Temperature Field Distribution Testing and Improvement of Near Space Environment Simulation Test System for Unmanned Aerial Vehicles

Highlights

What are the main findings?

• The strong agreement between experimental and numerical simulation results validates the feasibility of using CFD numerical simulation to study the temperature field distribution characteristics in the near space environment simulation test system.
• Additional wind field to the near space environment simulation test system can improve the temperature uniformity greatly.

What is the implication of the main finding?

• The main findings will provide a robust theoretical foundation for reliability verification of near space unmanned vehicles.

Abstract

Temperature distribution inside the vacuum chamber of the TRX 2000(A) near space environment simulation test system (NSESTS) was investigated through both experimentation and computational fluid dynamics simulation. Comparison between the experimental result and the simulation result showed that these two results were very close to each other, validating the feasibility of using the simulation method to study the temperature distribution inside the NSESTS. Then, the effect of wind, either downwind or upwind, on temperature uniformity inside the NSESTS was investigated through the simulation method. The simulation result showed that the non-uniformity coefficient will be reduced from 0.2757 to 0.2012 (by 27.1%) in the case of downwind and to 0.2055 (by 25.5%) in the case of upwind. Then, the simulation result was validated by experiment. The result of this research indicates that the temperature uniformity can be greatly improved through installment of additional fans inside the NSESTS.

1. Introduction

Near space is the atmospheric region approximately 20–100 km above sea level and is of great significance for human beings [1,2,3,4,5]. The stratospheric airship is one of the main unmanned aerial vehicles (UAVs) that can fly in near space (see Figure 1). Due to its capability of staying at a high altitude for a long time, typically several months, the stratospheric airship exhibits a high potential in earth observation, remote sensing, and communication. The harsh near space environment poses a huge challenge to the stratospheric airship. Hence, an accurate ground environment simulation test should be performed to validate the reliability of the stratospheric airship [6,7].

The near space region extends across multiple atmospheric layers and is characterized by a highly complex environment, influenced by factors such as temperature, pressure, ozone concentration, and solar ultraviolet radiation [8,9]. Unlike the ground environment where temperature decreases with altitude, the vertical distribution of atmospheric temperature in the near space region is shown in Figure 2a. As we can see from Figure 2a, the atmospheric temperature remains constant at −57 °C at the altitude of 10~20 km. At the altitude of 20~50 km, the temperature increases with altitude at a rate of approximately 2–3 °C per km. At the top of the stratosphere (50 km), the temperature reaches −3 °C [10]. The atmospheric pressure in the near space region decreases approximately exponentially as the altitude increases, as shown in Figure 2b [10]. At 20 km, the atmospheric pressure is about 5–6 kPa; at 30 km, it drops to about 1170 Pa; and at 100 km, it further decreases to approximately 2.64 × 10⁻² Pa [10,11].

In 1971, the United States conducted an analysis of equipment failure in a full year, and the results showed that more than 50% of the failures were environment-related [12]. Similarly, most of near space vehicle failures would also be caused by environment-related factors. Hence, an accurate environment simulation test on the ground should be performed to validate the reliability of near space vehicles before flight. However, the knowledge on how to perform a near space environment simulation test accurately is still insufficient, which will greatly reduce the validity of the environment simulation test, especially for long duration stratospheric airships [13,14,15].

The near space environment simulation test system (NSESTS) is a ground-based facility designed to simulate the environmental conditions of near space, such as temperature, air pressure, and radiation, to validate the performance of near space vehicles. It makes an important contribution to the design of near space unmanned vehicles [16]. The temperature uniformity inside the vacuum chamber of the NSESTS is crucial for the near space environment simulation test [17,18]. However, since the airflow inside the vacuum chamber of the NSESTS is very weak, the temperature uniformity will be impaired greatly. How to quantify the temperature uniformity inside the vacuum chamber of the NSESTS has not been presented in the literature.

The computational fluid dynamics (CFD) simulation method has become an important research tool in recent years due to its cost advantage and convenience. Researchers usually use the CFD method to study not only the temperature distribution characteristics and internal flow field of the enclosed space but also the improvement of the temperature uniformity of the temperature field. Research also shows that the temperature field improved by changing the air supply speed [19,20].

The objective of this paper is to investigate the temperature uniformity inside the vacuum chamber of the TRX-2000(A) NSESTS, which is developed by Beijing Tianrui Xingguang Thermal Technology Co. Ltd. (Beijing, China), by using both experimental and CFD simulation methods. The rest of this paper is organized as follows. Section 2 gives a detailed description on the TRX-2000(A) NSESTS. Then, temperature distribution inside the vacuum chamber of the TRX-2000(A) NSESTS was obtained in Section 3, using both experimental and CFD simulation methods. The effect of wind on temperature uniformity is presented in Section 4. Then, Section 5 concludes this paper.

2. Near Space Environment Simulation Test System

2.1. Principles of Near Space Temperature Field Simulation Tests

Near space environment simulation equipment is usually modified from space environment simulation equipment. Space environment simulation equipment mainly consists of a vacuum chamber, a heat sink, a vacuum system, a liquid nitrogen system, a solar simulation system, and a measurement and control system [21,22]. Under the vacuum condition, convection and conduction can be neglected, and radiation is the primary mode of heat exchange.

The TRX-2000(A) NSESTS draws extensively on the design of existing space environment simulation equipment and consists of six subsystems: pressure vessel, heat sink system, refrigeration system, infrared heating cage, solar simulation system, lifting and pressure control system, and measurement and control system, as shown in Figure 3. Shielding plates are placed within the chamber cylinder, at the rear of the chamber cylinder, and beside the door of the chamber cylinder. The body and the rear of the chamber cylinder are both equipped with a heat sink, which is composed of copper plates and refrigeration copper tubes. The refrigeration system employs a cascade Freon phase-change refrigeration method. An infrared heating cage is installed inside the chamber to compensate for excessive cooling brought by the heat sink through during temperature control. During the temperature control process, the heat sink reduces the temperature in the space through thermal radiation, and the heating cage increases the space temperature also through thermal radiation. The interaction of these two parts creates a temperature gradient where higher temperatures are maintained near the heating cage and relatively lower temperature are around the heat sink. Thus, the natural convection develops from the heating cage toward the heat sink. The near space environment simulation test system mainly uses two methods of heat transfer: thermal radiation and convection. The pressure control system adopts a combination of roots pumps and vane pumps to evacuate the vacuum, and the vacuum regulating valve regulates the pumping speed of the vacuum pump.

2.2. System Setup

The test system consists of the TRX-2000(A) NSESTS, a regulated power supply, a PT100 industrial platinum resistance temperature detector (RTD), and data acquisition (DAQ) units. As illustrated in Figure 3, the TRX-2000(A) NSESTS primarily consists of a pressure vessel, heat sink system, refrigeration system, pressure regulation system, infrared heating array, measurement and control system, and solar simulator. The key technical parameters are as below:

• Chamber dimensions: Φ2400 mm × 3500 mm
• Temperature range:

  ①

  −80 °C to +25 °C (within heat sink)

  ②

  −80 °C to +100 °C (within heating cage)

• Adjustable chamber pressure: 101–0.05 kPa.
• Measurement accuracy of the temperature measurement system: ±1 °C.
• Deviation in temperature uniformity: ±5 °C.

The pressure vessel is an external-pressure vacuum chamber with a horizontal cylindrical structure. One end features a large access door (with a dished head design), while the other end is also sealed with a dished head. Radiation shielding plates are installed on the cylindrical section, rear end, and door side. The vessel’s shell and rear end are equipped with a copper-made heat sink, with its layout illustrated in Figure 3c.

The refrigeration system employs a cascade freon phase-change cooling method, consisting of two independent subsystems: a high-temperature stage and a low-temperature stage. The high-temperature stage uses a medium-temperature refrigerant, while the low-temperature stage utilizes a cryogenic refrigerant.

The pressure regulation system incorporates an electrically vacuum regulating valve for gas charging, ensuring rapid repressurization when required.

Figure 3d shows the infrared heating cage actual unit; it utilizes armored heating strips to form an enclosed space where work pieces can be uniformly heated, providing a stable high-temperature environment. Its power output is adjustable, with target temperatures settable via the control cabinet or computer interface.

The measurement and control system monitors and regulates the pressure vessel, vacuum pumping, refrigeration system, heat sink system, and test specimens.

The supporting equipment of the test system is summarized in

Table 1. Key specifications of supporting equipment for test system.

Equipment Name	Manufacturer	Model	Key Performance Parameter
Industrial platinum resistance temperature detector	Beijing Sai Yiling Technology Co., Ltd., Beijing, China.	PT100	Accuracy class: complies with Class A
Regulated power supply	GWINSTEK, Beijing, China	PSW800-2.88	Rated voltage: 0–800 V; rated current: 0–2.88 A; rated power: 720 W
Data acquisition unit	Beijing Shuo Hua Xingye Electronics Technology Co., Ltd., Beijing, China.	ADAM-4150	Wide power input range: (10–48) VDC

.

2.3. Temperature Probe Setup for Test System

The temperature probes inside the TRX-2000(A) NSESTS were positioned according to the coordinates specified in

Table 2. Coordinates of temperature probes in the environmental simulation test system.

Probe ID	X-Axis (m)	Y-Axis (m)	Z-Axis (m)
T05	−1.45	0	0
T07	0	0	0
T08	−1.45	0	−0.9
T09	−1.45	−0.9	0
T11	0	0.9	0
T12	0	0	−0.9
T13	0	−0.9	0
T14	0	0	0.9
T16	1.45	0.9	0
T17	1.45	0	0
T24	−1.45	0.9	0
T26	−1.45	0	0.9
T30	1.45	0	0.9

. The middle of the chamber is set to be the origin of the coordinate system. The temperature probe layout inside the TRX-2000(A) 3D model and the physical arrangement of the temperature probes are shown in Figure 4.

3. Experimental Testing and Simulation of Temperature Field of NSESTS with Only Natural Convection

3.1. Thermal Simulation Model Construction for Near Space Wind Field

The flow that is driven by non-uniform temperature field in fluids without external driving forces (e.g., pumps or fans) is termed natural convection. The buoyancy force induced by density differences serves as the driving mechanism. Natural convection can be classified into laminar flow and turbulent flow.

The process by which objects transfer energy through electromagnetic waves is called radiation. Objects emit radiant energy due to various reasons, and the phenomenon of emitting radiant energy due to thermal causes is specifically referred to as thermal radiation. The combined effect of radiation and absorption processes results in heat transfer among objects via radiation—known as radiation heat transfer [23].

Based on the working principle and operational condition of the environmental simulation system, the applying process involves both natural convection and thermal radiation. The gas within the system is assumed to be an incompressible fluid with low flow velocity. Therefore, the laminar flow model is selected for natural convection, while the discrete ordinate (DO) model [24]—the most widely applicable for radiation model—is adopted for radiation heat transfer calculations.

The simulation procedure consists of the following steps: first, a three-dimensional model of the NSESTS is established and meshed; subsequently, an appropriate solver is selected with corresponding boundary conditions configured; finally, suitable fluid and radiation models are applied to perform the simulation calculations.

When calculating, the gas within the system is modeled as an incompressible fluid with low flow velocity, approximated as two-dimensional laminar flow. The effects of viscous dissipation and thermal radiation are neglected, with only temperature differences being considered. Specifically, except for the volume force terms in the momentum equation, the density in all other governing equations is treated as constant. This simplification is known as the Boussinesq approximation [25]. Consequently, all thermophysical properties of the medium remain constant except for the density in the buoyancy term.

The following fluid governing Equations (1)–(3) are established:

$$\nabla ·\mathrm{u}=0,$$

(1)

$${\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{t}}}+\nabla \left(\mathrm{u}\mathrm{u}\right)=-{\displaystyle \frac{1}{\mathsf{\rho }}}\nabla \mathrm{p}+\nabla ·\mathsf{\mu }\left(\nabla \mathrm{u}+\nabla {\mathrm{u}}^{\mathrm{T}}\right)+{\displaystyle \frac{{\mathsf{\rho }}_0\mathrm{g}}{\mathsf{\rho }}}+{\mathrm{F}}_{\mathsf{\sigma }},$$

(2)

$$\mathsf{\rho }{\mathrm{c}}_{\mathrm{P}}\left[{\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}+\left(\mathrm{u}·\nabla \mathrm{T}\right)\right]=\nabla ·\mathsf{\lambda }\nabla \mathrm{T},$$

(3)

Based on Equation (1), the fluid momentum conservation equation can be expressed as below:

$${\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{t}}}+\nabla \left(\mathrm{u}\mathrm{u}\right)=-{\displaystyle \frac{1}{\mathsf{\rho }}}\nabla \mathrm{p}+\nabla ·\mathsf{\mu }\left(\nabla \mathrm{u}+\nabla {\mathrm{u}}^{\mathrm{T}}\right)+\left[1-\mathsf{\beta }\left(\mathrm{T}-{\mathrm{T}}_0\right)\right]\mathrm{g}+{\mathrm{F}}_{\mathsf{\sigma }}$$

(4)

In the equations, u represents the velocity vector (unit: m/s); u^T denotes the transpose of the velocity gradient; ρ is the local average density of the fluid (unit: kg/m³); ρ₀ indicates the reference density; T₀ is the reference temperature (unit: K); p stands for pressure (unit: Pa); ▽ is the Hamiltonian differential operator; λ signifies the local average thermal conductivity of the fluid; μ represents the local average dynamic viscosity of the fluid (unit: Pa·s); and F_δ refers to the volumetric force acting on the fluid [24,26].

3.2. Simulation and Experimental Verification of Thermal Field in Near Space Wind Conditions

3.2.1. Numerical Simulation of Near Space Thermal Field

The gas flow and temperature distribution in the temperature field distribution can be accurately modeled through computational fluid dynamics (CFD) simulation. The CFD approach enables the construction of multi-physics models incorporating radiation, convection, and diffusion mechanisms, effectively simulating the coupled radiation–convection temperature field interactions in near space environments. Therefore, this study employs CFD simulations to investigate the temperature field under near space wind condition.

Based on the average pressure and temperature at 35 km altitude in mid-latitude regions of the Northern Hemisphere, the environmental conditions were configured in the CFD simulation, with the system pressure set at 0.6 kPa and the temperature at the center of the pressure vessel (location of temperature probe T07) maintained at −49 °C.

The CFD simulation model for the fluid is shown in the Figure 5. The entire fluid domain was discretized using unstructured tetrahedral meshes, with approximately 2.7 million grid cells. This study employs a self-developed fluid equation solver for numerical computation. The working fluid in the domain is air, which satisfies the Boussinesq approximation. The specific heat capacity (C_p) is set to 1004.43, and the thermal conductivity is set to 0.0242.

Considering the experimental setup where cold air pipes are uniformly distributed on the heat sink surface, this heat sink surface is modeled as a fixed no-slip wall (no heat exchange occurs) with a temperature of 193.15 K (−60 °C) in the simulation. The gate of the cylinder is treated as a fixed no-slip adiabatic wall. In accordance with the experimental condition, several cold air pipes are arranged on the rear wall, so the rear wall is set as a fixed no-slip wall with a temperature of 213.15 K (−60 °C). The infrared heating cage is modeled as a fixed no-slip wall, and its temperature is set to be 275.15 K (2 °C), consistent with the experimental temperature. The center point (T07) is controlled as a constant temperature point at 224.15 K (−49 °C).

Given the near space environment, the gas is highly rarefied, and Reynolds number is small at high altitude, a laminar flow model is adopted. For radiative heat transfer, the discrete ordinate (DO) model—one of the most widely used models—is employed.

This problem involves low-velocity flow in an enclosed space, so an incompressible steady pressure-based solver is used for computation. The simple algorithm, a pressure–velocity coupling method, is utilized to indirectly satisfy the mass conservation equation. This method solves the momentum equation and pressure correction equation iteratively, adjusting the velocity field gradually to meet the continuity condition, and is suitable for low-velocity flow scenarios. Convergence is deemed to be achieved when the velocity residual falls below 0.001.

Figure 6a,b show the temperature distribution contour plots on the centrally symmetric planes z = 0 and x = 0, respectively. As observed, the heat sink and heating cage radiate heat outward; the heating cage elevates temperatures in its vicinity; the heat sink reduces surrounding temperatures; and the spatial temperature distribution is non-uniform, with higher temperatures inside the heating cage and lower temperatures near the heat sink, which is consistent with physical reality. Figure 6c,d present the spatial flow fields plots on the central symmetry planes z = 0 and x = 0, respectively. The simulation results visually demonstrate the complete convective process and the temperature field distribution characteristics within the domain. Key phenomena observed are below:

(a)

The heat sink reduces ambient temperature through radiation cooling;

(b)

The heating cage elevates surrounding temperature via thermal radiation.

Their interaction of the two aspects creates higher temperatures inside/near the heating cage and lower temperatures around the heat sink. The temperature gradient drives natural convection from the heating cage toward the thermal sink, forming two distinct vortices.

3.2.2. Experimental Verification of Near Space Temperature Distribution

Uncertainty Analysis for Test Data

To confirm the reliability of the test data, an uncertainty analysis was performed on the experimental data. Uncertainty is primarily categorized into Type A and Type B uncertainties. Type A uncertainty was calculated using the Bessel formula. The calculation formulas for both types of uncertainty are as follows [27]:

Type A uncertainty:

$${\mathsf{\mu }}_{\mathrm{A}}=\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{T}}_{\mathrm{i}}-\overline{\mathrm{T}}\right)}^2}{\mathrm{n}(\mathrm{n}-1)}}},$$

(5)

In the above equation, ${\mathsf{\mu }}_{\mathrm{A}}$ indicates Type A uncertainty; ${\mathrm{T}}_{\mathrm{i}}$ represents temperature value at measuring point i (unit: °C); $\overline{\mathrm{T}}$ denotes the mean value across all measuring points (unit: °C); and n refers to the number of measuring points.

Type B uncertainty:

$${\mathsf{\mu }}_{\mathrm{B}}={\displaystyle \frac{\mathrm{U}}{\mathrm{k}}},$$

(6)

In the above equation, ${\mathsf{\mu }}_{\mathrm{B}}$ indicates Type B uncertainty; U represents expanded uncertainty, based on the technical specifications of the environmental simulation test system, U = 1 °C; and $\mathrm{k}$ denotes coverage factor, take √3 for k.

Combined uncertainty:

$${\mathsf{\mu }}_{\mathrm{C}}=\sqrt{{\mathsf{\mu }}_{\mathrm{A}}+{\mathsf{\mu }}_{\mathrm{B}}},$$

(7)

In the above equation, ${\mathsf{\mu }}_{\mathrm{C}}$ indicates the combined uncertainty.

The temperature within the test system was set to 10 °C, 22 °C, and −40 °C, respectively. After the temperature of the system was stabilized, temperature data were collected at each measuring points. Data were sampled at a frequency of 30 s, with 10 readings recorded per point. The average of these readings was designated as the experimental value shown in the table below.

Based on Formulas (5)–(7) and data in

Table 3. Temperature data for all the probes at three different setting points in the environmental simulation test system.

No.	Temperature Probe	Test Data (°C, Setting Point is 10 °C)	Test Data (°C, Setting Point is 22 °C)	Test Data (°C, Setting Point is −40 °C)
1	T05	10.5	21.7	−39.4
2	T07	10.9	21.9	−40.0
3	T08	10.9	22.9	−40.8
4	T09	10.1	20.6	−40.2
5	T11	11.9	22.7	−39.9
6	T12	11.1	21.8	−39.6
7	T13	10.7	21.5	−39.2
8	T14	10.2	21.7	−39.8
9	T16	9.9	21.1	−40.7
10	T17	11.1	22.0	−40.1
11	T24	10.6	22.2	−40.6
12	T26	10.3	11.7	−49.3
13	T30	10.4	21.5	−39.6

, the uncertainty of the test value was calculated. The results were rounded to three significant figures and are presented in

Table 4. Uncertainty of the test data.

Temperature Point (°C)	10	22	−40
Type A Uncertainty (°C)	0.147	0.794	0.729
Type B Uncertainty (°C)	0.500	0.500	0.500
Combined Uncertainty (°C)	0.521	0.939	0.884

. The maximum combined uncertainty (0.939 °C) was taken as the uncertainty of the test values. This value is lower than the measurement accuracy (±1 °C) of the environmental simulation test system; therefore, the experimental data obtained are reliable.

Analysis of Experimental and Simulation Results

Based on the average pressure and temperature at 35 km altitude in mid-latitude regions of the Northern Hemisphere, the environmental condition was configured, with the system pressure set at 0.6 kPa and the temperature at the center of the pressure vessel (location of temperature probe T07) maintained at −49 °C.

When the ambient temperature in the test system reached the steady state, both the experimental and simulation data of pressure inside the environmental simulation test system were 0.6 kPa. The experimental (steady state) and simulation temperature value in the environmental simulation test system were presented below.

Table 5. Experimental and simulation results of the temperature inside the vacuum chamber.

No.	Temperature Probe	Experimental Value (°C)	Simulation Value (°C)	Deviation Between Experimental Value and Simulation Value (°C)
1	T05	−46.6	−44.6	2.0
2	T07	−48.9	−49.0	−0.1
3	T08	−49.8	−49.3	0.5
4	T09	−60.5	−52.8	7.7
5	T11	−29.9	−21.4	8.5
6	T12	−38.0	−38.3	−0.3
10	T17	−56.2	−62.3	−6.1
11	T24	−37.5	−35.0	2.5
12	T26	−52.8	−49.4	3.4
13	T30	−64.1	−70.1	−6.0

and Figure 7 show the experimental and simulation results of the temperature inside the vacuum chamber.

• Consistency Assessment of Experimental and Simulation Results

Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are used to analyze the consistency of simulation and experimental data. The calculation formulas are as follows [28]:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{︱}{\mathrm{f}}_i-{\mathrm{g}}_i\mathrm{︳},$$

(8)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{f}}_{\mathrm{i}}-{\mathrm{g}}_{\mathrm{i}}\right)}^2},$$

(9)

In the equations, ${\mathrm{f}}_{\mathrm{i}}$ represents the simulation value at measuring point i (unit: °C); ${\mathrm{g}}_{\mathrm{i}}$ denotes the test value at measuring point i (unit: °C); and n refers to the number of measuring points.

Table 5 shows the experimental value, simulation value, and deviation between them. The deviation is between −0.1 °C and 8.5 °C. The deviation is rooted from the potential limitations existing in the simulation: (1) The laminar flow model used fails to capture local turbulent states, and unsteady flow is not considered. (2) The discrete ordinate radiation model may be inadequately to the radiative properties of rarefied gases. (3) The entire wall is set to be 193.15 K (−60 °C), but in the experiment, we will set the heat sink temperature to be −60 °C, and the simulation does not account for the cooling effect of these distributed heat sinks. Based on the above potential limitations, there is deviation between simulation and experimental results. The calculated mean value for all test points are −48.43 °C (experimental value) and −47.22 °C (simulation value). The MAE and RMSE between the simulation and experimental results are 3.71 °C and 4.76 °C, respectively. Both MAE and RMSE values are smaller than the temperature non-uniformity (±5 °C) of the environmental simulation test system. Furthermore, as shown in Figure 6, although there is deviation between experimental and simulation results, they exhibit the same trend with each other for the temperature field distribution, validating that the deviation is acceptable and it is appropriate for applying the above numerical simulation method to analyze temperature field distribution characteristics in this environmental test system.

2.

Analysis of Temperature Field Uniformity

The non-uniformity coefficient (${\mathsf{\sigma }}_{\mathrm{T}}$) is introduced to evaluate the uniformity of the temperature field within the environmental simulation test system. A smaller (${\mathsf{\sigma }}_{\mathrm{T}}$) value indicates better temperature field uniformity. The calculation formula is given below [29]:

$${\mathsf{\sigma }}_{\mathrm{T}}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}}-\overline{\mathrm{T}}}{\overline{\mathrm{T}}}}\right)}^2},$$

(10)

In the equations, ${\mathsf{\sigma }}_{\mathrm{T}}$ represents temperature non-uniformity coefficient; ${\mathrm{T}}_{\mathrm{i}}$ represents temperature value at measuring point i (unit: °C); $\overline{\mathrm{T}}$ denotes the mean value across all measuring points (unit: °C); and n refers to the number of measuring points.

Using the experimental and simulation results from Table 5 along with Formula (10), the non-uniformity coefficients are calculated. The ${\mathsf{\sigma }}_{\mathrm{T}}$ values for experimental and simulation results are 0.2114 and 0.2759, respectively.

4. Optimization Design of NSESTS Based on Wind Field Analysis

Both the experimental and simulaton results presented in the section “Analysis of Experimental and Simulation Results” show that the temperature uniformity within the environmental simulation test system is poor, which is due to insufficient air convection inside the environmental simulation system. To improve the temperature uniformity, more air convection should be involved. This study employs a fan to provide airflow to enhance convective heat transfer in the environmental simulation test system.

As shown in the section “Analysis of Experimental and Simulation Results”, the simulated temperature distribution with only natural convection shows great consistence with the experimental temperature distribution, implying the feasibility of the simulation method. In this section, the simulation method is still used to evaluate the temperature distribution after wind involved in the environment simulation test system.

4.1. Simulation of Temperature Field in NSESTS with Wind Involved

This paper investigates the following two configurations: (1) downwind configuration, where the fan is located in the front of the chamber and faces backward to the back of the chamber; and (2) upwind configuration, where the fan is located in the back of the chamber and faces forward to the gate of the chamber.

In the simulation, the system pressure is set to be 0.6 kPa, and the temperature at the center of the pressure vessel (location of temperature probe T07) is set to be −49 °C. The fan outlet is assigned a velocity inlet boundary condition, and the boundary condition for velocity magnitude is 5 m/s. The other parts of the fan are set as adiabatic fixed no-slip walls. This problem involves low-velocity flow in an enclosed space, so an incompressible steady pressure-based solver is used for computation. The simple algorithm, a pressure–velocity coupling method, is utilized to indirectly satisfy the mass conservation equation. This method solves the momentum equation and pressure correction equation iteratively, adjusting the velocity field gradually to meet the continuity condition, and is suitable for low-velocity flow scenarios. Convergence is deemed to be achieved when the velocity residual falls below 0.001. Figure 8 illustrates the fan configuration for the near space downwind simulation and the physical arrangement of the fan when tested. The fan is modeled as a cylindrical body with a radius of 15 cm, whose central axis coincides with the central axis of the environmental simulation test system. It blows wind in the direction from the gate side to the rear side of the test system and is located 350 mm away from the gate of the test system.

Figure 9 displays the temperature distribution contour plots and spatial flow field plots on the centrally symmetric planes z = 0 and x = 0, respectively. The simulation results visually demonstrate the convective process and temperature distribution throughout the entire space. The white rectangle in Figure 9a,c is the longitudinal section of the fan model. The heat sink reduces the ambient temperature through thermal radiation, while the heating cage raises it via radiant heating. Their interaction results in higher temperatures inside and near the heating cage and lower temperatures around the heat sink. The introduction of the wind field enhances convective heat transfer, generating multiple vortices within the test system and creating a more complex spatial flow field, leading to better spatial temperature uniformity.

Table 6. Comparison of simulation value before and after introducing the fan in the environmental simulation test system (gate side).

No.	Temperature Probe	Simulation Value before Introducing the Fan (°C)	Simulation Value after Introducing the Fan (°C)
1	T05	−44.6	−45.4
2	T07	−49.0	−49.0
3	T08	−49.3	−47.7
4	T09	−52.8	−55.8
5	T11	−21.4	−30.1
6	T12	−38.3	−41.3
10	T17	−62.3	−59.4
11	T24	−35.0	−38.5
12	T26	−49.4	−50.4
13	T30	−70.1	−64.8

and Figure 10 present a comparative analysis of simulation results before and after the involvement of the fan near the gate side of the environmental simulation test system. The simulation results confirm that after involving the wind, the non-uniformity coefficient reduces to 0.2012, reflecting a 27.1% decrease versus the simulation without fan (=0.2759). This demonstrates that after introducing wind near the gate of the environmental simulation test system, the temperature distribution exhibits significantly reduced dispersion and markedly improved uniformity compared with the simulation without additional wind.

In this paper, we also consider another configuration of fan placement and airflow direction: the near space upwind simulation, which is defined as having the fan located near the rear end of the test system, directing airflow toward the gate side.

The environmental condition configuration is the same with that of the near space upwind simulation. Figure 11 illustrates the fan configuration for the near space upwind simulation and the physical arrangement of the fan when tested. The fan is also modeled as a cylindrical body with a radius of 15 cm, whose central axis coincides with the central axis of the environmental simulation test system. It blows wind with the direction from the rear side to the gate side of the test system and is located 350 mm from the rear side of the test system.

Figure 12 displays the temperature distribution contour plots and spatial flow field plots on the centrally symmetric planes z = 0 and x = 0, respectively. The simulation results visually demonstrate that the introduction of the wind field enhances convective heat transfer, generating multiple vortices within the test system and creating a more complex spatial flow field, leading to better spatial temperature uniformity, which brings the similiar improvement as with the near space downwind situation.

Table 7. Comparison of simulation value before and after introducing the fan in the environmental simulation test system (rear side).

No.	Temperature Probe	Simulation Value Before Introducing the Fan (°C)	Simulation Value After Introducing the Fan (°C)
1	T05	−44.6	−46.8
2	T07	−49.0	−49.0
3	T08	−49.3	−48.8
4	T09	−52.8	−47.4
5	T11	−21.4	−30.7
6	T12	−38.3	−37.9
7	T17	−62.3	−58.5
8	T24	−35.0	−36.6
9	T26	−49.4	−48.2
10	T30	−70.1	−65.2

and Figure 13 present a comparative analysis of simulation results between the fan involved near the rear side of the environmental simulation test system and the TRX-2000(A) running without the fan. Numerical results confirm that after involving the upwind simulation, the non-uniformity coefficient reduces to 0.2055, reflecting a 25.5% decrease versus the simulation without fan ($=0.2759$). This demonstrates that after introducing wind near the rear section of the environmental simulation test system, the temperature distribution exhibits significantly reduced dispersion and markedly improved uniformity compared to the simulation without wind, which brings the similiar improvement as with the near space downwind situation.

From the near space downwind and upwind simulations, we can conclude that after introducing the wind, the non-uniformity coefficient of the temperature field within the environmental simulation system decreases significantly and the temperature uniformity markedly improves compared with the simulation without wind.

4.2. Experimental Validation of Temperature Field Simulation for Near Space Wind Field Environment

In Section 4.1, the introduction of airflow into the near space temperature field simulation was implemented to improve the temperature distribution within the environmental simulation test system, resulting in a more uniform internal temperature distribution. Simultaneously, by accounting for the wind field conditions in near space, the near space wind field environment was considered to better replicate the actual near space conditions.

To experimentally validate the simulation results from Section 4.1, this section incorporates airflow into the environmental simulation test system through the use of a fan.

In the near space downwind simulation, the fan was positioned on the central axis of the environmental simulation test system, a 350 mm distance from the gate side, blowing toward the rear section of the system. The fan is powered by an external power source. Figure 8c shows the physical arrangement of the fan installed near the door.

The environmental simulation test system was set with the pressure target to be 0.6 kPa and the temperature target to be −49 °C at the central location (where temperature probe T07 is positioned). After the temperature and pressure reached their set value, the fan was activated. The airflow brought by the fan enhanced convection within the system. Temperature readings for all probes are recorded after the fan was running for 1.5 h, 2 h, and 2.5 h.

Table 8. Experimental temperature value for all probes inside the chamber (fan is positioned at the gate side).

No.	Temperature Probe	Experimental Value Before Introducing the Fan (°C)	Experimental Value After Introducing the Continuous Fan Running for 1.5 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2.5 h (°C)
1	T05	−48.6	−55.8	−54.8	−54.5
2	T07	−49.0	−49.1	−49.3	−49.0
3	T08	−50.5	−48.7	−48.3	−48.3
4	T09	−61.6	−62.9	−63.1	−63.2
5	T11	−30.3	−33.3	−32.8	−31.8
6	T12	−38.2	−37.9	−37.6	−37.7
7	T17	−56.4	−51.8	−52.1	−51.8
8	T24	−38.1	−38.4	−38.0	−37.8
9	T26	−52.7	−49.7	−49.2	−49.0
10	T30	−64.4	−61.3	−61.5	−61.4

presents the experimental temperature value recorded by each probe in the environmental simulation test system before fan activation and after the fan was running for 1.5 h, 2 h, and 2.5 h from the gate side.

Table 9. Non-uniformity coefficient of experimental data for different continuous fan running (gate side) duration.

Fan Running Duration	Experimental Value Before Introducing the Fan (°C)	Experimental Value After Introducing the Continuous Fan Running for 1.5 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2.5 h (°C)
Non-uniformity coefficient	0.2094	0.1920	0.1961	0.2001

shows the non-uniformity coefficient of the environment simulation test system after the fan (located near the gate side) was running for 1.5 h, 2 h, and 2.5 h and the experimental values without the fan running. Non-uniformity coefficient decreases from 0.2094 when there is no fan to 0.1920 after the fan was running for 1.5 h, which is an 8.3% decrease for non-uniformity improvement. This indicates that after introducing the fan near the gate side, it shows a more concentrated temperature distribution and improved temperature uniformity within the system. Furthermore, the temperature uniformity across all probes stabilized after 1.5 h of fan operation. The observed trend aligns with the simulation results presented in Section 4.1, reaffirming that applying the numerical simulation method to analyze the temperature field distribution characteristics in the environmental simulation test system described in this study is appropriate.

With respect to the near space upwind simulation, we also validated the results through experiment. We also incorporated airflow into the environmental simulation test system through the use of a fan.

The fan is positioned on the central axis of the environmental simulation test system, a 350 mm distance from the rear section, blowing toward the gate side of the system. Figure 11c shows the physical arrangement of the fan installed near the rear section.

The environmental simulation test system was set with the pressure target to be 0.6 kPa and the temperature target to be −49 °C at the central location (where temperature probe T07 is positioned). After the temperature and pressure reached their setting values, the fan was activated. The airflow brought by the fan enhanced convection within the system. Temperature data for all probes are recorded after the fan was running for 1.5 h, 2 h, and 2.5 h.

Table 10. Experimental temperature value for all probes inside the chamber.

No.	Temperature Probe	Experimental Value Before Introducing the Fan (°C)	Experimental Value After Introducing the Continuous Fan Running for 1.5 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2.5 h (°C)
1	T05	−46.6	−50.0	−49.8	−49.7
2	T07	−49.0	−49.1	−49.0	−49.1
3	T08	−52.1	−53.9	−53.7	−53.6
4	T09	−61.6	−55.1	−55	−55.0
5	T11	−28.4	−30.7	−30.8	−30.9
6	T12	−37.4	−32.5	−32.5	−32.4
7	T17	−55.4	−53.7	−53.7	−53.7
8	T24	−38.5	−37.5	−37.5	−37.5
9	T26	−50.7	−54.7	−54.7	−54.5
10	T30	−64.3	−64.0	−64.4	−64.3

presents the experimental temperature values recorded by each probe in the environmental simulation test system before fan activation and after the fan was running for 1.5 h, 2 h, and 2.5 h at the gate side.

Table 11. Non-uniformity coefficient of experimental data for different continuous fan running (rear side) duration.

Fan Running Duration	Experimental Value Before Introducing the Fan (°C)	Experimental Value After Introducing the Continuous Fan Running for 1.5 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2 h (°C)	Experimental Value After Introducing the Continuous Fan Running for 2.5 h (°C)
Non-uniformity coefficient	0.2184	0.2153	0.2158	0.2153

shows the non-uniformity coefficient of the environment simulation test system after the fan (located near the gate side) was running for 1.5 h, 2 h, and 2.5 h and the experimental values without the fan running. Non-uniformity coefficient decreases from 0.2184 when there is no fan to 0.2153 after the fan was running for 1.5 h, which is a 1.4% decrease for non-uniformity improvement. This indicates that after introducing the fan near the gate side, it shows a more concentrated temperature distribution and improved temperature uniformity within the system. Furthermore, the temperature uniformity across all probes stabilized after 1.5 h of fan operation. The observed trend aligns with the simulation results presented in Section 4.1, reaffirming that applying the numerical simulation method to analyze the temperature field distribution characteristics in the environmental simulation test system described in this study is appropriate.

Through the experiment validation for the near space downwind and upwind simulation, we can conclude that after introducing the fan, the non-uniformity coefficient of the temperature field within the environmental simulation system decreases and the temperature uniformity improves compared to the TRX-2000(A) NSESTS running without wind.

5. Conclusions

This paper investigates the temperature distribution inside the TRX-2000(A) NSESTS and the effect of wind on temperature uniformity through the experimental method and the simulation method. The key findings are as follows:

• Comparison between the experimental and the simulation results show that these two results are very close to each other, validating the feasibility of using the simulation method to study the temperature distribution inside the NSESTS.
• Analysis of the effect of the wind on temperature uniformity through simulations show that the non-uniformity coefficient will be reduced from 0.2757 to 0.2012 (by 27.1%) in the case of downwind and to 0.2055 (by 25.5%) in the case of upwind. Then, the simulation result was validated by experiment. The result of this research indicates that the temperature uniformity can be greatly improved through installment of additional fans inside the NSESTS. Optimization of position and direction of these fans will be investigated in the future.