Aerodynamics Modeling of Sounding Rockets A Computational Fluid Dynamics Study Kristoffer Hammargren Engineering Physics and Electrical Engineering, master's level 2018 Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Abstract Any full scale rocket consists of four main components: the structural system (or frame), the payload system, the guidance system and the propulsion system. The guidance system of a rocket includes sophisticated sensors, on-board computers and communication equipment. The guidance system provides stability for the rocket and controls the rocket during maneuvers. When developing guidance systems, reliable aerodynamic models of the rockets are required. This report conducts a comparative study between CFD-simulations and the current aerodynamic models of two sounding rocket configurations used at RUAG Space in Link¨oping;the Maxus configuration and the two-stage Terrier-Black Brant configuration. Three parameters related to rocket stability are evaluated: the zero-lift drag coefficient CD0 , the stability derivative CNα , and the center of pressure Xcp. The parameters are evaluated in terms of behavior and parametric val- ues, ultimately determining how accurate the current aerodynamic models are compared to the CFD-simulations. Previous studies are used to deter- mine which data is most plausible in case of any deviations. All parameters are evaluated as a function of Mach number for complete configurations. The CFD-simulations are performed using Ansys CFX 18.2. Ansys is an American company that develops and markets engineering simulation soft- ware. Ansys is one of the leading commercial CFD-softwares. The results of this report show that the current aerodynamic model for the Maxus configuration corresponds well with the CFD-simulations, both in terms of behavior and parametric values. Data obtained from the current aerodynamic model are physically plausible and also corresponds well with earlier studies. Data provided from the current aerodynamic model for the first stage of the Terrier-Black Brant configuration show a mainly identical behavior to the CFD-simulations, but with varying accuracy in terms of parametric 2 values. Although the behavior of the current model is physically plausible, the provided data predict the position of the center of pressure to be too far from the nose. Data provided from the current aerodynamic model for the second stage of the Terrier-Black Brant configuration show an, at times, inconsistent and physically implausible behavior. These deviations are, however, limited to certain flight sequences, and not to the data as a whole. Apart from the inconsistencies shown at times, the provided data correspond well with the CFD-simulations in terms of parametric values. The aerodynamic model of the Maxus configuration is concluded to be accurate and sufficient for continued analysis. There are no indicators the current aerodynamic model could be faulty in any way. The aerodynamic model for the first stage of the Terrier-Black Brant configuration accurately represents the physical behavior of the rocket, but lacks accurate parameter value predictions in some cases. The current aero- dynamic model is concluded to be sufficiently accurate for continued analysis, provided the limitations of the model is taken into consideration. The aerodynamic model for the second stage of the Terrier-Black Brant configuration corresponds well compared to the CFD-simulations in terms of parametric values, but fails to predict the stabilization of CD0 at high Mach numbers and the rearward movement of the position of the center of pressure during transonic flight. The current aerodynamic model is concluded to be sufficiently accurate for continued analysis, provided the limitations of the model is taken into consideration. 3 Sammanfattning Varje storskalig raket best˚arav fyra huvudkomponenter: raketkroppen, nyt- tolasten, styrsystemet och framdrivningssystemet. Styrsystemet best˚arav sofistikerade sensorer, datorer och kommunikationsutrustning. Styrsystemet avser h˚allaraketen stabil och man¨ovreraraketen under flygningen. N¨arman utvecklar och tillverkar styrsystem kr¨avsp˚alitligamodeller ¨over raketernas aerodynamik. Den h¨arrapporten utf¨oren komparativ studie mellan CFD-simuleringar och dagens modeller f¨oraerodynamikmodellering f¨ortv˚asondraketskonfigurationer vid RUAG Space i Link¨oping.Konfigura- tionerna som unders¨okts¨arMaxus och en tv˚astegsTerrier-Black Brant. Tre parametrar relaterade till raketernas stabilitet har unders¨okts:mot- st˚andskoefficienten d˚aden effektiva anbl˚asningsvinkeln ¨arnoll CD0 , stabilitets- derivatan CNα , och tryckcentrum Xcp. Parametrarna ¨arutv¨arderadei form av beteende och parameterv¨ardenf¨oratt avg¨orahur noggranna dagens mod- eller ¨arj¨amf¨ortmed CFD-simuleringarna. Vid avvikelser j¨amf¨orsdata med tidigare studier f¨oratt avg¨oravad som ¨armest fysikaliskt troligt. Alla parametrar ¨arutv¨arderadesom funktion av Machtal f¨orfullst¨andigakon- figurationer. CFD-simuleringarna ¨arutf¨ordai Ansys CFX 18.2. Ansys ¨arett amerikan- skt f¨oretagsom utvecklar och s¨aljerprogramvara inom flera ingenj¨orsomr˚aden. Ansys ¨aren av de st¨orstakommersiella programvarorna f¨orCFD-simuleringar. Resultaten i denna rapport visar att dagens metod f¨oraerodynamikmod- ellering av Maxus ¨overensst¨ammerv¨almed CFD-simuleringarna, b˚ade vad g¨allerbeteende och parameterv¨arde.Data fr˚anden nuvarande modellen ¨ar fysikaliskt rimliga och st¨ammer¨aven v¨al¨overens med tidigare studier. Resultaten f¨orf¨orstasteget av Terrier-Black Brant uppvisar, f¨ordet mesta, ett identiskt beteende med CFD-simuleringarna, men med varierande noggrannhet vad g¨allerparameterv¨arden. Aven¨ om beteendet f¨orden nu- varande modellen ¨arfysikaliskt rimligt, f¨orutsp˚arden en position f¨ortryck- 4 centrum under den transsoniska fasen som ¨arorimligt l˚angtbak. Resultaten f¨orandra steget av Terrier-Black Brant uppvisar ett, i vissa fall, inkonsekvent och fysikaliskt orimligt beteende. Avvikelserna ¨aremeller- tid begr¨ansadetill vissa flygsekvenser, och inte till modellen som helhet. Bortsett fr˚ande f˚ainkonsistenser den nuvarande modellen uppvisar st¨ammer den nuvarande modellen v¨al¨overens med CFD-simuleringarna vad g¨allerpa- rameterv¨arden. Den nuvarande modellen f¨orMaxus bed¨omsvara noggrann och kan forts¨a- tta anv¨andasof¨or¨andratinom analyser. Det finns inga indikatorer p˚aatt den nuvarande modellen p˚an˚agotvis skulle vara bristf¨allig. Den nuvarande modellen f¨orf¨orstasteget av Terrier-Black Brant f¨orutsp˚ar ett korrekt fysikaliskt beteende, men med varierande precision vad g¨aller faktiska parameterv¨arden. Den nuvarande modellen bed¨omskunna forts¨atta anv¨andasinom analyser, f¨orutsattatt detta g¨orsmed bristerna med modellen i ˚atanke. Den nuvarande modellen f¨orandra steget av Terrier-Black Brant ¨overens- st¨ammerv¨almed CFD-simuleringarna vad g¨allerparameterv¨arden,men mis- sar att f¨orutsp˚astabiliseringen av CD0 f¨orh¨ogaMachtal samt den bak˚atf¨orfly- ttning av tryckcentrum som sker under den transsoniska fasen. Den nu- varande modellen bed¨omsvara tillr¨ackligt noggrann f¨orfortsatta analyser, f¨orutsattatt detta g¨orsmed bristerna med modellen i ˚atanke. 5 Acknowledgements Many people have helped me during the course of this thesis work. These are my acknowledgements to these people, whom I am greatly thankful for. First, I would like to thank Albert Thuswaldner at RUAG Space in Link¨opingwho was my initial contact at RUAG Space and who helped to actualize this thesis work. Thank you for initiating the process of actualizing this work and for always being a familiar and kind face whenever I would run into you. Second, I would like to thank Anders Helmersson, my supervisor at RUAG Space. Thank you for always taking time to answer my questions and for aiding me throughout this work. Third, I would like to thank Gunnar Hellstr¨om,my supervisor at Lule˚a University of Technology. Thank you for all the support, especially in the early phase of this work when I had seemingly endless technical problems. Fourth, I would like to thank my desk neighbours; Malin Thuswaldner, Johan Hedblom, Natasa Jankovic and Erik Sundberg. Thank your for making every day at RUAG Space a pleasant and fun day. Finally, I would like to thank the rest of the personnel at RUAG Space in Link¨opingfor giving me such a warm welcome and for being overwhelmingly kind to me since day one. You have given me a fantastic impression of RUAG Space. I will always cherish my time here. "Make it a habit to tell people thank you. To express your appreciation, sincerely and without the expectation of anything in return. Truly appreci- ate those around you, and you'll soon find many others around you. Truly appreciate life, and you'll find that you have more of it." -Ralph Marston 6 Contents 1 Introduction 10 1.1 Background . 10 1.2 Disposition of the thesis . 11 2 Sounding rockets 12 2.1 Maxus . 13 2.2 Terrier-Black Brant . 14 3 Fundamental concepts of fluid dynamics 16 3.1 Viscosity . 16 3.2 Laminar vs turbulent flow . 17 3.2.1 Relationship with Reynold's number . 17 3.3 Boundary layer . 18 3.4 Compressible vs incompressible flow . 19 3.5 The no-slip condition . 20 3.6 Newtonian vs non-Newtonian fluids . 20 4 Aerodynamic forces 21 4.1 Pressure . 21 4.1.1 Molecular definition of pressure . 22 4.2 Viscous shearing stresses . 26 4.2.1 Couette flow . 26 5 Parameters to be evaluated 31 5.1 Aerodynamic coefficients . 31 5.1.1 Drag coefficient . 32 5.1.2 Lift coefficient . 34 5.2 Center of pressure . 37 7 6 Computational fluid dynamics 38 6.1 Governing equations . 38 6.1.1 Conservation of mass . 39 6.1.2 Conservation of momentum . 39 6.1.3 Conservation of energy . 41 6.2 Approximation . 42 6.3 History . 42 6.4 Fields of application . 43 7 Model implementation 44 7.1 Geometry . 44 7.1.1 Maxus . 44 7.1.2 Terrier-Black Brant . 45 7.2 Fluid domain . 47 7.3 Mesh . 47 7.3.1 Yplus . 49 7.3.2 Orthogonal quality . 49 7.3.3 Aspect ratio . 49 7.3.4 Skewness . 49 7.4 Setup . 50 7.4.1 Flow analysis .