AeroCFD successfully determined drag
coefficient (Cd) verses Mach number from Mach 0.5 to Mach 5.0 for
the full scale V-2 rocket operating
at 4 degrees angle
of attack. AeroCFD predicts Cd = 0.279 at Mn = 2 and AOA = 4 degrees.
AeroCFD
is a "true" 3-D axisymmetric and 2-D
implicit finite volume CFD program that solves the inviscid Euler equations
for subsonic, transonic and supersonic flow to Mach 7 using automatic mesh generation and
graphical results visualization. AeroCFD provides a maximum of
100 cells in the axial direction, 50 cells in the transverse direction and
10 cells in the circumferential
(3-D) or thickness (2-D) direction. The outer boundary of the
computational region is specified as the far-field, meaning
captured shock waves pass through and are not reflected back into
the computational volume. The latest version of AeroCFD has
increased the number of discrete finite-volumes available for analysis from
18,000 cells to 50,000 cells. Due to its "true" 3-dimensional formulation, AeroCFD provides non-zero lift
and non-zero pitching moment for axisymmetric shapes at angle of attack without requiring computational
times exceeding one hour. Model geometry is specified by selecting from a library of standard shapes. Nose sections are defined using one of five basic shapes
that include Conical, Ogive, Elliptical, Parabolic and
Sears-Haack with power series coefficient. The user has the
option for adding up to two constant diameter sections,
one variable diameter transition section and one variable diameter
boat tail section to complete the library of user-defined shapes. For
added flexibility AeroCFD can import up to 1,000 X-R data points
for generating axisymmetric and two-dimensional designs that
require grid clustering in regions where shock waves and base flow dominate.
Base flow aerodynamics are estimated using wind tunnel
generated equations as a function of free stream Mach number and boat tail dimensions for subsonic and supersonic
flow.
The RESULTS section clearly displays FX, FY, MZ, CX, CY, CM, CD, CL,
base drag, surface friction drag and center of pressure location. Flow fields are
displayed using fill-contour plots, line-contour plots and surface
distribution plots for pressure coefficient, pressure ratio,
temperature ratio, density ratio and Mach number.
AeroCFD
allows the user to control
the mesh distribution around a body using simple point-and-click
operations and are explained in simple step-by-step operating instructions.
Model geometry is easily defined
by selecting from a number of standard shapes that are automatically
combined into one final shape with fins. In addition, transition shapes have a power
series shape control for defining very unusual three-dimensional axisymmetric and
2-D shapes. In addition, the Fin Geometry utility allows the user to attach complex fins having several
definition points to the final CFD airframe. Fin effects are superimposed on the final CFD solution using classical mechanics
that are not part of the
mesh definition. Using this methodology relatively thick fins
having complex geometry are modeled efficiently for subsonic,
supersonic and hypersonic flow to Mach 7.
AeroCFD
uses a very efficient
3-D numerical analysis technique to solve the
Euler equations for 1st, 2nd or 3rd order accuracy. An implicit
finite volume numerical scheme uses upwind differencing methods that are biased
in the direction determined by the signs of the characteristic
speeds. Specifically, Steger-Warming flux-vector-splitting and
Roe flux-difference-splitting methods are used for accurate solutions
in shock-wave dominated flows. Shock waves are captured in as
few as zero to one cell using the Roe flux-difference splitting
methods. Subsonic flows use standard finite volume differencing
methods. Engineering solutions are achieved in approximately
5 to 10 minutes using the default numerical settings for most
models after a "good" mesh is developed.
Final Note: AeroCFD uses the
compressible Euler equations for the aerodynamic analysis of high-speed rockets
for flights greater than 0.3 Mach. The compressible Euler equations are derived
from the full compressible Navier Stokes equations minus
viscosity terms. Tremendous increase in solution efficiency and
therefore computational speed are realized because for high-speed
flight when Reynolds number is high (on the order of 10 million) the
viscous forces are low and the boundary layer is thin indicating the
flow is essentially inviscid. The Euler equations are preferred when
modeling high-speed flight of aerospace vehicles even high-speed
model and high power rockets. Conversely, low Reynolds number flight
(on the order of 1 hundred) indicate viscous forces must be
considered because the boundary layer is thick and probably laminar
and not turbulent. Where, Reynolds number (Re = V L/v) is the ratio
of inertial forces to viscous forces.
AeroCFD
is a
registered trademark owned by John Cipolla used to promote sales of his
3-D axisymmetric and 2-D Computational Fluid Dynamics (CFD) software and other
related aerodynamics computer
programs.
Featured
AeroRocket CFD Codes
Nozzle 10:
Compressible Flow Analysis of
Converging-Diverging Nozzles
GO
HyperCFD
10:
Design of Supersonic and
Hypersonic Re-entry and Rocket Vehicles
GO
Latest Publications
Warp Drive
Propulsion Using Magnetic Fields to
Distort Space-Time OR
First
Successful Warp Drive Flight
(2024)
Three-Stage Rocket Equation Analysis of
the Saturn V Launch Vehicle
Excel Spreadsheet Multi-Stage Rocket Analysis, Technical Note 2023-1
FinSim Rocket Equation Burnout Velocity
Accuracy Compared to
Finite Difference and TR-10 Prediction, viXra
e-print archive (2022)
Ring Fin Rocket Center of
Pressure, Drag and Lift Slope Coefficients
Measured
Using the AeroRocket Wind Tunnel,
Technical Note
2022-2
Spool Rocket Center of
Pressure and Drag Coefficient Measured
Using the AeroRocket Wind Tunnel,
Technical Note
2022-1
(2022)
POF 291 Flutter Velocity Error Produces Negative Margins of
Safety Compared to NACA TN 4197,
Technical Note
2021-2
FinSim 10 Torsional Stiffness of Rocket Fins
Thickness-Tapered From Root to Tip,
Technical Note 2021-1
"Proving Shock Thickness Decreases for
Increasing
Mach Number", Shock Wave
Thickness Analysis (2020)
"Demonstrating the Relationship
Between Quantum
Mechanics and Relativity",
viXra e-print archive (2019)
"Computational and Experimental Interferometric
Analysis
of a Cone-Cylinder-Flare Body"
(1989, 2015)
viXra e-print archive
"Rocket Spin Stabilization Using Canted Fins",
SpinSim (2002)
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