Cordier diagram

The Cordier diagram is a diagram from the field of flow machines such as turbines , pumps , and compressors . It was named after Otto Cordier , who presented it in 1953. It shows the relationship between the running number σ (or the specific speed ) and the diameter number δ (or the specific diameter ) of single-stage turbo machines with high efficiency. The Cordier diagram is an important tool in the design of turbo machines and is also currently used continue to apply.

Basics

D_q, n_q diagram based on values from Cordier

Running number and diameter number are dimensionless key figures . The running number is calculated to

${\ displaystyle \ sigma = n \ cdot {\ frac {\ sqrt {\ dot {V}}} {(2 \ cdot Y) ^ {3/4}}} \ cdot 2 \ cdot {\ sqrt {\ pi} }}$

and the diameter number too

${\ displaystyle \ delta = D \ cdot {\ sqrt [{4}] {\ frac {2 \ cdot Y} {{\ dot {V}} ^ {2}}}} \ cdot {\ frac {\ sqrt { \ pi}} {2}}}$

The volume flow and the specific nozzle work are included in the formulas . If these two variables are assumed to be given by the conveying problem, the number of rotations depends only on the speed and the number of diameters only depends on the rotor diameter . ${\ displaystyle {\ dot {V}}}$ ${\ displaystyle Y}$ ${\ displaystyle n}$ ${\ displaystyle D}$

In his work for single-stage turbo machines of the best efficiency, Cordier calculated the running number and the diameter number at the operating point and entered them in a diagram (later referred to as the Cordier diagram). He realized that these values lie in a narrow band around a curve. ${\ displaystyle \ sigma, \ delta}$

The specific speed and the specific diameter are calculated equivalently ${\ displaystyle n_ {q}}$ ${\ displaystyle D_ {q}}$

${\ displaystyle n_ {q} = n \ cdot {\ frac {{\ dot {V}} ^ {1/2}} {H ^ {3/4}}}}$

${\ displaystyle D_ {q} = D \ cdot {\ frac {H ^ {1/4}} {{\ dot {V}} ^ {1/2}}}}$

and only differ from the running number and the diameter number by a constant in which the acceleration due to gravity is contained. H is the total head.

Applications

With a given volume flow and given specific nozzle work, the following project planning is possible with the Cordier diagram:

Determination of the optimal rotor diameter when determining the speed.
Determining the optimal speed when determining the rotor diameter.

Furthermore, it can be checked whether existing machines are optimally designed, i.e. have the highest possible efficiency.

Individual evidence

↑ ^a ^b Cordier, Otto: Similarity conditions for flow machines . In: BWK magazine . tape 5 , no. 10 , 1953, pp. 337-340 .
^ ^A ^b Fister, Werner: Fluid energy machines . Springer Verlag, Berlin 1984, ISBN 3-540-12864-6 .
↑ ^a ^b Bohl, Willi: Turbo machines 1 . Vogel Buchverlag, Würzburg 2008, ISBN 978-3-8343-3130-4 .
↑ ^a ^b Sigloch, Herbert: turbomachines . Carl Hanser Verlag, Munich 2006, ISBN 978-3-446-40288-1 .

literature

Bohl, Willi: Turbo machines 1 . Vogel Buchverlag, Würzburg 2008, ISBN 978-3-8343-3130-4 .
Daniel Wolf: The CORDIER diagram with special consideration of the axial turbo machine (PDF; 3.8 MB), diploma thesis, 2009

[cordier-1] Cordier, Otto: Similarity conditions for flow machines . In: BWK magazine . tape 5 , no. 10 , 1953, pp. 337-340 .

[fister-2] A ^b Fister, Werner: Fluid energy machines . Springer Verlag, Berlin 1984, ISBN 3-540-12864-6 .

[bohl-3] Bohl, Willi: Turbo machines 1 . Vogel Buchverlag, Würzburg 2008, ISBN 978-3-8343-3130-4 .

[sigloch-4] Sigloch, Herbert: turbomachines . Carl Hanser Verlag, Munich 2006, ISBN 978-3-446-40288-1 .