Properties of Pure Fluids - NIST Pure Fluids
Appendix D: SUPERFLUID HELIUM
Because of the unique superfluid transition in helium, an alternative program
is provided which calculates the properties of helium down to 0.8 K. This program
allows the calculation of the superfluid properties, including lambda line properties,
superfluid density fraction, and the speed of second and fourth sound. (For
temperatures above the lower lambda point, 2.17 K, either program can be used
to calculate the properties of helium.)
The interactive program is designed to be largely self explanatory and includes
help messages on some items. To start the NIST Thermophysical Properties of
Pure Fluids Database from the subdirectory or diskette in which it resides,
run the program NIST12HE. This program is nearly identical to that provided
in Version 3 of the NIST12 database. The directions given in the menu driven
user interface are straightforward. After the introductory banner is displayed,
the user can access a short description of program usage by entering a question
mark.
By entering "C" in the main menu, the user can choose a new set
of thermophysical properties to be calculated and displayed. The options are
given in Table D-1. To change parameters, type in the column number (1-7) and
enter the new parameter name. A question mark response to the interactive query
will result in a listing of the options. Only four characters are needed to
define a parameter; Table D-1 indicates the minimum abbreviations necessary.
If fewer than seven properties are desired, type the word "BLANK"
after entering a column number; the column specified and all columns to its
right will then be omitted from the display. Note that it is not permissible
to blank the first column. To restore columns that have been removed using "BLANK",
select C at the main menu. Each time this option is selected, a full set of
seven properties is displayed.
By entering "U", the user can choose a new set of units for the
specified thermophysical properties. Four standard sets are available: (1) SI
UNITS, (2) SI HYBRID, (3) CHEM, and (4) ENGINEER. The units for pressure, temperature,
density, enthalpy, and length associated with each of these sets are listed
in the menu; the units for other properties are determined from these quantities.
If one of these sets of units is desired, enter the corresponding number (1-4).
A fifth option allows the user to select units for each property selected for
display. After entering the selection "5", the optional units for
each property are displayed in turn. A choice of units for each property is
then selected by entering the corresponding number. (Although any thermophysical
property may be displayed in more than one column, the program does not allow
the user to use different units for the same variable; the last units option
selected will be used for each corresponding column.)
By entering "K", the user enters the interactive calculation menu
of the program. Because two variables are needed to define the state point of
a pure fluid, the program prompts the user to enter the desired independent
variables. The available choices are given in Table D-2. The list of options
will also appear if a question mark is entered in response to the "NAME
THE FIRST INPUT VARIABLE" or "NAME THE SECOND INPUT VARIABLE"
query. At these prompts, it is also possible to terminate the program (by entering
"Q") or back up one step in the interactive mode (by entering "B").
The two input parameters can be entered in either order, e.g., pressure (PRES)
and enthalpy (ENTH), or enthalpy and pressure. However, the program asks for
a single numerical value for the first parameter, but allows multiple calculations
with the second parameter. Thus, to form an isobaric table, enter the fixed
pressure as the first variable; to form an isenthalpic table, enter the fixed
enthalpy as the first variable. The interactive program allows up to 100 steps:
the program asks for an initial value, an increment, and a final value of the
second input parameter. To evaluate properties at a single point, enter zero
for the increment.
Possible input parameters include the saturation line (SAT for properties
of the coexisting vapor and liquid, SATL for the saturated liquid only, and
SATV for the saturated vapor), the melting line (MELT), and the lambda line
(LAMB, the phase boundary between the superfluid and normal fluid states). No
numerical values are requested for these parameters. If the requested pair of
parameters does not determine a thermodynamic state (for example DENS and VOLU,
or SAT and SATL) or is not supported, an error message is printed, and the program
requests a new pair of input parameters.
If the input parameters lead to a point in the single-phase region, one line
of output will be printed for each specified state point. If saturation properties
are requested, using SAT as one of the input parameters, two output lines will
be printed, first for the liquid phase properties and then for vapor phase properties.
However, if the user requests SATL or SATV, only the appropriate line is printed.
If the input parameters lead to a point within the two-phase region (corresponding
to a combination of liquid and vapor phases), three output lines are printed,
first for saturated liquid properties, then for the bulk properties, and finally
for vapor properties. Most derivative properties (heat capacities, sound speed,
etc.) and transport properties are undefined in the two-phase states, and are
printed as zero.
When an appropriate state point is entered, the program will calculate the
desired properties and display the output as well as write the information to
a file (NIST12HE.DAT). In exceptional circumstances, an error message is displayed;
these messages are self explanatory and usually relate to specified points being
out of the range of the correlation. The user may be given a warning message
if there is a convergence problem in the calculation (such as trying to find
a root of a very flat curve).
By entering "R", the user can input numerical data from a file.
The first four lines of this file are written to the screen, and the user is
asked for the column numbers (which must be one through seven) for the two named
input parameters. A fixed value of the first parameter may also be specified
(to produce data along a path which is isothermal, isobaric, etc.) at this point:
enter "K" instead of a column number, and the value of the constant
can then be entered.
The format of the data in the file is flexible. The program asks which of
the first four lines contains the first numerical input, in case labels or other
non-numeric information are contained at the head of the file. Within each line,
data can be separated by spaces, commas, or a solidus (/). Blank lines are simply
skipped, and the format need not be uniform from line to line. At the end of
the file, when alphabetic (or other non-numeric) characters are detected, or
after an error or warning message is given, the file reading is stopped, and
the program returns to the main menu.
Table D-1. Thermophysical properties available in NIST12HE
|
Thermophysical
Property |
Symbol or
Equation |
Abbreviation
n |
|
| Compressibility factor |
PV/RT |
PV/R |
| Conductivity function |
–q3/
T |
CON |
| Density |
 |
DENS |
| Dielectric constant |
|
DIEL |
| Enthalpy |
H |
ENTH |
| Entropy |
S |
ENTR |
| Gibbs energy |
G |
GIBB |
| Gorter-Mellink function |
AGM |
GORT |
| Gruneisen constant |
V( P/T)V/Cv
|
GRUN |
| Heat capacity ratio |
g=Cp/Cv |
GAMM |
| Internal energy |
U |
ENER |
| Isobaric heat capacity
|
CP |
CP |
| Isobaric T difference to l line |
T-Tl |
DT(P |
| Isochoric heat capacity |
CV |
CV |
| Isochoric T difference to l line |
T-Tl |
DT(V |
| Isothermal compressibility |
(/P)T/c |
COMP |
| Joule-Thomson coefficient |
(/T/P)H |
JT |
| Latent heat of vaporization |
L |
LATE |
| Normal fluid viscosity |
 n |
VIS |
| Prandtl number |
Cp/(M ) |
PRAN |
| Pressure |
P |
PRES |
| Quality (vapor mass fraction) |
Q |
QUAL |
| Refractive index |
N |
REFR |
| Sound speed |
W |
VSOU |
| Specific volume |
V |
VOLU |
| Speed of 2nd sound |
C2 |
V2S |
| Speed of 4th sound |
C4 |
V4S |
| Superfluid density fraction |
S/ |
RHOS |
| Surface tension |
 |
SURF |
| Temperature |
T |
TEMP |
| Thermal conductivity |
|
COND |
| Thermal diffusivity |
/
Cp |
THDI |
| Thermal expansivity |
(V/T)P/V |
EXPA |
| Viscosity (0 for superfluid) |
|
VISC |
|
