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Fig A.4.1.2.5.1: Mesh of 1Kg launch vehicle in GAMBIT (Jayme Zott, Chris Strauss, Brian Budzinski) After meshing was complete, we broke up the launch vehicle into zones. We designated the face of the rectangular prism in front of the launch vehicle as a pressure inlet, and the face behind the launch vehicle as a pressure outlet. We designated the face aligned with the symmetry plane of the launch vehicle as symmetry, and the remaining faces as walls. Once meshing was complete and the launch vehicle had been broken up into zones, we exported the mesh into Fluent. Table A.4.1.2.5.1 describes the settings and boundary conditions we chose within Fluent.
We based our choices for the settings and boundary conditions shown in table A.4.1.2.5.1 on Fluent tutorials^{1}, Fluent webinars^{2}, conversations with graduate students and professors^{3}, and trial and error. The solver was chosen to be pressure based because pressure based is most accurate for supersonic flows. The energy equation was turned on as a requirement for incompressible flow. The viscosity was chosen to be inviscid, because viscous forces are negligible at zero angle of attack. The boundary conditions for the pressure inlet and outlet were chosen based on the desired launch vehicle velocity. The remaining settings and boundary conditions were based more on trial and error than anything else. Overall, we attempted many different solution possibilities, from adapting the gradient of the grid to account for the formation of shock waves, to testing out a density based solver, to reducing the Courant number all the way to 0.01. There were many different options tested, and while our output seems intuitively reasonable, it is hard to say whether or not the settings displayed in table A.4.1.2.5.1 are the best for analyzing the supersonic flow of air around our launch vehicle. The results for the pressure distribution of the 1kg launch vehicle traveling 350 m/s at zero angle of attack can be seen in Fig. A.4.1.2.5.2. The scale on the left displays a color schematic representing the range of pressures distributed across the launch vehicle. The lowest pressure, colored blue, begins at 0.37 atm, and the greatest pressure, colored red, stops at 1.56 atm. The pressure is highest at the locations where a sharp edge occurs, and lowest in the areas immediately after them. Based on our initial boundary conditions, and the high probability that the flow is separating near the base of each skirt, these results seem reasonably accurate. Figure A.4.2.1.5.2 Pressure distribution of 1 Kg launch vehicle (Jayme Zott) The results for the velocity distribution of air surrounding the 1kg launch vehicle traveling 350 m/s at zero angle of attack can be seen in Fig. A.4.1.2.5.3. The scale on the left begins in blue at 5.89 m/s, and ends in red at 411 m/s. Figure A.4.2.1.5.3 Velocity distribution of air surrounding 1 Kg launch vehicle traveling 350 m/s (Jayme Zott) The velocity is greatest at the locations where the skirts end, and lowest slightly after that location. Shocks are most likely forming at the base of the skits where a significant change in the launch vehicle geometry occurs. These probable shock locations correlate well with the velocity distribution, and the velocity magnitudes correlate well with our initial boundary conditions. We therefore assume that the results are reasonably accurate for use in our aerodynamic analysis. Since the bottom line aerodynamic analysis for the launch vehicle design was completed using call_aerodynamics.m, we used CFD as a sanity check for the linear perturbation theory output. With both of these methods working together, we were able to get a solid idea of the type of aerodynamic loading the launch vehicle was likely to experience throughout its flight. References: ^{1}Ansys Fluent “Fluent 6.3 Tutorial Guides”, Fluent Inc. 2006. ^{2}^{ }Fluent: Fluid Flow Modeling Webinars, Compressible Flows  Solving Compressible Flow Problems; June 25, 2005. [http://www.fluent.com/elearning/resources/webinars/webinars_cfd.htm. accessed 1/29/08]. ^{3}Charles Merkle PhD, Reilly Professor of Engineering, Personal communication, Mechanical Engineering Building, Purdue University, 1/29/08. A.1.2.6 CMARC We now detail our process to determine the aerodynamic coefficients using the computational fluid dynamics package CMARC. This process is used in place of Fluent due to Fluent’s exceptionally long run time; also the results obtained in CMARC are reasonably close to those in calculated in Fluent. We found that while running a full three dimensional CFD simulation to obtain aerodynamic coefficients, took a long time to reach a converged solution. This led to our decision to come up with an alternative method to find these coefficients. We decided to use a panel method solver called CMARC and its postprocessing program POSTMARC for this analysis. The reason we chose this program is because of the time it takes to run a full three dimensional viscous case. Fluent, the program we were using prior to CMARC, took several hours to run only a small fraction of one case, while CMARC can run a full three dimensional viscous case in approximately five minutes. There is a slight difference between the results obtained from CMARC and Fluent. This is because Fluent is a full NavierStokes solver whereas CMARC is a panel method solver where the accuracy of the solution is based on the number of panels in the model. The results, however, are close enough to the Fluent solution to be useful. To begin our CMARC model, we enlisted the help of a doctoral student, Liaquat Iqbal, who has had much experience working with CMARC and POSTMARC. We used his method of creating CMARC input files in Excel to create our model geometry. A sample of the input prompt is shown in Figure A.1.2.5.1 below. Figure A.1.2.5.1: Sample CMARC Parameter Input (Chris Strauss) From Figure A.1.2.5.1, we can see that different design parameters of the launch vehicle such as stage length and diameter, nose cone length, skirt length, and (if a wing is present for an aircraft launch case) wing parameters can be easily changed to analyze the current configuration. The launch vehicle, for this case, had wings because this method was originally used to analyze aircraft launch configuration. The launch vehicle would have a wing attached to the first stage enabling it to pitch into a vertical trajectory. After the first stage burned out, the wing would be discarded along with the first stage. This method, however, is flexible enough so that nonwinged rockets can also be analyzed. We accomplished this by setting the wing span to zero. After the parameters are entered, the Excel sheet is saved in a format that is readable in CMARC. The input file is then run in CMARC which creates an output file for use in POSTMARC. Once this output file is entered into POSTMARC, the pressure distribution and aerodynamic coefficients are found using the program’s aerodynamic coefficient calculation routine. The pressure distribution on a winged aircraft launched vehicle can be seen below in Figure A.1.2.5.2. Figure A.1.2.5.2: Pressure distribution on winged air drop rocket at a 0 deg. angle of attack produced in POSTMARC (Chris Strauss) As seen in Figure A.1.2.5.2, the pressure is at a maximum on the nose cone and the leading edge of the wings. This is as expected and thereby supports the accuracy of using CMARC and POSTMARC for the calculation of the aerodynamic coefficients. The model’s flexibility is shown in Figure A.1.2.5.3 below. Figure A.1.2.5.3: Pressure distribution on wingless rocket at 0 deg angle of attack (Chris Strauss) Figure A.1.2.5.3 shows a modification to the original model. This model uses the same input sheet as the winged model except in this case the wingspan was set to zero to allow a wingless rocket to be analyzed. Again, the figure shows that the pressure distributions are as expected with the highest pressure on the nose cone and lower pressures along the rest of the rocket body. This again shows that the model is reasonable for aerodynamic analysis of the vehicle. While this model appears useful when the preliminary cases are run, a major flaw is present. This is not a flaw in the model, but rather with the limitations of the CMARC/POSTMARC package. We find that CMARC calculations are only valid up to Mach 0.9. This effectively ends the use of CMARC as a primary CFD tool because the launch vehicle quickly achieves supersonic velocities after being launched. Had these supersonic cases been run in CMARC, erroneous results would have been obtained and jeopardized the integrity of the project. A.1.2.7 Ascent Aeroheating Analysis Due to the nature of the coursework and limited time constraints, a thorough ascent aeroheating analysis was “black boxed”. A subsequent analysis would be necessary for a final design; however, we do not believe that glossing over this subject was detrimental to our design. A.1.3 Closing Comments The aerothermodynamics group survives trial and tribulation to bring you, the reader, reasonable aerodynamic data. This data includes aerodynamic coefficients and their corresponding forces. For example: drag, lift, moment, normal and axial, and shear. We also find the location of the center of pressure and aerodynamic heating. If the project is revisited, aerothermodynamics has several recommendations for the design. For future improvements, the launch vehicle geometry should be a prime driver. The large variance in stage to stage diameter produces excess drag that can be minimized with a more slender and uniform configuration. Additionally, the drag versus launch vehicle diameter should be taken into consideration when determining the nominal launch vehicle geometry. The consideration of drag was not taken into account when first determining a cost effective means of launch. Therefore, with more time and more tools, it is beneficial to further study the effects of drag with launch vehicle diameter. We find the aerodynamic coefficients to the best of our ability, though several complications arise in the transonic and hypersonic regimes. The models we implement are not applicable for transonic and hypersonic flows. Further study must be done in order to determine the exact flow effects in those regimes. The best method to determine the flow effects in the transonic regime is wind tunnel testing. As aforementioned, due to the nature of our coursework, making a model and performing wind tunnel tests is not viable. However, the predictions that we make for the transonic regions are unsound, they err on the high side. Being that our vehicle is making it into an acceptable orbit indicates that the aerodynamics experienced in reality would cause improved performance. As for the flow in the hypersonic region, the Newtonian method should be employed. Due to the launch configuration, the launch vehicle is far out of the atmosphere before reaching hypersonic speeds. This ensures that our model remains valid for the implemented configuration. On the other hand, if a different configuration is to be used, rather than the model that we implement, our model would need to be reformatted in order to take into account the hypersonic regime. All in all, the applied model is satisfactory for our launch configuration and all of the aerodynamic coefficients are reasonable for our specific design. A.1.4 User’s Guides for Aerothermal Codes User’s Guide for call_aerodynamics.m Written by Jayme Zott Revision 2.0 – 3/18/08 Description: The purpose of the code ‘call_aerodynamics.m’ is to output all aerodynamic loads pertinent to the launch vehicle design. These outputs include Mach number, coefficient of drag (both historically based and dimensionally based), normal coefficient, pitching moment coefficient, the center of pressure location, shear forces acting on the launch vehicle, and moments acting on the launch vehicle. All of these aerodynamic loads are output with respect to Mach number, and angle of attack (in essence, time). Files necessary to run call_aerodynamics.m: Filename Author Solve_cd_int.m (Jayme Zott) CP_Structure.m (Alex Woods) CP_Volume_two.m (Alex Woods) CP_overall_int.m (Jayme Zott) Atmosphere4.m (historical code) CP_Dimensions.m (Jayme Zott) CP_Linear_two.m (Alex Woods, Jayme Zott) Assumptions: There are quite a few assumptions made within the call_aerodynamics.m code. Assumptions can be broken down for each output. 