A comparison of two swirl measurement techniques

A Comparison of Two Swirl Measurement Techniques R. J. Edwards* K. Jambunathan B. L. Button Department of Mechanical Engineering, Nottingham Polytechnic, Nottingham, United Kingdom J. M. Rhine Midlands Research Centre, British Gas plc, Solihull, United Kingdom

-.Two experimental techniques for quantifying swirling airflow in the entrance region of annular ducts are presented. Swirl numbers derived from measurements of the torque on a pivoted honeycomb structure are compared with those obtained from the fringes on the inner surface of the duct sprayed with liquid crystals. The primary flow angles measured from the fringe patterns have been verified by using a Pitot tube and smoke trials. The swirl numbers range from 0.7 to 1.4 for Reynolds numbers of 4000-15,000. Data were obtained up to 11 hydraulic diameters from the entrance of two annular ducts that had diameter ratios of 0.66 and 0.79. The results show that the liquid crystal technique is an easy-to-use and attractive low-cost alternative to the more traditional approach, although the authors recognize that more expensive, nonintrusive, full-field velocity measurements, such as laser-Doppler anemometry, are superior to either of the methods considered here.

Keywords: Keywords: swirl, annular flows, liquid crystals, visualization, swirl meter, swirl number INTRODUCTION Numerous applications of swirl flows are found in engineering, including turbomachinery, gas turbine combustors, cyclone separators, heat exchangers, and flame stabilizers in gas, oil, and pulverized coal burners [1-5]. Extensive work has been undertaken by researchers investigating such flows, mainly in relation to combustion aerodynamics and heat transfer characteristics [6-8]. However, because swirling flows are complex, it is difficult to quantify the contribution this work can make to heat transfer enhancement. Most workers describe swirl flows by combining the axial and circumferential velocity components using a swirl number proposed by Chigier and Be6r [9], who defined it as

S = G/Gxr i

(1)

Where G and G, are axial fluxes of angular and linear momentum, respectively, given by

G =

2~rfouwr 2 dr

(2)

and

Gx = 21rfpw2rdr + 27rfprdr

(3)

* Present address: Stanton plc, P. O. Box 72, Nottingham NG10 5AA, United Kingdom.

Gx relies on knowledge of the velocity and pressure profile data; the latter are rarely available and are very difficult to measure. Kerr and Fraser [10] proposed a modified swirl number that assumes that the density variation and the pressureintegral contribution to the axial momentum flux is negligible. The modified swirl number can then be expressed as

f uwr dr S1

(4)

f wZr drri In this study, our main requirement for the measurement of swirl flow was to gain an understanding of the heat transfer characteristics in terms of the modified swirl number. To achieve this objective, we considered several measurement techniques. The obvious hot-wire and pressure probe methods of local velocity measurement were initially investigated. However, swirl flows have been found to be inherently sensitive to even the smallest disturbances. For example, Holman and Moore [11] reported a 50% change in static pressure caused by inserting a 1.5 mm diameter probe in the rear of a swirl chamber. Murthy [12] concluded that the use of immersed probes is open to question on account of the disturbances introduced into the flow. The use of hot-wire or Pitot probes were therefore discounted. Laser-Doppler anemometry (LDA) affords local flow velocity measurement by nonintrusive means. To measure the swirl velocity component effectively it is desirable that the laser system be aligned axially within the duct. This

Address correspondence to Dr. K. Jambunathan, Department of Mechanical Engineering, Faculty of Engineering, Nottingham Polytechnic, Nottingham NGI4BU, United Kingdom.

Experimental Thermal and Fluid Science 1993; 6:5-14 © 1993 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010

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6 R.J. Edwards et al. would affect the flow and, because of the limited focal length of the beams, prevent velocity mapping along the entire length of the duct. Such observations were corroborated by Dellenback et al [13], who concluded that the determination of the swirl velocity component in narrow duct flows is particularly difficult. Preliminary LDA measurements were made in an annular duct. Only axial and radial velocity components were obtained, and curvature effects prevented velocity mapping near the outer wall. Numerical techniques have been applied to the prediction of swirl flows [1, 2, 7]. Unfortunately, results have often been poor owing to the inability of turbulence models to simulate isotropic turbulent behavior. Sloan et al [7] evaluated the applicability of the standard k - e and other turbulence models to swirling recirculating flows. Their comparison with experimental data portrayed the relative advantages and disadvantages of the various modifications to the models. This extensive review concludes that the k - e model performs competitively with other model corrections in the recovery region and can, in some cases, be superior. The Reynolds stress model is seen to be the best way to improve predictions. Among the recommendations for further research, Sloan et al identify the need for more experimental data and particularly isothermal flow visualization. Beltagui et al [1] report satisfactory agreement between measurements and predictions from a noncombustion flow from a variable-swirl burner. Work at the International Flame Research Foundation [2] indicated that an analytical method based on making certain assumptions with basic flow equations to produce simplified expressions can be used to estimate many important characteristics of expanding swirling flows. The analysis is based on the use of the inviscid expanding flow equations to impart a disturbance to the cylindrical equations of motion. Hagiwara et al [2] claim that they can predict isothermal flow characteristics such as the form and strength of the internal recirculation zone to within "engineering accuracy" for the design of industrial burners. Karasu [14] and Morsi and Clayton [15] numerically predicted turbulent swirling flow in annular ducts; finitedifference solution algorithms were used that incorporated mixing length and the two-equation k - e turbulence models. Karasu's data agreed with the measurements of Scott and Rask [16] and Yeh [17] for the case of forced vortex flow, but the agreement was poor for initial axial locations for predominantly free vortex flow. Morsi and

1.2 m I~ ,

-,,

Clayton [15] found that extensive experimental input was required to obtain reasonable numerical results. Abujelala and Lilley [18] investigated numerical predictions of swirling flow in various geometries. They concluded that the standard form of the k - e model yielded poor results and recommended modifications that would improve its performance. However, the modifications were found to be problem-dependent. On the basis of this literature review, we concluded that a considerable amount of experimental a n d / o r numerical work is still required to fully quantify swirl characteristics. As a contribution to the understanding of swirl flows, this paper describes two novel, low-cost, techniques that were used in the entrance region of annular geometries. SWIRL G E N E R A T I O N The swirl was induced into the airflow by a radial-vane swirl generator mounted at the exit of a thermal wind tunnel [19], Fig. 1. The radial-vane swirl generator was similar to the one recommended by West [20] and used by Singh [21] and is shown in Fig. 2. The span length of the 12 guide vanes was 80 mm, and their exit angles were calculated using a method proposed by Gupta et al [6] to achieve a swirl number of approximately unity. The "hub" diameter of the swirl generator was 80 mm, and the swirl generator was made from a cylinder with a wall thickness of 1 mm to ensure minimum flow disturbance. The overall inside diameter was 200 mm. Measurements to evaluate swirl number were made in two 600 mm long annular ducts positioned immediately downstream of the swirl generator. The outside diameter of the annuli remained constant at 150 mm, and two diameter ratios were obtained by changing the inner cylinder diameter from 100 mm to 120 mm. SWIRL MEASURMENT USING A SWIRL METER The circumferential component of the flow is determined by the measurement of torque induced on a pivoted honeycomb structure situated downsteam of the swirl generator. The technique was used with success by Hassan [22] to quantify swirl flow in industrial gas and coal burners, and we have adopted it for measurements in annular geometries.

Test Specimen Rofafion

Air flow ~'~

i

Side E[evation

Figure 1. Thermal wind tunnel assembly.

Swirl Generafor

Two Swirl Measurement Techniques

Figure 2. Swirl Generator.

7

8 R.J. Edwards et al. The meter was essentially a honeycomb structure with a torque arm securely fastened to its circumference. The assembly was pivoted at the center by a 2 mm diameter rod machined to a point at each end and placed in PTFE bushes positioned in the guide rails as shown in Fig. 3. Torque measurements could be taken at the exit of the swirl generator or up to 300 mm downstream by sliding the guide rails in longitudinal slots placed in the outer tube. The cell geometry of the honeycomb was a compromise between total swirl removal and positional resolution. The cell had a length of 16 mm and length/width ratio of 8. To prevent the swirl component from mixing with the one-dimensional flow that passed through the hub of the swirl generator, an annular duct was formed between the swirl generator and the honeycomb. Tubes of various lengths were manufactured to enable measurements to be taken at several positions downstream of the swirl generator. The force exerted on the torque arm was measured by a precalibrated 120 ohm constantan strain gauge positioned on a 3 mm × 10 mm rectangular cross section aluminum bar that had a resolution of 4 × 103 N. The measured torque on the honeycomb gave a direct reading of G, which was used to form the modified swirl number S 1 given by Eq. (4). SWIRL MEASUREMENT USING LIQUID CRYSTALS The liquid crystals used in this study were organic compounds derived from esters of cholesterol. Their molecules are arranged in layers of parallel planes, with each layer rotated with respect to its neighbor. When they are subjected to an increase in temperature, the distance between the layers changes and incident white light is scattered through the complete visible spectrum. Certain colors are displayed at distinct temperatures; they are clear and reproducible and can be accurately calibrated. Hence

liquid crystals sprayed onto a surface afford an accurate and reliable means of measuring surface temperatures. Liquid crystals in sheet or solution form have provided an effective means of determining local heat transfer coefficients using either steady-state analysis (see Davies at al [23], Butcher [24]) or transient analysis (see Ireland and Jones [25], Edwards [19]). Rhine and Tucker [26] present a review of liquid crystal thermography and its application to the measurement of convective heat transfer in smallscale physical models of industrial furnaces and boilers. In this study, liquid crystals in solution were sprayed onto the inner cylinder of the annular duct, which was mounted at the exit of the thermal wind tunnel (Fig. 1) and supplied air at 20°C above the change temperature (42°C) of the crystals. These experimental conditions were found to be convenient and to produce data that were accurate and repeatable. When the annular duct was rotated in the heated flowfield, the liquid crystals changed color according to the local heat transfer coefficients (h) produced by the flow. The magnitude of h can be calculated by a transient analysis of wall heating [19]. When the duct was subjected to swirl flow, localized areas of high heat transfer were created that were displayed by the liquid crystals in the form of helical "streaks," as illustrated in Fig. 4. The angle at which these streaks occurred was assumed (see "Validation of the Techniques") to correspond to the angle of maximum velocity. The angles measured from photographs of the liquid crystal experiments were incorporated in Eq. (4) as follows. Rewriting the u and w component velocities in terms of the maximum velocity v m occurring at an angle 0, Eq. (4) becomes

fv~ (sin 2 0 ) r 2

(6) 2fv2(cos 20)rdrr

t,.6Omm

....... J ......-i

'i

fHoneycomb corners

3 across

I~I~I

x 16 wide

i

.... ~ }-i- I

Airflow ~L --4 Swirl j

Generat'or

I ~JE~,

I [ /

"----Interchangeable Hub

l] ~ S f r a i n (3auge ~1__~ ~

dr

S 1 =

71 d |

/

1

/

View on A'A

A

Figure 3. Swirl meter assembly.

i

Two Swirl Measurement Techniques

(a) Elapsed time 16.2s

(c) Elapsed time 53.2s Figure 4. Quantifying swirling flow in an annular duct using the liquid crystal technique.

9

10

R.J. Edwards et al.

(b) Elapsed time 31.Is

(d) Elapsed Time 77.6s

Two Swirl Measurement Techniques

would be expected in forced convective flow. However, the primary flow angle was observed using two methods:

Assuming radial independence of v,,, the equation can be directly integrated, resulting in

1. Smoke flow visualization trials 2. Measurement of the angle of maximum velocity using a Pitot probe

(sin 2 0 ) ( t o3 - r3) S 1 = 3(cos20)(r2o

_

(7)

ri2)ri

Smoke was introduced into the flow prior to the swirl generator and was found to progress through the annular duct at the same helical angle as the liquid crystal "streaks." The second method of validation involved inserting a 1.0 mm Pitot probe at intervals downstream of the inlet and measuring the angle of maximum velocity at the center of the duct. As discussed earlier, the insertion of probes in swirling flows in not recommended. However, the measurements were taken with the probe positioned parallel to the flow, which minimizes disturbances. A comparison of the angles measured from the liquid crystal streaks and the Pitot probe is shown in Fig. 6. Good agreement between the measured results from the two methods further confirms the assumption that the streaks indicated by the liquid crystals are coincident with the direction of the primary flow.

Figure 5 shows the computed swirl number S 1 from Eq. (7) for annular geometries with diameter ratios of 0.66 and 0.79 and with 0 varied from 2 ° to 84°d. VALIDATION OF T H E T E C H N I Q U E S The Swirl Meter Technique The swirl meter technique relies on the honeycomb eliminating the swirl component of the flow. Smoke flow visualization trials showed no trace of the swirl component downstream of the honeycomb. This observation was confirmed by inserting another honeycomb section downstream of the swirl meter. The torque on the second honeycomb was found to be less than the resolution of the strain gauge representing a modified swirl number of less than 0.01. The main source of error was assumed to occur from a flow disturbance effect of the honeycomb. The smoke trials showed some disturbance at the leading edge of the honeycomb, but the effect upstream was difficult to quantify and requires further work. However, Hassan's own work [22] suggests that these effects are minimal and do not affect the overall accuracy of the technique.

RESULTS Figures 7 and 8 show comparisons of the results from the two techniques for a = 0.66 and 0.79, respectively, at various Reynolds numbers based on the mean velocity prior to entering the swirl generator. Due to the size of the swirl meter, only limited distances downstream of the generator could be analyzed. Reasonable agreement between the two techniques has been noted, particularly at c~ = 0.66, which is similar to the diameter ratio of the swirl meter. The overall shapes of the two sets of curves are the same, but differences in swirl number between the two diameter ratios are appar-

The Liquid Crystal Technique The crucial factor in the liquid crystal technique is the assumption that the helical "streaks" indicating high areas of heat transfer follow the primary flow direction, which

I

I

I

Oiameter

I

|

60

75

ratio

0.79 _ 0.66

Si

4

I

0

t5

30

11

45

Figure 5. The distribution of the swirl number assuming a uniform velocity profile.

90

12

R . J . Edwards et al.

Re Liquid Crystal Pilot Tube 1 2

5500 8000

A A

O

3

10800

A

o

15000

A

O

o

~N

57.5

e"

L I

\\

I

~

~

3

52-!5

51)0

6,50'

~

½

~

L

~;

6

.> 1

X/D h

Figure 6. Measured angle of primary flow direction in turbulent flow in a smooth annulus, a = 0.66.

ent, with greater values obtained at the larger diameter ratio. This is not unreasonable because the larger diameter ratio has a smaller flow area, which would tend to prevent axial dissipation of the swirl component. The decay in swirl number along the annular duct shows characteristics similar to those measured by Morsi and

1.4

I

i

i

~, 1.3

i.2

Clayton [15], again showing a weak dependence on Reynolds number. The variation of the swirl number with Reynolds number is relatively small, as can be seen in Figs. 7 and 8. It was estimated to be less than 10%, which appears to be in agreement with Hassan [22].

i

i

i

REYNOLDS NUMBER SWIRL METER LIQUID CRYSTALS ~ 4000 + 5500 o 7000 [] 8000 o 10000 v 10800

~\ \~ ~\~\

Si 1.1

1.0

0.9

O.B

i

i

i

i

i

,

!

2

3

4

5

6

7

xl~ Figure 7. Swirl number distribution obtained by means of the color patterns from liquid crystals and the honeycomb swirl meter, a = 0.66.

Two Swirl Measurement Techniques

t.50

!

m

I

I

13

1

REYNOLDS NUMBER SWIRL METER LIQUID CRYSTALS

t.35

o ! .20

4000

+

7000

[] 7000 v 10000

¢ I0000 x 14000

4000

• 14000

Si t. tt

0.90

0.75

0.60 0

2

4

6

B

iO

12

X/Oh Figure 8. Swirl number distribution obtained by means of the color patterns from liquid crystals and the honeycomb swirl meter, c~ = 0.79. The data show that the two techniques recorded similar swirl numbers. The swirl meter, however, becomes insensitive at swirl numbers less than 0.95 mainly because of inertia in the system becoming significant compared to low circumferential momentum. The swirl number obtained by the liquid crystal technique is of particular interest as it represents the flow affecting convective heat transfer related to the surface under investigation. In contrast, the swirl meter measures an overall swirl number that has contributions from the inner and outer boundary layers. PRACTICAL S I G N I F I C A N C E / USEFULNESS Liquid crystal thermography is already established as an accurate and reliable method of determining convective heat transfer data for a wide range of flow and geometric situations. This study has demonstrated that the technique can be extended to quantify characteristics in swirling flows in confined geometries. The nonintrusive nature and simplicity of this technique should prove useful in practical situations where cost considerations outweigh the need for precise measurement of the flow parameters, such as those one would expect to obtain using LDA systems. CONCLUSIONS From the range of parameters considered in this investigation, 4000 < Re < 15,000, 0.7 < S~ < 1.4, and up to 11 hydraulic diameters from the inlet, it has been found that 1. The swirl number is independent of Reynolds number. 2. The swirl number results obtained with the swirl meter and the liquid crystal techniques are not significantly different.

3. The leading peaks of the liquid crystal fringes coincide with the maximum velocity peaks of the airflow around the annuli. 4. Both techniques provide the engineer with a practical method of determining the strength of swirl flow. To apply the liquid crystal technique it is necessary to have an isothermal gaseous flow at a higher temperature than the transformation temperature of the liquid crystals. The shape of the liquid crystal fringes obtained depends on the type of swirl generator used, and the shape of the fringes may be difficult to measure with other types of swirl generators. Since the liquid crystal technique is a surface measurement, it is likely to accurately evaluate the swirl number for the whole airflow only when the width of the annulus is small. The liquid crystal technique has greater resolution than the swirl meter, is nonintrusive, and can also be used to evaluate full-field heat transfer coefficients. The swirl meter technique can be used in liquid or gaseous flows but is intrusive and requires modification to the outer cylinder of the duct. This work was carried out in the laboratories of the Department of Mechanical Engineering, Nottingham Polytechnic. Support for the project and for Dr. R. J. Edwards as a CASE research student by the Science and Engineering Research Council and British Gas plc is gratefully acknowledged.

NOMENCLATURE D h

D

hydraulic diameter ( D O diameter of cylinder, m

Di) , m

14

R . J . Edwards et al.

G axial flux of angular m o m e n t u m , N . m G x axial flux of axial m o m e n t u m , N p static pressure, N / m 2 r radius, m Re Reynolds number, dimensionless r m radius of m a x i m u m velocity, m S swirl n u m b e r , d i m e n s i o n l e s s S 1 m o d i f i e d swirl n u m b e r , d i m e n s i o n l e s s u c i r c u m f e r e n t i a l velocity, m / s Um m a x i m u m resultant velocity [ = ( u 2 + w2)1/2], m / s w x

axial velocity, m / s distance d o w n s t r e a m f r o m exit of the swirl g e n e r a tor, m

Greek Symbols a p 0

a n n u l a r d i a m e t e r ratio D i / D o , d i m e n s i o n l e s s fluid density K g / m 3 primary flow angle o f m a x i m u m velocity, deg

i o

inner outer

Subscripts

REFERENCES 1. Beltagui, S. A., Fuggle, R. M., and Ralston, T., Aerodynamics and Mixing Within the Quarl of a Variable-Swirl Burner, First European Conf. on Industrial Furnaces and Boilers, Lisbon, Portugal, 1988. 2. Hagiwara, A., Bortz, S., and Weber, R., Theoretical and Experimental Studies on Isothermal Expanding Swirling Flows with Application to Swirl Burner Design, International Flame Research Foundation Rep. F259/a/3, February 1986. 3. Horvay, M., and Leuckel, W., LDA-Measurements of Liquid Swirl Flow in Converging Swirl Chambers with Tangential Inlets, First International Syrup. on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 1982. 4. Ikeda, Y., Nakajima, T., and Hosokawa, S., and Matsumoto, R., Flow Characteristics Measurement in a Model of Gas Turbine Combustor, Second International Syrup. on Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 1984. 5. Syred, N., Sidnu, B. S., and Styles, A. C., Characteristics of Swirling Flow Exhausting from Nozzles with Curved Walls, Fifth International Symp. on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 1990. 6. Gupta, A. K., Lilley, D. G., and Syred, N., Swirl Flows, Abacus Press, Tunbridge Wells, Kent, U.K., 1984. 7. Sloan, D. G., Smith, P. J., and Smoot, L. D., Modelling of Swirl in Turbulent Flow Systems, Prog. Energy Combust. Sci., 12 (3), 163-250, 1986. 8. Leuckel, W., Swirl Intensities, Swirl Types and Energy Losses of Different Swirl Generating Devices, International Flame Research Foundation Rep. G O 2 / a / 1 6 , 1967. 9. Chigier, N. A., and Be6r, J. M., Velocity and Static Pressure Distributions in Swirling Air Jets Issuing from Annular and Divergent Nozzles, J. Basic Eng., Ser. D, 86, 788-796, 1964.

10. Kerr, N. M., and Fraser, D., Swirl--Effect of Axisymmetrical Turbulent Jets, J. Inst. Fuel, 38, 519-526, 1965. 11. Holman, J. P., and Moore, C. D., An Experimental Study of Vortex Chamber Flow, Trans. ASME J. Basic Eng., Ser. D, 83, 632-637, 1961. 12. Murthy, S. N. B., Containment Problems in Electrical and Nuclear Propulsion, Aerospace Research Laboratories Rep. ARL 71-0126, 1971. 13. Dellenback, P. A., Metzger, D. E., and Neitzel, G. P., Heat Transfer to Turbulent Swirling Flow Through a Sudden Axisymmetric Expansion, J. Heat Transfer, 108 (3), 613-620, 1987. 14. Karasu, T., Numerical Prediction of Incompressible Turbulent Swirling Flows in Circular-Sectioned Ducts and Annuli, Ph.D. Thesis, Imperial College of Science and Technology, London, 1980. 15. Morsi, Y. S. M., and Clayton, B. R., Determination of Principal Characteristics of Turbulent Swirling Flow Along Annuli. Part 3. Numerical Analysis, Int. J. Heat Fluid Flow, 7 (3), 208-222, 1986. 16. Scott, C. J., and Rask, D. R., Turbulent Viscosity for Swirling Flow in a Stationary Annulus, Trans. ASME Fluid Eng., 95, 557-566, 1973. 17. Yeh, H., Boundary Layer Along Annular Walls in a Swirling Flow, J. Basic Eng. Trans. ASME, 80, 767-776, 1958. 18. Abujelala, M. T., and Lilley, D. G., Limitations and Empirical Extensions of the k e Model as Applied to Turbulent Confined Swirling Flows, Chem. Eng. Commun., 31, 223-236, 1984. 19. Edwards, R. J., Enhancement of Heat Transfer in Smooth Annular Ducts Using Longitudinal Fins or Swirling Flow, Ph.D. Thesis, Trent Polytechnic, Nottingham, 1987. 20. West, P. D., Heat Transfer in Free Swirling Flow in a Pipe, M. Phil. Thesis, Univ. Nottingham, 1973. 21. Singh, G., Heat Transfer in Swirling Flow, Polytechnic Diploma Project Report, Trent Polytechnic, Nottingham, 1974. 22. Hassan, M. M. A., Study of Natural Gas and Pulverised Coal Diffusion Flames, Ph.D. Thesis, Imperial College of Science and Technology, London, 1983. 23. Davies, R. M., Rhine, J. M., and Sidhu, B. S., The application of the Liquid Crystal Technique to the Experimental Modelling of Forced Convective Heat Transfer in Industrial Heating Processes, First U.K. National Heat Transfer Conference, Leeds, 3-5 July, 1984. 24. Butcher, M. R., Fluid Flow and Heat Transfer in Converging/Diverging Annular Ducts, Ph.D. thesis, Coventry (Lanchester) Polytechnic, 1987. 25. Ireland, P. T., and Jones, T. V., Detailed Measurements of Heat Transfer On and Around a Pedestal in Fully Developed Passage Flow, Presented at the Eighth International Heat Transfer Conf., San Francisco, 1986. 26. Rhine, J. M., and Tucker, R. J., Modelling of Gas-Fired Furnaces and Boilers, British Gas and McGraw-Hill Book Company, Maidenhead, U.K., 1991.

Received October 18, 1989; revised March 18, 1992