<p>To assess the feasibility of implementing a slotted return guide vane with the jet flow in a compact multi-stage centrifugal compressor, this study utilised a cylindrical slotted return guide vane as the simplest shape example within a return channel with a large inner and outer diameter ratio and an inadequate mixing channel. The impact on internal flow, pressure recovery, and residual angular momentum at the device outlet was primarily examined through computational fluid dynamics, in addition to the suppression of the flow instability that may occur in an inward swirling flow. The study also delved into determining the optimal dimensionless momentum for the application of a slotted return guide vane through Bayesian optimisation, with the power ratio serving as the objective function. The findings revealed that the proposed slotted return guide vane with jet flow effectively curbs the occurrence of flow instability, resulting in an improved flow field compared with that of the conventional return guide vane under the constant dimensionless momentum condition. Additionally, the residual angular momentum at the device outlet was reduced, and the outlet static pressure coefficient was higher than that of the conventional return guide vane. Furthermore, under the dimensionless momentum condition identified through Bayesian optimisation as the minimum power ratio from device inlet to outlet, improvements were observed in the residual angular momentum and static pressure coefficient. The study findings are expected to improve the overall system performance and power ratio of multi-stage centrifugal compressors.</p>