Thermal Mass Flow Factor Theory and Derivation for Model Families: SLA Series, 5850E Series, 5850EM Series, 5700 Series, 5850I Series, and 5850TR
When a thermal mass flow controller or meter operates with a different gas than the one it was calibrated for, a scale shift will occur in the relation between the output signal and the mass flow rate. This happens due variations in heat capacities or specific heat between the two gases. See example of scenarios below where sensor factors could be used.
Scenario 1: Factor Application to Existing Calibration with Different Gases
Scenario 2: Factor Application to Existing Calibration with Change in Gas Mixture
Scenario 3: Re-Calibration/Verification Using a Surrogate Gas with a Factor
- Cost: Calibrating with specialty or hazardous gases can be expensive. Using a surrogate can reduce calibration expenses.
- Safety: Using a safe/inert gas will reduce safety risks during calibration.
- Availability: Surrogate gases maybe easier to source and plentiful.
Scenario 4: Re-Calibration/Verification Using Process Gas with No Factor Required, Factor = 1
- Accuracy: Calibrating on actual process gas will get you the highest accuracy possible.
- No Conversion Errors: No risk with conversion errors or inaccuracies.
- Critical Applications: Some applications require very accurate and precise measurements. Calibrating on actual gas will get you as accurate and precise as possible.
- Simplified Calibration Process: No calculations necessary. Reduces the complexity and potential human error.
Variations in Specific Heat between Two Gases
What is Specific heat? Specific heat is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius/Kelvin. It measures how much energy a substance can absorb before its temperature increases. The specific heat is often denoted by the symbol Cp and is expressed in units of joules per kilogram per degree Celsius (J/kg·°C) or joules per kilogram per Kelvin (J/kg·K).
Mathematically, it can be defined as:
In thermal wire-based sensors, specific heat is taken at 80°C because of the sensor operation at 59 °C above ambient. This scale shift can be approximated by using the ratio of the molar specific heat of the two gases or by a sensor factor. Derivation of the sensor factor from mass flow relationships is shown below:
Definitions to consider:
Equations to consider:
A list of sensor factors is given in the Brooks Thermal Mass Flow Sensor Factor Table.
FPO: Button
The specific heat of most gases is not strongly pressure, and/or temperature, dependent. However, gas conditions that vary widely from reference conditions may cause an additional error due to the change in specific heat caused by pressure and/or temperature. Additional considerations in sensor factor accuracy include reference database consistency of specific heat, Reynolds Number effects (flow path geometry, gas density/viscosity), and thermophysical similarity of surrogate/process gas. The highest accuracy will always result from calibration on actual gas.
To change to a new gas, multiply the output reading by the ratio of the sensor factor for the desired gas to the sensor factor of the calibration gas.
See example calculation:
To calculate flow for a new gas mixture, use the following equations:
Operating the thermal mass flow controller or meter at gas conditions, operating pressure, or flow range different from the factory built and calibrated conditions may also require new sizing of the orifice and restrictor. Such resizing will require support from the Brooks Technical Services Team to ensure your device’s internal components are compatible with the new process conditions.
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