ISTP-16, 2005, PRAGUE 16TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA

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Abstract

The paper deals with control or influence of synthetic jets on the flow field at conditions near boundary layer separation. It is well known fact that the boundary layer separation has a considerable effect on efficiency of turbomachines and fundamental effect on aircraft wing sections performance. By the boundary layer control, it is possible to obtain both operational economy and extension of efficient operational region of turbomachines. Traditional methods of boundary layer control are very complex and their application needs complex facilities. Modern methods based on the control by synthetic jets are simpler, but their design has to be carried out at rather well experience and detailed knowledge about boundary layer and its interaction with the actuator.

1. Introduction

The design of turbomachines is based on given parameters, for instance mass flux, compression ratio, rotor speed, etc. The turbomachine is designed for operation under values of these parameters. Mainly due to appearance of separation, the efficiency of the turbomachine working under off-design conditions is decreased considerably.

There are some possibilities to improve efficiency of turbomachine. First choice is to assume chance to run the turbomachine under wider value of working conditions (implicate off-design in value of working condition) and to design it with respect to them. But the efficiency will be lower. The second possibility is to

control boundary layer, especially its separation. For control boundary layer passive and active methods can be used. Because the flow field in front of the blades inside the channel (turbomachines) has higher intensity of turbulence and dimensions of the blade are smaller comparing to conditions seen on airplane wing, passive methods does not appear preferable.

In this paper the problem of application of active methods to control boundary layer separation on turbomachines will be discussed.

2. Theoretical background

At first we should summarize, which active method can be used. There are three possibilities

• Synthetic jet • Steady suction • Steady blowing

Synthetic jet excitation is more effective and efficient then steady blowing or suction [6], [4]. Great advantage of this method is zero mass flux supplied to, or taken from main flow. Therefore as was written, in this paper will be discuss synthetic jet boundary layer control.

There are two possibilities to control boundary layer by synthetic jet. The first can be call low power control. Because turbulent boundary layer is more resistant to separation, we can control position of transition point applying synthetic jet to laminar boundary layer. This method is more sophisticated and assumes good knowledge of the physical process

A STUDY OF INFLUENCE OF SYNTHETIC JETS TO THE BOUNDARY LAYER SEPARATION

Milan Matejka

Czech Technical University in Prague, Faculty of Mechanical Engineering Corresponding author: milan.matejka@fs.cvut.cz, phone: +420224352661, fax:

+420224310292

Keywords: synthetic jet, boundary layer separation, boundary layer control, turbomachinery

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description. This method is very close to passive boundary layer control (turbulators).

Second method is based on conception of supplying energy to the flow, accelerating boundary layer to delay the separation point. Boundary layer velocity profile is changed by jet from the orifice to be more resistant to separation. Generating high frequency synthetic jet form strong flow from the orifice very similar to continuous jet. Main problem is to construct synthetic jet with sufficient power output.

Flow field on turbomachines has different characteristics then flow field on airfoils. Extent of laminar boundary layer on the blades of turbomachines is smaller than on airfoils. Therefore using low power control is not so preferable.

To determine intensity of synthetic jet can be used the total momentum coefficient which is defined [3], [5]:

cU

hUC jj

2

2

2/1 ∞∞

=ρ

ρµ

(1)

where U∝ and ρ∝ velocity of the jet fluid and fluid density respectively, Uj, ρj are the same quantities related to outer flow, h is the jet orifice diameter, c is the typical dimension of the body. Its value is changed from 0.01% to 3%. Lower values are for active low power control and higher for high power control.

2.1. Synthetic jet generator

Synthetic jet is a generator of zero-net-mass-flux. This flow control actuator is designed as a cavity with periodically moving boundary and with orifice or slot which generates a synthetics jet. ([1], [2], [3]).

Fig. 1 depicts direction of the flow round the orifice. There exist two main lines of the flow caused by two phase of the jet. First heads direct along the central line of the orifice and the jet direction and its intensity depends on the power of the spurt. Second phase (suction) of synthetic jet bring on air suction along the wall.

Fig. 1 Model of zero net mass flux.

2.2. Synthetic jet actuator design – Lumped Element Model (LEM)

At relatively low frequencies, where the characteristic length scales of the physical phenomena are larger than largest geometric dimension, the governing partial differential equations of the dynamic system can be easily transferred into a set of coupled ordinary differential equations. Individual parts of actuator components are modeled as elements of an equivalent electrical circuit using conjugate power variables (see Fig.2). The frequency response function of the circuit is derived to obtain an expression for Qout/Vac, the volume flow rate to applied voltage. Idea of the LEM has been introduced in [1], [2], where detailed derivation of the model is also shown.

Fig. 2 Lumped Element Mode - equivalent

electrical circuit

Change of various actuator parameters has

significant effect to its dynamical behavior, to the amplitude-frequency response and namely to the velocity amplitude of the air coming out of the orifice. On the Fig. 3 and 4 it can be seen influence changes of actuators parameters. Both “LEM” case have the same cavity volume, radius and length of the orifice, but the different diameter of the diaphragm.

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A STUDY OF INFLUENCE OF SYNTHETIC JETS TO THE BOUNDARY LAYER SEPARATION

We can clearly see possibility to optimize the actuator parameters to obtain output velocity maximum or momentum of the flow, wide frequency period with high velocity output etc. [2]. But there are problems to estimate constants, for example material constants as an impact of the wall acoustic rigidity etc. It is necessary to verify them experimentally.

Fig. 3 LEM – smaller diaphragm

Fig. 4 LEM – bigger diaphragm

3. Model design and experimental setup

Boundary layer on the model could be to control by the three actuators. It is practicable to operate arbitrary number of the actuators. The position of the actuators and base dimension of the model are depicted on the Fig. 5. The angle of flaps was varied from 22° to 27°.

Synthetic jet actuators were designed with speakers of 52mm diameter as exciters. Cavity has five orifices, to get 3D flow field, on diameter 1mm and length 2,8mm. Distances

between the orifices are 4mm. Amplitude-frequency characteristic of the actuator was obtained experimentally using HW anemometry. Excite amplitude was 2V and amplitude-frequency characteristic of the actuator is plotted in Fig. 6. Maximum of the synthetic jet mean velocity 1mm above orifice is 15 m/s and to this correspond frequency of 300 Hz. On that account it was used this value as the exiting frequency.

Fig. 5 The design of measured model

Fig. 6 Amplitude-frequency characteristic of

actuator

Free stream velocity in the measurement area varies from 0.9 to 5.5 m/s.

4. Results

Measurement has been carried out by PIV method and visualization. For more accurate results of PIV measurement adaptive correlation was used.

To compare the differences flow fields of control and no control boundary layer are shown.

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4.1. Field of velocity

Fig. 7 Free stream velocity c=1 m/s, angle of flap

α=22°, bottom figure shows flow field with synthetic jets.

Fig. 8 Free stream velocity c=1.7 m/s, angle of flap α=22°, bottom figure shows flow field with

synthetic jets.

Fig. 9 Free stream velocity c=3.7 m/s, angle of flap α=22°, bottom figure shows flow field with

synthetic jets.

Fig. 10 Free stream velocity c=3.6 m/s, angle of flap α=26°, bottom figure shows flow field with

synthetic jets.

Fig. 11 Free stream velocity c=5.3 m/s, angle of flap α=26°, bottom figure shows flow field with

synthetic jets.

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A STUDY OF INFLUENCE OF SYNTHETIC JETS TO THE BOUNDARY LAYER SEPARATION

4.2. Field of vorticity

Fig. 12 Free stream velocity c=3.7 m/s, angle of flap α=22°, bottom figure shows flow field with

synthetic jets.

Fig. 13 Free stream velocity c=5.3 m/s, angle of flap α=26°, bottom figure shows flow field with

synthetic jets.

4.3. Comments

Effect of the synthetic jet to the boundary layer is clearly depicted on the pair of the figures for given free stream velocity. When we compare both of them we can see differences of velocity profile of boundary layer. The boundary layer with influence of synthetic jet is seemed to be thinner and without exciting to be thicker. First actuator causes change of the

boundary layer thickness to 31% (1 m/s) Fig. 7, 61% (1.7 m/s) Fig. 8, 66% (3.6 m/s) Fig. 9 and 10, 72% (5.3 m /s) Fig. 11 of their nominal value.

Significant impacts of synthetic jet to the thickness of boundary layer except velocity have the direction and intensity of synthetic jet. This effect is shown on the flap of model. On the figures there are big differences between actuated and unactuated flow field, which depend on the velocity of the free stream flow field. Higher free stream velocity comparing to synthetic jet velocity cause higher wake behind the flap. But when we look to the figures very carefully, we can note strong effect in direction of the jets. To reduce angle of synthetic jet to the surface is suitable. Optimal is to design the jet to make use of the Coanda effect.

On the Fig. 12 and 13 fields of vorticity for angle of flap α=22° and 26° at free stream velocity 3.7 and 5.3 m/s are depicted. There is clear change of position of intensity vorticity field, which is caused actuator on the flap. Aero-shaping effects form the surface of the flap. It is evident that rate of aero-shaping depends on proportion of free stream and synthetic jet velocity.

5. Conclusion and future work

Experiment proved effect of both actuators, on the top side and on the flap, to the flow field. Considerable impacts of synthetic jet to the thickness of boundary layer have the direction, the free stream velocity and the intensity of the synthetic jet. In many cases has indispensable influence actuator position too.

One of the major problem is to project small high power actuator and to place it in to the blade or wall to control various types of shear flows. Appropriate choice is to use Coanda effect to steady synthetic jet near wall to show off its impact.

It is possible to shape the surface using synthetic jet actuator, but is needed high power actuator and to define control process of the actuators.

Future work will be to design blade cascade with actuators to control boundary layer and to

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make the extension of operational region possible.

The research was supported by the Grant Agency of the Czech Republic under the projects No. 101/05/2537.

References

[1] Quentin Gallas, Jose Mathew, Anurag Kaysap, Ryan Holman, Toshikazu Nishida, Bruce Carroll, Mark Sheplak, and Louis Cattafesta. Lumped Element Modeling of Piezoelectric-Driven Synthetic Jet Actuators. AIAA 2002-0125, 2002.

[2] Gallas, Q., Wang, G., Papila, M., Sheplak, M., Cattafesta, L. Optimization of Synthetic Jet Actuators, AIAA 2003-0635, 2003

[3] Ari Glezer and Michael Amitay. Synthetic Jet. Annu, Rev. Fluid Mech. 2002.

[4] R. Mittal P. Rampunggoon, H. S. Udaykumar. Interaction of a Synthetic Jet with a Flat Plate Boundary Layer. AIAA 2001–2773, 2001

[5] V.Uruba. Flow Control Using Synthetic Jet Actuators. Inženýrská Mechanika 2004

[6] B.L. Smith, G.W. Swift, A comparison between synthetic jets and continuous jets, Experiments in Fluids 34 (2003) 467–472, 2003