Surface pressure determination: a comparison between PIV...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Surface pressure determination: a comparison between PIV-based methods and PSP measurements

A. Tagliabue*, M. Bitter, S. Scharnowski, C.J. Kähler Department of fluid mechanics and aerodynamics, Universität der Bundeswehr München, Germany

* Correspondent author: [email protected]

Keywords: Pressure estimation, PIV processing, transonic flow, PSP

ABSTRACT

The present work investigates the challenges in measuring the surface pressure d istribution using particle image

velocimetry (PIV) in comparison with pressure sensitive paint (PSP) measurements. With the aim to assess if PIV

may be regarded as a complementary method to PSP, or even as a possible replacement at least for 2D flow analysis

or at low speed were PSP fails. The investigation is based on two d ifferent test cases: 1. the attached flow around a

NACA-0012 airfoil, 2. the separated flow around a backward -facing step (BFS). Both cases are investigated at

transonic flow conditions. For the airfoil both PIV and PSP measurements were conducted for a d irect comparison.

At such high Reynolds number, the boundary layer thickness is very small and therefore the pressure in the flow

field outside the boundary layer can be easily determined from the velocity data with an isentropic flow

assumption. The results of the PIV-based surface pressure reconstruction and the one of PSP are compared with the

static pressure taps installed on the model surface. For the BFS test case synthetic PIV images are produced from a

2D LES simulation. In this case flow separation as well as strong viscous effects appear which inhibit the use of the

isentropic flow assumption. Therefore, the Reynold averaged momentum equation is d irectly used and the pressure

is determined solving the Poisson equation which is obtained applying the d ivergence operator to the momentum

equation. The results are compared with the pressure d istribution on the surface given by the LES simulation. This

case aims to analyze the accuracy of PIV-based surface pressure determination in case of massive flow separation. It

w ill be shown that the deviations to the expected results are caused by the spatially d iscretization as well as by

spatially averaging, which occurs in a standard PIV measurement. Additionally, the effect of the velocity

uncertainty on the estimated surface pressure d istribution biases the result significantly. This implies that PSP will

be hard ly replaced by PIV.

1. Introduction

The aerodynamic load is conventionally measured with force balancing or pressure sensitive

paint (PSP) in case of complex 3D models or surface pressure taps and Pitot-tube in case of

simple 2D models. These methods are well established and lead to highly reliable results.

However, point-wise pressure taps suffer from low spatial resolution (that coincides with the

pressure taps location) and the intrusive effect. Furthermore, the implementation is costly and

the location and spacing of the pressure ports must be specified before the manufacturing

process which makes a later ad justment impossible. To overcome these drawbacks PIV-based

post-processing techniques were developed in recent years to measure the flow pressure in a


non-intrusive way with high resolution. To estimate the surface pressure in case of complex

flows with separation for instance, it is essential to resolve the near wall flow features in detail.

Thanks to the strong improvement in the field of PIV and PTV image analysis techniques in the

last years, this is possible in many applications (Kähler et al, 2012). This is also of fundamental

importance for delivering a high resolution pressure field in the entire flow domain down to the

wall. For the understanding of the governing flow physics a review of PIV-based pressure

measurements concepts developed in the last years can be found in van Oudheusden (2013). By

using tomographic PIV, the pressure in a 3D volume can be estimated , whereas with classical

pressure transducers, only pointwise measurements on the surface are possible. However, it has

to be kept in mind that the volumes that can be resolved are relatively small and resolving near

wall flow features is challenging due to model reflections. The majority of research has been

carried out at low speed and incompressible flow conditions, where state-of-art 2D2C PIV

techniques allow for measuring the instantaneous velocity and the material acceleration term of

the Navier-Stokes equations simultaneously. Very little has been published for high

subsonic/ transonic flow experiments. At such high velocities it becomes more challenging to

obtain time-resolved data, which is necessary for the computation of the accelerations in the full

momentum equations. One possibility is to use a four-pulse tomographic-PIV system

(Schneiders et al, 2014) that allows the reconstruction of the acceleration in a flow field from two

tomographic PIV velocity measurements, separated by a small time delay. This solution is quite

expensive in terms of experimental preparation, equipment and alignment and it is questionable

if the near wall region of complex models can be resolved adequately for surface pressure

determination.

The Pressure-Sensitive Paint measurement technique (PSP) is a well-established method for the

optical determination of the surface pressure d istributions (Bitter, 2012). The physical principle is

based on the detection of the luminescence emitted by excited luminophors which interact with

the oxygen molecules. The intensity of the emitted rad iation is dependent on the oxygen

concentration in the wall surrounding region. The oxygen concentration is d irectly proportional

to the oxygen partial pressure and , according to the Henry’ s law, to the flow static pressure. This

process was firstly d iscovered in 1935 by Kautsky and Hirsch for detecting the oxygen

concentration. Unfortunately, the luminescence is strongly affected by temperature variations.

Only in the last 10 years, with the introduction of a second dye in the paint (Gouterman et al,

2004) PSP became an established technique for the pressure determination on wind tunnel

models where high thermal effects occur. Thus, PSP is more and more replacing the classical

pressure-tap measurements especially if complex models at flow speeds larger 30 m/ s are

examined in costly wind-tunnels.

The objective of the present study is to investigate whether PIV may be regarded as a

complementary method to PSP, or even as a possible replacement, to determine the model


surface pressure in future applications from a single measurement. That would safe wind-tunnel

time and less expert knowledge would be required if only one measurement technique is

required .

2. Theoretical background

There are a number of possibilities to derive the mean pressure field from the mean velocity field

and a lot of development has been performed in the past especially in the field of numerical flow

simulations to optimize these approaches. Each method has its advantages and drawbacks and is

therefore suited for d ifferent flows, depending on the physics of the problem. For this reason, it

is important to know the fundamentals of the flow being analyzed , in advance.

In many cases, where the viscosity effect can be neglected , the flow is considered as inviscid and

adiabatic. With these assumptions the isentropic flow relation can be used to compute the

pressure d irectly from the velocity field (van Oudheusden, 2013):

(1)

where u and v represent the velocity magnitude in x and y d irection ,

Ma and u

the free

stream Mach number and free stream velocity respectively. If the viscous effects strongly affect

the flow behavior the problem becomes more complex and the momentum equation has to be

used:

(2)

In Charonko et al (2010) the challenges associated with the determination of in-field pressure

d istribution from PIV are analyzed and d ifferent topologies of integration methods are

compared . Two different techniques exist that are used to integrate the pressure field from the

momentum equation: a d irect pressure integration from the momentum equation and the

solution of the Poisson problem, which is obtained by applying the d ivergence operator to the

momentum equation. A d irect integration method was developed at first by Liu and Katz (2006),

where a four-exposure PIV system was used for measuring the material acceleration term. Omni-

d irectional path integration was then used for the integration of the pressure gradient. The

pressure was then averaged from the value obtained for d ifferent integration paths. This method

2( )pt

uu u u

2 122

2

11 1

2

p u vMa

p u


presents two main d isadvantages: the high integration time and the effect of the errors which are

transported through the integration path. In the last years the Poisson problem became of broad

interest for reconstructing the pressure field to avoid both drawbacks (van Oudheusden, 2013).

Furthermore, this approach is also well suited for applications of fast flows were no time

resolved PIV measurements are possible. In this case the analysis is based on the Reynolds

equation. As we are interested in transonic flows, in this work the mean pressure field is

investigated using the Poisson solution of the Reynolds equation:

(3)

where p represents the mean pressure, the mean density, u and v the mean velocity

component in the x and y direction respectively, 'u and 'v their fluctuations. In Equation 3 all

the components in the z direction are neglected as a 2D model was used for the PIV

experiments. In case of flows around 3D models a volumetric measurement technique is

required to resolve all terms in the Reynold s equation. All the kinetical quantities on the righ t

side of Equation 3 can be obtained with a classical window -correlation PIV using an ensemble of

individual measurements. For compressible flows, the density is an unknown variable that

also has to be determined and which is dependent on both, the pressure and the temperature.

Therefore, additional equations have to be introduced , i.e. the ad iabatic flow condition and the

ideal gas law. The use of the ad iabatic flow assumption is also reasonable for the viscous region,

if the heat transfer is not significant, as reported in Souverein et al (2010). For the Poisson

equation, boundary conditions are needed at each boundary point. The conditions could be both

of Neumann and Dirichlet type, where the latter gives more stability to the calculation process

(Englisch and Seba, 1985). The Neumann boundary condition can be easily derived from the

Reynolds averaged momentum equation. The Dirichlet boundary condition can be represented

from pressure-taps installed on the model surface, PSP pressure data, or pressure values derived

with the isentropic flow assumption in the undisturbed potential flow region (Equation 1).

Different mathematical procedures are then available to solve Equation 3 (van Oudheusden,

2013).

Next two d ifferent flow cases will be analyzed in order to examine in which case PIV could

represent a possible PSP replacement and when PSP can be seen as the only possible technique

for measuring the pressure d istribution on the model surface.

2 2 2 22 2 2 2 2 2

2 2 2 2 2 2

' '' '( ) ( )2 2

u vu vuvp p u v

x y x yx y x y x x

c

d


Figure 1: Experimental setup for the PSP and PIV measurements: 5-MPx sCMOS camera for PIV (a), two 11-MPx

PCO 4000 CCD camera for PSP (b), 405 nm high power LED (c), laser light sheet (d )

3. Experimental arrangement

3.1 NACA 0012

A NACA 0012 profile with a chord length of 150c mm was used for the first investigation.

The model is made out of steel and has 48 pressure taps split across the top and the bottom sides

of the model, in order to be able to simultaneously measure the pressure on both sides. The

experiments were conducted in the Trisonic Wind Tunnel Munich (TWM) which is described by

Bitter et al (2010). The model was mounted between the glass windows in the sidewalls of the

test section. The angle of attack was varied in the range between -4° and -6°. An illustration of the

combined PIV and PSP experimental setups is shown in Figure 1.

The PIV camera was installed on a mount d irectly connected to the model, so that the field of

view (FOV) remained the same for each angle of attack. A 5-MPx sCMOS camera with a 50 mm

Zeiss macro planar objective was used for the standard 2C2D PIV measurements. The FOV

covered a region of 200 × 150 mm² . A Nd:YAG double pulse laser with 100 mJ pulse energy at

15 Hz was used for particle illumination. The laser was operated with two double pulses and the

pulse separation time Δt was 3 µs. The light sheet, with a thickness of roughly 1.6 mm, was

positioned several millimeters next to the PSP paint in order to reduce the intensity of scattered

light by the paint. The light sheet illuminated the seeding particles from the top of t he model, in

order to illuminate the whole velocity field around the model (also in the proximity of the nose).

A standard multi-pass cross-correlation processing, with decreasing interrogation window size

(64px² → 16px² ), was applied to the masked -out double-frame images. The PIV results were

ensemble-averaged using 500 double frame images.

(a)

(b)

(d )

(c)

(b)


On the model surface a PtTFPP based binary paint (ISSI, Binary FIB PSP) was used for

comparison. The paint is composed from a reference dye emitting at 500 < λ < 580 nm and an

active dye emitting at λ > 650 nm. This paint is characterized by a strong model adhesion and

negligible temperature dependence. A white screen layer below the paint was used to

homogenize the surface background. The paint was illuminated with a 10 Watt high-power-LED

operating in a pulsed mode at 400 nm. For PSP measurements two 14 bit PCO 4000 CCD

cameras were mounted on the top. Their view was deflected by around 80° with a mirror. Two

35 mm Zeiss objectives were installed . On each objective lens of the cameras, a filter was

mounted in order to separate the two signals. A red filter enables to acquire the pressure signal

and a green one records the reference signal. Before the image acquisition, all components were

allowed to reach thermal equilibrium.

3.2 Backward-facing Step

The transonic flow around a backward -facing step (BFS) was investigated because it is of great

scientific interest and it is well-documented in Bradshaw and Wong (1972), Eaton and Johnston

(1981), Weiss et al (2009), Scharnowski and Kähler (2015). Furthermore, the flow topology

preserves various features which are of strong aerodynamic interest, such as flow separation and

periodic and stochastic reattachment, strong and thin shear layers, and significant pressure

gradients. The pressure reconstruction method was tested with 2D data ob tained from an LES

simulation (Statnikov et al, 2010). From this data set, 600 velocity fields were extracted for the

analysis to generate synthetic images which possess realistic measurement quality and

resolution of a standard PIV experiment. An example of one-time step of the LES velocity field

and a corresponding PIV particle image d istr ibution is presented in Figure 2.

Figure 2: Velocity and pressure flow field delivered from the LES simulation (left) and instantaneous synthetic PIV

snapshot (right)


4. Results

4.1 NACA 0012

The flow around the NACA 0012 profile w as investigated for d ifferent angle of attack at Mach

number Ma = 0.6 and Reynolds chord number 2.3 × 106. In Figure 3 the PIV and PSP results for

the angle of attack =6° and a stagnation pressure 0p =1.3 bar are presented . The velocity field

was obtained by averaging 500 instantaneous velocity field s. The spatial resolution is about 10

pixels mm -1. The PSP surface pressure d istribution was estimated by averaging 10 wind -on

images. The data was projected and processed on a rectangular surface grid with 1 × 1 mm²

spatial resolution. The pressure coefficient pc was derived as follows:

(4)

2

/ 1

1

2

p

p p p pc

qM

Figure 3: Mean-time velocity field from PIV and PSP pressure d istribution on NACA 0012 airfoil


From the pressure surface d istribution, it can be seen that the flow is characterized by a 2D

behavior in spanwise d irection which permits to compare the PSP with the PIV-based pressure

results which were measured next to each other. Unfortunately, it was impossible to resolve the

near wall flow field due to the light laser scattered on the model surface and a lack of seeding

close to the wall.

Figure 4: Pressure d istribu tion comparison; dots: pressure orifices data; solid line: PSP data; dashed line: PIV-based

data taken at 4 mm from the surface; dotted line: critical cp


Figure 6: Pressure deviation to the pressure-taps data for the PIV-based reconstruction (empty) and for PSP (filled)

However, at such high Reynolds number the boundary layer thickness is very small as long as

the flow is fully attached and therefore, the pressure in the flow field outside the boundary layer

can be easily determined with an ad iabatic flow assumption as reported in Equation 1. Figure 4

shows the comparison between the PIV-based pressure reconstruction and the PSP data which

was extracted on the plane of symmetry at y = 0 for a d irect comparison. Both measurements

can be d irectly compared with the pressure-tap measurements. The tests at an angle of attack of

2° and 4° were also performed for -2° and -4° because in this way the pressure flow field on both

sides of the model can be reconstructed employing the symmetry of the airfoil. The

Figure 5: Pressure compared through lines normal to the profile; dot: pressure orifices; triangle: PIV-based pressure

based on the isentropic relation; line: extrapolated data


measurements at an angle of attack of = 4° show a pressure d istribution with the maximum

value of pc near the critical region. Therefore, at higher angle of attack a superson ic flow region

is expected . At = 6° a supersonic region appears and a quasi-normal shock occurs at

approximately /x c = 0.1.

The PSP pressure d istribution fits very well with the pressure taps data. Some higher

d iscrepancies appear only at = 6° in the leading edge region because of the low spatial

resolution in that region due to the strongly curved model surface, together with the high

pressure gradient. The PIV-based surface pressure d istribution shows significant systematic

d iscrepancies with both the PSP and the pressure tap data. Due to the laser light reflections at the

model surface no velocity information was measured in the n ear wall region and the pressure

d istribution can be only derived up to 4 mm above the model. Therefore, in the leading edge

region, where the pressure gradient normal to the surface is large, high d iscrepancies occur. To

better analyze the PIV-based results, it was decided to extrapolate the pressure d istribution also

in the region where no PIV information could be measured by using a second order

extrapolation line. The extrapolation is presented in Figure 5. The pc profiles were extracted

along lines perpendicular to the airfoil contour close to the pressure taps position in order to

have a d irect comparison. With that extrapolation the d iscrepancies between the PIV-based and

the pressure orifices data reduce drastically. In order to better quantify the d iscrepancies

between the d ifferent measurement processes a new parameter was introduced

(5)

where p represent either the PIV-based or the PSP pressure value. The results are presented in

Figure 6. It can be seen that despite the drastic reduction of the d iscrepancies with the

extrapolation, the d iscrepancies remain pretty high in the leading edge region (up to 10%). In the

same region PSP presents uncertainties in the order of up to 2.7%. Only after 30% of the chord

length the d ifference between the pressure-tap measurement and the PIV-based resu lts are

below 3%.

[%] 100

orifice

dev

orifice

p p

p


4.2 Backward-facing Step

A total number of 600 synthetic double frame PIV images were evaluated in order to derive the

mean velocity field and the Reynolds stresses needed to solve Equation 3. The d igital resolution

of the synthetic PIV images is about 4.25 pixels mm -1. The double frame images were evaluated

using a standard multi-pass window-correlation algorithm with decreasing correlation window

size (48px→12px) and 50% overlap, resulting in a vector grid spacing of about 5% of the step

height. For the pressure reconstruction, central d ifferences were used to derive all the spatial

derivatives. A schematic view of the applied boundary conditions is presented in Figure 7. In the

outer main flow, the pressure can be evaluated using the isentropic relation. Therefore the

Dirichlet boundary condition is used on the top of the frame. Neumann boundary conditions,

extracted from Reynolds averaging the momentum equation, were used where this assumption

cannot be used because the viscosity effects become relevant. The density was derived with an

iterative method: the temperature in the domain was estimated based on an ad iabatic flow

assumption. At each iteration step the density was computed from the ideal gas law using the

pressure value from the previous iteration step. The calculation converged after about 20

iterations, which takes about 20 seconds for this grid (272 × 122 pixel2) using a common binary

conjugate solver.

In order to analyze the stability of the pressure field result, d isturbances w ith a standard

deviation of 0.6% of the free-stream velocity were added to the velocity field . The pressure

surface d istribution for both the d isturbed an d undisturbed case is presented in Figure 8. In the

near-step region a deviation from the expected value up to 3% is reached. This is due to the high

velocity gradients that occur in this region which suffer more from averaging the motion of

several particle images within the interrogation window (Kähler et al, 2012) and because the

calculation of the first and second order derivatives. The deviation trend then presents a smaller

peak in the reattaching region, which becomes much more relevant if any noise is introduced .

Figure 7: Schematic representation of the model, the flow field and the boundary condition

p

x

p

x

p

y

isp


5. Summary and Conclusions

The present work has investigated the accuracy in PIV-based surface pressure reconstruction on

an airfoil model and on a backward -facing step in the transonic flow regime. Furthermore, it was

examined weather PIV may be regarded as a complementary method to PSP or even a possible

replacement.

For the attached flow around a NACA 0012 airfoil, real 2D2C PIV experiments were conducted .

The PIV-based pressure surface d istribution and the PSP data can be d irectly compared with the

pressure-tap measurements. The PIV-based pressure reconstruction deviates with respect to the

pressure-taps data by up to 10% in the lead ing edge region. After 30% of the chord length the

deviation reduce to about 3%. The PSP data matches the classical pressure tap data very nicely.

Therefore, PSP surface pressure measurements should be performed if high accuracy surface

pressure results are needed.

For the separated flow around the backward -facing step synthetic double frame PIV images

from a LES simulation were analyzed to avoid limitations due to seeding and wall reflections.

The pressure flow field was derived and compared with the expected value of the LES

simulation. In the near-step region, where high velocity gradients occur, a deviation with the

expected value of up to 3% was observed . The deviation trend then presents a smaller peak in

the reattaching region, which becomes much more relevant if any noise is introduced . It can be

concluded that measurement uncertainties in the velocity data strongly affect the quality of the

final pressure d istribution. Furthermore, in the case of strong velocity gradient high

measurement resolution and sophisticated methods for determination of gradients are necessary.

Acknowledgements: The authors gratefully acknowledge the Grant Agreement (GA 605151) of

the FP 7 project NIOPLEX funded by the European Union supporting this ongoing research.

Figure 8: Pressure coefficient d istribution with and without noise compared to the original LES d istribution (left)

and deviation to the LES value (right)


6. Literature

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a generic rocket model in sub- and supersonic flows. Experiments in Fluids, DOI

10.1007/ s00348-010-0988-8

Bitter M, Hara T, Hain R, Yorita D, Asai K, Kähler CJ (2012) Characterization of pressure

dynamics in an axisymmetric separating/ reattaching flow using fast-responding

pressure-sensitive paint. Experiments in Fluids, DOI 10.1007/ s00348-012-1380-7

Bradshaw P, Wong FYF (1972) The reattachment and relaxation of a turbulent shear layer.

Journal Fluid Mechanics, 52:113–135

Charonko JJ, Cameron VK, Barton LS, Vlachos PP (2010) Assessment of pressure field

calculations from particle image velocimetry measurements. Measurement Science

and Technology 21 105401

Eaton JK, JP Johnston (1981) A Review of Research on Subsonic Turbulent Flow

Reattachment. AIAA Journal, 19:1093–1100

Englisch H, Seba P (1985) The stability of the Dirichlet and Neumann boundary conditions.

Reports on mathematical phisics doi:10.1016/ 0034-4877(86)90028-5

Gouterman M, Callis J, Dalton L, Khalil G, Copper KR, Granier M (2004) Dual luminophor

pressure-sensitive paint: III. Application to automotive model testing. Measurement

Science and Technology doi:10.1088/ 0957-0233/ 15/ 10/ 007

Kähler CJ, Scharnowski S, Cierpka C (2012) On the resolution limit of d igital particle image

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four exposure PIV system. Experimental Fluids, 41, 227-240

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layer by means of PIV. Theoretical and Applied Mechanics Letters, 5:30–34

Schneiders JFG, Lynch K, Dwight RP, van Oudheusden BW, Scarano F (2014) Instantaneous

pressure from single snapshot tomographic PIV by Vortex-in-Cell. 17th International

Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal

Souverein LJ, van Oudheusden BW, Scarano F (2007) Particle image velocimetry based loads

determination in supersonic flows. AIAA Journal, 2007-0050

Statnikov V, Bolgar I, Scharnowski S, Meinke M, Kähler CJ, Schröder W (2015) Analysis of

characteristic wake flow modes on a generic planar transonic space launcher

configuration. Sixth European conference for aeronautics and space sciences

Van Oudheusden BW (2013) PIV-based pressure measurement. Measurement Science and

Technology 24(3):032001


Weiss PE, Deck S, Robinet JC, Sagaut P (2009) On the dynamics of axisymmetric turbulent

separating/ reattaching flows. Phys Fluids, 21:075103

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