Printing number

Surname

Printing number

{\ displaystyle {\ mathit {\ psi}}}

dimension

dimensionless

definition

{\ displaystyle \ psi = {\ frac {2 \ cdot Y} {u ^ {2}}}}

${\ displaystyle Y}$	specific nozzle work
${\ displaystyle u}$	Peripheral speed

scope of application

Turbo machines

The pressure number is a dimensionless number used to describe single-stage flow machines . In connection with the flow rate , the pressure rate is also described as the size of the power conversion of the stage. In the definitions described under slight transformations, the pressure coefficient is also referred to as the blade work parameter , work coefficient , performance figure or enthalpy figure . ${\ displaystyle \ psi}$

The pressure number relates the specific nozzle work to the square of the circumferential speed of the machine's impeller : ${\ displaystyle Y}$ ${\ displaystyle u}$

{\ displaystyle \ psi = {\ frac {Y} {{\ frac {1} {2}} \ cdot u ^ {2}}}}

In this definition, the nozzle work , neglecting friction forces, can be replaced by the mass-specific technical work and further described using Euler's main turbine equation with velocity components: ${\ displaystyle Y}$ ${\ displaystyle w_ {t}}$

{\ displaystyle \ psi = {\ frac {w_ {t}} {{\ frac {1} {2}} \ cdot u_ {2} ^ {2}}} = 2 \ cdot \ left ({\ frac {c_ {u2}} {u_ {2}}} - {\ frac {u_ {1}} {u_ {2}}} \ cdot {\ frac {c_ {u1}} {u_ {2}}} \ right)}

It should be noted that the peripheral speed is not uniformly defined. In the case of axial machines, it mostly relates ${\ displaystyle u}$

on the outside diameter (for pumps , fans , compressors ) or
to a medium diameter ( steam and gas turbines ).

When defining the circumferential speed, either the change in the static or the absolute total pressure is balanced. The balancing of the nozzle work describes a change of state along a polytropic .

In gas flows

For pressure ratios between pressure and suction side that are less than 1.30, the compressibility can often be neglected even with gas flows:

{\ displaystyle {\ frac {p_ {D}} {p_ {S}}} <1.30 \ Rightarrow \ kappa \ approx 0}

In these cases, the pressure number can be calculated with the change in the total pressure of the flow machine and the mean density of the working medium: ${\ displaystyle \ Delta p_ {ges}}$ ${\ displaystyle \ rho _ {m}}$

{\ displaystyle \ psi \ approx {\ frac {\ Delta p_ {ges}} {{\ frac {1} {2}} \ cdot \ rho _ {m} \ cdot u ^ {2}}}}

Typical values

In modern axial compressors for aircraft :: 0.30 to 0.35 ${\ displaystyle \ psi \ approx}$
for axial compressors in stationary gas turbines: 0.60 to 0.65
In turbines: negative and less than -1.30.

literature

Willi Bohl: Turbo machines 1, structure and mode of operation . Vogel, Würzburg 1998, ISBN 3802317378 .
Walter Bitterlich, Sabine Ausmeier, Ulrich Lohmann: Gas turbines and gas turbine systems, presentation and calculation . Teubner, Stuttgart / Leipzig / Wiesbaden 2002, ISBN 3-519-00384-8
Walter Traupel: Thermal Turbomachines, 3rd, revised and expanded edition . Springer-Verlag, Berlin / Heidelberg / New York 1977, ISBN 3-540-07939-4
Willy JG Bräunling: Aircraft engines, 3rd, completely revised and expanded edition . Springer-Verlag, Berlin / Heidelberg 2009, ISBN 978-3-540-76368-0
Reinhard Mönig, Ulrich Waltke in: Stationary gas turbines, 2nd, revised edition - Chapter 7 Compressors . Christof Lechner, Jörg Seume (eds.), Springer-Verlag, Heidelberg / Dordrecht / London / New York 2010, ISBN 978-3-540-92787-7