Steam properties.docx

1、Steam properties30/10/2014Steam and silencersSummary2 methods can be used to determine the parameters of the sonic neck: A graphical method with EXCEL from the steam tables (saturated steam) by using the ratio x which is the ratio of the mass of the gaseous phase divided by the mass of the mixture.

2、A method using relationships similar to those of perfect gases, with an isentropic coefficient k instead of .They give the same results as the Bertin calculation of a typical case.Then, concerning the velocity of the jet downstream infinite (where the pressure is the atmospheric pressure): We have t

3、o consider that it is an adiabatic expansion.One can find very detailed steam tables on the following site:site http:/webbook.nist.gov/chemistry/fluid.Table des matires1 Goal 32 Steam table 33 Case of study 43.1 Personal interpretation 54 Steam 54.1 Enthalpy diagrams 54.2 Isentropic curves 64.3 Rela

4、tionship between pressure and density 74.4 Isentropic expansion relationships 84.4.1 Zeuner relationship 84.4.2 Euler equation 84.4.3 Sound speed definition 84.4.4 Continuity 94.4.5 Additional laws 95 Back to the case study 105.1 Using isentropic relationships 105.2 Current Bertin calculation 115.3

5、Downstream 121 GoalExplain the thermodynamical behaviour used to compute and design the Bertin silencers.2 Steam tableWeb site where one can download very accurate data:http:/webbook.nist.gov/chemistry/fluid/http:/webbook.nist.gov/cgi/fluid.cgi?TLow=100&THigh=300&TInc=1&Applet=on&Digits=5&ID=C773218

6、5&Action=Load&Type=SatP&TUnit=C&PUnit=MPa&DUnit=kg%2Fm3&HUnit=kcal%2Fmol&WUnit=m%2Fs&VisUnit=uPa*s&STUnit=N%2Fm&RefState=DEF3 Case of studyThe important parameters for the silencer design are: The total section necessary for the flow rate at the required pressure (sonic neck) The jet speed at the do

7、wnstream infinite condition which is used to calculate the acoustic power for a free jet.We choose a numerical application for which we have the results of calculation: NI Steam Dump Silencers - Dumping Module and Acoustics Dimensioning - Rf. : 05483-005-DC002-A Pages 5 et 6, it is written : 3.1 Per

8、sonal interpretationAs the valve behaviour is unknown, we just consider the upstream conditions (3) of the valve Then we admit that the expansion is adiabatic (isentropic) for 2 reasons: As the steam velocity at the neck will be high (sound speed) we admit that there is no heat exchange with environ

9、ment; We have simple relationships in this case.Then we manage to have a sonic flow at the neck.Then, we admit that at the outlet, the pressure decreases to reach the atmospheric pressure in the far field. We have still an adiabatic expansion and we can calculate the steam velocity at the atmospheri

10、c pressure.4 SteamThe steam is not a perfect gas.4.1 Enthalpy diagramsWe use the enthalpy diagrams versus entropy for saturated steam because the transformation is assumed to be isentropic (adiabatic).Above: Enthalpy for various x coefficients.The curve x = 1 is the saturated steam curve.On this gra

11、ph: The initial enthalpy is 2765 kJ/kg. Then we have an isentropic expansion up to h1. The titre x is 0,9. It means that the corresponding steam mixture contains 90% of gas (in mass).4.2 Isentropic curvesThey are easy to build when the enthalpy decreases because we can use the titre x.For the entrop

12、y, we have:Where is the entropy of the liquid phase and the entropy of the gaseous phase.It is the same with enthalpy and volume (in m3/kg).We can easily compute the x coefficient corresponding to the entropy where x = 1 which is the entropy for saturated steam. For x = 1 we have:Therefore for each

13、line of the table we can compute :Then we compute for each line :The pressure and temperature do not change when x changes.Nota Bene : x cannot exceed 1.4.3 Relationship between pressure and densityThanks to the steam table, we have now on an isentropic curve the values of the density and pressure o

14、f the mixture. We can see that:Hereafter are some isentropic coefficients for some values of the entropy:S (kJ/kg/K)k6,98941,13766,0141,12135,77391,10935,50261,09095,29151,07334.4 Isentropic expansion relationshipsIn the following equations we never assume that steam is a perfect gas.4.4.1 Zeuner re

15、lationshipONLY if the transformation is adiabatic (isentropic):The enthalpy is h and u is the fluid velocity.Between the initial state and any current point:We derive this relationship:In fact, it is the thermo dynamical equation in the particular case of an adiabatic transformation.4.4.2 Euler equa

16、tionWithout external forces work:Using Zeuner equation, we have also:4.4.3 Sound speed definitionThe sound speed is given by the partial derivative of pressure versus density in isentropic conditions:4.4.4 ContinuityIt is the conservation of the mass, and thus of the mass flow rate :Where A is the s

17、ection.Therefore:4.4.5 Additional lawsWe can obtain additional laws which are very similar to those for perfect gases.Using:Where k depends upon the entropy (but is constant for a given entropy) we obtain after boring calculations the following relationships: When the downstream velocity is neglecte

18、d:Mass flow rate for a subsonic flow :Critical pressure for a sonic flow rate:Velocity at the neck (sound velocity):Mass flow rate for a sonic flow:5 Back to the case studyInlet (i)Dumping Module (3)Sonic neck (c)Outlet (o)Pi=7.6 MPa absTi=292CHi=2765 kJ/kgP3=4.56 MPa absT3=258CTcPo=0.1 MPa absTo=14

19、5CHo=Hi=2765 kJ/kgNota: V3 is about 80 m/s. The condition (V3)/2 Hi is verified but must be checked for every case.Upstream we have:Pi=7.6 MPa absTi=292CHi=2765 kJ/kg5.1 Using isentropic relationships Neck section:The equation Gives:With:k =1,1213cte1=0,61543621cte2=1,05718192P0 =4,56MpaP0 =4560000P

20、arho_0 =23,013kg/m3For:Qm=90kg/sWe find:A =1,3884E-02m2 Critical pressure (at the sonic neck):Pc/P0 =0,580P0/Pc=1,723Pc =2,646Mpa Sound speed:We find:c2=2,095E+05c =457,69m/s5.2 Current Bertin calculationIt gives the same result.5.3 DownstreamWe use the relationship :At the atmospheric pressure: k =1,1213P0 =4,56MpaP0 =4560000Parho_0 =23,013kg/m3Uj =1113,56138m/s