Modeling of dielectric barrier discharge (DBD) flow actuator

A dielectric barrier discharge (DBD), operating at kHz and kV conditions, can generate almost a uniform non-thermal plasma and induces fluid flow similar to a wall jet. The discharge gaps usually range an order of millimeters separated by a dielectric insulator, and a stable gas discharge can be obtained using radio frequency high voltage.

Since it provides uniform plasma volume at atmospheric pressure, the dielectric barrier discharge has been focused for industrial applications. Though the exact mechanism of induced flow generation is not sufficiently understood, it is known that the localized force acting on the neutral fluid is caused by collisions between neutral and charged particles driven by the electric field.

<Charge density and electric field evolution>

In order to better understand the mechanism of the momentum coupling between the plasma and the fluid flow, it is beneficial to apply computational models. In particular, the focus is on the operating mechanism and thermo-fluid effects of the DBD actuator that is efficient enough for flow control applications. Since there exists huge length and time scale disparities, for example, the time scale ratios between convection, diffusion, and reaction/ionization mechanisms are about O(10⁷), the effect of plasma on the fluid dynamics can be modeled via a body force treatment. The picture shows the evolution of the species of charged particles and electric field based on a first principle-based hydrodynamic plasma model. The present research is focused on low Reynolds number applications where the plasma dynamics is hardly influenced by the surrounding fluid flow.

In order to minimize the computational cost, a reduced order plasma model using a linearized force field to approximate the discharge structure is also proposed. The actuators typically operate on low power consumption (2-40 W/ft of wing span) operated with either a steady or unsteady mode. Typical examples of plasma-based flow control have been to enhance lift, excite 3-D boundary layer instabilities, control separation for low-pressure turbine blades and wings, control dynamic stall on oscillating airfoils control acoustic effects in subsonic cavity flows, etc. For example, as shown in the picture, the Reynolds stress over a low Reynolds number airfoil SD7003 is substantially decreased by steady actuation near the leading edge.

<Reynolds stress with and without actuation>

Researchers

Faculty advisor: Professor Wei Shyy
Dr. Balaji Jayaraman
Graduate student: Young-Chang Cho

References

Shyy, W., Jayaraman, B. and Andersson, A., “Modeling of Glow Discharge-Induced Fluid Dynamics”, Journal of Applied Physics, Vol. 92-11, (2002), pp. 6434-6443.
Jayaraman, B. and Shyy, W., “Flow Control and Thermal Management Using Dielectric Glow Discharge Concepts”, 33rd AIAA Fluid Dynamics Conference and Exhibit, Orlando, June 25-28, AIAA Paper No. 2003-3712, 2003
Jayaraman, B., Thakur, S. and Shyy, W., “Modeling of Dielectric Barrier Discharge and Resulting Fluid Dynamics”, 44th Aerospace Sciences Meeting & Exhibit, Paper No. 2006-0686, 2006
Jayaraman, B., Shyy, W. and Thakur, S., “Modeling of Fluid Dynamics and Heat Transfer Induced by Dielectric Barrier Plasma Actuator”, Journal of Heat Transfer 129-4 (2007) 571-525
Jayaraman, B., Cho, Y. and Shyy, W., “Modeling of Dielectric Barrier Discharge Plasma Actuator”, 38th AIAA Plasmadynamics and Lasers Conference, 25-28 June 2007, Miami, Florida, Paper No. AIAA-2007-4531
Jayaraman, B., Lian, Y. and Shyy, W., “Low-Reynolds Number Flow Control Using Dielectric Barrier Discharge Actuators”, 37th AIAA Fluid Dynamics Conference and Exhibit, Miami, FL, Jun 25-28, AIAA paper 2007-3974, 2007
Jayaraman, B., Cho, Y., and Shyy, W., “Modeling of Dielectric Barrier Discharge Plasma Actuator”, Journal of Applied Physics, Vol. 103, 053304, 2008.

Surrogate models and dielectric barrier discharge (DBD) flow actuator performance

For the efficiency of the DBD flow actuator, it is important to maximize the force generation with minimal power input. The DBD flow actuator has various parameters – geometry of electrodes, insulator material, magnitude and waveform of excitation voltage, etc – which affect its operational efficiency, the ability to produce a desirable flow field with minimal power.

The final effect on the flow field, the generation of aerodynamic force, is also determined by various factors such as ionized particle densities, strength and direction of the time-variant electric field. Though there are some physical understandings of the relationship between the specific operational parameter and its effect, it is difficult to assess their effect on the flow field in a whole for the purpose of designing a flow actuator, considering their complicated interactions. The computational simulations enable tests with less limited conditions and provide data in detail which may be hard to measure in experiments. However, it is very burdensome or almost impossible to simulate all the cases which are necessary to evaluate the correlations between variables, especially due to its expensive computational cost. As an efficient design tool, using surrogate models offers ideas about the correlation of variables as well as information of the optimal operational conditions.

<Iso-force contours predicted by RBNN>

Instead of the numerical simulations to solve governing transport equations, the surrogate models enable us to generate reliable approximations and assess parameter sensitivity and degree of interaction. For example, by constructing a radial basis neural network (RBNN) using simulation results for the selected design points, iso-force contours can be drawn as presented in the picture. There are widely adopted surrogate models such as polynomial response surface, Kriging, RBNN and combination of them. It is known that model fitting error is problem-dependent and a reliable model can be chosen based on a sound design of experiments and various error measures. Once a reliable surrogate model is realized, the whole picture of variables in the design space can be obtained with a negligible cost compared to the numerical simulations.

<Pareto front and design space refinement>

A surrogate-based optimization can be applied to the optimization process which in many cases consists of multiple objectives containing competing factors. For example, force generation by the actuator and the average power input to maintain the discharge can be chosen as two objective functions. And the iterative design refinement facilitates to keep the number of numerical simulations as small as possible. Also, Pareto front analysis that demonstrates all the candidates of the optimum solution can efficiently suggest the set of parameters desirable for operational requirements -to minimize power and/or maximize force-, as well as ideas about the variable correlations to each other.

Researchers

Faculty advisor: Professor Wei Shyy
Graduate student: Young-Chang Cho
Dr. Balaji Jayaraman

References

Cho, Y., Jayaraman, B., Viana, F.A.C., Haftka, R.T., and Shyy, W., “Surrogate Modeling for Characterizing the Performance of Dielectric Barrier Discharge Plasma Actuator”, AIAA paper 2008-1381, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan 7-10, 2008.

Adaptive flow control of low Reynolds number aerodynamics

The dielectric barrier discharge (DBD) actuator provides a responsive control method with a relatively simple installation, suppressing flow separation by either inducing additional momentum to the retarded flow or facilitating transition to turbulent flow. For high angle of attack conditions, however, the flow actuation introduces instability in the wake structure, resulting in the unsteady vortex evolution as shown in the picture. For a low Reynolds number airfoil SD7003 with the Reynolds number of 60,000, a DBD actuator located at the blue circle induces unsteady vortex formation and evolution. Despite the increase in the average performance such as lift-to-drag ratio, the severe variation of aerodynamic forces needs to be avoided for most applications. Moreover, unsteady forces caused by the disturbance in the free stream hinder stable flights of low Reynolds number flyers.

Considering that the operational time scale of a DBD actuator is several mili-seconds, a closed-loop control scheme using an adaptive algorithm is introduced to effectively control the unsteady flow structure. In discrete-time systems, time-variant variables at any instant can be represented using Markov parameters that compose the system parameters and relate past/current system input and past output. The retrospective correction of the controller parameters along with knowledge about system Markov parameters enables an effective adaptive control with a minimal modeling approach.

In order to obtain optimal controller output that minimizes the current performance cost, system and control parameters in discrete-time representation are necessary. A regulated noise signal and the system response data set can be used to identify the Markov parameters of the system. Those parameters are identical to the impulse response of the system and in the picture the identified parameters using the recursive least squares (RLS) algorithm show a good agreement with the impulse response. The controller parameters can be obtained by searching the parameters that minimize performance cost measures such as drag or difference between a command signal and measured quantities.

<Block diagram of adaptive flow control>

The picture is a schematic diagram for exploring the impact of the adaptive algorithm on the flow structure. It is shown that the airfoil lift is favorably regulated by combining the DBD actuator and closed-loop adaptive controller.

Researchers

Faculty advisor: Professor Wei Shyy, Professor Dennis S. Bernstein
Graduate student: Young-Chang Cho, Matthew Fledderjohn, Matthew Holzel

References

Cho, Y., Fledderjohn, M., Holzel, M., Jayaraman, B., Santillo, M., Bernstein, D.S., and Shyy, W., “Adaptive flow control of low Reynolds number aerodynamics using a dielectric barrier discharge actuator”, AIAA-2009-378, 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, Jan. 5-8, 2009.