Rocketry - Camera Fairing Analysis

Attributes linked to this design project (CEAB's Graduate Attributes):

> Knowledge base for engineering

> Problem analysis

> Investigation

> Design

> Use of engineering tools

> Communication skills

> Professionalism

> Impact of engineering on society and the environment

> Life-long learning

INTRODUCTION

As part of our plan to document the flight of the Defiance[1] rocket, we intend to install a GoPro[2] camera on the rocket body, utilizing a 1.2 cm diameter hole, preferably in the Avionics Bay section of the rocket. However, we recognize that this hole may create potential aerodynamic challenges for the rocket during its flight. While we are not expecting significant issues, we have decided to conduct simulations to determine the precise effects on stability and overall performance. By confirming our suspicion, we aim to ensure that the addition of the hole does not compromise the rocket's performance. The findings of our simulation will be presented in this report which will examine and analyze the effects of the camera hole, providing detailed insights into any challenges it may pose for the Defiance rocket.

METHODOLOGY 

2.1. SIMULATION AND MODELING APPROACH 

All required modelling and modifications to existing models were done using Autodesk Fusion 360[3] , Ansys[4] Spaceclaim[5] and SolidWorks[6] . To complete the simulation and analysis, Ansys software was used, including SpaceClaim, Discovery[7], Workbench[8], and Fluent[9] . A to-scale model of the Defiance rocket was used, occasionally excluding the fins during some of the simulations to streamline the simulation to focus on the direct effects of the hole in the body as the fins would have no change during this analysis. 

2.2. TEST SCENARIOS 

Three situations were tested in the simulations to compare the overall effects of creating a hole in the body and how its diameter plays a role: the rocket’s body without any modification (i.e. no hole), the body with the hole to the exact required dimensions (12 mm diameter), and lastly, the body with a relatively larger hole in terms of diameter (200 mm diameter). Throughout this analysis, the depth of the hole was kept constant (30 mm). 

2.3. INITIAL ASSUMPTIONS 

2.3.1. TURBULENCE INTENSITY 

For high-speed flows like those around the rocket, a value between 0.05 and 0.1 is commonly used[10]. The choice of 0.1 for turbulence intensity was made for our simulations. 

2.3.2. TURBULENT KINETIC ENERGY 

By using a turbulence intensity of 0.1 at a velocity of approximately 607 m/s, we get a turbulent kinetic energy (TKE) as follows: 

k = 3/2 * (0.1 * 607)^2 ≈ 5545 m^2 /s^2 

2.3.3. SPECIFIC DISSIPATION RATE (ω) 

To set the specific dissipation rate (ω) value for a rocket moving at approximately 607 m/s, we can estimate the specific dissipation rate using the following formula: 

ω = k^(1/2) / (Cµ^(1/4) * L) 

where k is the turbulent kinetic energy, Cµ is a model constant (approximately 0.09), and L is the turbulent length scale. 5 We previously calculated the turbulent kinetic energy (k) assuming a turbulence intensity of 0.1 as: 

k = 5545 m^2 /s^2 

To get the turbulent length scale (L), we use a typical percentage for external flows (around 1- 5% of the characteristic length (D) ), where D is the diameter of the rocket (14 cm = 0.14 m): 

L ≈ 0.01 * D to 0.05 * D 

We will assume that the turbulent length scale (L) is 1% of the rocket's diameter: 

L ≈ 0.01 * D 

Therefore, 

L ≈ 0.01 * 0.14 m ≈ 0.0014 m 

Now, using the k-ω SST model formula, we calculate the specific dissipation rate (ω): 

ω = (5545)(1/2) / (0.09(1/4) * 0.0014)
ω ≈ 97,110 s^-1 

ANALYSIS AND RESULTS 

3.1. AERODYNAMICS 

In this subsection, we will analyze the effects of the camera hole on various areas of aerodynamics, including the maximum velocity, drag coefficient, apogee, and the stability of the Defiance rocket in each situation mentioned in section 2.2. 

3.1.1. MAXIMUM VELOCITY 

Using the original model (without any modifications), we can see that the maximum velocity near the Avionics Bay is approximately 607 m/s (Mach 1.820) (Fig. 3.1.1.1). 

After running an airflow analysis on the modified model with a 12 mm diameter hole, we can see that at the location of the 12 mm hole (location shown by red circle in Fig. 3.1.1.2), the maximum velocity has decreased to 606 m/s (Mach 1.817), a change of only 1 m/s from the original model. 

3.1.2. DRAG COEFFICIENT 

The drag coefficient of the original model was obtained as approximately 0.8885 at the apogee (6981 m) (Fig. 3.1.2.1). 

After running a simulation on the model with the 12 mm diameter hole, we obtained a change of 0.0047 in drag coefficient, resulting in a drag coefficient of 0.8838 at its apogee (6975 m). 

Similarly, using the 200 mm hole model resulted in a further change of 0.0032 to the drag coefficient, hence making its drag coefficient 0.8806 at its apogee (6971 m). 

3.1.3. APOGEE 

Using our original model, we get an apogee of 9681 m (Fig.3.1.3.1). 

Now, using the data achieved in section 3.1.1 and section 3.1.2, we can obtain the apogee for our modified models. We get an approximate of 9675 m for our model with the 12 mm hole (Fig. 3.1.3.2) and approximately 9671 m for our test model with the 200 mm hole (Fig. 3.1.3.3). 

3.1.4. STABILITY 

For our analysis, we used wall Yplus to examine the change in stability/turbulence (at maximum velocity). Wall Yplus is a dimensionless quantity used in CFD to determine the distance of the first cell center from the wall, normalized by the thickness of the first cell [12] . The wall Yplus graph for the original model is shown in Fig. 3.1.4.1. 

After modifying our model with the 12 mm hole, we obtained a TKE of approximately 5510 m2 /s2 , and hence a specific dissipation rate (ω) of approximately 96800 s-1 . Its wall Yplus graph can be seen in Fig. 3.1.4.2. 

For our 200 mm hole model, we obtained a TKE of approximately 5490 m2 /s2 , and specific dissipation rate (ω) of approximately 96626 s -1 . Its wall Yplus graph can be seen in Fig. 3.1.4.3. 

DISCUSSION 

4.1. INITIAL CONDITIONS 

As previously mentioned in section 2.2, we used three models, two with camera holes of different sizes to make this a controlled analysis. From our results, we can say that this was a good approach as it gave us a better insight on how slight modifications to the outer surface of the rocket’s body can have an effect on the aerodynamics of the entire rocket and how the change of diameter of the hole changes the aerodynamic factors. 

Furthermore, in section 2.3, we mentioned the calculation assumptions we were required to make in order to run the simulations. Our first assumption was the turbulence intensity. We obtained a range for it from Aerodynamics for Engineers, 6th ed. (J. J. Bertin and M. L. Smith) [10] . From the range we obtained, we took the upper end (10% i.e. 0.1) to make further calculations for the turbulent kinetic energy and the specific dissipation rate. 

4.2. RESULTS 

From the results achieved in section 3.1 of this report, we can see that making a 12 mm hole in the body of the rocket has minimal effects on its aerodynamics. 

From section 3.1.1, we can see that making a 12 mm hole in the rocket’s body reduces the maximum velocity by 1 m/s (from 607 m/s to 606 m/s), a change of 0.165%. 

From section 3.1.2, we saw the change in the drag coefficient at maximum velocity at the apogee. Adding a 12 mm hole resulted in a 0.0047 change in the drag coefficient (from 0.8885 to 0.8838), a change of 0.53%. 

A change of 1 m/s after adding the 12 mm hole (from section 3.1.1) resulted in a 6 m decrease in the apogee achieved (from 6981 m to 6975 m), but as it is a 0.06% change, it is not that significant. 

According to the graphs obtained in section 3.1.4, the inclusion of a 12 mm hole has an insignificant impact on the stability/turbulence of the rocket as measured by the wall Yplus values. Based on the results obtained, there is little difference in turbulence between the original model near apogee (Fig. 3.1.4.1) and the model with the 12 mm hole (Fig. 3.1.4.2), or the model with the 200 mm hole (Fig. 3.1.4.3). 

In section 3.1, we also saw that by increasing the diameter of the hole (from 12 mm to 200 mm) resulted in a lower maximum velocity and therefore, lower apogee. However, something to note is that the change in diameter was not exactly proportional to the change in the tested factors. 

CONCLUSION 

5.1. CONCLUSION 

In conclusion to our findings, summarized in section 4.2, we can say that making a hole with the dimensions tested will not have a significant effect on the aerodynamics of the rocket. Also, we can conclude that the increase in diameter of the hole will result in a decrease in the tested factors (i.e. maximum velocity, drag coefficient, apogee, and its stability), however, the change will not be proportional (i.e. the change in the factors will decrease as we increase the diameter). Therefore we can move forward on adding a 12 mm hole to body of the Defiance rocket. 

5.2. RECOMMENDATIONS 

Although the effect of the intended hole is negligible, there can be approaches taken to reduce even those effects. A transparent plastic or glass cover could be placed aligned with the outer surface of the body above the hole. This will ensure the purpose of the hole stays as well as minimize any effects the depth of the hole could have on the aerodynamics. 

[1] UTAT, Ed., “Rocketry - Defiance,” University of Toronto Aerospace Team, 2023. [Online]. Available: https://www.utat.ca/rocketry. [Accessed: 29-Mar-2023]. [2] GoPro, 2023. [Online]. Available: https://gopro.com/en/ca/. [Accessed: 29-Mar-2023]. [3] “Fusion 360: 3D CAD, CAM, CAE, & PCB cloud-based software,” Autodesk, 03-Feb-2023. [Online]. Available: https://www.autodesk.ca/en/products/fusion-360/overview. [Accessed: 29-Mar-2023]. [4] ANSYS Inc., "ANSYS: Engineering Simulation & 3D Design Software," 2023. [Online]. Available: https://www.ansys.com/. [Accessed: 29-Mar-2023] [5] “Ansys SpaceClaim | 3D CAD modelling software,” 2023. [Online]. Available: https://www.ansys.com/products/3d-design/ansys-spaceclaim. [Accessed: 29-Mar-2023]. [6] “3D CAD Design Software,” Solidworks, 2023. [Online]. Available: https://www.solidworks.com/. [Accessed: 29-Mar-2023]. [7] “Ansys Discovery | 3D product simulation software,” 2023. [Online]. Available: https://www.ansys.com/products/3d-design/ansys-discovery. [Accessed: 29-Mar-2023]. [8] “Ansys Workbench | Simulation Integration Platform,” 2023. [Online]. Available: https://www.ansys.com/products/ansys-workbench. [Accessed: 29-Mar-2023]. [9] “Ansys fluent | Fluid Simulation Software,” 2023. [Online]. Available: https://www.ansys.com/products/fluids/ansys-fluent. [Accessed: 29-Mar-2023]. [10] J. J. Bertin and M. L. Smith, Aerodynamics for Engineers, 6th ed. Upper Saddle River, NJ, USA: Pearson Prentice Hall, 2014, p. 394. [11] OpenRocket. (n.d.). OpenRocket – Open-Source Model Rocket Simulator. [Online]. Available: https://openrocket.info/. [Accessed: 29-Mar-2023]. [12] Fluent Inc. (2003). FLUENT 6.2 User's Guide. [Online]. Available: https://www.ansys.com/products/fluids/ansys-fluent/. [Accessed: 29-Mar-2023].