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