1. DENSITY OF LIQUID REFRIGERANTS
By
T SHYAMKUMAR
14TH14F
I sem, M Tech
Thermal Engineering
2. CONTENTS
Introduction
Methods of measuring density
Literature Review
ISH correlation
Rackett equation
Rackett equation by Yamada and Gunn
Spencer and Danner modification of Rackett method(RSD)
Hankinson and Thomson (HT) method(COSTALD)
Reidel method
NM Correlation
Programming
Results
Conclusion
3. INTRODUCTION
Designing refrigeration cycles require thermodynamic
properties of refrigerants, i.e., liquid density, vapour
density, enthalpy of vaporization and vapour pressure
Liquid density is needed for process simulation and
equipment design.
Equations of state (EoS) are used in commercial simulation
software for predicting phase behavior and thermodynamic
properties.But, equations of state are not accurate enough
for a wide range of applications. The popular EoSs such as
SRK and PR predict liquid density with an average absolute
error of about 8%, much higher than the correlations .
correlations have wider range of applicability and accuracy.
4. TWO SINKER DENSIMETER
Based on the
Archimedes'
buoyancy principle.
Both sinkers have
the same mass, the
same surface area,
and the same surface
material, but a
considerable
difference in
volume.
5. Continue...
This sinker support is connected to a commercial analytical
balance ( resolution 10 μg) by a thin wire via a magnetic
suspension coupling .
“apparent mass difference” Δm* = (mD* − mS*) of the
sinkers.
By means of the magnetic suspension coupling, the
suspension force is contactlessly transmitted from the
pressurized measuring cell to the balance at ambient
conditions.
ρ = (Δm* − ΔmVac) / (VS − VD),
where ΔmVac= ( mD − mS) corresponds to the very small
mass difference of the two sinkers which is accurately
determined by weighing in the evacuated measuring cell.
6. CORIOLIS FLOW METER
Based on coriolis principle.
An exciter causes tube to
oscillate constantly
Sensors are located at inlet
& outlet
Phase shift during flow is a
measure of mass flow rate.
Oscillating frequency is a
direct measure of density.
.
7. LITERATURE REVIEW
(a) ISH correlation (Iglesias et al [1])
= (2.1)
= 0.03 – (2.1.a)
= (1 - ) – 1 -
(2.1.b)
=
n=0.5 and β is the scaling exponent having a value between 0.32 and 0.34
9. Modified Rackett equation by
Yamada and Gunn
Yamada and Gunn (1973), [2] proposed
.....(Eq 2.3)
Acentric factor
=
] - 1
W represents accentricity or nonsphericity of a molecule.For
monoatomic gases w =0.
For higher hydrocarbon w increases.
10. Spencer and Danner modification of Rackett
method
By Kh.Nasrifar et al[3]
Popularly known as RSD equation
.....(Eq 2.4)
= ( )
ZRA = 0.29056- 0.8775w
11. Hankinson and Thomson (HT) method
By Hankinson et al[4]
.......(Eq 2.5)
( ) = [1- ]
= 1+a +b +c +d
a = -1.52816 ; b = 1.43907;
c = -0.81446 ; d = 0.190454 ;
e = -0.296123 ; f = 0.386914 ;
g = -0.0427258 ; h = -0.0480645 ;
is the characteristic volume
=
12. Reidel method
Reidel [3] suggested the following correlation
......(Eq 2.6)
= = 1 + 0.85 (1- + (0.53 + 0.2 )
= 1 + 0.85 (1- + (1.6916 + 0.984 )
is the slope of vapour pressure at critical temperature
13. NM Correlation
KhashayarNasrifar and Mahmood Moshfeghian proposed the following
correlation [5]
= [1+ ]
= 1+
+
+ +
d1 = 1.1688
d2 = 1.8177
d3 = -2.6581
d4 = 2.1613
δ is the characteristic parameter for each compound.
= <1
= >1
c1, c2 and c3 are vapour pressure dependent parameters
15. PROGRAMMING
Coding language:MATLAB
The program reads input data from excel sheet,
calculates saturated liquid densities and percentage
deviation from ASHRAE values for temperature ranges
specified in ASHRAE data hand book and writes it
back to another excel sheet.Average absolute
percentage deviation is also calculated.
Two plots for each refrigerant:
Density vs temperature
%error vs temperature
16.
17. ERROR ESTIMATION
Percentage deviation from ASHRAE values,
δ =(ρs –ρexp)*100 .... (Eq 7)
Average absolute percentage deviation = 1/N*Σ|δ|..(Eq8)
Where N is the number of data points .
35. CONCLUSIONS
NM correlation has been found the best the for
prediction of saturated liquid densities for R22, R32,
R134a, R152a, R600 and R12 with a maximum AAPD of
0.89878 % for R12
Equation predicted by Hankinson and Thomson.et al
is best suited for R290, R600a and R1270
Reidel’s correlation can be applied to R143a and R125
Modified Rackett equation by Yamada and Gunn and
Spencer and Danner gives fairly accurate results for
R123 and R718 respectively.
ISH correlation is best suited for R717 with AAPD of
0.555%.
36. REFERENCES
[1] Gustavo A Iglesias-Silva,Kennath.R.Hall,”A saturated liquid density
equation for refrigerants”,Fluid Phase Equilib 131(1997) 97-105
[2]The properties of Gases and Liquids, Fifth Edition, Bruce E poling, John M
Prausnitz John P O’Conell , McGraw Hill, ’Rackett equation’(145-146)
[3]Khashayar Nasrifar, Mahmood Moshfeghian, ”Evaluation of saturated
liquid density prediction methods for pure methods”, Fluid phase Equilib
158-160(1999),437-445
[4]Risdon W Hankinson, George H Thomson, AIChE Journal (vol25, no4)
(1979), 653-663
[5]Khashayar Nasrifar, Mahmood Moshfeghian, “A saturated liquid density
equation in conjunction with the Predictive-Soave–Redlich – Kwong
equation of state for pure refrigerants and LNG multi component systems”,
Fluid phase Equilib 153(1998),231-242
37. [6]Kh.Nasrifar,Sh.Ayatollahi,M.Moshfeghian,”An extended saturated liquid
density equation”,Fluid phase Equilib166 (1999),163-181
[7]Kh.Nasrifar,Sh.Ayatollahi,M.Moshfeghian,”Generalised saturated liquid
density prediction method for pure compounds and multi-component
mixtures”,Fluid phase Equilib168(2000),71-90
[8]”Refrigerants-Physical properties”, http://www.EngineeringToolBox.com
[9] “Liquid density by volume translated method-
Part1”,http://www.jmcampbell.com/tip-of-the-month/2011/03/liquid-density-
by-volume-translated-method-%e2%80%93-part-1-pure-compound/
[10]“Liquid density by volume translated method-
Part2”,http://www.jmcampbell.com/tip-of-the-month/2011/07/liquid-density-
by-volume-translated-method-%e2%80%93-part-2-recent-development/
