Large Scale Optimization of Transonic Axial Compressor Rotor Blades

Abstract

I.Problem Formulation n the present work the Multipoint Approximation Method (MAM) by Toropov et al. (1993) has been applied to the shape optimization of an existing transonic compressor rotor (NASA rotor 37) as a benchmark case. Simulations were performed using the Rolls-Royce plc. PADRAM-HYDRA system Lapworth 2003, Lapworth andShahpar 2004) that includes the parameterization of the blade shape, meshing, CFD analysis, postprocessing, and objective/constraints evaluation. The parameterization approach adopted in this system is very flexible but can result in a large scale optimization problem.For this pilot study, a relatively coarse mesh has been used including around 470,000 nodes. The parameterization was done using 5 engineering blade parameters like axial movement of sections along the engine axis in mm (XCEN), circumferential movements of sections in degrees (DELT), solid body rotation of sections in degrees (SKEW), and leading/trailing edge recambering (LEM0/TEMO) in degrees. The design variables were specified using 6 control points at 0 % (hub), 20%, 40%, 60%, 80%, and 100% (tip) along the span. Thus the total number of independent design variables N was 30. B-spline interpolation was used through the control points to generate smooth design perturbations in the radial direction.The objective function is the adiabatic efficiency that has to be maximized where P and T are total mass averaged pressure and temperature, respectively. The constraints are the pressure ratio and mass flow rate that have to be within 1% of the same characteristic for the datum blade, i.e. 2.15 ± 1.0% for pressure ratio and 20.1 kg/s ± 0.5% for mass flow rate. II. Software ToolsIn this work the Rolls-Royce SOFT-PADRAM-HYDRA design system (SOPHY) is used. SOPHY (Shahpar 2004) is a fully integrated flexible aerodynamic design optimization system. The main elements of the SOPHY system are as follows:SOFT provides four state-of-the-art optimization libraries namely, local and global optimization algorithms, Design of Experiment (DoE), Statistical Variational Analysis (ANOVA) and Response Surface Methodology (RSM). SOFT also provides an integrating platform to define the automation strategy, see Figure 1.PADRAM is a multi-passage, multi-stage parametric geometry modeller and rapid meshing system. The PADRAM design space for the blades consists of global parameters such as stagger angle, camber angles at leading and trailing edges, lean and sweep at different spanwise locations and pitch (rotor and stator). The PADRAM design space has recently been extended to include an endwall profiling and fillet design capability. PADRAM uses an automatic multiblock mesh generator to create the grid consisting of O-H-C topology. The mesh generation is very fast and does not require user interaction during the optimization. The parametric design system has been extended to non-blading applications, for example nacelle design and exhaust design systems (Lapworth and Shahpar 2004

Structurally Constrained Aerodynamic Adjoint Optimisation of Highly Loaded Compressor Blades

“…In-depth analysis of previous optimisations studies conducted on this test case were documented in [2] and [3]. The authors show the wide range of methods explored in the literature, evolving from simple, single-objective, unconstrained optimisation problems with only three design parameters [4] to multi-objective [5], constrained [5][6][7], higher number of variables [7] optimisation methods.…”

“…The optimisation methods used vary with the evolution of optimisation algorithms in general, and cover both high and low fidelity analyses. This includes evolutionary algorithms [5], metamodeling approaches [6,7] or, more recently, adjointbased methods [8]. Most of the blade parametrisations were done using either engineering parameters or camber and thickness distribution [5][6][7][8], with some work being done using free-form deformation [2,9].…”

“…This includes evolutionary algorithms [5], metamodeling approaches [6,7] or, more recently, adjointbased methods [8]. Most of the blade parametrisations were done using either engineering parameters or camber and thickness distribution [5][6][7][8], with some work being done using free-form deformation [2,9]. The large variety of optimisation methods and number of optimisation parameters also results in a great variety of incurred computational costs.…”

“…From the early work in the filed it was clear that an unconstrained optimisation leads to solutions with increased efficiency but decreased rotor pressure ratios [4]. Therefore, further efforts focused on constraining the pressure ratio [6][7][8]. However, most of the constraints were purely aerodynamic, referring either to the pressure ratio or mass flow rate.…”

Mid-range metamodel assembly building based on linear regression for large scale optimization problems

“…The approach undergoes continuous development (van Keulen and Toropov 1997;Polynkin et al 2008;Shahpar et al 2008). The objective is to produce better quality approximations that are applicable to large-scale optimization problems.…”