Automated shape optimisation of a plane asymmetric diffuser using combined Computational Fluid Dynamic simulations and multi-objective Bayesian methodology

Abstract

An approach for shape optimisation of the flow through a diffuser is presented in this work. This multi-objective problem focuses on maximising the diffuser performance by simultaneously increasing the static pressure recovery across the geometry and the flow uniformity at the outflow. The hydrodynamic analysis of the geometry was conducted using the Computational Fluid Dynamics (CFD) software OpenFOAM, while a recently proposed multi-objective Bayesian approach was used for optimisation. The CFD and Bayesian methodology have been combined for fully automated operation using a Python-based framework. The proposed design parameterisation focuses on reshaping the diffuser in the expansion region. Catmull–Clark subdivision curves were employed to represent the shape of the diffuser wall; the influence of the number of control points (design points) for the curves on the optimum design was investigated. The optimal designs exhibit a reasonable performance improvement compared with the base design.

Keywords:

• Buice diffuser
• Catmull–Clark subdivision curves
• flow uniformity index
• pressure recovery
• shape optimisation
• multi-objective
• Bayesian optimisation

Acknowledgments

The CFD simulations were performed on the ISCA HPC in the Advanced Computing Facility in the University of Exeter, UK.

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

A	=	cross-sectional area (m${}^2$)
$C_p$	=	pressure recovery factor (–)
$C_{\mathrm{pw}}$	=	wall pressure coefficient (–)
$p_w$	=	wall static pressure (kg m${}^{-1}$ s${}^{-2}$)
${\mathcal{F}}^{\ast }$	=	estimated Pareto front
$\mathcal{F}$	=	optimal Pareto front
$\mathbf{l}$	=	reference vector for computing hypervolume
${\mathcal{P}}^{\ast }$	=	estimated Pareto set
$\mathcal{L}$	=	turbulent length scale (m)
$\mathcal{P}$	=	optimal Pareto set
AR	=	aspect ratio (–)
$C_{p,\mathrm{ideal}}$	=	ideal pressure recovery (–)
h	=	height of inflow section (m)
l	=	length of section (m)
p	=	static pressure (Kg m${}^{-1}$ s${}^{-2}$)
1, 2, 3	=	index for diffuser sections (inflow, expansion, and tailpipe regions)
γ	=	flow uniformity index (–)
λ	=	frictional loss coefficient for straight pipe (–)
k	=	tailpipe height (m)
$K_{\mathrm{loss}}$	=	frictional loss coefficient for expanding sections (–)
m	=	number of control points (–)
$\mathrm{out}$	=	outflow boundary
$\mathrm{ref}$	=	reference position
U	=	velocity magnitude (ms${}^{-1}$)
$u_b$	=	bulk velocity (ms${}^{-1}$)
$u_c$	=	velocity along the inflow centreline (ms${}^{-1}$)
$U_{\mathrm{ave}}$	=	average velocity magnitude (ms${}^{-1}$)
X, Y	=	nondimensional streamwise and vertical distances (–)
$y_1^{+}$	=	nondimensional wall-normal distance (–)

Notes

1 Maximising a function $f_i(\cdot )$ is equivalent to minimising $-f(\cdot )$

2 Python code for the MBO framework is available at: http://bitbucket.org/arahat/gecco-2017.

Additional information

Funding

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeter's College of Engineering, Mathematics, and Physical Sciences.