AIAA 2017-3740 AIAA AVIATION Forum 5-9 June 2017, Denver, Colorado 35th AIAA Applied Aerodynamics Conference
On the Aerodynamic Design of the Hyperloop Concept Max M. J. Opgenoord and Philip C. Caplan† ∗
Massachusetts Institute of Technology, Cambridge, MA, 02139
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The Hyperloop is a ground-bas ground-based ed transporta transportation tion system concept slated to drasticall drastically y reduce travel times over medium range distances, for example between San Francisco and Los Angeles. This paper discusses discusses aerodynami aerodynamic c design design consideration considerations s for the Hyperloop Hyperloop pod. A Hyperloop Hyperloop capsule travels travels in an unconvent unconventional ional flow regime – very very low Reynolds Reynolds numbe numbers rs with with high high Mach Mach numbe numbers rs – which which bring brings s with with it uniqu unique e chall challeng enges. es. This This work work focuses focuses on the aerodyna aerodynamic mic design design of the the MIT Hyperloo Hyperloop p Team. eam. For this design, design, it is crucial to delay separation over the pod as much as possible by forcing the boundary layer to transition transition further upstream, upstream, resulting resulting in a droplet droplet shape for the aerodynami aerodynamic c shell. shell. We discuss the nominal performance of the aerodynamic design as well as its performance in transonic flow. The overall overall design of this team’s Hyperloop po d won the design competition of the SpaceX Hyperloop Competition in January 2016.
I.
Intr Introdu oduct ctio ion n
Hyperloop is a concept for high speed ground transportation, consisting of passenger pods traveling at transonic transonic speeds in a partially partially evacuate evacuated d tube. The concept concept was originally originally proposed in a white paper 1 published by SpaceX in 2013 as an alternative to the high-speed rail system currently being developed between between Los Angeles Angeles and San Francisco, rancisco, which was deemed deemed too expensive expensive and slow. slow. The Hyperloop concept could fill a growing need for an alternative transportation mode for short-haul travel. For short routes, such as Los Angeles – San Francisco, or Boston – New York, the time spent traveling at the cruise speed is quite low compared to overall end-to-end travel time due to inescapable ine fficencies in air travel travel (runwa (runway y taxiing, taxiing, climb, climb, descent, descent, holding patterns, patterns, etc.). etc.). The high-frequenc high-frequency y throughpu throughputt of ffi Hyperloop pods could alleviate some of these ine ciencies. Recently, KPMG published a preliminary study commissioned by Hyperloop One – one of the companies commercializing the Hyperloop concept – on the Helsinki–Stockholm corridor where they found that the Hyperloop could cut down end-to-end travel time by 75% to 28 minutes. 2 Furthermore, the market share for high-speed transport is projected to grow rapidly over the next few decades, 3 and the Hyperloop concept could take some pressure o ff increasingly increasingly congested airports and flight routes.
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Momentum is growing in the Hyperloop movement, with a number of newly founded companies attempting to commercialize it. In addition, SpaceX is sponsoring a student competition to encourage innovation and to help accelerate the development of a working prototype, starting June 2015 a . Over 1,000 teams submitted their intent to compete, and over 100 teams made it to Design Weekend in January 2016. The student team from the Massachusetts Institute of Technology – the MIT Hyperloop Team b – won first place overall in that design weekend.4 The aerodynamic design of that team’s prototype is the subject of this paper. Academic Academic research research into into the Hyperloop concept has focused focused mostly mostly on system integration. integration. A conceptual conceptual 5 sizing tool using the OpenMDAO framework focuses primarily on the aerodynamic and thermodynamic interactions between the pod and tube, with recent work focusing on the energy consumption of the system. 6 The pods for the SpaceX Hyperloop Competition were the first physical prototypes of the Hyperloop concept. Recently, one team reported on their aerodynamic design. 7 For that design, a low-fidelity aerodynamic model Graduate Graduate student, student, Departmen Departmentt of Aeronautics Aeronautics and Astronautics Astronautics,, Team Lead & Aero/Structu Aero/Structures res Lead, MIT Hyperloop Team,
[email protected], Student Member AIAA † Graduate Graduate student, student, Departmen Departmentt of Aeronautics Aeronautics and Astronautics Astronautics,, Aero/Structu Aero/Structures res Engineer, Engineer, MIT Hyperloop Team, Team,
[email protected], Student Member AIAA a www.spacex.com/hyperloop b hyperloop.mit.edu ∗
1 of 16 16 American Institute of Aeronautics and Astronautics Copyright © 2017 by M. Opgenoord and P. Caplan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
was used to optimize the outer mold line, which was subsequently analyzed using a three-dimensional RANS solution with a turbulence model. This paper describes the approach taken by the MIT Hyperloop Team. For rapid design iterations, we use an axisymmetric viscous/inviscid coupled boundary layer method to accurately predict predict flow separation and transition. transition. The final design design is then analyzed analyzed using a three-dim three-dimensio ensional nal CFD solver, which is also used to characterize the aerodynamics at higher velocities to investigate the potential issues related to Hyperloop pods traveling through a partially evacuated tube at transonic speeds. Section II discusses historic background of the Hyperloop concept, as well as the SpaceX Hyperloop competition competition.. Section Section III explains the design philosophy chosen by the MIT Hyperloop team, as well as a brief overvie overview w of the overall overall pod design. design. Section Section IV then IV then describes the aerodynamic design methodology. Section V Section V focuses focuses on the final aerodynamic design and its performance for di ff erent erent flow conditions. Finally, Section VI Section VI concludes the paper.
II.
Bac Backg kgro roun und d
Concepts for high-speed trains in vacuum or evacuated tubes can be traced back as far as 1909, when rocket pioneer Robert H. Goddard proposed high-speed passenger-carrying pods traveling through evacuated tubes.8 Bac Bachelet helet introduced introduced the core idea behind magnetically magnetically levitating levitating trains trains as early as 1910.9 Over the years these ideas have been further refined, for instance by the Rand Corporation in 1972 with their “Very High Speed Transport System”.10 The Hyperloop Alpha white paper combined combined several several of these historic concepts concepts1 and spurred a great deal of public public inter interest est in the concept, concept, someth something ing the earlie earlierr ideas ideas were were somewh somewhat at lackin lacking. g. This This white white paper paper discusses a Hyperloop pod that travels at 1220 km/h in km/h in a partially evacuated tube (1/ (1 /1000th of atmospheric pressure) pressure) levitating levitating using air bearings. The use of wheels at these high speeds would be quite problemat problematic ic because of the massive centripetal forces on them. Air bearings are proposed as a more e fficient mechanism, where the pod floats on a thin film of compressed air. In the Hyperloop Alpha concept, this compressed air is supplied by an onboard compresso compressor. r. Propulsion Propulsion is provided provided by a linear induction induction motor. motor. The benefit of this is that the heavy components are built track-side and the pod only has to carry a rotor which makes the propulsion quite e fficient. cient. Furthermor urthermore, e, that same linear induction induction motor can also be used for braking at the other end of the tube to recover a substantial amount of energy. The onboard compressor is also used to improve the e fficiency ciency of the pod at higher higher speeds. speeds. Once Once the pod reaches transonic speeds, the flow around the pod will start to choke, i.e. the flow around the pod will become sonic. sonic. At this sonic condition condition – the so-called so-called Kantrowitz limit 11 – the mass flow around the pod is at its maximum. Therefore, when the speed is further increased, not all flow can travel around the pod and is therefore therefore collected collected in front of the pod. The result is a column column of air being pushed by the p od throughout throughout its run. That pressure pressure build-up results results in significan significantt additional drag. The Hyperloop Alpha concept therefore therefore introduces the on-board compressor to compress the additional flow and suck it through the pod, while at the same time supplying compressed air to the air bearings. Two years after publishing the Hyperloop Alpha white paper, SpaceX announced the Hyperloop student competition to advance the concepts proposed in that white paper to the next level, while at the same time garnering garnering more interest interest from students, students, universities universities and the general general public for the concept. concept. In this competition, students are to design and build Hyperloop pods which are then tested on a 1 mile long, 6 f t diameter tube built by SpaceX. The tube has a flat concrete base on which aluminium (Al 6101) track plates and an aluminium I-beam are installed. The com competi petitio tion n is inten intentio tional nally ly kept kept very very open, open, allow allowing ing for a variet ariety y of diff erent erent designs. designs. Taking the levitation levitation concepts concepts as an example, wheels, air bearings, and magnetic levitation levitation are all allowed. allowed. The Hyperloop Alpha concept used a linear induction motor to get up to speed. Because such a system requires a great deal of integration between the pod and track, and it is quite hard to handle this integration with a large number of teams, SpaceX provides a pusher vehicle to bring pods up to speed. The most important scoring criteria for the competition are the overall run time (therefore favoring high cruise speeds and fast braking), and the potential to scale up the technologies used in the competition vehicle to a full-scale full-scale Hyperloop vehicle. vehicle.
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III.
MIT MIT Hyperl Hyperloop oop Desi Design gn
The competition goal is to advance the Hyperloop concept to the next level by designing technologies that one day could be used in full-scale Hyperloop and by using these technologies in a working Hyperloop prototype. Here we cover the final Top-Level Design of the MIT Hyperloop pod. The overall goal of the MIT Hyperloop Team within this competition was to design and build a pod that scores scores well in both aspects aspects of the competit competition ion,, i.e speed and scalabil scalabilit ity y of systems systems used. The speed goal favo favors rs a light lightwe weigh ightt design design,, while while the scalabil scalabilit ity y goa goall com comes es back back in every every aspect of the pod. There There are several approaches that could be taken to design for scalability, for instance to design a full Hyperloop pod with a large passenger compartment and scale it down for the competition. The MIT Hyperloop team took the approach of focusing on the most important technologies for the Hyperloop concept, and developing scalable scalable technologies technologies for those. Therefore, Therefore, a major focus was the scalabilit scalability y of the levitation levitation design, the braking braking design, design, and the aerodynamic aerodynamics. s. Other major driving requiremen requirements ts for the design were were imposed by the team itself. itself. Firstly Firstly,, the pod had to be built in four months (February 2016 start of manufacturing – May 2016 fully assembled), which meant that simpler/easier simpler/easier-to-to-man manufact ufacture ure designs designs were were often favored. favored. Secondly Secondly,, the pod p od needed needed to accelerat acceleratee at 2.4G – the maximum proposed acceleration o ff ered ered by the SpaceX SpaceX pusher. Finally Finally, the p od had to be robust to changes in performance specifications and track tolerances.
Figure Figure 1. Explode Exploded d view of the MIT Hyperloop Hyperloop Design. Design.
An overview of the MIT Hyperloop design is shown in Fig. 1. The prototype is 2. 2.4 m long, weighs 258 k 258 k g , and is designed for a top speed of 400 km/h. km/h. The pod has no propulsion on board, as we rely on the SpaceX pusher to get up to cruising speed. Passive magnetic levitation (maglev) is used to levitate above the track, specifically the pod uses an
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electrodynamic suspension (EDS) system. (EDS) system. Although the original Hyperloop Alpha concept uses air bearings, the track tolerances were poor enough that a large pressure vessel would be required to keep su fficient track clearance (> (> 2 mm 2 mm), ), and it was therefore therefore decided decided not to use air bearings. EDS works with larger gap heights heights (on the order of a few milimeters), and additionally becomes more e fficient at higher speeds. The levitation system does not require power, therefore it scores well for scalability because of its safety and e fficiency at high speeds. Magnetic Magnetic levitation levitation is notorious notorious for being underdamped, underdamped, therefore therefore a suspension suspension is added between the magnet arrays and the pod. The eddy-current braking system uses the same physical principle as the levitation design, only now the design design is optimi optimized zed for drag rather rather than than lift. lift. The design design is simila similarr to an eddy-c eddy-curr urren entt brake brake on a rollercoast rollercoaster. er. As discussed earlier, earlier, linear induction induction motors will likely likely be b e the best technolog technology y for propulsion propulsion and deceleration. However, track-side infrastructure is required for that. In the case of an anomaly mid-run (e.g. a problem with a p od further down the track, track, tube de-pressur de-pressurizatio ization/bre n/breach ach,, etc.) the pod still has to brake. brake. Therefore Therefore,, the braking braking system on the MIT Hyperloop po d is designed designed as an emergency emergency braking braking system for a full-scale Hyperloop, decelerating the pod upwards of 2. 2 .4G. The pod does not have an onboard compressor, both because of the lower speeds in the competition and because the pod does not have air bearings that need to be supplied with air. The Kantrowitz limit will be further discussed in Section V Section V..
IV.
Aerodynam Aerodynamic ic Design Design Methodo Methodolog logy y
This section details the design approach used for the aerodynamic shell, and dicusses any analysis tools used in the design. IV.A. IV.A.
Requir Requireme ement ntss
The main performance requirement for the aerodynamic shell is to keep the overall C D A for the pod below 0.5, to adhere adhere to the overall overall pod run time requiremen requirement. t. Furthermore urthermore,, the rules require require that a dummy dummy is carried carried in the p od “in a reasonable reasonable position” position” during the test. test. We chose to use a 3 f t dummy dummy. Other selfimposed requirements are to keep the total weight of any aerodynamic covers below 10 kg, kg , and to be able to access the inside of the pod within 2 minutes.
Figure 2. The aerodynamic aerodynamic shell cover coverss the systems inside the pod.
Of course, the aerodynamic shell has to cover the structural frame, while leaving enough room for the dummy dummy, electronic electronics, s, hydraulics, hydraulics, etc. inside the pod, as shown in Fig. 2. In this case, the other subsystems drive the size of the shell. IV.B. IV.B.
Flow Flow Regime Regime
The choice of analysis tools for the aerodynamics of this pod depends strongly on the flow regime the pod experiences. experiences. Even though the Hyperloop system system consists consists of a large partially partially evacuat evacuated ed tube, the remaining remaining air in the tube still necessitates necessitates a careful aerodynamic aerodynamic design design of the outer shape of the pod. Therefore Therefore,, the 4 of 16 16 American Institute of Aeronautics and Astronautics
MIT Hyperloop pod has an aerodynamic aerodynamic shell to cover cover the internals internals of the p od. To reduce manufactu manufacturing ring risk, the aerodynamic shell is decoupled from the structural frame of the pod, motivated by the aggressive manufacturing timeline in this project. Because a Hyperloop pod travels at high speed through a partially evacuated tube, it operates in an unconven unconventiona tionall flow regime. For the SpaceX SpaceX Hyperloop competition, competition, the tube pressure is 860 P a, and the pod will travel at 250 mph. mph. Even Even though though the pressur pressuree is quite quite low, low, the fluid fluid can still be modele modeled d as a continu continuum. um. The Knudsen number number Kn is a dimensionless parameter that is typically used to describe the boundary of continuum flow, and is defined as the ratio between the molecular mean free path λ and a characteristic length scale in the flow. 12 For this condition, the Knudsen number is Kn = O 10 6 , flow which is still far below the continuum limit ( O 10 1 ).13 The Reynolds number for this flow regime is around 60,000, which means that the flow will transition from laminar laminar to turbulen turbulentt flow somewhere somewhere on the pod. Capturing Capturing this transition transition accurately accurately is crucial crucial and therefore therefore drives drives the selection selection of appropriat appropriatee aerodynamic aerodynamic analysis analysis tools. This Reynolds number number is of the same order of magnitude as the full-scale Hyperloop pod in the Hyperloop Alpha paper which travels at a higher higher speed and is longer, longer, but the pressure pressure in the tube is ten times lower. lower. Finally, Finally, the Mac Mach h number for the SpaceX Hyperloop competition is around 0.3, requiring compressibility of the fluid to be taken into account. For a full-scale Hyperloop at higher speeds, this Mach number is considerably higher. As mentioned earlier, the Kantrowitz limit is not significant for this competition due to the lower speeds, and therefore no compressor is included in design analyses. −
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IV.C. IV.C.
Flow Flow Analys Analysis is
During the preliminary design phase, extensive flow analyses are carried out to characterize the design space. Relying Relying on a 3D Navier-Stok Navier-Stokes es CFD simulatio simulation n for each design tweak tweak is simply simply too expensive. Therefore, Therefore, in the preliminary design phase we relied on an axisymmetric viscous/inviscid analysis code, MTFLOW. 14 Moreov Moreover, er, this viscous/inviscid viscous/inviscid analysis code allows allows for capturing transition transition of the bounda b oundary ry layer layer from lamina lam inarr to turbul turbulen entt accura accuratel tely y, which which is critic critical al to the design. design. MTFLO MTFLOW W is typic typicall ally y used used to design design axisymmetr axisymmetric ic bodies b odies and axisymmet axisymmetric ric flow passages. This throughflow throughflow code uses an integral integral boundary layer method to solve for the laminar or turbulent boundary layer and a streamline curvature formulation to solve for the inviscid outer flow. The coupling between the inviscid and viscous flow is achieved through the displacemen displacementt body b ody model. MTFLOW MTFLOW uses the e the e n method to capture boundary layer transition. 15,16 We used MTFLOW v2.12, which improves its accuracy of blunt trailing edges. In order to analyze the final 3D shape of the pod we resorted to a 3D Navier Stokes solver. Unfortunately, these solvers in general are worse at capturing transition than a viscous/inviscid analysis code like MTFLOW.
Figure 3. Design parameters parameters for shell geometry geometry..
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IV.D IV.D..
Geom Geomet etry ry
To facilitate facilitate rapid design iterations iterations,, we parametrize parametrize the aerodynamic aerodynamic shell in terms terms of a few geometric geometric parameters, which can be used for trade-o ff studies. studies. The curvature curvaturess in the geometry geometry are generated generated using Lam´ e curves. The geometry for the aerodynamic shell as shown in Fig. 3 is parameterized in terms of the overall length of the pod, nose length l n , width of the pod w, w , height of the nose hn , tail height h height h t, and the Lam´e parameters parameter s for the nose λn , the side of the nose λsn , the back λb , and the side of the back λsb . The geometry shown in Fig. 3 Fig. 3 is is a three-dimensional geometry, whereas for preliminary design studies we rely on an axisymmetric solver. The conversion from such a three-dimensional geometry to an axisymmetric one is never perfect; for one the pod actually does not travel in the middle of the tube but travels towards the bottom of the tube. The tube is also not perfectly perfectly circular because because of the concrete concrete base. Howeve However, r, by using a variable axisymmetric tube radius, we can minimize the discrepancies between the axisymmetric and three-dimensional geometries. The variable axisymmetric tube radius is chosen such that the area ratio between the axisymmetric tube and axisymmetric pod is the same as the area ratio between the actual tube and three-dimensional pod. This process is illustrated in Fig. 4 Fig. 4.. For the axisymmetric shape we revolve the top centerline of the outer mold line on itself. . Move pod to center of tube and make tube circular
Use top center line as axisymmetric geometry and find variable axisymmetric tube radiu radiuss MTFLOW MTFLOW geometry geometry with initial mesh
Figure 4. Illustration Illustration of recoveri recovering ng the axisymmetric axisymmetric geometry geometry from the full three-dimen three-dimensional sional geometry geometry.
V.
MIT Hyperloop Hyperloop Aerodyna Aerodynamic mic Design Design
The main trade-off s for the aerodynamic design of the MIT Hyperloop pod are discussed in this section. We discuss the final aerodynamic aerodynamic shape, its performanc performancee at competition competition speeds, and characteri characterize ze its performance at transonic speeds.
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V.A.
Kantro Kantrowitz witz Limit Limit Conside Consideratio rations ns
When When a pod trave travels ls at transo transonic nic speeds speeds throug through h a tube, tube, it could choke choke the flow around around the pod. This This happens when the Mach number of the flow around the pod is equal to 1. When the pod speeds up further, a large pressure increase in front of the pod results, because the mass flow that can go around the pod is limite limited. d. This This sonic sonic condit condition ion is known known as the Kantro Kantrowit witzz limit. limit.11 There are two main ways to avoid the Kantrowit Kantrowitzz limit. The first option is to increase the ratio between between tube cross-sect cross-sectional ional area and po d cross-sect cross-sectional ional area, thereby allowing allowing relatively relatively more air to pass around around the pod at a lower lower velocity. velocity. The other option uses a compressor that sucks in air through the front of the pod and feeds the compressed air through a duct in the pod which subsequently exits through a nozzle at the back, which is the approach taken in the Hyperloop Alpha white paper. 1 Neither option is perfect, it either means limiting the crosssectional area of the pod, hence decreasing payload or increasing tube construction costs, or it means adding an expensive, expensive, high-maintenan high-maintenance ce compresso compressorr to each each pod. Furthermore urthermore,, transonic transonic compressors compressors at such low Reynolds numbers would require a large research and development e ff ort, ort, because they are not in use in any aerospace application today. 0.9
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Figure Figure 5. Area Area ratio ratio (pod-to-tube (pod-to-tube)) versu versuss Mach Mach numbe number. r. M ext ext is the maximum Mach number of the flow around the pod – if M if M = 1 the flow is exactly exactly choked. The red line indicates indicates the Kantrowi Kantrowitz tz limit.
As shown in Fig. 2 Fig. 2,, the pod does not have a compressor, because it is not worthwhile to use one for the SpaceX SpaceX Hyperloop Hyperloop competition. competition. Fig. 5 Fig. 5 shows the variation of the external Mach number to the pod-to-tube ratio and the freestrea freestream m Mach number. The external Mach number number is the maximum maximum Mach number of the flow around around the p od, the flow is choked choked when that external external Mach number number equals 1.0. Fig. 5 clearly shows that for a reasonably sized pod without a compressor, the Kantrowitz limits the speed of the pod without an additional additional drag increase. increase. At an area ratio of 0.3 and a Mach number number of 0.3, the flow around around the p od is not even close to choking, as seen in Fig. 5. Because compressors also have a large risk associated with them in terms of design, manufacturing, and cost, the MIT Hyperloop team decided not to use a compressor. V.B. V.B.
Axisym Axisymmet metric ric design design
First, an axisymmetr axisymmetric ic aerodynamic aerodynamic shell was designed using MTFLOW. MTFLOW.14 All of the results in this section are generated using MTFLOW. In the aerodynamic design we relied on sweeps over the design parameters in Fig. 3, Fig. 3, rather than going for a purely purely numerical numerical optimization optimization method. The main reason for this was to gain more physical insight in this design problem with a large unexplored design space, and to use constraints that would be harder to capture in mathematical statements. Additionally, this allowed for a more aggressive design schedule.
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Cp 1 0.75 0.5 0.25 0 -0.25 -0.5 -0.75 -1 -1.25 -1.5 -1.75 -2
Figure 6. Laminar Laminar flow separation separation on a Hyperloop pod at a Reynolds number number Re Re = 60, 60, 000 and Mach number M = 0.3. The boundary layer layer and wake wake are indicated indicated in gray. gray. ∞
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Figure 7. Shape parameter parameter and momentum momentum defect for diff erent erent dummy positions. The shape in gray positions positions the dummy in the middle resulting in a flatter shape (C ( C D A = 0.0553), the shape in red positions the dummy in the nose (C (C D A = 0.0431).
At these low Reynolds numbers (Re (Re ' 60 60,, 000) the boundary layer separates very easily, and proper aerodynamic design is needed to reduce that as much as possible to keep the pressure drag to a minimum. As an example, consider the sleek axisymmetric shape in Fig. 6. The laminar boundary layer separates at a very low adverse pressure gradient – just after the inflection point on the geometry – and therefore this shape results in large amounts of pressure drag. Thus, even though the skin friction drag is low due to laminar flow existing on the surface, the pressure drag is high because of the large wake. This laminar separation has to
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be prevent prevented ed in order to reduce reduce drag. Turbulent urbulent boundary layers can handle larger pressure gradients, gradients, and a key part to this aerodynamic design is therefore to ensure that the boundary layer transitions to turbulent towards the nose of the pod. The transition transition location location depends depends on N on N crit crit , which is a measure for the ambient disturbance level as well as some degree of receptivity. 17 Because Because we expect the environmen environmentt in the tube to b e fairly noisy – e.g. dust in the tube or vibrations due to track disturbances – we use N crit crit = 4 throughout the design. The dummy is the largest “component” that has to be fitted inside the shell, and its position is therefore an important important consideration consideration in the design of the aerodynamic aerodynamic shell. Here, we show the trade-o trade-o ff between between two options. The first option is to put the dummy in the nose of the pod in an upright position, thereby leaving more room for components components towards towards the rear of the pod but resulting resulting in a higher nose. The second option option is to lay the dummy more flat over the components inside the pod, thereby reducing the height of the pod and allowing for a more gradual ramp-up to the highest point of the pod. Fig. 7 Fig. 7 shows shows the results results for both of these shapes. For the shape with the dummy in the nose, the boundary layer transitions much closer to the nose, therefore delaying separation and reducing pressure drag. For the shape with the dummy laying flat, the laminar boundary layer separates close to the highest point on the pod, resulting resulting in large pressure drag. Therefore, Therefore, even even though the shape with the dummy dummy in the nose has a larger larger cross-sectional cross-sectional area, area, the drag is lower. The reason for this is the blunt nose which which is known known to 18 promote early transition. Several diff erent erent sweeps over design parameters have been performed during the design stage, although only a few of them are discussed here. Fig. 8 shows the influence of the nose Lam´ e parameter and the tail height on the drag coe fficient. cient. When the nose is too shallow (e.g. (e.g. λn = 1.5) transition will occur later on the pod and more pressure drag results. However, too blunt of a nose increases the curvature on the highest point of the nose, which also induces induces separation. separation. For the tail height, height, the higher the tail the higher the pressure drag. However, too low of tail does not add any benefit because the flow separates anyway. 0.080 0.070
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Figure 8. Nose bluntness bluntness and tail height height influence on drag for axisymmetric axisymmetric pod.
We also investigate investigate the use of an aerodynamic aerodynamic tail section section to reduce reduce drag. The idea is to keep a straight straight sectio section n of most most of the componen components ts on the pod to provid providee max maxim imum um paylo payload ad capaci capacity ty,, and then add a lightw lightweigh eightt aerodynamic aerodynamic tail section section to keep keep drag to a minimum. minimum. We compare such a design to our final design in Fig. 9. The concept with an aerodynamic tail has a smaller cross-sectional diameter to keep the 9 of 16 16 American Institute of Aeronautics and Astronautics
internal internal volume volume (excluding (excluding tail) similar. The momentum momentum defect defect on the pod surface surface is much much bette b etterr for the pod with an aerodynamic aerodynamic tail because there there is no adverse adverse pressure gradient gradient on the p od. Howeve However, r, the flow separates separates as soon as the aerodynamic aerodynamic tail is reached, reached, dramatically dramatically increasing increasing the momentum momentum defect. The large increase in pressure pressure drag therefore therefore renders renders the aerodynamic aerodynamic tail useless. c
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1.6
Figure 9. Comparison Comparison between between designs with aerodynamic tail (gray – C – C D A = 0.0950) and without aerodynamic tail (red – C D A = 0.0431).
The flow field around the final geometry is shown in Fig. 10. As mentioned several times, if we can delay separation, we can dramatically reduce the pressure drag, because a turbulent boundary layer can handle adverse adverse pressure gradients gradients much much better. better. Therefore Therefore,, the final design design has a blunt blunt nose section which triggers transition transition slightly slightly downstream downstream of the tallest point of the pod. This results in no flow separation separation until until the very very back of the pod. The back of the po d is not tapered down further, further, because trying to close it completely completely (i.e. such such that the cross-sectio cross-sectional nal area of the back is 0) is futile futile because because the flow would separate separate anyway anyway.. Additionally, this shape results in clean separation o ff the back of the pod, which aids stability, although this is less of a problem here because the ratio of aerodynamic forces to intertial forces on the pod is quite low. Lastly, we investigate the sensitivity of the performance of the final axisymmetric design to Reynolds number. number. The variation variation of drag as a function function of Reynolds Reynolds number number is similar similar to the well-know well-known n variation ariation of 19 drag over a cylinder as a function of Reynolds number. The results for low turbulence free stream are computed with N crit roughness is quite important important for the drag of the po d. Trying crit = 7.0. We see that the roughness to trip the boundary layer layer near the nose could therefore therefore be helpful. helpful. This could be achieve achieved d by roughening roughening up the nose section. section. Howeve However, r, Reθ may not be high enough to e ff ectively ectively use an physical trip on the nose c section . In the end, we decided decided against tripping the boundary layer, layer, because this would require detailed detailed c
Reθ is the Reynolds number based on the momentum thickness of the boundary layer. Transition from laminar to turbulent flow is only possible when locally Reθ ≥ 150 . . . 250.
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Cp 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3
Figure 10. Flow field around the final axisymmetric axisymmetric design at Reynolds Reynolds number Re number Re = 60, 60, 000 and Mach number M = 0.3. The boundary layer layer and wake wake are indicated indicated in gray. gray. ∞
wind tunnel experiments to get right, and it was decided to spend valuable resources elsewhere instead. 10 0.050 N
0.040
[
A
D
D
, g a r D
C0.030
0.020 0.010 5000 50000 0
1000 100000 00 1500 150000 00 2000 200000 00 Reynolds number, number, Re
2500 250000 00
(a) Drag coefficient versus Reynolds number
Total (N crit = 4.0)
8
]
Pressure (N crit = 4.0) Friction (N crit = 4.0)
6
Total (N crit = 7.0)
4 2 0 500 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 Tube pressure, p [ P a]
(b) Drag versus tube pressure. pressure. Note that the tube pressure is proportional to Reynolds number, because the pod velocity and tube temperature are kept constant constant here.
c
∞
5
∞
H , 4 r e t e m3 a r a p 2 e p 1 a h S
2
V 0.025 ρ
/ 0.020 P
, t c 0.015 e f e D0.010 m u t n 0.005 e m0.000 o 0.0 M
0.5
1.0
1.5
2.0
2.5
3.0
0 0.0
50k 80k 110k 140k 170k 200k 230k 250k
0.2
0.4
0.6
0.8
1.0
x/c
x/c
(c) Momentum Momentum defect
(d) Shape parameter over body
Figure 11. Sensitivit Sensitivity y of final axisymmetric axisymmetric shape to Reynolds number. number.
V.C.
Final Three-Dime Three-Dimensio nsional nal Shape
To generate the three-dimensional shape from the final axisymmetric shape, the axisymmetric shape is used as the center centerline line for the pod. The other other design design paramet parameters ers from Fig. 3 are determined from packaging constrain constraints ts with the other subsystems subsystems (e.g. structura structurall frame, frame, electronics electronics,, hydraulic hydraulics, s, etc.). etc.). We study the performance performance of this design using STAR-CCM STAR-CCM+. +. For these simulations simulations we solve solve the laminar Nav Navier-S ier-Stok tokes es equations on a very fine grid (2.58 million cells). Adding a turbulence model would overestimate the transition location location to be too far upstream upstream and therefore therefore underestima underestimate te separation separation to occur too far downstream downstream.. These simulations have to be unsteady because flow separation o ff the the back is an inherently unsteady phenomenon. Total flow conditions (total temperature, total pressure) are set at the inlet to the domain and a pressure outlet is used at the outflow. The results for the laminar Navier-Stokes simulations over the pod are shown in Fig. 12. We can see a small degree of vortex shedding o ff the back of the pod, but the overall influence on the drag coe fficient is low, as shown in Fig. 12(a) Fig. 12(a).. Vortex shedding is to be expected at these low Reynolds numbers. 20 The drag 11 of 16 16 American Institute of Aeronautics and Astronautics
coefficient is of course quite di ff erent erent from the axisymmetric case due to 3D interference e ff ects. ects. However, However, the trends that are deduced from the axisymmetric axisymmetric flow results results are still valid. valid. We see that the flow over the top of the pod stays stays attached attached until the back, agreeing agreeing with the axisymmet axisymmetric ric results. results. The drag could be lowered lowered by covering covering the skis with aerodynamic aerodynamic covers. covers. Howeve However, r, this would reduce accessibility accessibility to critical critical components on the skis, and therefore no aerodynamic covers for the skis are used. 0.106 0.104 0.102 A0.100 D C0.098 0.096 0.094 0.092 0
10 20 30 40 Non-dimensional time, t¯ = V t/l
50
∞
(a) Drag coefficient versus non-dimensional time ¯t.
(b) Velocity field contours at ¯t = 48. Figure 12. Laminar Laminar Navier Stokes Stokes solution of the final aerodynamic aerodynamic design 110 m/s ( m/s (Re Re = = 60, 60, 000, 000, M = 0.32).
V.D.
Perform Performance ance at Transo Transonic nic Speed
Although the pod will not see any transonic speeds during the competition, we still investigate its performance at higher higher speeds speeds here here because because it is such such an importan importantt part part of the Hyperloo Hyperloop p concep concept. t. In this part part of the work, work, we rely on turbulent turbulent 3D Nav Navier-S ier-Stok tokes es simulations. simulations. At these higher higher speeds – we increase increase the po d velocity, thereby increasing both Mach number and Reynolds number – turbulent flow is expected over a larger larger portion of the pod, and therefore therefore using a turbulence turbulence model is more justified. justified. We use the κ-ω SST 21,22 turbulence model, which is known for handling separated flows and adverse pressure gradients well. 23 Any simulation near and above the Kantrowitz limit has to be unsteady. The choking of the flow around the pod po d and the subsequen subsequentt pressure pressure build-up is an inherently inherently unsteady unsteady phenomenon, phenomenon, and prevent prevent a steady steady simulation simulation from convergin converging. g. This also requires requires careful set-up of the inlet and outlet outlet boundary boundary conditions, conditions, i.e. specifying specifying total pressure and temperature temperature at the inlet, and a pressure outlet at the outflow outflow bounda b oundary ry.. Note that the meshes for each run are di ff erent erent to ensure that y+ y + ≤ 1 everywhere on the pod boundary.
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(a)
(b)
M ∞
M ∞
= 0 .65, below Kantrowitz Kantrowitz limit.
= 0 .675, below Kantrowitz limit, a small shock develops.
(c)
M ∞
= 0 .70, above Kantrowitz limit.
Figure Figure 13. Contou Contours rs of local local Mach Mach numbe number r around the pod for diff erent erent freestream Mach numbers.
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0.450 0.400 0.350 A0.300 D C0.250 0.200 0.150 0.100 0.45 0.45 0.50 0.50 0.55 0.55 0.60 0.60 0.65 0.65 0.70 0.70 0.75 0.75 0.80 0.80 0.85 0.85 Mach number, M ∞
Figure 14. C D A as a functi function on of Mach number number for the final design. design. The large drag build-up build-up starts starts around around M = 0.675. 675. Note Note that that the freestr freestream eam densit density y is kept kept consta constant nt,, theref therefore ore the Reynol Reynolds ds numbe number r increa increases ses proportionall proportionally y with Mach number. ∞
The change in C D A as a function of Mach number is shown in Fig. 14. The small drag increase from M = 0.5 to M to M = 0.65 can be explained by the flow turning supersonic over the highest point of the pod (as shown in Fig. 13(a)), 13(a)), which results results in a small shock with associated associated wave wave drag. Although Although part of the flow over the pod is supersonic at those freestream Mach numbers, the flow has not choked yet, because the supersonic supersonic region does not reach all the way way to the tube boundaries. boundaries. The flow around the pod chokes chokes around M around M = 0.675, resulting resulting in a large drag increase for larger Mach numbers. numbers. Due to the fact that not all flow can continue continue past the pod, a pressure build-up build-up in front front of the pod results. results. Fig. 15 15 shows shows the pressure coefficient along the tube, 1 m above the pod, which clearly shows a large pressure increase in front of the pod for freestream freestream Mach numbers numbers higher than 0.675 0.675.. The drag build-up build-up due to exceeding the Kantrowitz Kantrowitz limit is signficant, the drag coe fficient is three times as high for M = 0.8 compared to M = 0.65. Note Note that part of the drag increase is also the result of the wave drag increase due to the associated strong normal shock, as shown in Fig. 13(c). 13(c). Furthermor urthermore, e, the shock-induced shock-induced boundary layer separation separation for M > 0.70 also increases the pressure pressure drag. The drag increa increase se due to the exceedin exceedingg the Kantro Kantrowit witzz limit limit is substa substant ntial: ial: a threethree-fol fold d increa increase se in C D A between M = 0.65 and M = 0.80. That That additio additional nal drag increas increasee result resultss in a power power loss of 31 kW . kW . Howeve However, r, it is questionabl questionablee that a compresso compressorr used to avoid avoid exceeding exceeding the Kantrowitz Kantrowitz limit could compress compress the air to feed it through the pod for less power. For example, the Hyperloop Alpha concept’s concept’s first 1 stage compressor has a power requirement of 276 kW , kW , and Chin et al. found found that for their configuratio configuration n the compressor power requirement exceeded 300 kW . kW .5 For our configuration, if we assume an isentropic efficiency for the compressor of 80% and a duct d area of 0. 0.05 05 m m 2 , the power requirement for the compressor is 204 kW at M = 0.80. Of course, if the power requireme requirement nt for a compresso compressorr to avoid avoid the Kantrowitz Kantrowitz limit is higher than the power loss due to the additional drag from exceeding the Kantrowitz limit, adding a compressor would be futile. ∞
∞
∞
∞
∞
∞
∞
∞
∞
p
C 0.500
, t n e i c 0.000 fi f e o -0.500 C e r u s -1.000 s e r -30 P
M ∞ = 0.55 M ∞ = 0.60 M ∞ = 0.65 M ∞ = 0.675 M ∞ = 0.70 M ∞ = 0.75 M ∞ = 0.80
-20
-10
0
10
20
30
x [ m]
Figure Figure 15. 15. Pressur Pressure e coefficient at 1 m above the base of the shell along tube for di ff erent erent Mach numbers.
d
The duct feeds the compressed air from the compressor outlet to the nozzle at the back of the pod.
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VI. VI.
Conc Conclu lusi sion on
This paper presented the aerodynamic design of the MIT Hyperloop pod, which participated in the SpaceX Hyperloop Competition from 2015–2017, where it won best overall design at Design Weekend in January January 2016. The aerodynamic aerodynamic design strategy strategy was two-fo two-fold. ld. First, geometry geometry sweeps sweeps were performed performed using a fast axisymmetric viscous/inviscid analysis tool, while accounting for di ff erent erent flow rates between the axisymme axisymmetri tricc and 3D shape. shape. In the aerodyna aerodynamic mic design design it was was crucia cruciall to transi transitio tion n the boundary boundary layer to turbulent close to the front of the pod such that higher adverse pressure gradients are tolerated before separation. separation. Such Such a design strategy strategy increases increases friction drag but dramatica dramatically lly reduces reduces pressure drag. Once the axisymmetric shape was decided upon, the final three-dimensional geometry was analyzed using a three-dime three-dimensiona nsionall Nav Navier-S ier-Stok tokes es solver to characte characterize rize its final performance performance at design design speed. Finally, Finally, we investigated the performance of the design at transonic speed, where it was found that violating the Kantrowitz limit could lead to three-fold increase in drag coe fficient.
Acknowledgements This engineering project’s successful outcome was the result of a massive team e ff ort ort by the MIT Hyperloop Team, consisting of 35 team members across the Mechanical Engineering, Aeronautical & Astronautical Engineering, and Electrical Engineering & Computer Science departments, as well as the Sloan School of Managemen Management. t. This work could not have been completed completed without their contributio contribution n to the project. The MIT Hyperloop Team was fortunate to have an array of sponsors, who generously provided advice and funding for this project e , their support is hereby hereby acknowledge acknowledged. d. For this work work in particular, particular, Siemens Siemens Product Lifecycle Management is thanked for sponsoring the use of STAR-CCM+, as are Main & Partners and Cameron Cameron Paget for their help with graphics graphics of the pod. Additionally Additionally,, we would like to thank SpaceX for organizing and hosting hosting this competition. competition. Finally, we would like to thank Professor Mark Drela for his initial advice on the aerodynamic design, allowing the use of MTFLOW, and adapting MTFLOW to handle blunt trailing edges better.
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e
The full list of sponsors can be found at hyperloop.mit.edu/sponsors.
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14
Drela, M., “A User’s Guide to MTFLOW MTFLOW 2.01,” Tech. Tech. rep., Massachusett Massachusettss Institute Institute of Technology echnology,, Cambridge, Cambridge, MA,
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