Design and testing of an external drag balance for a hypersonic shock tunnel

Measurement 46 (2013) 2110–2117

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Design and testing of an external drag balance for a hypersonic shock tunnel P. Vadassery, D.D. Joshi, T.C. Rolim, F.K. Lu ⇑ Aerodynamics Research Center, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019, USA

a r t i c l e

i n f o

Article history: Received 3 July 2012 Received in revised form 14 February 2013 Accepted 17 March 2013 Available online 26 March 2013 Keywords: Force balance Hypersonic shock tunnel Drag measurement Finite element analysis Stress wave force measurement technique

a b s t r a c t An external force balance for a hypersonic shock tunnel was developed. The design utilized finite element analysis that identified the dynamics of the balance. A simulated impulse and a step load were applied to the design, the former for determining the simulated transfer function and the latter to validate the design. The numerical modeling showed the feasibility of this approach for designing stress wave force balances. A force balance based on the design was fabricated, calibrated statically and dynamically, and implemented in a shock tunnel for measuring drag of a blunt cone at Mach 9.4. The measured drag compared well with modified Newtonian theory. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Short-duration facilities such as shock tunnels and their variants are well-known for their hypersonic testing capabilities. Unfortunately, such facilities have test times in the micro to millisecond range which complicates force measurement [1]. Of particular concern is the dynamics of the force balance when subjected to sudden aerodynamic loading. The short test time also likely prevents the force balance from attaining a steady state. A unique consideration related to the test environment and the short test time is that the sensors must be robust and fast. Typical sensors are fast-response accelerometers and strain gages. A method known as the stress wave force measurement technique (SWFM) [2] can address the complications from the short test duration by measuring the stress waves propagating within the force balance. Another force measurement approach is accelerometer based [3], which requires the model to be free floating. This type of internal balance requires springs and rubber flexures mounted in

⇑ Corresponding author. Tel.: +1 817 272 2083. E-mail address: [email protected] (F.K. Lu). 0263-2241/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.03.011

a model suspension system [4,5]. The measured acceleration–time history can then be related to obtain the force history. As with conventional aerodynamic facilities, force balances for impulse facilities are either internal where the sensing elements are placed within the test model or external otherwise. Robinson et al. [6] showed that high accuracy of the recovered force and moment loads was attained using an external force balance. Also, for a blunt body, these authors found that the interaction of an external balance on the model forces was less than that of an internal balance. Moreover, authors in [7,8] have discussed the possibilities of using finite element modeling techniques in the design process for developing aerodynamic force measurement devices in hypersonic flows. The present work involves a further development of the SWFM technique. The emphasis is to apply finite element analysis (FEA) in designing a drag balance through investigating the propagation of stress waves. A number of preliminary designs were evaluated using FEA. Other than developing an understanding of stress wave propagation, FEA identified stress concentrations and was used to identify suitable locations for strain gage placement. A drag balance was fabricated as a monolithic item and it was cal-

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ibrated dynamically to obtain the system transfer function. This transfer function was used to recover the force acting on the model by a deconvolution procedure [9]. The balance was used to measure the drag of a spherically blunted cone mounted in a hypersonic shock tunnel in a nominal Mach 10 flow. The measured drag was compared against the modified Newtonian theory. 2. Force balance The SWFB technique utilizes the wave reflections in a so-called stress bar for determining model forces in impulse facilities. The force balance is considered to be a linear system. The general approach, therefore, is to perform a dynamic calibration to determine the system transfer function. The force of a subsequent test can then be obtained from the stress measurement and the established transfer function. The design of the present force balance is facilitated by finite element analysis and will be summarized next. 2.1. Force balance design A requirement for the force balance is its ability for mounting a variety of models. Design requirements such as size (to fit into the test core of the shock tunnel), strength of balance, model and support attachment, strain gage/transducer placement and machining simplicity were considered. For ease of manufacture, reduced weight and high strength, aluminum (Al-6061) was chosen as a suitable material. A rigid support was made using hardened steel. The design made use of finite element analysis (ANSYSÒ Workbench™ 12 explicit dynamics solver) to assist in selecting a suitable force balance design amongst a number of candidates. (Details of the selection process can be found in [10].) This novel approach was carried out to understand the propagation of stress waves in solids. An impulse and a step load were applied to the front of the balance. In some of the designs, stresses concentrated more at joints where members are fastened together.

Fig. 1. Mesh generated with explicit dynamics solver.

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Therefore, it was decided to fabricate the force balance as a single solid piece. Details of the analysis settings are seen in Fig. 1. The top surface remained as a fixed support. Location 1 is just behind the tip of the axial bar while location 2 is 25 mm up the forward leg from the axial bar as indicated in Fig. 1. These two locations are potential sites for strain gages. The mesh was initially generated with a total of 34,088 uniform tetrahedral elements. The size of the elements was dictated to respond to high frequencies associated with the stress wave. Mesh refinement was then applied for computational efficiency, by maintaining larger elements to insignificant areas and increase density in areas of higher stress concentration. FEA solves the general differential equation of motion in structural dynamic analysis

€ þ cu_ þ ku ¼ f ðtÞ mu

ð1Þ

where m is the mass of the system, c is the damping coefficient, k is the stiffness constant, u is the displacement vector and f(t) is the vector of the time-varying load. Forces at nodes are calculated by a central difference time integration scheme used by the solver with a uniform time step of 0.08 ls. The time step is limited by the smallest element in the mesh. Simulations were carried out on an Intel Pentium 4, 2.6 GHz machine with 2 Gb of RAM. The simulation required 16,250 steps to converge, which required approximately 2 h. Damping was not included in the simulation so as to capture the high-frequency stress waves. The dynamical behavior of the force balance depends solely on the impulse response which ideally is the output when an impulse load is applied. The output y(t) is given by the convolution of the input x(s) and the impulse response g(t  s), namely,

yðtÞ ¼

Z

t

gðt  sÞxðsÞds

ð2Þ

0

It is more convenient to express Eq. (2) in the Fourier domain and after rearranging one obtains

Gðf Þ ¼ Yðf Þ=Xðf Þ

ð3Þ

Eq. (2) or (3) provides the key for determining the transfer function. In practice, an ideal impulse x(t)  d(t) cannot be achieved. However, such an ideal impulse can be approximated to a high degree by a narrow triangular loading [11]. For the present, a triangular loading with a peak of 350 N and pulse width of 220 ls is applied at the front of the force balance. A few frames of the simulation are shown in Fig. 2. The time after the application of the impulse is indicated in the individual frames. The frames show primarily the propagation of stress waves within the force balance, omitting most of the subsequent reflections. The forward slant member is considered for strain gage placement and hence it is named the ‘‘stress bar.’’ The initial stress wave at the front face transmits to the rear of the axial bar as well as to the forward and aft stress bars. The strain histories observed on the axial bar at locations 1 and 2 are shown in Fig. 3. This figure shows that the strain history at location 1 follows closely the trend of the impulse with minor reflection right after the pulse. Location 2, however, shows that there are numerous wave

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Fig. 2. Stress wave propagation in force balance.

−5

x 10

350

4

Strain location 2 Strain location 1 300 Simulated pulse

3.5

250

4.5

Strain

3

200

2.5 150

2 1.5

100

1

Impulse force (N)

5

50 0.5 0 0

0.2

0.4

0.6

Time (s)

0.8

1

0

1.2 −3

x 10

Fig. 3. Response to the simulated impulse starting at 90 ls.

interactions during the same period. A standard deconvolution approach using Eq. (3) was used to obtain the impulse transfer function.

The next step of the analysis was to find the response of the force balance to a simulated step load using the previously determined impulse response. The simulated step

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load was chosen as an idealized form of the drag signal obtained from the shock tunnel [12]. The step load of 222.4 N with a 100 ls rise time was applied to the model for 2 ms, see Fig. 4. The response of the stress bar is shown in the figure. Deconvolution of the strain output with the impulse transfer function restored the step input, which is also seen in Fig. 4. The figure shows that it is possible to recover the step loading with good accuracy even from the strain determined at location 2. The above indicates that finite element analysis can be used to guide the force balance design process. It was used to analyze the dynamic behavior of the balance due to impulsive forces and also helped to locate possible positions for strain gage placement on the balance.

2.2. Drag balance construction The drag balance was fabricated from a single aluminum block for rigidity and to prevent spurious oscillations from joints and welds. It had a dimension of 209 mm in length, 108 mm in height and 25 mm in width. The stress bars had a thickness of 8.8 mm. Also, a 12.7 mm threaded hole in the front of the balance is used for model attachment. Two 12.7 mm threaded holes were available at the top to attach the balance conveniently into the test section. Two 6.3 mm threaded holes were located at the bottom for attachment as needed. Fig. 5 shows the fabricated force balance; flow is right to left. Fig. 6 shows a schematic of the force balance subjected to dynamic calibration using an impulse hammer that will be described later. A blunt cone model was chosen to validate the drag balance by comparing the measured value with that obtained from modified Newtonian theory. The blunt cone model was made of steel with a base radius of 40 mm and a semi-angle of 18.5°. The model was 88.9 mm long and its mass was 0.907 kg. For simultaneous pitot pressure measurements, the model was designed to hold a PCB

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113A21 pressure transducer at its nose. A pressure transducer holder was designed to firmly embrace the transducer in the nose of the cone with a 4.5 mm recess. This holder was tightened from the centerline through the base of the model to the nose of the cone. A steel bolt was screwed into the base of the model with required wiring lead taken out. This assembly consisting of the model and the hardened steel bolt was attached to the front of the force balance, aligned with the axial bar. Piezoelectric film gages (Measurement Specialties Model DT1-052k) were used to measure the stress waves. Two gages were used, one on the stress bar and the other behind the model on the balance aligned with the axis. Piezoelectric film was chosen due to its high sensitivity and higher frequency response than conventional strain gages [13]. All instruments were protected from the flow by rubber padding which was further covered by electrical and aluminum tape. It was noticed that there occurred an interaction between the exposed balance structure with the oncoming flow. However, it was seen from experimental test results that these interaction would happen after the steady test time. Given that the steady test time was very short and the stress waves traveled faster than the flow, it was concluded that this interaction had minimal effect on the measured drag during the steady test time. Further research is presently being carried out to study these effects in detail.

2.3. Dynamic calibration Static calibration was performed in a standard manner by loading the force balance with discrete loads and by measuring the strain gage outputs at each loading. The results showed excellent linear behavior and further discussion of static loading is omitted for brevity. Dynamic calibration was performed to find the force balance characteristics, also known as the transfer func-

Fig. 4. Response to the simulated impulse starting at 90 ls.

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Fig. 5. Fabricated force balance mounted in the shock tunnel.

Fig. 6. Schematic of dynamic calibration using an impulse hammer.

tion. Dynamic calibration was performed by striking the model/balance by an instrumented impact hammer, as shown schematically in Fig. 6. The PCB Model 086C01 impulse hammer was instrumented to measure the input impulse while the output strain was measured by the piezoelectric film. An example of the input impulse and the output strain is shown in Fig. 7. From the measured input and output, an impulse transfer function is determined in agreement with Eq. (2). With the established transfer function and measured output, the input can be reconstructed. This system transfer function was then used to recover the actual drag, which is discussed in the results.

rates the driver from the driven tube, so-called because it is used to hold two diaphragms. The driven tube is constructed in three segments of 2.74 m length each. The three segments are connected to each other with a flange at each end identical to the one on the driver section. The internal diameter is the same as the driver tube. The end of the driven tube has a special coupling for the nozzle insert and secondary diaphragm. The nozzle has interchangeable throat inserts to provide test Mach numbers of 5–16. The nozzle has a length of 2.57 m, with an exit diameter of 33.6 cm at the test section. The test chamber has a dimension of 53.6 cm in length and 44 cm in diameter. It has two diametrically opposed access windows of 23 cm diameter. The rear of the test section leads into the diffuser and then to a dump tank. The diffuser with a supersonic conical section is unusual for shock tunnels and is an artifact from being used previously as a hypervelocity tunnel. The diffuser does not appear to have an adverse effect on the performance of the shock tunnel. Dried air was used for filling the driver and driven sections. An advantage of the double-diaphragm operation is that precise rupture can be obtained by venting the double diaphragm section. Upon diaphragm breakage, a shock wave is propagated into the driven tube. The shock propagation is picked up by two PCB Model 111A23 transducers, located at 82.5 cm (32.5 in.) and 219.7 mm (86.5 in.) upstream from the end of the driven section. The shock velocities for the tests were calculated using the time-of-flight method described in [14].

3. Hypersonic shock tunnel facility 4. Results The test article was mounted in a reflected shock tunnel which was operated with a cold air driver, thereby achieving only a low enthalpy. The shock tunnel is shown schematically in Fig. 8. The main components of the hypersonic shock tunnel include the driver section, driven tubes, nozzle, test chamber, diffuser and dump tank. The driver tube is 3 m long with an internal diameter of 15.24 cm and a wall thickness of 2.54 cm. One end is closed off with a hemispherical end cap. The other end has a 48.26 cm diameter, 11.43 cm thick flange, which allows the driver tube to be bolted to the diaphragm section and the driven section. The double diaphragm section sepa-

Tests were conducted at a nominal Mach 9.4 conditions, see Table 1. Pressure and force signals were recorded using a Tektronix oscilloscope Model DPO 4054, sampled at 25 MS/s. A trigger level was set to record the response to the incident shock wave. The test conditions are shown in Table 1 and the percentage values represent the repeatability margins based on multiple test results. To remove noise from the raw data, the pitot pressure signal was filtered using a 20 kHz low-pass Butterworth filter while the strain output was filtered using a 10-point moving average. The filtered strain data were then decon-

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0.2 Impact hammer 600

Strain gage (axial) 0.15

400

200

0.05

0

0

Voltage (V)

Force (N)

0.1

−0.05

−200

−0.1

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Time (s) Fig. 7. Hammer pulse and resulting strain.

Fig. 8. Shock tunnel schematic.

Table 1 Test conditions. Free stream Mach number M1 Stagnation pressure po Stagnation temperature To Stagnation enthalpy ho Free stream static pressure p1 Free stream static temperature T1 Free stream velocity V1 Free stream Reynolds number Re1

9.43 ± 0.13% 2.69 ± 2.2% (MPa) 920 ± 1% (K) 0.65 ± 1.6% (MJ/kg) 73 ± 2.6% (Pa) 52 ± 1.4% (K) 1350 ± 0.54% (m/s) 1.9  106 ± 0.89% (m)

volved with the transfer function obtained from the dynamic calibration to recover the drag acting on the blunt cone model. Fig. 9 presents the recovered drag on the blunt cone model and also shows the simultaneous pitot pressure at the stagnation point. The flow starting stage is seen to have a duration of approximately 150 ls. This is associated to the nozzle starting process, which is due to unsteady occurrence after the shock enters the nozzle until a steady flow is established [15]. After the flow arrival the force remains steady for a period of approximately 150 ls and is then noticed to decrease. The experimental drag force was 16.9 N and the overall uncertainty was estimated to be ±9%.

Modified Newtonian theory is suitable for application to a blunt body in hypersonic flow [16]. The theory yields an expression for the pressure coefficient as 2

C p ¼ C pmax sin h

ð4Þ

where C pmax is the maximum pressure coefficient behind a normal shock wave and is found using the Rayleigh pitot formula, and h is the angle between the flow vector and the surface of the model. The axial force coefficient is then found from integrating the pressure coefficient. The drag coefficient is approximated by [17]

2

3 2

6 C D  4

cþ1 2

½ðcþ1Þ=ð1cÞ

c½c=ðc1Þ S

7 D 5 Ppit

ð5Þ

where c is the specific heat ratio, D is the experimentally recovered drag, S is the reference area of the blunt cone which in the present case is the base area and ppit is the measured pitot pressure. Fig. 10 plots the coefficient of drag history obtained from the recovered force. The figure shows a flow initiation and establishment process of about 150 ls followed by the quasi-steady test of 150 ls. The

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Fig. 9. Recovered drag and pitot pressure.

were performed by pulse excitation using an impulse force hammer. From the impulse hammer tests an experimental transfer function was established. The strain data were processed and deconvolved with the transfer function to recover the drag. The simple balance design was validated by comparing the measured drag with the modified Newtonian theory. Ease of operation and different model attachment are some of the force balance benefits.

0.8 Coefficient of drag Average from175 µs to 275 µs Predicted drag coefficient

Drag coefficient , Cd

0.6 0.4 0.2 0 −0.2

Acknowledgments

−0.4

The assistance by Raheem Bello, Derek Leamon and Nitesh Manjunath Gupta is greatly appreciated. Also, we thank Kermit Beird and Sam Williams for machining the force balance and model.

−0.6 0.5

1

1.5

2

2.5

Time (s)

3

3.5

4 −4

x 10

Fig. 10. Drag coefficient.

References average experimental drag coefficient was 0.199 and the overall uncertainty was estimated to be ±8%. 5. Conclusions An external drag balance for hypersonic shock tunnel applications was designed and fabricated, and applied to a blunt cone. Finite element analysis (FEA) was used extensively to design and determine the dynamic characteristics of the force balance under impulsive loading. Stress wave propagation was analyzed using an explicit dynamics solver. FEA also provided guidance in locating the placement of strain gages. Several designs were investigated before the actual fabrication bearing in mind certain constraints such as being able to fit into the shock tunnel with room for support and model attachment, maximum impulse loading and machining simplicity. Piezoelectric film gages were used to measure stress waves. Dynamic calibrations

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