How to design a solar radiation shield for weather station temperature sensors?
/QUESTION: What features make an excellent solar radiation shield for weather station temperature sensors?
ANSWER: A high-quality solar radiation shield for weather stations will ideally maintain clean attached airflow internally, have a large air gap between louvers/plates, and keep the temperature sensor shielded from 360° of direct, reflected solar and thermal radiation as described below:
Plate spacing should be at least 4x the thermal boundary layer thickness at low wind speeds of less than 1 m/s (3.6 kph or 2.2 mph) so that the temperature of at least 50% of the air entering the shield is not affected by thermal exchange with the radiation shield louvers before reaching the sensor.
Airflow to the sensor should be free of obstructions if possible. A solar shield’s or solar screen’s louvers should be shaped aerodynamically so as to minimize obstruction to the airflow by minimizing turbulence and flow separation. This can be a real challenge at very low wind speeds since laminar airflow does not like turning.
The sensor should not be exposed to any direct solar irradiation or its ground or wall reflections from any angle as the sun traverses the sky so as not to expose the sensor to solar heating, from which the solar radiation shield is supposed to protect it.
A detailed explanation of the above design points follows:
1. Plate spacing should be at least 4x the thermal boundary layer thickness.
In the air gap between two radiation shield louvers (or solar screen plates), the thermal boundary layers of the upper plate and the lower plate will significantly reduce the amount of air whose temperature is not affected by the radiation shield surface temperature. Taking this into consideration, we recommend that at least 50% of the air entering the shield is free from any shield induced thermal effects or flow obstructions, which results in a louver spacing of at least 2 * Thermal boundary layer thickness / 50% = 4 * Thermal boundary layer thickness.
From the below table of calculated thermal boundary layer results, one can see the minimum air gap between the plates or louvers of a multi-plate radiation shield design. The same constraints apply to a helical radiation shield design. However, many multi-plate radiation shield designs do not meet this criterion.
| Thermal boundary layer thickness at 0.5 m/s air speed for different louver widths (0.5 m/s = 1.8 kph or 1.1mph) | ||||
|---|---|---|---|---|
| Louver widths | Reynolds Number Range (Laminar Flow) | Velocity boundary layer thickness Blasius solution =5*x/(√Re) | Thermal boundary layer thickness | Minimum recommended gap between radiation shield plates/louvers |
| 30 mm | 783+60°C to 1490-40°C | 3.89-40°C to 5.36 mm+60°C | 2.84-40°C to 3.73 mm+60°C | 3.73 * 4 = 14.9 mm min gap |
| 40 mm | 1044+60°C to 1987-40°C | 4.49-40°C to 6.19 mm+60°C | 3.28-40°C to 4.30 mm+60°C | 4.30 * 4 = 17.2 mm min gap |
| 50 mm | 1306+60°C to 2483-40°C | 5.02-40°C to 6.92 mm+60°C | 3.66-40°C to 4.81 mm+60°C | 4.81 * 4 = 19.2 mm min gap |
| 60 mm | 1567+60°C to 2980-40°C | 5.50-40°C to 7.58 mm+60°C | 4.01-40°C to 5.27 mm+60°C | 5.27 * 4 = 21.08 mm min gap |
| 70 mm | 1828+60°C to 3476-40°C | 5.94-40°C to 8.19 mm+60°C | 4.33-40°C to 5.69 mm+60°C | 5.69 * 4 = 22.76 mm min gap |
| Thermal boundary layer thickness at 1 m/s air speed for different louver widths (1 m/s = 3.6kph or 2.2mph) | ||||
|---|---|---|---|---|
| Louver widths | Reynolds Number Range (Laminar Flow) | Velocity boundary layer thickness Blasius solution =5*x/(√Re) | Thermal boundary layer thickness | Minimum recommended gap between radiation shield plates/louvers |
| 30 mm | 1566+60°C to 2979-40°C | 2.75-40°C to 3.79 mm+60°C | 2.01-40°C to 2.63 mm+60°C | 2.63 * 4 = 10.5 mm min gap |
| 40 mm | 2088+60°C to 3973-40°C | 3.17-40°C to 4.38 mm+60°C | 2.32-40°C to 3.04 mm+60°C | 3.04 * 4 = 12.2 mm min gap |
| 50 mm | 2611+60°C to 4966-40°C | 3.55-40°C to 4.89 mm+60°C | 2.59-40°C to 3.40 mm+60°C | 3.40 * 4 = 13.6 mm min gap |
| 60 mm | 3133+60°C to 5959-40°C | 3.89-40°C to 5.36 mm+60°C | 2.84-40°C to 3.73 mm+60°C | 3.73 * 4 = 14.9 mm min gap |
| 70 mm | 3655+60°C to 6952-40°C | 4.20-40°C to 5.79 mm+60°C | 3.06-40°C to 4.02 mm+60°C | 4.02 * 4 = 16.1 mm min gap |
2. & 3. Airflow to the sensor should be free of obstructions while maintaining 360° sensor protection
At very low air speeds, the air has a hard time turning around obstacles since viscous forces are more dominant than at higher speeds. When encountering shaped radiation shield plates or angled solar screen louvers, unless they are properly shaped, flow separation will occur and cause flow blockage or flow reduction to the temperature sensor inside. The resulting effect is convective heat buildup of the air inside the shield and an increase in sensor response time to temperature changes. In a multi-plate radiation shield design, it is geometrically impossible to shape the plates to meet good airflow criteria while keeping the sensor hidden from 360° of direct or reflected solar or thermal radiation and meeting the above-mentioned minimum plate spacing requirement.
Geometrically, a helical radiation shield design allows for meeting all three of these criteria, even at very low wind speeds:
Maintain attached flow.
Keep the air gap between plates 4x larger than the thermal boundary layer.
Keep the sensor shielded from 360° of direct, reflected solar or thermal radiation.
Definitions and math behind the results
Reynolds Number (Re) gives the ratio of how much inertial forces dominate over viscous forces in the flow and is used to calculate the velocity and thermal boundary layer thickness. Re = (x)*v*ρ/μ (v = wind speed, x = length along the radiation shield louver, ρ = air density, μ = dynamic viscosity of air)
Prandtl Number (Pr) gives the relative thickness of the thermal boundary layer as a fraction of the aerodynamic velocity boundary layer thickness. For air, the Prandtl number indicates that the thermal boundary layer is 0.73 to 0.695 of the aerodynamic velocity boundary layer thickness between -40 °C and +60 °C.
Nusselt Number (Nu) gives the ratio of how much convective heat transfer increases heat transfer rate over purely conductive heat transfer in a fluid. In this example, the heat transfer rate to air is increased by 16 to 35 times for 0.5 m/s wind speeds and by about 23 to 50 times for 1 m/s wind speeds than for conductive heat transfer alone.
References
Gnielinski, V., "Berechnung mittlerer Warme- und Stoffubergshoeffizienten an laminar und turbulent uberstromten Einzellkorpern mit Hilfe einer einheitlichen Gleichung," Forschung im Ingenierwesen, Vol. 41, pp 145-153, (1975).
https://www.sfu.ca/~mbahrami/ENSC%20388/Notes/Forced%20Convection.pdf