Additional resistance due to boundary layer separation in model testing

ADDITIONAL RESISTANCE DUE TO BOUNDARY LAYER SEPARATION IN MODEL TESTING

by L. S. Aztjushkov Translated by Michail Aleksandrov and Geoffrey Gardner

The Department

of Naval Architecture and Marine Engineering

The University of Michigan College Of Enineering

Contemporary methods for calculating the results bf model tests are based on the assumption that there is no boundary layer separation for all scales of models. But,

tests carried out recently, ReferenCeS[l] and [21 proved that in some cases, separation exists and must be taken into account. The additional resistance due to this can approach 10 - 20% of the total model resistance. In

Reference [3], a method was presented to account for this additional resistance under conditions of infinite flow.

When moving in restricted waters the distribution of ship hull pressure varies primarily due to different excited water velocities. These velocities and their distribution

lead to ear.lier boundary layer separation. This paper deals with the influence of the mentioned separation for

the models moving in restricted waterson the model resis-tance.

Because of the complex nature of this problem, we accept the assumption that the influence of waves on the layer separation is negligible. Thus, we can replace the model moving in a channel by the model and its reflection moving in a tunnel. l½nother assumption is that we can replace the actual model by an ellipsoid of revolution, and the tunnel by a round pipe. The pressure distribution on the surface of an ellipsoid in an ideal liquid was

ob-tained in Reference [4]. Using this reference the velocity distribution for ellipsoids with L/B ratio = 3.5, 5 and 7 were calculated for different area ratiOs (ratio of model area to pipe area). The values Of excited velocities ex-pressed in terms of flow velocity and pressure coefficient are given in figures 1 and 2.

To determine the position of boundary layer separation, the method described in Reference [5] was used.

The condition of flow without separation can be expressed

as:

2.0 "5 1,0 0,5

Figure 1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,1 0.9

Figure 2

P I

,0z

I 2 S 4 5 6 7

1.

lIIiui

01 0.2 0.3 0.4 0.5 0.6 01 0R Oq 4L

where x - the coordinate of the section under consideration. U - the flow velocity at the outer edge of the

boun-dary layer.

U' (x) - velocity derivative

Re

-

local Reynold's number

Replacing the local Reynold's number by the general

Re and transferring to the relative velocities and coordinates we have i TT -0,8 'lx -Z

r U1,2

E

0,015, where

UL

-

U R_eL = ; = 00 - Flow velocity L - model length

It is convenient to calculate the criterion of separa-tion, without referring the Reynold's number

!',&_ y0.8

U1,2

and to determine the position of separation for a given Re graphically as the absissa of the intersection between (3) and the line 0.015 Re). An example of this solution is

given in figure 3, for Re = 1 x

i05, 1 x 106, 1

x

1 x 108,

lx i09.

We can see the dependence of this position on Reynold's number and the area ratio. The separation point when m = 0 corresponds to the infinite fluid. On Figure 4

the position of the separatiOn point is given for an ellipsoid with Re = 1 x Reference [3].

o.g Xsep I., 40 0,Q 0,8 f L: & Figure 4

On the same drawing, point A corresponds to an ellipsoid with L/B = 4 which was tested in a Swedish wind tunnel with Re = 1.28 x lOp, Reference [6] 3 - _U'2 A - Re=f109

I/u

=08b

44

4lI1JJIl.

4Wi1II

C f10

-

A__JII1i

-dIr

VIII

106 . _____ilm__ Re = I f0 4#

-i

_{ref 17}

2. #'e

[57

,re/[J

I I I I 0,5 06 0.7 0,9 Figure 3 2 5 6 7 8 9 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2

We can see the similarity of results. The lower curve was obtained using Reference [51. This method predicts

earlier separation than was actually obtained, with approxi-mately 4% difference. This figure may be used to obtain the correction coefficient, but we must assume that this correction is constant for any given Reynold's number. On

figure 3 the corrected value of criterion 3 is shown as a dashed line. Figure 5 gives the dependence of the separation point on Re, and L/B, accounting for this correction.

Assum-ing the described method can be applied to restricted flows, the corresponding charge was introduced for flows in the

pipes. The corrected position of separation for an ellipsoid with L/B = 7, (in a pipe) is given in figure 6.

L

0,9

0.8

Figure 6

We ca.n detect a very strong dependence of the point of separation on the area ratio and ReP. When the area ratio increases, the point of separation moves gradually upstream and then at a certain point the rate of movement increases rapidly as shown in figure 6. For restricted flow, the in-fluence of Re is much stronger. This can be understood by studying figure 2. For increased area ratio the minimum

part of the curve becomes less shallow and the kinetic energy of the flow becomes insufficient to overcome the counter

pressure. This leads to earlier flow separation. The lessening of Re produces a decrease in kinetic energy as well.

The critical values of area ratio which are. marked by arrows on figure 6 are given on figure 7 for all three ellip-soids, as a function of Re.

20 50 40 30 go 0

L:Br7

5

3,5

/

4 6 7 Figure 7

To account for additional resistance caused by boundary layer, separation we may use Reference [3]. It was found that the ratio of the additional resistance to the functional

resistance of an equivalent plate is directly proportional to the relative sectional area at the point of separation.

LK5=

(4)

where, w - area of an ellipsoid section at the point of -flow separation.

- wetted surface.

From the experiment, Reference [6], the numerical coefficient in formula 4 is equal to 14.1, which can be accepted as

sufficient. For the calculation of additional resistance caused by separation, let's introduce the form coefficient:

7O7'..

FPL

(5)

If we accept n according to experimental results with ellipsoids, then the additional resistance expressed in terms of resistance without flow separation is

4 /(

-

p

(6)

The values of n can be given according to References [3] and [7].

The ratios were calculated using figure 5 and the addit-ional resistance due to flow separation for the considered ellipsoids was found ccording to formula 6. The results are presented in figure 8. For Re = 1

x 106

the additional resistance is approximately equal to 8,, 14 and 25% of the total resistance without separation for LIE ratios

corres-pondingly equal to 7.0, 5.0 and 3.5. _{Similarly, the} addit-ional resistance was calculated for ellipsoids moving in

pipes. Farther from the value was

subtracted to obtain the additional resistance caused by pipe interaction. The results are presented in figures 9,

10 and 11. This analysis indicates the substantial influence of the area ratios on flow separation resistance. For example, the additional resistance for = 30%, Re = 1

x 106

and L/B =

5 is equal to 40%. _{The. considerable scale effect due to} boundary flow separation was also detected. In some cases the flow separation might take place for actual ships moving in narrow and shallow canals. It can be seen also that the increase of L/B ratio leads to a smaller additional resis-tance.

The point of sharp resistance increase coincides with the values of area ratio when the point of separation is moving

L:B

50

70

I00 .50 7

Figure 8

t,Re

Figure 9

0 40 30 20 10 4

50 L: B7 4

___

V

(:I0?A

V

i:io

I P 7₀₀ , '0 IC 20 30 40 50 60 70 Figure 10

The graphs mentioned previously may be used to account for the additional resistance in model tests. However, because the separation resistancet is subjected to scale effect an additional resistance must be subtracted from the total resistance. When rescaling the resistance to actual ships, we have to add the part of the resistance caused by separation, according to the corresponding Re. We have to mention that the offered tech-nique is conditional, and does not account fOr several factors such as interaction of the counterf low with the boundary layer. But, the method is acceptable as a first approximation.

100 50

Ie110

' 7Ep %

10 20 30

Figure 11

50 60

FERENCES

Townsin, R. L., "Boundary Layer Separation from Ship Models," Trans. RINA, VOl. _{107, 1965}

Clemënts, R. E., "The Control of Flow Separation at the Stern of a Ship Model _{Using Vertex Generators,"} Trans. RINA, Vol. 107, 1965

Mechailov1 V. 1g., "Turbulent _{Boundary Layer Separation} and its InfluenOe on Viscous Resistance," S.T.S.S. Proceedings, 1963

Artushkov, L. S., "The Calculation _{of Excited Velocities} for Axisynunetrical Flow in Round Pipes," Krilov's

Reaings, April 1966

[5,] Bam-Zelikovich, G. N., !'Boundary Layer Separation

Cal-culation," Sjiipbuilding, No. _{8, 1960}

[61 _{Petersohn1 E.G.M., "The Pressure Drag due. to Turbulent}

Separation on Bodies of Revolution _{with Varying}

Boundary Layer Thickness," Flygteknisko Forsoksanstalten, Meddeland 75, Stockholm, 1957

[7] Droblenkov, V. F., !'The Form Resistance _{of Ships,"}

Shipbuilding, No. 8, 1960

[81 _{Kempf, G., "Wirbelablosung bei volligen schiffsforinen,"}