**3.1 The sting balance description**

An aerodynamic balance has been developed to measure drag and lift forces in the MARHy operating flow conditions. The main difficulty comes from the fact that operating conditions concerns rarefied regime with low density flows, giving force values estimated between 1mN and 1 N. Aerodynamic balances applied to supersonic wind tunnels are ranged in two main balance groups' internal and external balances. Internal balances [32] are a test model extension and located inside the test section, on the contrary, external [33] are placed outside the test section and the model is supported with thin wires. For the present study, a sting balance was designed to measure drag and lift forces applied to the waveriders in supersonic and hypersonic flows. The design of this device had to meet to several constraints: be able to measure small forces values around mN, to have an aerodynamic design to not obstruct the test section and ability to measure aerodynamic model forces with different incidence angles without changing the balance calibration. This sting balance is composed in two parts, drag and lift modules as showed on **Figure 2**. The principle adopted for force measurement is based on the deformation of thin slats equipped with strain gauges, deforming when the test model is an incoming flow.

The drag module as can be seen on **Figure 3** is designed in three parts: upper part, slats, and lower part in order to facilitate manufacturing. There are six slats arranged in three rows and two columns. Indeed, many configurations have been dynamically simulated with a CAO software to optimized de number of lamelles, their arrangement and their thickness. The **Figure 3** shows the deformation of the drag module slats when subjected to a horizontal force. The results showed that this configuration is the best compromise to optimize the bending, and to minimize the

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

**Figure 1.** *3D CAO design of the waverider used in this experimental work.*

**Figure 2.** *View of the sting balance two modules, drag and lift.*

lateral and vertical deformations. Indeed, other configurations such as a row of three wider slats showed lateral and vertical deformations that could weaken the balance of the sting, optimizing the bending which is the most important part for this module.

The drag slats are 0.2 mm thick and made of AISI 304 steel to avoid plastic deformation. Once all the components of the drag module are assembled, the lower

**Figure 3.** *Detail of the drag module and simulation of the strain stresses.*

part is static and only the upper part is mobile. Therefore, the most sensitive part of the slats is the upper area, where the strain gauges will be placed. The strain gauges are glued to the central slat and there is one on each side to create a complete Wheatstone bridge. The lifting module is made up of a single part and there are only two superimposed slats. This module is also made of AISI 304 and it measures 10 cm. The purpose of having two superimposed slats is to reduce the bending of the heavy test models when the flow is deactivated. Indeed, if the test model creates a bending due to its mass, it can have an impact on the lift values in the presence of the flow. The maximum mass of the test model that this sting balance can support is 140 g. This lift module, like the drag module, has a full Wheatstone bridge with two strain gauges per side, as shown in **Figure 4**.

Drag module measurements are dependent on the position of the balance center of gravity (COG). A change in the position of the center of gravity will change the measurement of the associated forces for the same test model and flow conditions. To avoid this problem, a counterweight is placed at the back of the balance and its position is adapted according to the mass of the test model. The higher the mass of the test model, the further the counterweight will be from the drag module. On the contrary, if the test model is light, the counterweight will be closer so that the center of gravity is always aligned with the two slats equipped with strain gauges.

**Figure 4.** *Detail of strain gauges of the lift module.*

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

Another important point for this type sting balance is to avoid that the flow has a direct impact on the deformation of the slats. Indeed, if the drag and lift modules are in the flow without protection, the drag and lift values will be overestimated. In addition to the shock produced by the presence of the test model, a second shock can be created on the drag module itself and increase the deformation of the slats and thus the drag value. To solve this problem, a cover was modeled and installed. It is dimensioned to allow the drag and lift modules to deform without touching the cover which could create friction and in turn distort the measurements. On the other hand, this cover also allows to protect the strain gauges from the temperature increase caused by the shock in hypersonic flow condition. For the experimental conditions of this work in supersonic regime, the shock does not produce any heating.

To validate this sting balance, we have performed a study with spheres in order to compare our experimental results with those of the literature. In his study, Aroesty determines the drag coefficients for spheres in a supersonic flow at Mach 4 and low density and establishes a curve that relates the drag coefficients of the spheres with the Reynolds number after shock Re2 [34]. In our case we measured the drag forces for spheres of different diameters in the three flow conditions at Mach 4. **Figure 5** plots the experimental data from Aroesti and our experimental results. As shown in the graph, the drag coefficients for the sting balance are consistent with the reference values. The numerous preliminary tests we have conducted have shown that without the stinger cover, the drag coefficients for small diameter spheres (less than 15 mm) and low Re2 (less than 200) are indeed overestimated as explained in the previous paragraph. For larger diameter spheres, the results are close to the Aroesty values without the protective cover. This is due to the fact that the shock created by the large diameter spheres is large enough to protect the scale elements that will be in the wake, which is not the case for the small diameter spheres.

**Figure 5.** *Drag coefficients of spheres in near rarefied regime: Aroesty and Noubel data.*

## **3.2 Strain gauges**

Strain gauges are used to measure the slat deformation. It is a sensor whose resistance varies with the applied force, then it converts force into an electrical resistance which can then be measured [35]. Strain gauge elements are electrically connected to form a Wheatstone bridge circuit used for the measurement of static or dynamic electrical resistance. The output voltage of the Wheatstone bridge is expressed in millivolts output per volt input. At the end a calibration curve of the lift and drag modules will convert the out put signal in a mesure of the corresponding fonce expressed in newton. For the experimental conditions of the MARHy wind tunnel forces are estimated between 1 mN and 1 N so strain gauge need to have a high gauge factor. There are essentially two types of strain gauges, the so-called semiconductor strain gauges whose gauge factor is greater than 180 and the metallic strain gauges whose gauge factor is between 2 and 3. In order to optimize the measurement of forces we have opted for the first type, however they are very sensitive to the value of excitation applied which can easily damage them [36, 37]. For this balance, the gauge used is the KYUOWA: KSPB-2-1 K-E4, with an excitation voltage of 1 Volts.

### **3.3 Calibration procedure**

Calibration of the balance is necessary to convert the electrical signal from by strain gauges into applied force. The purpose of calibration is to reproduce known forces on the sting balance and relate them to the variation of the measured voltage. We designed a calibration bench composed of a digital newton meter mounted on a motorized micrometric displacement, which aligned with the lift or drag modules, apply a stable and known force in the same geometric configuration as those of the experience. Both during calibration and during wind tunnel experiments, the models are screwed onto the model holding sting so as to align their center of gravity with the end of the sting. Finally a curve is obtained expressing the force as a function of the voltage measured for each module: drag and lift. The accuracy of the force measurement on the lift and drag module is estimated at 0.1 mN.

A counterweight is added so that the position of the center of gravity remains constant regardless of the size and mass of the model. This preserves the calibration performed with the balance provided that, during wind tunnel measurements, the balance's center of gravity is in the same position as during calibration. For this purpose, the position of the counterweight is adjusted for each test model.

It should be noted that if the aerodynamic forces are to be studied as a function of the angle of incidence of the test model with respect to the flow, it must be ensured that the center of gravity remains unchanged. For this reason, the balance is positioned horizontally so that the angle of incidence in the horizontal plane (x-y) is changed and the position of its center of gravity is not affected [38].

## **4. Experimental conditions**

#### **4.1 Marhy facility description**

The first version of the wind tunnel, then named SR3, was built in 1961, at the Aerothermic Laboratory. Since 2000, this wind tunnel, renamed MARHy, has been installed at the ICARE Laboratory of the CNRS in Orléans, and many technical improvements have been made.

In particular the pumping unit which is a key element allowing to ensure in continuous mode without time limit low density flows with Mach numbers ranging *Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

from 0.8 to 21. The two main components of the Marhy facility are the large capacity test chamber and the pumping unit. The wind tunnel consists of three main parts: the settling chamber, the test chamber and the collector-diffuser chamber as presented in **Figure 6**.

The facility is supplied with exchangeable nozzles to generate laminar subsonic, supersonic and hypersonic stationary flows [39]. Only the supersonic configuration is described in this paper.

Subsonic and supersonic conditions flows are generated by contoured nozzles, using air or nitrogen at ambient temperature. Nozzles are housed into the settling chamber, a cylinder of 2*:*6 m length and 1*:*2 m in diameter with a large access port at the bottom (200 *kg*), placed on a trolley with wheels on a guide rail for easy opening and closing. The relevant components of the facility MARHy in supersonic configuration is skecthed on **Figure 7**.

The divergent section of the nozzles opens into the experimental chamber, a cylindrical test section with a diameter of 2 m and a length of 3.5 m.

This chamber is placed perpendicular to the direction of the flow, so that there is enough space on either side of the flow to install diagnostic systems and supports without disturbing the flow. The experimental chamber is large enough to allow the

**Figure 6.** *The wind tunnel MARHy and the pumping group.*

**Figure 7.** *Sketch of the wind tunnel MARHy in supersonic configuration.*

integration of specific instrumentation such as probe supports, electron gun and aerodynamic balances and to avoid interactions between the flow and the wall of the wind tunnel. Two rounded bottoms laterally close the cylinder, one of them is provided with a door of 1*:*2 m in diameter, giving access to the interior of the experimental chamber as can be seen in **Figure 8**. Four port flanges with a diameter of 0.6 m, closed by optical windows made of quartz and fluorine, are distributed around its cylindrical section. Six other smaller diameter flanges are available for instrumentation.

The pressure in the experimental chamber is recovered by means of a central diffuser to match the test section pressure to the inlet pressure for the vacuum pumps, specially at hypersonic operating conditions. The collector-diffuser is a 1.4 m diameter cylinder connects the experimental chamber to the pumping group by means of a motorized butterfly valve with a diameter of 1.5 m. The pumping group consists of 2 primary pumps, 2 roots-type intermediate pumps and 12 rootsvacuum pumps,ensuring continuous operation. The number of pumps commissioned depends on the operating conditions of the flow (Mach number and static pressure).

**Figure 8.** *View of the experimental chamber of the facility MARHy.*

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*
