estimation of pressure profile from piv data for the wake...

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

Estimation of Pressure Profile from PIV Data for the Wake Flow behind Vehicle

Y. Fukuchi1,*, Y. Murakumo1, M. Yonezawa2, K. Matsushima3 1: Automobile R&D center, Honda R&D Co., Ltd, Japan

2: Formerly Automobile R&D center, Honda R&D Co., Ltd, Japan 3: Dept. of Mechanical Engineering, University of Toyama, Japan

* Correspondent author: [email protected]

Keywords: PIV processing, Pressure estimation, Aerodynamics

ABSTRACT

The accuracy of pressure estimation methods from PIV data for the wake flow behind a ground vehicle was

investigated. The measurable domain of PIV and the boundary conditions are main issues to adopt the pressure

estimation method to the flow around a ground vehicle. To solve the first issue, the scanning stereoscopic PIV which

can measure the meter-scale flow structure was developed using the pneumatic seeder and was applied to the wake

flow of a ground vehicle. The averaged particle diameter of the pneumatic seeder is two times larger than it of

Laskin nozzle. The measured PIV data was applied to the input velocity of 2D/2.5D Poisson’s equation. The

estimated pressure profile using 2D Poisson’s equation shows the discrepancy from it of 2.5D Poisson’s equation at

the shear layer from the roof end of a vehicle model. Concerning about the second issue, the effect of boundary

conditions to the estimated pressure profile was investigated. The measurable domain of PIV with the pneumatic

seeder enables to use the isentropic process for the top boundary and the side boundaries. The pressure which is

calculated using the isentropic process corresponds to the measured pressure within the accuracy of differential

pressure sensors at the measured points by adopting the correction of the static pressure gradient of the wind-

tunnel, even the case of a low Mach-number condition. Nueman boundary condition is suit for the bottom

boundary for the case of the flow around a ground vehicle, because the flow is sensitive to the intrusive pressure

measurement probe at the boundary around the ground plane. The pressure measurement method using the

combination of the isentropic process boundary condition and Nueman boundary condition is a completely a non-

intrusive pressure measurement technique. The error analyses indicate the advantage of this method to the intrusive

pressure measurement probe for the case of the wake flow behind a ground vehicle.

1. Introduction

The importance of fuel efficiency is increasing year by year for the mass production ground

vehicles. The ratio of the aerodynamic drag in the running resistance is about 75-80 [%] at 100

[km/h] (Nakamura 2015), so the reduction of the aerodynamic drag is one of the key technology

to achieve high fuel efficiency.


To reduce the aerodynamic drag efficiently, the aerodynamic drag is resolved into the pressure

drag and the longitudinal vortex drag using CFD data (Machida 2015). Lots of optimization

works are conducted at a wind-tunnel, so it is desirable to realize the same method to resolve the

aerodynamic drag in a wind-tunnel with less time consumption.

The pressure estimation methods from PIV data are growing mature (Schmeiders 2014) due to

the recent progress of Tomographic PIV. Several examples of application in practical flow field

are reported (Oudheusden 2013). On the other hand, due to the size of flow structure, the

application of Tomographic PIV has still some issues, so multi-planes planner PIV is a realistic

measurement method in the case of flow around a ground vehicle. To compare with

Tomographic PIV and multi-planes planner PIV, the spatial resolution and grid points in the

out-of-plane direction have large difference, so the influence of resolution in the out-of-plane

direction was investigated (Matsushima 2011). In the study, the velocity data of CFD was used

instead of PIV data, so experimental validation is required.

Concerning about the boundary conditions for Poisson’s equation, Dirichlet boundary condition

is widely used in the case of the flow around a simple surface body. The hypothesis of the

isentropic process for the boundary condition is applied to the transonic flow around an air foil

(Ragni 2009). The combination of the isentropic process and Nueman boundary condition is

applied to the transonic flow around a simple bluff body and shows the accurate estimation of

pressure profile (Schneiders 2014).

In the case of a ground vehicle in a low Mach-number condition, there are some issues to apply

these boundary conditions, for example the accuracy of an absolute pressure sensor or the

presence of the static pressure gradient of a wind-tunnel along the flow direction. The boundary

condition around ground plane is also an issue. The use of a wind-tunnel with a rolling road

system will be common in the near future to simulate the flow of the real world with high

accuracy, so the investigation of suitable boundary conditions around a ground plane is required.

In this study, various kinds of boundary conditions in a low Mach-number condition around a

ground vehicle were investigated using large scale planner PIV.

2. Estimation method of pressure profile from PIV data

For the case of aerodynamic drag of commercial vehicles, the time dependence does not have

significant importance, so three-dimensional Poisson’s equation for pressure is expressed as

Equation (1) to assume the time depend terms are zero.


{(

)

(

)

(

)

(

)

}

(

) (1)

Where

(2)

It is not difficult to calculate the terms of x-derivatives of velocity vectors using scanning

stereoscopic PIV or Tomographic PIV. On the other hand, to provide a pressure profile using a

Dirichlet condition for x-direction is an unrealistic boundary condition, so second order x-

derivatives of pressure in the left-hand-side of Equation (1) should be eliminated. To take an x-

derivative of Navier-Stokes equation (3) and to assume the time depend terms are zero, Equation

(4) is obtained.

(

) (3)

(

)

(

) (4)

Equation (5) is formulated by subtracting Equation (4) from Equation (1). The second order x-

derivative of pressure term is eliminated in Equation (5). As a result, the input pressure data at

the boundary is only required in a plane where the pressure profile is estimated. Equation (5)

and Equation (6) are considered as 2.5-dimensional Poisson’s Equation (Kat 2008, Matsushima

2011).

{(

)

(

)

(

)

𝐸

𝐸

𝐸

}

( 𝐸

𝐸

𝐸

) (5)

Where

(6)

2-dimensional Poisson’s Equation is also shown in Equation (6) and (7) by assuming the terms of

x-derivatives are zero. The results from each equations were compared in this study.


{(

)

(

)

𝐸

𝐸

}

( 𝐸

𝐸

) (7)

These equations are computationally solved by a finite difference discretization and the SOR

method.

The influence of several boundary conditions, Dirichlet boundary condition, Neuman boundary

condition and the isentropic process boudanry condition, to the accuracy of the estimated

pressure profile were also studied. To avoid confusions, “Dirichlet boundary condition” means

that Dirichlet boundary condition was given using the pressure measurement data and

“isentropic process boudary condtion” means that Dirichlet boundary condition was given using

the isentropic process in this study. Dirichlet boundary condition was given by pressure rake

sensors at top, bottom, left and right boundary of measured domain. Nueman boundary

condition was applied at the bottom boundary because the boundary layer at ground plane was

sensitive to the blockage of pressure rake sensors. The pressure gradient was assumed as zero

along z-direction at the bottom boundary for Nueman condition in this study.

In the case of the isentropic process condition, the pressure profile at the boundary of the

measured domain was estimated by Equation (8). Where is the heat capacity ratio of air, M is a

Mach number, U∞ is a velocity of free-stream and P∞ is an absolute pressure of free-stream.

[{

(

)}

] (8)

Where (9)

The pressure profiles were estimated at sevral boundary conditions as shown in Table1.

Table 1 Models of Poisson’s equation and boundary conditions.

Poisson’s eq. Top B.C. Left & right B.C. Bottom B.C.

Case 1 2D model Dirichlet Dirichlet Dirichlet

Case 2 2.5D model Dirichlet Dirichlet Dirichlet

Case 3 2.5D model Isentropic process Isentropic process Dirichlet

Case 4 2.5D model Isentropic process Isentropic process Nueman


3. Experimental setup and conditions

Experiments were conducted in the in-house wind-tunnel as shown in Figure 1, for a quarter

scale vehicle model, with a 2.3 x 1.3 [m2] nozzle, open-jet and Gottingen type. A boundary layer

is suctioned in front of the test section. A rolling road system (RRS) with 5 belts is installed at the

test section.

The quarter scaled wind-tunnel model of the second generation of FIT/JAZZ (Length=975.00

[mm], Width=423.75 [mm], Height=381.25 [mm]) as shown in Figure 2 was made of aluminum

with mat black alumite treatment to reduce the reflection from the body. This model has rolling

tires, simplified under-floor structures and has not an engine room. The model was fixed to the

rolling road system using four rods from balance system.

The test conditions are shown in Table 2. The free stream velocity was set to 27.7778 [m/s]. Re#

was based on the length of the vehicle model. The temperature was maintained constant by the

radiator of the wind-tunnel.

Table 2 Test conditions.

RRS U

[m/s]

Static absolute

pressure [Pa]

T

[oC]

Humidity

[%]

Re# [kgf/m3] Speed of

sound [m/s]

Off 27.7778 101430 21.2 20.2 1.4 1.8x106 1.19884 344.0

Figure 1 shows the diagram of the pressure measurement. The reference pressure for the

pressure rake probe was measured at the nozzle of the wind-tunnel using a pitot tube. The origin

was set at just behind the vehicle model and on the ground. The absolute static pressure for the

input of the isentropic process was measured using an atmosphere pressure sensor (M2.10670JA-

A, ±30Pa, VAISALA Co., Ltd.) at the contraction area of the wind-tunnel.

In the case of using the hypothesis of the isentropic process for the boundary condition, the static

pressure gradient along x-direction in the wind-tunnel is not negligible small when the data is

compared with the measured pressure data behind the vehicle model. The level of static

pressure was set as zero at the center of wheel-base. Figure 1 shows the static pressure gradient

at test condition along the center line of the wind-tunnel at z=200 [mm] line. The measured

pressure data at the test section was corrected using this pressure gradient curve for the

validation of the estimated pressure profile and the Dirichlet boundary condition.


Fig. 1 Diagram of pressure measurements and the static pressure gradient along the center line

of the wind-tunnel.

Total pressure profile behind the model was measured using the pressure rake probe as shown

in Figure 2 to provide the boundary condition and the validation data. The pressure rake probe

was swept by the traverser from the ceiling of the wind-tunnel. The data was averaged in 10

[seconds]. The pressure rake probe has 30 ports of sensors and the spacing of each sensor in y-

direction is 12.5 [mm]. Two of DSA3217 sensors (F.S. 1 [psi], 16 [channels], Scanivalve

Corporation) were used. Total pressure profile was measured with 50 [mm] pitch in z-direction,

and the pressure measurement points were interpolated to fit the vector grid of PIV using a bi-

linear interpolation method.

Fig. 2 Total pressure measurement probe.


Figure 3 shows the configuration of large-scale PIV for the wake flow of a vehicle. A double-

pulsed Nd: YAG laser (200 [mJ], 15 [Hz], PIV solo200, New Wave Research) was set up one side

of the rail and sCMOS camera (2560x2160 [pixels], Imager sCMOS, LaVision GMBH) with Nikon

f = 50 [mm] lens (AF-S NIKKOR 50mm f/1.8G, Nikon CORPORATION) were set up on both

sides of the rails which were set beside the test section of the wind-tunnel. The measured plane

was shifted using this rail system without any extra alignment and calibration.

Fig. 3 Schematics of the scanning stereoscopic PIV.

The measured domain should be enough large to measure free stream velocity for the use of the

isentropic process as a boundary condition. To enlarge the measurement domain, the pneumatic

seeding nozzle (Fukuchi 2016) was used. Figure 4 (a) shows the schematics of the pneumatic

seeding nozzle. A pneumatic seeding nozzle is covered by a cylindrical-type fairing to reduce

large particles which do not follow the flow and contaminate the wind-tunnel and models.

Figure 4 (b) shows a probability density function (PDF) of the particle diameter generated by the

pneumatic seeding nozzle and Laskin nozzle (PIV part40, SEIKA Digital Image Corporation).

DEHS is used as seeding oil for each nozzle. Laskin nozzle is widely used for PIV, and the mean

diameter of the Laskin nozzle is abount 1 [m]. On the other hand, the red line shows the PDF of

particles seeded by the pneumatic seeding nozzle. Tracer particles which are smaller than 4 [m]

tend not to attach to the walls of the wind-tunnel or vehicle in normal test conditions of

automobiles. It is clear that larger particles are eliminated by a cylindrical-type fairing. The mean

diameter of this pneumatic seeding nozzle with the fairing is about 2 [m].

The particle generation rate is also important to realize PIV in the large wind-tunnel. The particle

gerenaration rate of the pneumatic seeding nozzle is 2x108 [particles/s]. The seeding time for the

quater scale wind-tunnel was less than 20 [seconds].


Fig. 4 Pneumatic seeding nozzle for large scale PIV (a) Schematics of pneumatic seeding nozzle

with cylindrical fairing (b) Comparison of particle diameter.

The effect of the spatial resolution in x-direction to the accuracy of the estimated pressure

distribution was investigated prior to this experiment (Matsushima 2011). The accuracy becomes

worse when the spatial resolution in x-direction decrease from 2.5 [mm] to 10 [mm], but the

averaged error of estimated pressure which is caused by the high x-velocity gradient is 2.56 [%]

even in the case of 10 [mm] resolution. To consider about the thickness of laser sheet and the

accuracy of pressure sensors, the resolution in x-direction is set to 10 [mm], so the wake

distributions were measured using the scanning stereoscopic PIV at 380 [mm], 390 [mm] and 400

[mm] behind the model as shown in Figure 5. The measurement plane was shifted to the next

one after taking 1000 shots of particle image pairs. The measurement time including the shifting

the measurement system was enough long to take no account of time dependency of the wake

flow. The pressure distribution was estimated at the section of 390 [mm], and the others were

used to calculate the derivatives in x-direction. The measured region of PIV was set enough large

to make it possible to introduce the hypothesis of the isentropic process for the top and side

boundary condition. To ensure the enough quality of velocity data for Poisson’s equation, the

actual measured domain was set to 2400 [mm] x 1000 [mm] and then the high quality region

which was used as an input data of Equation (5) and (6) was cut out from the original measured

area. Interrogation window size was 32 x 32 [pixels] with 75% overlap, the spacing between

vectors was in y-direction and z-direction was 4.32 [mm] as a result. 1000 shots of flow field

distributions were averaged at 10 [Hz]. DaVis8.3 (LaVision GMBH) was used for this analysis.

The accuracy of PIV around the bottom boundary is sensitive to the estimated pressure

distribution, so the measured data which was higher than 50 [mm] above the ground was used

to avoid the effect of reflection from the rolling road system.

(a) (b)


Fig. 5 Measurement region of the scanning stereoscopic PIV.

4. Results and discussion

4-1. Comparison of the pressure estimation model

Figure 6 (a) and (b) shows the estimated total pressure field of Case 1 and Case 2 respectively.

The wake distributions are almost same, so to emphasis on this difference, the pressure

distribution of Case 2 is subtracted from it of Case 1. Figure 6 (c) shows the delta of the pressure

distribution. Figure 6 (d) shows the schematics of the wake flow behind this vehicle model. The

shear layer from the roof edge which is shown by dashed line locates around z=280 [mm] in the

measured plane. The large difference can be found at the shear layer. The difference is up to 10

[%] of total pressure of free stream in the area. This result indicates that 2D Poisson’s equation

model has not sufficient accuracy for the flow which has a strong velocity gradient in the out-of-

plane direction, like the wake flow of a ground vehicle.


Fig. 6 Comparison of estimated total pressure distribution (a) Result of Case 1, (b) Result of Case

2, (c) Delta of estimated pressure (d) Schematics of the wake flow behind the vehicle model.

To investigate the influence of x-derivatives, the equation of continuity is calculated for each case

as shown in Figure 7 (a) and (b). The divergence of velocity in Figure 7 (a) contains only dv/dy

and dw/dz. On the other hand, the divergence of velocity in Figure 7 (b) contains du/dx in

addition to the components of Figure 7 (a). The value of divergence of velocity is up to ±3 [1/s]

in Case 1, though it of the equation of continuity should be zero in this test condition. The values

of first order derivatives in Equation (5) are around ±10 [1/s], so the error of Case 1 is estimated

up to 30 [%]. On the other hand, the divergence of velocity is less than ±1 [1/s] in Case 2, so the

error of Case 2 is reduced to 1/3 of Case 1. The divergence of velocity in Case 2 becomes large

where not only du/dx becomes large but also dv/dy and dw/dz becomes large. This means that

the cause of error in Case 2 is not the accuracy of a difference scheme in x-direction.

The spacing of vectors is 4.32 [mm], so the maximum fluctuation error of the averaged velocity is

estimated 0.004 [m/s]. This value is 0.014 [%] of the free stream velocity and mainly dominated

by the number of averaged snap shots.

(a) (b)

(c) (d)


Fig. 7 Comparison of divergence of velocity (a) Result of Case 1, (b) Result of Case 2.

4-2. Comparison of boundary conditions

Figure 8 shows the comparison of the static pressure profile at the boundary between the

measured value and the calculated value using the hypothesis of the isentropic process at each

boundary. The measured static pressure value was calculated by subtracting the dynamic

pressure which is calculated using PIV data from the total pressure measured by pressure rake

sensors.

The discrepancy can be seen at the boundary layer which is lower than z=50 [mm]. The

hypothesis of the isentropic process is not satisfied in this region due to the boundary layer of

ground plane and has high accuracy at the other region. The calculated pressure profile using

isentropic process corresponds with the measured value within 5 [Pa]. This accuracy is 0.07 [%

F.S.] and almost corresponds to the accuracy of differential pressure sensors.

Fig. 8 Comparison of pressure profile estimated by the isentropic process condition (a) Top

boundary, (b) Left boundary, (c) Right boundary.

-40

-20

0

20

40

-600 -400 -200 0 200 400 600

Ps(measured)

Ps(Isentropic)

y [mm]

Ps

[Pa]

-50

0

50

100

150

0 100 200 300 400 500 600 700 800

Ps(measured)

Ps(Isentropic)

z [mm]

Ps

[Pa]

-50

0

50

100

150

0 100 200 300 400 500 600 700 800

Ps(measured)

Ps(Isentroic)

z [mm]

Ps

[Pa]

(a) (b) (c)

(a) (b)

[1/s]


The estimated pressures profile by several boundary conditions were compared with the

measured total pressure value along z=100 [mm], z=200 [mm] and z=300 [mm] as shown in

Figure 9, Figure 10 and Figure 11.

Figure 9 and Figure 10 show that the estimated total pressure of all cases well correspond with

the measured total pressure value in the wake region (-200 [mm] < y <200 [mm]). On the other

hand, the estimated total pressure profiles in all cases at the center of the wake region (-100 [mm]

< y <100 [mm]) is lower than that of measured one in Figure 11.

The total pressure profiles of Case 2 and Case 3 correspond within 5 [Pa]. This means that the

accuracy of the boundary condition using the hypothesis of the isentropic process has the same

accuracy concerning about at the top, left and right boundary.

The discrepancy between Case 4 and the others can be found at the free stream region in each

section. The estimated pressure profile of Case 4 is well correspond to the measured pressure

profile at free stream region, though the pressure profile using Dirichlet condition (Case 2 and

Case 3) shows higher value than experimental one. This fact indicates that Nueman boundary

condition is a suitable method for the bottom boundary in the case of a ground vehicle.

These errors are studied in the next section in detail.

0

100

200

300

400

500

600

-600 -400 -200 0 200 400 600

Pt(Measured)Pt(Case2)Pt(Case3)Pt(Case4)

y [mm]

Pt

[Pa]

Fig. 9 Comparison of pressure profile estimated by each boundary conditions at z=100 [mm].


0

100

200

300

400

500

600

-600 -400 -200 0 200 400 600


y [mm]

Pt

[Pa]


200

250

300

350

400

450

500

550

-600 -400 -200 0 200 400 600


y [mm]

Pt

[Pa]


4-3. Error analysis

Experimental error of total pressure measurement is assessed in this section, because the error of

the scanning stereoscopic PIV is already assessed in Section4-1. Figure 12 (a) shows the total

pressure distribution measured by the pressure rake probe. Figure 12 (c) is the calculated static

pressure distribution by subtracting the dynamic pressure distribution which is calculated using

PIV data from the total pressure distribution measured by the pressure rake probe.

The static pressure distribution shows high value around z=300 [mm] line in the wake region.

This static pressure distribution around the shear layer from the roof end of the vehicle model is


a non-physical static pressure distribution. To compare with the position of its shear layer

between Figure 12 (a) and Figure (b), the position of the shear layer measured by the pressure

rake probe located lower than it of the shear layer measured by PIV. There are some possibilities

of this reason about that the position of the shear layer from the roof end of the vehicle model is

forced down due to the blockage of the pressure rake probe with the traverse system from the

ceiling of the wind-tunnel. This blockage is not sensitive to the shear layer from the side edge of

the vehicle model and in the wake, so the measured pressure profile and the estimated pressure

profile correspond at z=100 [mm] and z=200 [mm] line.

Fig. 12 Error analysis of pressure measurement value in the wake (a) Total pressure distribution

measured by the pressure rake probe, (b) Dynamic pressure distribution measured by PIV, (c)

Static pressure distribution.

The deviation at the outer region of wake was also investigated. The blockage of the pressure

rake probe with the traverse system also affect to the boundary layer around the ground plane,

because the static pressure shows high value at the outer region of wake in Figure 12 (c). To

investigate this issue, the static pressure was measured using single pitot tube. The pressure

holes of a pitot tube spread from the traverse system to reduce the effect of its blockage as shown

in Figure 13 (a). Figure 13 (b) shows the comparison of static pressure profile from y=-300 [mm]

to -500 [mm]. White symbols are the static pressure value in the Figure 12 (c), and black symbols

are the results of pitot tube measurements. The static pressure profiles measured by a pitot tube

are constant along z-direction, on the other hand, the static pressure profile measured by

pressure rake probe decrease along z-direction. The results of pressure rake probe shows higher

value along z=50 [mm] and z=60 [mm] line. This fact indicates that the pressure data for

Dirichlet condition for the bottom boundary includes large error at the outer region of wake, so

the estimated pressure profile using Nueman boundary condition shows the higher accuracy for

the bottom boundary.

(a) (b) (c)


Fig. 13 (a) Static pressure measurement around ground plane using a pitot tube, (b) Static

pressure profile besides the vehicle.

5. Conclusion

The scanning stereoscopic PIV which can measure meter-scale flow structure was developed

using the pneumatic seeder and was applied to the wake flow of a ground vehicle. The

measured PIV data was applied to the input velocity of 2D/2.5D Poisson’s equation. The

estimated pressure profile using 2D Poisson’s equation shows the discrepancy from it of 2.5D

Poisson’s equation at the shear layer from the roof end of a vehicle model.

The measurable domain of PIV with the pneumatic seeder enables to use the isentropic process

for the top boundary and the side boundaries. The pressure which is calculated using the

isentropic process corresponds to the measured pressure within the accuracy of differential

pressure sensors at the measured points by adopting the correction of the static pressure

gradient of the wind-tunnel, even the case of a low Mach-number condition.

Nueman boundary condition is suit for the bottom boundary for the case of the flow around a

ground vehicle, because the flow is sensitive to the intrusive pressure measurement probe at the

boundary around the ground plane.

The pressure measurement method using the combination of the isentropic process boundary

condition and Nueman boundary condition is a completely a non-intrusive pressure

measurement technique. The error analyses indicate the advantage of this method to an intrusive

pressure measurement probe for the case of the wake flow behind a ground vehicle.

(a) (b)


6. Future works

In this study, the height of the bottom boundary is relatively high to consider about the

importance of the flow structure around the ground plane. The accuracy of PIV data around the

ground plane is affected by the reflection from the ground plane and the velocity gradient along

z-direction exist. The method to set Nueman boundary condition using such data should be

studied as a future work.

7. Acknowledgements

The data analysis for the estimation of pressure profile was supported by Etsuya Kimura and

Ryodai Namba, graduate students of University of Toyama. Their careful works are greatly

acknowledged.

8. References

o Yuichi Fukuchi, Jun Sawada, Masato Nakajima, Yutaka Murakumo (2016) Development of a

New Pressure Measurement Technique and PIV to Validate CFD. SAE technical paper. o R de Kat, Bas W. van Oudeusden, Fulvio Scarano (2008) Instantaneous planar pressure field

determination around a square-section cylinder based on time-resolved stereo-PIV. 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics.

o Kentaro Machida, Munetsugu Kaneko, Atsushi Ogawa (2015) Aerodynamic Development of

the New Honda FIT/JAZZ. SAE technical paper. o K. Matsushima, M. Yonezawa, A. Ogawa, H. Motohara (2011) Examination of a Pressure

Estimation Method using PIV Measurement Data for Automobile Development. 11th Asian Symposium on Visualization.

o Daisuke Nakamura, Yasuyuki Onishi, Yoshiyasu Takehara (2015) Flow Field Analysis in the Development of the 2013 Model Year Accord Hybrid. SAE technical paper.

o Bas W. van Oudeusden (2013) PIV-based pressure measurement. Measurement science and technology 24.

o Jan F. G, Schneiders, Kyle Lynch, Richard P. Dwight, Bas W. van Oudeusden, Fulvio Scarano

(2014) Instantaneous Pressure from single Snapshot Tomographic PIV by Vortex-in-Cell. 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics.

o D. Ragni, Bas W. van Oudeusden, Fulvio Scarano (2009) Surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image Velocimetry. Measurements science and technology 20.

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