciably from the Gaussian distribution. Surface no '4 shows up two sharp-edged intrusions which cause extremely large
slopes and therefore long t ils in the slope distribútion and high flatness factor. One can ask whether this type of iÌ'regularities is important in the generation of resistance. Local flow separatiOns probably make the effects of
such small, sharp intrusions on the resistance negligible. The main problem
is still to find the link between the hydrodynamical behaviour of the surface and its surface characteristics.
4. PREDICTIONS OF THE INCREASE IN FRICTIONAL RESISTANCE ON FULL-SCALE SHIPS
DUE TO ROUGHNESS
Theoretical considerations (Clauser [16]) and experimental results (Perry & Joubert (17]) strongly suggest that the roughness function Eq. (3) is indepen-dent of pressure gradients. The fact that the roughness functions in this ex-periment were determined in a flow with zero pressure gradient does therefore not impose any restrictions regarding the use of the results in flows with pressure gradients. In this paper, however, the calculations are limited to flat-plate flows.
'4.1. Calculation Method
The ship is represented by a flat plate with the same length and speèd as the full-scale ship. Two-dimensional flow is assumed. A skin-friction laW for smooth flat plates is coupled to the roughness function, and local skin fric-tion coefficients for smooth and rough walls are obtained by an iterative method. As skin-friction law for smooth walls is chosen the law given by Coles [18],
2.(!)2 [UO.X + 2
; :
eK21)l
u* z C2
= 2C1e
eK(Uou5)
[1 s (2+
2s
(1 + _)] (12)The constants appearing in Eq. (12) have the values given by Coles:
The reason for choosing Coles' skin-friction law was that previous measure-ments of skin friction on smooth walls by the author (Karisson [.9]) in the same experimental set-up as the one used here, yielded a skin-friction rela-tion which agreed very well with Coles' law.
Eq.. (12) is solved for u with known values on U0, x, and y by an iterative
method, and Cf is calculated from the definition
s CLA S F ' Peak-to-valley height Correla-tion length Slope
(inn) (um) (um) (pm) (°)
Present investi-gation . 23 29 0.3 3.3 154 2190 1.2 University of Liverpool 30.0 37.2 0.1 2.8 189.5 1241 3.7 C1 = '4.05 C2 = 29.0 K 0.40 = 7.90.
Cfs
2(U!)Z
The roughness function is written in the following form
U0 U0 k
- = g( )
s r
where the right-hand side is known from Table 1. For given values on U0,
\,
k,and u, the only unknown variable is u which is solved by iteration. The
local skin friction coefficient for the rough-wall flow is then calculated in analogy with Eq. (13). The increment in local skin friction is
Cf Cf - Cf (14)
r s
The local skin friction coefficients for smooth and rough wall are then cal-culated for all values of U0, x, and k. The coefficients of total skin friction are calculated by numerical integration of the local skin friction coefficients over the plate length, and the increment in total skin friction is calculated from the équation
ACF CF - CF (15)
r s
Calculations were made with the following variàtion of free-stream velocity
and plate length: U0 3.0, 4.0,..., 18.0 m/s, L 1.0, 2.O,.., 406.0 rn. The
kinematic viscosity was in all calculations \ 1.1873 l0 m/s.
4.2. Results of Computations
Typical results
of
the computations a:re presented in Fig. 13, where a) local skin friction coefficients and b) total sk-in friction coefficients for the smooth walland the rough surfaces no 1 - 4 are shown as functions of the distance x from the leading edge (or R) for the free-stream velocity 8.0 m/s. The increase in skin friction (both absolute and relative) due to roughness islargest for small values of x. This result is of course expected, since the viscous length sdàle is smallest for small values of x. For constant speed, the viscous length scale is increasing with increasing values of x, and the effect of roughness ön the frictional resistance should therefore decrease with increasing ship length.
A more suitable form of presentation is to give the ratio between the in-örement in total skin friction due to roughness and the total skin friction for the corresponding smooth ship, as a function of the ship length L with the free-stream velocity U0 as parameter. Charts of this tyDe with the
rela-tive increase 100 LCr/CF on the ordinate axis have been prepared for each
s
rough surface tested in this investigation and are presented in Fig. 14 a - d. The increase in percent of the total skin friction of ships with hull surface conditions correspondi-np tò rough surfacés no 1 - 4 can thus be estimated from these charts. An additional advantage with this presentation is that the
choice of smooth-wall skin-friction law for the computations only gives a
minor influence on the ratio CF/CF , since both numerator and denominator
are affected in a similar way.
Surfaces no 1 and 4 correspond approximately to hull surface conditions of new
ships, whileas surface rio 2 is slightly more irregular. Surface no 3 is from
an older ship and is probably painted without prior sandblasting. Further details aboUt these particular surfaces will become available later.
As an illustration of the use of the charts, two hypothetical ships with
identical Reynolds numbers R are considered. Ship no 1 is a typical tanker
with L= 350 m and U07.0 rn/s. Ship no 2 has the length L175 m and thus the
speed 114 m/s. With knowledge of length and speed, the relative increase in
(13)
total skin friction can be read from the charts. The results are presented in the following Table.
Table i. Relative increase in total frictional resistance due to roughness for
two hypothetical ships. R=2.O6 lO for both ships.
Several interesting features are noted.
The relative increase in total frictional resistance for a given surface is not a unique function of R. This is, of course, a direct consequence of the fact that the viscous length scale v/ut itself is not uniquely re-lated to R
X
ii Also very small roughness heights, such as those for surfaces no 1 and 4,
cause an increase in the total frictional résistance of large, slow-going ships. Since the surfaces no 1 and 4 approximately represent the surface on new ships, this result indicates that the surfaces on new ships are not sufficiently smooth to assure hydrodynamically smooth flow conditions.
iii High speeds give considerable incr'eases in the total frictional resistance
also for fairly smooth surfaces.
iv It is possible to make lai'ge savings by improving ttie surface finish of
both new and old ships.
Ït is suggested that charts of this type are valuable for the marine engineer. With knowledge of the relative increase in the total frictional resistance (from a chart), the extra fuel consumption due to roughness can easily be
estimated and related to the côsts for different hull surface treatments,
and optimum docking intervals can be chosen.
4.3. Limitations of Predictions
The most serious limitation of the results presented in Fig. 14 is that the roughness functions could not be measured in the whole ±'ange of roughness Reynolds numbers covered in the predictions The extrapcla-ted roughness
functions were thus used in the ppedictioris for free-stream velocities higher than about 6 m/s. However, it is suggested that the extrapoiatons are reason-able (see section 2.5) in lack of further information and that the errors due to the extrapolation are reasonably small.
In view of our limited knowledge of the three-dimensional flow around ships, the simplification to two-dimensional flat-plate flow in the predictions is considered adequate.
5. SUMMARY AND CONCLUSIONS
The results of the present work can be summarized as follows.
It has been shown that the effect of irregular ship hull roughness on the frictional resistance of full-scale ships can be investigated by experi-ments made in a flat-plate turbulent boundary layer in a wind tunnel with moderately large subsonic free-stream velocities. The necessary criterion to be satisfied in such experiments is that the roughness Reynolds number Rk shall be identical in the test situàtion and on the full-scal.e ship.
Measurements of local skin friction with the floating element method were carried out in a wind tunnel on replicas of four different ship hull sur-faces, and roughness functions according to Hama's theory were determined.
912 Surface no 100 CF/CF. 1 ¡ 2 Ship no 1: Ship no 2: L L 350 m, U07.0 rn/s (l4 knots)
175 in, U0lLt.0 rn/s (28 knots)
6.5 114 37.5 '4.5
It was found that the roughness function ¿U/u* varies linearly with Rk for small values of Rk. Reasonable extrapolations of the roughness functions were made for the cases where the maximum wind tunnel speed was -too low to yield sufficiently high values of Rk. With the roughness height taken as the rms value ay of the roughness amplitude, the onsetof the effect of surface roughness on the local skin friction occurred in the region
3.0 Rk 6.6.
3. Measurethents were made of the surface structure, and various statistical
moments of the amplitude and slope distributions ere calculated. No
con-clusive results were reached regarding which roughness parameters are of hydrodyriamical relevance-. This was partly caused by an insufficient number of samples in the statistiòal eva]uation and partly by the complexity of the whole problem. Further research in this area is highly needed.
L4 PredictiOns of the effect of surf-ace-roughness on the frictional resistance
of full-scale ships were made with a sithple method. Charts, presenting the
re]ative increase 100 CF/CF in total skin friction on full-scale ships as
a function of the ship -length and with the free-stream velocity as para-meter, are given for each rough surface tested in this investigation. It is suggested that charts of this type äre valuable for the naval architect, since they provide means to est-imate the increáse in total skin friction on full-scale ships. The extra fuel consumption due to roughness can then be estimated and related to different hull surface treatments to obtain optimum ship operation. Further measurements of local skin friction on different types of rough surfaces, evaluated in the manner described i-n this paper, should provide additional useful information.
ACKNOWLEDGEMENTS
Financial support from the Swedish Ship Research Foundation (SSF) and the Swedish Bôardfor Téchnicâl Development (STU) is gratefully acknowledged.
REFERENCES
[11. Lackenby, H.: Resistance of Ships with Special Reference to 3k-i-n Friction and Hull Surface Condition. Proc. Inst. Mech. Erigrs 176, pp 981-101Li, London
1962.
[21 Karlsson, R., Appelqvist, B. & Frössling, N.: Frictional Resistance of Ships. Thick Boundary-Layer Simulation in Wind Tunnel. (In Swedish) SSF-rapport 106, The Swedish Ship Research Foundation, Göteborg l97'4.
[3] P-réston, J.. H.: The Determination of Turbulent Skin Friction by Means of
Pitot Tubes. J-. Roy. Aero. Soc. 58, p-p 109-121, 1954.
['4] Mama. F.R.: Boundary-Layer Characteristics for Smooth and Rough Surfaces.
Soc. Naval Architects Marine Engrs. Trans. 62, pp. 333-358, 195Li.
Mùs-ker, A.J., Lewkowïcz, A.K. & Preston, J.H.: Investigation of the Effect of Surf-ace Roughness of a Ship on the Wall Friction Using a Pipe Flow Technique. Report FM/24/76. University of Liverpool, Dept of Mechanical Engineering, June 1976
Kempf, G.: Neue Ergebnisse der Widerstandsforschung. Werft-Reederei-Hafen, 10, No 11, pp. 23'4-239: No 12, pp. 247-25-3, 1929.
Smith, D.W. & Walker, J.H.: Skin-Friction Measurements in Incompressible Flow. NACA TN '4231, 1957-.
Winter, K.G. & Gaude-t, L.: Turbulent Boundary-Layer Studies at H-igh Reynolds Numbers at Mach Numbers between 0.2 and 2.8. ARC R&M No -3712, London:
9:14
Karlsson R.I.: Studiés of Skin Friction in Turbulent Boundary Layers on Smooth and Rough Walls. Part 2: Skin-Friction Measurements in a Flat-Plate Turbulent Boundary Layer on a Smooth Wall. Chalmers Tekniska Högskola, Inst.
fOr Tillämpad termodynarnik och strömningslära. Publikation Nr 78/2. (Report in
preparation. )
Karisson, RI.: Studies of Skin F'iction in Turbulent Boundary Layers on
Smooth and Rough Walls. Part 1: Measur&ments of BoundaryLayer Development on
a Wind Tunnel Wall Chalmers Tekniska Hogskola, Inst for Tillamoad
termodyna-mik och strömningslra. Publikation Nr 78/1, 1978.
Karlsson. R.I.: Studies of Skin Friction in Turbulent Boundary Layers on Smooth and Rough Walls. Part 3: SkinFriction Méasurements in Flat-Plate Tur-bulent Boundary Layers on Rough Walls. Chalmers Tekniska Högskola, Inst. fOr
Tillämpad termodynamik och trömningsIära. Publikation Nr 78/3. (Report in
preparation.)
Karisson, R.I.: A New Response Equation for Hot-wire Anemometry, Suitable
j
for Digital Linearization. Chalmers Tekniska Högskola, Inst. för. Tillmpad termodynamik och strömningslära. Publikation Nr 77/L, Göteborg 1977.
Colebrook., C..F. & White, C.M.: ExDeriments with Fluid Friction in Rough-ened Pipes. Proc. Roy. Soc. A 161, pp. 367-381, London 1937.
[lu] Coles, D..E.: The Turbulent Boundary Layer in a Compressible. Fluid. Appendix A. Rand Corporation, Report No. R-403-PR, 1962.
[15] Peklenik, J.: New Developments in Surface Characterization and Measure-merits by Means of Random Process Analysis. Proc. Inst. Mech. Engrs. 182, Pt 3K, pp. 108-126, 1967-68.
[16) Clauser, F.H.: The Turbulent Boundary Layer. Adv. in Applied Mechanics, Vol IV, pp. l-61, Academic Press, New York, 1956.
Perry, A.E. & Joubert, P.N.: Rough-wall Boundary Layers in Adverse
Press-ure Gradients. J. Fluid Mech. 17, pp.. 193-211, 1963.
Coles, D.: Measurements in the Boundary Layer on a .mooth Fiat. Plate in Supersonic Flow. 1. The Problem of the Turbulent Boundary Layer. Report No. 20-69, Jet Propulsion Laboratory. Calif. Inst. of Technology, California.
02 Pstot
'
pU/2
iLl smooth wait,_rough watt
WatI contour LnU'y/)'Fig. i Definition of the downward shift of the logarithmiô velocity distribution
-4000 -2000
Pressure distribution. Bern. eq.) 1-dim)
Experiment x1J0-6rn/s --QU0-50Is
/
fljppJg device x 685rirn)
Detail of front edge
wood rough wail
685 .u5
Fig. 2. Schematic representation of local skin-friction results, súitàble for evaluatiön
of the roughness function
F I I
-©Ij)
i©6501 1770 11270
Stort. working sectiôn
-,,,,f,ff,,,,f///,,/,2f,f,/f,/;
);,;,;/
585 1050 x=685-.
x='c50 2000 xlmmj 1735 IRouggfl
Floating elementFig. 3 Geometry of the wind tunnel waJi, coordinates, static pressure distribution alongthe smooth wall, and location of rough-wall replica and floating element
'Jo
R-Front edge 5 FLoating element
Station
=1800
j
u,
a' Ø///W///4'
SF,
FF,+p
Fig. 5 Principle 'of the floating element
30, 20 10 o
o
I I I I1.1
I 03 0h5
OE6 0.7 08 09 1 U2.44Ln.5.O o cta:
Surface station 7' 'o U08.6m/s -Uç15.9 rn/s o I.l-22.3 rn/S o UO352 rn/s U,L9.3 rn/s D Surface 3 Surface 2 Q Surface I Surface 4 - Smooth-waLL resuLts 10 100 1000 10000Fig 8 Measured roughness functions and their analytical approximations for rough surfaces no 1-4 as functions of the roughness Reynolds number Rk
9:16' . ,
Fig.6
Rough-wall replica mounted on the floating, element
t 5%
ED0
4,.
AA . A ±2% 3 4 10 U5 ¡y (m1)Fig. 7 Experimental results. on local skin friction for smooth wall (Karlsson/9/) and rough surfaces no 1-4
as functions
of the únit Reynolds ñumber U0/v
o
2 5 10 50
uk/v Fig. 9 Measured mean velocity distributions at station 7 (on 'the floating element) för different free-stream velocitiès on rough surfaôe no 3
103Cr as 3.0 2.5
lo
0.1 mm u h.iOmmF-tA
0.125 0.10 0 0075 200- Surfàce I ioo-o
--N
-100-a' - 200-io= - o -200- 400- 300- 200- 100-w o n Lfl -100- -200- -300- -400-o.ós'ó . 0.050 . .. ._ 0._oso 0.025 0.025 O -100 0 100 -200 :100. VFig. 10 Measured surface profiles on the floating element for rough surfaces no 1-4
17 Gussian Surface 2 Surface, 3 0.125 -0.100 -0.075
!
I
4
100 - -ir 0 I 2 -40. 1.0. -60, 0 40.-40,0
¿0,Fig. 11 Probability density distributions of roughness amplitude (äbové) änd slope G,elow) for rough surfaces no 1-4.
0.12 5 0100 0.0 75 0.025 200l,.) -600 -400 -2do 37 6y -30, 0 30, 0.20 010 0.05 o 30, 0.20 "'ç 0.10 0.05 -2 -30, 0 2Ç 0.20 0_15 0.10 -0_.05 --6 -4 -2 o 2 4 30, 6Ç W
¿00 600 (ITIi -200 -100 0 tOO 200 i'nm)
9:18 s 6 smooth wall o surface ñumber
Fig. 12 Normalized auto-correlatioñ functions of the roughness amplitude for rough surfaces no. i-4 lo olmi 103CF 5 6 io 10 surface nùrnber 3 50 100 500 x 1ml
Fig. 13 Computed values of a) local skin friction and b) total skin friçtion for smooth and rough surfaces as fUnctions of x (or R). U0
8.0 rn/s. vl.l873 106 m2/s
10 50 loo 500i
...lo
Fig. b 50 100 300 10R 50 100 300 lo-7.R, 2 5 Fig. a 10110
r
LFiø
Fig. c 90 80 70 60 50 40 30 20 10 o 18 17 16 15 11. 13 12 11 10 9 8 u0 1!T/SI 500 I:'lo
Fig. 14 Predictions of the percentage increase in the total skin friction on füll-scale ships due to roughness-as a function
of the ship length and with the free-stream velocity Uas parameter. The predictions were made with the roughness functions specified in Table 1 and with y = 11873 1O m2/s a)- surface no i = 31 pm b) surface no 2 = 65 pm, c) surface no 3.Oy = 183 pm. d)- surface no 4, os,, = 29 pm
920
Ptb,td r.Swedev Gote,. KiMv. 1978.24314
50 lOO 500
