PART
1
SUBSONIC PANEL METHOD
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SUBSONIC PANEL METHOD FEATURES
VisualCFD
uses 3D source panels
for the body to rapidly solve the frictionless potential flow
equations in minutes to approximate subsonic compressible flow
up to Mach 0.80. A complete set of graphical tools such as velocity
and pressure contour plots are provided to allow the user to
visualize 3D flow around the model. The subsonic portion of
VisualCFD computes the pressure (form) drag which is the integral
of the normal pressure forces acting parallel (CX) to the axis
of the model and perpendicular (CY or CN) to the axis of the
model.
1. Determine pressure coefficient (Cp), static pressure, dynamic
pressure and velocity around threedimensional bodies in subsonic
flow (M < 0.8).
2. Compute axial drag coefficient (CX), normal drag coefficient
(CN), moment coefficient (CM), base drag coefficient (Cbase) and center of
pressure location (XCP).
3. Generate models using builtin SphereCone, Elliptical, Conical
and Ogive shapes.
4. Generate models by importing shapes having up to 1,000 X,
R points.
5) Automatically incorporates flow compressibility using the
PrandtlGlauret rule for flight analyses to Mach 0.80.
6. Generate color contour plots of pressure coefficient (Cp),
static pressure, dynamic pressure and velocity with a single
click.
7. Units include, MKS (meternewtonsecond), CGS (centimeterdynesecond),
FPS (footpoundsecond) and IPS (inchpoundsecond).
8. Define atmospheric properties up to 150,000 feet.
9. Send tabulated surface data to a text file in the following format:
AXIAL LOCATION (I), MERIDIAN (K), PSTATIC, PDYNAMIC, CP, VELOCITY.
10. Send all plots directly to a color printer.
11. Operating instructions always available, up to date and located
online.
12. Maximum mesh dimensions of 150 X 75 grids.
13. A series of ten project
files
(input data) are available. Simply unzip Projects.zip
and transfer to the EulerCFD directory.
GENERAL PROCEDURE
A) BASIC
UNITS
From the menu on top of the main startup screen, select units
(MNS, CGS, FPS or IPS) from the Units menu.
B) MODEL GEOMETRY
Begin model definition by clicking the GEOMETRY icon in the
toolbar. First, in the GEOMETRY definition section the user must
define the Outer Surface Shape of the solution region (exterior
region of flow away from the body) by selecting either the CIRCULAR
or ELLIPTICAL options in the Outer Surface Shape pulldown menu.
CIRCULAR and ELLIPTICAL outer shapes are intended for subsonic
flow and the SUPERSONIC outer shape is intended for supersonic
flow. The CIRCULAR and ELLIPTICAL outer boundary shapes cannot
be used to define supersonic outer boundary shapes because the
MacCormack spacemarching procedure requires the mesh in the
marching direction to be vertical, parallel and separated by
constant intervals from the initial plane of data to the end
of the computational region. Therefore, to perform a subsonic
analysis please select either the CIRCULAR or ELLIPTICAL Outer
Surface shape.
Second, the shape of the model must be defined. The model or
surface shapes available will depend on whether the outer boundary
shape is CIRCULAR, ELLIPTICAL or SUPERSONIC. For the subsonic
Outer Surface Shapes of CIRCULAR and ELLIPTICAL the model shapes
available are SPHERECONE, ELLIPTICAL, CONICAL and IMPORTED.
The user can import up to
1,000 XR airframe geometry points from a text file. To create
a model based on imported geometry, define the project geometry
in NotePad and then Import the shape and finally save the Project
file as usual. To read the Project file, open the Project file
as usual and then Import the shape. The Import feature is located
in the File command as Import Shape. The data has the following
format. First line: Total number of XR point locations. Second
and subsequent lines: X, R airframe locations separated by commas.
Third, depending on which Outer Surface Shape is selected and
which Body Shape is chosen various geometry definitions appear.
The following matrix of inputs are defined for each Outer Surface
selected in relation to each Model Shape. These geometry inputs
are automatically displayed when the Body Shape and the associated
Outer Surface is selected.
CIRCULAR and ELLIPTICAL Outer Shapes
SPHERECONE Body Shape
Number of grids in axial direction (NI). Please limit the number
of grids to 150.
Number of Grids in vertical direction (NJ). Please limit the
number of grids to 75.
Height of exit flow field above body surface (H)
Distance before nose stagnation point (DS) [Not required for
CIRCULAR Outer Shape. Required for ELLIPTICAL Outer Shape]
Spherical nose radius (RNOSE)
Total sphereconical body length (LBODY)
Angle of conical afterbody (THETA)
Initial spacing off body in vertical direction (S1)
Vertical grid distribution as either LINEAR or TANH (Hyperbolic
Tangent)
Number of grids on circumference of model (NM)
ELLIPTICAL Body Shape
Number of grids in axial direction (NI). Please limit the number
of grids to 150.
Number of Grids in vertical direction (NJ). Please limit the
number of grids to 75.
Height of exit flow field above body surface (H)
Distance before nose stagnation point (DS) [Not required for
CIRCULAR Outer Shape. Required for ELLIPTICAL Outer Shape]
Body radius at base of model (RBODY)
Total body length (LBODY)
Elliptical body clustering in the axial direction (1 < Beta
< 100)
Initial spacing off body in vertical direction (S1)
Vertical grid distribution as either LINEAR or TANH (Hyperbolic
Tangent)
Number of grids on circumference of model (NM)
CONICAL and IMPORTED Body Shapes
Number of grids in axial direction (NI). Please limit the number
of grids to 150.
Number of Grids in vertical direction (NJ). Please limit the
number of grids to 75.
Height of exit flow field above body surface (H)
Distance before nose stagnation point (DS) [Not required for
CIRCULAR Outer Shape. Required for ELLIPTICAL Outer Shape]
Body radius at base of model (RBODY)
Total body length (LBODY)
Initial spacing off body in vertical direction (S1)
Vertical grid distribution as either LINEAR or TANH (Hyperbolic
Tangent)
Number of grids on circumference of model (NM)
C) CFD ANALYSIS
PANEL METHOD CFD ANALYSIS FOR SUBSONIC FLOW
Begin the CFD analysis by clicking the PANEL CFD icon for subsonic
flow in the toolbar. Then enter the following.
1) Define altitude effects on pressure and density in the Operational
Altitude pulldown menu. Select from Sea Level to 150,000 feet.
2) Define velocity in the Free field velocity data entry box.
3) Define angle of attack in the Angle of attack data entry box
in degrees.
4) Specify the velocity in FT/SEC, MPH, M/SEC or Mach number
and see the velocity in the Basic Units displayed just above.
5) Perform a subsonic CFD
analysis and view results by clicking the Solve icon (below)
in the 3D PANEL ANALYSIS (SUBSONIC) section on the main screen.
Then, after the solution is found view filledcontour plots and
property surface plots for pressure coefficient (Cp), static
pressure, dynamic pressure and velocity. Toggle between various
properties such as Static Pressure, Dynamic Pressure, Cp and
velocity by clicking the option buttons. Select Plot contours
or surface plots by clicking either the Plot Contours or Plot
Surface Curves check boxes. Note: linecontour plots are not
available for subsonic flow results, but linecontour plots are
available for supersonic flow results.
Toolbar Operations
1) Exit the VisualCFD computer program.
2) Reset the analysis to the default startup CFD model (spherecone).
3) Save all flow properties (X,Y, Velocity etc) at each panel
control point to a data file.
4) Show/Hide the Model Geometry definition section.
5) Show/Hide the 3D Panel Analysis (Subsonic) section.
6) Show/Hide the Euler CFD Analysis (Supersonic) section.
7) Show/Hide the Contour Plots and surface plot section.
VALIDATION RESULTS
#1: 3:1 ELLIPTIC BODY, SUBSONIC PRESSURE DISTRIBUTION
Figure1: Main VisualCFD
screen  Model Geometry. Grid generation inputs.
Figure2: Main VisualCFD
Screen. 3D PANEL ANALYSIS (SUBSONIC), CFD performed..
Figure3: Main VisualCFD
screen. CONTOUR PLOTS, Plot surface curves.
Figure4: Main VisualCFD
screen. CONTOUR PLOTS, Cp filled contours.
Figure5: VisualCFD Subsonic Results Validation. VisualCFD results
and data from the paper, LowSpeed Pressure Distribution on Axisymmetric
EllipticNosed Bodies (red dots). From Journal of Aircraft, page
969, October 1988. Data from Figure 3, Pressure coefficient distribution
on semiinfinite axisymmetric bodies with elliptical noses.
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PART
2
SUPERSONIC SPACE MARCHING
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SUPERSONIC SPACEMARCHING
FEATURES
VisualCFD
uses a spacemarching approach based on the MacCormack
method to solve the hyperbolic Euler equations for supersonic
flow (Mn > 1). When the flow is entirely supersonic the equations
of fluid motion are hyperbolic and any spacemarching technique
will be appropriate. The spacemarching method will not
work if the flow is locally subsonic and elliptic. The supersonic
blunt body problem, where the flow is locally subsonic near the
stagnation point, is an example where the spacemarching methods
do not work. However, this analysis assumes the flow is totally
supersonic and that no subsonic regions in the flow exist and
that the flow is entirely hyperbolic. The following list of features
apply to the spacemarching supersonic analysis.
1. Determine
pressure ratio (P/Pinf), temperature ratio (T/Tinf), density
ratio (R/Rinf) and Mach number around 2D and axisymmetric bodies
and ramps for M > 1.
2. Compute axial drag coefficient (CX) and normal drag coefficient
(CN).
3. Generate models using builtin Conical and Ogive shapes.
4. Generate arbitrary axisymmetric models by importing shapes
having up to 1,000 X, R points.
5. Generate filledcontour and linecontour color plots of pressure
ratio (P/Pinf), temperature ratio (T/Tinf), density ratio (R/Rinf)
and Mach number with a single click.
6. Generate surface plots of pressure ratio (P/Pinf), temperature
ratio (T/Tinf), density ratio (R/Rinf) and Mach number .
7. View tabulated listings of station data in RichText format.
8. Send tabulated data to a text file in the following format:
I,J,X,Y,P/PINF,R/RINF,T/TINF,M
9. Send all plots directly to a color printer.
10. Operating instructions always available, up to date and located
on line.
11. Maximum mesh dimensions of 500 X 500 grids.
12. Improve stability and the odds of a solution by using artificial
viscosity to dampen numerical oscillation around shocks.
13. A series of ten project
files
(input data) are available. Simply unzip Projects.zip
and transfer to the EulerCFD directory.
GENERAL PROCEDURE
A) UNITS
From the menu on top of the main startup screen, select units
(MNS, CGS, FPS or IPS) from the Units menu. Not required because
all values are inviscid and are normalized by the free stream
conditions.
B) MODEL GEOMETRY
Begin model definition by clicking the GEOMETRY icon in the
toolbar. First, in the GEOMETRY definition section that appears,
the user must define the Outer Surface Shape of the solution
region (exterior region of flow away from the body) by selecting
either the CIRCULAR, ELLIPTICAL or SUPERSONIC options in the
Outer Surface Shape pulldown menu. CIRCULAR and ELLIPTICAL outer
shapes are intended for subsonic flow and the SUPERSONIC outer
shape is intended for supersonic flow. Therefore, to perform
a supersonic analysis please select the SUPERSONIC Outer Surface
shape.
Second, the shape of the model must be defined. The model or
surface shapes available will depend on whether the outer boundary
shape is CIRCULAR, ELLIPTICAL or SUPERSONIC. However, for the
SUPERSONIC outer boundary shape the available model shapes are
CONICAL, OGIVE and IMPORTED. The
user can import up to 1,000 XR airframe geometry points from
a text file. To create a model based on imported geometry, define
the project geometry in NotePad and then Import the shape and
finally save the Project file as usual. To read the Project file,
open the Project file as usual and then Import the shape. The
Import feature is located in the File command as Import Shape.
The data has the following format. First line: Total number of
XR point locations. Second and subsequent lines: X, R airframe
locations separated by commas.
Third, depending on which Outer Surface Shape is selected and
which Body Shape is chosen various geometry definitions appear.
The following matrix of inputs are defined for the SUPERSONIC
Outer Surface and the CONICAL, OGIVE and IMPORTED Body Shapes.
These geometry inputs are automatically displayed when the Body
Shape and the associated Outer Surface is selected.
SUPERSONIC Outer Shape
CONICAL, OGIVE, IMPORTED Body Shapes
Number of grids in axial direction (NI), Please limit the number
of grids to 500.
Number of Grids in vertical direction (NJ). Please limit the
number of grids to 500.
Height of exit flow field from centerline (H)
Distance before nose stagnation point (DS)
Nose cone base radius (RNOSE)
Nose cone length (LNOSE)
Angle of conical afterbody (THETA)
Conical afterbody length (LBODY)
Number of grids on circumference of model (NM)
C) CFD ANALYSIS
EULER CFD ANALYSIS FOR SUPERSONIC FLOW
Begin the CFD analysis by clicking the EULER CFD icon for supersonic
flow in the toolbar. Then enter the following.
1) CFL stability criterion, normally in the range of 0.0 to 1,
but practically the value of CFL should be limited to 0.5 to
1.
2) Artificial viscosity. Sometimes improves the stability
of a solution across shock waves by reducing the oscillatory
response of a solution. Please see page 391 in Computational
Fuid Dynamics, by John D. Anderson for further explanation of
the concept of using artificial viscosity to improve solution
stability. Artificial viscosity should be limited to the range
of 0 to 0.9.
3) Xtabular increment ( Limit to 0 to NI or the number of grids
in the axial direction) for printing to a scrolling RichText
box. A value other than 0 allows VisualCFD to output the data
in tabular form to a text box. A small nonzero value of this
value makes the program output each marched plane of data to
the scrollable text box. Printing large amounts of data to a
scrollable text box is very memory intensive and may cause the
program to crash. It is recommended the value for this input
be NI or NI/2 at first and then reduce this value as needed.
4) Ytabular increment (Limit to1 to NJ1) for limiting the vertical
data output at each data plane. This value allows the user to
limit the data output to the RichText file along each plane of
data. Greatly reduces memory requirement for storage of data.
5) Perform a supersonic
CFD analysis and view results by clicking the Solve icon (below)
in the EULER CFD (SUPERSONIC) section on the main screen. Then,
after the solution is found view vertical property plots, property
surface plots and see the tabulated results for pressure ratio
(P/Pinf), density ratio (R/Rinf), Mach number (U/a), XVelocity
ratio (Ux/a) and YVelocity ratio (Uy/a). The pullbar locates
the vertical property plots at each station in the marching direction.
Surface property plots are generated when the option button is
selected for the property on the surface in the marching direction.
The maximum and minimum values for the entire flow are located
in the boxes above Max Value and Min Value, respectively. The
maximum value for the plots may be altered by modifying the Max
Value box entry. The Max Value entry will be used to define the
maximum plot value for contour plots on the main screen. Linecontour
plots and filled contour plots may be generated on the main screen.
Finally, the maximum and minimum for each vertical plot location
(station number) are labeled, Maximum curve value and minimum
curve value, respectively.
Note: the height (H) of the exit flow field must enclose the
shock wave as it forms. Many times a solution will fail because
a smaller value than necessary is used for H. Simply increasing
H in many cases resolves solution problems for supersonic flow.
Toolbar Operations
1) Exit the VisualCFD computer program.
2) Reset the analysis to the default startup CFD model (spherecone).
3) Save all flow properties (X,Y, Velocity etc) at each panel
control point to a data file.
4) Show/Hide the Model Geometry definition section.
5) Show/Hide the 3D Panel Analysis (Subsonic) section.
6) Show/Hide the Euler CFD Analysis (Supersonic) section.
7) Show/Hide the Contour Plots and surface plot section.
VALIDATION RESULTS
#2: 10 DEGREE, 2D CONECYLINDER AT M = 2
Figure6:Main VisualCFD screen.
MODEL GEOMETRY  SUPERSONIC FLOW.
Figure7: Figure6:Main VisualCFD
screen. EULER CFD (SUPERSONIC) results
Figure8:EULER CFD results
at station 2.2, where 2D conecylinder is 10 degrees and P/Pinf=1.7
Figure9: EULER CFD results
along surface along 2D conecylinder
Figure10: EULER CFD results
at station 5.16, where 2D conecylinder is 0.0 degrees
Figure11: EULER CFD results
at station .62, where 2D conecylinder is 10 degrees and P/Pinf=1.7
at surface
Figure12: P/Pinf 10 degree
conecylinder linecontour plot on main screen.
Figure13: P/Pinf 10 degree
conecylinder filledcontour plot on main screen.
Figure14: VisualCFD
Supersonic Results Validation. NACA 1135 results
for a 2D, 10 degree conecylinder at Mach = 2 indicate P/Pinf
= 1.70 and shock angle equal to 39.3 degrees. VisualCFD spacemarching
results on the 10 degree cone are: P/Pinf = 1.70 and shock angle
approximately 39 degrees from plot of P/Pinf in Figure14 (above).
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VALIDATION RESULTS #3: 5.352 DEGREE EXPANSION,
M = 2, Pages 374  414,
Computational Fluid Dynamics
Figure15, VisualCFD
Supersonic Results Validation.
VisualCFD
results compared to a 5.352 degree PrandtlMeyer expansion wave
example from the book, Computational Fluid Dynamics by John D.
Anderson, pages 374  414 where the forward Mach line of the
expansion fan should be 30 degrees and the rearward Mach line
of the expansion fan should be 27.04 degrees. The green region
on the VisualCFD filledcontour plot indicates a forward Mach
line set at approximately 30 degrees and the rearward Mach line
set at approximately 25 degrees. For the methodology used to
compute the properties of a PrandtlMeyer expansion, please see
page 113 of the book Modern Compressible Flow with Historical
Perspective.
Figure16: VisualCFD
Supersonic Results Validation.
VisualCFD
results for an expansion corner compared to a 5.352 degree PrandtlMeyer
expansion wave example from the book, Computational Fluid Dynamics
by John D. Anderson, pages 374  414 where the exact results
are stated to be: M 2= 2.2, P2/Pinf = .732, R2/Rinf = .80 and
T2/Tinf = .916. VisualCFD results are: M2 = 2.11, P2/Pinf = .730,
R2/Rinf = .80 and T2/Tinf = .910.
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Euler Code Theory Report (EulerCode.pdf)
Table of Contents
Two
Dimensional Planar and Axisymmetric Euler Equations
MacCormack Method SpaceMarching Theory
EULER90 Program Listing
Program Definitions
Shock Capturing Analysis
VisualCFD References
Program Listing
Derivation of the MacCormack Finite Difference Equations
FreeField Points Derivation
Wall Points Derivation
UpperBoundary Points Derivation
Note: After installation the report is located at:
c:/Program Files/EulerCFD/EulerCode.pdf 
1
2
310
3
3
4
510
1116
1112
1314
1516 
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VisualCFD Project Files (Projects.zip)
STANDARD GEOMETRY
TEST CASES
5.352 DEG 2D EXPANSION  Pages 374  414, Computational Fluid
Dynamics
10 DEG 2D CONECYLINDER  NACA 1135 Test case
10 DEG CONE 2D  NACA 1135 Test Case
10 DEG CONE 3D  NACA 1135 Test Case
15 DEG CONE 2D  NACA 1135 Test Case
6 DEG CONECYLINDER 3D  NACA 1135 Test Case
OGIVE NOSE  SUPERSONIC
ELLIPTICAL BODY  LowSpeed Pressure Distribution on Axisymmetric
EllipticNosed Bodies
SPHERECONE30 DEG  Subsonic (M = 0.10) high resolution spherecone
analysis
IMPORTED GEOMETRY TEST CASES
CONECYLINDER IMPORT SHAPE  10 DEG CONECYLINDER 2D
CONECYLINDER PROJECT  SUBSONIC
CONE  CYLINDER PROJECT SUPERSONIC  NACA 1135 Test case
Note: After installation the project files and code listing is
located at:
c:/Program Files/EulerCFD/Projects.zip 
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System Requirements
(1) Screen resolution: 800 X 600
(2) System: Windows 98, XP, Vista, Windows 7 (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
PROGRAM REVISIONS
AeroEuler 2.0.0.2
Modifications
1) Corrected the output error that occurred when attempting to save subsonic
surface data by clicking SAVE DATA. By clicking SAVE DATA
the user now correctly saves static pressure, dynamic pressure, Cp
(pressure coefficient) and velocity along the axial length of the body
and at each meridian or circumferential location. The subsonic results
use the following format. Axial Location (I), Meridian Location (K),
PSTATIC, PDYNAMIC, CP, VELOCITY.
AeroEuler 2.0.0.3 Modifications (09/19/2009)
1) For AeroEuler, fixed all input data text boxes for 32 bit and 64 bit
Windows Vista. When operating earlier versions of AeroEuler 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.
VisualCFD
3.0.0.1 Modifications (12/01/2015)
Program name changed from AeroEuler to VisualCFD
VisualCFD
3.0.0.5 Modifications (08/31/2016)
1) Fixed error that caused velocity contour plot to disappear after
completion.
2) Added value displays for center of pressure location (XCP), moment
coefficient (CM) and base drag coefficient (Cbase).
3) When completing each subsonic contour plot, VisualCFD outlines the
computational region of the analysis for clarity.
4) Changed the title displayed on top of the main VisualCFD screen.
5) For this program description the supersonic plots require
modification.
For more information about VisualCFD
please
contact AeroRocket.
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