Christopher Porter

Plasma Actuator Force Measurements

In previous work at the U.S. Air Force Academy, the phenomenology and behavior of the aerodynamic plasma actuator, a dielectric barrier discharge plasma, was investigated. To provide insight into the phenomenology associated with the transfer of momentum to air by a plasma actuator, the velocity distributions upstream and downstream of a plasma actuator with an induced boundary layer were measured using freestream velocities of approximately 4.6 and 6.8 m/s for a range of frequencies (5-20 kHz) and voltages (5-10-kV amplitude). The body forces on the air were calculated using a control volume momentum balance. In a second experiment, time-averaged results were also obtained by measuring the reaction force using a pendulum. A third experiment uses an accelerometer to gain insight into the time-dependent forces or, more specifically, the direction of the forces. The results show that the body force acts within the first 4 mm above the surface of the actuator (within the boundary layer). For a constant peak-to-peak voltage, the body force is proportional to frequency, producing a constant impulse per cycle, and the energy dissipation per cycle and efficiency are independent of frequency. The time-dependent measurements support the theory that the body force of the actuator consists of one large push followed by one small pull during each cycle.

Momentum Transfer for an Aerodynamic Plasma Actuator with an Imposed Boundary Layer

In previous work at the United States Air Force Academy, the phenomenology and behavior of the aerodynamic plasma actuator (a dielectric barrier discharge (DBD)) has been investigated. In order to provide additional insight into the phenomenology associated with the transfer of momentum to air by a plasma flow actuator, the velocity distributions upstream and downstream of a plasma actuator with an induced boundary layer were measured using freestream velocities of approximately 4.6 and 6.8 m/s for a range of frequencies (5-20 kHz) and voltages (7.5-10 kV amplitude). The body forces on the air were calculated using a control volume momentum balance. The results show that the body force acts in the sub-boundary layer region. For constant voltage, the body force is proportional to frequency producing a constant impulse per cycle, and the energy dissipation per cycle and efficiency are independent of frequency. The body forces are not affected by the freestream velocity.

Spatially Distributed Forcing and Jet Vectoring with a Plasma Actuator

volume momentum balance was used. By shaping the buried electrode along the span of the actuator, the local volume of plasma generated can be controlled, which is related to the local body force. Pressure measurements were takenintheboundarylayerbehindtheactuatortocalculatethemomentumimpartedtothe flowatvariousspanwise locations corresponding to different electrode widths. Particle image velocimetry data were then used to show that spatially varying, steady jets could be created with the use of only one actuator by varying the width of the buried electrode in a quiescent flow. The angle of the jet created, relative to the dielectric, by a plasma synthetic jet is also investigated. By pointing two plasma actuators at each other, an inverted impinging jet can be created as a result of the two independent jets colliding. By altering the strength of one of the jets relative to the other, the angle of separation can be changed. Particle image velocimetry data were taken to show the effects of altering the voltage (strength)appliedtooneoftheactuatorsrelativetotheother.Itwasfoundthat,withthismethod,jetvectoringcould beachieved.Theangleofthejetcouldbecontrolledafull180degthroughsmallchangesinthevoltageappliedtothe electrodes, also in a quiescent flow. Nomenclature D = diameter FB = body force FS = shear force P = power qd;off = dynamic pressure downstream of the actuator (0.035 m) with the plasma off qd;on = dynamic pressure downstream of the actuator (0.035 m) with the plasma on Re = Reynolds number St = Strouhal number U = freestream velocity ud;off = velocity downstream of the actuator (0.035 m) with the plasma off ud;on = velocity downstream of the actuator (0.035 m) with the plasma on W = waviness amplitude � = angle of jet measured counterclockwise � V = voltage differential between exposed electrodes relative to ground � = wavelength

Circular Cylinder Wake Control using Spatially Distributed Plasma Forcing

This work investigates the use of spatially-distributed open-loop forcing for threedimensional control of vortex shedding from a circular cylinder. Force-shaped plasma actuators were used to control the flow, with the aim of reducing drag on a circular cylinder at a Reynolds number of 6500. Traditional approaches to cylinder drag reduction have typically involved two-dimensional forcing of the flow field. Spatially-distributed forcing, however, involves a spanwise modulation of the forcing on the flow. A new configuration of the dielectric-barrier discharge plasma actuator was implemented where the momentum addition could be directed either normal or tangential to the surface, as well as spatially tailored in a spanwise fashion to optimize control efficacy. The actuator configuration enables targeted manipulation of the wake-vortex structure shed from a bluff body. The goal of the flow control blowing profile is to break up the spanwise coherency in the vortex street, thereby promoting phase cancellation between spanwise portions of the wake structure. Wake profile measurements were made at several spanwise locations to evaluate the resulting drag reduction and modification of the wake.

Predictive Flow Control to Minimize Convective Time Delays

To overcome the convective time delay issue for active closed-loop flow control, a model based predictive control algorithm is analyzed. From a controls perspective, forms of internal model control or model predictive control can be used to accommodate and minimize the effect of systems with pure time delays. Moreover, the Smith predictor is a commonly employed control technique to negate the pure time delay in a closed-loop system. This form of model predictive control is applied to the asymmetric vortex problem of an axisymmetric forebody (specifically a von Karman ogive with fineness ratio of 3.5). The full-order Navier-Stokes equations are numerically solved on the forebody at a high angle of attack and provide the plant process. Small port and starboard blowing patches are used to introduce fluidic disturbances at the nose of the ogive to augment the global flow state and produce a deterministic vortex state. As the active flow control technique exploits a convective instability, a convective time delay exists. Linear-time-invariant and non-linear time-invariant models are developed from the open-loop dynamics. A Smith predictor is employed within the full order CFD simulation. The results of the predictive control are compared to open-loop and model-free closed-loop behavior. It is shown that the predictive control developed in this paper while very suitable for control of this type of flow, is very sensitive to modeling uncertainties.

Optical Method for Measuring Low Wall Shear Stresses Using Thermal Tufts

A thermal tuft method for the measurement of low wall shear stresses is described. Previous work described how the thermal tuft method can be used for flow visualization, but this work extends the technique to quantitative measurements of low values of wall shear stress. The laser thermal tuft involves heating a spot on a surface with a laser, which produces a teardrop-shaped surface temperature distribution pointing downstream of the heated spot. The temperature profile can be determined with liquid crystals, infrared thermography, or other methods. In the present study, it is demonstrated by theory and experiment that the lengths of these teardrop-shaped tufts are determined by the wall shear stress. Theoretical results evaluate the effects of laser power, laser spot size, and liquid crystal cutoff temperature on the tuft length. Effects of the thermal boundary-layer thickness are evaluated and found to be negligible for heights up to half of the hydrodynamic boundary-layer thickness. Experimental results agree with theoretical predictions, indicating shorter tuft lengths as shear stress increases. Thermal tufts can be used to measure the wall shear stress at multiple locations, thereby mapping out the wall shear stress distribution.

Closed-Loop Flow Control of a Tangent Ogive at a High Angle of Attack

The flowfield around an axisymmetric forebody at a moderate angle of attack (40 � < � < 60 � ) produces a significant side force as the result of an asymmetric pressure distribution around the body resulting from an asymmetric vortex flow state. Numerical studies of open-loop control using mass-blowing slots near the tip of the model have shown proportional control of the side force by varying the momentum coefficient of the blowing slots. From the open-loop simulations, a prediction-error minimization method (PEM) was used to develop a linear time invariant (LTI) model which captures the dynamics of the side force response to different mass flow rates applied to the port or starboard actuator. Based on the model, a PI controller was developed for reference tracking a prescribed side force profile. The development of the LTI model, and corresponding controller simulations of the closed-loop system are presented to illustrate the models capabilities as well as its limitations. The ability to track a prescribed reference signal based on the LTI model and corresponding PI control scheme is shown. The results indicate that the bandwidth of the controller is limited to frequencies below half the convective frequency due to the convective time delay as well as the actuator and sensor placement. Finally, the closed-loop controller simulations are compared to Navier-Stokes feedback simulations.

Effects of the Plasma Actuation on the Asymmetric Vortex around an Ogive Body at High Incidence

Time accurate numerical simulations are performed for the flow field around a vonKarman ogive with fineness ratio of 3.5 under the plasma actuation near the nose tip in a freestream of M=0.1 and ReD=220,000 to evaluate the effects of the actuation. The moving wall boundary condition is employed to model the plasma actuation. The velocity of the moving wall is correlated by the momentum produced by the plasma actuator on a flat plate using PIV measurements. The flow separation is promoted so that the pressure increases and the vortex is lifted up on the actuation side. Steady side forces with increasing magnitude are observed with increasing moving wall velocity. Increasing the moving wall velocity increases the rate of spatial evolution of the vortex asymmetry in the axial direction. The behavior of the side force observed in the simulation in terms of direction and magnitude in response to the actuation agrees with the observations in the wind tunnel test conducted by the authors under the same model geometry and freestream condition. Nomenclature Cp = pressure coefficient Cz = force coefficient in the yaw direction (positive toward the port from the starboard) D = Base diameter of the ogive model M = Mach number ReD = Reynold’s number based on D U∞ = Magnitude of the freestream velocity Uw = Magnitude of the moving wall velocity u = Velocity component in the horizontal direction v = Velocity component in the vertical direction x = Longitudinal axis of the ogive model (positive toward the base from the nose)  = Angle of attack

Curvature Effects of a Cycloidally Rotating Airfoil

A cycloidally (including prolate, curtate and traditional cycloids) rotating airfoil (CRA) has very unique aero/hydrodynamic characteristics, unlike any other device which interacts with a surrounding fluid flow. A system employing a CRA is one where the airfoil is mounted such that the span is aligned parallel with the axis of rotation, which is different to conventional rotors where the blades are oriented perpendicularly to the axis of rotation. This fundamental difference between the two aero-interactive systems provides CRAs the ability to interact with the incoming fluid flow in any direction perpendicular to the axis of rotation. Thus, from a propulsion standpoint, this unique characteristic allows the system to generate thrust in any direction perpendicular to the main shaft. Conversely, from an energy extraction standpoint, the device is able to generate shaft torque with any directional freestream perpendicular to the rotational axis. However, despite these stark advantages of these unique devices, many complex and poorly understood aero/hydrodynamic challenges are also procured. For instance, aerodynamic complexities such as: virtual camber, radial velocity (pressure) gradients, blade-wake interaction, and highly unsteady pitch-heave motions can be identified. This paper assesses a tier of computational fluid dynamic tools (complex potential, panel methods, and Navier-Stokes simulations) to illustrate the effects of curvature on a CRA. A non-dimensional parameter, regarding relative curvature, is formulated which relates resulting lift to arbitrary airfoil shapes with a constant curvature. Additionally, it is found that the attachment location, or pivot point, of the airfoil is a critical factor, and, interestingly, a three quarter chord attachment location produces a zero lift for all relative curvatures.

Vortex Dynamics of a Tangent Ogive at a High Angle of Attack

The flowfield around an axisymmetric forebody at a moderate angle of attack (40 o < � < 60 o ) can produce a significant side force as the result of an asymmetric pres- sure distribution around the body. The asymmetry of the pressure distribution results from a steady, asymmetric vortex configuration around the body even though the body is axisymmetric. Unsteady laminar simulations were performed on a von Karman tangent ogive forebody with a fineness ratio of 3.5, angle of attack of 50 degrees, and a diameter based Reynolds number of 220,000. As a first step towards feedback flow control of the asymmetric vortex state, open-loop disturbances similar to those produced by a Dielectric Barrier Discharge (DBD) plasma actuator near the tip of the model were simulated. The resulting side force from the open-loop simulations are compared to the unforced simu- lations. In the unforced case, a large side force was observed with maximum amplitudes similar to those observed in a companion experiment. However, the side force fluctuates between the port and starboard sides, in contrast to experimental observation where the side force is relatively steady. When forcing is turned on, the resultant asymmetric vortex state locks into one position where the magnitude of the side force is proportional to the strength of the applied forcing. These simulations, both forced and unforced, are used to develop a flow state database through Proper Orthogonal Decomposition (POD) for the development of reduced order models. It is shown that the second POD mode (including the mean) captures the asymmetry of the different vortex states tested.