12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

MIXING AND LARGE-SCALE MODULATION OF A TURBULENTBOUNDARY LAYER PERTURBED BY AN EFFUSION FILM

Jeremy Basley
LAMIH, CNRS UMR 8201
Université Polytechnique Hauts-de-France, INSA
Le Mont Houy, 59300 Valenciennes, France
jeremy.basley@uphf.fr

Kevin Gouder
Department of Aeronautics
Imperial College London
London SW7 2AZ, UK
kevin.gouder04@imperial.ac.uk

Jonathan F. Morrison
Department of Aeronautics
Imperial College London
London SW7 2AZ, UK
j.morrison@imperial.ac.uk

ABSTRACT

respectively (for a review, see Krewinkel, 2013). For higher
engine efficiency, a better understanding of the momentum
and heat exchange between the effusion film and the boundary
layer is required to deduce a minimal cooling flow rate while
maintaining the integrity of the film.
These highly distorted flows conform to the description of
suddenly perturbed boundary layers. Generally, the turbulence
does not adjust immediately to changes in the mean strain rate.
In any case, these flows are far from equilibrium as the effectsof the new surface condition are unlikely to have permeated thewhole layer (for a review, see Smits & Wood, 1985). Detailed
studies of perturbed boundary layers with changes to both momentum and heat flux are few: some exceptions are those by
Subramanian & Antonia (1981); Andreopoulos (1983).
This experimental study focuses on low velocity ratios(VR < 0.4) using an idealised, large geometry at low speed
to enable spatial and temporal resolution that are much better than those available in typical turbine rigs. This allows
us to highlight the momentum exchange mechanisms between
the injected film and the incoming boundary layer at the costof reduced relevance in neglecting such effects as blade rotation, freestream unsteadiness and turbulence, roughness andpressure gradients. A canonical turbulent boundary layer is injected with, in this case, an isothermal effusion film for a rangeof film velocity ratios (Figure 1, Bottom). The analysis focuseson the correlations between the concentration of injected fluid
and the large-scale fluctuations of velocity. The solid surface
condition is taken to be isothermal.
While the present measurements are isothermal, further
simultaneous measurements of temperature and velocity (reported elsewhere) are made where the film emerges at a temperature of a few ◦ C below that of the boundary layer so thatthe scalar field is passive and results are directly comparable tothose herein. It is well known that, even in unperturbed flows(close to a state of equilibrium), Reynolds analogy is a poor
assumption (see, for example Kays & Moffat, 1988). For perturbed flows (such as boundary layers on turbine blades), thesituation is even worse and large departures from Reynolds
analogy are likely.
In fact, exact correspondence between the temperatureand momentum fields should never be expected. A clue to

The large-scale modulation of an effusion film injected
into a high Reynolds-number boundary layer is investigatedfor a wide range of film-velocity to freestream-velocity ratios.
Particle Image Velocimetry (PIV), visualisations and hot-wiremeasurements are used to characterise the momentum effects
underlying the mixing of the effusion film. For this experiment, the geometry of a turbine blade is idealised in a largescale facility with a canonical upstream boundary layer where
the effusion film and the boundary layer are isothermal. Spectral analysis shows that the injection of the effusion film firstpromotes near-wall turbulence until the film breaks away fromthe surface when the velocity ratio reaches a critical value. For
higher velocity ratios, large-scale motions from the incoming
boundary layer no longer penetrate the sublayer. The associated spectral signature is accompanied by enhanced inter-scale
exchanges, as shown by the skewness of the streamwise velocity component and the amplitude modulation coefficients.
Use of seeding in the film flow enables the estimation of
the concentration of injected fluid in the laser sheet. Joint
momentum-concentration data show that the mixing of thefilm is strongly modulated by the large-scale motions of the
turbulent boundary layer, although in different ways depending on the velocity ratio. For very low velocity ratios, largescale motions are largely unaffected by the film. They encompass the boundary layer down to the injected sublayer andmodulate locally the concentration of injected film. For higher
velocity ratios, mixing intensifies as the effusion film is injected with momentum and reaches further from the wall. As
a result, the concentration of injected fluid in the near-wall region is remotely, yet more intensively modulated by the largescale motions above the sublayer.

INTRODUCTION
In order to withstand the high temperature flows coming
out of a combustion chamber, jet engine turbine blades requirecooling by the use of low temperature bleed flows producing
an effusion film. Typically, cooling flow rates are large: velocity ratios VR = U f /U∞ range from 1 to 3, where U f and U∞ arethe characteristic velocities of the film and the incoming flow,

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 1. (Top) Rendered snapshot of streamwise velocity fluctuations superimposed with concentration of injected fluid (yellow
line denotes 5% contour). Acquired in the plane passing by the centre of effusion holes (for VR = 0.37). (Bottom) side view of theexperimental set-up.

these differences lies in the fact that equations for both themean temperature and mean-square temperature fluctuations
do not contain terms for the pressure gradient while those forthe momentum and turbulence kinetic energy do. Using direct numerical simulations, Guezennec et al. (1990) show thatheat is a poor marker of the instantaneous vorticity field. They
also show that, except very close to the wall, pressure-gradient
forces are significantly larger than viscous forces (Batchelor& Townsend, 1956) but play no role in the exchange of heat.
This is because velocity and pressure fluctuations extend overmuch shorter distances than temperature fluctuations, the latterstages of mixing of the scalar field occurring by molecular diffusion even though large eddies are brought together by mean
flow advection and turbulent mixing. For a discussion of thesechallenges within the context of suddenly perturbed boundary
layers, see Morrison (2005)
These ideas appear not yet to have been considered fully,
owing partly to the difficulty of making the necessary measurements at high Reynolds numbers, which are a prerequisite
for rational modelling techniques for film cooling design. Thisis the purpose of the current set of experiments.

fusion panel fed through a plenum supplied with compressed
air, and enclosed with a thick perforated plate. The temperature can be independently controlled, although in the present
experiment, all measurements are isothermal. The effusion
film was generated through a staggered grid of inclined D = 16mm diameter holes with a pitch of 5D.
Time-resolved planar PIV data were acquired in a streamwise wall-normal plane above the effusion plate, along the hole
centres, as shown in Figure 1. Visualisation images were acquired in the same way, but with targeted seeding. This allows
us to reconstruct the concentration C of injected fluid (saturated with seeding) with respect to incoming flow (largely unseeded) using the scattered light intensity as a surrogate forconcentration.

C% (x, y,t) =I(x, y,t) − Imin
× 100
Imax − Imin

(1)Here, I(x, y,t) is the light intensity at position (x, y) of the visualisation image acquired at time t, and Imin and Imax are theminimal light intensity (far field) and maximal light intensity(directly out of the effusion holes), respectively. Since enoughresidual particles are still present everywhere in the flow, velocity fields can be calculated synchronously with concentration fields. A wide range of low velocity ratios were investigated, in the range 0 ≤ VR ≤ 0.4 with the holes open. For
VR= 0, hole discontinuity is the only change of boundary conditions to the turbulent boundary layer. These data sets werecomplemented by hot-wire measurements of the streamwise
velocity.

EXPERIMENTS
The large-scale, low-velocity experiment was carried out
in the closed-loop 10 × 5 wind tunnel at Imperial College. The
incoming boundary layer was generated using a large, selfsimilar turbulent boundary layer, tripped and developed over
15 m, yielding a range of Reynolds numbers 2700 ≤ uτ δ /ν ≤4700, with uτ the friction velocity and δ ' 0.2 m the boundary
layer thickness upstream of the plate (Figure 1). This turbulent
boundary layer was perturbed with a geometrically similar ef-

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 2. Streamwise velocity statistics from hot-wire measurements. Plain lines correspond to profiles at (x = 594 mm =37.1D, z = 40 mm = 2.5D) mid-way between two rows of effusion holes. Colours from dark to light depict different effusion cases
VR={0, 0.10, 0.16, 0.27, 0.38}, respectively.
a) VR = 0b) VR = 0.10c) VR = 0.37

Figure 3. Pre-multiplied power spectral densities of streamwise velocity PSDu,x as a function of wavelength λx and wall distance yfor three VR, from PIV datasets along centre-line of holes. Contour levels are shown every 0.3 u2τ . The horizontal dashed lines markthe cut-off wavelength λx = 1.5δ .

RESULTS & DISCUSSION

depicted in Figure 3, where pre-multiplied spectrograms arecalculated using PIV velocity fields. For VR=0, the behaviour
is consistent with high Reynolds number boundary layers(Ganapathisubramani et al., 2005; Squire et al., 2016; Basley
et al., 2018). There is a scale separation between small-scale
turbulence confined in the roughness sublayer – here generated by the perforated plate – and large-scale motions that are
particularly intense in the log layer. The gap between smallscale turbulence populating the ‘roughness sublayer’ and thelarge-scale motions allows for the decomposition of velocity fluctuations into u = uL + us , where uL = u(λx > 1.5δ )is the large-scale component obtained through unbiased lowpass filtering, while us represents the remaining fluctuations at
smaller scales. With this decomposition, the skewness can be
defined as in Equation (2),Measurements of the streamwise velocity component are
performed with a single hot wire. Figure 2 shows wall-normal
profiles of the first- (U/U∞ ), second- (σu /U) and third-ordermoments (skewness, Su ) acquired mid-way between two adjacent rows of holes. The mean velocity profile of the perturbed
boundary layers no longer show the log-law exhibited by the
incoming boundary layer. The roughness of the effusion holes
also results in lower turbulence rate in the near-wall region due
to enhanced mixing. When VR > 0, the turbulence rate firstincreases throughout the boundary layer. With increasing VR
the levels of turbulence concentrate around D < y < 3D, corresponding to film lift-off.
Typically, the skewness upstream of the effusion panel issignificant (0 < Su < 1) close to the wall, is zero in the buffer
layer and log layer and then decreases to large negative peak(Su ≈ −3) at edge of the boundary layer due to the highly contorted turbulent / non-turbulent interface. Like the turbulence
rate, the roughness layer induced by the perforated plate drastically attenuates the skewness close to the wall but leaves therest of the BL unchanged. The introduction of the effusion film
increases the skewness significantly in the buffer layer. Thisevolution suggests a higher correspondence between high momentum events and the enhancement of the turbulent kinetic
energy.

Su =hu3 i hu3L i + 3hu2L us i + 3huL u2s i + hu3s i
=
σu3
σu3

(2)

where h.i denotes time averaging. The decomposition of theskewness profile seen in Figure 2 is plotted in Figure 4. Except
for the negative spike close to y = δ (typical of the turbulent/ non-turbulent interface), these expansion terms show the relative effects of large- and small-scale processes in inter-scale
exchanges.
Triadic exchanges within the large-scale range exclusively are associated with hu3L i. They remain near zero. The
term hu2L u2s i represents the influence of small scales on the amplitude of large-scale fluctuations. It is weak but, interestingly,

Further insight from the skewness is provided by separating fluctuations into two distinct ranges: large-scale motions
and small-scale turbulence. To that aim, the spectral signatureof the streamwise velocity in the perturbed boundary layer is3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 4. Skewness decomposition into large and small scales, from hot-wire measurements. Profiles are obtained at (x = 594 mm= 37.1D, z = 40 mm = 2.5D) mid-way between two rows of effusion holes. Colours from dark to light depict different effusion cases
VR={0, 0.10, 0.16, 0.27, 0.38}, respectively.
a) VR = 0b) VR = 0.10c) VR = 0.37

Figure 5. Amplitude modulation coefficient for (a) VR = 0, (b) VR = 0.10, and (c) VR = 0.37. (Top) single point correlation AM(x, y)
at reference point (x0 = 28D, y0 = 1.2D), and (bottom) two-point correlation profile AM(y0 , y) at x0 = 28D. White vertical dotted lines
mark the intersections with top maps at y0 = 1.2D and black dashed diagonals mark the no-shift correlation (y = y0 ).

goes from negative at low VR to positive when VR increases
significantly. This might be indicative of the appearance ofintermediate scales generated by the introduction of the film.
The terms hu3s i and huL u2s i relate to the amplitude ofsmall-scale turbulence. The former represents exclusively
small-scale, triadic exchanges (skewness), while the latter corresponds to correlations between large-scale fluctuations andthe amplitude of small-scale fluctuations. Both terms become
increasingly positive for low VR < 0.3. However, at the highest velocity ratio, VR = 0.37, this trend reverses and values
tend to zero near the wall. On the contrary, the correlation between small-scale turbulence and large-scales motions keeps
increasing at the top of the film (D < y < 2D) with increasing
VR. This indicates that the injection of the film indeed promotes mixing with the incoming boundary layer, but the increasing VR changes the nature of the film under the mixing
layer which is pushed further away from the wall.
Mathis et al. (2011) have highlighted the relationship between the skewness expansion in Equation (2), specifically theterm huL u2s i, and the amplitude modulation approach used innumerous papers recently (Mathis et al., 2009; Marusic et al.,2010; Mathis et al., 2011). This approach consists in quantifying the amplitude modulation of small-scale turbulence bylarge-scale motions as a correlation coefficient between large
scales uL and (u2s )L , the large-scale envelope of small-scale
fluctuations, obtained by low-pass filtering u2s .

Often restricted to temporal correlations of hot-wire measurements, AM has recently been extended to two-point spatial correlations (Basley et al., 2018; Yao et al., 2018). Inclined, meandering large-scale motions modulate the amplitude of small scales in the roughness sublayer, so that turbulence is intensified directly beneath these large structures.
Here, the single-point modulation coefficient is calculatedwith respect to the large-scale motions at a reference position
denoted (x0 , y0 ):AM(x0 , y0 , x, y) =huL (x0 , y0 ) ∗ (u2s )L (x, y)iσuL (x0 , y0 ) σ(u2s )L (x, y)(3)

where σ denotes a standard deviation. AM represents a generalisation of the covariance between uL and u2s that is the term
huL u2s i. Figure 5 shows the momentum exchange between
scales. At low VR the amplitude modulation is enhanced near
the wall. As VR increases, the injection of momentum alters
this mechanism but amplitude modulation of small-scale turbulence still occurs. Notably, amplitude modulation is significantly amplified further from the wall at y ≈ y0 ≈ D, corresponding to the mixing layer that hovers after the effusion film
lifts off (see also Basley et al., 2021).
The present work builds on these findings to expand themodulation approach to passive tracers within the effusion
film.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022a) VR = 0.10b) VR = 0.37

Figure 6. Correlation coefficient maps between large-scale fluctuations of velocity and large-scale fluctuations of concentration for
two VR cases. (Top) single point correlation γu,c (x, y) at reference point (x0 = 28D, y0 = 1.2D), and (bottom) two-point correlation
γu,c (y0 , y) at x0 = 28D. White dotted lines mark the intersections with top maps at y0 = 1.2D and black dashed diagonals mark the
no-shift correlation (y = y0 ).

CONCLUSIONSThe coefficienthuL (x0 , y0 ) ∗ cL (x, y)iγu,c (x0 , y0 , x, y) =σuL (x0 , y0 ) σcL (x, y)This study comes within the framework of turbine blade
effusion cooling. This paper highlights the importance offilm detachment at much lower VRs than typically used ingas turbines. The underlying mechanisms of the mixing andbreaking-up of an effusion film are investigated in an idealisedcase of a canonical turbulent boundary layer.
The mixing of passive tracers injected with the effusion
film is analysed in depth with respect to synchronous PIV
data. This results in joint data sets of concentration and momentum fields, which reveal a striking change in the dynamics of the perturbed boundary layer when velocity ratios exceed VR = 0.15: from low-momentum diffusion confined to
the near-wall region, where mixing is limited to small-scale
turbulence, the injected sublayer breaks up to shreds drifting
towards the edge of the outer layer, where more intense mixing occurs. Consequently, not only the excessive momentumof higher VR promotes mixing of the film but it also renders
the near-wall film more susceptible to intense modulations bylarge-scale motions passing in the outer layer.
It is worthwhile noting the threshold VR = 0.15 is likely
quite sensible to geometry and flow conditions. However thisvalue is remarkably low with respect to typical velocity ratios
encountered in gas turbines, generally well over VR = 1. The
resulting time-resolved and space-extended data sets explain
the favourable outcome of low velocity ratios, for which theshear-driven mixing of the effusion film is limited to near-wallregion of the boundary layer. Results also suggest that the effusion film effectively restricts the penetration of fluid from theouter region into the near-wall region of the boundary layer.

(4)

quantifies the spatial correlation between the large-scale fluctuations of streamwise velocity at (x0 , y0 ) and the large-scale
fluctuations of concentration at (x, y). Examples of correlation maps are displayed in Figure 6. The reference point(x0 = 28D, y0 = 1.2D) for the single-point maps (Figure 6 top)
was chosen to depict a representative picture of the dynamics.
Streamwise, x0 = 28D is a midway point between two successive holes (5th and 6th ), downstream enough for the sublayer
to be established, while y0 = 1.2D corresponds to the edgeof the sublayer where the high levels of kinetic energy were
measured. The two-point correlation maps (Figure 6 bottom)
identify correlations between distant features of the flow, taken
at different wall-distance.
Two regimes can immediately be identified from thesemaps. For low velocity ratio VR = 0.10, there is a strong local
anti-correlation between concentration and momentum within
the film confined near the wall. The distribution in Figure 6(a)top is inclined as it follows the flow in the sublayer. This signature results from the injected fluid carrying relatively lessmomentum compared to the incoming flow. The modulation
by outer-layer dynamics is non-existent.
The scenario for higher velocity ratio VR = 0.37 is completely different (Figure 6b). Since the local anti-correlation
with local velocity fluctuations is the signature of recently
injected (unmixed) fluid, it is logically pushed much further
away from the plate. However a stronger modulation appears
in the near-wall region of the effusion film with the distantlarge-scale motions in the outer-layer, as shown by the bottomright corner of Figure 6(b) bottom.
This implies that, despite keeping the large-scale motions
away from the near-wall region, higher VR cases enhancerather than reduce the influence of incoming turbulence on theinjection of the effusion film. Such a remote correlation between large-scale motions and near-wall concentration of injected fluid suggests an interplay via wall pressure and is the
subject of ongoing work.

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Osaka, Japan (Online), July 19-22, 2022
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