Modeling pulsed blowing systems for active flow control.

摘要

A model for predicting the performance of pulsed-blowing actuator systems commonly used for many flow control applications is presented and compared with experiments. The actuator system consists of a regulated air supply, oscillatory valve, transmission tubing and actuator. The actuator is a chamber and slot at the location in the flow to be controlled. The typical design objective is to achieve the largest possible velocity fluctuation levels at the actuator slot exit for a given fluctuating pressure input. However, the performance of the system is strongly dependent on geometry, flow rate and frequency of pulsation. Lumped-element models are useful for predicting the performance of the actuator chamber and slot, but fail to account for the effects of the transmission tubing. A distributed model for the tubing combined with a lumped-element model for the actuator accurately predicts system resonance and amplitudes. Comparisons with experiment are made for a wide range of tubing lengths, slot widths, mean flow velocities and forcing frequencies. The resonance of a pulsed blowing system is characterized with open-end resonance and closed-end resonance using the reflection coefficient of the system. Unexpected behavior such as reversed flow at the slot exit is predicted by considering the open-end resonance.; The impedance estimation in the lumped-element model for an actuator plays an important role in predicting the pulsed blowing systems. The exit fluctuating velocity is dependent on the thickness of slots or orifices and the forcing frequency in the linear regime if the thickness is finite and St > $8$. However in most active flow control applications the actuator velocity is in the nonlinear regime, where the fluctuating pressure is proportional to the square of the fluctuating velocity. The nonlinear acoustic effects dominate the impedance, which is proportional to the exit velocity. In a pulsed blowing system, the mean velocity is inevitably superimposed on the fluctuating velocity, so that the nonlinear impedance must be estimated with the superimposed mean flow. The nonlinear phenomena of the flows through an orifice or slot can be understood with the Bernoulli equation in which the pressure drop between an orifice or slot is proportional to the velocity squared. When the fluctuating velocity is superposed with a mean flow at the exit of slots or orifices, it was found that the nonlinear resistances for the mean flow and resistance for the fluctuating flow can be different. Furthermore, the nonlinear resistance is independent of the r.m.s. of the fluctuating velocity u ′, if the minimum of the instantaneous velocity is greater than zero. This is due to the fact that the high acoustic resistance for high instantaneous velocities and the low acoustic resistance for low instantaneous velocities are averaged constant. In this case, the resistance for the fluctuating velocity can be obtained based on experimental measurements of the resistance at steadying blowing conditions.