Fluid Mechanic Interface

in a Francis Runner Turbine

A Case Study

Michelle de Abreu

Andritz Hydro Inepar

Araraquara – SP

PRESENTATION TOPICS

• Company Overview;

• Problem Description

• Hydraulic design on the Blade Runner Turbine

• Structural and Modal Analysis

• Methodology;

• Goals;

• Conclusion and next steps.

Andritz Hydro Overview

• Global supplier for

hydropower plants:

– Hydraulic systems

– Mechanical systems

– Services and

– Electrical systems

“From water to wire”

• Areas of Competence:

– Large new installations

– Compact hydropower

– Modernization and rehab

• A leader in world market

hydro power generation

Design

Design – Francis Turbine

Design - Runner

Geometry and Meshing

• Runner - Total Blades: 13

• 1 Blade modeled

• ASTM A 743 CA6NM

(12%Chromium 4%Nickel)

Sy = 550 MPa; Su = 755 MPa

Crown

Band

Blades

Meshing Details on Crown

Meshing Details on Band

Load Cases and Boundary Conditions

• Runaway Speed

n = 26,7 rad/s

No pressure

• Normal Operation (Hmax – Pmax)

n = 14,5 rad/s

Hydraulic Load Pressure

Cyclic Symmetry

Hydraulic Load Pressure

Radial Gap – Crown and Band

Crown – radial gap = 3,7 / 2 = 1,85 mm – máx.

3,1 / 2 = 1,55 mm – mín

Band – radial gap = 3,28 / 2 = 1,64 mm – máx.

2,68 / 2 = 1,34 mm – mín.

Crown

Band

Radial Gap - Band

Allowable radial displacement =

25% of labyrinth gap =

ux_all = 0,34mm

Radial Gap - Crown

Allowable radial displacement =

25% of labyrinth gap =

ux_all = 0,39 mm

Von Mises Stress – Normal Operation

Normal Operation (Hmax-Pmax)

• Maximum Von Mises Stress:

81,14 MPa

• Allowable Stress:

150 MPa

Von Mises Stress – Normal Operation

Maximum Von Mises

Stress: 53 MPa

All. Stress - Crown: 175 MPa

All. Stress - Band: 125 MPa

Normal Operation

(Hmax-Pmax)

Von Mises Stress - Runaway

Runaway • Maximum Von Mises Stress: 174,4 MPa

• Allowable Stress: Sm/2 = 755/2 = 377 MPa

Modal Analysis in Water

Natural frequencies and the corresponding mode

shapes (nodal diameter modes ND)

ND is a line on a structure that does not move while the rest

of the structure is vibrating.

ND= i.z2 - z0 = 2

NDmax = (z2 - 1) / 2 = 6,

the maximum number

of ND-modes.

ND<=NDmax

z2= number of runner blade = 13

z0= number of guide vane = 24

Coarse mesh without fillets

Cilinder – Element Fluid (Fluid 221)

Runner – Element Solid

Modal Analysis in Water

Excitation Frequency (fe)

fe = fn / 60 x z0 = 55,44 Hz

n =138.46 rpm;

f = 138.46 / 60 = 2.31 Hz

SF = +/- 15%

The natural frequency does

not be included between:

47.07 and 63.69 Hz.

The result ND=2 is the Mode 4

Natural Frequency = 18,8Hz

NEXT STEP

• Dynamic Analysis (harmonic)