Using CryoComp 5.3

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 immediately 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 gradients.

                Resistivity                                            Resistance, at higher, lower, and

                                                                                across the natural temperature gradient.

                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. for some materials , the Δ(L/Lo) data may be used to directly calculate thermal expansion coefficients that are satisfactory for use in determining specific heats (R. P. Read and A. F. Clark, Materials at Low Temperatures, ASM, 1983, Pg, 106). This feature is useful when sparse specific heat data is available.

 

Since the density is given at 273K, the density of isotropic materials at any temperature, those without phase changes, may be approximated by the equation density(T)= density(273K)*(1-3*Δ(L(T)/Lo)). 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 cool-down/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 cool-down. 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 when 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 (see 7075 Al material notes). 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 creating 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 a material in CryoComp having incomplete data. For 7075, if the user’s temperature range of interest is from 70 to 300K, a new “material” having a complete data set may be created having a temperature range corresponding to the specific heat data range in the material notes.

 

Enabling Parameters.

I2t. This parameter, part of the design computations, 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.  Similarly, 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 section parameters add like conductances in series.

 

Estimating the coefficient expansion.

In version 5.3 the number of significant figures for thermal contraction output to Excel has been increased to allow more precision should the user need to determine the coefficient of thermal expansion by numerical differention and curve fitting. An abbreviated form of the Gruneisen relation may be useful to bridge gaps in the available specific heat data for some solid isotropic materials exhibiting no phase changes.