Simultaneous Measurement of Velocity and Temperature

1 Copyright © 2011 by ASME

SIMULTANEOUS MEASUREMENT OF VELOCITY AND TEMPERATURE DOWNSTREAM OF A HEATED CYLINDER

Péter Bencs Department of Fluid and Heat Engineering,

University of Miskolc Miskolc, Hungary

Szilárd Szabó Department of Fluid and Heat Engineering,

University of Miskolc Miskolc, Hungary

Róbert Bordás Laboratory of Fluid Dynamics

and Technical Flows, University of Magdeburg

“Otto von Guericke” Magdeburg, Germany

Katharina Zähringer Laboratory of Fluid Dynamics



Dominique Thévenin Laboratory of Fluid Dynamics



INTRODUCTION Bluff bodies placed in a flow, such as electrical

transmission lines, cartridge heaters, pipes of heat exchangers,

factory chimneys and so on, often have a different temperature

compared to that of the surroundings. The structure of the flow

developing around bluff bodies has been investigated for a long

time (Adrian, 1991; Williamson, 1996). The Kármán vortex

street was and is examined by numerous researchers, both

experimentally and numerically. Nevertheless, the question

arises as to how this vortex street is modified by a heated

cylindrical bluff body. What is the influence of heating on the

frequency of the detaching vortices, the structure of the vortices

and the location of the detachment? Many of these questions

have already been answered by the help of numerical

simulations and of measured velocity distribution using Particle

Image Velocimetry (PIV) and the vortex distributions obtained

from this (Venkatakrishnan and Meier, 2004). A further

question is the heat loss caused by the vortex structure and the

forced convection. To tackle this question, the Background

Oriented Schlieren (BOS) method is applied here. At the same

time, first steps have been taken towards determining

temperature and vortex distributions simultaneously, which are

introduced in this paper. Main objective and novelty of this

work is the solution for the mentioned measurement problem

with a single camera.

The objective of this work was to carry out non-intrusive

measurements of both temperature and flow fields, by means of

BOS and PIV respectively, using the experience from previous

research (Wang and Trávniček, 2001; Baranyi et al., 2008;

Bencs et al., 2009; Baranyi et al., 2009; Bencs et al., 2010). The

flow was investigated behind a heated cylinder, mounted in a

Göttingen-type (closed-loop) wind tunnel, with suitable

conditions. Future intention is to validate existing numerical

calculations. This project is a fundamental research, which is

supported by Hungarian, German and European Union projects.

1. EXPERIMENTAL SETUP The experimental setup (Fig. 1) is mounted in a closed-

loop wind tunnel. The cross section of the test area had the

dimensions of 500x600 mm.

Figure 1. Schematics of the experimental setup

Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference PVP2011

July 17-21, 2011, Baltimore, Maryland, USA

PVP2011-57789


Mean velocity was set to v=0.3 m/s, since this was the

minimum stable velocity of the wind tunnel in this

configuration. This led to a wind tunnel Reynolds number of

Re=11,000, calculated from the mean flow velocity in the test

section, the hydraulic diameter of the wind tunnel and the

viscosity of air at ambient temperature. Two transparent

windows were mounted on both sides of the measurement

section, with a hole in the middle, used to mount the heated

cylinder perpendicular to the main flow direction (see Fig. 1).

The cylinder with a diameter of d=10 mm was electrically

heated by an adjustable transformer. The mean temperature of

the cylinder was measured by a thermocouple and the power of

the transformer was set to the required value. The cylinder

Reynolds number was Recyl=200, calculated with the mean flow

velocity, the diameter of the cylinder and the viscosity of air at

ambient temperature.

2. PIV/BOS SYSTEM The system used for the present measurement was a

regular 2D-PIV system, consisting of the components listed in

Table 1.

Table 1. Description of the PIV/BOS system Component Remarks Manufacturer

Double frame

CCD camera

Flow Sense 2M/E with

8 bit resolution, recording

frequency: 15 Hz

Dantec

Dynamics

Lens

Manual Focus Nikkor

180 mm; f-number: 11,

focus set to ~4 m

Nikon

Double pulse

Nd-YAG laser

Power: 2x300 mJ at

532 nm, max. frequency:

fr=15 Hz

Litron

High-energy

mirrors

for a wavelength of

532 nm

CVI Melles

Griot

Laser sheet-

optics f = -10 LaVision

Timer box TTL logical electronic unit

to trigger laser and LEDs

Self-

produced

PC with a

frame grabber

card and PIV

software

For image data acquisition

and for processing of

acquired data

Dantec

Dynamics

The applied software for the acquisition and evaluation of

data was commercial PIV software package (Dynamics Studio

3.0 from Dantec Dynamics), used for both PIV and BOS

measurements. The PIV measurements are only briefly

discussed here, since there are numerous publications

describing the principles of PIV (e.g., Wang and Trávniček,

2001). The same camera was used for both PIV and BOS

measurements. The camera was calibrated with the help of a

calibration plate to set the pix/mm factor and to eliminate

possible distortion. Camera optics was focused on the

calibration plate and the f-number (the focal length of the lens

divided by the “effective” aperture diameter) was set to 11.

2.1.Timer Box and synchronization PIV and BOS pictures were recorded successively (timing

scheme is shown in Fig. 2). The measurement area was lit by

the laser (at PIV recordings). The background (during BOS

measurements) was lit by LEDs (shown in Fig. 4). This timer

box (with timer electronics) was developed for the present

PIV/BOS measurements. A block diagram of the timer box is

shown in Fig. 3. Main task of the timer box was to trigger the

laser and LEDs during the alternating PIV/BOS recordings so

that the timing scheme in Fig. 2 was assured. The essence was,

that one single camera could record successive PIV and BOS

images with relatively small time intervals. For PIV evaluation

double frame images were recorded, while in case of BOS

recordings, only the second frame was lit and used for the

correlation. The reference image for BOS was taken prior to the

measuring sequence.

Figure 2. Timing diagram

The timing diagram of the synchronization method

assuring that the temperature and velocity information were

synchronized as shown in Fig. 2, with the time-intervals:

1,2 1A s , 1,500B= s , 66,667C = s .

TTLDelay

Generator

HUB

Laser Q-Switch 2

Converter

LEDs

Flashlamp 2

Laser Q-Switch 1

Flashlamp 1

AC 230 V

Q1

(in)

Q2

(in)

Q1

(out)

Q2

(out)

+ -

-+

Figure 3. Schematics of the timer box setup

Both PIV and BOS images were made in the same

recording. The measurement area was lit by the laser (at PIV

recordings). The background (for BOS measurements) was lit

by LEDs (Fig. 4). LEDs were placed between the wind tunnel

and the background plane (Fig. 1).


LEDs

Background

Figure 4. Experimental LEDs setup

The time lag between two succeeding frame pairs was

specified by the recording frequency of the applied camera:

1/ 1/ 15 66,666 .C fr Hz s (1)

Therefore, the time difference between two PIV and two BOS

recordings was:

2 .P B= = C = 136,333 s (2)

This means a recording frequency of 7.33P Bfr = fr = Hz for

separate PIV and BOS image sequences. According to previous

research (Baranyi et al., 2009), the vortex shedding frequency

for the present case is vfr 4.85 Hz , considering both branches

of the vortex street. Thus, the recording frequency is about 3

times larger than that of the vortex shedding, when considering

a single branch. Therefore, even the present camera with a

recording frequency of 15 Hz is suitable to capture each vortex.

Thus, an interpolation of the velocity field and its derivatives

was possible for time instances between two recordings. Of

course, the accuracy of interpolation is expected to increase

with higher recording frequencies.

From the timing scheme (Fig. 2) it can be seen that the PIV

(velocity) and BOS (temperature) distributions are not recorded

simultaneously but successively: PIV1, BOS1; PIV2, BOS2; …

PIVi, BOSi,; …. Time instances belonging to the recordings are

P,1 , B,1 ;

P,2 , B,2 ; …

P,i , B,i ; …, respectively. Therefore,

during the evaluation, each deflection vector pair of two

consecutive BOS images was linearly interpolated according to

the time instance of the enclosed PIV image. The temperature

P,iT belonging to the velocity P,iv of a given time

instance P,i can be interpolated using the relation:

, , 1

, , 1 , , 1

, , 1

.P i B i

P i B i B i B i

B i B i

T = T T T

(3)

3.2. Particle Image Velocimetry Measurements For PIV measurements the background was not illuminated

and the TTL electronics turned on the laser light. Oil droplets of

3 µm in diameter were added to the flow as tracer particles and

the measurement plane was lit through the light sheet optics by

a doubled Nd:YAG double pulse. The velocity field was

calculated from the scaled images using cross-correlation with

a 64x64 pixel interrogation area, using 75% overlap. The

resulting vector maps were then exported to ASCII files for

later visualization using Matchad® v14 and Matlab® R2009a.

3.3. Background Oriented Schlieren Measurements For BOS measurements a background with white noise

dots was printed and placed 519 mm behind the plane of focus.

The background was illuminated homogeneously with LEDs

(every second double frame), such that the same f-number

could be applied as in case of the PIV measurements. The

Schlieren recordings were carried out in double frame mode

(where only the second frame was used). The time lag between

two double frames, B=1,500 µs (see Fig. 2), was important for

the calculation of the deflection from the exported correlation

information. The cross-correlation was carried out with an

interrogation area of 32x32 pixels and an overlap of 75%. The

results were also exported into an ASCII file for later post

processing and visualization in Matchad® and Matlab®. The

displacement vectors resulting from PIV analysis must be

translated into density gradient vectors in order to move the

BOS analysis towards completion. By assuming the flow is

strictly two-dimensional, the density gradient along any given

light ray passing through the Schlieren object can then be

assumed constant (Richard and Raffel, 2001). Given these

assumptions, the relation between image displacement and

density gradient can be simply written using two algebraic

equations. Eq. (4). defines the relationship between angular

deflection of a light ray and image displacement d as

/ ,Ddh z (4)

where h is the physical dimension of a pixel in the background

plane (i.e., a conversion between displacement in pixel units to

a length unit) and Dz is the distance between background plane

and Schlieren object. Eq. (5). defines the relation between

density gradient and angular deflection as

,K W (5)

where W is the width of the Schlieren object. The variable K

is the Gladstone-Dale constant, which is found using the

relation between density and the index of refraction n

as shown in Eq. (6).

1 .n K (6)

Finally, the temperature field was calculated using the ideal gas

law and presented as a contour plot.

4. RESULTS Raw PIV (tracers with laser lighting) and BOS

(background with LED lighting) recordings are presented in

Fig. 5.

Figure 5. PIV and BOS raw pictures (300 oC)


The vortex shedding can be clearly recognized in the PIV

image (Fig. 5, left). Even this image shows the connection

between the vortex shedding and the temperature field. The

dark regions represent the change in physical condition of the

oil fog used for the visualization. These dark regions appear

due to higher temperatures and mark at the same time the

vortices. The diffraction, caused by the air density change near

the heated cylinder, can slightly be seen slightly in the BOS

picture near the heated cylinder (white circle in Fig. 5).

The periodicity of vortices and temperature are shown in

Figs. 6 and 7. The origin 0, 0x = y = is defined by the

intersection of the ,x y plane and the axis of the cylinder,

which is perpendicular to this plane. Figure 6 depicts the

positive (yellow) and the negative vortices (magenta) and the

vorticity (amplitude). The vorticity peaks decrease

progressively downstream of the cylinder.

Vorticity [1/s]

x y, ω, ( ) Vorticity [1/s]

x y, ω, ( )

Figure 6. Vorticity field

In Fig. 7 the temperature field is presented. Directly behind

the cylinder two peaks representing high temperatures are

followed by two rapidly decreasing but explicit wakes.

These temperature regions follow the path of the vortices

and indicate that the heat is transported in packages from the

cylinder. It can also be noticed that the temperature equalization

increases downstream of the cylinder, i.e., the distance grows

between the parallel wakes.

Figure 8 shows both measured and interpolated contour

plots of vorticity and temperature in two successive time

instances. For comparison, the interpolation was carried out for

vorticity (right) as well. Although it is a vector field, and the

interpolation was carried out separately for both vector

components, the result is satisfactory. The vortex street is not

decomposed; moreover it suits both the preceding and the next

following vorticity fields.

Temperature [oC]

x 1000 y 1000, T, ( )

Figure 7. Temperature field

Regarding the temperature and vorticity fields, presented in

Figs. 8 and 9, following statements can be made:

The experimental setup is suitable for simultaneous velocity

and temperature measurements for the present case, even with a

relatively slow camera.

Velocity and temperature fields can be determined using a

single camera and the developed timer box.

Examining the vortices, we find that the lower branch of the

vortex street is more regular. A possible reason for this is the

rising heat packages collapsing with the upper branch. This can

also be seen in the temperature field, where the upper branch is

much less ordered.

The temperature field diverges more than the vortex street.

This is probably also caused by the previously mentioned

phenomenon of heat diffusion.

The high peaks behind the cylinder in the temperature field

can be explained by the closeness of the heated cylinder.

However, the high temperature differences - i.e., the large

density gradients - might require an additional BOS

background image. It is an interesting question whether a

relation could be found between the resolution of the BOS

background and the expected density gradients. This might

improve the accuracy of the temperature measurement (results

of the cross correlation).

Comparing the two image sequences, it is clear that the

distribution of the temperature peaks is similar to that of the

vortices, but not identical. The reason for this is probably an

optical problem: PIV visualizes an image at a well defined

plane, illuminated by the laser sheet, whereas BOS recordings

represent light refraction in the whole focal depth. Furthermore,

light rays arriving to the camera chip are not parallel to each

other, thus in particular at the boundary region of the recorded

BOS image the light ray crosses vortices in different phases and

incident rays of light are not parallel to the heated cylinder (see

Fig. 10).


BOS (temperature) s

x 1000 y 1000, T,

0

x 1000 y 1000, T,

65,1

67

x 1000 y 1000, T,

133,

333

198,

500

measured

interpolated

measured

y [

mm

] y [

mm

] y [

mm

] y [

mm

]

interpolated

Figure 8. Temperature field behind the cylinder

The goal of the research is to determine the relationship

between the momentum and heat transfer from a heated

cylindrical machine elements. These effects influence the

components placed around and behind the cylinder.

s PIV (vorticity)

0

65,1

67

x y, ω, ( )

133,

333

x y, ω, ( )

198,

500

x y, ω, ( )

measured

measured

y [

mm

] y

[m

m]

y [

mm

]

y [

mm

]

interpolated

interpolated

Figure 9. Vorticity field behind the cylinder

This temperature measurement method does not have an upper

limit. It should be clarified how to adjust the structure of

background to the larger changes in the temperature and

density.


Figure 10. Geometrical properties of the optics

5. CONCLUSIONS This method is applicable for the determination of the

velocity and temperature fields around a heated cylindrical

body of arbitrary cross-section. We are planning to investigate

this issue in future. However, to ensure the homogeneous

heating of cylinders with non-circular cross-sections will mean

a new challenge compared to that of the circular cylinder. The

developed Matchad® and Matlab® codes were successfully

applied to the calculation of the temperature field from the

measured deflection, resulting from density variations in the

flow. Thanks to the employed timer box, temperature and

velocity measurements could be reasonably synchronized.

However, considerable improvements - especially concerning

timing method and optics (a convex lens to generate field of

view parallel to the cylinder) - are still required in the existing

system to make more reliable and comparable measurements.

In order to analyze images in a further step, the recording

quality and frequency must be increased to get more reliable

images (a high speed camera to decrease time delay between

two recordings). It should also be checked whether it is

necessary to change the resolution of the BOS background

according to the expected density changes in the flow.

6. ACKNOWLEDGEMENTS The authors are grateful to NKTH-OTKA (68207 and 76085)

and to the Hungarian-German Intergovernmental S&T

cooperation programs P-MÖB/386 for the financial support of

this research. The work was carried out as part of the TÁMOP-

4.2.1.B-10/2/KONV-2010-0001 project in the framework of the

New Hungarian Development Plan. The realization of this

project is supported by the European Union, co-financed by the

European Social Fund.

REFERENCES Adrian, R.J., 1991, “Particle-Imaging Techniques for

Experimental Fluid Mechanics,” Annual Reviews in Fluid

Mechanics, 23(1), pp. 261-304.

Williamson, C.H.K., 1996, “Vortex dynamics in the cylinder

wake,” Annual Review of Fluid Mechanics, 28(1), pp. 477-539.

Venkatakrishnan, L. and Meier, G.E.A., 2004, “Density

measurements using the Background Oriented Schlieren

technique,” Experiments in Fluids, 37(2), pp. 237-247.

Wang, A.B. and Trávniček, Z., 2001, “On the linear heat

transfer correlation of a heated circular cylinder in laminar

crossflow using a new representative temperature concept,”

International Journal of Heat and Mass Transfer, 44(24), pp.

4635-4647.

Baranyi, L., Szabó, S., Bolló, B., and Bordás, R., 2008,

“Analysis of Flow Around a Heated Circular Cylinder,”

Proceedings, 7th JSME-KSME Thermal and Fluids

Engineering Conference, Sapporo, Japan, (No. 08-201.), A 115.

pp. 1-4.

Bencs, P., Bordás, R., Zähringer, K., Szabó, S., and Thévenin,

D., 2009, “Towards the Application of a Schlieren

Measurement Technique in a Wind-Tunnel,” Proceedings,

MicroCAD International Computer Science Conference,

Miskolc, Hungary, pp. 13-19.

Baranyi, L., Szabó, S., Bolló, B., and Bordás, R., 2009,

“Analysis of Flow Around a Heated Circular Cylinder,” Journal

of Mechanical Science and Technology, 23, pp. 1829-1834.

Bencs, P., Bordás, R., Zähringer, K., Szabó, Sz., Thévenin, D.,

2010, “Application of Schlieren Measurement Technique for

Forced Convection from a Heated Circular Cylinder,”

Proceedings, 7th International Conference on Mechanical

Engineering, Budapest, Hungary, No. E., pp. 203-208.

Richard, H. and Raffel, M., 2001, “Principle and applications of

the background oriented Schlieren (BOS) method,”

Measurement Science and Technology, 12, pp. 1576-1585.

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Simultaneous Measurement of Velocity and Temperature