SCIENTIFIC SOFTWARE TOOL FOR CALCULATION OF STATIC HEAT
LEAK AND MATERIALS SPECIFIC HEAT FOR CRYOGENIC
APPLICATIONS
D.Sonara, V. Tanna, S. Pradhan Institute For Plasma Research, Gandhinagar, India
Abstract
The scientific software tool 'Qdot' is being developed to
calculate the static heat leaks in cryogenic system. 'Qdot'
readily calculate conduction and radiation heat leak for
cryogenic applications. This software tool uses NIST
published cryogenic material property database along
with well-known formulae for heat leak computation and
specific heat calculation. In this software, 49 different
materials property database are embedded in the
developed program. Application is GUI based, user
friendly and all calculations are done on the fly and
instantaneously. In this paper, details of calculation flow
chart, algorithms and software usage will be discussed.
INTRODUCTION
The design phase of cryogenic system requires
intensive calculation of various parameter of the
envisaged system. The designer has to first look for
thermodynamic property of selected material from
reference books or online. In this software tool “Qdot” we
have tried to embed design formulas along with required
constants and thermodynamic property of various
cryogenic materials in single platform. This calculation
formulas and material property data integration into
software makes it easy to compute heat leaks of the
system and specific heat of various cryogenic materials.
OVERVIEW OF “Qdot”
The “Qdot” program code and Graphical User Interface
(GUI) is developed using Labwindows C for Virtual
Instrument (CVI) Integrated Development Environment
(IDE) for windows operating system. Figure 1 show
overall logical integration of Qdot application tool.
Application combines the low temperature physics
formulas, NIST (National Institute and Standard
Technology) material property data, programming code,
computation algorithms and user input. “Qdot” provides
conduction heat leak, Thermal radiation heat leak and
specific heat calculation. Application is designed with
different menus for each calculation. It comprises three
different user interface screen corresponding to mode of
calculation. The output values are calculated on the fly.
Means valid calculation output is displayed in
corresponding result box immediately after user changes
any one of input field. The governing equation for the
heat leak is displayed on the user interface for user’s
understanding. In general, cryogenics systems design
incorporate higher vacuum better than 10-5 mbar. The
contribution due to residual gas conduction is negligible.
Figure 1: Overview of Qdot.
Therefore, the major source of steady state heat-in leak is
considered as solid conduction and radiation only.
CONDUCTION HEAT LEAK
COMPUTATION
In conduction heat load calculation Integral thermal
conductivity of material in consideration is important for
precise calculation. NIST has publish 8th order
polynomial coefficient equation [4] for various 49
cryogenic grade material. The values of coefficients are
embedded in software for all materials. By clicking on
material drop box list of material is displayed on separate
panel, user can select the material in consideration. The
lower
temperature T1 and higher temperature T2 are
user input in Kelvin. The geometrical parameter like
length (L) and cross-sectional area (A) of the material
shape under
consideration are fed as an input to the
program. The equations are in form of given below.
𝑇2
𝑘𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 = ∑[𝐾 ∗ 𝛿𝑇]
𝑇1
𝑙𝑜𝑔10 𝑘 = 𝑎 + 𝑏(𝑙𝑜𝑔10 𝑇) + 𝑐(𝑙𝑜𝑔10 𝑇)2 + 𝑑(𝑙𝑜𝑔10 𝑇)3 +
𝑒(𝑙𝑜𝑔10 𝑇)4 + 𝑓(𝑙𝑜𝑔10 𝑇)5 + 𝑔(𝑙𝑜𝑔10 𝑇)6 +
ℎ(𝑙𝑜𝑔10 𝑇)7 + 𝑖(𝑙𝑜𝑔10 𝑇)8
𝑇2
𝑄̇ = ∫
𝑇1
𝐾(𝑇)𝑑𝑇 ∗
𝐴
𝐿
Figure 2: GUI of conduction menu.
Inside computation algorithm k is evaluated from
temperature T1 to T2 in step of 0.01. The value of
coefficient a,b,c,d,e,f,g,h and i are selected by program
corresponding to material selection by the user. Along
with heat leak program also displays calculated integral
thermal conductivity for material for selected temperature
range. Figure 2 shows screen of conduction menu of
application.
RADIATION HEAT LEAK
COMPUTATION
Radiation heat leak from high temperature surface to
low temperature surface can be calculated easily by
supplying lower temperature (T1) surface area (A1) and
lower temperature (T1 in kelvin) surface’s area (A1 in sq.
m) and emissivity (E1), higher temperature (T2) surface’s
area (A2) and emissivity (E2). The remaining constant
and equation evaluation will be done in program code.
The resultant radiation heat load is displayed on screen in
watt. The value of emissivity (or reflectivity) is highly
variable among different material & depends on surface
condition and temperature. The emissivity of metal is
more sensitive to surface contamination than that of
Figure 3: GUI of thermal radiation menu
Non-conductive material. Contamination includes
oxidation and alloying. Figure 3 shows the screen of
radiation heat calculation menu of application
SPECIFIC HEAT COMPUTATION
“Qdot” can radially calculate specific heat of twenty
seven various materials for user defined specific
temperature, further more software also provides integral
average specific heat of material for range of temperature
specified by user. The integral average specific heat is
computed by evaluating the Cp in step of 0.1 K for
temperature range specified by user.
𝑇
𝐶𝑝 𝑖𝑛𝑡 𝑎𝑣𝑔 =
2
∫𝑇 𝐶𝑝 𝑑𝑇
1
𝑇2 − 𝑇1
Specific heat computation is based on NIST published
curve fitting coefficient. The software will only calculate
specific heat within the equation range; the equation
range is displayed on the screen. If user specifies temperature beyond this equation range a pop-up message
REFERENCES
[1] Experimental techniques for low temperature
measurements: Cryostat design, Material properties
and superconductor critical- current testing – 2006
Author: Ekin, Jack W
Publisher: Oxford
University Press
[2] “Case studies in superconducting magnet design and
operational issue” second edition by Prof Yukikazu
Iwasa page no.251. Publisher: Springer
[3] Randall F. Barron, Cryogenic Systems 2nd Ed.
(Clarendon University Press, Oxford,1985).
[4] Web site:
Figure 4: GUI of specific heat calculation
“Specified Temperature is out of range” will be displayed
and result box displayed as “0.00000”.Figure 4 shows the
specific heat calculation screen of program.
CONCLUSION
The scientific application “Qdot” is being developed on
Windows Operation system using Labwindows/CVI
program development tool and distributed among the
cryogenic users. The computation results are compared
with available reference and it matches within acceptable
margins. For computation of integral thermal conductivity
and specific heat of material we have used NIST
published material property data. The application
provides necessary properties of wide range of various
cryogenic materials quickly on few clicks.
ACKNOWLEDGMENT
Throughout this application program we have used
cryogenic material property data, equation and coefficient
published by NIST. We are very thankful to them for
making all data accessible.
http://cryogenics.nist.gov