Muhammad Luqman Hakim, Bagus Nugroho, I Ketut Suastika, I Ketut Aria Pria Utama

Corresponding email: kutama@na.its.ac.id

Corresponding email: kutama@na.its.ac.id

**Published at : ** 06 Oct 2021

**Volume :** **IJtech**
Vol 12, No 4 (2021)

**DOI :** https://doi.org/10.14716/ijtech.v12i4.4692

Hakim, M.L., Nugroho, B., Suastika, I.K., Utama, I.K.A.P., 2021. Alternative Empirical Formula for Predicting the Frictional Drag Penalty due to Fouling on the Ship Hull using the Design of Experiments (DOE) Method.

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Muhammad Luqman Hakim | Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia |

Bagus Nugroho | Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia |

I Ketut Suastika | Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia |

I Ketut Aria Pria Utama | Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia |

Abstract

Biofouling is known as one of
the main problems in the maritime sector because it can increase the surface
roughness of the ship’s hull, which will increase the hull’s frictional
resistance and consequently, the ship’s
fuel consumption and emissions. It is thus important to reduce the impact of
biofouling by predicting the value of *R*^{2}

Added frictional resistance; Biofouling; Design of experiments; Empirical formula; Ship resistance

Introduction

The
impact of fouling or biofouling on ship performance is important (Molland et al., 2014). Biofouling makes the hull’s surface rough, and hence, increases its
frictional resistance (_{2} emissions and global warming. Moreover, biofouling
mediates the distribution of invasive species that can damage the water
ecosystem structure (Ulman et al., 2019). To prevent these unwanted problems due to biofouling, a more efficient
hull may be designed (Sulistyawati and Suranto, 2020) or a more efficient propeller (Abar and Utama, 2019), or a
device may be installed (Suastika
et al., 2017), but the
easiest solution is to predict the impact of biofouling.

When
the fluid passes through the rough surface, the turbulence boundary layer
structure will be shifted downward. Mathematically, the value of the downward
shift can be estimated using what is called a *roughness function* [ *k*^{+}

Each
of the existing empirical methods is challenging to use. While the similarity
law scaling boundary layer method of Granville (1958, 1987) yields accurate results
because it can accommodate all types of roughness by entering the

Therefore,
this paper proposes an alternative formula for predicting the value of
that is easy to use and flexible because it
can accommodate several types of . This
formula was established with the help of the Design of Experiments (DOE)
method, which is a branch of modern statistics. The DOE is known to be useful
for modeling with small amounts of data and even with many parameters (factors)
(Lye, 2002). The type of DOE used in this study was the two-level factorial design
with four factors, followed by factor code translations using the nonlinear
regression and optimization method. To our knowledge, factor code translations
are rarely used. Some statistical software that we often encounter also do not
do factor code translations but stop at the result of a formula whose input
factor is still a code (-1 or +1), which is not the actual value of the factor.
Islam and Lye (2009) predicted the value of the hydrodynamic performance of the propeller
without translating the factor code to the actual value, so their resulting
formula became difficult to use. Therefore, in this study, we developed a
different formula for predicting the impact of biofouling. We tested the result
of the formula against the result of the similarity law scaling method of Granville (1958), which was used with iterative
calculations. The error rate was calculated from all the error results of 1,000
random calculations.

Conclusion

This paper described the process of establishing an alternative formula
for the prediction of the increased frictional resistance (*k*. Then, the formula was created
while still inputting the code of the factor (Equation 9), after which the
codes were translated into functions (Equations 10–13) that represented the
actual value of each factor. The functions were substituted in Equation 9 to
come up with the final alternative formula in Equation 14.

The alternative formula was validated by comparing its calculation
result with that of the Granville method and computing the error. The results
were quite good, with values of *R ^{2}*

We should be grateful for the DOE, followed by the translation of
factors, for allowing the creation of a formula that can calculate a response
with good accuracy using minimal initial data. The initial data were generally
obtained from measurements in the field, laboratory tests, or numerical
simulations, all of which required resources. The resulting formula was also
quite easy to use.

Using this alternative formula, predicting the
increased frictional resistance of ships due to fouling will be easier, faster,
and cheaper. The formula’s error rate, which the author considers still quite
good, makes the formula suitable as an initial tool for determining how much
impact fouling has on ship performance. In addition, this formula has
considerable flexibility in the type of roughness function it can be applied to
because of its roughness constant variable *C _{s}*

Acknowledgement

This
research project was supported by the Ministry of Research, Technology, and
National Innovation and Research Agency (Kemenristek – BRIN) of the Republic of
Indonesia under Master to Doctorate Program for Excellent Graduate (PMDSU)
scholarship program batch III (Contract No. 1277/PKS/ITS/2020).

Supplementary Material

Filename | Description |
---|---|

R1-ME-4692-20210609234243.pdf | Revised Supplementary File -PDF format |

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