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NASA NTRS2015

Overview of the 2nd Gen 3.7m HIAD Static Load Test

To support NASAs long term goal of landing humans on Mars, technologies which enable the landing of heavy payloads are being developed. Current entry, decent, and landing technologies are not practical for human class payloads due to geometric constraints dictated by current launch vehicle fairing limitations. Therefore, past and present technologies are now being explored to provide a mass and volume efficient solution to atmospheric entry, including Hypersonic Inflatable Aerodynamic Decelerators (HIADs). In October of 2014, a 3.7m HIAD inflatable structure with an integrated flexible thermal protection sys-tem (F-TPS) was subjected to a static load test series to verify the designs structural performance. The 3.7m HIAD structure was constructed in a 70 deg sphere-cone stacked-toroid configuration using eight inflatable tori, which were joined together using adhesives and high strength textile webbing to help distribute the loads throughout the inflatable structure. The inflatable structure was fabricated using 2nd generation structural materials that permit an increase in use temperature to 400 C+ as compared to the 250 C limitation of the 1st generation materials. In addition to the temperature benefit, these materials also offer a 40 reduction in structure mass. The 3.7m F-TPS was fabricated using high performance materials to protect the inflatable structure from heat loads that would be seen during atmospheric entry. The F-TPS was constructed of 2nd generation TPS materials increasing its heating capability from 35W sq cm to over 100W sq cm. This test article is the first stacked-torus HIAD to be fabricated and tested with a 70 deg sphere-cone. All previous stacked-torus HIADs have employed a 60o sphere-cone. To perform the static load test series, a custom test fixture was constructed. The fixture consisted of a structural tub rim with enough height to allow for dis-placement of the inflatable structure as loads were applied. The tub rim was attached to the floor to provide an airtight seal. The center body of the inflatable structure was attached to a pedestal mount as seen in Figure 1. Using an impermeable membrane seal draped over the test article, partial vacuum was pulled beneath the HIAD, resulting in a uniform static pressure load applied to the outer surface. During the test series an extensive amount of instrumentation was used to characterize deformed shape, shoulder deflection, strap loads, and cord loads as a function of structural configuration and applied static load. In this overview, the 3.7m HIAD static load test series will be discussed in detail, including the 3.7m HIAD inflatable structure and flexible TPS design, test setup and execution, and finally results and conclusions from the test series.

HIAD↗

NASA NTRS1971

Calculation of inviscid surface streamlines and heat transfer on shuttle type configurations. Part 2: Description of computer program

A description of the computer program used for heating rate calculation for blunt bodies in hypersonic flow is given. The main program and each subprogram are described by defining the pertinent symbols involved and presenting a detailed flow diagram and complete computer program listing. Input and output parameters are discussed in detail. Listings are given for the computation of heating rates on (1) a blunted 15 deg half-angle cone at 20 deg incidence and Mach 10.6, (2) a blunted 70 deg slab delta wing at 10 deg incidence and Mach 8, and (3) the HL-10 lifting body at 20 deg incidence and Mach 10. In addition, the computer program output for two streamlines on the blunted 15 deg half-angle cone is listed. For Part 1, see N71-36186.

Dejarnette, F. R.↗

NASA NTRS1953

The similarity law for hypersonic flow and requirements for dynamic similarity of related bodies in free flight

The similarity law for nonsteady, inviscid, hypersonic flow about slender three-dimensional shapes is derived. Conclusions drawn are shown to be valid for rotational flow. Requirements for dynamic similarity of related shapes in free flight are obtained. The law is examined for steady flow about related three-dimensional shapes. Results of an experimental investigation of the pressures acting on two inclined cones are found to check the law as it applies to bodies of revolution.

Hamaker, Frank M↗

NASA NTRS1991

Local and overall aerodynamic coefficients for bodies in hypersonic, rarefied flow

A computational method is given for the prediction of local pressure and viscous shear stress on windward surfaces of bluff, convex, axisymmetric or quasi-axisymmetric, hypersonic bodies in the transitional, rarefied flow regime. Overall aerodynamic forces and moments are computed by integration of the local quantities. The method is based upon a correlation of local pressure and shear stress computed by the direct simulation Monte Carlo (DSMC) numerical technique for cold wall, real gas conditions and some supplemental data from low-density, hypersonic wind tunnels. The relative simplicity of the method makes it feasible to do the necessary calculations with a personal computer. Two-dimensional shapes and leeward surfaces are not included in the scope of the method as it is presented here. Results are compared with DSMC computations for both local and overall coefficients. The latter includes sphere and blunt cone drag as well as lift and pitching moment coefficients for the NASA AFE vehicle at various angles of attack. Very satisfactory agreement is shown.

Potter, J. Leith↗

NASA NTRS2016

Manufacturing Challenges and Benefits When Scaling the HIAD Stacked-Torus Aeroshell to a 15m-Class System

HIAD↗

NASA NTRS2016

Manufacturing Challenges and Benefits when Scaling the HIAD Stacked-Torus Aeroshell to a 15m-Class System

Over a decade of work has been conducted in the development of NASAs Hypersonic Inflatable Aerodynamic Decelerator (HIAD) deployable aeroshell technology. This effort has included multiple ground test campaigns and flight tests culminating in the HIAD projects second generation (Gen-2) aeroshell system. The HIAD project team has developed, fabricated, and tested stacked-torus inflatable structures (IS) with flexible thermal protection systems (F-TPS) ranging in diameters from 3-6m, with cone angles of 60 and 70 deg. To meet NASA and commercial near term objectives, the HIAD team must scale the current technology up to 12-15m in diameter. Therefore, the HIAD projects experience in scaling the technology has reached a critical juncture. Growing from a 6m to a 15m-class system will introduce many new structural and logistical challenges to an already complicated manufacturing process.Although the general architecture and key aspects of the HIAD design scale well to larger vehicles, details of the technology will need to be reevaluated and possibly redesigned for use in a 15m-class HIAD system. These include: layout and size of the structural webbing that transfers load throughout the IS, inflatable gas barrier design, torus diameter and braid construction, internal pressure and inflation line routing, adhesives used for coating and bonding, and F-TPS gore design and seam fabrication. The logistics of fabricating and testing the IS and the F-TPS also become more challenging with increased scale. Compared to the 6m aeroshell (the largest HIAD built to date), a 12m aeroshell has four times the cross-sectional area, and a 15m one has over six times the area. This means that fabrication and test procedures will need to be reexamined to ac-count for the sheer size and weight of the aeroshell components. This will affect a variety of steps in the manufacturing process, such as: stacking the tori during assembly, stitching the structural webbing, initial inflation of tori, and stitching of F-TPS gores. Additionally, new approaches and hardware will be required for handling and ground testing of both individual tori and the fully assembled HIADs.There are also noteworthy benefits of scaling up the HIAD aeroshell to a 15m-class system. Two complications in working with handmade textile structures are the non-linearity of the material components and the role of human accuracy during fabrication. Larger, more capable, HIAD structures should see much larger operational loads, potentially bringing the structural response of the material components out of the non-linear regime and into the preferred linear response range. Also, making the reasonable assumption that the magnitude of fabrication accuracy remains constant as the structures grow, the relative effect of fabrication errors should decrease as a percentage of the textile component size. Combined, these two effects improve the predictive capability and the uniformity of the structural response for a 12-15m HIAD.In this presentation, a handful of the challenges and associated mitigation plans will be discussed, as well as an update on current 12m aeroshell manufacturing and testing that is addressing these challenges

Infatables↗

NASA NTRS1995

Dual-Code Solution Strategy for Chemically-Reacting Hypersonic Flows

A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flow fields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three-dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a non-catalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the non-catalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated in both the radial and streamwise directions. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three-dimensional case in comparison to an all thin-layer Navier-Stokes solution.

Wood, William A.↗

NASA NTRS2016

Manufacturing Challenges and Benefits when Scaling the HIAD Stacked-Torus Aeroshell to a 15m Class System

Over a decade of work has been conducted in the development of NASA's Hypersonic Inflatable Aerodynamic Decelerator (HIAD) deployable aeroshell technology. This effort has included multiple ground test campaigns and flight tests culminating in the HIAD project's second generation (Gen-2) aeroshell system. The HIAD project team has developed, fabricated, and tested stacked-torus inflatable structures (IS) with flexible thermal protection systems (F-TPS) ranging in diameters from 3-6m, with cone angles of 60 and 70 deg. To meet NASA and commercial near term objectives, the HIAD team must scale the current technology up to 12-15m in diameter. The HIAD project's experience in scaling the technology has reached a critical juncture. Growing from a 6m to a 15m class system will introduce many new structural and logistical challenges to an already complicated manufacturing process. Although the general architecture and key aspects of the HIAD design scale well to larger vehicles, details of the technology will need to be reevaluated and possibly redesigned for use in a 15m-class HIAD system. These include: layout and size of the structural webbing that transfers load throughout the IS, inflatable gas barrier design, torus diameter and braid construction, internal pressure and inflation line routing, adhesives used for coating and bonding, and F-TPS gore design and seam fabrication. The logistics of fabricating and testing the IS and the F-TPS also become more challenging with increased scale. Compared to the 6m aeroshell (the largest HIAD built to date), a 12m aeroshell has four times the cross-sectional area, and a 15m one has over six times the area. This means that fabrication and test procedures will need to be reexamined to account for the sheer size and weight of the aeroshell components. This will affect a variety of steps in the manufacturing process, such as: stacking the tori during assembly, stitching the structural webbing, initial inflation of tori, and stitching of F-TPS gores. Additionally, new approaches and hardware will be required for handling and ground testing of both individual tori and the fully assembled HIADs. There are also noteworthy benefits of scaling up the HIAD aeroshell to 15m-class system. Two complications in working with handmade textiles structures are the non-linearity of the materials and the role of human accuracy during fabrication. Larger, more capable, HIAD structures should see much larger operational loads, potentially bringing the structural response of the materials out of the non-linear regime and into the preferred linear response range. Also, making the reasonable assumption that the magnitude of fabrication accuracy remains constant as the structures grow, the relative effect of fabrication errors should decrease as a percentage of the textile component size. Combined, these two effects improve the predictive capability and the uniformity of the structural response for a 12-15m class HIAD. In this paper, the challenges and associated mitigation plans related to scaling up the HIAD stacked-torus aeroshell to a 15m class system will be discussed. In addition, the benefits of enlarging the structure will be further explored.

Decellerators↗

NASA NTRS2016

Manufacturing Challenges and Benefits When Scaling the HIAD Stacked-Torus Aeroshell to a 15 Meter Class System

Over a decade of work has been conducted in the development of NASA's Hypersonic Inflatable Aerodynamic Decelerator (HIAD) deployable aeroshell technology. This effort has included multiple ground test campaigns and flight tests culminating in the HIAD project's second generation (Gen-2) aeroshell system. The HIAD project team has developed, fabricated, and tested stacked-torus inflatable structures (IS) with flexible thermal protection systems (F-TPS) ranging in diameters from 3-6 meters, with cone angles of 60 and 70 degrees. To meet NASA and commercial near-term objectives, the HIAD team must scale the current technology up to 12-15 meters in diameter. Therefore, the HIAD project's experience in scaling the technology has reached a critical juncture. Growing from a 6-meter to a 15-meter class system will introduce many new structural and logistical challenges to an already complicated manufacturing process. Although the general architecture and key aspects of the HIAD design scale well to larger vehicles, details of the technology will need to be reevaluated and possibly redesigned for use in a 15-meter-class HIAD system. These include: layout and size of the structural webbing that transfers load throughout the IS, inflatable gas barrier design, torus diameter and braid construction, internal pressure and inflation line routing, adhesives used for coating and bonding, and F-TPS gore design and seam fabrication. The logistics of fabricating and testing the IS and the F-TPS also become more challenging with increased scale. Compared to the 6-meter aeroshell (the largest HIAD built to date), a 12-meter aeroshell has four times the cross-sectional area, and a 15-meter one has over six times the area. This means that fabrication and test procedures will need to be reexamined to account for the sheer size and weight of the aeroshell components. This will affect a variety of steps in the manufacturing process, such as: stacking the tori during assembly, stitching the structural webbing, initial inflation of tori, and stitching of F-TPS gores. Additionally, new approaches and hardware will be required for handling and ground testing of both individual tori and the fully assembled HIADs. There are also noteworthy benefits of scaling up the HIAD aeroshell to a 15m-class system. Two complications in working with handmade textile structures are the non-linearity of the material components and the role of human accuracy during fabrication. Larger, more capable, HIAD structures should see much larger operational loads, potentially bringing the structural response of the material components out of the non-linear regime and into the preferred linear response range. Also, making the reasonable assumption that the magnitude of fabrication accuracy remains constant as the structures grow, the relative effect of fabrication errors should decrease as a percentage of the textile component size. Combined, these two effects improve the predictive capability and the uniformity of the structural response for a 12-15-meter HIAD. In this presentation, a handful of the challenges and associated mitigation plans will be discussed, as well as an update on current manufacturing and testing that addressing these challenges.

Infatables↗

NASA NTRS2017

Fabrication of the HIAD Large-Scale Demonstration Assembly and Upcoming Mission Applications

Over a decade of work has been conducted in the development of NASAs Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology. This effort has included multiple ground test campaigns and flight tests culminating in the HIAD projects second generation (Gen-2) deployable aeroshell system and associated analytical tools. NASAs HIAD project team has developed, fabricated, and tested inflatable structures (IS) integrated with flexible thermal protection system (F-TPS), ranging in diameters from 3-6m, with cone angles of 60 and 70 deg.In 2015, United Launch Alliance (ULA) announced that they will use a HIAD (10-12m) as part of their Sensible, Modular, Autonomous Return Technology (SMART) for their upcoming Vulcan rocket. ULA expects SMART reusability, coupled with other advancements for Vulcan, will substantially reduce the cost of access to space. The first booster engine recovery via HIAD is scheduled for 2024. To meet this near-term need, as well as future NASA applications, the HIAD team is investigating taking the technology to the 10-15m diameter scale.In the last year, many significant development and fabrication efforts have been accomplished, culminating in the construction of a large-scale inflatable structure demonstration assembly. This assembly incorporated the first three tori for a 12m Mars Human-Scale Pathfinder HIAD conceptual design that was constructed with the current state of the art material set. Numerous design trades and torus fabrication demonstrations preceded this effort. In 2016, three large-scale tori (0.61m cross-section) and six subscale tori (0.25m cross-section) were manufactured to demonstrate fabrication techniques using the newest candidate material sets. These tori were tested to evaluate durability and load capacity. This work led to the selection of the inflatable structures third generation (Gen-3) structural liner. In late 2016, the three tori required for the large-scale demonstration assembly were fabricated, and then integrated in early 2017. The design includes provisions to add the remaining four tori necessary to complete the assembly of the 12m Human-Scale Pathfinder HIAD in the event future project funding becomes available.This presentation will discuss the HIAD large-scale demonstration assembly design and fabrication per-formed in the last year including the precursor tori development and the partial-stack fabrication. Potential near-term and future 10-15m HIAD applications will also be discussed.

Swanson, G. T.↗

NASA NTRS2017

Fabrication of the HIAD Large-Scale Demonstration Assembly

Over a decade of work has been conducted in the development of NASA's Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology. This effort has included multiple ground test campaigns and flight tests culminating in the HIAD projects second generation (Gen-2) deployable aeroshell system and associated analytical tools. NASAs HIAD project team has developed, fabricated, and tested inflatable structures (IS) integrated with flexible thermal protection system (F-TPS), ranging in diameters from 3-6m, with cone angles of 60 and 70 deg.In 2015, United Launch Alliance (ULA) announced that they will use a HIAD (10-12m) as part of their Sensible, Modular, Autonomous Return Technology (SMART) for their upcoming Vulcan rocket. ULA expects SMART reusability, coupled with other advancements for Vulcan, will substantially reduce the cost of access to space. The first booster engine recovery via HIAD is scheduled for 2024. To meet this near-term need, as well as future NASA applications, the HIAD team is investigating taking the technology to the 10-15m diameter scale. In the last year, many significant development and fabrication efforts have been accomplished, culminating in the construction of a large-scale inflatable structure demonstration assembly. This assembly incorporated the first three tori for a 12m Mars Human-Scale Pathfinder HIAD conceptual design that was constructed with the current state of the art material set. Numerous design trades and torus fabrication demonstrations preceded this effort. In 2016, three large-scale tori (0.61m cross-section) and six subscale tori (0.25m cross-section) were manufactured to demonstrate fabrication techniques using the newest candidate material sets. These tori were tested to evaluate durability and load capacity. This work led to the selection of the inflatable structures third generation (Gen-3) structural liner. In late 2016, the three tori required for the large-scale demonstration assembly were fabricated, and then integrated in early 2017. The design includes provisions to add the remaining four tori necessary to complete the assembly of the 12m Human-Scale Pathfinder HIAD in the event future project funding becomes available.This presentation will discuss the HIAD large-scale demonstration assembly design and fabrication per-formed in the last year including the precursor tori development and the partial-stack fabrication. Potential near-term and future 10-15m HIAD applications will also be discussed.

Swanson, G. T.↗

NASA NTRS1974

Experimental investigation at Mach 8 of the effects of projections and cavities on heat transfer to a model of the Viking aeroshell

An experimental investigation into the aerodynamic heating on a Mars entry vehicle shape with several types of local surface distortion is presented. The configurations tested were 0.033-scale models of a spherically blunted 70 deg half-angle cone with two protuberances of different length, representing the tube leading to the gas chromograph mass spectrometer, and two aeroshell-bioshield attachment points of different size. These models were tested at free-stream Reynolds numbers per meter of 3.7 million and 17 million over an angle-of-attack range from 0 to 18 deg in the Langley Mach 8 variable density hypersonic tunnel. The phase change-coating technique was used to measure heat transfer coefficient. The long protuberance caused more severe interference heating than the short protuberance for the same conditions. When the short projection was located close to the edge of the aeroshell, the interference heating was greater than that on the same projection when located near the vertex. A significant increase in heat transfer coefficient was measured only on the larger aeroshell-bioshield attachment point.

Creel, T. R., Jr.↗

NASA NTRS1993

Zonally-decoupled DSMC solutions of hypersonic blunt body wake flows

Direct simulation Monte Carlo (DSMC) solutions are presented for the hypersonic flow behind a blunt body in which the wake region is solved in a zonally-decoupled manner. The forebody flow is solved separately using either a DSMC or a Navier-Stokes method, and the forebody exit plane solution is specified as the inflow condition to the decoupled DSMC solution of the wake region. Results are presented for a 70-deg, blunted cone at flow conditions that can be accommodated in existing low-density wind tunnels with the Knudsen number based on base diameter ranging from 0.03 to 0.001. The zonally-decoupled solutions show good agreement with fully-coupled DSMC solutions of the wake flow densities and velocities. The wake closure predicted by the zonally-decoupled solutions is in better agreement with fully-coupled results than that predicted by a fully-coupled Navier-Stokes method indicating the need to account for rarefaction in the wake for the cases considered. The combined use of Navier-Stokes for the forebody with a decoupled DSMC solution for the wake provides an efficient method for solving transitional blunt-body flows where the forebody flow is continuum and the wake is rarefied.

Wilmoth, Richard G.↗

NASA NTRS2015

Structural Testing of a 6m Hypersonic Inflatable Aerodynamic Decelerator System

NASA is developing low ballistic coefficient technologies to support the Nations long-term goal of landing humans on Mars. Current entry, decent, and landing technologies are not practical for this class of payloads due to geometric constraints dictated by current and future launch vehicle fairing limitations. Hypersonic Inflatable Aerodynamic Decelerators (HIADs) are being developed to circumvent this limitation and are now considered a leading technology to enable landing of heavy payloads on Mars. At the beginning of 2014, a 6m diameter HIAD inflatable structure with an integrated flexible thermal protection system (TPS) was subjected to a static load test series to verify its structural performance under flight-relevant loads. The inflatable structure was constructed into a 60 degree sphere-cone configuration using nine inflatable torus segments composed of fiber-reinforced thin films. The inflatable tori were joined together using adhesives and high-strength textile woven structural straps. These straps help distribute the load throughout the inflatable structure. The 6m flexible TPS was constructed using multiple layers of high performance materials that are designed to protect the inflatable structure from heat loads that would be seen in flight during atmospheric entry. A custom test fixture was constructed to perform the static load test series. The fixture consisted of a round structural tub with enough height and width to allow for displacement of the HIAD test article as loads were applied. The bottom of the tub rim had an airtight seal with the floor. The rigid centerbody of the HIAD was mounted to a pedestal in the center of the structural tub. Using an impermeable membrane draped over the HIAD test article, an airtight seal was created with the top rim of the static load tub. This seal allowed partial vacuum to be pulled beneath the HIAD resulting in a uniform static pressure load applied to the outer surface. Using this technique, the test article was subjected to loads of up to 50,000lbs. During the test series an extensive amount of instrumentation was used to provide a rich data set, including deflected shape, structural strap loads, torus cord loads, inflation pressures, and applied static load. In this paper the 2014 6m HIAD static load test series will be discussed in detail, including the design of the 6m HIAD test article, the test setup, and test execution. Analysis results will be described supporting the conclusions that were drawn from the test series..

Hypersonic↗

NASA NTRS1990

Stability theory for chemically reacting flows

Linear stability theory for chemically reacting (equilibrium and nonequilibrium) flows is applied to study the stability of hypersonic boundary layers under the equilibrium assumption. The results for Mach 15 flow indicate that the second mode instability shifts to lower frequencies, as compared to the perfect gas results. The peak second mode growth rate is also increased for the equilibrium gas model. However, the results for Goertler instability show very little real gas effect. The present theory has been applied to a sphere-cone flight transition experiment performed at freestream Mach of about 20.

Malik, Mujeeb R.↗

NASA NTRS1961

A Semigraphical Method of Applying Impact Theory to an Arbitrary Body to Obtain the Hypersonic Aerodynamic Characteristics at Angle of Attack and Sideslip

A simple semigraphical method of applying impact theory to obtain the aerodynamic characteristics of an arbitrary body at combined angle of attack and sideslip is presented. The necessary equations are derived, a general procedure for application is outlined, and the effects of graphical errors and areas of application are discussed. One of the features of the present method is the requirement of only one graphical construction for any combination of angle of attack and sideslip. As an example application the present method is applied to a blunted elliptical cone in order to obtain the longitudinal aerodynamic characteristics at an angle of attack of 40 degrees and an angle of sideslip of 0 degrees.

Jackson, Charlie M., Jr.↗

NASA NTRS1993

On magnetodynamic effects initiated by a high-speed impact of a large cosmic body upon the Earth's surface

The impact of a large cosmic body with typical size R approximately = 1 km (mass M approximately = 4-10 Gt for a stony or icy body) moving with velocity V approximately = 50-70 km/s (kinetic energy of the order of 10 exp 21 J or 10 exp 6 Mt of TMT) on the Earth's surface leads to a full vaporization of a body and of a significant part of substance of the upper layers of the Earth and even to the ionization of this vapor cloud. As a result, a hypersonic jet of air and erosion plasma is formed. The kinetic energy E sub J is far above the total energy of the geomagnetic field of the Earth (approximately equivalent to the energy of 100 Mt) and the total mass of a fast-moving part of the jet M sub j approximately = 10 exp 12 kg is far above the mass of atmosphere in the jet expansion cone. Thus, the jet will propagate practically inertially with the constant mean velocity U approximately = 10-20 km/s and even higher. The interaction of this plasma jet with the Earth's magnetic field causes magnetodynamic effects similar to those which are produced by cosmic nuclear explosions but of a larger scale. The preliminary results of experimental and numerical modeling of the plasma jet-magnetosphere interaction are presented.

Nemchinov, I. V.↗

NASA NTRS1991

Hypersonic merged layer blunt body flows with wakes

An attempt is made here to understand the basic physics of the flowfield with wake on a blunt body of revolution under hypersonic rarefied conditions. A merged layer model of flow is envisioned. Full steady-state Navier-Stokes equations in spherical polar coordinate system are computed from the surface with slip and temperature jump conditions to the free stream by the Accelerated Successive Replacement method of numerical integration. Analysis is developed for bodies of arbitrary shape, but actual computations have been carried out for a sphere and sphere-cone body. Particular attention is paid to set the limit of the onset of separation, wake closure, shear-layer impingement, formation and dissipation of the shocks in the flowfield. Validity of the results is established by comparing the present results for sphere with the corresponding results of the SOFIA code in the common region of their validity and with the experimental data.

Jain, Amolak C.↗