Multi-objective optimisation of K-shape notch multi-way spool valve using CFD analysis, discharge area parameter model, and NSGA-II algorithm

Multi-way spool valves (MWSVs) with K-shape notches (KSNs) provide advantages such as improvement of the actuator speed control, micro-action, and response performance. However, the pressure drop (PD) associated with the energy consumption is larger of MWSVs under the high-pressure and large-flow condition. Meanwhile, extremely complex flow coefficient and multi-parameter, highly coupled KSNs are the chief factors restricting the flow-pressure characteristics exploration and optimisation design of MWSVs. To address these problems, complete numerical research and experiment are performed in this study, especially concerning the method of MWSV flow-pressure characteristics modelling, and surrogated model-based optimal design of KSN structures. First, the relationships between KSN structure parameters and flow-pressure properties of MWSV are modelled on the innovative discharge area parameter model (DAPM) and response surface methodology (RSM) (RSM-DPAM) using the CFD dataset. Second, to reduce the PD combining the flow control performance, surrogate model-based optimisation design is addressed. During optimisation, six KSN structure parameters are chosen as design variables, PD and flow area relative deviation (FARD) are selected as objective functions, and the RSM is employed as the projected model. Depended on the created surrogate model, the non-dominated sorting genetic algorithm (NSGA-II) is established to search for the optimal KSN structure. To certify the performance of the optimisation, flow field characteristics are analysed. The results demonstrate that the proposed RSM-DAPM-RSM model achieves reliable prediction for PD and FARD with a great correlation coefficient (0.9757 and 0.9946). The average PD reduces as much as 7.23% while the FARD is only 1.28%. Moreover, the region of low-pressure, high-velocity, and high-turbulent kinetic energy in the flow field are reduced. The proposed framework enhances the performance in KSN spool optimisation and could be applied to other kinds of notches.Abbreviations: BOI: Body of influence; BSV: Bucket spool valve; CFD: Computational fluid dynamics; CM: Construction machinery; DAPM: Discharge area parameter model; FARD: Flow area relative deviation; FCC: Flow control characteristic; GSA: Global sensitivity analysis; KSN: K-shape notch; MHAs: Meta-heuristic algorithms; MODE: Multi-objective differential evolution; MOGA: Multi-objective genetic algorithm; MOO: Multi-objective optimisation; MOPSO: Multi-objective particle swarm optimisation; MWSV: Multi-way spool valve; NRMS: Non-road mobile source; NSGA-II: Non-dominated sorting genetic algorithm; OLHD: Optimal Latin hypercube design; PD: Pressure drop; PDCs: Pressure drop characteristics; RSM: Response surface methodology; SA: Sensitivity analysis; TKE: Turbulent kinetic energy; TOPSIS: Technique for order preference by similarity to ideal solution; VFR: Volume flow rate