Using CryoComp Software

Summary:  CryoComp provides engineering estimates of low temperature thermal transport properties of listed materials, engineering computations of some parameters germane to cryogenic analysis, and some supporting computed parameters enabling other useful computations. These are listed below:

Transport properties             Engineering Computations               Enabling Parameters

(Tabular)

Thermal conductivity                     One dimensional contraction                    i2t.

between temperatures with both           Thermal conductivity

isothermal and natural gradients.             integral.

Specific heat                                      Heat flow with natural gradients.

Thermal expansion                         Cooldown enthalpy with isotheral

and natural thermal gradients.

Resistivity                                           Resistance, at higher, lower, and

across the natural temperature

Diffusivity

Enthalpy

Density.

Tabular Properties.

The tables of properties generated use the lowest temperature input for the reference temperature for integrated properties, i.e., enthalpy, I(k*dT), and Δ(L/Lo). If a User wants the full expansion curve relative to some reference, say 273K, then a table is generated from lowest allowed temperature to 300K. The table is then launched in Excel. A column is inserted to the right of the Δ(L/Lo) column and the Δ(L/Lo) at 273K is subtracted from all column elements with the result placed in the new column, a formula manipulation. This gives the expansion/contraction relative to 273 or any other value chosen.

Since the density is given at 273K, the density at any temperature may be approximated by the equation density(T)= density(273K)*(1-3*Δ(L(T)/Lo)) for isotropic materials without phase transitions. Δ(L(T)/Lo) is found from the table produced by the method described in the preceding paragraph.

Diffusivity is useful in its own right and can also be used to estimate the cooldown/warm-up “time constant” for simple geometries by the following equation, “time constant” = (1/b)*(L2/α)0.5 where L is a characteristic length in the heat flow direction, α is the thermal diffusivity, and b is a dimensionless constant approximately equal to π.  The value of “b” varies slightly with geometry but π is a good approximation in most cases, enabling good engineering estimates of cooldown time. The thermal “time constant” is the time required to transfer 62.3% of the relative enthalpy from or to the component and three time constants approximate thermal equilibrium time.

Engineering Computations.

The computational capability of CryoComp is straight forward except that all of the data required may not be available. CryoComp can help in these cases with its user property entry capability. Properties from like species may be copied into the User file from CryoComp’s data base and then edited to bound the unknown property. All of CryoComp’s capabilities are available for the User’s materials and hence the performance of the material with missing data may be bounded. An example could be 7075 Al. Scant data is available for 7075 specific heat. The data for 7075 Al from CryoComp may be copied into the User’s data base and renamed, perhaps 7075L. The specific heat data of 1100 Al may then be entered in the data table of 7075L for a lower bound on 7075 performance. A very simple upper bound could be established by copying 7075L into a new material, 7075H. Then, multiplying the 1100 specific heat by 1.1 and entering it creates an upper bound material. Frequently data is available for materials, but it is partial, or single source, or perhaps conflicting with logic so that the User may have a reasonable estimate of the performance of the material in CryoComp having incomplete data. Another method redefining the temperature range of a material in the CC5.1 data base may be used. For example if the user’s temperature range for A-286 is between 172K and 300K, the data in the A-286 notes may be used to generate a new complete “material” set for A-286 having a temperature range from 172K to 300K.

Enabling Parameters.

I2t. This parameter describes the temperature rise vs time for the component when carrying current. Dividing the I2t value by the current squared yields the time to rise from the lower temperature in the design to the higher.  Similarily, dividing I2t by the time and taking the square root gives the current allowable for the given temperature rise.

Thermal Conductivity Integral. For design elements with a cross-sectional area change, the effective thermal conductivity integral may be computed from the CryoComp design output by the following formula:

Q = {[(A/L)|L)*(A/L)|H]/[(A/L)| L +(A/L)| H ]}*{I| H -I| L}

Where: Q is the heat flow.

I L is the thermal conductivity integral evaluated at the lower temperature.

I H is the thermal conductivity integral evaluated at the higher temperature.

(A/L)|L is the colder cross sectional area-to-length ratio.

(A/L)|H is the warmer cross sectional area-to-length ratio.

For multiple cross-sectional area changes in a design element, the above equation can be generalized and the A/L parameters add like electrical conductances in series.