Engineering task and calculation objective
The HE module calculates the properties of helium gas as a function of temperature and pressure. If you need to calculate helium properties — density, specific heat capacity, thermal conductivity, viscosity, enthalpy and entropy, as well as derived quantities such as Prandtl number and thermal diffusivity — you obtain them for the temperature range from 20 to 1500 °C and pressures from 1 to 100 bar. The data basis is the property correlations of the Jülich Research Centre (Forschungszentrum Jülich), developed in the course of high-temperature reactor development.
As a monatomic noble gas, helium is chemically inert, has the highest thermal conductivity of all gases after hydrogen, and a high specific heat capacity of about 5.19 kJ/(kg·K) that is practically constant over wide temperature ranges. These properties make it the preferred working and cooling gas for high-temperature processes: gas-cooled high-temperature reactors, helium turbine cycles, inert gas applications, leak-testing and cryogenics peripherals, and high-temperature heat exchangers.
In addition to the temperature- and pressure-dependent values, the module provides the molar mass, specific gas constant, standard density and the critical data (critical temperature, critical pressure, critical density).
Standard and calculation basis: Forschungszentrum Jülich
Calculation workflow
- Specify the state point: The user enters temperature and pressure within the validity range (20 to 1500 °C, 1 to 100 bar). In this range, helium is always a gas far above its critical point — the critical temperature is only about 5.2 K.
- Calculate the thermal state properties: Density and real-gas behavior are determined from the built-in equation of state; because of the weak intermolecular interactions, helium deviates only slightly from ideal gas behavior in this range. Molar mass and specific gas constant are available as constants.
- Determine the caloric properties: Specific heat capacity, enthalpy and entropy are evaluated. As a monatomic gas, helium has no contribution from internal degrees of freedom, so cp remains nearly constant over the entire temperature range and the isentropic exponent is κ ≈ 5/3.
- Determine the transport properties: Thermal conductivity and dynamic viscosity are calculated as functions of temperature and pressure using the Jülich correlations; both increase markedly with temperature. From these follow the kinematic viscosity, thermal diffusivity and Prandtl number.
- Use the results in heat transfer and cycle calculations: The property values enter directly into Nusselt correlations for helium-cooled channels and heat exchangers, into pressure drop calculations, and into the thermodynamic balancing of helium cycles.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Density | ρ ρ | kg/m³ |
| Density | ρ ρ | kg/m³ |
| Thermal conductivity | λ λ | W/(m·K) |
| Thermal conductivity | λ λ | W/(m·K) |
| Dynamic viscosity | η η | mPa·s |
| Dynamic viscosity | η η | mPa·s |
| Kinematic viscosity | ν ν | m²/s |
| Kinematic viscosity | ν ν | m²/s |
| Specific enthalpy | h h | J/kg |
| Specific enthalpy | h h | J/kg |
| Specific entropy | s s | J/(kg·K) |
| Specific entropy | s s | J/(kg·K) |
| Temperature | ϑ1 ϑ2 | °C |
| Temperature | ϑ1 ϑ2 | °C |
| Pressure | p1 p2 | Pa |
| Pressure | p1 p2 | Pa |
| Specific heat capacity | cp cp | J/(kg·K) |
| Specific heat capacity | cp cp | J/(kg·K) |
| Specific heat capacity | cv cv | J/(kg·K) |
| Specific heat capacity | cv cv | J/(kg·K) |
| Prandtl number | Pr Pr | - |
| Prandtl number | Pr Pr | - |
| Coeff. of thermal expansion | β β | 1/K |
| Coeff. of thermal expansion | β β | 1/K |
Worked example
For the preliminary design of a helium-cooled heat exchanger, the density of helium at the inlet at 20 °C and 10 bar is required. The calculation uses the ideal gas law with the specific gas constant; the small real-gas deviation of helium is neglected — a worked example of a typical gas density calculation.
Given values
| Temperature T | 20 °C = 293.15 K |
| Pressure p | 10 bar = 1.0 · 10⁶ Pa |
| Molar mass M | 4.0026 g/mol |
| Universal gas constant R | 8.3145 J/(mol·K) |
Solution
Specific gas constant of helium
RHe = R / M = 8.3145 / 0.0040026 = 2,077.3 J/(kg·K)
Density from the ideal gas law
ρ = p / (RHe · T) = 1.0 · 10⁶ / (2,077.3 · 293.15) = 1.0 · 10⁶ / 608,960 = 1.642 kg/m³
For comparison: at 1 bar and 20 °C, the corresponding result is ρ = 0.164 kg/m³ — in the ideal range, the density scales linearly with pressure.
Result
| Specific gas constant R_He | 2,077.3 J/(kg·K) |
| Density ρ (20 °C, 10 bar) | 1.642 kg/m³ |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
May helium be treated as an ideal gas within the module's range?
Largely, yes. Helium has extremely weak intermolecular forces; between 20 and 1500 °C, the compressibility factor is only slightly above 1 even at 100 bar (slightly positive deviation). For approximate density and balance calculations, the ideal gas law with the specific gas constant R = 2077 J/(kg·K) is therefore quite usable. For accurate designs, especially at high pressures, the correlation values of the module should be used — above all for the transport properties, which follow no simple law.
Why is helium such a good cooling gas for high-temperature processes?
Three properties act together: the high specific heat capacity of about 5.19 kJ/(kg·K) — roughly five times that of air —, the highest thermal conductivity of all technically usable gases except hydrogen, and complete chemical inertness even at very high temperatures. Unlike hydrogen, helium is not flammable and does not embrittle materials; unlike CO2, it does not dissociate. Its disadvantages are its price, its low density (high compression effort) and its high diffusivity, which is demanding in terms of sealing technology.
Why is the Prandtl number of helium smaller than that of air?
For monatomic gases, the ratio of momentum to heat transport is fixed by kinetic gas theory; theoretically Pr = 2/3, and in reality helium lies at about 0.66 to 0.68, below air (approx. 0.7). Moreover, the Prandtl number is nearly independent of temperature and pressure, because viscosity and thermal conductivity grow in the same way with temperature while cp remains constant — which considerably simplifies heat transfer calculations over large temperature spans.