Hi all,

For different problems in gasdynamics/thermofluids, different thermodynamic inputs are most convenient for expressing and solving the problem. For example, if I have a stagnation process, in which kinetic energy goes to enthalpy, the steady flow energy equation can be written:

h1 + V2/2 = h2

If the process is isentropic:

s2 = s1

If the fluid is a pure fluid and is non-reacting, and the upstream thermodynamic state and the velocity are specified, this is readily solved with eg. REFPROP, Cantera (using PureFluid), CoolProp; state two can be defined with enthalpy-entropy inputs, and we have our stagnation state.

[Please note that I am not interested in the perfect-gas approximation (constant-gamma analytical solutions); I am interested in the general problem, and solving it with computationally-implemented equations of state.]

However, I am unclear as to whether, for a non-reacting multicomponent mixture (such as air!), enthalpy-entropy-composition inputs define a unique thermodynamic state.

The issue of non-uniqueness of thermodynamic states, for various inputs, is discussed in the documentation for REFPROP [https://www.nist.gov/system/files/documents/2018/05/23/refprop10a.pdf, p. 4]:

"There are cases where an input state point can result in two separate valid states. The most common is temperature-enthalpy inputs. Viewing a T-H diagram will help show how there can be two valid state points for a given input. For example, nitrogen at 140 K and 1000 J/mol can exist at 6.85 MPa and at 60.87 MPa. When this situation occurs, REFPROP returns the state with the higher density."

Clearly the equation of state determines which inputs will define a unique state; T-h, T-s or T-g inputs for an ideal gas defined by [h(T), s(T), g(T)] will of course not define a unique state. However, it is not clear to me how I can determine which sets of inputs will result in the definition of a unique state, and why enthalpy-entropy-composition inputs for mixtures, each component of which is specified in the manner above, are not permitted in eg. Cantera.

My question is: are there hard-and-fast rules regarding which sets of thermodynamic properties define unique thermodynamic states? Similarly, apart from the obvious non-independence of pressure and temperature for pure fluids in the saturation region, are there other sets of intensive state variables that are not independent? Can anybody point me to good resources that explain the what and why of this issue?

This question is motivated by my desire to understand why certain inputs are permitted in Cantera only for pure fluids, and not for mixtures. I have already asked a related question in the Cantera Users Google Group [https://groups.google.com/forum/embed/#!topic/cantera-users/HS5eVTkStN0] but have as yet had no reply, and hope someone on here may be able to help me. Similar issues arise when I tried enthalpy-entropy inputs in CoolProp for multicomponent mixtures; all works well for pure fluids, but not for mixtures.

Thanks in advance,

Nick Mason-Smith

Melbourne, Australia