In-plane transverse momentum injection to disrupt large-scale eddies in a turbulent boundary layer
Systems and methods are described herein to implement transverse momentum injection at low frequencies to directly modify large-scale eddies in a turbulent boundary layer on a surface of an object. A set of transverse momentum injection actuators may be positioned on the surface of the object to affect large-scale eddies in the turbulent boundary layer. The system may include a controller to selectively actuate the transverse momentum injection actuators with an actuation pattern to affect the large-scale eddies to modify the drag of the fluid flow on the surface. In various embodiments, the transverse momentum injection actuators may be operated at frequencies less than 10,000 Hertz.
1. A turbulent boundary layer control system, comprising:
a plurality of actuators on a surface of an object, wherein each actuator is selectively controllable to inject momentum into a turbulent boundary layer of a fluid in-plane with the surface and transverse to a flow direction of the turbulent boundary layer of the fluid relative to the surface; and
a controller to operate the plurality of actuators according to an actuation frequency, f, based on a time scale multiplier, T + , of at least 300 for fluid flows having friction Reynolds numbers, Re τ , greater than 1,500,
wherein the time scale multiplier, T + , and the actuation frequency, f, are related by a function of a kinematic viscosity, v, of the fluid divided by the square of a friction velocity, u τ 2 , of the fluid.
2. The system of claim 1 , wherein the time scale multiplier, T + , is expressible as:
1
T
+
=
f
*
v
u
τ
2
.
3. The system of claim 1 , wherein the actuation frequency, f, is between 100 and 20,000 Hz for friction Reynolds numbers, Re τ , greater than 1,500.
4. The system of claim 1 , wherein at least some of the actuators are spaced on the surface in a direction transverse to the flow direction of the fluid with a spacing distance between one-tenth and one-half of a boundary layer thickness, δ, of the fluid, where the boundary layer thickness, δ, of the fluid is calculated as a function of the fluid, the friction velocity, u τ , of the fluid, and the kinematic viscosity, v, of the fluid.
5. The system of claim 1 , wherein the object is selected from a group of objects consisting of: a fixed-wing aircraft, a rotary-wing aircraft, a rocket, a missile, a projectile, a pump, a fan, a turbine, a wind turbine, a mast, an airfoil, a hydrofoil, a sail, a boat rudder, a boat hull, a rocket nozzle, and a vehicle.
6. The system of claim 1 , wherein the object is a pipe that operates to implement at least one fluid operation selected from a group of fluid operations consisting of:
transporting the fluid;
mixing the fluid with one or more other substances;
transferring heat from or to the fluid; and
managing a chemical reaction of the fluid with a reactant.
7. The system of claim 1 , wherein the fluid comprises at least one fluid selected from a group of fluids consisting of: air, water, and oil.
8. The system of claim 1 , wherein at least some of the actuators comprise oscillating surface actuators that are actuated via at least one type of actuation selected from a group of actuation types consisting of: piezoelectric actuation, electromagnetic actuation, and electromechanical actuation.
9. The system of claim 1 , wherein at least some of the actuators comprise dielectric-barrier discharge (DBD) devices.
10. A power-saving method, comprising:
identifying a friction velocity, u τ , and a kinematic viscosity, v, of a fluid flowing over a surface that is moving relative to the fluid with a friction Reynolds numbers, Re τ , greater than 1,500;
selecting a timescale multiplier T + greater than 300;
calculating an actuation frequency, f, based on the selected time scale multiplier, T + , wherein the actuation frequency, f, is calculated as a function of the friction velocity, u τ , the selected time scale multiplier, T + , and the kinematic viscosity, v; and
actuating a plurality of actuators on the surface at the actuation frequency, f, to reduce a friction characteristic of a turbulent boundary layer of the fluid flowing over the surface, wherein the timescale multiplier, T + , is selected such that power consumption to actuate the plurality of actuators at the actuation frequency, f, is less than an amount of power saved due to the reduced friction characteristics of the fluid flowing over the surface.
11. The method of claim 10 , wherein identifying the friction velocity, u τ , and the kinematic viscosity, v, of the fluid comprises estimating fluid flow characteristics based on one or more real-time measurements of the fluid flow.
12. The method of claim 10 , wherein identifying the friction velocity, u τ , and the kinematic viscosity, v, of the fluid comprises calculating fluid flow characteristics based on a velocity of the fluid relative to the surface.
13. The method of claim 10 , further comprising identifying a friction Reynolds numbers, Re τ , of the fluid flowing relative to the surface of the object.
14. The method of claim 13 , wherein the time scale multiplier, T + , is a function of the identified friction velocity squared, u τ 2 , divided by the product of the calculated actuation frequency, f, and the identified kinematic viscosity, v.
15. The method of claim 13 , wherein the actuation frequency, f, is less than 20,000 Hz for friction Reynolds numbers, Re τ , greater than 1,500.
16. The method of claim 10 , wherein the time scale multiplier, T + , is expressible as:
1
T
+
=
f
*
v
u
τ
2
.
17. The method of claim 10 , wherein at least some of the actuators comprise dielectric-barrier discharge (DBD) devices.
18. A method to modify drag on a surface, comprising:
identifying fluid flow characteristics of a turbulent boundary layer of a fluid flowing relative to a surface of an object, the fluid flow characteristics including a friction velocity, u τ , of the fluid and the kinematic viscosity, v, of the fluid;
calculating an actuation frequency, f, for injecting momentum along the surface of the object and perpendicular to a direction of fluid flow relative to the surface of the object to disrupt large-scale eddies in the turbulent boundary layer, where the large-scale eddies have a time scale that is at least 300 times larger than a viscous time scale, η′, where η′ is calculated as the identified kinematic viscosity, v, divided by the square of the identified friction velocity, u τ 2 ; and
actuating a plurality of actuators on the surface of the object with the calculated actuation frequency, f, to disrupt the large-scale eddies to selectively increase or decrease the drag of the fluid on the surface of the object.
19. The method of claim 18 , further comprising identifying a friction Reynolds numbers, Re τ , of the fluid flowing relative to the surface of the object, and
wherein actuating the plurality of actuators on the surface of the object comprises actuating the plurality of actuators on a time scale multiplier, T + , of at least 300 for fluid flows having friction Reynolds numbers, Re τ , greater than 1,500, and
wherein the time scale multiplier, T + , is a function of the identified friction velocity squared, u τ 2 , divided by the product of the calculated actuation frequency, f, and the identified kinematic viscosity, v.
20. The method of claim 19 , wherein the time scale multiplier, T + , is expressible as:
1
T
+
=
f
*
v
u
τ
2
.