miniature rainbow schlieren deflectometry system for quantitative measurements in microjets and...

Miniature rainbow schlieren deflectometry system forquantitative measurements in microjets and flames

Rajani P. Satti, Pankaj S. Kolhe, Semih Olcmen, and Ajay K. Agrawal

Recent interest in small-scale flow devices has created the need for miniature instruments capable ofmeasuring scalar flow properties with high spatial resolution. We present a miniature rainbow schlierendeflectometry system to nonintrusively obtain quantitative species concentration and temperature dataacross the whole field. The optical layout of the miniature system is similar to that of a macroscale system,although the field of view is smaller by an order of magnitude. Employing achromatic lenses and a CCDarray together with a camera lens and extension tubes, we achieved spatial resolution down to 4 �m.Quantitative measurements required a careful evaluation of the optical components. The capability of thesystem is demonstrated by obtaining concentration measurements in a helium microjet (diameter,d � 650 �m) and temperature and concentration measurements in a hydrogen jet diffusion flame froma microinjector �d � 50 �m�. Further, the flow field of underexpanded nitrogen jets is visualized to revealdetails of the shock structures existing downstream of the jet exit. © 2007 Optical Society of America

OCIS codes: 120.0120, 120.1740, 120.4640, 120.6780.

1. Introduction

Over the past two decades, the scientific communityhas seen remarkable progress in the area of microscaledevices with applications ranging from biochemicalanalysis to propulsion and power generation. The mi-croscale systems offer several advantages over theirmacroscale counterparts including compact size, dis-posability, and improved functionality. In particular,microfluidics has emerged as an important area of re-search with interdisciplinary applications such asdrug delivery, thermal management of micro-electro-mechanical systems (or MEMS), micropropulsion andmicrocombustion, and ink jet printing.1,2 An under-standing of the flow and heat transfer processes inthese devices requires miniature diagnostics systemscapable of measuring various flow properties withmicron-scale spatial resolution. The diagnostic toolsare needed to investigate the small-scale flow phenom-ena as well as to develop new theoretical and empiricalmodels for related systems. The present study deals

with the development and application of a miniaturerainbow schlieren apparatus to obtain quantitativescalar measurements in microscale flow systems.

The small size of microscale flow systems generallyprecludes the use of traditional intrusive probes forflow measurements. Hence nonintrusive optical diag-nostic techniques are sought to resolve the flow char-acteristics of microscale systems. In the past fewyears, the development of micro-particle image ve-locimetry (micro-PIV) has led to velocity measure-ments in micron-size channels. Santiago et al.3 usedmicro-PIV to measure the velocity field in the Hele–Shaw flow around a 30 �m elliptical cylinder. Mein-hart and Zhang4 examined the flow in an inkjetprinter cartridge using a micro-PIV system. Synner-gren et al.5 employed digital speckle photography tomeasure the velocity field in a micron-size fiber net-work. In recent years, novel adaptations of the laserDoppler velocimetry technique have also been devel-oped for microfluidic applications.6,7

Although several techniques are available to mea-sure the velocity field, the diagnostics of scalar fields(e.g., temperature and species concentration) in mi-croscale flows has received little attention. Kihm8 re-viewed flow visualization techniques for applicationsin microscale heat and mass transport measure-ments. Scroggs and Settles9 used a conventionalknife-edge schlieren system to visualize the scalarflow structure in converging–diverging nozzles of di-ameter ranging from 600 to 1200 �m. Phalnikaret al.10 used a knife-edge schlieren system to visualize

R. P. Satti is with the University of Oklahoma, Norman, Okla-homa 73019, USA. P. S. Kolhe, S. Olcmen, and A. K. Agrawal([email protected]) are with the University of Alabama, Tus-caloosa, Alabama 35487, USA.

Received 14 August 2006; revised 10 December 2006; accepted11 December 2006; posted 19 January 2007 (Doc. ID 74047); pub-lished 1 May 2007.

0003-6935/07/152954-09$15.00/0© 2007 Optical Society of America

2954 APPLIED OPTICS � Vol. 46, No. 15 � 20 May 2007

the shock cell structure in underexpanded nitrogenjets from tubes of inside diameter varying from 100 to400 �m. Note that the knife-edge schlieren techniqueallows only the qualitative flow visualization. Hencequantitative details of the scalar flow field were notobtained in the above experiments.

In recent years, the quantitative rainbow schlierendeflectometry (RSD) technique has been developedand applied to obtain temperature and species con-centration measurements in several nonreacting andreacting flow configurations.11–19 In the RSD tech-nique, the knife-edge filter in a schlieren system isreplaced by a computer-generated color filter to relatethe angular ray deflection to color (or hue) in therainbow schlieren image.11 The RSD technique hasbeen used in nonreacting flows, for example, to mea-sure species concentration in helium jets12,13 andtemperature in a heated air jet.14 The RSD techniquehas also been used to measure the temperatureand�or species concentration in diffusion flames,15–17

partially premixed flames,18 and premixed flames.19

The schlieren apparatus employed in these studieswas macroscale in size. For example, Albers andAgrawal15 used a lens-based system with an 80 mmfield-of-view to characterize the temperature field of aflickering gas-jet diffusion flame with spatial resolu-tion of 140 �m and temporal resolution of 60 Hz.

Two obvious questions provided the motivation forthe present study: (i) Could a miniature RSD appa-ratus be developed using mainly off-the-shelf opticalhardware, and (ii) would the miniature RSD appara-tus yield quantitative measurements in nonreactingand reacting microscale flows? The results and dis-cussion presented in this paper provide an affirma-tive answer to both of these questions. To the bestof our knowledge, our system is the smallest lens-based schlieren apparatus reported in the literature.Through a careful selection of optical components andthe rainbow filter, we were able to obtain quantita-tive measurements across the whole-field in nonre-acting and reacting microscale axisysmmetric flowsat a spatial resolution of 20 �m. Further, the shockflow structure of an underexpanded nitrogen jet wasvisualized at a spatial resolution down to 4 �m. Theexperimental details, results, and discussion are pro-vided in the following sections.

2. Experimental Details

The optical configuration of the miniature schlie-ren apparatus is similar to that of macroscale sys-tems.12–15 However, its development required acareful evaluation of each optical component. Inthis section, we provide details of the optical hard-ware followed by brief descriptions of the test me-dia, analysis procedure, and uncertainty analysis.

A. Optical Hardware

Figure 1 shows a schematic diagram of the rail-mounted miniature schlieren apparatus. Broadbandlight from a 150 W halogen light source is transmit-ted by a 600 �m fiber optics cable to a 5 �m wide,3 mm high source aperture. The source aperture is

placed at the focal point of an achromatic lens of10 mm diameter and 40 mm focal length � f1�. Thecollimated light rays pass through the test medium,and deflected rays are decollimated by a 10 mm di-ameter lens of 100 mm focal length � f2�. The image ofthe source aperture displaced by the test medium isformed at the focal point of the decollimating lens,wherein a rainbow filter is placed. The filtered imageis acquired by a CCD array together with a cameralens and extension tubes.

1. Light Source, Fiber Optics Cable, and SourceApertureThe light source and the fiber optics system used inthis study are identical to those in the macroscaleschlieren apparatus.13 The light source consists of a150 W halogen lamp with a focusing optics assembly tofocus light onto the upstream end of a multimode fiberof 600 �m diameter. Light rays following differentpaths inside a multimode fiber result in concentricbands of low and high intensity at the downstreamterminal of the fiber. A single-mode fiber could providemore uniform light distribution, although the smallcore diameter of these fibers reduces the light through-put to adversely affect the exposure time (or temporalresolution) of the CCD array. In this study, a 5 �mwide source aperture (the smallest width availablecommercially) was used. In contrast, the macroscalesystems typically use 50 to 200 �m wide source aper-ture.13 In general, a source aperture of smaller widthimproves the measurement resolution and sensitivity.However, the light throughput also decreases by de-creasing the aperture width. Nevertheless, the sourceaperture used in this study allowed acquisition ofschlieren images at exposure time down to 100 �s. Thesmall width of the source aperture compared to thefiber diameter also alleviated the problem of nonuni-form light distribution at the fiber terminal. Thesource aperture was positioned directly in front of thebright region of the optical fiber terminated with anSMA (subminiature version A) connector. A custom-ized holder was fabricated in-house to ensure precisepositioning of the optical fiber with respect to thesource aperture. A separation distance of 2 to 3 mmwas maintained between the fiber terminal and sourceaperture.

2. Collimating and Decollimating LensesChromatic aberration is the most serious concern inthe lens-based rainbow schlieren apparatus. Thusachromatic lenses are necessary for collimation anddecollimation to obtain quantitative data from therainbow schlieren images. Accurate alignment oflenses is another key requirement. Initially, we used6 mm diameter lenses with self-adjusting lens hold-ers. However, the vertical and horizontal alignmentof lenses with this type of holder proved to be ex-tremely cumbersome. Thus we switched to the small-est off-the-shelf fixed lens holder of 10 mm diameter.The fixed lens holder accurately positioned the lensby a set of circular rings, which limited the field-of-view to 7 mm.

20 May 2007 � Vol. 46, No. 15 � APPLIED OPTICS 2955

The focal length of the collimating lens � f1 �40 mm� was chosen to maximize the collection of thelight from the source aperture and also to minimizethe total length of the system. The light rays de-flected by the test medium are focused at the focalpoint of the decollimating lens or the filter plane. Akey parameter affecting the measurement accuracyis the transverse ray displacement at the filterplane give as

d�y� � f2 tan��y�� f2��y�, (1)

where d�y� is the transverse ray displacement at thefilter plane, f2 is the focal length of the decollimatinglens, and ��y� is the angular deflection of a ray at theprojected transverse location y. As explained in Sub-

section 2.C, the d�y� is related to the hue detected inthe rainbow schlieren image using the filter calibra-tion curve.

A large value of f2 increases the transverse raydisplacement and hence improves the measurementsensitivity. Initially, we employed a lens combinationusing off-the-shelf achromatic lenses to obtain f2 ex-ceeding 300 mm. However, the minor chromatic ab-errations were magnified by the lens combination,and hence the rainbow schlieren images were notamenable to quantitative analysis. Finally, an off-the-shelf achromatic lens of the largest available fo-cal length of 100 mm was used for decollimation.Note that the image of the source aperture at thefilter plane is magnified by a factor of 2.5, i.e., theratio of the focal lengths of the decollimating andcollimating lenses � f2�f1�.

Fig. 1. Optical layout of the miniature schlieren apparatus.


3. Rainbow FilterThe transverse ray displacement at the filter planedepends upon the angular ray deflection, which isproportional to the density gradient integrated overthe path length of the test medium [see Eqs. (1) and(2)]. The smaller path length of the microscale testmedium results in a smaller angular ray deflection.The transverse ray displacement is also constrainedby the small f2 of the miniature schlieren apparatus.Accordingly, severe restrictions are placed on themaximum usable width of the rainbow filter. Afterseveral trials, a 0.5 mm wide symmetric filter withhue varying from 70 to 350 degrees was used, com-pared to the 2–3 mm wide filters used in macroscalesystems. The rainbow filter is a 35 mm slide printedwith spatial resolution of 115 pixels per mm. Thusthe 0.5 mm wide color band provides nearly 30 dis-tinct colors (or hues) on each side of the filter plane.Figure 2 shows the filter calibration curve obtainedby traversing the filter without the test media, insteps of 0.01 mm, and recording the correspondingbackground schlieren image. The average calibrationcurve in Fig. 2 represents the average hue in thebackground schlieren image, which differs from cal-ibration curves for the individual pixel locations, inpart because of the pixel to pixel variations in thesensitivity of the CCD array. As discussed in Subsec-tion 2.C, the calibration curves for each pixel locationwere used in this study to postprocess the schlierenimages. For a helium jet, owing to the very smallangular ray deflections, only one side of the symmet-ric filter was utilized. However, both sides of the filterwere used for a hydrogen jet diffusion flame and anunderexpanded nitrogen jet.

4. Camera SystemThe filtered image of the test section was acquired bya CCD array with a lens. Obtaining schlieren imageswith high spatial resolution required a detailed eval-

uation of the camera system. We used a 50 mm cam-era lens for a helium jet and hydrogen flame and a100 mm lens for the nitrogen jet experiments. How-ever, the minimum working distance of the lens ex-ceeded the small optical length of the system. Thus aset of extension tubes was placed in between the CCDarray and camera lens to decrease the minimumworking distance of the camera lens. The extensiontubes magnified the image as illustrated in Fig. 1.Thus the field-of-view and hence the spatial resolu-tion in the schlieren image were determined by thelength of the extension tubes and the focal length ofthe camera lens. The camera shutter was controlledelectronically to yield the exposure times down to100 �s.

B. Test Media

The miniature schlieren system was used with thefollowing microscale flows: helium jet in air, hydro-gen jet diffusion flame, and underexpanded nitro-gen jet. Commercially available hypodermic tubes ofstainless steel with inside diameter (d) ranging from100 to 1500 �m were used. Similar to Phalnikaret al.,10 injectors were fabricated by starting out withlarger diameter tubing and then concentrically in-serting smaller straight sections of hypodermic tub-ing until the tube diameter of the desired size wasobtained. The junctions of different size tubes weremade leak proof by a careful process of soldering andthen applying high-strength glue. This procedureproved unsuccessful for the 50 �m diameter tube be-cause of the difficulty in cutting and holding the tinytube without creating dents or bends. Thus experi-ments with a 50 �m injector were conducted using anO’Keefe micro-orifice. Figure 3 shows a photograph ofdifferent size injectors used for the experiments to-gether with the lens and fixed lens holder.

Injectors for helium jet and hydrogen flame exper-iments were mounted vertically upward through aplenum, and hence the schlieren system sensed den-sity gradients in the transverse direction. The injec-tor for the nitrogen jet experiments was orientedhorizontally to visualize the density gradients in thestreamwise direction. The gas flow was supplied froma compressed gas cylinder fitted with a pressure reg-ulator and a control valve to regulate the mass flowrate measured by a mass flowmeter.

Fig. 2. Filter calibration curves.Fig. 3. (Color online) Optical components and injectors used forexperiments.


C. Analysis Procedure

In a rainbow schlieren image, the color representedby hue according to the HSV (hue–saturation–value)model relates to the transverse ray displacement atthe filter plane according to the filter calibratingcurve. As discussed previously, the filter calibrationcurve is obtained by traversing the filter without thetest media and then measuring the hue in the back-ground schlieren image taken at each traverse loca-tion. However, the inaccuracies in printing a smallwidth filter with large hue gradients, minor opticalmisalignments, and chromatic aberrations produce abackground schlieren image with nonuniform huedistribution, as depicted by the error bars of the stan-dard deviation of hue for the average hue curve inFig. 2. To minimize associated errors, a filter calibra-tion curve was obtained for each pixel location in thebackground schlieren image; two such calibrationcurves are shown in Fig. 2.

The analysis begins by converting the hue mea-sured at a pixel location in the schlieren image totransverse ray displacement according to the filtercalibration curve at that particular pixel location.Then, the angular ray deflection is obtained from Eq.(1), and local distribution of the refractive index dif-ference is found from Abel inversion given as

��r� � �1r�

r

��y�

��y2 � r2�dy, (2)

where � � �� 1� is the refractive index difference,and � is the refractive index of the test medium nor-malized by that of the surrounding air. Note that therefractive index difference varies with the radial co-ordinate r only for the axisymmetric test media in thepresent study.

The integral in Eq. (2) is written in discrete form as

��ri� � ��i�r� � j�i

N

Dij��yi�, (3)

where Dij are the geometric coefficients given by Al-bers and Agrawal.15 The mixture density and concen-trations of species are related to the refractive indexdifference using the Gladstone–Dale equation

� � i

iYi, (4)

where � is the Gladstone–Dale constant and Y is themass fraction, and the summation is taken over allspecies in the mixture. For reacting flows, the densityis related to temperature according to the chemicalequilibrium and ideal gas law.15

D. Uncertainty Analysis

In the miniature schlieren system, the uncertaintiesin the measurements are directly related to the imageprocessing procedures. Uncertainty analysis was per-formed to understand how the errors in direct mea-surements of hue in the color schlieren image affected

the measurement accuracy of angular deflection, re-fractive index difference, and thereby temperature orconcentration. The precision and bias error in tra-versing the filter was estimated to be 0.25 �m. Ac-cordingly, the uncertainty in the slope of the filtercalibration curve was found to be 5.0 � 10�4. Theuncertainty in angular ray deflection was calculatedassuming bias error of 1% in the focal length of lensand precision error of 1% in optical alignment of thelens. Accordingly, the maximum uncertainty in an-gular deflection was found to be 1.0 � 10�3 degree.Error propagation analysis for the Abel inversionshowed maximum uncertainty at the center of theflow. The maximum uncertainty in refractive indexdifference in the jet diffusion flame was 7.5 � 10�6 atthe axis, and it decreased to approximately 1.4 �10�6 near the flame surface. Further, the uncertaintyin temperature was approximately 160, 80, and 20 K,respectively, at local temperatures of 2400, 2000, and1000 K.

3. Results and Discussion

A series of experiments were conducted with heliumjets (nonreacting) and hydrogen jet diffusion flames(reacting) to obtain quantitative data across the wholefield. Experiments were also conducted to visualize thescalar flow structure of an underexpanded nitrogen jet.

A. Helium Jet

Figure 4(a) shows an instantaneous color schlierenimage of the helium jet for d � 650 �m and jet Reyn-olds number, Re � 375. The image depicts the near-

Fig. 4. (Color online) (a) Rainbow schlieren image and (b) huecontours for the helium jet, d � 650 �m, Re � 375.


field laminar region at spatial resolution of 20 �m.The tube exit and the outer surface are visible asblack regions in the image. Figure 4(a) clearly showscolor gradations in the shear layer region �r�d �0.5� with large density gradients. In the center regionof the jet, the density gradients are small, and hencethe color matches that in the background. Interest-ingly, the schlieren image of the microscale helium jetis similar to that of the macroscale helium jet (d �7.2 mm and 10.4 mm) obtained by Alammar et al.12

Because of the flow symmetry, Fig. 4(b) shows huecontours on only one side of the jet, whereby the axialand radial coordinates are normalized by the tube in-side diameter. The contour plot reveals hue varyingfrom 140 to 180 degrees, corresponding to the latterhalf of the filter calibration curve in Fig. 2. The rangeof hue in Fig. 4(b) pertains to the maximum transverseray displacement of 0.05 mm in the helium jet.

Figure 5 shows the radial profiles of helium molepercentage at three axial locations. Results depict sig-nificant mixing of helium with air, which is consistentwith measurements in macroscale flows.12 The profilesclearly show increased diffusion of the jet flow in thedownstream direction. Toward the jet center, the den-sity gradients and hence transverse ray displacementsare small. Further, the measurement errors propagateexponentially toward the jet center during the Abelinversion process, as documented in Ref. 12. Thus thepresent measurements are considered inaccurate forr�d � 0.2 . Figure 6 shows the contour plot of heliummole percentage across the whole field. The wavinessFig. 5. Radial profiles of helium mole percentage, d � 650 �m,

Re � 375.

Fig. 6. Contours of helium mole percentage, d � 650 �m, Re� 375.

Fig. 7. (Color online) (a) Rainbow schlieren image and (b) huecontours for the hydrogen diffusion flame, d � 50 �m, Re � 410.


in the instantaneous contours is reminiscent of thebuoyancy-induced flow oscillations observed in mac-roscales systems.13 Results show that the miniatureschlieren system is capable of providing quantitativemeasurements at high spatial resolution. Further-more, the structural features of the flow field are sim-ilar in both macroscale and microscale helium jets.

B. Hydrogen Jet Diffusion Flame

Figure 7(a) shows instantaneous rainbow schlierenimage of a hydrogen jet diffusion flame at spatialresolution of 20 �m for d � 50 �m, Re � 410. Theschlieren image depicts an axisymmetric laminarflame in the near field. Figure 7(b) shows the corre-sponding hue contours with hue varying from 60 to

110 degrees. According to the filter calibration curve,this hue range signifies a maximum transverse raydisplacement of 0.05 mm. Figures 8(a) and 8(b)show, respectively, the radial profiles of temperatureand oxygen concentration at three axial locations. Inthese figures, the radial location with the peak tem-perature or zero oxygen concentration pertains to theflame boundary, located between 12 � r�d � 18. Thepeak temperature of 2400 K and the trends of ra-dial profiles match with similar measurements takenin macroscale hydrogen jet diffusion flames.15,17 Fig-ures 9(a) and 9(b) show the instantaneous contourplots of temperature and oxygen concentration acrossthe whole field. Only one side of the flame is shown

Fig. 8. Radial profiles of (a) temperature distribution and (b)oxygen mole percentage, d � 50 �m, Re � 410.

Fig. 9. Contours of (a) temperature distribution and (b) oxygenmole percentage, d � 50 �m, Re � 410.


because of the flow symmetry, and the coordinatedimensions are normalized by the injector inside di-ameter. Figure 9 depicts an increase in radial gradi-

ents toward the flame surface. The curvature of thecontours reveals large axial gradients near the injec-tor exit that decrease in the axial direction. Overall,these results are similar to those obtained in mac-roscale systems.15,17

C. Underexpanded Nitrogen Jet

Figure 10 shows instantaneous color schlieren im-ages of an underexpanded nitrogen jet from injectorswith d � 650 �m and 300 �m at different supplypressures. The spatial resolution in the image is4 �m. The formation of shock diamonds at supplypressure of 60 psi is depicted in Fig. 10(a). Theschlieren image shows color gradations caused bydensity gradients in the shock cells. The shock celldiamonds in the image represent the characteristicfeatures of an underexpanded jet. Interestingly, theoverall shock flow structure is similar to that ob-served in macroscale jets. The supply pressure wasvaried between 300 psi and 450 psi for both injectorsto obtain the near-field flow structure depicted inFigs. 10(b) and 10(c). Images show expansion andcompression fans, free jet boundary, oblique shockwaves, and Mach disks. The shock cell spacing, theformation and length of the Mach disk, supersoniccore length, and angle of the oblique shock waveswere affected by the supply pressure. Although theflow characteristics of underexpanded jets have beendocumented at different scales,10 the color schlierenimages at such a high spatial resolution have notbeen presented before to our knowledge. Togetherwith appropriate state relationships, one could obtaindensity, temperature, and�or pressure fields from therefractive index difference field determined by therainbow schlieren technique.

4. Conclusions

A miniature rainbow schlieren apparatus has beendeveloped using off-the-shelf optical hardware. Thespatial resolution of the system was determined bythe focal length of the camera lens and the length ofthe extension tubes placed between the CCD arrayand camera lens. The miniature schlieren systemwas built on principles of the macroscale rainbowschlieren apparatus together with a careful evalua-tion of the optical components. The miniature systemwas used to measure species concentration and�ortemperature across the whole field of nonreactingand reacting microscale flows at spatial resolution of20 �m. Results show that the structural features ofmacroscale flows are replicated in microscale flows.The miniature schlieren apparatus was also used tovisualize the shock flow structures of an underex-panded nitrogen jet at spatial resolution of 4 �m. Theschlieren apparatus presented in this study is thesmallest system of its kind, and it offers the prospectsof developing a readily portable schlieren device forquantitative scalar measurements in nonreactingand reacting flows.

This work was supported by the Physical SciencesDivision of NASA’s Office of Biological and Physicalresearch under grant NNC04GA22G.

Fig. 10. (Color online) Schlieren images showing (a) formation ofshock diamonds, d � 650 �m at 60 psi, (b) effect of supply pressureon shock cell structure, d � 650 �m, and (c) effect of supply pres-sure on shock cell structure, d � 300 �m.


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miniature rainbow schlieren deflectometry system for quantitative measurements in microjets and...

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