# Surrogate-Based Optimization of a Biplane Wells Turbine

• Tapas K. Das
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 23)

## Abstract

Oscillating Water Column (OWC) is one of the most popular wave energy converters being used for the last two decades. The pneumatic energy from water waves inside the air chamber of OWC is converted into mechanical energy with the help of Wells turbine. Biplane Wells turbine has inherent advantage over the monoplane turbine in terms of starting characteristics and operating range. The main parameters affecting the performance of biplane Wells turbine are the gap between the planes and the offset angle between blades in two planes. Surrogate-based optimization represents the optimization methodologies that use surrogate modelling techniques to find out maxima or minima. Surrogate modelling techniques are very useful for design analysis that uses computationally expensive codes such as Computational Fluid Dynamics (CFD). In the present work, flow over a biplane Wells turbine is simulated using CFD and optimized using surrogate approach. Radial Basis Neural Network (RBNN) method is used to create the surrogate. Blade thickness and the offset angle defining the circumferential position of blades in two planes are considered as the two variables and the objective function is taken as efficiency of the turbine rotor. The comparison of performance between the reference blade and the optimized blade is presented in this article.

## Keywords

Wells turbine Biplane Surrogate model Radial basis function

## Nomenclature

ρ

Air density (kg/m3)

ω

c

Chord length (m)

η

Efficiency

$$\varphi$$

Flow coefficient

R

T

Torque (N-m)

CT

Torque coefficient

$$\Delta P_{0}$$

Total pressure drop (Pa)

$$\Delta P_{0}^{*}$$

Pressure drop coefficient

Q

Volume flow rate (m3/s)

ua

Inlet air velocity (m/s)

ut

Tip speed velocity (m/s)

## Abbreviation

OWC

Oscillating Water Column

RMS

Root Mean Square

SST

Shear Stress Transport

RSM

Response Surface Methodology

ANN

Artificial Neural Network

KRG

Kriging

RBNN

## References

1. 1.
Raghunathan S (1995) The wells air turbine for wave energy conversion. Prog Aerosp Sci 31:335–386.
2. 2.
Gato LM, Curran R (1996) Performance of the biplane wells turbine. Trans ASME 118:210–215Google Scholar
3. 3.
Raghunathan S, Tan CP (1983) The performance of biplane wells turbine. J Energy 7:741–742
4. 4.
Raghunathan S, Setoguchi T, Kaneko K (1989) The effect of inlet conditions on the performance of wells turbine. J Energy Res Technol 111:37.
5. 5.
Shaaban S (2012) Insight analysis of biplane wells turbine performance. Energy Convers Manag 59:50–57.
6. 6.
Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Kevin Tucker P (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41:1–28.
7. 7.
Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45:50–79.
8. 8.
Halder P, Samad A (2016) Optimal wells turbine speeds at different wave conditions. Int J Marine Energy 16:133–149.
9. 9.
Halder P, Samad A, Thevenin D (2017) Improved design of a wells turbine for higher operating range. Renew Energy 106:122–134.
10. 10.
Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Opt 23:1–13.
11. 11.
Myers RH, Montgomery DC, Anderson-cook CM (2017) Response surface methodology. Metallurgia Italiana.