Main start-up screen for the Aerospike Nozzle and Minimum Length Nozzle (MLN) analyses

Aerospike Rocket Motor Designed Using AeroSpike 3.1 NEW

PART 1: AEROSPIKE NOZZLE DESIGN
ANNULAR (3-D) & LINEAR (2-D) CONTOURS BACK TO TOP

Summary of Features
1. Determine the shape of an annular or linear aerospike nozzle given the thruster exit area ratio (Aei/At), projected area expansion ratio (Ae/At), pressure ratio (Pc/Pa), thruster internal radius (Ra), radius to lip of cowl (Re), total nozzle length from origin (Lnozzle), chamber temperature (Tc), chamber pressure (Pc), ratio of specific heats (g) and gas constant.
2. Click the UpDown command button to move a locator to one of seven points in the flow field.
3. All important flow properties are displayed in real time as the locator moves from point to point in the flow field described by the characteristic mesh of the aerospike.
4. Generate color contour plots of Mach number (Mn), Pressure (P/Pc), Temperature (T/Tc) and density (R/Rc) with a single click.
5. Plot Mn, P/Pc, T/Tc, R/Rc, CF, CFvac, ISP, ISPvac as a function of aerospike nozzle axial location at a particular Pc/Pa.
6. Plot CF, Thrust, CFvac, ISP, and ISPvac verses pressure ratio (Pc/Pa) on a semi-log scale.
7. Units include, MKS (meter-newton-sec), CGS (centimeter-dyne-second), FPS (foot-pound-second) and IPS (inch-pound-second).
8. Graphically display the outer flow boundary for under expanded flow, over expanded flow and the angle of the outer boundary flow.
9. Graphically display the initial shock wave formed at the lip of the cowl for over expanded flow (Pa/Pc > Pe/Pc) and the shock angle from the lip.
10. Define gas properties for inert gases, liquid propellant gases and solid fuel propellant gases or insert your own values.
11. Define the analysis for annular (3-D) or linear (2-D) aerospike nozzles.
12. Define the angle the sonic section of the thruster makes with the axis of the aerospike nozzle.
13. Added a hybrid rocket motor propellant having the following fuel and oxidizer to the list of combustion gases: 85% Nitrous Oxide, 15% HTPB.
14. Added the ability to save F(x) verses PR (Pressure Ratio) and F(x) verses x to a CSV file for use with Notepad or Excel.
15. In the Aerospike Nozzle Data section added a display of Truncation as percent of total aerospike length.
16. In the Aerospike Nozzle Data section added a display of Distance from throat (origin) to end of thruster.
17. In the Aerospike Nozzle Data section added a display of Distance from end of thruster to end of ramp.
18. NEW! Added the ability to include base thrust for truncated aerospike nozzles.

General Discussion
AeroSpike performs an expansion-wave analysis from the throat of the thruster nozzle, where Mn = 1.0, to the thruster nozzle internal-exit as a series of simple wave expansions. Then, for the external ramp AeroSpike performs a series of Prandtl-Meyer expansions from the lip of the cowl, where R=Re, to the entire length of the external ramp of the aerospike nozzle. The ideal contour or shape of the external ramp of the aerospike nozzle is determined using isentropic supersonic flow theory. Then, depending on whether the flow is underexpanded or if the flow is overexpanded AeroSpike performs either a Prandtl-Meyer expansion analysis or an oblique shock wave analysis to determine the angle of the outer flow boundary from the lip of the cowl. As a by product of the oblique shock wave analysis AeroSpike determines the shock wave angle for overexpanded flow and plots both the outer boundary contour and the initial shock wave from the lip of the cowl. If the Check to Include base thrust check box is not checked then base pressure is assumed equal to atmospheric pressure (Pb = Patm) which means base thrust is zero and only the centerbody and thrusters contribute to total aerospike thrust. However, if the Check to Include base thrust check box is checked then base pressure and atmospheric pressure are non-equal resulting in the following aerospike nozzle total thrust equations, F_total = F_centerbody + F_base + F_thruster. and CF = F_total  / (At * Pc).

Procedure
From the menu on the top of the main start-up screen, select units (MNS, CGS, FPS or IPS) from the Units menu and then the propellant gas from the Gases menu. A number of inert gases, liquid fuel propellants and solid fuel propellants are available. The value for the ratio of specific heats (g) are determined from the Units and Gases menus and are passed on to the Aerospike Nozzle program after clicking the Aerospike Nozzle command button on the main start-up screen. The ratio of specific heats, gas constant (Rgas), chamber pressure (Pc), and pressure ratio (PR) are required for the Aerospike Nozzle analysis. Additionally, the pressure ratio (PR) represents the maximum value for Pc/Pa that AeroSpike will use to plot CF, Thrust, CFvac , ISP and ISPvac as a function of PR. The chamber pressure is computed based on the atmospheric pressure (Pa) and the pressure ratio (Pc/Pa). These values are automatically passed to the Aerospike Nozzle analysis when the command button is clicked. However, the user can over-ride any input value by inserting new data directly into each data entry box on the Aerospike Nozzle Design screen. Each time the user changes any data entry the results are automatically updated and displayed. The user only needs to click the Plot button to see a new contour plot of the results or the UpDown button to see flow results at any of the characteristic mesh points.

Toolbar Operations

1. Click [X] to switch between the main data entry area (Figure-2) and the secondary data entry area (Figure-3). The main data entry area is displayed by default. Specify either annular aerospike geometry or linear aerospike geometry by clicking one of two option buttons in the secondary data entry area. In addition, the thruster sonic-section angle (60 degrees to 120 degrees) is located in the secondary data entry area. The thruster sonic-section angle is measured from the axis of the aerospike nozzle to the section that defines the throat of the thruster (where Mach number = 1). Default = 90 degrees. Finally, check the Check to Include base thrust check box to include base thrust for the determination of total thrust and thrust coefficient (CF) for truncated aerospike nozzles.
2. Send all flow properties (X, Y, Mn etc.) at each characteristic mesh point to the printer.
3. Send an image of the screen to the printer.
4. Save all flow properties (X,Y, Mn etc) at each characteristic mesh point to a data file.
5. Read the nozzle description file from a previous session.
6. Save the nozzle description file from a previous session.
7. Refresh the displayed analysis to the default analysis seen during start-up.
8. Return to the main start-up screen.

Input Variable Definitions
1. Thruster exit area ratio (Aei/At): Ratio of thruster internal exit area (Aei) to thruster throat area (At). Equation 1 is inverted to find Pc/Pei from Aei/At.
2. Thruster pressure ratio (Pc/Pei): Ratio of chamber pressure to thruster exit pressure. Found by interation of Equation 1 and displayed in lower data region.
3. Aerospike expansion ratio (Ae/At): The projected area of the aerospike nozzle (Ae = p * Re^2) divided by the total thruster throat area.
4. Ratio of specific heats (g): Selected from a pull-down menu or user-defined.
5. Gas constant of exhaust (Rgas): Selected from a pull-down menu or user-defined.
6. Aerospike pressure ratio (Pc/Pa): Ratio of the chamber pressure (Pc) to the atmospheric pressure (Pa).
7. Thruster internal circular radius (Ra): Radius of the internal portion of the thruster duct from point 1 (throat) to point 2 (Ra).
8. Radius to lip of cowl (Re): Radius that defines the projected area of the aerospike nozzle (Re).
9. Aerospike length from origin (Lnozzle): Total length of the aerospike nozzle from the origin (throat) of the thruster to the end of the ramp.
10. Chamber temperature (Tc): Chamber temperature in either degrees Rankine or degrees Kelvin depending on the units selected.
11. Chamber pressure (Pc): Chamber pressure whose units depend on the units selected.
12. Width of ramp for linear aerospike nozzles (Lramp).
.
Equation 1: Thruster Cross-Sectional Area and Pressure Ratio Relationship.


Figure 1. Aerospike Nozzle Displaying Basic Geometry and the External Expansion Fan.

AeroSpike Validation-1
EXTERNAL FLOW FIELD FOR AN ANNULAR AEROSPIKE NOZZLE

Figure 2. Aerospike Nozzle - Optimum Expansion (PR = 71.5) and 20% plug nozzle configuration


Figure 3. Aerospike Nozzle - Secondary Input Data Entry Area for Annular/Linear nozzle and thruster angle inputs.

Truncated Aerospike Nozzle Base Pressure, Total Thrust and Thrust Coefficient
To determine truncated aerospike nozzle base pressure (Pb) for computing total thrust and pressure coefficient (CF) simply check the Check to Include base thrust check box in the Annular or Linear Ramp Selection and Thruster Angle data entry area. When checked this check box activates base pressure computation for truncated aerospike nozzles where base pressure is included for determination of total aerospike thrust and thrust coefficient. Truncated aerospike nozzle base thrust is determined using two curve-fit relationships for computing base thrust. The first relationship is atmospheric pressure (Patm) verses pressure ratio (PR=Pc/Pa) and the second relationship is base pressure verses percent truncation. Where, X% truncation refers to an aerospike nozzle where (100-X)% of the expansion ramp has been removed leaving a blunt base region. The plots in Figure 4 and Figure 5 illustrate the relationship between Patm verses PR and Pb verses Percent Truncation for the computation of base thrust, total thrust and thrust coefficient. The curve-fit for base pressure verses percent truncation displayed in Figure 5 was developed using several Computational Fluid Dynamics (CFD) analyses using aerospike nozzles having 20%, 30%, 40% and 50% truncation.

Aerospike nozzle total thrust is computed using the following equations knowing PR and percent truncation.
F_base= (Pb - Patm) * A_base, F_total = F_centerbody + F_base + F_thruster and CF = F_total  / (At * Pc) where Patm = fn(PR) and Pb = fn(% Truncation)

Figure 4. Atmospheric pressure (Pa) verses pressure ratio (PR=Pc/Patm)

Figure 5. Base pressure (Pb) verses percent truncation curve-fit using CFD analyses of aerospike nozzles having 20%, 30%, 40% and 50% truncation.

CF vs. PR Validation		Flow Field Validation
Figure 6. CF verses Pressure Ratio (Pc/Pa)  - Semi-Log plot, Maximum PR = 1000. AeroSpike CF verses PR compared to 20% (80% truncated) plug nozzle  Base Flow CFD analysis includes base pressure coefficient. Reference: AIAA 2001-1051, T. Ito, K. Fujii, Flow Field Analysis of the Base Region of Axisymmetric Aerospike Nozzles. "I used (AeroSpike) to design several types of nozzle(s) and found your software is really useful". Takashi Ito, JAXA
Reference: "Aerospike Nozzle Flow Fields", AIAA 2001-1051, by Takashi Ito. Contour plots used with permission from reference.		Figure 7. AeroSpike program nozzle flow field results compared to Base Flow CFD analyses for PR=9, PR=71 and PR=500.

Aerospike Rocket Motor Design Example
		AeroCFD 5.2 Analysis by John Cipolla
Annular aerospike designed to produce 225,000 pounds of thrust.		AeroCFD analysis of an aerospike rocket. M = 1.5.

The annular aerospike rocket motor pictured above (left) is a design developed and rendered by Richard Caldwell (Rocket Nut) intended to produce 225,000 pounds of thrust at sea level. This design concept was developed using AeroSpike 2.6 software to specify the internal thruster and external ramp geometries for efficient operation from sea level to orbital altitude. Rocket Nut's design uses an untruncated Annular Aerospike ramp as illustrated in Figure-3. Please click here for more information.

AeroSpike Validation-2
X-33 XRS-2200 AEROSPIKE ROCKET ENGINE ANALYSIS EXAMPLE
In this example the Linear Ramp or 2-D option is used to determine sea level and vacuum thrust for the X-33 XRS-2200 aerospike rocket engine. Click the Hide or Show Aerospike Nozzle Data (X in the toolbar) to select the Linear Aerospike option and then insert 90 for the 2-D Ramp width in the space provided. The data from Figure-9 were used as input for the aerospike analysis illustrated in Figure-10 where vacuum  thrust and specific impulse (Isp) are predicted to be 264,600 lbf and 454.7 sec where Pc/Pa = 100000. Dimensional data for this analysis are based on Boeing's results for the XRS-2200 linear aerospike rocket engine where vacuum thrust and Isp are 266,230 lbf and 436.5 sec for a 0.6% variation in thrust and 4.2% variation in Isp. Due to unavailable thruster dimensions and conflicting dimensional and performance information provided by NASA and relevant technical papers this aerospike rocket engine analysis is an approximation.

NASA Description of the X-33 Spaceplane: The X-33 was to have been a wedged-shaped subscale technology demonstrator prototype of a potential future Reusable Launch Vehicle (RLV) that Lockheed Martin dubbed VentureStar. The company hoped to develop VentureStar early this century. Through demonstration flight and ground research, NASA's X-33 program was to have provide the information needed for industry representatives such as Lockheed Martin to decide whether to proceed with the development of a full-scale, commercial RLV program. The X-33 design was based on a lifting body shape with two revolutionary linear aerospike rocket engines and a rugged metallic thermal protection system. The vehicle also was to have had lightweight components and fuel tanks built to conform to the vehicle's outer shape. Time between X-33 flights was planned to normally be seven days, but the program hoped to demonstrate a two-day turnaround between flights during the flight-test phase of the program. The X-33 was to have been an unpiloted vehicle that took off vertically like a rocket and landed horizontally like an airplane. It was planned to reach altitudes of up to 50 miles and high hypersonic speeds. The X-33 Program was managed by the Marshall Space flight Center and was planned to have been launched at a special launch site on Edwards Air Force Base. Technical problems with the composite liquid hydrogen tank resulted in the program being cancelled in February 2001.

	XRS-2200 Engine 5K ft Vacuum Thrust, lbf 204,420 266,230 Specific Impulse, sec 339 436.5 Propellants Oxygen, Hydrogen Mixture Ratio (O/H) 5.5 Chamber Pressure, psia 857 Cycle Gas Generator Area Ratio (Ae/At) 58 Throttling, Percent Thrust 50 - 100 Dimensions, inches Forward End Aft End Forward to Aft ---- 134 wide x 90 long 42 wide x 90 long 90
Figure-8 aerospike engine side view.	Figure-9, XRS-2200 aerospike rocket engine description data repeated in Figure-10.

Figure-10, XRS-2200 vacuum (Pc/Pa=100,000) analysis. Input data for the results in Figure-10 based on data from Figure-9 using AeroSpike version 2.6.0.5.

Aerospike Engine Results Compared	5K ft (Pc/Pa = 70.0621)		Vacuum (Pc/Pa = 100,000)
	Thrust, lbf	Isp, sec	Thrust, lbf	Isp, sec
AeroSpike 3.1	155,500	267	264,600	454.7
Boeing XRS-2200 Results	204,420	339	266,230	436.5

BOUNDARY SHAPE: The outer boundary angle from the lip of the thruster cowl to the end of the external ramp increases as altitude increases. The pressure ratio (Pc/Pa) defines the extent to which the outer boundary expands as altitude and pressure ratio increase. For pressure ratio, Pc is the thruster chamber pressure and Pa is the local atmospheric pressure. This section compares the XRS-2200 expansion boundary shapes at 5K feet (Pc/Pa = 70.0621) and 50K feet (Pc/Pa = 509.21) determined by Navier Stokes and AeroSpike.

 

AeroSpike Rocket Motor Designed Using AeroSpike 2.6 NEW

Aerospike hot fire jet and inset illustrating AeroSpike 2.6 results superimposed on aerospike.

This section for the design and test of an actual aerospike rocket motor/thruster displays the geometry, fabrication methods and photographic results for a model rocket scale aerospike rocket motor. Click here to see a 10-second 400KB QuickTime movie of an aerospike rocket motor designed using AeroSpike 3.1. Requires QuickTime from Apple Computer. This design continues to evolve so updated information will appear as results are available.

Aerospike Input Data, 1st column. Some Results, 2nd column
Thruster exit area ratio (Aei/At)	2.0		Chamber temperature	1047.0
Aerospike expansion ratio (Ae/At)	10.5		Chamber pressure	154.0
Ratio of specific heats for exhaust	1.2		Aerospike thrust	2.802
Gas constant of exhaust (Rgas)	247139		Ramp base radius (Rbase)	0.0
Aerospike pressure ratio (Pc/Pa)	10.5		CF - Thrust coefficient	0.888
Thruster internal circular radius (Ra)	0.2		CF - Vacuum thrust coefficient	1.748
Radius to lip of cowl (Re)	0.25		Isp - Specific Impulse	51.3
Aerospike length from origin (Lnozzle)	0.96		Isp - Vacuum specific impulse	101.0
Propellant weight (lbs)	0.0077		Estimated burn time (sec)	0.172

Aerospike generated using AeroSpike 3.1. This plot properly scaled was used as a template.

Aerospike Ramp Fabrication		Aerospike Rocket Motor: Exploded View
Aerospike fabricated from a solid bar of 6061-T6 aluminum using a lathe to machine the article using a template generated by AeroSpike 2.6.		Exploded view of the aerospike rocket motor. Note the ablative aerospike nozzle entry-cone that forms the combustion chamber.
Aerospike Rocket Motor Test (Tburn = 0.0 sec)		Aerospike Rocket Motor Test (Tburn = 0.172 sec)
Aerospike rocket motor primed and ready for hot fire testing.		Aerospike image clipped from QuickTime movie. Requires QuickTime from Apple.

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PART 2: 2-D & 3-D MINIMUM LENGTH NOZZLE DESIGN USING
THE METHOD OF CHARACTERISTICS (FREE BONUS ADDITION) BACK TO TOP

Summary of Features
1. Determine shapes and flow properties of 2-D Minimum Length Nozzles (MLN) given exit Mach number (Mdesign) and throat diameter (Dt).
2. Determine shapes and flow properties of 3-D Minimum Length Nozzles using an approximation procedure based on 2-D results.
3. Click the UpDown command button to move a locator from point to point in the flow field.
4. All important flow properties are displayed in real time as the locator moves from point to point in the flow field described by the characteristic mesh.
5. Generate color contour plots of Mach number (Mn), Pressure (P/Pc), Temperature (T/Tc) and density (R/Rc) with a single click.
6. Units include, MKS (meter-newton-second), CGS (centimeter-dyne-second), FPS (foot-pound-second) and IPS (inch-pound-second).
7. Define gas properties for inert gases, liquid propellant gases and solid fuel propellant gases or insert your own values.
8. Output all flow variables to the printer or text file for use with spreadsheet applications.

General Discussion
The Minimum Length Nozzle routine performs a minimum length nozzle (MLN) design using the method of characteristics. A minimum length nozzle has the smallest possible throat-to-exit length that is still capable of maintaining uniform supersonic flow at the exit. Strictly speaking a minimum length nozzle requires a sharp corner at the throat. However, sometimes a sharp corner at the throat may be impractical. A nearly minimum length nozzle may be generated by specifying a very small but finite radius of curvature at the throat with the inflection point of the throat-curve just downstream of the throat. For a nearly minimum length nozzle simply specify the streamline from the throat-curve so the curvature lines up with the nozzle wall shape generated by MLN.

A straight sonic line is assumed to occur at the throat of the minimum length nozzle. For the example presented in Figure 2 and Figure 3, where the exit Mach number is 2.4, the first characteristic (C_ ) propagating from the corner of the throat is inclined by a small amount (q = 0.375 deg) from the normal sonic line. The slope of the first characteristic is dy/dx = (q - m) = -73.725 deg. See Figure 1 below. The remaining expansion fan is divided into six increments. The Mach number at each point in the flow is determined from the Prandtl-Meyer function using the Newton-Raphson iteration method and the unit processes dictated by the method of characteristics. The nozzle contour is drawn by starting at the throat corner where the maximum expansion angle of the wall, qw_max is equal to one-half the Prandtl-Meyer function, n(Mn) / 2, at the design exit Mach number. For a minimum length nozzle the maximum expansion angle is equal to one-half the Prandtl-Meyer function for the design exit Mach number. For other nozzles the maximum expansion angle must be less than n(Mn=Mdesign) / 2. For a detailed discussion of the method of characteristics please refer to the reference, Modern Compressible Flow, With Historical Perspective, by John D. Anderson, pages 260 to 282.

PLEASE NOTE: For the 2-D Minimum Length Nozzle selection the "X" and "Y" coordinates of the nozzle contour represent the horizontal and vertical dimensions that define the 2-D characteristic mesh. Therefore, the Exit Area Ratio (Aexit/Athroat) = [2*Yexit*WIDTH] / [2*Ythroat*WIDTH] = Yexit/Ythroat because the flow is 2-Dimensional. Likewise, for the 3-D Minimum Length Nozzle selection the "X" and "Y" coordinates of the contour represent the horizontal and radial dimensions that define the 3-D axisymmetric mesh. Therefore, the Exit Area Ratio (Aexit/Athroat) = [p*Yexit^2] / [p*Ythroat^2] = (Yexit/Ythroat)^2 because the flow is 3-Dimensional and not 2-Dimensional. Finally, MLN Project files generated by previous versions of MLN must be updated by adding "1" for 2-D flow or "2"  for 3-D flow at the bottom of the MLN file. Do not forget to save each Project file with an MLN extension when updating older Project files for use with AeroSpike 2.5 or higher.

Procedure
From the menu on the top of the main start-up screen, select units (MNS, CGS, FPS or IPS) from the Units menu and then the propellant gas from the Gases menu. A number of inert gases, liquid propellants and solid fuel propellants are available. The value for the ratio of specific heats (g) are determined from the Units and Gases menus and are passed on to the MLN program after clicking the Minimum Length Nozzle command button on the main start-up screen. Only the ratio of specific heats are required for the MLN analysis. The other values including the gas constant (Rgas), chamber pressure (Pc) and pressure ratio (PR) are not required for the MLN analysis. When performing an MLN analysis the only values required are the Inclination angle from the sonic line (see above), Design Mach number (Mdesign), and throat diameter (Dt). The ratio of specific heats has already been specified from the main screen selection. However, the user can over-ride the inserted ratio of specific heats by simply inserting his own ratio of specific heats in the data entry box. Each time the user changes any data entry the results are automatically updated and displayed. The user only needs to click the Plot button to see a new contour plot of the results or the UpDown button to see flow results at any of the characteristic mesh points.

Toolbar Operations

1. Show or hide the main data window from view or from being printed.
2. Send all flow propeties (X, Y, Mn etc) at each characteristic mesh point to the printer.
3. Send an image of the screen to the printer.
4. Save all flow properties (X,Y, Mn etc) at each characteristic mesh point to a data file.
5. Read the nozzle description file from a previous session.
6. Save the nozzle description file from a previous session.
7. Refresh the displayed analysis to the default analysis seen during start-up.
8. Return to the main start-up screen.

Input Variable Definitions
1. Ratio of specific heats (g): Selected from pull-down menu or user-defined.
2. Inclination angle from sonic line: This angle is used to compute the slope of the first characteristic from the edge of the throat.
3. Design Mach number (Mdesign): The Mach number at the exit of the nozzle where the flow is uniform.
4. Throat diameter (Dt): The entrance to the minimum length nozzle where Mn = 1.0
5. Area ratio (Aexit/Athroat): The resulting exit area ratio of the nozzle determined by the method of characteristics.
6. Specify whether the nozzle is 2-D or 3-D by clicking either the 2-D characteristics or 3-D approximation option buttons.


Figure 1. Description of the inclination angle (q) from the sonic line (at throat) where Mn =1.0

Minimum Length Nozzle Validation-1
Example 11.1, on page 282 from Modern Compressible Flow, With Historical Perspective, by John D. Anderson

Figure 2. Example 11.1, on page 282 from Modern Compressible Flow, With Historical Perspective, by John D. Anderson

NOTE ABOUT MLN ANALYSIS ACCURACY: The Minimum Length Nozzle (MLN) analysis illustrated in Figure-2 uses exact input data from Modern Compressible Flow With Historical Perspective. For maximum accuracy simply insert 0.0 degrees in the Inclination angle from sonic line input block. When this simple modification is performed the exit Area ratio (AR) becomes 2.43 which compares to AR = 2.403 for exact 2-D isentropic flow and represents a 1.124% difference from isentropic theory.


Figure 3. MLN Characteristic Mesh For exit Mach number of 2.4 where Inclination angle from sonic line = 0.0 degrees produces AR = 2.43.

Minimum Length Nozzle Validation-2
Figure 17.5, Gasdynamics: Theory and Applications, 2-D and Approximate 3-D MLN Validation at M = 3.0
The following table compares 2-D and 3-D MLN results with data scaled from Figure 17.5, Gasdynamics: Theory and Applications. Two wall-points, one from the center and one at the end of the nozzle contour have been selected for comparison. Notice that 3-D Minimum Length Nozzles are substantially shorter than equivalent 2-D Minimum Length Nozzles that have identical Area Ratio (Aexit/Athroat). For comparison purposes all results are referenced to the curved sonic line analysis for 2-D and 3-D axisymmetric nozzles. Please reference Gasdynamics: Theory and Applications* page 325, Figure 17.15 where g = 1.4 and Mexit = 3. Finally, please note that MLN uses the straight sonic line method of characteristics analysis.

Figure 4. 2-D MLN Characteristic Mesh when g =1.4 and exit Mach number = 3


Figure 5. Approximate 3-D Axisymmetric MLN Characteristic Mesh when g =1.4 and exit Mach number = 3
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AeroSpike System Requirements
(1) Screen resolution: 800 X 600
(2) System: Windows 98, XP, Vista, Windows 7, Windows 10 (32 bit and 64 bit), NT or Mac with emulation
(3) Processor Speed: Pentium 3 or 4
(4) Memory: 64 MB RAM
(5) English (United States) Language
(6) 256 colors

Please note this web page requires your browser to have
Symbol fonts to properly display Greek letters (a, m, p, ∂ and w)

ADDITIONAL REQUIREMENT: Input data for all AeroRocket programs must use a period (.) and not a comma (,) and the computer must be set to the English (United States) language. For example, gas constant should be written as  Rgas = 355.4 (J / kg*K = m^2 / sec^2*K) and not Rgas = 355,4. The English (United States) language is set in the Control Panel by clicking Date, Time, Language and Regional Options then Regional and Language Options and finally by selecting English (United States). If periods are not used in all inputs and outputs the results will not be correct.

AEROSPIKE REVISIONS
AeroSpike 2.3 Features and Error Fixes
1. Fixed plot resolution problem that occurred for some high aspect ratio aerospike nozzles.
2. Fixed the ratio of specific heats (g) manual entry error that would not accept gamma (g) = 2 and some other minor errors.
3. Fixed the incorrect gas constant (Rgas) value for hydrogen. For hydrogen, Rgas = 4122.11 m^2/(sec^2*K).
4. Added the ability to specify thruster sonic-section (throat) angle. Throat angle can vary from 60 to 120 degrees, the default is 90 degrees.

AeroSpike 2.4.1 Features and Error Fixes
1. Added a hybrid rocket motor propellant having the following fuel and oxidizer to the list of combustion gases: 85% Nitrous Oxide, 15% HTPB.
2. Added the ability to save F(x) verses PR (Pressure Ratio) and F(x) verses x to a CSV file for use with Notepad or Excel.
3. In the Aerospike Nozzle Data section added a display of Truncation as percent of total aerospike length.
4. In the Aerospike Nozzle Data section added a display of Distance from throat (origin) to end of thruster.
5. In the Aerospike Nozzle Data section added a display of Distance from end of thruster to end of ramp.
6. Corrected a few Status Bar display errors for plots of F(x) verses x.

AeroSpike 2.4.2 Error Fix (11/26/2006)
1) The gas Nitrogen Dioxide in the Gases pull-down menu should be labeled Nitrous Oxide (N2O). (Fixed)

AeroSpike 2.5.0 Features (01/23/2007)
1. Added ability to determine shapes and flow properties of 3-D Minimum Length Nozzles using an approximation procedure based on 2-D results.

AeroSpike 2.6.0.1 Features (09/21/2008)
1. Added the ability to include base thrust of truncated aerospike nozzles to determine total thrust and thrust coefficient.
2. To modify or change units in previous versions of AeroSpike the user needed to close the main aerospike nozzle analysis screen and then redefine units in the start-up screen. However, starting with this new version the user goes directly to the start-up screen without closing the aerospike nozzle analysis screen to modify pressure ratio, units, gases and altitude to instantly included those changes on the main aerospike nozzle analysis screen.
3. Darkened all data display boxes to prevent confusion with white data entry boxes for the MLN and aerospike analyses.

AeroSpike 2.6.0.2 Features (09/14/2009)
1) For AeroSpike, fixed all input data text boxes for 32 bit and 64 bit Windows Vista. When operating earlier versions of AeroSpike in Windows Vista the input data text boxes failed to show their borders making it difficult to separate each input data field from adjacent input data fields. This simple change did not alter any computational result.

AeroSpike 2.6.0.3 Features (04/27/2011)
1) For the Minimum Length Nozzle routine corrected the 3D axisymmetric mesh-data display. This simple change did not alter any computational result.

AeroSpike 2.6.0.4 Features (09/21/2011)
1) For AeroSpike the color contour plots and aerospike nozzle shape data are now displayed to scale. In previous versions aerospike color contour plots and aerospike nozzle shape displays were not to scale to allow full use of the available display area. However, recent work indicates it is more useful to display scaled aerospike geometry than to fill the entire plot area. The factor 0.5390 was used to properly scale the X-coordinates of the X, R plot data. This simple change did not alter any computational result.

AeroSpike 2.6.0.5 Features (09/25/2011)
1) For AeroSpike the Truncation as percent of total aerospike length data field displayed incorrect values intermittently based on UNITs selection. This simple change did not alter any other computational result.

AeroSpike 3.1.01 Features (01/21/2021)
1) Increased numerical analysis speed for aerospike and minimum length nozzle (MLN) computations.
2) In the Gases pull down menu added properties for Liquid Oxygen and Liquid Methane (LOX/LMH4) gases for mass ratios; 2.70, 2.80 and 2.90.

For more information about AeroSpike please contact AeroRocket.

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