*2.3. Parameter Nondimensionalization*

In this paper, the Reynolds number and the dimensionless methods of the results are defined as follows:

$$\text{Re} = \frac{2\pi m R D\_2}{\nu} \tag{1}$$

$$K\_v = \frac{V}{\sqrt{2gH}}\tag{2}$$

$$C\_p = \frac{\left(p - p\_{ref}\right)}{\rho \text{g}H} \tag{3}$$

$$C\_m = \frac{M}{0.5\rho V\_{ref}^2 A\_{ref} L\_{ref}} \tag{4}$$

Here, *Re* is the Reynolds number, *Kv* is the velocity coefficient, *Cp* is the pressure coefficient, and *Cm* is the moment coefficient (a positive moment direction was defined as the closing direction of the guide vane). In addition, the rated rotational speed *n* = 500 rpm, outlet radius of the runner R = 1.0225 m, outlet diameter of the runner *D2* = 2.045 m, water density (20 ◦C) *<sup>ρ</sup>* = 998.2 kg/m3, water viscosity (20 ◦C) *<sup>μ</sup> <sup>=</sup>* 1.003 × <sup>10</sup>−<sup>3</sup> Pa.s, head of the pump turbine H = 610 m, reference pressure *Pref* = 0, reference velocity *Vref* = 1 m/s, reference area *Aref* =1m2, and reference length *Lref* = 1 m; in this paper, *Re* = 6.55 × <sup>10</sup>6.
