Image Analysis of the Influence of the Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) on the Mars Environmental Dynamics Analyzer at Extremely Low Reynolds Number

Abstract

This study analyzes the influence of the Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) on the Mars Environmental Dynamics Analyzer (MEDA) station located on board the Perseverance rover (Mars 2020). A novel visualization methodology was developed using a hydrodynamic towing tank and 3D-printed models created through additive manufacturing. This experimental approach, not previously applied in this context, proved to be a cost-effective alternative for studying thermal interactions while providing accurate preliminary insights into the behavior of thermal plumes under Martian-like conditions. Key factors such as the extremely low Reynolds number, an increasing temperature of the model, and atmospheric properties similar to those in Mars were incorporated. The findings suggest that the MMRTG’s thermal plume may significantly influence MEDA’s performance due to the plume’s height and its interaction with the surrounding environment.

1. Introduction

The Mars Environmental Dynamics Analyzer (MEDA) is an instrumental suite installed on NASA’s Perseverance rover designed to monitor the Martian atmosphere (Sebastián-Martínez et al. (2021) [1]). The proper operation and accuracy of MEDA are essential for understanding the planet’s meteorological conditions and planning future missions. However, the presence of the Multi-Mission Radioisotope Thermoelectric Generator (MMRTG), which provides the rover with power, introduces potential thermal perturbations that could affect the accuracy of the MEDA measurements.

Previous studies, such as those conducted by Lorenz et al. (2020 and 2014) [2,3] and Hess et al. (1977) [4], have already highlighted the potential thermal impact of the MMRTG on nearby instruments. These perturbations, ranging from 2 to 5 K depending on wind conditions and the relative positions of the instruments, could influence the data collected, particularly under low wind speeds where thermal convection plays a significant role.

It is worth noting that Reynolds numbers around ${10}^3$, considered extremely low in this study, are a consequence of the unique Martian atmospheric conditions. On Earth, such values are typically encountered in highly viscous or low-velocity flows, like microfluidic systems, whereas on Mars, they represent mesoscale flows due to the reduced atmospheric density and the thin atmosphere. As emphasized in studies like Sun and Boyd (2004) [5] and Srinath and Mittal (2009) [6], such low Reynolds numbers present unique aerodynamic challenges, with laminar wakes and minimal turbulence dominating the flow dynamics.

In addition, it will be interesting to analyze the geometry of the flows in the affected area, as demonstrated in studies by Rodríguez-Sevillano et al. (2022) [7], Bardera-Mora et al. (2024) [8], and Viúdez-Moreiras et al. (2019) [9]. Understanding the flow patterns around the MEDA station and its interactions with the MMRTG is crucial, as the localized geometry can enhance or mitigate the influence of thermal convection on the instruments. The local flow structures generated by the interaction between the MMRTG, the MEDA station, and the rover geometry exhibit significant sensitivity to low Reynolds number effects, where viscous forces dominate over inertial forces, altering convection and flow separation patterns.

A detailed analysis of these flow structures may provide further insights into potential disturbances and improve the accuracy of environmental measurements on Mars. Furthermore, a recent study by Bardera-Mora et al. (2024) [10] demonstrates that the complex flow phenomena in the Martian atmosphere, particularly the importance of the Grashof number, can introduce additional uncertainties in measurements obtained from the MEDA system, which is located at the front of the Perseverance rover. Their research emphasizes the feasibility of conducting experiments on Earth that simulate Martian atmospheric conditions without the need for a vacuum chamber, allowing for more streamlined methodologies.

This paper aims to provide a preliminary analysis of the influence of the MMRTG on the MEDA station using a novel experimental method. A hydrodynamic towing tank and ink flows are employed to simulate the thermal emission patterns, representing a more economical approach while maintaining accuracy in reproducing Mars-like scenarios. To further validate this method, the experimental results are compared with established Reynolds and Grashof numbers for Mars, as well as with known thermal behaviors studied in prior research (Lorenz et al. (2020) [2]). Additionally, this study investigates wind velocities below 1 m/s, a critical range for thermal interactions between the MMRTG and MEDA. The typical wind speeds on Mars, between 1 and 3 m/s, represent a low range with significant thermal disturbances, especially when the wind passes directly over the MMRTG. The analysis concludes by discussing the potential implications of these findings on the environmental measurements collected by MEDA, emphasizing the need to take these thermal influences into account in future analyses.

2. Materials and Methods

2.1. Materials and Apparatus

The tests were conducted in the hydrodynamic towing tank at the Department of Aircraft and Space Vehicles (ETSI Aeronáutica y del Espacio), Universidad Politécnica de Madrid. The towing tank dimensions are 3000 × 420 × 720 mm, with an effective working width of 335 mm, ensuring sufficient space for controlled fluid dynamics experiments. The towing tank was equipped with an engine-driven trolley, which allowed for adjustable speeds based on the experiment’s requirements. This setup enabled precise control over the experimental conditions and ensured accurate simulation of different scenarios. The trolley can reach frequencies of 0 to 155 Hz, as will be discussed in the Section 2.3.

It is worth noting that the blockage ratio of the prototype adheres to standard guidelines for wind tunnels, ensuring reliable experimental results. Additionally, the height of the model can reach approximately 12 cm when the angle of attack is adjusted, allowing for flexibility in studying varying flow and thermal interaction scenarios.

The ink delivery system used a Mariotte bottle, 3.2 mm diameter pipes, and various valves. This allowed us to keep the pressure constant along the circuit and ensure a homogeneous distribution of the fluid. The experiment employed a mixture of 28% cosmetic colorings (environmental friendly) and 72% water, selected to minimize contamination during the tests.

To simulate MMRTG heating, a variable-temperature resistor was installed, capable of adjusting between 291 and 307 K (18–34 °C). A thermostat was integrated to regulate the resistor’s temperature, and an additional thermostat was used to control both the cavity and atmospheric temperatures. After preliminary tests, a stable temperature of 301 K (28 °C) was selected to maintain consistency during the experiments. It should also be emphasized that the water temperature in the towing tank remained constant at approximately 289 K (16 °C) throughout the tests. This setup ensured precise temperature control during the experiment, allowing for accurate simulation of thermal conditions similar to those expected on Mars.

2.2. MMRTG and Mast Models

The engineering design software CATIA V5 [11] was chosen to create the models, with dimensions obtained from the Mars 2020 mission website (JPL-MARS 2020 Perseverance [12]) and relevant articles of the MEDA station (Sebastián-Martínez et al. (2021) [1]). These models, MMRTG and Mast (Figure 1), were fabricated using additive manufacturing on an Ultimaker 3 Extended 3D printer. A 1:10 scale was selected due to the hydrodynamic towing tank constraints. Standard grey PLA material was used.

The symmetry of the original MMRTG model was used to simplify the structure of the study model. In addition, a shell similar to the real model was manufactured, which also allowed us to tilt the MMRTG by 30°, equal to the actual tilt of the vehicle. This setup enabled a more accurate analysis of the thermal plume propagation generated by the MMRTG. Additionally, the MMRTG model included a watertight cavity to house resistors and ink pipes, with twelve 1 mm orifices specifically designed for the ink flow experiments (Figure 2).

Regarding the mast, the model was simplified to include only the MEDA station modules of the mast booms and the TIRS (Thermal Infrared Sensor). Although the design of the mast head was drafted, it was excluded from the study as it would not initially impact the analysis of the MEDA station’s effects. In addition, this allowed for zenithal photos to be taken.

Both models were mounted on a methacrylate artificial floor reinforced with a stiffening device to prevent vibrations. The floor dimensions ensured a 200 mm offset between the MMRTG and the mast, scaling the real 2 m separation (Figure 3).

2.3. Hypotheses and Environmental Control Calculations

The primary hypothesis of this study is based on the assumption of extremely low Reynolds numbers in the Martian atmosphere. This is attributed to its very low density atmosphere, coupled with the relatively low velocities of atmospheric flows and the high viscosity of the air. The Martian atmosphere is much thinner than Earth’s, resulting in a small numerator in the Reynolds number formula (Equation (1)). This classification aligns with prior studies, which highlight the unique atmospheric dynamics on Mars. For instance, Spiga (2011) [13] discusses how mesoscale meteorological phenomena, including boundary layer convection, are significantly influenced by the low atmospheric density. Similarly, Martínez et al. (2017) [14] review the near-surface Martian climate and emphasize the impact of the atmosphere’s thinness on fluid dynamics and heat transfer processes. Additionally, Alam et al. (2008) [15] and Sun and Boyd (2004) [5] emphasize that at Reynolds numbers below ${10}^4$, viscous forces dominate, leading to laminar wakes and weak turbulent structures. Aprovitola et al. (2020) [16] and Koning (2010) [17] further analyzed aerodynamic performance at low Reynolds numbers relevant to Martian conditions, where thin atmospheres and reduced gravity amplify viscous effects and inhibit boundary layer separation recovery. These references support the designation of Reynolds numbers on the order of ${10}^3$ as extremely low in the Martian context, as follows:

(1)$\mathrm{Re}={\displaystyle \frac{\rho ·v·L}{\mu }}$

where

• $\rho$ is the fluid density (kg/m³);

• v is the characteristic velocity of the fluid flow (m/s);

• L is the characteristic length (m), which is a relevant dimension of the object or flow system;

• $\mu$ is the dynamic viscosity of the fluid (Pa·s or N·s/m²), which measures the fluid’s resistance to shear.

The low atmospheric pressure and resulting slow wind speeds contribute to a small value for Reynolds number. This means that viscous forces dominate over inertial forces in Martian atmospheric flows, significantly influencing the aerodynamics of any objects interacting with the Martian air.

Based on this hypothesis, the speeds of the carriage and ink injection must be adjusted to achieve Reynolds numbers around ${10}^3$. Moreover, the ink injection must be matched to the carriage speed. However, this alignment was not feasible for very high flow rates (Table 1), as will be discussed in the results.

The forward velocity of the trolley can be calculated using the following mathematical relation:

(2)$u_t=\left(0.022·F+0.0565\right)·{\displaystyle \frac{1}{60}}$

where

• $u_t$ is the trolley’s velocity [m/s];

• F is the frequency of the engine [Hz].

It is essential to calculate the influence of the engine on the Martian atmosphere to determine the importance of conducting laboratory studies with thermal variation and to verify their proper execution. To this end, the Grashof number was calculated to study the impact of the engine on the atmosphere and, subsequently, on the MEDA station. This dimensionless number, which represents the ratio of buoyancy forces to viscous forces, is critical for understanding flow behavior in low Reynolds number environments, such as Mars. Previous studies have indicated that the Grashof number significantly affects thermal convection processes under Martian conditions (Bardera-Mora et al., 2024) [10], influencing how heat from the MMRTG propagates through the atmosphere. Temperature data from the MMRTG obtained from previous studies by Lorenz et al. (2020) [2] were used, corresponding to 414 K (141 °C).

(3)$\mathrm{Gr}={\displaystyle \frac{g·\beta ·\Delta T·L^3}{{\nu }^2}}\sim 8.544·{10}^6$

where

• g is the Martian gravity, with a value of 3.72 m/s²;

• $\beta$ is the thermal expansion coefficient, with a value of 0.0033 1/K;

• $\nu$ is the kinematic viscosity, calculated as the ratio of dynamic viscosity to density, with a value of 0.0005 m²/s;

• L is the characteristic length, set at 1 m for the MMRTG (real dimension);

• The temperature difference ($\Delta T$) is based on the ambient temperature of the Martian atmosphere, which is 240 K (−33 °C).

These values were obtained from the mission’s database (MARS CLIMATE DATABASE v6.1 [18]). The data obtained were intended to correspond to a standard scenario rather than to dust storms or any other undesired conditions.

Furthermore, the interplay between the Reynolds number and the Grashof number, expressed as ${\displaystyle \frac{Gr}{R{e}^2}}$, delineates the convection regime: when ${\displaystyle \frac{Gr}{R{e}^2}}\ll 1$, the system is dominated by forced convection; when ${\displaystyle \frac{Gr}{R{e}^2}}\sim 1$, a mixed regime occurs; and when ${\displaystyle \frac{Gr}{R{e}^2}}\gg 1$, free convection prevails (Bardera-Mora et al., 2024) [10]. This relationship allows for a comprehensive understanding of the thermal dynamics and flow patterns around the MMRTG in Martian conditions.

3. Results and Discussion

3.1. Scenario Verification

To verify the correct performance of the tests conducted, an analysis of the isolated MMRTG model was performed both dynamically and statically.

3.1.1. Thermal Scenario

As demonstrated in the Section 2.3, previous calculations of the thermal scenario for the actual MMRTG on Mars suggest that the Grashof number should be on the order of ${10}^6$ to ensure proper test conditions. To achieve this, the laminar flow of the ink emitted from the model was measured under the condition of active resistance at 301 K (28 °C) (Table 2), using this value as the characteristic length in the calculation (Equation (3)). It was calculated that for flow rates greater 0.3 mL/s, the Grashof number reached the order of ${10}^6$ (Table 3), confirming the correct execution of the thermal tests.

As shown in Figure 4 and Table 2, it is important to highlight that there is a significant increase in the length of the laminar flow as the internal temperature of the model rises. This phenomenon occurs because while the temperature of the ink emission increases, its buoyancy relative to the water also increases due to a considerable decrease in its density. As it is shown in Table 4, this also leads to an increase in the height of the plume, which could potentially affect the MEDA station. It is also important to note that the increase in the height of the laminar flow appears to converge for flow rates greater than 0.7 mL/s. Specifically, when comparing the 289 K (16 °C) and 301 K (28 °C) scenarios, the increase remains consistent at 70% for both the 0.7 mL/s and 1.4 mL/s flow cases.

Although the experimental conditions feature considerably lower temperatures than those expected in the actual MMRTG environment, this discrepancy does not invalidate this study. Even with the laboratory temperature around 28 °C significantly lower than the MMRTG’s operating temperatures, the key to ensuring the experiment’s relevance lies in maintaining the similarity of dimensionless parameters. For example, the Grashof number, exposed in this section, which relates buoyancy forces to viscous forces, remains of a similar order of magnitude. This guarantees that buoyancy-driven effects and the resulting radiative and convective patterns observed at lower temperatures are representative of those that would occur under higher temperature conditions.

3.1.2. Dynamic Scenario

The dynamic scenario was also verified by measuring the experimental Reynolds number. Based on the hypotheses already mentioned, the length of the laminar ink flow was measured for a scenario of non-active resistance at 289 K (16 °C). As illustrated in Table 5, it can be observed that, regardless of the flow rate used in the experiment, Reynolds numbers on the order of ${10}^3$ were obtained, thus verifying the correct implementation and validation of the hypotheses in the dynamic scenario.

3.2. Wind Analysis

The influence of the wind is considered in our study, as shown in Hess et al. (1977) [4] and Lorenz et al. (2013) [3]. When the wind flow velocity is below or close to 0.5 m/s and it directly crosses the RTG (Radioisotope Thermoelectric Generator), a thermal perturbation of between 2 and 5 K can occur. It is important to emphasize that the influence will always be greater for wind flows that hit the RTG directly, heading towards the mast. Given a separation of approximately 2 m between the MMRTG and the mast, and an MMRTG width of approximately 1 m, there will be a potential influence from surrounding elements over an angle of 30°. Considering that the MMRTG has a width of approximately 0.7 m and the distance between it and the mast is around 2 m, the total influence will be 9.9° rather than 30°. Therefore, the probability that the wind direction vector directly passes through the MMRTG is calculated as ${\displaystyle \frac{30}{360}}={\displaystyle \frac{1}{12}}\approx 8.33\%$.

Although, as seen in the mission’s database, typical wind speeds on the Martian surface range between 1 and 3 m/s, the objective of this study was to preliminarily verify previous studies on the potential influence of the MMRTG on the measurement instruments mounted on the mast (Lorenz et al., 2013, 2020 [2,3]). Therefore, the wind speeds selected for this study were below 1 m/s, while respecting the constraints and hypotheses based on the Reynolds number. It is important to emphasize that, as mentioned earlier, these lower wind speeds will show a clear thermal perturbation in the surrounding temperatures.

Studies conducted by the Department of Aircraft and Space Vehicles at the Technical University of Madrid (School of Aeronautics and Space Engineering) and the National Institute for Aerospace Technology (INTA) (Rodríguez-Sevillano et al., 2022 [7]) indicate that wind flow incidents on the MEDA station generate two types of flow regions around the mast and booms. These two regions are separated by the upstream and downstream sides of the mast. Around the booms, the mast induces a strong influence, creating a large region of disturbed flow, generally characterized by detached flow. This factor can significantly increase the influence of thermal convection on the station and alter measurements if this influencing factor is not considered. The increase in convective influence arises from the enhanced turbulence generated by the wind flow interacting with the mast and booms. This turbulence facilitates greater mixing of air layers, leading to a more effective heat transfer between the atmosphere and the measurement instruments. Additionally, the separation of the flow can create localized areas where warm air accumulates, further affecting the thermal dynamics around the station.

3.3. MMRTG Emissivity Analysis

The MMRTG is estimated to emit ∼ 2 kW of thermal power (Harmon et al., 2008 [19]), which will be transferred through both radiative and convective processes. A straightforward method to model this heat transfer is to parameterize the MMRTG as a cylinder, as suggested by Lorenz et al. [3]. In our study, the MMRTG was modeled as a cylinder with a diameter of 0.66 m and a length of 1 m. According to Mohan et al. (1997) [20], it is important to highlight that there are models for studying heat emissivity that take cooling systems into account. These models are based on the use of the Nusselt number (Piedrahita et al. [21]).

3.3.1. Convective Heat Transfer

(4)$\dot{Q_{ac}}=h_{amb}{A}_b(T_b-T_a)\sim 1250.7\mathrm{W}$

(5)$h_{amb}=0.32R{e}^{0.675}P{r}^{0.4}({\displaystyle \frac{k}{l_e}})\sim 3.47(\mathrm{W}/{\mathrm{m}}^2·\mathrm{K})$

where

• $\dot{Q_{ac}}$: convective heat transfer rate (W);

• $h_{amb}$: convective heat transfer; coefficient of the ambient air (W/m²·K).

• $A_b$: surface area of the body (m²);

• $T_b$: temperature of the body (K);

• $T_a$: ambient temperature (K);

• $h_{amb}$: convective heat transfer coefficient of the ambient air (W/m²·K);

• $Re$: Reynolds number (dimensionless), a measure of the flow regime;

• $Pr$: Prandtl number (dimensionless), a measure of the relative thickness of the thermal and velocity boundary layers;

• k: thermal conductivity of the fluid (W/m·K);

• $l_e$: characteristic length (m).

To calculate the Prandtl number, we can initially simplify by assuming that the Martian atmosphere consists solely of C${\mathrm{O}}_2$. However, based on actual atmospheric data, the specific heat capacity $c_p$ will be set to $7.4\times {10}^2$ J/kg·K. For the thermal conductivity k, we will use a simplified value of 0.0163 W/m·K.

3.3.2. Radiative Heat Transfer

(6)$\dot{Q_{ar}}={\epsilon }_{amb}\sigma A_b(T_b^4-T_a^4)\sim 1348\mathrm{W}$

where:

• $\dot{Q_{ar}}$: radiative heat transfer rate (W);

• ${\epsilon }_{amb}$: emissivity of the ambient environment (dimensionless);

• $\sigma$: Stefan–Boltzmann constant ($5.67\times {10}^{-8}$ W/m²·${\mathrm{K}}^4$);

• $A_b$: surface area of the body (m²);

• $T_b$: temperature of the body (K);

• $T_a$: ambient temperature (K).

The materials used in the construction of the MMRTG are metal alloys known for their high resistance to heat and radiation. To simplify this study, the radiative emissivity of the block surface will be approximated to that of cast iron, ${\epsilon }_{amb}=0.44$.

These data will help us estimate the potential influence of the MMRTG’s thermal emission on the MEDA station. Davy et al. (2010) [22] and Lorenz et al. (2020) [3] show that the sensed plume perturbation was approximately $\sim 2\mathrm{K}$, while the temperature of Lander’s deck was about 15 K higher than that in the region without thermal disturbance. These values could have a significant impact on the measurements if they are not properly accounted for.

In the Martian environment, the extremely low atmospheric density substantially limits the effectiveness of convective heat transfer. As a result, heat exchange between the MMRTG and the MEDA station positioned approximately 2 meters apart is dominated by radiative processes. The scarcity of atmospheric particles capable of transporting thermal energy makes convection negligible. Consequently, even though convective effects could theoretically occur at such a distance, their contribution is minimal compared with the radiative component. This observation aligns with prior studies, such as Spiga (2011) [13], which highlight the significant influence of the Martian atmosphere’s low density on limiting convective dynamics and emphasizing radiative processes as the dominant mechanism of heat transfer. This justifies focusing the analysis and modeling efforts predominantly on radiative heat exchange.

3.4. Plume Height Analysis

3.4.1. Buoyancy Flux

Before presenting the experimental results, preliminary calculations were made to estimate the height of the thermal emission plume in the Martian atmosphere. To calculate this, it is first necessary to determine the buoyancy flux, $F_B$, and then the height, $h_B$.

(7)$F_b={\displaystyle \frac{g·Q_E}{\pi ·{\rho }_a·c_p·T_a}}$

(8)$h_B={\left({\displaystyle \frac{3}{2{\beta }^2}}\right)}^{1/3}{\displaystyle \frac{F_B^{1/3}{x}^{2/3}}{u}}$

where

• g: gravitational acceleration = 3.72 (${\mathrm{m}/\mathrm{s}}^2$);

• ${\rho }_a$: atmospheric density = 0.02 (${\mathrm{kg}/\mathrm{m}}^3$);

• $c_p$: specific heat at constant pressure = 7.4 ($\mathrm{J}/(\mathrm{kg}·\mathrm{K})$);

• $\beta$: thermal expansion coefficient $\sim 0.6$ ($1/\mathrm{K}$);

• Q: heat emitted by the MMRTG $\sim 2$ (${\mathrm{W}/\mathrm{m}}^2$);

• $T_a$: ambient temperature (K);

• x: downstreams coordinate x (m);

• u: wind speed (m/s).

As can be observed in Table 6, the height of the thermal plume decreases as wind speed increases. Therefore, it will be particularly interesting to analyze lower wind speeds, as they are more likely to generate a significant influence on the mast. This is due to the fact that at lower wind speeds, the plume remains more concentrated and rises higher, increasing the potential for thermal interaction with the MEDA station’s sensors.

3.4.2. Dynamic Tests Influence MMRTG/Mast

The influence of the thermal emission plume was analyzed for a scenario with a non-active resistor at 289 K (16 °C) and for an active resistor at 301 K (28 °C). Flow rates of 0.3, 0.7, and 1.4 mL/s, corresponding to wind speeds approximately equivalent to 1 m/s, were examined (Table 1). A representative case from these experiments is illustrated in Figure 5 and Figure 6. It is important to note that the booms on the mast were positioned approximately 100 mm above the ground, and the total surface area of the complete model was 0.027 ${\mathrm{m}}^2$. It can be observed from the data (Table 4 and Figure 5 and Figure 6) that the plume height increases with an increasing flow rate and temperature. Furthermore, this increase is more pronounced in the non-active resistance scenario at 289 K (16 °C).

Regarding the comparison between the active and non-active resistor cases, a slight increase in plume height is observed for the same flow rates. This can be attributed to the fact that the increased temperature of the ink flow enhances its buoyancy relative to the water in the towing tank.

Thus, it can be preliminarily determined that since the height of the plume is equal to or greater than the height of the MEDA station for flow rates exceeding 0.75 mL/s (wind speeds of ∼1 m/s), regardless of the model temperature, the influence on the station is possible and a factor to be considered.

3.5. Thermal Emission Plume Affected Area

Thanks to the images captured from the zenithal plane, a study of the affected area of the thermal emission plume and its exit angle over the rover’s deck was carried out. As shown in the following table (Table 7), the deck of the rover is completely affected. By analyzing the exit angles of the emission plume, we can estimate the potential impact of the MMRTG on its surroundings in a 2D plane. A representative case from these experiments is illustrated in Figure 7 and Figure 8.

4. Conclusions

The objectives of this study focused on analyzing the potential influence of the MMRTG electrical generation module on the MEDA environmental station, which has already been studied in other articles (Lorenz et al., 2020 [2]). Additionally, this study aimed to validate the obtained results through an experimental method not previously applied to this case, the hydrodynamic towing tank analysis. It should be noted that this method is more cost-effective, and preliminary results are accurate, yielding realistic simulations of the study scenarios, as shown by the Grashof number (Table 3) and Reynolds number (Table 5) results.

First, the experimental Grashof number closely resembles the calculated values for a realistic scenario of the rover on Mars, with values on the order of ${10}^6$. This initial validation supports the thermal simulation in our study, despite the fact that the experimental temperatures were much lower than the actual conditions on Mars. However, it is important to note that this method does not allow for a fully realistic analysis of the phenomena that may occur at high temperatures. For example, in high-temperature conditions, the buoyancy effects could be significantly more pronounced, leading to more complex convection patterns that are not accurately captured in our experimental setup. Additionally, the thermal expansion of materials and changes in fluid properties, such as viscosity or specific heat, could alter the heat transfer dynamics, which this preliminary study cannot fully replicate.

On the other hand, the experimental Reynolds numbers (Table 5) match the hypothesized Reynolds number on the order of ${10}^3$, which has also been found in numerous studies (Rodríguez-Sevillano et al., 2022 [7]). This verification supports the dynamic scenario of the study. Similarly, Bardera-Mora et al. (2019) [23] analyzed the impact of the Mars 2020 rover on wind measurements under similar constraints, acknowledging the challenges of replicating higher Reynolds number conditions experimentally. These constraints align with our current limitations, as the experiments were conducted at wind speeds below 1 m/s, focusing on conditions where the MMRTG influence is most likely to occur.

Moreover, the most critical scenario was considered, where the air flows directly across the MMRTG. Analyzing the plume height, it can be observed that it exceeds 100% for flow rates above 0.7 mL/s (Table 4) (wind speed of 3.5 cm/s; Table 1), allowing us to preliminarily conclude a possible influence of the MMRTG on the MEDA station.

Some calculations by Lorenz et al. (2013) [3] and Hess et al. (1977) [4] suggest that this potential influence could result in a thermal perturbation of 2–5 K. It is also important to highlight that, as shown in Rodríguez-Sevillano et al. (2022) [7], wind flow incidents on the MEDA station generate two types of flow regions around the mast and booms. These regions are separated by the upstream and downstream sides of the mast. Around the booms, the mast induces a strong influence, creating a large region of disturbed flow, generally characterized by detached flow. As explained earlier, this can exacerbate convection phenomena in the area, increasing the potential influence.

In conclusion, a potential effect on the MEDA station from the MMRTG module has been observed through preliminary studies under extremely low Reynolds number conditions and wind speeds below 1 m/s. If not accounted for, this could affect environmental measurements on Mars. Furthermore, this study validates the use of a hydrodynamic towing tank and ink flows to simulate thermal emission flows as a valid methodology for preliminary studies, offering a lower cost and shorter experimental time compared with other methods found in the literature. Notably, this approach eliminates the need for a costly infrastructure, such as hydrodynamic channels with Laser Doppler Velocimetry systems, which typically require investments of approximately USD 200,000, while still providing valuable qualitative insights.

Author Contributions

Conceptualization, Á.A.R.-S., M.J.C.-C. and R.B.-M.; methodology, Á.A.R.-S., M.J.C.-C. and R.B.-M.; software, E.F.-R.; validation, Á.A.R.-S., M.J.C.-C., R.B.-M., J.C.M.-G. and E.B.-B.; formal analysis, Á.A.R.-S., M.J.C.-C., R.B.-M., J.C.M.-G., E.B.-B. and E.F.-R.; investigation, Á.A.R.-S., M.J.C.-C., R.B.-M., J.C.M.-G., E.B.-B. and E.F.-R.; resources, Á.A.R.-S. and M.J.C.-C.; data curation, Á.A.R.-S., M.J.C.-C. and E.F.-R.; writing—original draft preparation, E.F.-R.; writing—review and editing, Á.A.R.-S., M.J.C.-C., R.B.-M., J.C.M.-G., E.B.-B. and E.F.-R.; visualization, Á.A.R.-S., M.J.C.-C. and E.F.-R.; supervision, Á.A.R.-S., M.J.C.-C. and R.B.-M.; project administration, Á.A.R.-S., M.J.C.-C. and R.B.-M.; funding acquisition, Á.A.R.-S., M.J.C.-C. and R.B.-M. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. (left (Mast)) Modular mast design with mounting of the booms, TIRS, and rover head. (right (MMRTG)) Modular design of the MMRTG with shell and main module assembly.

Figure 2. MMRTG cavity (left) in addition to the resistor housing and the presence of the ink holes. MMRTG’s shell (right) with 30° angled brackets.

Figure 3. MMRTG and mast on the experimental floor: the 200 mm spacing between the mast and the MMRTG can be seen.

Figure 4. Comparison of laminar length fluxes (marked in a green line) for active and non-active resistor: (a) non-active resistor (289 K); (b) active resistor (301 K).

Figure 5. Side view flow rate 0.7 [mL/s]—dynamic mast/MMRTG—non-active resistor; in green and blue lines, the thermal plume near the mast and downstream is marked.

Figure 6. Side view flow rate 0.7 [mL/s]—dynamic mast/MMRTG active resistor; in green and blue lines, the thermal plume near the mast and downstream is marked.

Figure 7. Zenithal view exit angle flow rate 0.7 [mL/s]—dynamic mast/MMRTG-non-active resistor. Upper images (from 1 to 4) show the ink emission flow evolution; lower image details (green lines) the measurement of the exit angle.

Figure 8. Zenithal view exit angle flow rate 0.7 [mL/s]—dynamic mast/MMRTG active resistor. Upper images (from 1 to 4) show the ink emission flow evolution; lower image details (green lines) the measurement of the exit angle.

Table 1

Engine frequency for different flow rates r.

Ink Flow [mL/s]	Velocity [cm/s]	Engine Frequency (Trolley) [Hz]
0.3	1.5	39
0.7	3.5	93
1.4	6.7	180 1

¹ Maximum frequency of the trolley, 155 Hz. The frequency was adjusted from 180 Hz (exceed the maximum) to 155 Hz in the test.

Table 2

Thermal plume height for non-active (289 K) and active (301 K) resistor.

Ink Flow [mL/s]	Laminar Flow Height (289 K) [%] 1	Laminar Flow Height (301 K) [%] 1
0.3	47	88
0.7	72	145
1.4	120	198

¹ The % of height is measured with respect to the height of the fins, which corresponds in our study to 32 mm.

Table 3

Grashof number for active (301 K) resistor as a function of ink flow rate.

Ink Flow [mL/s]	Grashof Number (301 K) [$\times {10}^6$]
0.3	0.64
0.7	3.15
1.4	7.86

Table 4

Thermal plume height for non-active (289 K) and active (301 K) resistor.

Ink Flow [mL/s]	Plume Height (289 K) [%] 1	Plume Height (301 K) [%] 1
0.3	81	86
0.7	106	116
1.4	129	123

¹ The % of height is measured with respect to the height of the booms, which corresponds in our study to ∼ 100 mm.

Table 5

Experimental Reynolds number as a function of the ink flow rate.

Ink Flow [mL/s]	Reynold Number
0.3	1239
0.7	2817
1.4	5408

Table 6

Thermal plume height (mathematical calculations—real scenario).

Air Velocity [m/s]	Downstreams Coordinate x [m] 1	Plume Height [m]
0.3	2	7.4
0.5	2	4.5
1.0	2	2.2
2.0	2	1.1

¹ Real separation distance between mast and MMRTG (2 m). Note: An ambient temperature of 240 K has been chosen as for the previous heat flux calculations.

Table 7

Thermal plume affected area and exit angles for non-active (16 °C) and active (28 °C) resistor.

Temperatures [K]	Ink Flow [mL/s]	Exit Angle [°]	Affected Area [%] *
289	0.3	13	133
	0.7	7	115
	1.4	9	122
301	0.3	22	159
	0.7	14	137
	1.4	7	119

* The % of affected area is measured with respect to the experimental rover’s deck, which corresponds in our study to 0.027 ${\mathrm{m}}^2$.

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