ArticlePDF Available

Abstract and Figures

Flow visualization is necessary in fields such as engineering, since it allows us to know what is happening around the element being studied by means of a preliminary method, although it is relatively close to future research and computation methodology. The present project studies the interference at the anemometers of the Mars rover Perseverance, caused by the mast holding one of its cameras. After obtaining the model, manufactured by a 3D printer, it was placed inside a hydrodynamic towing tank, and red dye was added for a visual observation of the interference during the experiment. A comparison was made between the results achieved and those seen in a wind tunnel, realizing the high correlation they have. Finally, this paper promotes the use of the hydrodynamic towing tank in preliminary studies due to its low costs, considering the adequate comparison with other higher precision methodologies.
Content may be subject to copyright.
Appl. Mech. 2022, 3, 1385–1399. https://doi.org/10.3390/applmech3040079 www.mdpi.com/journal/applmech
Article
Flow Study on the Anemometers of the Perseverance Based on
Towing Tank Visualization
Ángel Antonio Rodríguez-Sevillano 1,*, María Jesús Casati-Calzada 1, Rafael Bardera-Mora 2,
Alejandro Feliz-Huidobro 1, Claudia Calle-González 1 and Jaime Fernández-Antón 1
1 Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid,
28040 Madrid, Spain
2 Experimental Aerodynamics Branch, Instituto Nacional de Técnica Aeroespacial (INTA), 28850 Torrejón de
Ardoz, Spain
* Correspondence: angel.rodriguez.sevillano@upm.es
Abstract: Flow visualization is necessary in fields such as engineering, since it allows us to know
what is happening around the element being studied by means of a preliminary method, although
it is relatively close to future research and computation methodology. The present project studies
the interference at the anemometers of the Mars rover Perseverance, caused by the mast holding one
of its cameras. After obtaining the model, manufactured by a 3D printer, it was placed inside a
hydrodynamic towing tank, and red dye was added for a visual observation of the interference
during the experiment. A comparison was made between the results achieved and those seen in a
wind tunnel, realizing the high correlation they have. Finally, this paper promotes the use of the
hydrodynamic towing tank in preliminary studies due to its low costs, considering the adequate
comparison with other higher precision methodologies.
Keywords: flow visualization; Perseverance; ultra-low Reynolds number; towing tank
1. Introduction
Visualization can be defined as the necessary technique to create an image, video,
etc., with the main purpose being to send a message. The first tests were carried out in a
high Reynolds number tunnel to study changes in aerodynamic characteristics by modi-
fying the airfoil of a sailplane (simulating the presence of insects) or the Reynolds number
itself [1]. A few years later, there was interest in optimizing the lift-to-drag ratio at lower
Reynolds numbers to attempt to understand the behavior of the wings during the soaring
maneuver of some species of birds [2]. It was not until a decade after that the scientific
community became interested in the ultra-low Reynolds number experiments [3]. The
flight environment of the insects was studied, attempting to build a man-made aircraft
that could work under the same conditions. That same author went into more detail by
studying micro air vehicles at ultra-low Reynold numbers, developing and testing appro-
priate rotors for those conditions [4]. Thanks to this knowledge, it was possible to try to
understand the flow behavior with Reynolds numbers between 400 and 1200, where the
model was validated by comparing the solutions obtained with the ones achieved by
Kunz [5]. To fully understand the micro air vehicles, tests were performed on flat-plate
airfoils with Reynolds numbers between 1 and 200 [6]. Having studied the low and ultra-
low Reynolds number spectrum, researchers tried to visualize the effect that the number
had on the turbulence downstream of an airfoil [7,8], or the effect it had on the laminar
separation bubble at the leading edge of an airfoil [9]. Others preferred to study the aero-
dynamics of some birds and insects, such as a dragonfly at Re below 8000 [10], or an owl
[11], due to their interest in micro air vehicles with fixed wings. Having studied the be-
havior of aerodynamic structures (such as airfoils), there was interest in knowing what
Citation: Rodríguez-Sevillano, Á.A.;
Casati-Calzada, M.J.; Bardera-Mora,
R.; Feliz-Huidobro, A.;
Calle-González, C.;
Fernández-Antón, J. Flow Study on
the Anemometers of the Perseverance
Based on Towing Tank
Visualization. Appl. Mech. 2022, 3,
1385–1398. https://doi.org/10.3390/
applmech3040079
Received: 31 October 2022
Accepted: 5 December 2022
Published: 8 December 2022
Publisher’s Note: MDPI stays neu-
tral with regard to jurisdictional
claims in published maps and institu-
tional affiliations.
Copyright: © 2022 by the authors. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (http://crea-
tivecommons.org/licenses/by/4.0/).
Appl. Mech. 2022, 3 1386
behavior the flow displays on bluff bodies at low Reynolds numbers [12]. It is also inter-
esting because this study was placed in the same hydrodynamic towing tank as in this
project.
Similarly, to the previous field of study, an interest in knowing the similarities be-
tween Mars and Earth appeared. The reason for this is a desire to look for new places to
obtain raw materials and even in the future to live. To achieve this, a study of the Martian
atmospheric boundary layer was carried out [13]. This study suggested the need to take
new measurements, which could constrain the models so that the next missions would
know the requirements. Following that path, the Rover Environmental Monitoring Station
(REMS) was taken to Mars [14]. Its main purpose was to collect more data concerning the
thermal environment, ultraviolet radiation, and water cycling. With these data, it could
be possible to have more precision during the landing maneuver or by calculating the
perturbations the lander may produce on its final approach, no matter the wind speed
[15].
It is at this point where both paths (the low Reynolds number study and the Mars
study) converge. Researchers are improving both the design and the performance of rov-
ers, beginning with the Sojourner, and currently with the Mars 2020 Rover (known as
Perseverance). For the latter, numerous studies were carried out. One such report was the
study of the flow around the vehicle, showing how the atmosphere of Mars behaves and
the perturbations the rover may have as a result of that flow [16]. Linked to it, there was
an investigation about how well the anemometers worked in the presence of the men-
tioned perturbations, and the regions where each of them measures the best [17]. The next
step was to design space drones, because they allow access to places where the rover can-
not reach. There were studies of fixed-wing space drones in different solar system bodies
[18]. The rotary-wing space drone was selected for its first mission and was inside the
Mars 2020 rover. To achieve this, it was necessary to study the shape of the rotor, the
blades, and the airfoils [19–21].
The reason why flow visualization is important in this project is to find out if the
anemometers placed at the mast of the Mars rover Perseverance are recording proper data
concerning the wind speed on the surface of the mentioned planet. In order to understand
the results obtained during the experiment, it is important to comment on the necessary
knowledge of fluid mechanics and aerodynamics and how they are connected.
For valid results, the interference study must be done by simulating, as much as pos-
sible, the atmospheric conditions which the Perseverance would encounter. For that reason,
it was decided that the Reynolds number (Re) in the experiment must be the same as on
Mars. This number established the importance of the convective acceleration, compared
to the viscous stresses. That in mathematics terms is:
 = · ·
(1)
where is the density on the surface of Mars, U is the wind speed, Lc is the characteristic
length of the Perseverance, and µ is the dynamic viscosity of Mars.
For that study, the characteristics of the atmosphere of Mars must be known. Assum-
ing that the temperature on the surface of that planet is the mean value of [16], the density
used would have been the following:
= 1.9 × 10 
(2)
In addition, the dynamic viscosity at the surface of Mars can be calculated by apply-
ing its equation:
= 9.82 × 10 ·
(3)
where the sub-index “M” refers to Mars.
Appl. Mech. 2022, 3 1387
The maximum wind speed observed on the surface of Mars has been measured [22],
and its value is as follows:
27.7
(4)
The last parameter needed to obtain the Reynolds number at which the Mars rover
Perseverance works is the characteristic length. Since the aim of the project was to study
the interference of the anemometers, the diameter of one of them was selected as this
length [23]:
= 5 × 10
(5)
The Reynolds number looked for is the following:
 2680
(6)
To understand the experimental results obtained, it is necessary first to learn how the
flow will act around the tested element. Because both the mast and the anemometers have
a bluff shape, there will be von Karman vortex streets downstream. The shape of them
varies with the value of the Reynolds number [12] so, considering that the test will be
performed at very low Re (seen in Equation (6)), one approximation of the expected results
would be given in Figure 1.
Figure 1. Variation of the von Karman vortex streets as a function of the Reynolds number
Adapted from [12].
2. Materials and Methods
Once a brief introduction of the project is made, it is necessary to comment on the
manufacturing of the element to be tested, as well as the hydrodynamic towing tank
where the test is going to be placed.
The Mars rover Perseverance is designed with CATIA V5 (Dassault Systèmes,
https://www.3ds.com/products-services/catia/). Since the test wants to show preliminary
results of the interferences between the mast and the anemometers, the designed part only
covers that area. To make the results as realistic as possible, both the main components of
the camera held by the mast and the largest volume elements attached to it have been
added. The prototype was built based on [23] with a geometrical scale of 1:5. The result
can be seen in Figure 2.
Appl. Mech. 2022, 3 1388
Figure 2. Details of the Mars rover Perseverance. (a,b) Main dimensions of the real rover, in meters;
(c) left view of the final model of the mast and booms; (d) right view of the final model of the mast
and booms; (e) detailed view of the mast and booms, from [23].
This figure shows that, in addition to the above mentioned, a circular base was de-
signed, so that the entire item could be attached to the hydrodynamic towing tank. That
base has segments that are separated by 30 degrees, allowing for a higher precision when
testing it. Its function is to simulate the slip angle (that is, the projection of the incident
current velocity with the plane OXZ) at which the rover may be. A graphic definition of
the slip angle (β), and the axes criteria taken, can be seen in Figure 3.
Figure 3. (a) Isometric view of the Mars rover Perseverance with its coordinate axes OXYZ; (b) plan
view of the Mars rover Perseverance, and definition of the slip angle [16].
At the height where the anemometers are located, 6 holes were designed. They allow
the dye to flow downstream to appreciate the behavior in that region. The direction of
reference is selected as if the camera was pointing at the negative direction of the X axis
Appl. Mech. 2022, 3 1389
(shown in Figure 3). The tests are performed at slip angles of 60°, 90°, 210°, 240°, 270° and
300°.
Having fully defined the shape of the model, the manufacturing process of the model
is introduced. The fused deposition modelling technique (FDM) is the most common form
of additive manufacturing. It consists of the fusion of a filament that is subsequently ex-
truded through the nozzle, building the piece layer by layer. Many materials can be used
in the process; however, plastics such as PLA (Polylactic acid) or ABS (Acrylonitrile Buta-
diene Styrene) are frequently utilized. Software plays a key role as it controls the printing
process. It must be flexible, trustworthy, standardized, and efficient. To succeed in 3D
printing, a proper integration of software, hardware, and materials must be realized. To
do so, studies must be carried out to optimize results by changing the different parameters
that can be configured.
The 3D printing process begins with a concept and some requisites given to the piece.
Then, CAD (Computer-Aided Design) software is used to create a digital model that rep-
resents the accurate geometry of the piece (seen in Figure 2). Afterwards, this file is ex-
ported to a CAM (Computer-Aided Manufacturing) program where the printing param-
eters are set, and the model is laminated in as many layers as needed to reproduce the
structure. Finally, manufacturing and most of the post-processing take place. All of these
steps have a great influence on each other, so it is essential to take all of them into consid-
eration during the entire manufacturing process to ensure success.
In this case, the outside geometry of the piece is known and scaled to focus only on
the area of interest, which is the mast and anemometers of the Mars rover. However, to
conduct the experiment, thin channels are designed in the piece so that the ink used to
visualize the flow can be carried and ejected through the small holes on the surface of the
model. The diameter of these holes and the position of the conducts must be precisely
chosen for each 3D printing material and configuration.
The 3D printing parameters that have a stronger influence on the resulting dimen-
sions of the holes and conducts are the printing speed and layer height. Setting up a higher
speed and thicker layer height makes the manufacturing process faster; however, it can
also cause a loss in geometric accuracy and surface quality. A calibration probe is designed
to compare the different combinations of these two parameters. It consists of a rectangular
prism that contains 11 holes whose diameters vary between 8 mm and 0.8 mm. This prism
is printed 9 times, for printing speeds of 50, 60 and 70 mm/s and for layer heights of 0.1,
0.2 and 0.3 mm. The color code in calibration probes is detailed in Figure 4. Then the di-
ameters are measured, and the relative error between the given measures on the CAD file
and the real measures obtained is calculated.
Figure 4. Parameters and color code in calibration probes.
The results obtained show that a thicker layer height and/or a faster printing speed
reproduce less accurately the nominal measures given to the model; thus, a slower print-
ing speed and a thinner layer height display the smallest relative error. This can be seen
in Figure 5.
Appl. Mech. 2022, 3 1390
Figure 5. Relative error in holes as a function of the nominal diameter varying the printing speed.
However, an unexpected result has been derived by comparing the relative error us-
ing the same layer height and varying the printing speed. Figure 6 shows how for a small
value of the nominal diameter, the relative error will be small for the combinations of
parameters (printing speed=50 mm/s, layer height=0.1 mm); (printing speed=60 mm/s,
layer height=0.2 mm); and (printing speed=70 mm/s, layer height=0.3 mm). This can be
explained by the fact that the amount of extruded material (which depends on the set of
layer height set) must be in accordance with the speed at which it is placed on the piece.
Appl. Mech. 2022, 3 1391
Figure 6. Relative error in holes as a function of the nominal diameter for a fixed layer height, var-
ying three different printing speeds.
These results have been considered when manufacturing the model of the Mars rover
Perseverance, and both the printing speed and the layer height have been adapted to ensure
an accurate reproduction of the geometry of the piece.
The 3D printer used to manufacture the model is an Ultimaker 3 Extended. In addi-
tion, the filament selected was PLA. Due to the height of the mast being greater than the
enclosure available for printing, it will be sectioned. These sections have been selected to
waste as little support material as possible. Figure 7 shows the sections of the base and
anemometers into which it has been divided and the result once they have been glued. A
male–female union between the first two sections has been designed to avoid leaks and
blockages, allowing the mixture to flow exclusively through the proper conduit.
Appl. Mech. 2022, 3 1392
Figure 7. (a) Printed section between the bottom and the beginning of the prism attached to the
mast; (b) printed section between the beginning of the prism and the end of the ring, including
dimensions in cm; (c) result of the design and manufacture of the mast of the Mars rover Persever-
ance, including dimensions in cm.
The hydrodynamic towing tank is the element where the test takes place. The channel
is a parallelepiped formed by methacrylate panels, the dimensions of which are 3000 mm
× 410 mm × 410 mm. Figure 8 shows a simplified version of the hydrodynamic towing
tank [12].
Figure 8. Simplified version of the hydrodynamic towing tank [12], including dimensions in mm.
To appreciate the flow behavior downstream, a dye that can be observed in the water
must be selected. The formula will consist of mixing 400 mL of concentrated liquid red
dye for each liter of water. This causes the final solution to have approximately the same
density as the water. This mixture was placed on the top of the model car, inside a Mar-
iotte flask. The main advantage of the flask is that it ejects the mixture (for a single valve
position) at the same pressure regardless of the volume of mixture inside the flask.
The previous mix will exit directly from the mast. Due to the effect the interference
of the mast has on the anemometers, there are tests at the slip angles commented before.
The aim is to place the mixture outlet orifice as if it were the first point on the mast at
which the flow arrives. That allows observation of the two streamlines that arrive at the
two anemometers. Because of that, there is only one orifice that ejects the mixture per slip
angle.
1
0.8
1.2 2.1
4.7
2.7
2.1
10.6
19.6
6.3
3.3
6.7
(a) (b) (c)
Appl. Mech. 2022, 3 1393
The way the mixture moves from the Mariotte flask to the model tested is by rubber
hoses. Due to the fact that the diameter of the hose in the flask is much larger than in the
model, it will be necessary to splice the hoses until the desired diameter is achieved
The car model (including the Mariotte flask and the element to be tested) is moved
by an AC engine through the driving belt. The speed of the engine can be selected by
modifying the frequency at which it will be rotating. The equation showing the relation
between speed and frequency is shown below [12].
 = 0.022 · [] + 0.0565
(7)
The AC engine can operate at frequencies between 0 Hz and 150 Hz. This parameter
is selected in the engine control box. In addition, there are multiple buttons there. These
buttons consist of a green button that allows the model car to move forward at the selected
frequency, an orange button that makes the model car move backward at the maximum
speed (that is, the maximum frequency), a red button that stops the model car from its
movement, and an emergency button that shuts down the engine.
To achieve the Reynolds number at which the Perseverance would be working, the
frequency of the AC engine must be determined. Knowing that the fluid in which the
experiment is going to take place is water and that the scale of the impressed model is 1:5,
the only unknown element is the velocity of the car model.
= = 2680 0.268
(8)
where the subindex “E” identifies the experiment in the hydrodynamic towing tank.
Combining Equations (7) and (8), the frequency at which the AC engine must operate
can be obtained.
0.268 · 60 = 0.022 · + 0.0565 728 
(9)
Because the AC engine can only achieve a maximum frequency of 150 Hz, the atmos-
phere at Mars when the wind speed is maximum cannot be simulated. However, the av-
erage wind speed at Mars is between 1 and 4
[24] so, for these cases, the Reynolds
number can be achieved. By selecting the mean value of the interval mentioned above, the
Re obtained is the following one.
 193
(10)
where the sub-subindex “LS” refers to the fact that the Reynolds number is calculated for
low speeds.
Using (8), the new speed at which the AC engine has to work can be obtained.
 = = 193 0.0193
(11)
This value, in terms of frequency, is the one shown below.
0.0193 · 60 = 0.022 · + 0.0565 50.1 
(12)
The channel capacity is around 500 L, which is filled with a flexible hose. The empty
process is done by opening the drain valve. This process may take 30 min, so, to do it more
quickly, there is a hydraulic bomb that reduces that time to half.
The mast of the Perseverance will be tested in a horizontal position. This allows the
creation of bigger models without changing the results. If it was tested in a vertical posi-
tion, there could be interactions between the model and the surface of the water, modify-
ing the results downstream.
If the von Karman vortex streets want to be captured, it is necessary to place a camera.
For this project, a Sony DSC-QX100 (Sony Europe B.V.) is used. It is placed at the top of
the hydrodynamic towing tank, attached to the model car, allowing photographs to be
taken from the beginning through to the end of the channel.
Appl. Mech. 2022, 3 1394
The testing procedure is as follows. First, the hydrodynamic towing tank must be
filled with water. Then, the model must be screwed to the model car at the desired slip
angle. The next step is to connect the Mariotte flask with the desired outlet orifice. After
the conduct is purged (that is, making sure that there is no air inside the hose), it is neces-
sary to wait until the water remains calm to simulate a stationary experiment. Then, after
the camera is connected to a smartphone and the valve of the flask is opened, the green
button is pressed in the engine control box. At this point, the experiment has begun, and
it is necessary to take as many photographs as possible. When the model reaches the end
of the channel, the flask valve is closed, and the orange button must be pressed to restart
the experiment at another slip angle.
3. Results and Discussion
After explaining the technique of the experiment, the main results obtained are pre-
sented. Then, the computational (with a CFD simulation) and experimental (with a wind
tunnel) solutions are used to validate the veracity of the one obtained in the hydrody-
namic towing tank.
As evidenced in [16], the test was carried out at slip angles of 0°, 90°, 180° and 270°.
Since it was not possible to create outlet orifices every 30° (because of the presence of the
prisms that hold both anemometers), the only results that can be compared are those with
a slip angle of 90° and 270°. We can observe slip angles in three different orientations of
the model in Figure 9.
Figure 9. Different slip angles in three orientations of the model: (a) orientation at β = ; (b) orien-
tation at β = 90°; (c) orientation at β = 270°.
3.1. Previous Test with the Mars Rover “Curiosity”
Our first test campaign was carried out with a previous model of a “Curiosityrover.
The main definitions of the geometrical parameter of this prototype are the same; it is not
necessary to include further explanations. This model allows us to validate extensively
our technique, because the booms are in different vertical planes, and their interference to
each other is less complex. Furthermore, this experience allows us to improve our tech-
nique and to improve our knowledge of this geometry.
This test campaign was compared with the experimental results with the PIV tech-
nique [17]. In this comparison, the results are quite promising, and the main conclusions
are:
At β = 180° the upstream deviation in our test is less noticeable than in [17] but
shows the same tendency.
At β = we observed strong differences between the upstream deviation in our
tests and the results presented in [17].
Appl. Mech. 2022, 3 1395
At β = 270° we do not observe any upstream deviation, but there is a slight devia-
tion curving the streamlines up in [17].
We can observe these conclusions in Figure 10.
Figure 10. Previous tests with the Mars Rover “Curiosity”. (a) Mast and booms prototype tested; (b)
Comparison results at β = 180°; (c) Comparison results at β = ; (d) Comparison results at β =
270°.
Based on these promising results, we face the study of the Perseverance model consid-
ering that the technique will be appropriate to reach adequate conclusions.
3.2. Test at a Slip Angle of 90°
Beginning with the test at 90° of the slip angle, Figure 11 shows the comparison with
the hydrodynamic towing tank and the CFD simulation code, adding an overlap in order
to compare and validate them.
Figure 11. (a) Test done in a hydrodynamic towing tank at a slip angle of 90°; (b) PIV experimental
results according to earlier tests; (c) overlap of the previous ones.
Figure 11a shows that both the outlet orifice at the mast and the current line are com-
pletely visible. The wake left behind is the classic wake of a bluff body. The flow, once it
impacts both the anemometer and the prism that holds it to the mast, generates a turbulent
wake in which there are von Karman vortex streets.
Looking at the results obtained at [16] for this slip angle, the ones obtained by a CFD
simulation are approximately the same as in the wind tunnel. Because of that, a compari-
son is made between the towing tank experiment and the PIV experimental campaign. The
PIV results has been selected as a model for further comparison (Figure 11b). Finally, Figure
11c shows a comparison between the towing tank experiment and the wind tunnel results
(PIV). Due to these results, it can be proved that the result obtained in the towing tank has
Appl. Mech. 2022, 3 1396
the same tendency as in the wind tunnel. Once the flow arrives at the mast (and later the
smallest anemometer), it bifurcates, generating two turbulent paths with numerous recir-
culation bubbles, simulating the blue region (characterized for having small velocities).
3.3. Test at a Slip Angle of 270°
If the model is tested at a slip angle of 270°, the results obtained in the hydrodynamic
towing tank, in the wind tunnel and their overlap are shown in Figure 12.
Figure 12. (a) Test carried out in a hydrodynamic towing tank at a slip angle of 270°; (b) wind tunnel
test results; (c) overlap of the previous tests.
In this case, as can be seen in Figure 12a, the influence the mast has on the anemom-
eters is very little, because the streamlines catch only the prism holding the anemometers.
This allows them to take the correct measures of the wind speed around them.
Once again, by reviewing the results obtained in the CFD simulation and in the wind
tunnel [16], the first ones are not correlated with the second ones, since the region where
the recirculation bubbles predominate is smaller than expected. Due to this, a comparison
is performed using the wind tunnel test as a model (Figure 12b). This overlap (Figure 12c),
shows that both experiments have the same tendency. Upstream, the streamlines placed
near the studied anemometers are contracted, trying to avoid the anemometer curving
them up. If the towing tank experiment is observed, it is possible to detect that the red
mixture follows the same path as the streamlines on the wind tunnel experiment.
4. Conclusions
The aim of this project was to study the interference the mast of the Mars rover Per-
severance has over its anemometers, and to validate the experimental results obtained by
INTA (Instituto Nacional de Técnica Aeroespacial) [16]. Our study has focused on β =
90° and β = 270° because we try to validate our method with the scientific results of
other colleagues. Furthermore, we cannot test β = 180° due to the strong interference of
the MMRTG (Multi-Mission Radioisotope Thermoelectric Generator).
This research has compared the results (the streamlines) of our flow visualization
facility around the Mars rover with other experimental and computational techniques that
are carried out in the industry, proving the validity of this method. These other industrial
techniques would therefore not lead to the same results, but nonetheless required much
more expensive equipment. A comparative study is carried out analyzing the deviation
of the streamlines above these bluff bodies. Moreover, the technique allows us to analyze
not only the deviation but also the size of the separation bubble and the wake behind any
bodies.
The importance of knowing the flow behavior lies in the study of the interference
effect between the Rover head mast and the booms installed in the mast, because these
Appl. Mech. 2022, 3 1397
booms include the sensors that will take the atmospheric data of Mars. This interference
analysis is essential to determine the flow behavior of the wind around MEDA (Mars En-
vironmental Dynamics Analyzer); that is, if the interference caused by the mast were not
considered, the data sent would be wrong. It is necessary to quantify the deviation of the
results through tests to apply an adequate correction to the data collected.
According to [13,18,24] we have assumed the main parameters characterizing the cli-
mate and atmosphere for Mars and Earth, due to modelling but also due to recent mis-
sions and in situ observations. It is true that our model is a simplified study, and we are
not capable of distinguishing some complex Martian flows, such as dust devil vortices.
The main objective of our research is not that, but to offer a proper procedure to analyze
the impact of the rover mast on its anemometers and its influence based on our flow vis-
ualization technique.
The main conclusion drawn is that the experimental results received in the hydrody-
namic towing tank are very similar to those in the wind tunnel [16]. We have observed in
our results, and according to [16], two types of flow regions around the mast and the
booms. Two regions separated by upstream and downstream of the mast. Around the
booms, the mast generates a strong influence, a strong and massive region of perturbated
flow and, generally, a detached flow. This shows that, in preliminary studies, this method
is an option to be considered, since its associated cost is cheaper than, for example, testing
in a wind tunnel.
Therefore, in this paper we did not focus on studying how much the data (stream-
lines or speed velocity) are modified due to the interference of mast booms, but on demon-
strating that the flow visualization technique is an appropriate technique to carry out flow
correction analysis due to this mast boom interference. In addition, the installation of the
hydrodynamic towing tank is simpler than that of a wind tunnel (when talking about its
materials and the space it occupies).
Author Contributions: Conceptualization, Á.A.R.–S., M.J.C.-C., R.B.-M.; data curation, Á.A.R.–S.,
R.B.-M., C.C.-G., A.F.-H.; formal analysis, Á.A.R.–S., M.J.C.-C., R.B.-M., C.C.-G.; funding acquisi-
tion, Á.A.R.–S., M.J.C.-C., R.B.-M.; investigation, Á.A.R.–S., M.J.C.-C., R.B.-M., A.F.-H., C.C.-G., J.F.-
A.; methodology, Á.A.R.–S., M.J.C.-C., R.B.-M.; project administration, Á.A.R.–S., M.J.C.-C.; re-
sources, Á.A.R.–S., M.J.C.-C.; software, C.C.-G., A.F.-H.; supervision, R.B.-M.; validation, Á.A.R.–S.,
M.J.C.-C., R.B.-M., C.C.-G.; visualization, Á.A.R.–S., R.B.-M., C.C.-G., J.F.-A.; writing—original draft
preparation, Á.A.R.–S., R.B.-M., C.C.-G., A.F.-H., J.F.-A.; writing—review and editing, Á.A.R.–S.,
R.B.-M., A.F.-H., C.C.-G., J.F.-A. All authors have read and agreed to the published version of the
manuscript.
Funding: This research received no external funding.
Data Availability Statement: Not applicable.
Acknowledgments: The authors thank all the engineers and analysts from the Department of Aer-
odynamics of the ‘Instituto Nacional de Técnica Aeroespacial Esteban Terradas’ (INTA) and the
enthusiastic efforts of R. Corredor-Morales, and L. Rico-Establés from the Escuela Técnica Superior
de Ingeniería Aeronáutica y del Espacio.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Boermans, L.M.M.; Selen, H.J.W. On the Design of some Airfoils for Sailplane Application. XVIIth OSTIV Congr. 1981, Vol. 16,
18–39.
2. Pfenninger, W.; Vemuru, C.S. Design of Low Reynolds Number Airfoils: Part I. In Proceedings of the AIAA 6th Applied Aero-
dynamic Testing Conference, Williamsburg, VA, USA, 6–8 June 1989.
3. Kunz, P.J.; Kroo, I. Analysis and Design of Airfoils for Use at Ultra-Low Reynolds Numbers. Am. Inst. Aeronaut. Astronaut. 2001,
195, 36–60.
4. Kunz, P.J. Aerodynamics and Design for Ultra-Low Reynolds Number Flight; Stanford University: Stanford, CA, USA, 2003.
5. Mateescu, D.; Abdo, M. Aerodynamic Analysis of Airfoils at Very Low Reynolds Numbers; Department of Mechanical Engineering,
McGill University: McGill, QC, Canada, 2004.
Appl. Mech. 2022, 3 1398
6. Sun, Q.; Boyd, I.D. Flat-Plate Aerodynamics at Very Low Reynolds Number. J. Fluid Mech. 2004, 502, 199–206.
7. Alam, M.M.; Zhou, Y.; Yang, H.X.; Guo, H.; Mi, J. The ultra-low Reynolds number airfoil wake. Exp. Fluids 2010, 48, 81–103.
8. Wang, S.; Zhou, Y.; Alam, M.M.; Yang, H. Turbulent intensity and Reynolds number effects on an airfoil at low Reynolds num-
ber. Phys. Fluids 2014, 26, 115107. https://doi.org/10.1063/1.4901969
9. Samson, A.; Sarkar, S. An experimental investigation of a laminar separation bubble on the leading-edge of a modelled aerofoil
for different Reynold numbers. J. Mech. Eng. Sci. 2016, 230, 2208–2224.
10. Levy, D.E.; Seifert, A. Simplified dragonfly airfoil aerodynamics at Reynolds numbers below 8000. Phys. Fluids 2009, 21, 071901.
https://doi.org/10.1063/1.3166867
11. Anyoji, M.; Wakui, S.; Hamada, D.; Aono, H. Experimental Study of Owl-Like Airfoil Aerodynamics at Low Reynolds Numbers.
J. Flow Control. Meas. Vis. 2018, 6, 185–197.
12. Rodríguez-Sevillano, Á.A.; Barcala-Montejano, M.Á.; Bardera-Mora, R.; Batuecas-Fuejo, J. Flow Study over Bluff Bodies Based
on Visualization Technique. Am. J. Sci. Technol. 2017, 4, 97–104.
13. Petrosyan, A.; Galperin, B.; Larsen, S.E.; Lewis, S.R.; Määttänen, A.; Read, P.L.; Vázquez, L. The Martian atmospheric boundary
layer. Rev. Geophys. 2011, 49, RG3005. https://doi.org/10.1029/2010RG000351
14. Gómez-Elvira, J.; Armiens, C.; Castañer, L.; Domínguez, M.; Genzer, M.; Gómez, F.; Martín-Torres, J. REMS: The Environmental
Sensor Suite for the Mars Science Laboratory Rover. Space Sci. Rev. 2012, 170, 583–640. Available online:
https://link.springer.com/article/10.1007/s11214-012-9921-1 (accessed on 27 September 2022).
15. Lorenz, R.D.; Sotzen, K.S. Buoyant thermal plumes from planetary landers and rovers: Application to sizing of meteorological
masts. Planet. Space Sci. 2014, 90, 81–89.
16. Bardera-Mora, R.; Sor, S.; Garcia-Magariño, A.; Javier Gomez-Elvira, J.; Marin, M.; Torres, J.; Carretero, S. Characterization of
the flow around the Mars 2020 Rover. In Proceedings of the 35th AIAA Applied Aerodynamics Conference, Denver, CO, USA.
5–9 June 2017; p. 4228.
17. Bardera, R.; Garcia-Magariño, A.; Sor, S.; Urdiales, M. Mars 2020 Rover Influence on Wind Measurements at Low Reynolds
Number. J. Spacecr. Rocket. 2019, 56, 1107–1113.
18. Hassanalian, M.; Rice, D.; Abdelkefi, A. Aerodynamic performance analysis of fixed wing space drones in different solar system
bodies. In Proceedings of the AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 8–12 January 2018.
19. Désert, T.; Moschetta, J.; Bézard, H. Aerodynamic Design of a Martian Micro Air Vehicle. In Proceedings of the 7th European
Conference for Aeronautics and Aerospace Sciences (EUCASS), Milan, Italy, 3–6 July 2017.
20. Koning, W.J.F.; Romander, E.A.; Johnson, W. Low Reynolds Number Airfoil Evaluation for the Mars Helicopter Rotor. In Pro-
ceedings of the AHS International 74th Annual Forum & Technology Display, Phoenix, AZ, USA, 14–17 May 2018.
21. Li, C.; Dong, H.; Cheng, B. Tip vortices formation and evolution of rotating wings at low Reynolds numbers. Phys. Fluids 2020,
32, 021905. https://doi.org/10.1063/1.5134689
22. Agency, T.E.S. La acción de los vientos de Marte. Available online: https://www.esa.int/Space_in_Member_States/Spain/La_ac-
cion_de_los_vientos_de_Marte (accessed on 27 September 2022).
23. NASA. Mars 2020 Perseverance Rover. Available online: https://mars.nasa.gov/mars2020/ (accessed on 27 September 2022).
24. CSIC-INTA. Mars Atmosphere. Available online: http://cab.inta-csic.es/rems/en/mars-atmosphere/ (accessed on 14 October
2022).
... 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], [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. ...
... 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. ...
... 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. ...
Article
Full-text available
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.
... It is interesting to first understand the flow behavior around a body. Karman vortices will appear and their shape depends on the Reynolds number that is considered [9]. It can be seen in Figure 2 that, at very low Reynolds numbers, below 5, the flow is unseparated. ...
... Variation of the Von Karman vortex streets as a function of the Reynolds number, adapted from[9]. ...
... Estimated Reynolds number for Mars. The velocity was obtained from[9,14,19]. ...
Article
Full-text available
This article aims to highlight the importance of utilizing flow visualization techniques in the preliminary analysis of streamlined and bluff bodies, especially the potential use of visualization with ink in a water channel as a tool for a preliminary approach during fluid mechanics analysis. According to this, the study compares the results obtained using a classical flow visualization technique, ink injection in water, with those obtained through the employment of a laser-based measurement and visualization technique, called PIV, in a low-speed wind tunnel. The article briefly presents both techniques and highlights the importance of flow visualization in the analysis of aerodynamic bodies. This study focuses on flow over NACA airfoils at extremely low Reynolds numbers, which is of great interest for application in extraterrestrial atmospheres, such as on Mars. After obtaining images of the flow streamlines over the NACA 0018 airfoil, the results of both techniques were compared. The results indicated that there was good agreement between the visualization with the water channel and the PIV results, suggesting that the results obtained in the water channel represented a scientifically valid approximation and an essential complement to computational models that require experimental validation.
... This phenomenon is also used for anemometric measurements. The measured flow velocity is related to the frequency of the vortices formed [43][44][45][46]. The flow velocity can also be determined by measuring the velocity of naturally existing or artificially introduced markers into the flow. ...
Article
Full-text available
This article presents an innovative design of a tachometric anemometer for measuring wind velocity and direction, which does not contain electronic components and systems or power supply systems in the measurement area. This device can be used in extremely unfavourable environmental operating conditions, in locations exposed to direct atmospheric discharges, in conditions requiring restrictive and intrinsic safety, in special military applications, and in measurements in the presence of extreme electromagnetic fields. An innovative optical–mechanical transducer is used in the anemometer. This transducer generates a light pulse signal, the frequency of which is a function of the flow velocity, and the duty cycle is a function of the wind direction. This signal is transmitted via optical fibre from the sensor assembly to the measuring station, located outside the measurement area. The design of the device is simple, durable, and resistant to environmental conditions.
... For this reason, it is essential to know the aerodynamics of the rover, as a function of the wind direction, to be able to correct the velocity measurements recorded by the rover during its recordings. In this context, Rodriguez-Sevillano et al. [7] compare the aerodynamics of the Mars rover 2020 wind sensors obtained in a water channel with those obtained in a wind tunnel. On the other hand, García-Magariño et al. [8] studied the aerodynamics of the Mars Rover 2020 wind sensors using a PIV system for high Reynolds numbers, in order to obtain the correction functions of the incident wind speed as a function of its direction. ...
Article
Full-text available
Although the towing tank is a standard piece of equipment used to investigate fluid phenomena, it primarily exists as custom-built hardware that takes up a significant footprint. The size, cost, and custom-built nature have heretofore inhibited the production of this equipment in the authors’ context, an African university. This paper presents a small-scale (1000 mm x 200 mm x 200 mm), low-cost (<$1,000) towing tank made using readily available components and basic digital fabrication tools. Other universities on the continent and beyond can hence create this foundational platform for fluid mechanics-related teaching and research. Leveraging an Arduino microcontroller loaded with the GRBL firmware, G-code is sent from the computer to stepper motors to execute movements in two axes. This allows for automation capabilities, controlled towing speeds, and consistent experimental conditions. Validation tests revealed motion accuracy within 1 %. A glitter-based flow visualization approach to measuring surface phenomena is demonstrated here. Experiments conducted successfully visualized relevant flow characteristics generated by bluff bodies being towed in the tank. As the Reynolds number increased within the operating range, wider wakes and larger, more distinct vortices were generated, as expected. This platform can be replicated widely in institutions that may otherwise forego experimentation in fluid mechanics.
Article
Full-text available
The wake structures generated by rotating wings are studied numerically to investigate the complex vortex formation and evolution in both near-wake and far-wake regions. Flat rectangular wings with finite aspect ratios (AR = 1–8) that rotate from rest at an angle of attack ranging from 15° to 90° in a low Reynolds number regime (200–1600) are considered. Simulations were carried out using an in-house immersed-boundary-method-based incompressible flow solver. A detailed analysis of the vortex formation showed that the general wake pattern near the wingtip shifted from a single vortex loop to a pair of counter-rotating vortex loops with the enhancement of the leading-edge vortex (LEV) strength. Specifically, a stronger LEV due to the high angles of attack or high aspect ratios can induce an enhanced counter-pair trailing-edge vortex (TEV). As the TEV intensifies, a secondary tip vortex will be generated at the bottom corner of the wingtip, regardless of the wing geometry. This forms a pair of counter-rotating vortex loops around the wingtip. This type of wingtip vortex formation and evolution are found to be universal for the range of angle of attack and aspect ratio investigated. In addition to the vortex formation, surface pressure distribution and aerodynamic performance are also discussed. The findings from this work could help advance the fundamental understanding in the vortex dynamics of finite-aspect ratio rotating wings at a high angle of attack (>15°).
Article
Full-text available
Email address angel.rodriguez.sevillano@upm.es (Á. A. Rodríguez-Sevillano), miguel.barcala@upm.es (M. Á. Barcala-Montejano), barderar@inta.es (R. Bardera-Mora), j.batuecas@alumnos.upm.es (J. Batuecas-Fuejo) Abstract Flow visualization is a very important part of the study of fluid dynamics processes analyzed in many fields of physics and engineering. The present study explores flow visualization experiment technique applied to blunt shaped bluff bodies placed inside towing tank. Vortex shedding in circular cylinders has been studied in depth, being able to visualize the classical von Kármán vortex street. Moreover, the vortex shedding in cylinders of square section has been studied so that the differences between bodies with different section can be compared. A comparison between theoretical and experimental values of vortex shedding frequencies has been obtained; a high correlation with them shows the appropriate experimental procedure. Finally, this paper tries to advocate the use of the towing tank technique as a method to support the theoretical lectures related with some fluid mechanics concepts quite difficult to understand.
Conference Paper
The present research provides a performance comparison between several low Reynolds number airfoil profiles for the Mars Helicopter. The low density of the Martian atmosphere and the relatively small Mars Helicopter rotor result in very low chord-based Reynolds number flows, Re𝒸 = O(10³ - 10⁴). At low Reynolds numbers, flat and cambered plates can out-perform conventional airfoils, making them of interest for the Mars Helicopter rotor. Performance models are generated for the Mars Helicopter rotor based on a free wake analysis, and the results are compared with Mars Helicopter isolated rotor performance from previous work. A Reynolds-Averaged Navier-Stokes based approach is used to generate the airfoil deck using OVERFLOW. The model is constructed using airfoil data tables (C81 files) that are used by the comprehensive rotor analysis code CAMRADII. Performance results for the Martian atmosphere show improved performance for the cambered plate rotor over conventional airfoils, in terms of thrust for equal power and Figure of Merit for equal blade loading. The cambered flat plate airfoil produces 7% larger maximum rotor thrust versus the Mars Helicopter airfoils, and 5% larger Figure of Merit over the design thrust coefficient range. Larger maximum thrust allows an increase of design blade loading for the same thrust range for control authority, whereas the larger Figure of Merit reduces power requirements.
Article
The Mars 2020 rover is the new vehicle dedicated to the Martian surface investigation. This vehicle will transport Mars Environmental Dynamic Analyzer, the new meteorological station, including two wind sensors installed in the camera mast. An experimental characterization was conducted to investigate the influence of the Mars 2020 rover in the Mars Environmental Dynamic Analyzer wind measurements at low Reynolds numbers. Wind tunnel experiments were conducted using a 1:45th scaled model in a wind tunnel specially designed for these experiments. The velocity was measured using laser Doppler anemometry. A method is proposed in this investigation to calculate a correction factor for the data measurements of wind sensors embarked on rovers dedicated to planetary exploration missions. In particular, the method was applied to wind measurements taken by Mars Environmental Dynamic Analyzer in the Mars 2020 rover using the laser Doppler anemometry measurements, and corrections up to 40% in the velocity magnitude and 23 deg in the deflection angle were found.
Article
This paper describes the dynamics of a laminar separation bubble formed on the semi-circular leading edge of constant thickness aerofoil model. Detailed experimental studies are carried out in a low-speed wind tunnel, where surface pressure and time-averaged velocity in the separated region and as well as in the downstream are presented along with flow field visualisations through PIV for various Reynolds numbers ranging from 25,000 to 75,000 (based on the leading edge diameter). The results illustrate that the separated shear layer is laminar up to 20% of separation length and then the perturbations are amplified in the second half attributing to breakdown and reattachment. The bubble length is highly susceptible to change in Reynolds number and plays an important role in outer layer activities. Further, the transition of a separated shear layer is studied through variation of intermittency factor and comparing with existing correlations available in the literature for attached flow and as well as separated flow. Transition of the separated shear layer occurs through formation of K-H rolls, where the intermittency following spot propagation theory appears valid. The predominant shedding frequency when normalised with respect to the momentum thickness at separation remains almost constant with change in Reynolds number. The relaxation is slow after reattachment and the flow takes about five bubble lengths to approach a canonical layer.
Article
Growing interest in micro-air-vehicles has created the need for improved understanding of the relevant aerodynamics. A reasonable starting point is the study of airfoil aerodynamics at Reynolds numbers below 10,000, here termed ultra-low Reynolds numbers. The effects of airfoil geometry on performance are explored using an incompressible Navier-Stokes solver. Variations in thickness, camber, and the shape of leading and trailing edges are studied. Results indicate an increase in maximum lift coefficient with decreasing Reynolds number, but the lift to drag ratio continues to decrease, making the power required for flight a more restrictive consideration than lift. This performance penalty can be mitigated by careful airfoil design. Contrary to the notion that viscous fairing reduces airfoil geometry effectiveness, the computational results indicate that geometry still has a profound effect on performance at ultra-low Reynolds numbers. To further explore this design space, the flow solver has been coupled with an optimizer, resulting in the first airfoils quantitatively designed for this flow regime and demonstrating that unconventional camberlines can offer significant performance gains. Building on these results, tools are developed for ultra-low Reynolds number rotors combining enhanced classical rotor theory with airfoil data from Navier-Stokes calculations. This performance prediction method is coupled with optimization for both design and analysis. Performance predictions from these tools are compared with three-dimensional Navier-Stokes analyses and experimental data for several micro-rotor designs. Comparisons among the analyses and experimental data show reasonable agreement both in the global thrust and power, but the spanwise distributions of these quantities exhibit deviations, partially attributable to three-dimensional and rotational effects that effectively modify airfoil section performance. While these issues may limit the applicability of blade-element type methods for detailed rotor design at ultra-low Reynolds numbers, such methods are still useful for evaluating concept feasibility and rapidly generating initial designs for prototyping and for further analysis and optimization using more advanced tools. Moving toward controlled powered flight at centimeter scales, several prototype rotorcraft have been fabricated and tested, exploring both the aerodynamics and system integration issues.
Article
This work investigates the aerodynamics of a NACA 0012 airfoil at the chord-based Reynolds numbers (Re c ) from 5.3 × 103 to 2.0 × 104. The lift and drag coefficients, C L and C D , of the airfoil, along with the flow structure, were measured as the turbulent intensity T u of oncoming flow varies from 0.6% to 6.0%. The analysis of the present data and those in the literature unveils a total of eight distinct flow structures around the suction side of the airfoil. Four Re c regimes, i.e., the ultra-low (<1.0 × 104), low (1.0 × 104–3.0 × 105), moderate (3.0 × 105–5.0 × 106), and high Re c (>5.0 × 106), are proposed based on their characteristics of the C L -Re c relationship and the flow structure. It has been observed that T u has a more pronounced effect at lower Re c than at higher Re c on the shear layer separation, reattachment, transition, and formation of the separation bubble. As a result, C L , C D , C L /C D and their dependence on the airfoil angle of attack all vary with T u . So does the critical Reynolds number Re c, cr that divides the ultra-low and low Re c regimes. It is further noted that the effect of increasing T u bears similarity in many aspects to that of increasing Re c , albeit with differences. The concept of the effective Reynolds number Re c ,eff advocated for the moderate and high Re c regimes is re-evaluated for the low and ultra-low Re c regimes. The Re c ,eff treats the non-zero T u effect as an addition of Re c and is determined based on the presently defined Re c, cr. It has been found that all the maximum lift data from both present measurements and previous reports collapse into a single curve in the low and ultra-low Re c regimes if scaled with Re c ,eff.