System and method for simulating turbulence
A system and method for simulation of fluid flow. The system being configured to remove loops in a vortex filament in a simulation model and reconnect the filament. The system may also be configured to model fluid flow in relation to a moving object and to correct errors in surface vorticity.
1. A system for simulation of computational fluid dynamics (CFD), the system comprising:
an input device configured to receive an input parameter of a set of parameters indicative of:
rotor blades rotating in a rotor plane associated with a vertical take-off and landing (VTOL) vehicle,
rotor blades rotating in a rotor plane associated with a wind turbine,
a moving automotive vehicle body shape, or
a moving aerospace vehicle body shape;
a vortex sheet construction unit configured to model the geometric shape of: the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape; and
a processing unit for modeling in a model fluid flow in relation to: the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape, the processing unit configured to:
compute a position of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape in an inertial frame model;
transform velocity and vorticity data for the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape to non-inertial frame;
integrate equations in a non-inertial frame of each of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape in time by employing one or more boundary conditions of each of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape;
transform vorticity data for the non-inertial frames to the inertial frame;
compute a vorticity field for all the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape objects in the inertial frame;
integrate equations in the inertial frame and compute inertial velocity and vorticity; and
release, advect and remove any vortex tube generated by a vortex sheet velocity processing unit in the inertial frame model.
2. The system of claim 1 , wherein the processing unit is further configured to perform each of the steps for each of a plurality of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape in the inertial frame model at each of a plurality of time intervals.
3. The system of claim 1 , wherein the processing unit comprises a vortex sheet velocity processing unit configured to perform the step of:
computing a position of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape in the inertial frame model using r| B =R·{tilde over (r)}, where {tilde over (r)} is a position vector of the rotor blades rotating in a rotor plane associated with each of the VTOL or the wind turbine, or the moving automotive or aerospace vehicles' body shape in the inertial frame and is a time dependent rotation matrix constructed by multiplying rotation matrices about each coordinate of the moving object.
4. The system of claim 3 , wherein the rotation R matrices are defined as:
ℛ
x
(
α
)
=
(
1
0
0
0
cos
(
α
)
-
sin
(
α
)
0
sin
(
α
)
cos
(
α
)
)
ℛ
y
(
β
)
=
(
cos
(
β
)
0
sin
(
β
)
0
1
0
-
sin
(
β
)
0
cos
(
β
)
)
ℛ
z
(
γ
)
=
(
cos
(
γ
)
-
sin
(
γ
)
0
sin
(
γ
)
cos
(
γ
)
0
0
0
1
)
5. The system of claim 3 , wherein the vortex sheet velocity processing unit is configured to perform the step of: transforming vorticity data for each non-inertial frame to the inertial frame by calculating the vorticity data for each non-inertial frame's w, using:
ℛ
-
1
=
(
cos
(
β
)
cos
(
γ
)
sin
(
α
)
sin
(
β
)
cos
(
γ
)
-
cos
(
α
)
sin
(
γ
)
sin
(
α
)
sin
(
γ
)
+
cos
(
α
)
sin
(
β
)
cos
(
γ
)
cos
(
β
)
sin
(
γ
)
sin
(
α
)
sin
(
β
)
sin
(
γ
)
+
cos
(
α
)
cos
(
γ
)
cos
(
α
)
sin
(
β
)
sin
(
γ
)
-
sin
(
α
)
cos
(
γ
)
-
sin
(
β
)
sin
(
α
)
cos
(
β
)
cos
(
α
)
cos
(
β
)
)
and then calculating absolute vorticity (W) in the inertial frame using:
W=ω+ 2Ω
where Ω is the angular velocity of the non-inertial frame.
6. The system of claim 1 , wherein the system is a vertical takeoff and landing (VTOL) design system.
7. The system of claim 6 , wherein output from the system is provided to a VTOL control system.
8. A system for performing computational fluid dynamics (CFD) simulation, the system comprising: an input device configured to receive an input parameter of a set of parameters of rotor blades selected from a vertical take-off and landing (VTOL) vehicle, or a wind turbine, the rotor blades rotating in a rotor plane to be evaluated; a vortex sheet construction unit configured to model the geometric shape of the rotor blades rotating in the rotor plane; and a processing unit for simulating turbulence caused by rotor blades rotating in the rotor plane, the processing unit configured to:
generate; vortex tubes, of the rotating blades according to a rotor model selected from the group of actuator disk, actuator line and actuator surface; compute a velocity at the rotor plane due to vortex tubes, surface panels and vorticity sheets; and
correct the rotor model according to the computed velocity,
wherein the rotor model is an actuator line and at each time interval, N tubes are ejected from N prescribed points on each of the M rotating virtual blades with non-dimensional circulation F of each tube defined by: Γ=Ct*R 2 *Ω/M/N where Ct is a thrust coefficient, R is a rotor radius, and Ω is a rotor rotation speed.