# Flow control of a jet in cross-flow: film cooling effectiveness enhancement using surface DBD plasma actuator

Pierre Audier, Nicolas Bénard, Éric Moreau, Matthieu Fénot

► To cite this version:

Pierre Audier, Nicolas Bénard, Éric Moreau, Matthieu Fénot. Flow control of a jet in cross-flow: film cooling effectiveness enhancement using surface DBD plasma actuator. Applied Physics Letters, 2016, 108 (8), pp.084103. 10.1063/1.4942606. hal-03629383

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Submitted on 21 May 2025

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# Flow control of a jet in cross-flow: film cooling effectiveness enhancement using surface DBD plasma actuator

P. Audier,¹, a) N. Bénard,¹ E. Moreau,¹ and M. Fénot¹

Institut PPRIME (CNRS UPR 3346, Université de Poitiers, ISAE-ENSMA),
SP2MI Téléport 2 Bd Marie et Pierre Curie BP 30179, Futuroscope, 86962 Poitiers,
France

(Dated: 14 December 2015)

The case presented here deals with plasma flow control applied to a cross-flow configuration, more specifically to a film cooling system. The ability of a plasma DBD actuator for film cooling effectiveness enhancement is investigated through an experimental set-up including a film injection from a rectangular slot into a thermally uniform cross-flow. 2D PIV and IR-thermography measurements are performed. Results show that the jet can be deflected against the wall when the discharge is switched on. For all the tested blowing ratios, the injected jet flow covers a more significant part of the wall, leading to an improvement of the effectiveness of 15% compared to the standard baseline case.

<footnote>a) Electronic mail: pierre.audier@univ-poitiers.fr</footnote>
In turbojet engines, protecting combustion chamber walls and turbine blades from high thermal stresses induced by high temperature combustion gases is a necessity. Convective film cooling is one of the most frequently used techniques. In this process, a coolant jet flow is injected into the hot cross-flow from a row of holes to cover the wall as much as possible. Keeping the coolant jet attached to the wall is a primary purpose and quite few researches were realized, specially dealing with passive flow control strategies such as the shape of injection¹,², the injection hole position or the influence of the mass flow rate ratio between the injected air and the cross-flow (i.e. blowing ratio)³. However, all these methods are designed for specific flow conditions and can not be adjusted, for instance, for a varying cross-flow velocity. Furthermore, the unsteadiness of actual turbine flows requires a control mechanism which can be adapted in time to stay efficient, highlighting the needs for active cooling technologies.

The present experimental work investigates an active flow control strategy, using a plasma actuator, in case of a jet injected in a cross-flow through an elongated slot. The concept of using plasma actuators for active flow control in case of film cooling enhancement was firstly introduced by Roy and Wang⁴. Based on numerical simulations, their results underlined that application of plasma discharges can improve the film cooling efficiency up to 26% in case of a classical hole geometry. For the last 15 years, surface dielectric barrier discharge (DBD) devices have proved to be one of the most sophisticated actuator devices for flow control in a wide range of applications⁵,⁶. Unlike other type of active control devices, plasma actuators are lightweight, easy to use on in-lab models and able to produce a localized perturbation with a wide range of amplitudes and frequencies. Typically, a surface DBD plasma actuator operates by applying a strong electric field between two electrodes separated by a dielectric material to create a non-thermal plasma above the dielectric surface. By the mechanism of ion collision, a momentum exchange occurs between charged particles and neutrals, inducing an electrohydrodynamic (EHD) force. The forcing takes place mainly in a small region close to the edge of the air-exposed electrode where the electric field is more intense. The result is a wall tangential jet flow, called ionic wind⁷, which is used for flow control. In this study, the actuator consists of two copper electrodes mounted asymmetrically on both sides of a dielectric sheet composed of four layers of polyimide film, representing a total actuator thickness of 440 µm. The width of the electrodes is 10 mm in the stream-wise direction and 95 mm in the span-wise direction in order to obtain an actuation on 95% of the slot
length. There is a gap of 2 mm between both electrodes. The plasma is created by applying
a sinusoidal signal to the air-exposed electrode with a high voltage amplitude $V_{AC}=7.5$ kV
(15 kV peak to peak) and a frequency $f_{AC}=2$ kHz. The high voltage is provided by a Lecroy
signal generator (WaveStation 3082) and a Trek amplifier (model 30 kV/40 mA). The mean
volume force produced by this kind of actuator was previously estimated⁸ to be around
$2 \text{ kN.m}^{-3}$, which is of the same order of magnitude as the volume force used by Roy and
Wang⁴ in their numerical simulation.

The experiments are conducted in a low speed, closed-loop, thermoregulatory wind tunnel. A schematic diagram of the system is shown in Fig. 1. The test section is 1.19 m long with a square cross-section of 300 x 300 mm². A thermoregulatory unit allowed maintaining the cross-flow at a temperature level of $T_∞=293$ K. The top wall of the wind tunnel is composed with a thin high transmittance window allowing optical access for both particle image velocimetry (PIV) and infrared thermography measurements. The injected jet flow is heated at $T_j=313$ K before being injected in the wind tunnel as a film through a single central slot. It should be underlined that the choice was made to inject the jet from a slot, instead of the classical hole shape, to simplify the experimental model to facilitate the implementation of the plasma actuator. This slot is 100 mm long and a 20 mm wide (5:1 aspect-ratio) and is drilled in the bottom wall at an angle of 30° with respect to the stream-wise direction. The jet velocity is set to $U_j=5 \text{ m.s}^{-1}$ while the cross-flow velocity was monitored to obtain different averaged blowing ratios $M=ρ_jU_j/ρ_∞U_∞$, where the density ρ and the velocity U are respectively related to the jet and the cross-flow. The study is performed for three different blowing ratios of $M=0.4, 0.5$ and $1$ for a Reynolds number (based on the jet velocity and on the width of the slot) of $Re=6370$. Note that all the dimensions are normalized by the slot half-width $D=10$ mm, thus $x/D=0$ corresponds to the middle of the slot. The actuator is set on the downstream edge of the slot, in a way that the plasma is created at $x/D=1$.

2D PIV measurements are realized with a LaVision system to gain insight into the dynamics of this cross-flow configuration. The flow is seeded with Ondina oil droplets (0.4 µm) and illuminated with a laser sheet provided by a 532 nm Nd:YAG laser generator, set above the test section and fitted with divergent cylindrical lens. The images are acquired using a PCO Edge camera, with a resolution of 2560×2160 px², set on the side of the test section and combined with a 60 mm lens. In this study, velocity fields are computed in the XY plane, in the middle of the slot ($z/D=0$), with a final image size of 120×70 mm² and a final resolution
of 47 µm/px. Infrared thermography is performed to measure the wall temperature $T_w$ using a CEDIP Jade MWIR camera set above the wind tunnel at a vertical distance of 1 m. Heat transfer measurements are performed on a glass epoxy test wall (300×200 mm²), set 50 mm (x/D=5) downstream the middle of the slot. This test wall contains a thin copper circuit on the upper side, facing the flow and fed by a power supply (Agilent-E3634A) to generate a constant electrical flux density. The upper side of the test wall is also painted black to get a homogeneous emissivity of 0.95 all over the surface. The temperature field is composed of thermal images obtained at three consecutive positions along the stream-wise direction, with a final size of 250×160 mm². Type-K thermocouples are used to precisely measure $T_j$, $T_∞$ and the temperature at the rear of the test wall. The maximum uncertainty of temperature measurements is estimated at ±0.2 K.

<figure><img src="image_2.png" /><figcaption>FIG. 1. Schematic diagram of the experimental set-up.</figcaption></figure>

To obtain detailed local informations on film cooling performance, the convective heat transfer coefficient $h$ and the film cooling effectiveness $\eta$ (dimensionless form of the the adiabatic wall temperature $T_{ad}$) are conventionally used³. In this study, those values are determined using a multi heat flux method based on the Newtons law of cooling⁹. This method consists in imposing an electrical flux density $\varphi_{elec}$ to heat a test wall by Joule effect and calculating radiative $\varphi_{rad}$ and conductive $\varphi_{cond}$ losses, using $T_w$ and the temperature values provided by several thermocouples positioned below the epoxy-glass plate, to obtain the convective heat flux density exchange $\varphi_{conv}$ on the upper side of the test wall:
$$ \varphi_{conv} = \varphi_{elec} - \varphi_{cond} - \varphi_{rad} \quad (1) $$

For a given aero-thermal configuration (i.e. blowing ratio, Reynolds number, injection and ambient temperature), the Newton's law of cooling could be written:

$$ T_w = \frac{1}{h}\varphi_{conv} + T_{ad} \quad (2) $$

Four electrical flux densities are imposed to the test wall by varying the current intensity. For each electrical flux density $\varphi_{elec}$ and for a given position on the test wall, a couple ($\varphi_{conv}$, $T_w$) can be computed after thermal equilibrium is reached. Due to the linearity of Eq.2, $T_{ad}$ and $h$ are deduced from a linear regression using those four couples. The film cooling effectiveness is then obtained by normalizing $T_{ad}$ with the cross-flow temperature $T_\infty$ and the jet temperature $T_j$:

$$ \eta = \frac{T_{ad} - T_\infty}{T_j - T_\infty} \quad (3) $$

$T_{ad}$ represents the reference temperature of the fluid close the wall. The closer $T_{ad}$ to $T_j$, the higher the effectiveness. For $\eta=1$, the temperature of the fluid close to the wall is equal to $T_j$, meaning that the jet flow is perfectly covering the wall. On the contrary, $\eta=0$ attests that the temperature of the fluid close to the wall is equal to the one of the cross-flow.

To begin, 2D-PIV measurements are realized to characterize the plasma actuator. Fig.2 shows the mean distribution of the longitudinal $<u>$ and normal $<v>$ components of the induced ionic wind. The maximum ionic wind velocity is around $2.4 \text{ m.s}^{-1}$ (Fig.2(a)) and is reached just after $x/D=2$, over the downstream edge of the grounded electrode. From the distribution of $<v>$, it can be noticed that the airflow is sucked toward the wall with a maximum of $-0.5 \text{ m.s}^{-1}$ located few millimetres above the wall at $x/D=0.2$, over the upstream edge of the grounded electrode. From the mean velocity magnitude distribution of the ionic wind, the plasma momentum coefficient $C_\mu=2J/\rho U_j^2 L$ can be estimated by computing the actuator momentum $J = \rho \int U_{act}^2 dy$, where $U_j$ is the jet velocity, $U_{act}$ is the ionic wind velocity and $L$ the length of the slot. In this study, the plasma momentum coefficient of the actuator is estimated to be around $C_\mu=0.02\%$.
<figure><img src="image_3.png" /><figcaption>FIG. 2. Distribution of (a) the mean longitudinal component $\langle u \rangle$ and (b) the mean normal component $\langle v \rangle$ of the ionic wind velocity induced by the plasma actuator. $V_{AC}=7.5$ kV and $f_{AC}=2$ kHz.</figcaption></figure>

The effects of the plasma discharge on the free jet (without cross-low) are first investigated to better understand the control mechanism. Fig.3 shows the distribution of the normalized mean velocity of the free jet without and with the plasma actuation. From the baseline case, it can be observed that the free jet separates from the edge of the slot ($x/D=1$) and reattaches downstream around $x/D=7$. When the actuator is turned-on, the jet stays attached to the wall, meaning that the ionic wind produced by the plasma actuator (Fig.2) is able to induce a deflection of the jet flow towards the wall and thus a better wall coverage than without actuation.

The aerodynamic aspect of the cross-flow configuration is now investigated for a blowing ratio $M=0.5$ ($U_j=5$ m.s$^{-1}$ and $U_\infty=10$ m.s$^{-1}$). Fig.4 shows the distribution of the difference between the normalized mean velocity magnitude with actuation $\langle U_{on} \rangle$ and without actuation $\langle U_{off} \rangle$. The main difference between both cases can be observed close to the wall, over the grounded electrode, where the normalized mean velocity magnitude is higher. This underlines that the mean topology of the flow is affected by the discharge and that the mean velocity is significantly increased close to the wall. To put an emphasis on this phenomenon, normalized velocity profiles are added to the figure at two different positions ($x/D=1$ and 3) for both controlled and baseline cases. For all the positions along the x-axis, the velocity is increased close to the wall, showing that interactions between jet and cross-flow are modified in a way that more momentum is added in the boundary layer thanks to
the plasma actuator. According to the results obtained in case of the free jet Fig.3, it can
be inferred that plasma flow control guarantees that the injected flow stays attached to the
wall.

<figure><img src="image_4.png" /><figcaption>FIG. 3. Distribution of the mean velocity magnitude $<U>$ of the free jet, normalized with the mean output velocity of the jet $<U_j>$. (a) baseline case (b) with plasma actuation at $V_{AC}=7.5$ kV and $f_{AC}=2$ kHz.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIG. 4. Distribution of the difference between the mean velocity magnitude with actuation $<U_{on}>$ at $V_{AC}=7.5$ kV / $f_{AC}=8$ kHz and without actuation $<U_{off}>$, normalized with the mean cross-flow velocity $<U_\infty>$. Normalized velocity profiles are superimposed for $x/D=1$ and $x/D=3$. $M=0.5$.</figcaption></figure>

Results obtained from infrared thermography of the test wall are illustrated in Fig.5, with-
out and with actuation at V<sub>AC</sub>=7.5 kV / f<sub>AC</sub>=2 kHz, for the same blowing ratio M=0.5.
Without actuation, the effectiveness reaches a maximal value around 0.8 at the beginning
of the test wall (x/D=5), meaning that the jet and the cross-flow have started to mix.
Downstream, the effectiveness gradually decreases as the jet and the cross-flow keep mixing,
bringing the effectiveness down to 0.4 in the central plan ($z/D=0$). When the plasma actuator is turned-on, the effectiveness is around 15% higher all along the test wall. According to the results obtained in the case of the free jet (Fig.3), it can be inferred that plasma flow control guarantees that the injected flow stays attached to the wall, avoiding the cross-flow to row under the jet. The diffusion of the jet in the cross-flow is thus delayed and the wall coverage is enhanced. It can be noted that even if the jet is injected from an elongated slot, its thermal print on the wall is not bi-dimensional at all. This could be explained by the interaction between the jet and the cross-flow close to the edges of the slot ($z/D=\pm5$) as for classical hole shaped injection.

<figure><img src="image_6.png" /><figcaption>FIG. 5. Distribution of adiabatic effectiveness without actuation (upper part) and with actuation at $V_{AC}=7.5$ kV / $f_{AC}=2$ kHz (lower part) for $M=0.5$.</figcaption></figure>

A comparison of effectiveness profiles, obtained in the central plan ($z/D=0$) with and without actuation, is shown in Fig.6 for three different blowing ratios. By looking at the baseline profiles, blowing at $M=0.4$ provides the best wall coverage in our experimental conditions. The effectiveness obtained for $M=0.5$ is nearly as high as the one measured for $M=0.4$. For $M=1$, the effectiveness is around 15% lower than for the other blowing ratios. Indeed, as with jets ejected from holes, when the blowing ratio increases (i.e. the cross-flow velocity decreases), the penetration of the jet into the cross-flow is increased and the jet attaches later on the wall. The local low pressure area due to the separation is also increased, thus the cross-flow can easily row under the jet, decreasing the effectiveness close to the slot. When the plasma actuator is turned-on, the effectiveness is always higher and remains higher all along the test wall whatever the blowing ratio. This means that this
<figure><img src="image_7.png" /><figcaption>FIG. 6. Evolution of the adiabatic effectiveness along the test wall, in the central plan ($z/D=0$), without and with actuation at $V_{AC}=7.5$ kV / $f_{AC}=2$ kHz for three different blowing ratio.</figcaption></figure>

control strategy stays efficient even when the cross-flow velocity changes. To quantify the efficiency of the control, the gain in effectiveness $G_{\eta} = (\eta_{on} - \eta_{off})/\eta_{off}$ is computed and averaged all along the test wall. For the three cases, the mean gain in effectiveness is around 15% when the plasma actuator is turned-on, meaning that whatever the tested blowing ratio, using plasma actuator enhances the wall coverage and improves the effectiveness. Even if this gain in effectiveness is lower in comparison with the 26% predicted by Roy and Wang$^4$, both numerical and experimental results underlined that plasma flow control guarantees the jet flow stays attached to the wall and improves the effectiveness of film cooling.

To conclude, an experimental work was realized to assess the potential of a surface DBD plasma actuator for active flow control for film cooling system enhancement. In all the cases studied, results underlined the advantages of plasma actuators for improving film cooling effectiveness, as predicted by the numerical results available in literature. The actuator increases the wall coverage by keeping the injected flow attached to the wall surface, increasing its momentum and delaying its diffusion in the cross-flow. This control strategy has to be tested on other geometries to confirm its efficiency. A parametric study should also be done in the future to investigate the influence of the electric parameters on the effectiveness.
ACKNOWLEDGMENT

This work has been funded by the French Government program INVESTISSEMENT D'AVENIR (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01) and a part of the equipment was funded by (INOPLAS, ANR-13-ASTR-0015-01)

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