Numerical Study of the Thermal Model on High Uniformity Temperature Test Platform

The surface temperature uniformity of a test platform with an effective test area of 600 mm × 600mm was numerically studied. The conductive heat transfer model for the test platform and the device under test (DUT) installed on the surface was established in the present work, as well as the radiation heat transfer model from the platform surface to the background temperature. The platform surface was divided into 5 or 9 regions where heated independently to make the surface temperature consistent. The temperature uniformity of these two partition designs was compared. The result shows that the 9 regions design has higher temperature uniformity at both target temperatures of -10°C and +45°C.


Introduction
The spacecraft payload in orbit provides certain requirements for the thermal control system. These requirements of spacecraft mainly include operating temperature range, temperature uniformity, temperature stability, etc. The temperature uniformity requirement is generally put forward in the form of temperature difference or temperature gradient, which is determined by the thermal deformation of materials. For the main mirror of a 1m diameter solar telescope, the deviation of the mirror parabola is required to be less than λ/40 (λ=663nm), the focal distance difference is less than 0.15mm, and the displacement along the axis is less than 0.05mm. To maintain optical performance, the 3mdiameter main mirror of the Hubble telescope should be kept at a constant temperature of 21.1 ℃ and its temperature uniformity should be less than 0.1℃ [1,2].
By exploring the space interference measurement task of the next generation space telescope (NGST), the requirements of optical system were proposed by NASA as follows: 1. The stability of the optical element position should be maintained at the nanoscale. 2. The relative position sensitivity of parliamentary optical elements is subnanometer. 3. The torque of the optical element is controlled at the picometer level. Such high precision position and deformation requirements inevitably require the precise temperature control of scientific payload frame and precise support structure. Such as the temperature uniformity of the GRACE satellite is below 0.1 ℃, and 0.01 ℃ for the GOCE satellite [3].
Usually, the scientific payload is closely connected with the supporting structure. When the contact surface temperature is different, there is a heat conduction process between them. In this paper, a test platform with an effective test area of 600mm × 600mm was taken as the research object, which was placed in a 7m diameter and 6m length thermal chamber with vacuum pressure of 1.3×10 -5 Pa, background temperature of -173℃±5℃. The temperature control target was -10℃ and +45℃. The realization of surface temperature uniformity was studied numerically.

Thermal model
The heat transfer process of a control volume is governed by three basic physical laws, namely mass conservation, momentum conservation and energy conservation. By solving these equations, the heat transfer process and temperature field distribution in the space can be obtained. The heat transfer process between scientific payload, test platform and low temperature cold background is shown in Fig. 1: The heat generated by the scientific payload is transmitted to the central area of the test platform by conduction through the installation surface. The rest heat was transferred to other areas of the test platform through radiant heat transfer. All the heat is then radiated from the outside surface of the test platform to the low temperature cold background. Additionally, in order to keep the test platform at the target temperature, electric heating is required on the platform surface, which will eventually be taken away by radiation.

Methodology
In the space environment simulator where the high uniformity temperature simulation test platform is located, the gas pressure is lower than 1.3 × 10 -3 Pa. So its flow and heat transfer are very weak, and can be ignored. Only the internal heat conduction conservation [4] of solid materials is considered, which can be simplified as follows.
In the formula, ρ is the density. T is the temperature. λ is the thermal conductivity; c p is constant pressure specific heat. The Discrete Ordinates (DO) radiation model [5][6][7][8] was adopted for the radiation heat transfer between the surfaces. For a control volume, the radiation heat transfer equation is shown as follows: where r is the position vector. s is the direction vector. s' is the scattering direction vector. a is the absorption coefficient. n is the refractive index. σ s is the scattering coefficient. σ is the Stefan-Boltzmann constant. I is the radiation intensity, which depends on position (r) and direction (s). T is the local temperature. Φ is the phase function. Ω is the solid angle.
For gray diffuse radiation, the incident radiative heat flux q in at the wall is The net radiative flux leaving the surface is given by The boundary intensity for all outgoing directions at the wall is given by

Simulation and analysis
In order to achieve the high uniformity of the platform surface temperature, the platform surface was divided into 5 or 9 regions where heated independently to make the surface temperature consistent. Furthermore, the result of uniform heating flow was compared with these two partition forms. The results were calculated by Fluent. The working pressure is 1 × 10 -5 Pa. The temperature of the background is -173 ℃ . The background surface emissivity is 0.88. The test platform surface emissivity is 0.8. The calculation process is divided into three steps: 1) Set the temperature boundary condition of the simulator to isothermal boundary (e.g., T = -10 ℃), after convergence, obtain the heating power Q 1 ~ Q n for each heating region.
2) According to the required heating power calculated in 1), the boundary condition of the heating regions is set as heat flux boundary with Q 1 ~ Q n respectively. The surface temperature distribution will be obtained to verify whether the temperature control requirements are met.
3) Optimize the heat flow on each surface to make the surface temperature of the platform consistent.

Partition scheme
The two partition schemes are shown in Fig. 2.  Partition scheme 1: The platform is divided into 5 regions for independent temperature control, as shown in Fig. 2 a). The effective test area named Part 1 is 300mm × 300mm in the centre of the platform. The surrounding area is divided into 4 symmetrical L-shaped areas named Part 2 with equal heat flow.
Partition scheme 2: Based on the Partition scheme 1, the platform is further divided into 9 regions for independent temperature control, as shown in Fig. 2 b). The shape of the middle area remains the same and is named as Part 1. The surrounding areas are more specifically divided into the marginal areas Part 2 and the corner areas Part 3.

Target temperature of -10℃
When the platform temperature is stable to -10 ℃, the heat flux required for each partition is shown in Table 1.  Fig. 3 a), for the clod background temperature of 100 K (-173.15 ℃ ). The temperature range of the effective test area with 300 mm × 300 mm was from -10.75℃ to -10 ℃ as shown in Fig. b). It is indicated that the uniform heating method cannot meet the temperature uniformity requirement of ±0.025℃.  The surface temperature distribution of the platform surface is shown in Fig. 4 a) under the heat flux condition of Partition scheme 1, the platform surface temperature was -10.26 ℃ ~ 9.85 ℃. The temperature uniformity area at ±0.025℃ is shown in Fig. 4 b) with a surface temperature range from -10 ℃ to -9.95 ℃. The uniform temperature area was a circular area with a diameter of 478mm. The surface temperature distribution of the platform surface is shown in Fig. 5 a) under the heat flux condition of Partition scheme 2, the platform surface temperature was -10.23℃~ -9.87℃. The temperature uniformity area at ±0.025℃ is shown in Fig. 5 b) with a surface temperature range from -10.02 ℃ to -9.97 ℃. The uniform temperature area was 467 mm × 467 mm.

Target temperature of +45℃
When the platform temperature is stable to 45 ℃, the heat flux required for each partition is shown in Table 2.  Fig. 6 a). The temperature range of the effective test area was from 44.6℃ to 45.6 ℃ as shown in Fig. 6 b). The uniform heating method cannot meet the temperature uniformity requirement of ±0.025℃ for target temperature of +45℃ neither. a) Bottom of the platform b) Effective test area The surface temperature distribution of the platform surface is shown in Fig. 7 a) for the target temperature of +45℃ under Partition scheme 1 condition, the platform surface temperature was +44.53 ℃~ +45.09 ℃ . The temperature uniformity area at ±0.025℃ is shown in Fig.  7 b) with a surface temperature range from +45.04℃ to +45.09 ℃. The uniform temperature area was a circular area with a diameter of 430 mm. Under the heat flux condition of Partition scheme 2, the platform surface temperature was +44.58 ℃~ +45.05 ℃ as shown in Fig. 8 a). The temperature uniformity area at ±0.025℃ shown in Fig. 8 b) had a surface temperature range from +45℃ to +45.05℃. The uniform temperature area was 420 mm × 420 mm.

Temperature uniformity
As shown in Fig. 3 and Fig. 6, the uniform heating method is unable to make the temperature difference within ±0.025℃ in the effective test area with 300 mm × 300 mm under target temperature of -10 and 45 ℃ . However, both partition methods can achieve temperature uniformity.

Temperature uniform region
The temperature uniform region of partition scheme 1 is circular and that of Partition scheme 2 is a square. The area of the temperature uniform region is calculated as shown in Table 3. It can be seen from Table 3 that the area of temperature uniform region for partition scheme 2 is larger than that of scheme 1. Moreover, the shape of temperature uniform region for scheme 2 is consistent with the shape of the payload. Therefore, the 9 partition regions design is more appropriate.

Conclusion
The surface temperature uniformity of a test platform with an effective test area of 600 mm × 600mm was numerically studied in this paper. The conductive heat transfer model for the test platform and DUT installed on the surface was established, as well as the radiative heat transfer model from the platform surface to the background temperature. The surface uniformity of the test platform at the target temperature of -10, 45℃ is analysed under two partition schemes. The result shows that the 9 regions design has higher temperature uniformity.