Fluids¶

Calculation of thermodynamic properties for working fluids.

Turbomachinery design and analysis requires knowledge of thermodynamic properties of the working fluid. This module contains classes that abstract real or perfect gases, so that calculations of thermodynamic properties can be performed using a common interface independent of the fluid equation of state.

The general pattern of usage of these classes is as follows. First initialise a state using turbigen.fluid.PerfectState.from_properties() or turbigen.fluid.RealState.from_fluid_name() constructors. If the type of working fluid is not known at runtime, the copy() method of an existing state can be used. Second, specify a pair of two thermodynamic properties using, for example, turbigen.fluid.PerfectState.set_P_T(). Finally, other derived properties can be read off as attributes of the state, such as turbigen.fluid.PerfectState.rho. The examples below illustrate functionality of the classes; practical usages are found in the turbigen.meanline functions.

Example code¶

Create a state for real Air, print some properties, then if this is a stagnation state, find static pressure given a Mach number:

>>> import turbigen.fluid
>>> So1 = turbigen.fluid.RealState.from_fluid_name('Air')
>>> So1.set_P_T(16e5, 1600.)
RealState(Air, P=16.000 bar, T=1600.0 K)
>>> print('cp = %.1f kJ/kg' % So1.cp)
cp = 1220.9 kJ/kg
>>> print('ga = %.3f' % So1.gamma)
ga = 1.308
>>> S1 = So1.to_static(Ma=0.6)
>>> print('P1 = %.3e' % S1.P)
P1 = 1.271e+06

Initialise states for both perfect air and steam, then calculate the work required for an isentropic compression:

>>> S_water = turbigen.fluid.RealState.from_fluid_name('water')
>>> S_air = turbigen.fluid.PerfectState.from_properties(
...     cp=1005.,gamma=1.4, mu=1.8e-4
... )
>>> PR = 3.
>>> for S1 in (S_water, S_air):
...     S1.set_P_T(1e5, 300.)
...     S2 = S1.copy().set_P_s(S1.P * PR, S1.s)
...     print(f'wx12 = {(S2.h-S1.h)/1e3:.2f} kJ/kg')
RealState(water, P=1.000 bar, T=300.0 K)
wx12 = 0.20 kJ/kg
PerfectState(P=1.000 bar, T=300.0 K)
wx12 = 111.17 kJ/kg

Array states are also supported, by passing a shape tuple on initialisation. Broadcasting input values, and read-only iterating and slicing work:

>>> import turbigen.fluid
>>> S = turbigen.fluid.RealState.from_fluid_name('water', shape=(3,))
>>> S.set_P_T(1e5, [400., 500., 800])
RealState(water, P=[1. 1. 1.] bar, T=[400. 500. 800.] K)
>>> print(S.rho)
[0.54760542 0.43514008 0.27102399]
>>> for Si in S[1:]:
...     print(Si)
RealState(water, P=1.000 bar, T=500.0 K)
RealState(water, P=1.000 bar, T=800.0 K)

Property attributes¶

The state classes expose the following thermodynamic and fluid properties as attributes:

Attribute	Property	Units
a	Acoustic Speed	m/s
cp	Specific heat capacity at constant pressure	J/kg/K
cv	Specific heat capacity at constant volume	J/kg/K
gamma	Ratio of specific heats
h	Specific enthalpy	J/kg
mu	Dynamic viscosity	kg/m/s
P	Pressure	Pa
Pr	Prandtl number
rgas	Specific gas constant	J/kg/K
rho	Mass density	kg/m^3
s	Specific entropy	J/kg/K
T	Temperature	K
u	Specific internal energy	J/kg

Setting methods¶

The state classes expose the following methods to specify the thermodynamic state, each taking two properties as arguments:

Method	Properties specified
set_P_T(P,T)	Pressure, temperature
set_P_s(P,s)	Pressure, entropy
set_h_s(h,s)	Enthalpy, entropy
set_T_s(T,s)	Temperature, entropy
set_P_h(P,h)	Enthalpy, entropy
set_rho_u(rho,u)	Density, internal energy
set_rho_s(rho,s)	Density, entropy

Static/stagnation methods¶

Consider the problem of converting between static and stagnation conditions at a given Mach number \(\Ma=V/a\). If static conditions are known, it is straightforward to use Mach number and acoustic speed to evaluate velocity and hence enthalpy of the stagnation state; an ideal stagnation is an isentropic process, so static and stagnation states have the same entropy. The reverse problem, where static conditions must be found for known stagnation conditions, in general requires iteration because acoustic speed is unknown a-priori.

The state classes have two methods to streamline these conversions:

to_stagnation(Ma) returns a State object for stagnation conditions

to_static(Ma) returns a State object for static conditions

Constructor methods¶

class PerfectState(shape=(), order='C', typ=<class 'numpy.float64'>)[source]¶

Thermodynamic properties from perfect gas equations of state.

classmethod from_properties(cp, gamma, mu, shape=(), Pr=0.72)[source]¶

Create a state for a perfect gas with specified properties.

Parameters:

cp (float) – Specific heat capacity at constant pressure [J/kg/K]
gamma (float) – Ratio of specific heats [–].
mu (float) – Kinematic viscosity [kg/m/s].
shape (tuple) – Specify a tuple to allocate an array of states; defaults to scalar.
Pr (float) – Prandtl number [–], default to room-temperature air.

class RealState(shape=(), order='C', typ=<class 'numpy.float64'>)[source]¶

Thermodynamic properties for a real fluid using table lookups.

classmethod from_fluid_name(fluid_name, shape=())[source]¶

Create a state for a particular real working fluid.