DESIGN PROJECT-1 BANKI-MICHELL TURBINE

ME 5427 By

INDU SHEKHAR KUMAR

Introduction:-

The Banki-Michell Turbine also known as the cross-flow turbine, is primarily used in locations with low head and high flow rate. Due to its low manufacturing price, it can be used in a variety micro-hydraulic applications. One important characteristic of this turbine is which distinguishes it from other turbines is that, instead of having axial or radial flow it has flow across the blades. In other words water flows through the turbine.

The construction, includes a nozzle through which water enters the turbine. Next, the water falls over the distributor. This is followed by the runner or rotor where rotating blades are placed. The water passes through the blades twice per rotation. The turbines can be visualized using figures-(i) and (ii)

Figure-(i) Figure :(ii)

Given Data:-

Effective Head (H): 2.60 m

Volumetric Flow Rate (Q): 2.45 m3/s

Efficiency of the Inlet Pipe (p): 0.95

Frictions losses at inlet distributor (1): 0.97

Frictions losses at exit of each blade (2): 0.98

Procedure:-

1.) Optimization of Velocity triangles:- Firstly, the value of absolute inlet velocity was calculated using equation (2). A random value of inlet angle of absolute flow (1) was selected and corresponding values of blade speed and relative velocity was calculated by using velocity triangles. These triangles can be seen in figure-(iii). Equations relating angles between absolute and relative velocities with radial direction was found using velocity triangles. The equations can be seen as equation (3) and equation (4). After, obtaining all required angles for four stages of the rotor, the value of inlet angle of absolute velocity was optimized to achieve maximum efficiency. The maximum efficiency condition that relates the inlet absolute velocity and blade speed can be seen in equation (1). The equation used for finding efficiency is equation (6)

Figure-(iii)

2.) Design of Runner:- The distributor was designed using procedure given in Lecture 7 Notes slide- 18. Using this procedure value width of distributer at inlet S0 was obtained. This can be seen in figure-(iv). This was in-turn used to find the runner length using equation (5). Following this the number of blades were decided upon. The criteria used to determine this was high number of blades gives low volumetric flow rate but reduced axial loads on the blades. This blade design can be seen in figure: (v).

Figure: (iv)

Figure: (v)

Figure:6 (vi)

Results:-

Values for 1 = 67.5

Values for 1 = 75.0

Conclusion:-

The following were the optimized valued without exceeding constraints.

1 = 75.0

u1= 3.346 m/s

Power= 53.772 kW

Efficiency= 0.8605

S0 = 0.49 m

D1 = 1 m

B= 34.64 m

Z= 26

= 13.85

Equations Used:-

11 = 0.5 sin (1) (1)

1 = 2 . (2)

1 cos(1) = 1 cos(1) (3a)

1 sin(1) = 1 + 1 sin(1) (3b)

4 cos(4) = 4 cos(4). (4a)

4 sin(4) = 1 4 sin(4) (4b)

= 0 1.. (5)

h = /().. (6)

References:-

Lecture notes (ME 5427) Banki-Michell Optimal Design by Computational Fluid

Dynamics Testing and Hydrodynamic Analysis

Appendix