John W. Slater

Glenn Research Center, Cleveland, Ohio

Design and Analysis Tool for External-Compression

Supersonic Inlets

NASA/TM—2012-217660

August 2012

AIAA–2012–0016
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John W. Slater

Glenn Research Center, Cleveland, Ohio

Design and Analysis Tool for External-Compression

Supersonic Inlets

NASA/TM—2012-217660

August 2012

AIAA–2012–0016

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

50th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Nashville, Tennessee, January 9–12, 2012
Acknowledgments

The author would like to acknowledge the support of the Supersonics Project under the 

NASA Fundamental Aeronautics Program.

Available from

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7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217660 1 

Design and Analysis Tool for External-Compression 

Supersonic Inlets 

John W. Slater 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

A computational tool named SUPIN has been developed to design and analyze external-compression 

supersonic inlets for aircraft at cruise speeds from Mach 1.6 to 2.0. The inlet types available include the 

axisymmetric outward-turning, two-dimensional single-duct, two-dimensional bifurcated-duct, and 

streamline-traced Busemann inlets. The aerodynamic performance is characterized by the flow rates, total 

pressure recovery, and drag. The inlet flowfield is divided into parts to provide a framework for the 

geometry and aerodynamic modeling and the parts are defined in terms of geometric factors. The lowfidelity aerodynamic analysis and design methods are based on analytic, empirical, and numerical 

methods which provide for quick analysis. SUPIN provides inlet geometry in the form of coordinates and 

surface grids useable by grid generation methods for higher-fidelity computational fluid dynamics (CFD) 

analysis. SUPIN is demonstrated through a series of design studies and CFD analyses were performed to 

verify some of the analysis results. 

I. Introduction 

The pursuit of sustainable commercial supersonic flight has lead to recent conceptual studies for 

aircraft with cruise speeds between Mach 1.6 and 2.0 with the goal of supersonic flight over land (Refs. 1 

and 2). Among the challenges are reducing sonic boom signatures and developing an efficient propulsion 

system. The design of the inlet for the propulsion system is included among the challenges (Ref. 3). 

The role of the inlet is to capture a required amount of airflow and deliver it to the engine at 

conditions suitable for the stable and efficient operation of the propulsion system. For cruise speeds below 

Mach 2.0, an external-compression supersonic inlet is considered a good choice due to potentially high 

total pressure recovery with stable operating characteristics (Refs. 4 to 6). An external-compression 

supersonic inlet compresses the supersonic flow along the external surfaces of the inlet using shock and 

Mach waves while decelerating the flow to lower supersonic speeds. A strong shock situated at the 

entrance of the inlet decelerates the flow from supersonic to subsonic speeds. The subsonic flow is then 

ducted to a gas turbine engine while being decelerated and compressed through an increase in the crosssectional area of the subsonic diffuser. 

The design and analysis of external-compression supersonic inlets has been a topic of research and 

development for over 60 years. Ferri and Nucci provided some of the earliest design guidelines for the 

angles and placements of the centerbody cone and cowl for an axisymmetric inlet (Ref. 7). A conical 

centerbody turns the flow outward from an axis-of-symmetry and establishes conical shock and Mach 

waves, which compress and decelerate the supersonic flow. The use of a conical compression was 

facilitated in part by the ability to analytically compute the conical shock properties using equations such 

as those of Taylor and Maccoll for supersonic flow past a cone (Ref. 8). Oswatitsch also studied 

axisymmetric external-compression inlets and considered multiple stages for the centerbody with stage 

angles selected to maximize the total pressure recovery of the external supersonic diffuser (Ref. 9). The 

axisymmetric, external-compression inlet was used for a variety of ramjet missiles and supersonic 

military aircraft. Its use on the Mach 2.0 B-58 Hustler bomber provides an important example (Ref. 10). 
NASA/TM—2012-217660 2 

Axisymmetric inlets were used on the A-12/YF-12/SR-71 series of Mach 3.0+ aircraft for external 

compression; however, that inlet also incorporated internal supersonic compression to retain efficiency 

above Mach 2.0 (Ref. 11). Axisymmetric inlets continue to be studied for use for future supersonic 

transports. The conceptual study by Lockheed Martin suggested axisymmetric inlets for its supersonic 

transport (Ref. 2). The Gulfstream Aerospace Corporation has studied supersonic transports utilizing 

axisymmetric inlets and its low-boom, axisymmetric inlet has been analyzed and tested at the NASA 

Glenn Research Center (Refs. 3 and 12). 

Two-dimensional supersonic compression is another option for the external supersonic diffuser and 

involves compression through oblique shock and Mach waves. The flow properties through oblique shock 

and Mach waves can be determined analytically using compressible flow relations such as those in 

NACA Report 1135 or compressible flow textbooks (Refs. 13 and 14). Two-dimensional, externalcompression inlets have been studied and developed for a variety of aircraft. The US Air Force F-15 

Eagle aircraft has side-mounted two-dimensional inlets that each fed an engine (Ref. 15). The AngloFrench Concorde supersonic transport had a pair of two-dimensional inlets mounted under each wing with 

each inlet feeding an engine (Refs. 16 and 17). Both aircraft reached speeds in excess of Mach 2.0. An 

attractive feature of two-dimensional inlets for these aircraft was that variable-geometry elements, such as 

rotating ramps, could be more easily integrated into the inlet than for axisymmetric inlets. The inlets 

incorporated a throat slot at the end of the external diffuser ramps to reduce the adverse effects of shock/ 

boundary layer interactions and provide a bypass of flow to allow proper matching of flow for the engine. 

The two-dimensional inlet was an attractive option for supersonic transport aircraft studies in the 1990’s 

as part of NASA’s High-Speed Research Program (Ref. 18). The inlet concept centered on a twodimensional, bifurcated duct inlet in which two external-compression ramp systems mirrored about a 

plane-of-symmetry fed a single duct leading to the engine. That project involved a cruise speed of 

Mach 2.5, which meant the inlet also incorporated internal supersonic compression. For flight below 

Mach 2.0, the two-dimensional inlet remains a viable option. The conceptual study by the Boeing 

Company suggests a two-dimensional inlet as an option (Ref. 1). 

In addition to external compression of supersonic flow about axisymmetric or two-dimensional 

surfaces, it is possible to compress supersonic flow about “three-dimensional” surfaces through the 

process of streamline tracing. The process involves defining a compressive flow field, establishing a 

curve from which the streamlines originate, and then tracing the streamlines through the flow field to 

define the compression surface. This process has been used to develop inlet surfaces for hypersonic 

speeds. Mölder and Szpiro studied an inlet based on an axisymmetric, flow field proposed by Busemann 

in which the supersonic inflow and outflow are uniform and directed along the axis-of-symmetry 

(Ref. 19). The Mach waves isentropically compress the flow inward toward the axis-of-symmetry. An 

oblique, conical shock then turns the flow and the shock is cancelled at the inlet surface to yield axial, 

uniform outflow. The Taylor-Maccoll conical equations and oblique shock relations provide an analytic 

solution for the flow field. The streamline-tracing technique has been applied by various researchers to 

develop inlets for hypersonic missiles and aircraft (Refs. 20 and 21). The technique allows the generation 

of a wide variety of surface shapes depending on the shape of the curve from which the streamlines 

originate. The surfaces are potentially “three-dimensional” surfaces if the generated surfaces are nonplanar and asymmetric. Thus, streamline tracing can facilitate improved integration of the inlet with the 

aircraft, which is of increased importance at hypersonic speeds, but may also be of importance for 

supersonic speeds for which the reduction of sonic boom effects is desired. 

At speeds below Mach 2.0, it is possible to generate streamline-traced surfaces for external 

supersonic compression. However, the oblique shock is replaced with a stronger shock that yields 

subsonic outflow. The use of streamline tracing for external-compression inlets has been limited. Konscek 

studied the use of streamline tracing for Mach 2.5 flight as part of the NASA High-Speed Research 

Program in the late 1990’s and a patent was released in 2004 (Ref. 22). A parallel effort at NASA resulted 

in the so-called “Parametric Inlet”, which used an external-compression supersonic diffuser that 
NASA/TM—2012-217660 3 

compressed the flow isentropically by turning the flow toward the axis-of-symmetry. The curve from 

which the streamlines originated was located in the throat and had the shape of a partial co-annular 

section. This yielded flat sidewalls which did not contribute to the isentropic compression. The Parametric 

Inlet underwent an extensive design and analysis process involving CFD and a wind-tunnel model was 

fabricated and tested in 2004 (Ref. 23). A “three-dimensional” inlet concept derived from streamline 

tracing was studied by Vinogradov and Stepanov for a Mach 2.0 supersonic business jet (Ref. 24). 

The focus of this paper is to investigate inlet concepts suitable for supersonic commercial flight below 

Mach 2.0 and develop the computational tools for the design and analysis of those inlet concepts. Over 

the past 60 years, various methods and tools have been applied for the design of supersonic inlets. 

Analytic methods for shock waves and compressible flow such as documented in the NACA Report 1135 

formed a starting point for many of the methods (Ref. 13). Empirical methods derived from wind-tunnel 

and flight studies provided information on such things as shock stand-off distances and total pressure loss 

through subsonic ducts (Refs. 25 and 26). Such methods were coded into computational tools such as the 

US Air Force Level II Installation Code, the US Navy NIDA Code, and the NASA Inlet Performance 

Analysis Code (IPAC) (Refs. 27 to 29). The InletMOC and LercInlet codes incorporated the method of 

characteristics for planar compressible flow for the analysis and design of external and internal supersonic 

diffusers (Refs. 30 to 31). Forms of LercInlet are still being used despite being over 40 years old. The 

LAPIN code solves the unsteady, quasi-one-dimensional Euler equations to analyze steady and unsteady 

flow within mixed-compression inlets (Ref. 32). The methods of computational fluid dynamics (CFD) 

have been applied to solve the unsteady, three-dimensional, viscous flow through supersonic inlets 

(Ref. 23). The increased fidelity and flow field detail possible with CFD methods requires greater 

complexity and time for the analysis. 

The present work has the objective of retaining the capability of the various past tools while updating 

and documenting the coding and methods. The objective is to provide a capability to design and analyze 

traditional inlet types, such as the axisymmetric and two-dimensional inlets, as well as, develop tools to 

design and analyze newer inlet concepts, such as the streamline-traced inlets. The work has resulted in the 

computational tool named SUPIN (SUPersonic INlet design and analysis tool). SUPIN is being written in 

Fortran 95. The intent has been to provide a tool to design inlet geometry and perform analysis of an inlet 

using a small set of key input factors. The methods used are analytic, empirical, and numerical. While 

some compressible flow relations and method of characteristics solutions yield planar flow fields, much 

of the analysis is based on a one-dimensional representation of the inlet flow. Thus, the methods are of 

low fidelity. However, this allows an almost instantaneous computational time, which is beneficial for use 

in aircraft system studies that require basic supersonic inlet performance data and geometry properties 

(Ref. 33). Yet, we wish to retain the option to launch into higher-fidelity analysis of the inlet using CFD 

methods. SUPIN has capabilities to automatically generate surface grids that can be directly used for the 

generation of computational grids needed for analysis using CFD methods. When an axisymmetric or 

two-dimensional flow analysis is appropriate, SUPIN can create a planar grid at the symmetry plane of 

the inlet that can be directly input to CFD codes. 

This paper describes the models and methods for the geometry modeling, aerodynamic analysis, and 

design of supersonic external-compression inlets as implemented into the SUPIN tool. The types of inlets 

modeled within SUPIN are discussed in the next section and include: the axisymmetric outward-turning 

inlet, the two-dimensional single-duct inlet, the two-dimensional bifurcated-duct inlet, and the streamlinetraced inlet. These types encompass not only the traditional inlet types, but allow for modeling of newer 

inlet concepts. The modeling divides the inlet flow field into parts that allow natural segmentation of the 

modeling tasks. Section III discusses the parts of the inlet flow field. Section IV discusses the freestream 

and approach flow parts of the flow field, which provide the upstream boundary conditions for the inlet 

design and analysis problem. Section V discusses the engine face, which provides the downstream 

boundary conditions. Section VI discusses the external supersonic diffuser, which is an essential part that 
NASA/TM—2012-217660 4 

defines the character of the inlet. The nose is also discussed within this section. Section VII discusses the 

cowl lip and cowl exterior, which characterize the capture area and external drag of the inlet. Section VIII 

discusses the internal ducting of the inlet consisting of the throat and subsonic diffuser through which 

flow is subsonic leading to the engine face. Section IX discusses the primary performance measures 

calculated for the inlet, which include the flow rates, total pressure recovery, and drag. The use of SUPIN 

for the design and analysis of inlets is discussed in Section X and includes information on the input and 

output files of SUPIN and the modes of using SUPIN for geometry creation, design and sizing, and 

analysis. The output files include surface and planar grids usable for CFD analysis. Section XI presents 

some results of several design studies using SUPIN and results generated with planar CFD analyses that 

provide some verification of the methods used within SUPIN. 

II. Inlet Types 

The development of a computational tool for the design and analysis of supersonic externalcompression inlets is made simpler by limiting the possible inlets to a set of four inlet types: the 

axisymmetric outward-turning inlet, the two-dimensional single-duct inlet, the two-dimensional 

bifurcated-duct inlet, and the Busemann streamline-traced inlet. Figure 1 shows the four inlet types with 

each inlet cut along its vertical plane of symmetry. SUPIN does include a fifth inlet type of the 

axisymmetric pitot inlet; however, it is not considered an external-compression inlet since it does not have 

an external supersonic diffuser. Further, the poor performance of the pitot inlet at Mach numbers above 

Mach 1.6 does not make it an attractive inlet choice for the present work. The set of four inlet types 

encompass many of the traditional inlets and can be used as baseline inlets or initial concepts for inlet 

design studies. The streamline-traced inlet type has a number of factors that allow a wide variety of 

shapes that may integrate better with an aircraft. 

The geometry of the four inlet types are all constructed from planar geometric operations. The 

surfaces of the axisymmetric, outward-turning inlet are constructed from extruding the planar profile of 

the centerbody and cowl about the axis-of-symmetry. Much of the two-dimensional inlet is constructed 

from extruding the planar profile into the cross-stream or z-coordinate direction. The subsonic diffuser of 

the two-dimensional inlets transition from a rectangular cross-section to a circular cross-section; however, 

each cross-section is described by a super-ellipse defined within a reference plane. Even the threedimensional surfaces of the streamline-traced inlet are generated by defining planar profiles at 

circumferential planes coincident with the circumferential planes of the axisymmetric Busemann flow 

field. This basis of planar construction greatly simplifies the geometry modeling methods while allowing 

a wide variety of inlet shapes. Further details on the geometry modeling will be discussed in the sections 

below. 

Figure 1.—Set of supersonic external-compression inlet types (left to right: axisymmetric outward-turning, 

two-dimensional single-duct, two-dimensional bifurcated, and streamline-traced).
NASA/TM—2012-217660 5 

Figure 2.—Parts of the supersonic external-compression inlet flowfield. 

III. Parts of the Inlet Flowfield 

The inlet flowfield includes the streamtube of airflow that extends from the freestream to the engine 

face while passing over and through the inlet. This flow field is divided into parts which facilitate the 

geometric modeling and aerodynamic analysis of the inlet. Figure 2 shows the parts for an externalcompression inlet along with a schematic of an inlet showing the general location of the parts. 

The numbers or letters within circles indicate key stations within the flowfield. The stations are 

mostly located at boundaries between the parts. The numbers correspond to standard stations for an inlet 

for a turbo-fan engine (Ref. 34). Stations 0, 1, and 2 correspond to the freestream, cowl lip entrance, and 

engine-face stations, respectively. The stations with letters correspond to additional stations that further 

define the flow field. These are defined in the sections below in discussion of the individual parts of the 

inlet. 

IV. Freestream and Approach Flow 

The freestream and approach flow parts form the upstream boundary to the inlet design and analysis 

task. The freestream is described by uniform flow properties ahead of the aircraft at station 0. This 

includes the Mach number and angle-of-attack of the aircraft and the static pressure and temperature of 

the freestream, which can be determined from the standard atmosphere and a specified altitude. The 

specifications for the freestream are assumed to be explicitly defined as part of the mission analysis and 

operating point for which the inlet is to be designed. 

The approach flow considers the effects on the inlet streamtube as it washes over the forward parts of 

the aircraft prior to encountering the inlet. The approach flow effects occur between stations 0 and L with 

uniform and steady conditions at station L. The approach flow models possible installation effects for the 

inlet as part of the aircraft. The model assumes the flow encounters a combination of oblique shocks, 

conical shocks, and Prandtl-Meyer expansions. The result is the uniform flow conditions at station L. 

Inlet

Flowfield

Freestream Approach 

Flow Nose 

External 

Supersonic 

Diffuser

Cowl Lip Cowl

Exterior Throat SubsonicDiffuser

Engine

Face

Nose

Engine

Face Throat

External

Supersonic

Diffuser

Subsonic

Diffuser

Cowl Lip

Cowl Exterior

L

EX

TH SD

2 1

Shock

Wave

Mach

Waves

0

Aircraft Forebody

Freestream
NASA/TM—2012-217660 6 

V. Engine Face 

The engine face forms the downstream boundary to the inlet design and analysis task. It is assumed 

that the engine size and engine operating point to which the inlet is to be designed are known. Here it is 

assumed the engine face has a circular cross-section corresponding to a gas turbine engine and the engineface dimensions include the engine-face diameter (DEF). A spinner may exist to cover the engine-face 

hub. If a spinner exists, it is assumed that the hub diameter, spinner length, and planar profile shape are 

known. The spinner can be modeled to have a conical, circular, or elliptical profile. For an axisymmetric, 

outward-turning inlet, the centerbody surface is assumed to cover the spinner and match up to the hub 

diameter. The inlet examples shown in Figure 1 have spinners with elliptical profiles. For axisymmetric 

inlets, the axis of the engine is assumed to coincide with the axis-of-symmetry of the inlet. For twodimensional bifurcated inlets, the engine axis coincides with the line of intersection of the two symmetry 

planes. For two-dimensional, single-duct inlets and streamline-traced inlets the engine axis is on the plane 

of symmetry, but it can be moved vertically to adjust the subsonic diffuser shape. For the inlet design and 

analysis task, it is assumed that the engine flow rate is specified in some form. Section IX will discuss 

further the engine flow rate. 

VI. Nose and External Supersonic Diffuser 

The nose is the start of the external supersonic diffuser. The nose is a point for an axisymmetric 

outward-turning inlet and a linear edge for the two-dimensional inlets. The streamline-traced inlet does 

not have a nose, but rather the cowl lip defines the leading edge of the external supersonic diffuser. While 

it is common for supersonic inlets to have sharp noses and leading edges, a nose with a circular profile 

can be modeled. 

The external supersonic diffuser compresses the supersonic flow external to the interior duct of the 

inlet from station L to station EX. The compression involves a number of stages in which each stage turns 

the flow into itself with the creation of shock or Mach waves. Shock waves are generated when the stage 

involves sudden turning. Mach waves are created when the stage involves gradual turning. Station EX is 

located just upstream of the strong terminal shock that changes the inlet flow to subsonic. The flow 

properties at station EX are the one-dimensional, mass-averaged properties of the supersonic flow at the 

end of the external compression. These properties are used as the upstream conditions for the normal 

shock calculations that determine the properties at station NS, which is downstream of the terminal shock. 

The inlet is designed for critical conditions for which the terminal shock is located at station 1, which is 

the entrance to the internal ducting of the inlet. Thus, at the design point, stations NS and 1 are coincident 

and have the same flow properties. Thus, the external supersonic diffuser extends from the nose to 

station 1. The planar surface at station 1 is defined as the plane passing through the cowl lip and 

perpendicular to the external supersonic diffuser. The two sub-sections below discuss the specific design 

methods for the external supersonic diffusers. 

A. Axisymmetric and Two-Dimensional External Supersonic Diffusers 

The axisymmetric outward-turning inlet has an external supersonic diffuser consisting of an 

axisymmetric centerbody that turns the flow outward from the axis-of-symmetry to create conical shocks 

and Mach waves. The two-dimensional inlets turn the flow along planar ramps or curved surfaces of a 

specified width. The two-dimensional inlets also include sidewalls to contain the compression on the 

external supersonic diffuser. The leading edge of the sidewall is assumed to be a straight line from the 

nose to the cowl lip. 

The external supersonic diffuser is designed so that the shock and Mach waves created on each stage 

pass through focal points. Figure 3 is a schematic showing an external supersonic diffuser with three 

stages that creates shock waves that pass through a focal point near the cowl lip. While Figure 3 shows all 

three waves with the same focal points, each wave can have its own focal point. The focal points are 
NASA/TM—2012-217660 7 

Figure 3.—An external supersonic diffuser with three 

stages with oblique shocks with a common focal point. 

 

Figure 4.—Axisymmetric external supersonic diffusers with one (left), two (middle), and three 

(right) stages. 

placed with respect to the cowl lip. The so-called “shock-on-lip” condition involves placing the focal 

points coincident with the cowl lip. This results in zero supersonic spillage, which maximizes the airflow 

into the inlet. Placing the focal points above the cowl lip results in supersonic spillage, which may be 

advantageous for the stability of the inlet over its range of operations. 

Each stage of the external supersonic diffuser is characterized by a change in surface angle that 

results in the flow being turned. A stage consisting of a conical or ramp surface will create a shock wave. 

Compressible flow equations such as oblique shock and conical shock equations can be used to solve for 

the shock wave angles and change in flow properties for the stage (Refs. 8 and 13). Method-ofcharacteristic numerical methods can be used to solve more complex conical shocks and Mach waves 

through the stage (Ref. 31). Knowing the wave angles and focal point locations, the start and end of the 

stages can be determined. The analytic and numerical flow solutions provide the change in the total 

pressure through the stages. 

SUPIN provides the capability to explicitly specify the flow turning angles and start and end locations 

of the stages or to determine these quantities using design operations. SUPIN can design axisymmetric 

external supersonic diffusers with a single cone, two cones (bi-conic), and three stages in which the 

second stage is curved with an isentropic compression of Mach waves. The design methods require 

specification of the desired Mach number at the end of the external supersonic diffuser, which is at station 

EX and assumed to be at station 1. 

SUPIN can design two-dimensional external supersonic diffusers with one, two, or three stages. For a 

three-stage diffuser, the second stage can either be a ramp or be curved to provide for isentropic 

compression using Mach waves. For two-dimensional diffusers consisting of ramps, SUPIN provides a 

method to search for the ramp angles that result in the lowest total pressure loss for the diffuser. This 

solution corresponds to the observation of Oswatitsch that the total pressure loss through the external 

supersonic diffuser is minimized when the losses through each shock wave are equal (Ref. 9). 

Figure 4 shows three external-compression supersonic diffusers for axisymmetric inlets with one, 

two, and three stages. The middle diffuser is bi-conic. The diffuser on the right has an isentropic, curved 

second stage. As the number of stages increases, the total pressure losses decrease; however, the diffuser 

becomes longer. The design study below will provide more details on the properties of the external 

supersonic diffuser designs. 

External Supersonic 

Diffuser

Cowl 

Lip

Shock 

Waves

Focal 

Point
NASA/TM—2012-217660 8 

B. Streamline-Traced External Supersonic Diffusers 

The external supersonic diffuser for the streamline-traced inlet takes on a separate character than the 

multi-stage diffusers discussed. The streamline-traced diffuser is considered to consist of one stage 

involving isentropic compression. The nose and cowl lip are indistinguishable such that the leading edge 

of the diffuser is modeled as the cowl lip. 

The design of the diffuser starts with an axisymmetric Busemann flow field characterized by the 

inflow and outflow Mach numbers. The Taylor-Maccoll equations are solved for the axisymmetric 

conical flow field about a focal point (Refs. 8 and 14). Figure 5 shows an example of the conical flow 

field. The flow is uniform at the inflow and outflow and the direction is axial. The inflow Mach number 

corresponds to the Mach number at station L, ML. The design method involves specifying the desired 

outflow Mach number. An iteration scheme is performed on the angle of the shock wave to arrive at the 

desired inflow Mach number for the specified outflow Mach number. 

The surface of the diffuser is formed by tracing streamlines through the Busemann flow field. The 

process involves defining a tracing curve within the outflow and then integrating the streamlines in the 

upstream direction through the flow field. The tracing curve is a closed curve defined on a plane that is 

perpendicular to the flow. The tracing curve is built of separate super-ellipses for the top and bottom. The 

paper by Konscek presents one of the earliest applications of the super-ellipse for inlet design (Ref. 35). 

The super ellipse is characterized by the lengths of the semi-major (aST) and semi-minor axis (bST) and a 

super-ellipse parameter (pST). A parameter value of pST = 2 indicates an ellipse. The curve approaches a 

rectangle as the parameter is increased. The top and bottom sections of the tracing curve share the same 

semi-major axis length, but can have different values of the semi-minor axis length and parameter. 

Figure 6 shows two examples of tracing curves. The tracing curve on the left consists of circular arcs for 

the top and bottom sections. The curve on the right has a circular arc for the top section and a superelliptic curve for the bottom with the parameter equal to pSTbot = 10. The tracing curves are defined in a 

local coordinate system in which the center is on the x-z plane but can be translated in the y-direction by a 

value yST. This approach for defining the tracing curves and placing it with respect to the axis-ofsymmetry of the Busemann flow field provides a capability to generate a wide variety of shapes for the 

external supersonic diffuser. 

Figure 5.—Axisymmetric Busemann flow field. 

Figure 6.—Tracing curves for two streamline-traced. Inlets. 

y y

yST

z z

bSTtop

bSTbot

aST

pSTbot = 2 pSTbot = 10

pSTtop = 2

pSTtop = 2
NASA/TM—2012-217660 9 

Figure 7.—Integration of streamlines from the tracing curve. 

 

Figure 8.—Examples of streamline-traced inlets with the tracing curves of Figure 6. 

The tracing curve is placed in the uniform outflow of the Busemann flow field. The streamlines are 

then created by starting at points on the tracing curve and integrating the local velocity field in the 

upstream direction. Figure 7 shows an example of the creation of the streamlines (shown as dashed lines). 

Each point on the tracing curve is associated with a circumferential angle of the axisymmetric flow. Thus 

the integration of each streamline is a planar integration problem. 

The shape of the tracing curve and the placement of the tracing curve with respect to the axis-ofsymmetry provides for a variety of diffuser shapes. For an external supersonic diffuser, the tracing curve 

is placed away from the axis-of-symmetry such that the streamlines will not contain the focal point of the 

Busemann flow field. Figure 7 shows the tracing curve “above” the axis-of-symmetry. The tracing curve 

can also be placed below the axis-of-symmetry. Figure 8 shows two examples of streamline-traced inlets 

created from the tracing curve shapes of Figure 6. In these examples, the tracing curves were placed 

below the axis-of-symmetry. This created a shape with a “cut-out” at the top of the inlet. 

VII. Cowl Lip and Cowl Exterior 

The cowl lip is the start of the internal ducting of the inlet and the location of the cowl lip determines 

in part the amount of the inlet streamtube flow that is captured and delivered to the engine. The cowl 

exterior starts at the cowl lip exterior and encloses the inlet to provide a surface for which the cowl drag 

can be estimated. 

The cowl lip coordinate is either specified or determined as part of the sizing operation. For an 

axisymmetric inlet, the radius of the cowl lip corresponds with the circular shape of the capture area. For the 

two-dimensional inlets, the height of the cowl lip corresponds with the rectangular shape of the capture area 

and the specified width of the external supersonic diffuser. For the streamline-traced inlet, the cowl lip 

coordinates vary circumferentially and the locus of the points forms the outline of the capture area. 

The profile of the cowl lip can be sharp, circular, or elliptical. Figure 9 shows examples of each 

profile shape along with the geometric factors. The cowl lip is characterized by the surface angles of the 

cowl lip interior and cowl lip exterior. The angle of the cowl lip interior influences the subsonic diffusion 

at the entrance of the throat. The angle of the cowl lip exterior influences the supersonic flow at the start 

of the cowl exterior, which affects the cowl wave drag on the cowl exterior. The cowl lip angles should 

Minflow tracing curve
NASA/TM—2012-217660 10 

 

Figure 10.—Cowl exteriors for the axisymmetric (left), two-dimensional (center), and streamline-traced (right) inlets. 

align roughly to the angle of the flow at the cowl lip to minimize the generation of exterior shocks, 

especially strong shocks. The cowl lip exterior angle should be 3° to 5° greater than the cowl lip interior 

angle to allow some structural bulk for the cowl lip. 

The cowl exterior is washed by the portion of the inlet streamtube that does not enter the internal 

ducting of the inlet. The cowl exterior starts at the cowl lip exterior. The initial angle of the cowl exterior 

surface is equal to the angle of the cowl lip exterior. The end of the cowl exterior is set to the same axial 

coordinate as the engine face with the radial or cross-stream coordinates placed a certain factor of the 

engine-face radius. The cowl exterior surface is then formed between these two end coordinates. The 

cowl exteriors for the axisymmetric and streamline-traced inlets use a curved surface, while the cowl 

exteriors for the two-dimensional inlets are faceted planes. The sides of the cowl exterior for the twodimensional inlets require specification of an exterior sidewall angle. This simple model only requires a 

few input factors, but creates a realistic surface for which the cowl wave drag can be calculated. Figure 10 

shows examples of the cowl exteriors for the axisymmetric, two-dimensional, and streamline-traced 

inlets. The front views show the amount of axially-projected area of the cowl exterior that contributes to 

the cowl wave drag. 

VIII. Throat and Subsonic Diffuser 

The throat and the subsonic diffuser form the internal ducting of the inlets. The throat is the forward 

portion of the ducting and turns the subsonic flow downstream of the terminal shock into the entrance of the 

subsonic duct. While the throat and subsonic diffuser are both intended to be subsonic ducts, the throat may 

contain the terminal shock in the case of super-critical inlet flow. However, the modeling assumes that at the 

end of the throat at station SD, the flow is fully subsonic for entrance to the subsonic diffuser. 

The geometry model for the throat assumes the coordinates and angles at the inflow at station 1 are 

known. A “break angle” for the centerbody at station 1 can be specified in the inputs to indicate a 

discontinuous slope in the centerbody surface. The coordinates of the centerbody at station SD are 

specified in the inputs with respect to the centerbody coordinates at station 1. The angles for both the 

centerbody and cowl interior at station SD are also specified in the inputs. A smooth curve is created for 

the profile of the centerbody in which the specified end-coordinates and angles are matched. The curve 

for the profile of the cowl interior is created in a similar manner; however, the cross-sectional areas at 

stations TH and SD are used to determine the cowl coordinates at these stations. Station TH is an 

Figure 9.—Cowl lip shapes (left-right: sharp, circular, and elliptical) (right) cowl lips. 
NASA/TM—2012-217660 11 

 

Figure 11.—Geometry models for the throat. 

intermediate station. Three options exist for specifying the cross-sectional areas: 1) the area ratios 

between stations TH and 1 and stations SD and TH can be specified in the inputs, 2) a Mach number at 

station TH and the area ratio between stations SD and TH can be specified, and 3) the area ratio between 

stations SD and 1 can be specified. For option 2, the area ratio between stations TH and 1 is computed 

such as to yield the specified Mach number at station TH. With the cross-sectional areas at stations TH 

and SD known, the coordinate of the cowl can be calculated. This calculation assumes that the crosssectional shape is the same as at station 1. Thus, an axisymmetric inlet has a co-annular shape and the 

two-dimensional inlets have a rectangular shape. Figure 11 shows planar schematics of the throat. The 

drawing on the left is used for options 1 and 2. The drawing on the right is used for option 3. For option 3, 

station TH is not defined. 

For the streamline-traced inlets, the throat is modeled as a constant-area section that has the same 

cross-sectional shape as the tracing curve. The cross-sections are perpendicular to the axis-of-symmetry. 

The length of the throat is specified in the inputs. 

The subsonic diffuser connects the cross-section at the end of the throat with the engine face. The 

length of the subsonic diffuser can be directly specified as an input or computed to match a specified 

equivalent conical angle. 

For axisymmetric inlets, the annular cross-section at the end of the throat provides a straight-forward 

blending to the annular cross-section at the engine face. The planar profile of the centerbody assumes a 

smooth curve intersecting a cylindrical hub some distance (LCEX) upstream of the engine face. This 

models a centerbody that may translate axially on the hub. The planar profile of the cowl is determined 

based on the area distribution through the subsonic diffuser. The planar profiles are then extruded about 

the axis-of-symmetry to create the surfaces of the subsonic duct. The image on the left of Figure 12 shows 

the geometric factors and example geometry for the axisymmetric subsonic duct. 

For two-dimensional inlets, the subsonic diffuser is required to transition from a rectangular crosssection at the end of the throat to a circular cross-section at the engine face. This is performed by blending 

a distribution of rectangular and super-elliptic cross-sections. Both distributions use the same area 

variation. The image on the right of Figure 12 shows an example of the subsonic diffuser for a twodimensional, single-duct inlet. The image shows a cut at the symmetry plane. 

The subsonic diffuser for the streamline-traced inlet uses super-ellipses for the cross-sections through 

the axial length of the subsonic diffuser. The lengths of the semi-major and semi-minor axes and the value 

of the super-ellipse parameter are blended from the values at station SD to the values required to match 

the circular shape of the engine face at station 2. The cross-section at station SD matches the shape of the 

tracing curve. The cross-sections through the subsonic duct are all perpendicular to the x-axis. 
NASA/TM—2012-217660 12 

 

Figure 12.—Subsonic diffuser models for the axisymmetric outward-turning inlet (left) and 

two-dimensional, single-duct inlet (right). 

IX. Inlet Performance 

The aerodynamic performance of the external-compression supersonic inlet is characterized within 

SUPIN by the flow rates, total pressure recovery, and drag of the inlet. This section discusses each of 

these performance measures and the methods used to compute them. Other inlet aerodynamic information 

is certainly of interest for supersonic inlets, such as boundary layer properties, engine-face total pressure 

distortion, and buzz stability limits; however, SUPIN currently has no models for these properties. 

A. Inlet Flow Rates 

The inlet captures air from the freestream and delivers it to the engine. Figure 13 shows an example 

of the airflow about a two-dimensional inlet. The rate of flow entering the inlet is denoted as W1 with A1

as the cross-sectional area at station 1. The lower dashed line extending upstream from the cowl lip 

indicates the bounding streamline of the streamtube entering the inlet. At station L, the rate of flow is 

indicated by WL with a cross-sectional area of AL. For continuity, WL = W1. The solid horizontal line 

indicates the cowl lip height that defines the capture area, Acap. The image shows the capture streamline 

being turned by the shock waves such that AL  Acap. The potential airflow that does not enter the inlet is 

considered spillage and is shown flowing past the cowl exterior with the flow rate of Wspillage. The rate of 

flow entering the engine is W2 with a cross-sectional area of A2. 

The rate of flow is defined as 

 A T

p W

t

t (1) 

where  is the flow function or mass flow parameter expressed as 

   1 2 1

2

1 2

2

1 1

  





 



     

 



   

/ /

M

R

M (2) 

A theoretical capture flow rate can be defined as 

L

tL

tL A

T

p Wcap  cap  (3)

where Acap is a reference area called the capture area. The capture area is defined as the forward projection 

along the inlet axis (x) of the area defined by the cowl lip and any sidewalls edges. For an axisymmetric 

inlet, the capture area is bounded by a circle. For the two-dimensional inlets, the capture area is bounded 

(x,y)EF

1

(x,y)CBSD

(x,y)CWSD

(x,y)TEF

CWSD

SD

CBSD

(x,y)BEF

5
NASA/TM—2012-217660 13 

Figure 13.—A streamtube for a two-dimensional inlet flowfield. 

by a rectangle defined by the cowl lip and sidewall edges. For the streamline-traced inlet, the capture area 

can be a variety of shapes and is defined by the coordinates of the cowl lip about the circumference of the 

external supersonic diffuser. The theoretical capture flow rate is the maximum supersonic flow that can be 

accepted into the inlet and serves as the reference flow rate. 

For the external-compression inlets of interest in this work, it is assumed that no flow is extracted 

from the inlet streamtube due to bleed, bypass, or leakages and no flow enters the streamtube due to jets 

or auxiliary inlets. This simplification is consistent with the desire to keep the inlets for Mach 1.6 to 2.0 

as simple as possible. This simplification will eventually be relaxed within SUPIN as more complex 

analysis capabilities are introduced to model bleed and bypass. Thus, flow continuity is assumed through 

the inlet streamtube, 

WL  W1  W2 (4) 

The amount of the theoretical capture flow that does not enter the inlet is considered “spilled” past the 

inlet and represents a loss of the maximum flow that the inlet can capture. This spillage flow is denoted as 

Wspillage and flow continuity can be expressed as 

Wcap  WL Wspillage (5) 

A normalized flow continuity equation can be obtained for the inlet by combining Equations (4) and 

(5) and normalizing by Wcap to yield 

cap

spillage

cap

2 1

W

W

W

W   (6) 

Equation (6) can be used to either size the capture area of the inlet or determine the rate of spillage for 

an inlet. The sizing of the inlet involves determining W2 and estimating Wspillage and then solving 

Equation (6) for Wcap. From Wcap, the capture area Acap can be computed using Equation (3). For a specific 

type of inlet of Figure 1, the dimensions of the capture cross-section can be established. For example, for 

an axisymmetric inlet, which has a circular capture area, the cowl lip diameter can be computed easily 

from the capture area. For the two-dimensional inlets which have a rectangular capture area, the height of 

the cowl lip can be computed from knowing the capture area and the specified width of the capture area, 

which is the width of the external supersonic diffuser. For the streamline-traced inlet, the capture area 

shape is computed from the cross-section of the stream surface at the inflow. Iterations of the semi-major 

axis length of the tracing curve are performed to yield the tracing curve dimensions that will match the 

required capture area. The spillage Wspillage can be calculated using Equation (6) for inlet analyses for 

which Wcap and W2 are known. 
NASA/TM—2012-217660 14 

The engine flow rate W2 can be determined from the corrected engine flow rate WC2. For inlet design 

and analysis, it is assumed that the properties of the engine are known from a mission analysis and engine 

sizing. These properties include the diameter of the fan face D2 and spinner geometry such that the crosssectional area at the fan face A2 can be determined. These properties also include the corrected engine 

flow rate WC2 or equivalently the mass-averaged Mach number at the fan face, M2. The expression for the 

corrected engine flow rate is 

2

2

2

2

2 2   

 

tref

tref

C T

p A

W W (7) 

The 2 and 2 are the total temperature and total pressure ratios, respectively, referenced to the reference 

total temperature Ttref and total pressure ptref. The engine-face area A2 is calculated from the circular fan 

face diameter minus the circular area of the spinner hub (hub/tip ratio). Thus for a given engine face 

Mach number M2, Equation (7) is used to compute the corrected engine flow rate WC2. 

If the corrected engine flow rate WC2 is known, then Equation (7) can be used to compute the actual 

engine flow rate W2. However, Equation (7) requires estimates of the total pressure pt2 and total 

temperature Tt2 at the engine face. Adiabatic flow is assumed through the inlet, and so, Tt2 = TtL. Thus, the 

sizing involves an iteration of the inlet design and analysis process to gradually improve the estimation of 

the total pressure at the engine face. 

The flow ratio is a measure of how much of the theoretical capture flow rate enters the inlet. The WL

is normalized by the theoretical capture flow rate to form the flow ratio 

cap cap

FlowRatio

A

A

W

WL L   (8) 

The inlet is referred to as operating at full flow when AL = Acap, or the flow ratio equals unity. For 

subsonic flow at station L, the flow ratio can be less or greater than unity. For supersonic flow, the flow 

ratio can only be equal or less than unity. If the flow ratio is less than unity, then part of the flow that 

could have entered the inlet under ideal conditions is being “spilled” past the inlet. 

Key operating points of an external-compression inlet can be related to the flow ratio. At the “critical” 

operating point, the flow ratio is at its maximum with the normal shock sitting at the cowl lip plane. If the 

flow ratio is less than unity, then some of the flow is spilled supersonically. This will occur if the waves 

of the external supersonic diffuser have focal points outside of the cowl lip. The inlet can be operated at 

supercritical conditions in which the terminal shock enters the inlet; however, the flow ratio remains at its 

maximum value. If the flow ratio is below its maximum value, then flow is spilled subsonically, which 

requires the terminal shock to be located ahead of the cowl lip plane to allow the subsonic flow to spill 

past the cowl lip. 

B. Total Pressure Recovery 

The total pressure recovery at the engine face for an inlet is a measure of the amount of losses through 

the inlet and is denoted as (pt2/pt0) where pt2 is the mass-averaged total pressure at the engine face and pt0

is the total pressure at the freestream conditions. The total pressure recovery at the engine face is 

determined as the product of the total pressure ratios between the various stations through the inlet flow 

field, which is expressed as 

0

1

1

2

0

2

t

tL

tL

tEX

tEX

t

t

tSD

tSD

t

t

t

p

p

p

p

p

p

p

p

p

p

p

p  (9) 
NASA/TM—2012-217660 15 

Various methods evaluate each of the ratios on the right-hand side of the Equation (9). The ratio ptL / 

pt0 is evaluated as the total pressure losses through the oblique and conical shock waves of the approach 

flow. The ratio ptEX / ptL is evaluated as the total pressure losses through the oblique and conical shock 

waves of the external supersonic diffuser. The ratio pt1 / ptEX is evaluated as the total pressure loss through 

the terminal shock. The ratios of ptSD / pt1, and pt2 / ptSD are evaluated as total pressure losses due to 

viscosity of the subsonic flow through the throat and subsonic diffuser, respectively (Ref. 26). 

The total pressure recovery varies with respect to the flow ratio or engine flow ratio. The plot of the 

total pressure recovery pt2/pt0 with respect to the engine flow ratio W2/Wcap is called the total pressure 

characteristic curve or the “cane” curve due to its shape like a cane. The critical operating point is located 

at the “knee” of the cane curve. At sub-critical operating points, the terminal shock is pushed upstream 

and flow is spilled past the cowl lip. The engine flow ratio decreases; however, the total pressure recovery 

only varies slightly. As the flow becomes more sub-critical, the inlet will eventually experience buzz, 

which involves terminal shock oscillations. At supercritical operating points, the terminal shock is 

ingested into the inlet. The engine flow ratio cannot change, but the total pressure recovery drops sharply 

as the Mach numbers ahead of the terminal shock increase and losses due to shock / boundary layer 

interactions increase. 

C. Inlet Drag 

The inlet drag is the axial force opposing thrust that results from the operation of the inlet. The inlet 

drag contributions modeled within SUPIN include additive drag, cowl lip drag, and wave drag 

CDinlet  CDadd  CDclip  CDwave (10) 

The additive drag is the axial pressure force applied on the virtual surface of the inlet streamtube 

ahead of the cowl lip when the inlet flow ratio is less than unity. The flow field ahead of the cowl lip is 

integrated forward of the cowl lip to create the inlet streamtube and the static pressures are determined for 

each segment of the streamtube. The axial pressure force is computed from an integration of the static 

pressures along the streamtube surface, as of the form of Equation (11). The additive drag coefficient is 

normalized by the dynamic pressure at the local flow station L and the theoretical capture area. 

x

L L

D dA

pL

p

A M

C  













  



1

2

cap

add 1 2 (11) 

The cowl lip drag coefficient CDclip is determined from the axial force applied on the cowl lip due to 

suction, sharp lip flow separation, or a blunt cowl lip (Refs. 36 and 37). 

The wave drag coefficient CDwave is computed from the integration of the axial pressure forces caused 

by shock and Mach waves on the cowl exterior surface. The equation for the wave drag coefficient is 

similar in form to Equation (11). For the two-dimensional inlets, the static pressures on the cowl exterior 

are computed using oblique shock relations. This includes the shock waves generated by the sidewalls. 

For the axisymmetric inlet, the Mach number and pressure at the start of the cowl exterior are determined 

from a conical flow solution. A linearized pressure solver is then used to compute the pressure coefficient 

along the cowl exterior (Ref. 38). 
NASA/TM—2012-217660 16 

X. Inlet Design and Analysis Using SUPIN 

This section discusses the use of SUPIN for the design and analysis of external-compression 

supersonic inlets. This includes the design and analysis modes that control how SUPIN executes and an 

overview of the input and output files, including the grid files created for visualization and CFD analysis. 

A. SUPIN Input and Output Data Files 

SUPIN is a Fortran 95 program that operates in batch mode in which an input data file is read and an 

output data file is created. SUPIN has been developed and executed on Microsoft Windows (Microsoft 

Corporation) and Linux operating systems. Typical computational times range from seconds to less than a 

minute. The input data file (SUPIN.in) is in the format of an ASCII text file and contains blocks of input 

which control and provide inputs for SUPIN. While there are some requirements for the structure of the 

input file, there is flexibility which results in a simple input process that is usable. The output data file 

(SUPIN.out) is created as SUPIN is executed and also has the format of an ASCII text file. The output 

data file lists the values of the inputs, coordinates, geometric properties, aerodynamic properties, and 

performance results of the inlet. 

B. Inlet Surface Grids 

SUPIN represents the geometry of the inlet by distributing grid points along the planar profiles and 

creating surface grids for the inlet surfaces. The coordinates of the profiles are output to the output data 

file. The surface grids are output in Plot3D and stereo-lithography (STL) file formats (Ref. 39). These 

files can then be used by grid generation methods to create volume grids useful for CFD analysis. The 

generation of the grid points and surfaces is performed in an automated manner. The topology and 

geometric properties for the inlet are implied within the geometry model. The inputs to SUPIN include 

desired grid spacing values at key locations within the inlet, such as, the nose, cowl lip, throat, and engine 

face. Likewise, in the direction normal to walls, one may want to impose grid spacing values for 

resolution of boundary layers within CFD analyses. SUPIN applies an algorithm to calculate the number 

of grid points along the surfaces that provides for the desired grid spacing. Thus, the surface grid 

generation is automatically performed with minimal and logical inputs from the inlet designer. Figure 14 

shows some surface grids and grid spacing locations. 

 

Figure 14.—Grid spacing and surface grids for the inlets. 
NASA/TM—2012-217660 17 

C. Planar CFD Grids 

SUPIN can automatically generate a planar, multi-block structured grid for the symmetry plane of the 

inlet flowfield. The planar grid can be directly processed for use with a CFD code to obtain a flow 

solution. The planar flow solution can provide some useful information for the inlet aerodynamics since 

much of the inlet geometry is axisymmetric or two-dimensional and many of the methods assume 

axisymmetric or two-dimensional flow. The CFD flow solution can provide a verification check on the 

aerodynamic models within SUPIN. However, the results from a planar flow solution are limited for inlet 

flow fields that are inherently three-dimensional, such as the subsonic diffuser of the two-dimensional 

inlets and the entire flow field of the streamline-traced inlets. The inputs to SUPIN include specifications 

for the flow domain. The grid includes a block for the inlet outflow that attaches to the engine face. This 

block includes a converging-diverging nozzle with a variable nozzle throat area. This nozzle is used to 

impose a back-pressure for the CFD simulation and operates in an analogous manner as a choked exit 

plug for an inlet wind-tunnel test. The planar CFD grids are output in the Plot3D file formats. 

D. Design and Analysis Modes 

SUPIN can be executed in three modes: 1) generate the inlet geometry and surfaces from an explicit 

specification of the geometry factors or coordinates, 2) perform sizing and design operations for the inlet 

to generate the surfaces and calculate the aerodynamic performance of the inlet, and 3) generate the 

surfaces for a given inlet geometry and calculate the aerodynamic performance. 

The first mode reads in the inputs that specify the geometry and constructs the geometry coordinates 

of the inlet. If specified to do so, the surface grids and planar CFD grids are be generated. No design 

operations are performed and no aerodynamic performance properties are calculated. One way of 

specifying the inlet geometry is to specify the geometric factors of the individual parts of Figure 2. 

Another way is to specify the centerbody and cowl profiles in terms of a collection of line, polynomial, 

fitted curve, and NURBS entities. 

The second mode is used when one wishes to size the inlet and design the surfaces of the inlet for the 

freestream conditions, engine properties, and geometry factors specified in the input data file. It was 

discussed previously that the inlet sizing determines the inlet capture area Acap for a given corrected 

engine flow rate WC2 using Equation (6). This requires specifying a supersonic spillage ratio Wspillage/Wcap

and an initial guess for the inlet total pressure recovery pt2/pt0 in the input file. A fixed-point iteration is 

performed involving multiple analyses of the inlet to converge on the inlet total pressure recovery. 

Equation (7) can then be then used to compute the engine flow rate W2 and Equation (6) used to compute 

Acap. Knowing Acap, the dimensions of the cowl lip can be determined. 

The third mode is used if one wishes to perform off-design analysis of an inlet with known geometry. 

SUPIN has limited off-design analysis capabilities at this time. The terminal shock is assumed to be 

normal and located at station 1, thus subsonic spillage is not modeled. Off-design Mach numbers can be 

simulated for the two-dimensional inlets with ramps and for the single-cone axisymmetric inlet. Non-zero 

angles-of-attack can be simulated for the two-dimensional inlets with ramps. 

XI. Inlet Design Studies 

A series of design studies were performed to exercise and demonstrate the capabilities of SUPIN. All 

of the studies involve a basic set of specifications. The freestream properties are evaluated using the 

standard atmosphere at an altitude of 45,000 ft. The freestream assumes a cruise condition of Mach 1.8. 

No effects of an approach flow are modeled. Thus, the conditions at station L correspond to those at the 

freestream station 0. It is assumed that the engine operates at a constant corrected flow condition 

corresponding to an engine face Mach number of M2 = 0.5. The engine face has a diameter of 3.5 ft with a 

co-annular shape with a hub-to-tip ratio of 0.2. A spinner with an elliptical profile is specified. The axial 

length (semi-major axis) of the spinner is 0.5 ft. The radial length (semi-minor axis) of the spinner is 
NASA/TM—2012-217660 18 

0.35 ft, which matches to the hub of the engine face. The angle of incidence of the engine face is 0.0°. 

The outflow of the external supersonic diffuser at station EX is specified to be a mass-averaged Mach 

number of MEX = 1.3. The analyses assume the inlets are operated at the critical point with the normal 

shock at the cowl lip. 

A. Performance of the External Supersonic Diffusers 

The first study examined the variety of axisymmetric and two-dimensional external supersonic 

diffusers available within SUPIN. The diffusers are specified to be at zero angle-of-attack. Table 1 

summarizes the results. As the number of stages increase, the surface turning angle at station EX (EX) 

does not change significantly. While the turning for the axisymmetric diffuser is greater, the flow angles 

at the cowl lip (clip) are similar for the axisymmetric and two-dimensional diffusers. As the number of 

stages increase, the length of the external supersonic diffuser increases (Lexd/D2). The length of the 

isentropic diffuser is approximately 50 percent longer than the single-stage diffuser. The change from a 

single-stage diffuser to two or more stages results in a significant increase in the total pressure recovery 

(ptEX / ptL) and static pressure ratio (pEX / pL) for the diffuser. With a lower total pressure recovery, the 

single-stage diffusers are slightly smaller and result in less engine flow for the same engine corrected 

flow. The external supersonic diffuser for the two-dimensional bifurcated-duct inlet had the same 

performance as the two-dimensional single-duct inlet, and so, those results are not presented. However, 

the length of the external supersonic diffuser for the two-dimensional, bifurcated-duct inlet was 

approximately half of the length of the two-dimensional, single-duct inlet since the compression is 

mirrored about the plane-of-symmetry. 

B. Performance of the Inlet Types 

The second study examined the total inlet performance for the axisymmetric and two-dimensional 

inlets using the three-stage isentropic external supersonic diffuser. For each of the inlets, the cowl lip 

angles, cowl exterior factors, throat lengths and angles, and subsonic diffuser factors were all the same. 

Sharp cowl lips were specified for the inlets. The interior and exterior cowl lip angles were set to 10° and 

15°, respectively. The cross-sectional area through the throat was set to increase by 8 percent. The length 

of the subsonic diffuser was calculated to result in an equivalent conical diffusion angle of 3°. Table 2 

summarizes the results of the designs. The two-dimensional bifurcated-duct inlet resulted in the shortest 

inlet, which could yield a lower-weight inlet. The two-dimensional inlets had greater frontal area on the 

cowl exterior, which resulted higher wave drag coefficients. All three inlets had similar values for total 

pressure recovery and engine flow rate. 

TABLE 1.—SUMMARY OF THE EXTERNAL SUPERSONIC DIFFUSER DESIGN 

Inlet type EX clip Lexd / D2 ptEX / ptL pEX / pL hclip / D2 W2 / WC2 

Axi single cone 26.72 12.83 0.4443 0.9728 2.0172 0.9826 0.7035 

Axi double cone 26.33 12.53 0.5964 0.9936 2.0577 0.9963 0.7232 

Axi 3-stage isentropic 26.62 13.84 0.6551 0.9992 2.0720 0.9985 0.7265 

2D single ramp 13.76 13.76 0.6528 0.9667 2.0046 0.7584 0.7037 

2D double ramp 14.33 14.33 0.9067 0.9906 2.0542 0.7772 0.7211 

2D triple ramp 14.45 14.45 0.9975 0.9957 2.0648 0.7816 0.7251 

2D 3-stage isentropic 14.52 14.52 1.0004 0.9986 2.0709 0.7839 0.7273 

TABLE 2.—SUMMARY OF THE FULL INLET DESIGN

Inlet type Lexd / D2 Linlet / D2 hclip / D2 Acfex / A2 CDwave pt2 / ptL W2 / WC2

Axisymmetric 0.656 2.065 0.9985 0.337 0.1152 0.9687 0.7265 

2D single-duct 1.000 2.467 0.7839 0.491 0.1734 0.9680 0.7273 

2D bifurcated duct 0.500 1.880 0.7839 0.714 0.2759 0.9681 0.7273 
NASA/TM—2012-217660 19 

C. Variations in the Level of Supersonic Spillage 

The third study examined variations in the specified level of supersonic spillage for the twodimensional inlet with three ramps. Supersonic spillage can be implemented into an inlet design to allow 

a margin against the ingestion into the inlet of the external shock wave system or the vortices that 

originates from the external oblique/terminal shock interactions. Such ingestions have been shown to 

contribute to buzz. The specifications for the inlet geometry and conditions remain the same as those 

listed above. For a specified level of supersonic spillage, the design methods determined the single focal 

point for the oblique shock system. For zero spillage, the focal point coincides with the cowl lip. For 

spillage levels greater than zero, the focal point was placed above the cowl lip. All inlets operated with 

the same corrected engine flow rate. Table 3 summarizes the results. Since the total pressure recoveries 

were all the same, the actual engine flow rates were the same. With increased supersonic spillage, the 

length of the external supersonic diffuser and the height of the cowl lip increases. The cowl exterior 

factors were not changed, so increasing the height of the cowl lip resulted in a decrease in the forwardprojected area of the cowl exterior, which resulted in lower cowl wave drag. Increased supersonic spillage 

results in increased additive drag, but the decrease in wave drag more than compensates for the increase 

in additive drag. 

D. Analysis at Off-Design Mach Numbers and Angles-of-Attack 

The fourth study examined the two-dimensional single-duct inlet with three ramps analyzed for offdesign Mach numbers and angles-of-attacks. The design condition has the local Mach number ML = 1.8, 

local angle-of-attack L = 0°, and zero supersonic spillage. Table 4 summarizes the performance for offdesign increments of ML = 0.05 and L = 3.0°. The total pressure recovery seems to remain the same 

while the actual flow rate and drag vary significantly. 

E. CFD Analysis of the Axisymmetric Inlet 

The fifth study involved performing CFD analyses using the planar CFD grid for the axisymmetric, 

outward-turning inlet with the three-stage, isentropic external supersonic diffuser. The inflow was at 

Mach 1.8 and zero degrees angle-of-attack. A supersonic spillage ratio of 2 percent was specified. The 

inlet had a blunt cowl lip with a circular profile of radius 0.002 ft. The throat area increased 6 percent 

over its length of 1.0 ft. The subsonic diffuser was specified to be 4.0 ft in length. All other factors were 

the same as specified. Figure 15 shows the flow domain for the simulations. 

TABLE 3.—SUMMARY OF THE DESIGN OF A TRIPLE-RAMP, TWO-DIMENSIONAL 

SINGLE-DUCT INLET WITH VARIOUS LEVELS OF SUPERSONIC SPILLAGE 

Wspillage / Wcap W2 / Wcap pt2 / ptL Lexd / D2 Linlet / D2 hclip / D2 Acfex / A2 CDwave CDadd CDinlet

0.00 1.00 0.9652 0.9975 2.4638 0.7816 0.4941 0.1755 0.0000 0.1755 

0.01 0.99 0.9652 1.0410 2.5074 0.7895 0.4836 0.1663 0.0038 0.1701 

0.02 0.98 0.9652 1.0855 2.5518 0.7975 0.4729 0.1594 0.0075 0.1669 

0.04 0.96 0.9652 1.1771 2.6434 0.8141 0.4509 0.1455 0.0150 0.1605 

TABLE 4.—SUMMARY OF THE ANALYSIS OF A TRIPLE-RAMP, TWO-DIMENSIONAL 

SINGLE-DUCT INLET AT OFF-DESIGN MACH NUMBERS AND ANGLES-OF-ATTACK 

ML L W2 / WC2 pt2 / ptL CDwave CDadd CDinlet

1.80 0.00 0.7251 0.9652 0.1755 0.0000 0.1755 

1.75 0.00 0.6793 0.9652 0.1823 0.0079 0.1902 

1.85 0.00 0.7744 0.9651 0.1675 0.0000 0.1675 

1.80 3.00 0.7251 0.9659 0.1339 –0.0103 0.1236 

1.80 –3.00 0.7251 0.9625 0.2221 0.0202 0.2424 
NASA/TM—2012-217660 20 

Figure 15.—Flow domain and Mach number contours for the CFD simulation of the axisymmetric, 

outward-turning inlet at sub-critical operation. 

TABLE 5.—INLET PERFORMANCE FROM THE CFD ANALYSES AT 

VARIOUS LEVELS OF INLET BACK-PRESSURE 

Anoz / A2 W2 / Wcap M2 pt2 / pt0 p2 / p0 CDwave

0.720 0.9364 0.4825 0.9540 4.6457 0.1195 

0.730 0.9540 0.4892 0.9605 4.6640 0.1285 

0.735 0.9616 0.4926 0.9625 4.6670 0.1318 

0.740 0.9704 0.4968 0.9654 4.6683 0.1368 

0.745 0.9747 0.5113 0.9589 4.5564 0.1386 

0.750 0.9750 0.5190 0.9518 4.4890 0.1389 

0.760 0.9751 0.5239 0.9417 4.4431 0.1389 

The inflow and farfield boundaries were placed away from the inlet such that freestream boundary 

conditions could be imposed. The engine face station 2 was located at x = 5.35 ft. The nozzle block 

attached downstream of the engine-face shows a constant-area section followed by a convergingdiverging nozzle. The nozzle throat was sized to create a back-pressure for the critical operating point for 

the inlet. At the exit of the nozzle, a supersonic outflow boundary condition was imposed. The surfaces of 

the inlet were modeled as adiabatic, no-slip walls. The planar grid consisted of 27 structured-grid blocks 

with a total of 98361 grid points. The grid spacing values at the cowl lip, throat, and engine face were 

0.0001, 0.01, and 0.0625 ft, respectively. This resulted in 427 grid points distributed axially between the 

cowl lip and engine face. The grid spacing normal to the wall was 0.0001 ft, which corresponded to a y

+

for the first point off the wall of approximately y

+

 = 5. From the centerbody to the cowl, there were 135 

grid points. Figure 15 shows the Mach number contours and indicates the shock and Mach waves of the 

supersonic flow and the variations of the subsonic flow downstream of the terminal shock. 

The CFD simulations were performed over a range of outflow nozzle throat areas to vary the inlet 

flow from sub-critial to super-critical. Table 5 lists the various inlet performance measures over a range of 

inlet back-pressures as set by the outflow nozzle. As the nozzle is opened, the engine flow ratio (W2 / 

Wcap) increases to its maximum, choked value as the inlet becomes super-critical. The mass-averaged 

Mach number at the engine face (M2) varies about the design value of M2 = 0.5. The total pressure 

recovery (pt2 / pt0) increases and then drops. Figure 16 shows the characteristic “cane” curve of the 

variation of the total pressure recovery with engine flow ratio. Also plotted is the total pressure recovery 

for the critical operating point as computed by SUPIN. It is evident from Table 5 and Figure 16 that the 

CFD analysis indicates approximately 2.5 percent supersonic spillage rather than the 2.0 percent specified 

within SUPIN. The static pressure ratio similarly rises and then drops. The wave drag coefficient 

increases and then remains fixed for the super-critical flow rates. Figure 17 shows Mach number contours 

of the shocks and flow about the inlet entrance for the sub-critical, critical, and super-critical operating 

points. 
NASA/TM—2012-217660 21 

Figure 16.—Characteristic “cane” curve from the CFD 

simulations of the axisymmetric, outward-turning inlet. 

Figure 17.—Mach contours at sub-critical (left), critical (center), and super-critical (right) operation of the 

axisymmetric, outward-turning inlet. 

TABLE 6.—COMPARISON OF CFD AND SUPIN RESULTS AT 

THE CRITICAL OPERATING POINT 

Method W2 / Wcap M2 pt2 / pt0 p2 / p0 CDwave

SUPIN 0.9800 0.5000 0.9663 4.6802 0.1371 

CFD 0.9704 0.4968 0.9654 4.6683 0.1368 

% –0.98% –0.63% –0.09% –0.25% –0.21% 

Table 6 compares the various inlet performance measures at the critical operating point as computed 

from SUPIN and from the CFD analysis. The CFD results are those listed in Table 2 for Anoz / A2 = 0.740, 

which is assumed to approximate the critical operating point of the inlet. The CFD simulation indicates 

slightly greater supersonic spillage. This increased spillage is due to the blockage of the boundary layer 

on the centerbody. An inviscid CFD analysis of the inlet was performed and yielded a supercritical flow 

rate of W2 / Wcap = 0.9789, which is 0.11 percent below the supersonic spillage specified within SUPIN. A 

modification to SUPIN could be the estimation of the boundary layer displacement thickness on the 

external supersonic diffuser and the subsequent adjustment of the capture area to account for the 

boundary layer blockage. The mass-averaged Mach number of the CFD simulation is slightly different 

from the value specified within SUPIN (M2 = 0.5); however, this is most likely due to the use of the 

outflow nozzle to approximate the critical operating point. A CFD simulation could be performed for 

which the engine-face Mach number is specified as the boundary condition at station 2. However, the 

results of Table 6 were sufficient for the purpose of this paper. The total pressure recovery, static pressure 

ratio, and wave drag coefficient of the CFD simulation agreed well with the values indicated by SUPIN. 

Overall, this provides some confidence in the aerodynamic models within SUPIN for designing and 

analyzing axisymmetric, outward-turning inlets. 

0.90

0.92

0.94

0.96

0.98

1.00

0.90 0.92 0.94 0.96 0.98 1.00

pt2 / pt0

W2 / Wcap

SUPIN

CFD
NASA/TM—2012-217660 22 

Similar planar CFD analyses could be conducted for the two-dimensional inlets. However, the 

sidewalls of the two-dimensional inlets make the flow three-dimensional, and so, planar analyses would 

only provide a general sense of the flow through two-dimensional inlets. Likewise, the streamline-traced 

inlet is a three-dimensional flowfield. Thus, for these inlets, one should start with the surface grids and 

using a grid generation software system, create a three-dimensional CFD grid and perform a threedimensional flow analysis. 

XII. Summary 

The geometry and aerodynamic modeling of external-compression supersonic inlets is available 

within the SUPIN Fortran code. SUPIN models the geometry of a set of inlets using simple planar 

geometry constructs. The aerodynamic performance of the inlet is computed using low-fidelity and quick 

analytic, empirical, and numerical methods. The aerodynamic performance includes the flow rates, total 

pressure recovery, and drag. SUPIN provides surface grids suitable for higher-fidelity analysis using 

methods of computational fluid dynamics. Further development of SUPIN will provide greater 

capabilities for off-design analysis and modeling internal supersonic compression for the design and 

analysis of mixed-compression supersonic inlets. 

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Airplane,” SAE 595N, October 1962. 

11. Johnson, C.L., “Some Development Aspects of the YF-12A Interceptor Aircraft,” AIAA Journal of 

Aircraft, vol. 7, no. 4, p. 355-359, 1970. 

12. Hirt, S.M., Chima, R.V., Vyas, M.A., Conners, T.R., Wayman, T.R., and Reger, R.W., 

“Experimental Investigation of a Large-Scale Low-Boom Inlet Concept,” AIAA-2011-3796, 

June 2011. 

13. Ames Research Staff, “Equations, Tables, and Charts for Compressible Flow,” NACA Report 1135, 

1953. 

14. Anderson, J.D., Jr., Modern Compressible Flow, McGraw-Hill Book Company, New York, 1982. 

15. Imfeld, W.F., “Development Program for the F-15 Inlet,” AIAA Journal of Aircraft, vol. 13, no. 4, 

p. 286-291, April 1976. 
NASA/TM—2012-217660 23 

16. Rettie, I.H. and Lewis, W.G.E., “The Design and Development of an Air Intake for a Supersonic 

Transport Aircraft,” AIAA-1967-0752, October 1967. 

17. Candel, S., “Concorde and the Future of Supersonic Transport,” AIAA Journal of Propulsion and 

Power, Vol. 20, No. 1, January-February 2004, p. 59-68. 

18. Wasserbauer, J.F., Meleason, E.T., and Burstadt, P.L., “Experimental Investigation of the 

Performance of a Mach 2.7 Two-Dimensional Bifurcated Inlet With 30 Percent Internal 

Contraction,” NASA TM-106728, May 1996. 

19. Mölder, S. and Szpiro, E.J., “Busemann Inlet for Hypersonic Speeds,” AIAA Journal of Spacecraft 

and Rockets, vol. 3, no. 8, pp. 1303-1304, August 1966. 

20. Van Wie, D. and S. Mölder, “Applications of Busemann Inlet Designs for Flight at Hypersonic 

Speeds,” AIAA-1992-1210, February 1992. 

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Hypersonic Inlets,” AIAA-1999-4974, November 1999. 

22. Koncsek, J.L., “Supersonic External-Compression Diffuser and Method for Designing Same,” 

Patent 6793175, September 2004. 

23. Slater, J.W., Davis, D.O., Sanders, B.W., and Weir, L.J., “Role of CFD in the Aerodynamic Design 

and Analysis of the Parametric Inlet,” ISABE–2005–1168, 2005. 

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Aircraft,” AIAA-2008-4585, July 2008. 

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Waves Ahead of Plane or Axially Symmetric Bodies,” NACA TN 1921, 1949. 

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L56F05, 1956. 

27. Tindell, R. and Tamplin, G., “An Inlet System Installed Performance Prediction Program using 

Simplified Modeling,” AIAA-1983-1167, June 1983. 

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and Analysis,” JANNAF Propulsion Meeting, November 1993. 

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Perturbation Flow Field Analysis and Simulation for Supersonic Inlets - Final Report,” 

NASA CR 174576, September 1984. 

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Multifidelity Multidisciplinary Computer Codes for Design and Analysis of Supersonic Aircraft,” 

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Systems,” AIAA-1981-1395, July 1981. 

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Subsonic Speeds,” NACA Report 1193, 1954. 

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NASA-TM-101067, March 1990. 
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Design and Analysis Tool for External-Compression Supersonic Inlets 

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14. ABSTRACT

A computational tool named SUPIN has been developed to design and analyze external-compression supersonic inlets for aircraft at cruise 

speeds from Mach 1.6 to 2.0. The inlet types available include the axisymmetric outward-turning, two-dimensional single-duct, twodimensional bifurcated-duct, and streamline-traced Busemann inlets. The aerodynamic performance is characterized by the flow rates, total 

pressure recovery, and drag. The inlet flowfield is divided into parts to provide a framework for the geometry and aerodynamic modeling 

and the parts are defined in terms of geometric factors. The low-fidelity aerodynamic analysis and design methods are based on analytic, 

empirical, and numerical methods which provide for quick analysis. SUPIN provides inlet geometry in the form of coordinates and surface 

grids useable by grid generation methods for higher-fidelity computational fluid dynamics (CFD) analysis. SUPIN is demonstrated through 

a series of design studies and CFD analyses were performed to verify some of the analysis results.

15. SUBJECT TERMS

Supersonic inlets 

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