**Preliminary Design of Multistage Radial Turbines Based on Rotor Loss Characteristics under Variable Operating Conditions**

### **Zheming Tong 1,2,3,\*,**†**, Zhewu Cheng 1,2,**† **and Shuiguang Tong 1,2,\***


Received: 9 June 2019; Accepted: 28 June 2019; Published: 2 July 2019

**Abstract:** The loading-to-flow diagram is a widely used classical method for the preliminary design of radial turbines. This study improves this method to optimize the design of radial turbines in the early design phase under variable operating conditions. The guide vane outlet flow angle is a key factor a ffecting the o ff-design performance of the radial turbine. To optimize the o ff-design performance of radial turbines in the early design phase, we propose a hypothesis that uses the ratio of the mean velocity of the fluid relative to the rotor passage with respect to the circumferential velocity of the rotor as an indicator to indirectly and qualitatively estimate the rotor loss, as it plays a key role in the o ff-design e fficiency. Theoretical analysis of rotor loss characteristics under di fferent types of variable operating conditions shows that a smaller design value of guide vane outlet flow angle results in a better o ff-design performance in the case of a reduced mass flow. In contrast, radial turbines with a larger design value of guide vane outlet flow angle can obtain a better o ff-design performance with increased mass flow. The above findings were validated with a mean-line model method. Furthermore, this study discusses the optimization of the design value of guide vane outlet flow angle based on the matching of rotor loss characteristics with specified variable operating conditions. It provides important guidance for the design optimization of multistage radial turbines with variable operating conditions in compressed air energy storage (CAES) systems.

**Keywords:** preliminary design; optimization; rotor loss; guide vane outlet flow angle; radial turbine; CAES
