Low-density multi-fan wind tunnel design and testing for the Ingenuity Mars Helicopter

Abstract

Prior to its successful flights on Mars, the Ingenuity Mars Helicopter system underwent extensive flight dynamics testing in the 25-ft Space Simulator facility, a low pressure environmental chamber at NASA’s Jet Propulsion Laboratory (JPL), which can re-create relevant Martian conditions on Earth. This facility, while large, is not large enough for free or tethered forward flight tests. In this work, an open-jet, multi-fan wind tunnel concept is presented, which was integrated into the JPL facility to simulate the external freestream flow of forward flight scenarios in a low-density environment. A theoretical and experimental analysis was performed to evaluate the possibility of utilizing commercially available 80 x 80 mm axial flow cooling fan units for this type of wind tunnel. Sub-scale tests found that under Martian conditions, fans deliver approximately 30% reduced flow rates for the same RPM compared to Earth conditions due to decreased efficiencies at low Reynolds numbers. However, fans can run at higher RPM in low-density fluids, with the RPM increase being specific to the fan motor. While power consumption dropped by more than 90%, fans experienced higher thermal loads due to reduced heat convection. The study concludes that the investigated type of cooling fan can operate without modification in a low-density environment, offering a low-cost and easily adaptable wind tunnel solution. Informed by ambient flow field measurements on a comparable multi-fan wind tunnel, a low-density full-scale facility with 441 individually controlled fan units was constructed and used for aerodynamic testing of an engineering model of Ingenuity.

Graphic abstract

Supplementary Material

1.1 Estimation of fan efficiencies and maximum rotation rates in low-density environments

To predict the fan performance with varying Reynolds numbers based on Eqs. 7 and 10 requires an initial estimate of the efficiency at the reference Reynolds number, $\eta _1$ as well as information regarding the Re number at the test conditions. Lacking official information by the manufacturer, the efficiency at maximum flow rate and free delivery (zero static pressure) under ambient conditions was approximated via Eq. 6 and assuming that the total pressure rise equals the dynamic pressure of the flow within the fan duct:

$$\begin{aligned} \Delta p_1=\frac{1}{2}\rho _1 {V_{d,1}}^2, \, \, \text { with } V_{d,1}=Q_1/A_d \end{aligned}$$

(12)

where $A_d$ is the annular area of the fan duct. Using the manufacturer specified flow rate and power consumption at zero static pressure with an assumed electrical efficiency of $\eta _{el}=0.85$ yields a fan efficiency of $\eta _1\approx 0.46$.

For determining the machine Reynolds number at low-density test conditions, it also had to be considered that brushless motors of a fan can usually run slightly faster as density decreases due to reduced aerodynamic loading and a reduced torque demand. The steady-state torque of a fan can be assumed to be proportional the fluid density and to the square of the fan rotation speed $\tau =\tau (\rho , n^2)$, and was modeled here with the constant torque coefficient for a given geometry, which can be solved for the torque at low-density conditions:

$$\begin{aligned} \tau =C_Q \rho n^2 D^3 \end{aligned}$$

(13)

$$\begin{aligned} \tau _2=\tau _1 \frac{\rho _2 n_2^2}{\rho _1 n_1^2} \end{aligned}$$

(14)

For a constant voltage applied to the motor terminals, it can be assumed that the brushless motor driving the fan has a simple linear speed-torque characteristic (i.e., linearly decreasing RPM with increasing motor torque demand):

$$\begin{aligned} n_2=n_{0}-\frac{dn}{d\tau }\tau _2=n_{0}-\frac{n_{0}-n_1}{0-\tau _1}\tau _2 \end{aligned}$$

(15)

where $n_{0}$ is the motor speed under no-load conditions. Substituting Eq. 14 into Eq. 15 yields:

$$\begin{aligned} n_2 =n_{0}-\Big (\frac{\rho _2}{\rho _1}\Big ) \Big (\frac{n_2}{n_1}\Big )^2 (n_{0}-n_1) \end{aligned}$$

(16)

Using the front fan values of $n_0=16,000$ RPM and $n_1=13,500$ RPM for ambient conditions at ρ₁ = 1.225 kg/m³ (see Sect. 3.4), Eq. 16 predicts rotation rates of $n_2=15,957$ RPM for the low-density test conditions of ρ₂ = 0.012 kg/m³. This is close to no-load conditions, which can be explained by the drastically lower densities and reduced torque demand on the motor. This means that this fan model is expected to run $\sim 18\%$ faster in Martian-density environments compared to nominal ambient conditions, which was confirmed by the sub-scale test campaign. This increase in rotation rate was accounted for when determining the Re number for the test conditions for the fan model used in this work.

1.2 Heat transfer considerations

Heat transfer properties of a fluid are also a function of the fluid density, which can be critical for air cooling applications as decreasing gas density directly affects mass flow as well as the heat transfer coefficient. While these types of fans are typically used for cooling separate electronic components, the heat transfer characteristics are here closer analyzed to assess the fans’ capability to self-regulate the internal heat and maintain acceptable temperature limits when operating in low-density environments.

For forced-air-cooled systems, the rate of convective heat transfer from a surface to the local ambient fluid is described by (Belady 1996):

$$\begin{aligned} \dot{q}_{conv.}=h A (T_{s}-T_{f}) \end{aligned}$$

(17)

where h is the thermal convection coefficient, A is the area of heat transfer, and $T_s$ and $T_f$ is the temperature of the surface and fluid, respectively. To avoid confusion with the flow rate, Q, the heat transfer is here denoted as lowercase q. The heat transfer coefficient, h, can further be expressed in dimensionless form with the Nusselt number (Nu):

$$\begin{aligned} Nu=\frac{h D}{k} \end{aligned}$$

(18)

where k is the conductivity of the fluid and D the system geometry, both of which are assumed independent of density. Thus, the heat transfer coefficient is proportional to the Nusselt number, which is highly dependent on the flow structure and generally a function of Reynolds number and Prandtl number $Nu=Nu(Re,Pr)$ for forced convection. For laminar and fully developed turbulent flow in a circular duct the Nusselt number based on empirical correlations is given by:

$$\begin{aligned} Nu&= 4.36=const.&Re<2000\text { (laminar)} \end{aligned}$$

(19)

$$\begin{aligned} Nu&=0.023 Re^{0.8}Pr^{0.4} \,\,&Re>10000\text { (turbulent)} \end{aligned}$$

(20)

where Pr is the Prandtl number (0.7 for air) and $Nu_{lam} \ll Nu_{turb}$. Expressed in terms of the fluid density and flow rate, the heat transfer in a turbulent flow is:

$$\begin{aligned} h=\text {const. } \rho ^{0.8} Q^{0.8} \quad Re>10000\text { (turbulent)} \end{aligned}$$

(21)

Consequently, a decreasing fluid density reduces the heat transfer coefficient and thus forced convection if the flow can be considered turbulent. More substantial changes in density can, furthermore, lead the flow to being laminar, where the heat transfer coefficient is no longer varying with density, however, is considerably lower than in turbulent flows.

Equally, the heat capacity of a fluid, $q_{hc}$, scales with the fluid density, which can be rewritten in terms of the volumetric flow rate:

$$\begin{aligned} \dot{q}_{hc}=\dot{m} C_p (T_{f,o}-T_{f,i})=\rho Q C_p (T_{f,o}-T_{f,i}) \end{aligned}$$

(22)

where $C_p$ is the specific heat of the surrounding fluid and $(T_{f,o}-T_{f,i})$ the temperature difference between inlet and outlet. Hence, at constant volume flow, the advection of heat decreases drastically with density due to a reduced mass flow, resulting in an increased temperature rise from inlet to outlet of the system, $\Delta T$, for dissipating the same amount of heat, which in turn can negatively affect the convective cooling.

From the above-presented analysis, it can be concluded that the fluid density has severe adverse effects on the advection of heat by the forced air as well as the efficiency of heat exchange from the components to the fluid itself. Meanwhile, it was established that the fan power consumption similarly decreases with fluid density, leading to reduced currents and, therefore, reduced resistive heating of the fan unit. However, the maximum fan power consumption cannot be assumed to decrease proportional to the density as suggested by the fan laws ($\rho _2/\rho _1<P_2/P_1$), since fan efficiency decreases with Reynolds number and fans run faster due to reduced loading. Assuming that the heat generated by the fan unit is proportional to the power consumption (i.e., neglecting frictional heating and assuming a constant electric efficiency) and assuming a constant heat capacity $C_p$, an estimate for the magnitude of the component and fluid temperature at 100% duty cycle for ambient and Martian test conditions can be made. Using Eqs. 17, 21, and 22 and performance values from Table 3, the temperature deltas are:

$$\begin{aligned}&\frac{(T_{s}-T_{f})_2}{(T_{s}-T_{f})_1}= \frac{\dot{q}_{conv,2}}{\dot{q}_{conv,1}} \frac{h_1}{h_2}\nonumber \\&\quad =\frac{\lambda _2}{\lambda _1}\frac{\rho _2}{\rho _1}\Big (\frac{n_2}{n_1}\Big )^3 \Big (\frac{\rho _1}{\rho _2}\Big )^{0.8} \Big (\frac{\phi _1}{\phi _2}\frac{n_1}{n_2}\Big )^{0.8}\approx 2.3>1 \end{aligned}$$

(23a)

$$\begin{aligned}&\frac{(T_{f,o}-T_{f,i})_2}{(T_{f,o}-T_{f,i})_1}=\frac{\dot{q}_{hc,2}}{\dot{q}_{hc,1}} \frac{\dot{m}_1}{\dot{m}_2}\nonumber \\&\quad =\frac{\lambda _2}{\lambda _1}\frac{\rho _2}{\rho _1}\Big (\frac{n_2}{n_1}\Big )^3\Big (\frac{\rho _1}{\rho _2}\Big )\Big (\frac{\phi _1}{\phi _2}\frac{n_1}{n_2}\Big )\approx 5.9>1 \end{aligned}$$

(23b)

As a consequence of this, when fans are operating in an environmental chamber at room temperature and low density, they are expected to experience slower initial temperature rise due to reduced power consumption compared to ambient conditions, whereas the reduced convective cooling and heat capacity will lead to higher steady-state component and exhaust temperatures, both of which are undesirable, because it can affect long-term component reliability and changes the freestream temperature. It should be noted that for the convective cooling in Eq. 23a the flow was assumed fully turbulent for both scenarios, which may not necessarily be true. If the flow is indeed laminar under low-density conditions, the temperature difference is likely to be even higher. It also needs to be mentioned here that the above presented analysis is greatly simplified, but the general trends outlined here are supported by experimental findings of this study.

1.3 Ambient rotorcraft forward flight test

Rotorcraft operation introduces significant induced velocity perpendicular to the main freestream flow direction and is thus particularly sensitive to the overall test section size, adding further constraints on the required test section size. Here, experiments using a rotor model with similar size as the Ingenuity system were performed to further examine the minimum size requirements for a multi-fan wind tunnel.

Figure 11 depicts the experimental setup, in which, a single-rotor model ($D={1.14}\,\mathrm{m}$) with collective and cyclic pitch control was installed in front of the Caltech multi-fan wind tunnel. The rotor was oriented upside down with the rotor wake directed upward to circumvent the problem of ground effect aerodynamics. Orientation and size of the rotor model were chosen similar to the anticipated fixed-mounted forward flight tests of Ingenuity. The rotor plane was oriented parallel to the floor for simplicity and only collective pitch control was utilized. The rotor mounting was additionally instrumented with load cells for lift and drag recordings.

Fig. 11

Setup and terminology for rotorcraft wind tunnel sizing experiments including illustration of theoretical intake areas for different velocity ratios, and schematic visualization of the wind tunnel size reduction process. Note the rotor is oriented upside down

Using the wind tunnel’s unique capability of addressing and controlling each fan individually allowed us to actively reduce the overall test section horizontal and vertical dimensions by switching off columns or rows fans, respectively. Other relevant operational parameters (freestream velocity, rotor rotation rate and rotor collective pitch) remained constant throughout each test run, which permitted a direct assessment of the critical wind tunnel size at which edge effects become significant. These direction of size reductions occurred from below the rotor plane (intake of the rotor), from the sides, or from above the rotor plane (wake) separately in different test runs. For each test, the rotor was spooled up to a constant value of ${2700}\,\mathrm{{RPM}}$, similar to the Ingenuity system, and the collective pitch was adjusted for a maximum allowable rotor thrust of approximately ${97}\,\mathrm{N}$. Once the rotor reached steady-state operational conditions after an initial settling phase, all 36x36 fan units of wind tunnel were set to a predetermined, uniform velocity in the range of 5-12 m/s and the full-tunnel-lift and -drag baselines for the given velocity were quantified. Subsequently, maintaining a constant freestream velocity, rotor rotation rate and collective pitch, the operational fan wall size was incrementally reduced by switching off individual rows or alternatively columns of fans. After each wind tunnel size modification, the mean rotor forces and standard deviation were measured over 15 second periods. This process is schematically depicted in Fig. 11 (right). The experimental procedure was repeated for multiple freestream velocities for each of the three reduction directions (intake, sides, wake). Figure 12 shows the rotor forces against the horizontal or vertical distance from the rotor center to the wind tunnel edge of interest. In an attempt to generalize data, a scaling distance based on fluid mass flow through the rotor and tunnel was derived. With the mass flow through the rotor and the induced velocity of the rotor in hover according to the momentum theory approach being (Johnson 2012):

$$\begin{aligned} V_h=\sqrt{\frac{T}{2\,\rho \,A_{r}}} \end{aligned}$$

(24)

where T is the rotor thrust, and $A_r$ the rotor disk area, i.e., the area swept out by the blades. It follows that the mass flow through the rotor is:

$$\begin{aligned} \dot{m}=\rho \, A_{r} \, V_h=\sqrt{\frac{T \, \rho \, A_{r}}{2}} \end{aligned}$$

(25)

When assuming that the wind tunnel has to supply, at absolute minimum, the same mass flow of horizontally accelerated flow, the corresponding tunnel area becomes:

$$\begin{aligned} \dot{m}=\rho \, V_t \, A_t=\rho \, V_h \, A_{r} \end{aligned}$$

(26)

$$\begin{aligned} A_t=\frac{V_h}{V_t}A_{r}=\sqrt{\frac{T \, A_{r}}{2 \, \rho \, V_t^2}} \end{aligned}$$

(27)

where $A_t$ is the minimum planform wind tunnel area and $V_t=V_{\infty }$ the wind tunnel freestream velocity. Since the area ratio is directly related to the velocity ratio of the freestream to the induced velocity of the rotor, the following normalization of the forward speed (tunnel velocity) is defined, which is similar to the advance ratio $\mu =V_{\infty }/\Omega R$.

$$\begin{aligned} \mu ^*=\frac{V_t}{V_h} \end{aligned}$$

(28)

For the geometry of $A_t$, a further assumption is made that all flow is ingested from the intake direction of the rotor plane, which is below the rotor plane in this case, since the rotor is mounted upside down. The geometry minimizing the overall distance to the center of the rotor is a half circle with the radius:

$$\begin{aligned} R^{*}=\sqrt{\frac{2A_t}{\pi }}=\sqrt{\frac{2A_{r}}{\pi }*\frac{V_h}{V_t}}=\sqrt{\frac{1}{\pi } \sqrt{\frac{2T \, A_{r}}{\rho \, V_t^2}}} \end{aligned}$$

(29)

Fig. 12

Rotor force measurements vs. wind tunnel size (distance between rotor axis and wind tunnel edge) for different directions, refer to Fig. 11 for terminology

Figure 11 (middle) illustrates the derived projected intake areas for the given experimental conditions, a thrust of $T={97}\,\mathrm{N}$ and various, representative velocity ratios $V_t/V_h$. It can be seen that an increase in wind tunnel freestream velocity results in a decrease in required wind tunnel size. The hypothesis was qualitatively confirmed through the use of smoke visualization, in which glycerol smoke was injected at various points and freestream velocities upstream of the wind tunnel. It could be observed that only smoke injected within the confines of the projected intake radius $R^{*}$ entered the rotor disk. It is worth mentioning that the expression in Eq. 29 is merely a first-order approximation and does not necessarily reflect true flow characteristics. For instance, even fluid not passing directly through the rotor disk can influence the rotor aerodynamics.

Nonetheless, the expression from Eq. 29 was used as a scaling quantity to normalize the distance between the rotor center and the wind tunnel edge in Fig. 12, which shows the measured rotor thrust and drag with varying wind tunnel size. The abscissa denotes the vertical/horizontal distance from the rotor center to the edge of the wind tunnel normalized by the expression of $R^{*}$ (see Fig. 11 for terminology). It is worth mentioning again that only the distance of interest was reduced, while the other two distances remained unchanged at the full-wind-tunnel-dimension. The ordinate denotes the average thrust and drag measurements as well as the standard deviation relative to the full-tunnel baseline values for various $\mu ^{*}$.

The normalized experimental data shows only marginal changes in the rotor forces when wind tunnel size is varied above the critical distance of $d/R^{*}=1$ on the intake and sides. When the distance from the rotor center to the wind tunnel edge is reduced below this critical value, significant effects on the aerodynamic forces can be observed. This is particularly evident in the thrust and drag measurements. Furthermore, wind tunnel size reductions below $R^{*}$ lead to pronounced force fluctuations, as seen in the standard deviation of forces. Both, the reduction in thrust and strong fluctuations, are believed to derive from the blade tips entering the wind tunnel edge shear layer during the rotation. It should be noted here that effects of insufficient wind tunnel size can already be observed for values slightly greater than $d/R^{*}=1$ and according margins should be factored in. This is consistent with the results shown in Fig. 8, where edge effects and high levels of flow turbulence were found to occur for spanwise distances of $y>0.4L$. Meanwhile, even though it was previously assumed that flow is only ingested through the rotor from the intake side of the rotor plane, the data indicates that the wind tunnel dimension on the wake side of the rotor plane is quite relevant as well. However, identification of the critical wind tunnels dimension on the wake side of the rotor yields more ambiguous results. In this case, thrust measurements start to diverge from full-tunnel values at $d\approx 1 R^{*}$, but drag measurements at $d\approx 2 R^{*}$. Given the considerably lower drag forces compared to the thrust, causing the drag to be more prone to measurement noise, it is unclear whether the critical value for the wake side should be based on the thrust or drag measurements. Regardless, a conservative minimum dimension in the wake direction is $d=2 R^{*}$. When observing the standard deviation of both forces, it can be noted that reducing the wind tunnel dimension from the wake direction introduces only minor force fluctuations, starting at $d/R^{*}=1$.

The insights obtained by these ambient reference measurements help to establish absolute minimum requirements for the size of a multi-fan wind tunnel. Analysis of the unobstructed flow field in the main paper outlined a functional test section within the bounds of $y,z= [-0.4L, 0.4L]$ in the spanwise and vertical direction, and $6.75D<x<1.4L$ in the streamwise direction. When flow uniformity and low turbulence intensity are of concern for the application, downstream distances of $x>20D$ to the face of the fan wall should be maintained. Rotorcraft operation creates further constraints on the minimum wind tunnel size, those being that the freestream flow has to supply a sufficient mass flow to feed the rotor. The minimum wind tunnel edge distances from the rotor center outlined here are $d/R^{*}>1$ on the intake side of the rotor plane and within the rotor plane (sides) as well as $d/R^{*}>2$ on the wake side. Assuming a horizontal or inverted orientation of the rotorcraft, this yields an overall wind tunnel size of $2 R^{*} \times 3 R^{*}$ (W x H). Insufficient wind tunnel sizing may introduce significant edge effects causing erroneous force readings and strong fluctuations.

In accordance with these dimensioning guidelines, the recommended minimum wind tunnel size for the Ingenuity Mars Helicopter forward flight tests could be established for the given geometric and operational parameters provided in Sect. 3.1 ($m={1.8}\,\mathrm{kg}$, $D={1.21}\,\mathrm{m}$, height=${0.8}\,\mathrm{m}$, g = 3.72 m/s²), as well as an atmospheric full-scale test density of ρ = 0.019 kg/m³, and a freestream velocity of ${10}\,\mathrm{m/s}$. For the static rotorcraft model to be geometrically placed within the functional test section, a wind tunnel size of ${1.5}\,\mathrm{m}$ x ${1.0}\,\mathrm{m}$ (W x H) is required. Equation 29 yields a projected intake radius for the Ingenuity system of $R^{*}={0.95}\,\mathrm{m}$, requiring a wind tunnel size of ${1.9}\,\mathrm{m}$ x ${2.85}\,\mathrm{m}$ (W x H), which exceeds the static minimum requirements. Due to pragmatic reasons, including a limited number of sourecable fans within a short time period and the time intensive modifications for contamination requirements, the full-scale facility dimensions were limited to ${1.68}\,\mathrm{m}$ x ${1.68}\,\mathrm{m}$. As these dimensions fall short of the critical size outlined in Fig. 12, wind tunnel edge effects were expected to occur. Consequently, all experimental data obtained in the Ingenuity forward flight tests was sufficiently margined.