I am trying to simulate water-vapor as multiphase flow at room temperature using lattice Boltzmann method. In the selected method, we use an EoS to simulate multiphase flow. So, the flow follows the EoS in the simulation. All of the available EoSs (such as RK, vdW, C-S, P-R, ...) have been defined gases, so usually the density ratio at room temperature is overestimated. I want to know if there is any formula which defines density-temperature relation for a real substance (except gases) such as water, oil or ....
thanks
No - try getting a property database and just write a bit of code to look up the properties at each point. The NIST REFPROP database uses localized equations between measured data points and is probably the most trusted way to model water.
In air conditioning water vapour is treated as an ideal gas which obeys ideal gas laws and hence the equation of state (PV=mRT) is used specially if you are calculating the water content in a known volume of air. Where R for water vapour is taken as 4.615 kJ/kg K
For moderate accuracy requirements, the closed-form EOS's represent the liquid and the gas states (smallest and largest root for specific volume). If you want very high accuracy, you can use complex EOS's developed specifically for water like the IAPWS EOS. If you are only interested in ambient pressure, you can assume that water vapour will be an ideal gas and water will be an (almost) incompressible fluid regarding pressure, and you can tabulate the temperature dependence of density or use a thermal expansion coefficient. You can also tabulate NIST data as proposed by Susan if you need higher pressures and if you need high accuracy.
Have a look to my Ph.D. Thesis page 27 et.seq. where I cite different equations of state for water.
It may be outdated (1992) but I assume still quite valid.
Here is an equation is is commonly used for values of p/pinf not much greater than 1 (explosions and weak shock waves, etc OK ).
(p + B) / (pinf + B) = (rho / rhoinf)n
where pinf and rhoinf are the pressure and density at infinity, B is ~3000 atm, and n = 7
If you are only interested in water, you can use IAPWS 97 formulation which is one of the methods used to generate steam tables. The drawback of this method is that it can be only used for water and requires much more computation than a cubic EOS.
The problem of water is that it is a strongly associating fluid. Therefore an equation of state should take association into account such equation of state exist.
Also an equation of state is almost never universal so depending on the application you will have to use different equation of state. You may have to use a different equation of state for the density than for the enthalpy. For non-polar components the RKS or Peng-Robinson EOS are fair fits of enthalpy but you cannot use them for density prediction. You should use the BWRS or other complex EOS for density prediction. So using a consistent EOS treatment of a problem is some time impossible even for simple components (n-alkanes...).
Attached you will find recent work on water by Vincent Holten. He is a specialist on water EOS. His PhD thesis contains a review of EOS for water. You can contact him directly.
I use either Taits equation of state or the stiffened gas law for compressible water.
Usally the parameters B and n within the Tait equation are set by B = 3,01 * 10^8 Pa, n = 7.15 for water.
Kind regards,
Christian Dickopp
You need to take into account that the Taits EOS can be used only for the liquid state, so it does not represent the EOS which Ahad has asked for.
As Susan mentioned, use REFPROP from NIST. It is available as a "spreadsheet" that allows you to calculate/plot properties or available as callable FORTRAN subroutines that you can use in your code. You can also rewrite it in whatever language you want. REFPROP is the gold standard for EOS's of "real" substances. It is based on the MWBR EOS and it also included calculations for viscosity and thermal conductivity in addition to basic properties. You can order a copy from the NIST website (used to cost about $200 or so; might have gone up now).
As others coleagues said, you can use general EOS or some EOS specially developed for the water. Alternatively, as the substance is very well studied, you can look at property tables (such as NIST) as suggested by S. Krumdieck (first answer).
You may be interested to read this paper http://www.pnas.org/content/112/20/6341.full
You can find interesting information in the following papers
EQUATION OF STATE OF PURE WATER AND SEA WATER
F.H. Fisher and 0.E. Dial, Jr. 1975
Simple EoS (Tait , Tumlirz ) are fit with experimental date ...
http://www.dtic.mil/dtic/tr/fulltext/u2/a017775.pdf
Jeffrey and Austin (1999) New Analytic Equation of State for liquid water, J. Chem Phys. 110:484
You can refer to IAPS equation of state for the thermodynamical properties of water.L.Haar, J.S.Gallagher and G.S.Kell (1984).
Probably the parameters of the equation have been updated later for looking after higher precision.
IAPWS Formulation (http://www.iapws.org/relguide/IAPWS-95.html) is an extremely reliable analytical equation. Excel sheets, Fortran codes are available. The formulation is also available in many process simulation Software such DWSIM
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