Skip to main content
Log in

Performance predicting of 2D and 3D submerged hydrofoils using CFD and ANNs

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

In the present study, hydrodynamic performance of 2D and 3D submerged hydrofoils in terms of various geometries were simulated by computational fluid dynamic (CFD). Then, by selecting optimal artificial neural networks (ANN) hydrodynamic performance of hydrofoils are predicted. For this purpose, a finite volume method based on Navier–Stokes equation solver available in OpenFOAM, open-source CFD software, was used. After mesh size analyzing, to verify computational procedure, numerical results were compared with experimental ones which appropriate accuracy was observed. In this simulation, environmental and geometrical conditions such as, angle of attack, Reynolds number (Re), aspect ratio (AR) and taper ratio (TR) of hydrofoils are relevant on performance criteria of lift to drag ratio (LDR). To select a proper feed-forward ANNs to predict the performance of 2D and 3D hydrofoils under considered conditions based on the iterative algorithm, ANN architecture analysis was conducted. According to CFD results, larger value of AR and lower TR lead to greater LDR for 3D hydrofoils. Meanwhile, ANNs output showed that the maximum mean square error in predicting the LDR of 2D and 3D submerged hydrofoils are 0.0043 and 0.0035, respectively. In addition, based on the ANN weights and bias, two set of equations for predicting LDR of considered 2D and 3D submerged hydrofoils were proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

Abbreviations

CFD:

Computational fluid dynamics

ANNs:

Artificial neural networks

LES:

Large Eddy simulation

LDR:

Lift to drag ratio

CL:

Lift coefficient

CD:

Drag coefficient

AOA:

Angle of attack

Re :

Reynolds number

AR:

Aspect ratio

TR:

Taper ratio

MSE:

Mean square error

RMSE:

Root mean square error

MLA:

Marquardt–Levenberg algorithm

DLS:

Damped least-squares

PISO:

Pressure implicit with splitting of operators

\(c\) :

Chord of hydrofoil

U :

Fluid flow velocity

\({b_j}\) :

Bias of jth neuron

\({p_i}\) :

Output of ith neuron

r :

Number of neurons

R :

Correlation coefficient

N :

Number of evidence data

\({b_{\text{o}}}\) :

Output layer bias

\({O_i}\) :

Predicted results

\({y_{{\text{desired}}}}\) :

Number of reference data as desired values

\({\overline y _{{\text{desired}}}}\) :

Average of desired values

\(\overline {{S_{ij}}}\) :

Rate of strain tensor for filtered scale

\({y^ + }\) :

Distance to the wall in wall units

\(\tau _{ij}^{{\text{sgs}}}\) :

Sub-grid viscous stress tensor

\({k^{{\text{sgs}}}}\) :

Sub-grid scale kinetic energy

\(\mu\) :

Dynamic viscosity

\(\upsilon _{t}\) :

Turbulent kinematic viscosity

\(\bar \Delta\) :

Characteristic grid length scale

\(\rho\) :

Density

\({\omega _{ij}}\) :

Interconnection weight from ith neuron in previous layer to the jth neuron

λ:

Linear transfer function

\({\omega _{\text{L}}}\) :

Interconnection weights between last hidden layer with output layer

\({\phi _{\text{n}}}\) :

Normalized input

References

  • Armstrong JS, Collopy F (1992) Error measures for generalizing about forecasting methods: empirical comparisons. Int J Forecast 8:69–80

    Article  Google Scholar 

  • Beşikçi EB, Arslan O, Turan O, et al (2016) An artificial neural network based decision support system for energy efficient ship operations. Comput Oper Res 66: 393–401.

    Article  MATH  Google Scholar 

  • Brizzolara S, Bonfiglio L (2015) Comparative CFD investigation on the performance of a new family of super-cavitating hydrofoils. J Phys Conf Ser 656:012147.

    Article  Google Scholar 

  • Burrows CR (2000) Fluid power systems—some research issues. I Mech Eng C-J Mech 214:203–220.

    Article  Google Scholar 

  • Chiang YM, Chang LC, Chang FJ (2004) Comparison of static-feedforward and dynamic-feedback neural networks for rainfall–runoff modeling. J Hydrol 290(3):297–311

    Article  Google Scholar 

  • Choi B, Lee JH, Kim DH (2008) Solving local minima problem with large number of hidden nodes on two-layered feed-forward artificial neural networks. Neurocomputing 71(16–18):3640–3643

    Google Scholar 

  • Dahlstrom S (2000) Large Eddy simulation of the flow around a high-lift airfoil. Chalmers University of Technology, Goteborg.

    Google Scholar 

  • Demirci M, Üneş F, Aköz MS (2015) Prediction of cross-shore sandbar volumes using neural network approach. J Mar Sci Technol 20(1):171–179

    Article  Google Scholar 

  • Djavareshkian MH, Esmaeili A (2013) Neuro-fuzzy based approach for estimation of hydrofoil performance. Ocean Eng 59:1–8

    Article  Google Scholar 

  • Djavareshkian MH, Esmaeili A, Parsania A (2013) Numerical simulation of smart hydrofoil in marine system. Ocean Eng 73:16–24

    Article  Google Scholar 

  • Farzadpour F, Faraji F (2014) A genetic algorithm-based computed torque control for slider–crank mechanism in the ship’s propeller. I Mech Eng C-J Mech 228:2090–2099.

    Article  Google Scholar 

  • Garson GD (1991) Interpreting neural network connection weights. Artif Int Expert 6:47–51.

    Google Scholar 

  • Ghassemi H, Kohansal AR (2013) Wave generated by the NACA4412 hydrofoil near free surface. J App Fluid Mech 6(1):1–6

    Google Scholar 

  • Ghassemi H, Iranmeansh M, Ardeshir A (2010) Simulation of free surface wave pattern due to the moving bodies. Iran J Sci Tech Trans B Eng 34(B2): 117–134.

    Google Scholar 

  • Gosset A, DíazCasás V, Duro RJ et al (2010) Improving the analysis of hydrofoils undergoing cavitation by using artificial neural networks. Aust J Intell Inf Process Syst 12:41–45

    Google Scholar 

  • Harris CD (1981) Two-dimensional aerodynamic characteristics of the NACA 0012 airfoils in the langley 8 foot transonic pressure tunnel. NASA Technical Memorandum. Report no. 81927.

  • Herath MT and BGangadhara P (2012) Performance analysis and optimisation of bend-twist coupled composite hydrofoils using fluid-structure interaction. In: Proceedings of the 7th Australasian Congress on Applied Mechanics (ACAM 7), Adelaide, Australia, 9–12 December, pp. 827–836.

  • Issa RI (1986) Solution of the implicitly discretized fluid flow equations by operator-splitting. J Comput Phys 62:40–65

    Article  MathSciNet  MATH  Google Scholar 

  • Jacobs E and Sherman A (1937) Airfoil section characteristics as affected by variations of the Reynolds number. Annual report-national advisory committee for aeronautics, 227.

  • Kaastra I, Boyd M (1996) Designing a neural network for forecasting financial and economic time series. Neurocomputing 10(3):215–236.

    Article  Google Scholar 

  • Khataee AR and Kasiri MB (2010) Artificial neural networks modeling of contaminated water treatment process by homogeneous and heterogeneous nanocatalysis. J Mol Catal A Chem 331:86–100.

    Article  Google Scholar 

  • Khurana MS, Winarto H and Sinha AK (2008) Application of swarm approach and artificial neural networks for airfoil shape optimization. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, multidisciplinary analysis optimization conferences, Victoria, British Columbia, Canada, 10–12 September.

  • Ladson CL (1988) Effects of independent variation of mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA 0012 airfoil section. NASA TM-4071.

  • Lesieur M, Metais O (1996) New trends in large eddy simulations of turbulence. Annu Rev Fluid Mech 28(1):45–82

    Article  MathSciNet  Google Scholar 

  • Makarynskyy O, Makarynska D, Rayson M, et al (2015) Combining deterministic modelling with artificial neural networks for suspended sediment estimates. Appl Soft Comput 35: 247–256.

    Article  Google Scholar 

  • Makridakis S, Wheelwright S, Hyndman R (1998) Forecasting: methods and applications, 3rd edn. Wiley, New York

    Google Scholar 

  • McAlister KW and Takahashi RK (1991) NACA 0015 wing pressure and trailing vortex measurements. National aeronautics and space administration Moffett Field Ca Ames research center, No. NASA-A-91056.

  • Molland AF, Turnock SR (2007) Marine rudders and control surfaces: principles, data, design and applications, 1st edn. Butterworth-Heinemann, London

    Google Scholar 

  • Pope SB (2001) Turbulent flows (1st ed). Cambridge University Press, Cambridge

    Google Scholar 

  • Prechelt L (1998) Automatic early stopping using cross validation: quantifying the criteria. Neural Netw 11(4):761–767

    Article  Google Scholar 

  • Prechelt L (1999) Early stopping—but when?. In: Neural Networks: tricks of the trade. Springer, Heidelberg, pp 55–69

  • Radonjic A, Vukadinovic K (2015) Application of ensemble neural networks to prediction of towboat shaft power. J Mar Sci Technol 20(1):64–80.

    Article  Google Scholar 

  • Rediniotis OK, Wilson LN, Lagoudas DC et al (2002) Development of a shape-memory-alloy actuated biomimetic hydrofoil. J Intell Mater Syst Struct 13:35–49

    Article  Google Scholar 

  • Roohi E, Zahiri AP, Passandideh-Fard M (2013) Numerical simulation of cavitation around a two-dimensional hydrofoil using VOF method and LES turbulence model. Appl Math Modell 37:6469–6488

    Article  MathSciNet  Google Scholar 

  • Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Parallel distributed processing. MIT Press, Cambridge, pp 318–362

    Google Scholar 

  • Schumann U (1975) Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J Comput Phys 18(4):376–404

    Article  MATH  Google Scholar 

  • Tessicini F, Iaccarino GM, Fatica M et al (2002) Wall modeling for large-eddy simulation using an immersed boundary method. Annual research briefs. Stanford University Center for Turbulence Research, Stanford, pp 181–187

    Google Scholar 

  • Tessicini F, Temmerman L, Leschziner MA (2006) Approximate near-wall treatments based on zonal and hybrid RANS–LES methods for LES at high Reynolds numbers. Int J Heat Fluid Flow 27(5):789–799

    Article  Google Scholar 

  • Trenn S (2008) Multilayer perceptrons: approximation order and necessary number of hidden units. IEEE Trans Neural Netw 19 (5):836–844.

    Article  Google Scholar 

  • Veloudis I, Yang Z, McGuirk JJ (2008) LES of wall-bounded flows using a new subgrid scale model based on energy spectrum dissipation. J Appl Mech 75(2):021005

    Article  Google Scholar 

  • Xie N, Vassalos D (2007) Performance analysis of 3D hydrofoil under free surface. Ocean Eng 34:1257–1264

    Article  Google Scholar 

  • Zhang Z, Ma X, Yang Y (2003) Bounds on the number of hidden neurons in three-layer binary neural networks. Neural Netw 16(7):995–1002

    Article  Google Scholar 

  • Zhang C, Jiang J, Kamel M (2005) Intrusion detection using hierarchical neural networks. Pattern Recogn Lett 26(6):779–791.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hassan Ghassemi.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nowruzi, H., Ghassemi, H. & Ghiasi, M. Performance predicting of 2D and 3D submerged hydrofoils using CFD and ANNs. J Mar Sci Technol 22, 710–733 (2017). https://doi.org/10.1007/s00773-017-0443-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-017-0443-0

Keywords

Navigation