Design and Optimization of Thermal Vacuum Sensor Test System Based on Thermoelectric Cooling

Abstract

The performance of critical components in a sensor testing system may be compromised in a thermal vacuum environment as a result of the impact of extreme temperatures. Moreover, the precision of the angle measurement may be influenced by the thermal deformation effect. This paper presents a simulated analysis of the temperature regulation impact of the thermoelectric cooler (TEC) and outlines the design and optimization process of a sensor test chamber that can function within a consistent temperature range. The mathematical model of TEC is utilized to suggest a design choice, taking into account the aforementioned model, in a temperature-controlled environment with thermal vacuum circumstances. Moreover, the orthogonal test method is employed in combination with the FloEFD finite element analysis to validate the effectiveness of temperature control. In addition, the parameters of the radiation radiator are tuned and designed. Therefore, the temperature range difference inside the test system decreased by 20%. The thermoelectric temperature control system’s steady-state model is investigated using the PSpice simulation, based on the equivalent circuit theory. The discovered conclusions establish a theoretical foundation for improving the efficiency of temperature regulation. The design concepts presented in this work, particularly the optimization technique for radiation radiators in aerospace test equipment using thermoelectric cooling temperature control research and development, hold promise for practical implementation.

1. Introduction

A review of the historical record reveals that there have been more instances of significant accidents resulting from insufficient ground performance testing of space sensors than expected. In 2010, Russia had the unfortunate event of three GLONASS-M satellites crashing into the Pacific Ocean. This incident occurred as a result of an excessive amount of fuel generated by a malfunctioning fuel level sensor. As a consequence, the rocket was overweight and did not have enough velocity at the end of its trajectory, which hindered its proper entry into orbit and resulted in around USD 132 million in losses [1]. On 11 October 2018, a Russian Soyuz rocket experienced a launch failure as a result of a broken and deformed sensor that occurred during the construction process at the launch site. Consequently, there was an abnormality in the detachment of the strap-on booster, resulting in a collision with the fuel tank [2]. The tragedy had a substantial effect on the secure functioning of the International Space Station (ISS). Therefore, the progress of more efficient sensors is a crucial element in the advancement of the space industry [3,4,5]. Studying ground test equipment for space sensors is also crucial for the space industry’s advancement and the proper functioning of spacecraft in orbit [6,7,8].

Thermoelectric cooling is a type of refrigeration technology that relies on a thermoelectric cooler(TEC) as its main component, utilizing the Peltier effect of the TEC to realize the conversion of electrical energy into temperature difference. Thermoelectric technology has significantly progressed in practical applications since its inception in the 19th century [9,10]. Thermoelectric cooling, when compared to other major refrigeration technologies, has several advantages. These include the absence of pollution, no mechanical moving parts, precise temperature control, no need for a working fluid, a compact system size, and other benefits [11,12,13,14,15,16]. As a result, it has found extensive use in various fields such as biology, electronic devices, infrared lasers, aerospace, and others [17,18,19,20,21,22].

The heat sink, positioned on both sides of the heat exchange interface with the external environment, functions as a vital component in a thermoelectric refrigeration system, serving as the heat changer. This assembly typically comprises components such as heat sinks, fans, and liquid cooling devices. The efficiency of a thermoelectric cooling system is significantly influenced by the heat sink assembly. This assembly typically comprises components such as heat dissipation fins, fans, liquid cooling devices, and so on. The current study largely concentrates on augmenting the heat transfer capacity of the fins to enhance the system’s ability to dissipate heat and achieve more accurate temperature management. In their study, Ding et al. [23] created a new type of fin called Gilt Swallows and used numerical simulation to confirm its effectiveness in enhancing the heat transfer performance. The results showed that the Gilt Swallows fin outperformed both the wing and cross-wing fins, with an increase of around 6.3% and 6.9%, respectively. In addition, the analysis found the best structural parameters for various Reynolds numbers. Al Adel et al. [24] investigated the influence of several geometric parameters of fins on the efficiency of solar stills. They used a Computational Fluid Dynamics (CFD) model that has been experimentally tested to determine the ideal ranges for these parameters. Wang et al. [25] developed a new kind of perforated tree-shaped fin and showed that it can efficiently decrease the amount of fin material used and improve the heat exchange rate of the system. They achieved this by simulating the fin using the RSM method. Furthermore, Yiqi Zhao et al. [26] introduced three variations of microstructured fins (V-shaped ribs, curved ribs, and wave-shaped ribs) with the aim of increasing the radiative heat flow rate per unit mass of the fins. This was accomplished through the optimization of the microstructure of the fin surface and the adjustment of microstructural parameters, such as height and top angle. The simulation findings show that the rate of radiative heat flow per unit mass of the heat sink system, namely in the area where the fins have been tuned, has improved by 61%.

In this study, we designed and modeled a temperature-controlled angle sensor test system based on thermoelectric cooling (as shown in Figure 1) using finite element numerical simulation. Initially, a PSpice model was created to represent the thermoelectric cooling system. This model was used to examine how various control conditions affect the performance of thermoelectric cooling. Subsequently, the efficacy of temperature regulation in the system was examined with the utilization of FloEFD finite element analysis software (https://plm.sw.siemens.com/en-US/simcenter/fluids-thermal-simulation/floefd/, accessed on 11 July 2024). Afterward, the influence of the thickness, spacing, and section shape of the inner radiator fin on the uniformity of the internal fixture was assessed using orthogonal tests. Ultimately, the precision of the finite element simulation model was confirmed via numerical computations.

2. Simulation Methods

This section presents a brief overview of the theoretical model of the simulation, the boundary conditions, and the design and optimization concepts of the structure.

2.1. Mathematical Modeling of TEC

By the principles of thermoelectric refrigeration and the law of conservation of energy, the thermal power at the cooling side (Q_c) and the thermal power at the heating side (Q_h) are equal to the superposition of the Peltier, Fourier, and Joule heat, respectively [27]. The following equations are used to calculate thermal power:

$$Q_c={\alpha }_{m}I{T}_c-\frac{1}{2}{I}^2{R}_m-K_m(T_h-T_c)$$

(1)

$$N=UI={\alpha }_{m}I(T_h-T_c)+I^2{R}_m$$

(2)

$$U={\alpha }_m(T_h-T_c)+I{R}_m$$

(3)

$$Q_h=N+Q_c={\alpha }_{m}I{T}_h+\frac{1}{2}{I}^{2}R-K_m(T_h-T_c)$$

(4)

$$\epsilon =\frac{Q_c}{N}$$

(5)

where I, U, α_m, T_c, T_h, R_m, K_m, N, and ε represent the input current, input voltage, Seebeck coefficient of TEC, temperature at the cooling side, temperature at the heating side, TEC internal resistance, TEC thermal conductivity, input power, and refrigeration efficiency.

The derivation of Equations (1) and (5) regarding the current indicates that when I = α_m/R_m × T_c, the cooling side of the thermal power reaches its maximum value. Additionally, when $I=\frac{{\alpha }_m}{R_m(\sqrt{1+\frac{Z}{2}(T_c+T_h)})-1)}(T_h-T_c)$, the cooling efficiency is to achieve the maximum value (in the formula, Z is defined as the coefficient of merit, which equals α_m²/(R_m × K_m). It can be demonstrated that the thermal efficiency of the heating side (ε_h = Q/N) is always greater than one. If $M=\sqrt{1+\frac{1}{2}(T_h+T_c)Z}$, then the above equations can be simplified as:

$$I_{op}=\frac{{\alpha }_m}{R_m(M-1)}(T_h-T_c)$$

(6)

$${\epsilon }_{max}=\frac{T_c(M-\frac{T_h}{T_c})}{(T_h-T_c)(M+1)}$$

(7)

$$U_{op}=\frac{{\alpha }_{m}M(T_h-T_c)}{M-1}$$

(8)

$$N_{op}={(\frac{{\alpha }_m(T_h-T_c)}{M-1})}^2\frac{M}{R_m}$$

(9)

$$Q_{cop}=\frac{{{\alpha }_m}^{2}M(M{T}_c-T_h)(T_h-T_c)}{R_m(M+1){(M-1)}^2}$$

(10)

$$Q_{hop}=\frac{{{\alpha }_m}^{2}M(M{T}_h-T_c)(T_h-T_c)}{R_m(M+1){(M-1)}^2}$$

(11)

where I_op represents the input current, U_op represents the input voltage, N_op represents the input electric power, Q_hop represents the heating side thermal power, and Q_cop represents the cooling side thermal power, respectively, when the refrigeration efficiency takes the maximum value.

The parameters typically provided by manufacturers of thermoelectric coolers include the maximum thermal power at the cooling side (Q_cmax) at the specified temperature of the heating side, the maximum temperature difference between the two sides (ΔT_max), and the maximum current (I_max) and voltage (V_max) at which the maximum temperature difference can be generated. As the temperature difference between the two sides of the thermoelectric cooler increases, the cooling side’s thermal power decreases. Therefore, the maximum thermal power of the cooling side (Q_copt) refers to the thermal power when the temperature difference between the two sides is 0. At this time, the current flowing through the thermoelectric cooler is I_opt, and the applied voltage is V_max. The following expression can be derived from Equations (6)–(11).

$$V_{max}={\alpha }_m{T}_h$$

(12)

$$I_{max}=\frac{\sqrt{1+2T_{h}Z}-1}{{\alpha }_m}{K}_m$$

(13)

$$\Delta T_{max}=T_h+\frac{(1-\sqrt{1+2T_{h}Z})}{Z}$$

(14)

The formula mentioned above enables the determination of the Seebeck coefficient (α_m), internal resistance (R_m), and thermal conductivity (K_m) of the TEC by utilizing the data provided by the manufacturer.

$${\alpha }_m=\frac{V_{max}}{T_h}$$

(15)

$$R_m=\frac{V_{max}(T_h-\Delta T_{max})}{I_{max}{T}_h}$$

(16)

$$K_m=\frac{V_{max}{I}_{max}(T_h-\Delta T_{max})}{2T_h\Delta T_{max}}$$

(17)

2.2. Equivalent Circuit of TEC

The heat flow and temperature field distribution of a heat conductor are analogous to the current and electric field distribution laws of a conductor; its equivalent relationship is shown in

Table 1. Table of equivalent relationships between thermal and electrical.

Thermal Quantities	Units	Analogous Electrical Quantities	Units
Heat	W	Current	A
Temperature	K	Voltage	V
Thermal resistance	K/W	Resistance	Ω
Heat capacity	J/K	Capacity	F
Absolute zero temperature	0 K	Ground	0 V

:

To address heat transfer issues, an accurate temperature calculation can be achieved through the implementation of an equivalent circuit scheme [28]. The equivalent circuit model (as shown in Figure 2) can be used to create a corresponding simulation model. The TEC-TEG synergistic cooling system proposed by Ning et al. [29] demonstrates that the discrepancy between the currents flowing through the TEC in the experiments and the SPICE models is less than 4.8% on average.

2.3. Thermal Deformation and Goniometric Errors

Figure 3 illustrates the impact of the thermal deformation of the fixture within the test system on the goniometric error.

In this illustration, the BC section indicates that the drive shaft extends to the box part, while the AB section indicates the internal fixture part. In the event of heating or cooling conditions, the temperature T₃ represents the ambient temperature, T₂ represents the bearing temperature, T₁ represents the motor temperature, and the shaft radius deformation results from thermal expansion as l₁. The values φ₁ and φ₂ represent the rotation angle of sections AB and BC of the drive shaft, respectively. The parameter β is defined as the AB section and the horizontal line of the angle of deviation. Assuming that the coefficient of thermal expansion of the internal fixture is identical, the following equations can be derived:

$$\tan {\phi }_1=\tan {\phi }_2\times \cos \beta$$

(18)

$$\beta =\arctan \frac{l_1}{l_{AB}}$$

(19)

$$l_1=\alpha R(T_2-T_1)$$

(20)

where temperature range ε = T₂ – T₁, and the angular measurement error Δφ_AB of the AB section can be expressed as follows:

$$\Delta {\phi }_{AB}=\arctan (\frac{\tan {\phi }_2(1-\cos \beta )}{1+{\tan }^2{\phi }_2\cos \beta })$$

(21)

where α represents the coefficient of thermal expansion, and R represents the radial length of the internal fixture.

2.4. Numerical System and Boundary Conditions

In the insulation layer, only heat conduction occurs, and the temperature of the heat sinks on both sides can be utilized as boundary conditions in a mathematical model, represented by the equation $t{|}_{x=0}=T_{os},t{|}_{x=\delta }=T_{is}$. By focusing on the insulation layer as the object of study, it becomes possible to gain a deeper understanding of thermoelectric coolers’ performance in refrigeration and heating applications. Furthermore, the steady state of the insulation layer can be regarded as a stable one-dimensional flat-wall heat conduction process, as described by the following equations:

$$\frac{d}{dx}(\lambda \frac{dt}{dx})+\dot{Q}=0$$

(22)

$$\frac{d^{2}t}{d{x}^2}=0$$

(23)

The above equations can be integrated twice to obtain the general solution. This solution can then be used in conjunction with Fourier’s law to determine the heat flow of the insulation layer (Q₁) and the heat flow (q) density for:

$$Q_1=-\lambda S\frac{dt}{dx}=\lambda S\frac{T_{os}-T_{is}}{\delta }$$

(24)

$$q=-\lambda \frac{dt}{dx}=\lambda \frac{T_{os}-T_{is}}{\delta }$$

(25)

where S, λ, δ, and t represent the surface area of one side of the insulation layer along the thickness direction, the thermal conductivity of polyurethane of the insulation layer material, thickness of the insulation layer along the x-direction, and temperature distribution of the insulation layer along the x-direction.

To streamline the computational module and exclude irrelevant variables, the following fundamental assumptions were made for the numerical simulations in this study:

(1)

The values of temperature and heat flux are constant at both the control and non-control sides.

(2)

The values of thermal conductivity and emissivity of all materials are assumed to be constant.

(3)

The physical parameters of the thermoelectric cooler are all constants and do not vary with the external environment.

(4)

To improve the thermal emissivity, the surfaces of all devices are oxidized and blackened.

(5)

The initial temperature is 25 °C, and the ambient temperatures during heating and cooling conditions are −75 °C and 90 °C, respectively.

(6)

The simulation excludes the fluid domain. The transient analysis time is 200,000 s with a time step of 1000 s. The thermoelectric cooler starts operating when the internal fixture temperature reaches its boundary value.

3. Simulation Model

This section presents the conceptual framework and methodology used in constructing the simulation model.

3.1. TEC Selection

Selected a named ETX3-12-F2-3030-11-EP-W18 high-temperature special TEC. Its parameters are shown in

Table 2. ETX3-12-F2-3030-11-EP-W18 type thermoelectric cooler parameter.

${\mathit{V}}_{\mathbf{max}}(\mathbf{V})$	${\mathit{I}}_{\mathbf{max}}\left(\mathbf{A}\right)$	$\mathbf{\Delta }{\mathit{T}}_{\mathbf{max}}\left(\mathbf{K}\right)$	${\mathit{Q}}_{\mathit{c}\mathbf{max}}\left(\mathbf{W}\right)$
16.6	3.2	83	31.4

.

Mathematical modeling of the TEC allows for the calculation of its characteristic parameters, and the result is obtained as α_m = 0.0514 (V/K), R_m = 3.85 (Ω), K_m = 0.237 (W/K), and Z = 0.0029 (K⁻¹).

A study by Kominek et al. [30] found that the radiator temperature should generally be 20 °C higher than the ambient temperature. Based on the temperature requirements outlined in the design index, it can be assumed that the temperature of the outer radiator and the inner radiator during a specific refrigeration transient are T_h and T_c, respectively. According to Equation (6), the current (I_op) required to maximize the cooling efficiency at that temperature can be calculated. At this point, the refrigeration power is denoted as Q_uc. When considering the system under study, the total cooling power (Q_tc) should be greater than or equal to the sum of the radiation heat power from the external environment to the system as a whole (Q_f) and the internal heat generation of the system as a whole (Q_m), as described by the following equation:

$$Q_{tc}=n{Q}_{uc}\ge Q_m+Q_f$$

(26)

Following the radiation heat transfer formula [31], the required number of thermoelectric refrigeration modules (n) for refrigeration conditions can be determined by substituting the necessary data into Equation (26). In the heating condition, the total heating power (Q_th) should be greater than or equal to the difference between the overall radiation heat power (Q_f) from the external environment and the overall internal heat generation (Q_m). As the radiation heat power is proportional to the fourth power of its absolute temperature, the Q_f is smaller this time, while the Q_th is always greater than the Q_tc. Consequently, no further calculations are required.

3.2. Material Property Parameter Setting

The specific material properties of the main components were obtained from the FloEFD tool material library and literature [32], as illustrated in Table 3:

Table 3. Solid materials used in the simulation model and their physical parameters.

Material Name	Density (kg/m3)	Specific Heat Capacity (J/kg × K)	Thermal Conductivity (W/m × K)
Duralumin	2800	862	150
Bismuth telluride	7642	213	1
Polyimide	1300	1090	0.4
Steel616	7850	420	25
Polyurethane	1045	See Table 4	0.034

Table 3. Solid materials used in the simulation model and their physical parameters.

Material Name	Density (kg/m3)	Specific Heat Capacity (J/kg × K)	Thermal Conductivity (W/m × K)
Duralumin	2800	862	150
Bismuth telluride	7642	213	1
Polyimide	1300	1090	0.4
Steel616	7850	420	25
Polyurethane	1045	See Table 4	0.034

Table 4. Specific heat capacity of polyurethane versus temperature.

Temperature (K)	Specific Heat Capacity (J/kg × K)
150	720.5
200	1035.4
250	1320
300	1536.5

Table 4. Specific heat capacity of polyurethane versus temperature.

Temperature (K)	Specific Heat Capacity (J/kg × K)
150	720.5
200	1035.4
250	1320
300	1536.5

3.3. PSpice Model

The PSpice (https://www.pspice.com/, accessed on 11 July 2024) is electronic circuit simulation software that offers high levels of accuracy in its simulations. It supports a range of analysis techniques, including transient analysis, AC analysis, parameter scanning, Monte Carlo analysis, and others. Additionally, it can be used for both analog and digital circuit simulations.

According to the mathematical and equivalent circuit model of the TEC, the steady-state model of the PSpice simulation is established as illustrated in Figure 4. In this figure, V3, I7, and I9 represent the ambient temperature, input current, and the cooling power required by the load at the control side.

3.4. Finite Element Network Division

FloEFD is a comprehensive, general-purpose, synchronous CFD software program that offers several advantages over traditional CFD software:

(1)

It can reduce the time required to export and import three-dimensional models by up to 65%. This is because it has been designed to integrate seamlessly with traditional three-dimensional design software, such as SolidWorks. This integration allows users to perform simulations and analyses directly within the three-dimensional drawings, eliminating the need to convert them.

(2)

The meshing technique employed in FloEFD relies on the immersed boundary approach and rectangular adaptive mesh technology, hence obviating the necessity to take into account mesh quality. The simulation configures the global mesh to level 3. The computational domain has dimensions of 1001 mm (length), 1011 mm (width), and 1001 mm (height), and the dimensions of the assembly are 300 mm (length), 300 mm (width) 554 mm (height). A 3D mesh was applied to the model with a base size of 28 mm, resulting in a total of 601,517 elements. The utilization of local mesh refinement is implemented to enhance the convergence of intricate elements, with a refinement level of 4. Figure 5 illustrates the finalized model.

4. Results and Discussion

4.1. PSpice Simulation

This work presents a simulated analysis of the temperature regulation impact of the thermoelectric cooler (TEC) under a stable condition by using the PSpice software, as depicted in Figure 6. The research demonstrates that irrespective of the change in load power (I9), there is an optimal current operating point that guarantees the control side achieves the minimum temperature. The minimum temperature is attained when the load power is at its minimum. However, when the load power increases, the minimum temperature that can be achieved at the refrigeration side also increases, and the current operating point also increases accordingly. Furthermore, the input voltage and current of the TEC demonstrate a linear correlation with varying load power. This correlation can be represented by a function derived through a linear fitting technique, resulting in the curve equations presented in

Table 5. Specific heat capacity of polyurethane versus temperature.

Load Power (W)	Characteristic Equations	Coefficient of Determination
0	U = 5.48I + 1.47	0.995
5	U = 5.56I + 0.52	0.994
10	U = 5.61I − 0.34	0.997
15	U = 5.63I − 1.08	0.995
20	U = 5.64I − 1.82	0.995

. The average value of these equations is expressed in Equation (25). Figure 6c demonstrates that for an ambient temperature (V3) of 363 K, the refrigeration power is directly proportional to the temperature of the refrigeration side when considering a certain input current. This serves as the basis for our computations involving a system in a stable and unchanging condition. Figure 6d illustrates the presence of an ideal input current operating point that maximizes refrigeration efficiency under identical conditions. The aforementioned laws offer a theoretical direction for the thermoelectric cooler to get more accurate temperature regulation.

$$U=5.58I-0.25$$

(27)

4.2. FloEFD Simulation

4.2.1. Steady-State Analysis

Following the modeling of the thermoelectric cooler in FloEFD in Section 3.1, the maximum refrigeration efficiency current was then utilized to perform refrigeration, as indicated by the PSpice simulation results, and the temperature field cloud of the section of the converged test system (Figure 7a) with the heat flux of the thermal insulation layer (Figure 7b) can be obtained by transient simulation.

As illustrated in Figure 7a, the mean temperatures of the external radiator, internal radiator temperature, and inside test environment are 125.27 °C, 60.87 °C, and 63.76 °C, respectively. Moreover, the temperature distribution in the thermal insulation layer shows a descending gradient from the left side to the right side, suggesting that the effectiveness of temperature management has been enhanced. Moreover, the accuracy of the simulation data can be confirmed by comparing the numerical results with the computational results presented in the following section.

4.2.2. Transient Analysis

Figure 8a,b show that the thermoelectric cooling system effectively controls the temperature of the internal fixture in both high- and low-temperature test environments. When the system is refrigerating, the internal fixture temperature stabilizes at around 61.8 °C after 144,000 s. Under specific heating conditions, the temperature stabilizes at around −27.4 °C after 100,000 s. The temperature of the top cover has remained quite stable, allowing the sensor under test to be evaluated under the prescribed conditions.

Figure 9a,b depict the temperature distribution of the internal fixture during the near-steady conditions, showing the variation in their temperature ranges at high and low operating temperatures. The symmetrical design of the test system leads to a more even dispersion of temperature along the x-axis of the internal fixture. The temperature distribution shows a more consistent pattern from the motor to the bracket flange, with a diminishing gradient. The non-uniform distribution of temperature will lead to a decrease in the angular precision of the sensor. In order to evaluate the influence of this element, it is important to take into account the range of temperatures. Furthermore, it is necessary to carry out further optimization of this element for analysis. Figure 9c,d illustrate that at the near steady state, and the values of ε_c and ε_h before optimization are 1.28 °C and 3.22 °C, respectively.

4.3. Orthogonal Test Optimization

Several studies have demonstrated that the unique fin shape and aspect ratios of radiation radiators have different impacts on the efficiency of heat dissipation and the uniformity of temperature in the system [33,34]. The design of the orthogonal test table is partitioned into four levels for each group, encompassing a total of three optimization factors. The objective is to investigate and optimize the temperature range factor. The inner radiator was designed with four different fin sections, as shown in Figure 10 (where the H represents the height of the radiator, b represents the height of the radiator base and t represents the thickness of the fin). The temperature range of the internal fixture was employed as the assessment indices for refrigeration (ε_c) and heating conditions (ε_h). The outcomes of the orthogonal experiments are displayed in

Table 6. The result of the orthogonal experiment.

Experimental No	Factor A Shape	Factor B Space (mm)	Factor C Thickness (mm)	${\mathit{\epsilon }}_{\mathit{c}}$ (°C)	${\mathit{\epsilon }}_{\mathit{h}}$ (°C)
1	Rectangle	9	5	1.46	3.20
2	Rectangle	10	6	1.44	3.22
3	Rectangle	11	7	1.37	3.20
4	Rectangle	12	8	1.18	3.23
5	Isosceles trapezoid	9	6	1.24	3.19
6	Isosceles trapezoid	10	5	1.43	3.22
7	Isosceles trapezoid	11	8	1.22	3.21
8	Isosceles trapezoid	12	7	1.43	3.24
9	Hackle	9	7	1.12	3.22
10	Hackle	10	8	1.22	3.22
11	Hackle	11	5	1.36	3.20
12	Hackle	12	6	1.44	3.26
13	Slot	9	8	1.13	3.22
14	Slot	10	7	1.35	3.20
15	Slot	11	6	1.35	3.22
16	Slot	12	5	1.37	3.23

.

The simulation findings indicate that the variance of ε_c among different parameter groups is more noticeable, while the variation of ε_h is less apparent. This is because, while heating, the ambient temperature decreases, leading to a decrease in radiated heat power. Therefore, only the findings obtained under refrigerated circumstances are studied in terms of extreme deviation and comprehensive balance to determine the effects of different factor levels on the optimization index. The average answers of the evaluation indicators were computed and the findings are displayed in

Table 7. Mean response table for temperature uniformity under refrigeration condition.

Level	Fin Shape	Fin Spacing	Fin Thickness
1	1.362	1.238	1.405
2	1.330	1.360	1.367
3	1.285	1.325	1.317
4	1.300	1.355	1.188
Delta	0.077	0.122	0.218
Rank	3	2	1

and Figure 11.

Table 7 illustrates the effects of the three types of fin parameters on ε_c. In order of predominance, the fin parameters should be ranked as follows: fin thickness > fin spacing > fin type. Figure 11 demonstrates that the impact of fin shape and fin spacing on ε_c undergoes a turning process. However, the influence of εc reduces significantly as the fin thickness increases. The most significant influence on ε_c is observed when the fin type is rectangular, the fin spacing is 10 mm, and the fin thickness is 5 mm. In contrast, the smallest effect on ε_c is shown when the fin type is hackle, the fin spacing is 9 mm, and the fin thickness is 8 mm.

The contour plots (Figure 12) demonstrate the impact of the interaction among the three parameters on the ε_c index. To minimize ε_c, it is necessary to maximize the fin thickness. To address this situation, it is advisable to choose a fin type that has a hackle or slot cross-section and to minimize the fin gap as much as feasible. The data shown in Table 6 show that the most effective configuration for achieving temperature uniformity in both scenarios is a hackle fin cross-section with a fin spacing of 9 mm and a fin thickness of 7 mm. At these settings, the ε_c value is 1.12.

5. Numerical Verification

The results obtained using the methodology described in Section 2.4 are compared with the simulation results, and the findings of this comparison are reported in

Table 8. Comparison of simulation results with theoretical calculations.

Name	External Radiator Temperature	Internal Radiator Temperature	Insulation Layer Heat Flux
Simulation Value	398 K	334 K	11.12 W
Theoretical Value	383 K	333 K	11.73 W
Error	3.9%	0.3%	5.2%

. The table shows that the difference between the theoretical and simulated values is less than 5.2%, indicating a high level of confidence in the correctness of the numerical and simulation calculations.

6. Conclusions

In this paper, we design and optimize an angle test system for angle sensors in thermal vacuum environments based on thermoelectric cooling. The paper proposes a method for selecting thermoelectric coolers based on the maximum refrigeration efficiency formula, which is then subjected to verification through the use of PSpice and FloEFD simulations. The simulation results demonstrate that the use of the equivalent circuit simulation model can provide a reliable basis for the actual control of the system in a thermal vacuum environment with a high temperature of 90 °C and a low temperature of −75 °C; by applying the current that maximizes the cooling efficiency of the thermoelectric cooler, the test system is able to operate the sensor under test at the specified temperature conditions while effectively controlling the internal fixture temperature at 61.8 °C and −27.4 °C. The discrepancy between the theoretical calculations and the simulation results is within 5.2%.

Furthermore, the study examines how the section shape, thickness, and spacing of fins in the internal radiator affect the temperature range of the internal fixture. Through an orthogonal test, it is discovered that the temperature range under heating conditions (ε_h) remains relatively unchanged due to the low radiant heat power in the low-temperature environment. However, the temperature range under high-temperature conditions (ε_c) shows a more significant variation. The fin thickness has the most significant impact on the variation in temperature range, whereas the fin section shape has the least significant impact. Furthermore, a set of ideal parameters was chosen, leading to a 12.5% improvement in the uniformity of the optimized temperature (ε_c). Ultimately, the results of this study offer valuable knowledge for developing a testing method for angle sensors in a thermal vacuum setting. This will contribute to guaranteeing the stability and precision of the test results.