Journal of Wind Engineering and Industrial Aerodynamics, 36 (1990) 1095-1104 1095 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

Longitudinally and Transversely Spaced Cylinders in Cross Flow

Anwar Ahmed* Cyrus Ostowari**

ABSTRACT

An experimental investigation was conducted to determine the flow field around some arrangements of cylinders in cross flow. Results are presented in the form of surface pressure distributions, turbulence intensity and velodty maps, and flow visualization photographs. Results indicate that the forebody separated flow field influences the aft body flow characteristics significantly.

INTRODUCTION

Cylinders have historically been a fascinating geometry for a fluid dynamicist. The flow around a single cylinder in cross flow has been well established. With a circular cylinder in cross-flow, the viscous interactions of the fluid and the surface gives rise to the formation of boundary layer and it's thickness increasing downstream. The factors that determine the fluid dynamics in the boundary layer are the Reynolds number and the free-stream turbulence (Roshko, 1961). The large drag coefficients associated with circular cylinders is a result of separation of laminar/turbulent boundary layer which is highly dependent on the location of separation point along the surface.

In the sub-critical flow regime there is a tendency for the free shear layer to develop into an organized structure in the wake. This separation location is a result of an increasing pressure gradient. Turbulent wake is generated by this separation process, and in many cases regular/irregular vortex shedding is observed to occur (McCroskey, 1965). The vortex sheddin~ is normally considered to continue up to the limit of the critical flow, which is at Re = 6x10 ~. However, it has been shown that regular vortex shedding ex~ist in the critical flow region and, indeed, beyond it, i.e. at Re > 3.5x10 o. At very high Reynolds number the vortex shedding breaks down and the wake is dominated by random eddies (Roshko 1976). Measurements of the separation point on the cylinder has been reported to be between 90 to 140 degrees depending on the free-stream Reynolds number and local surface roughness. It has also been documented that the blockage factor, associated with wind tunnels, has little effect on the behavior of this separation point (Schlichting, 1968).

Cylinders are the most frequently used conduit geometry in majority of the engineering applications, especially in supporting structures and as heat exchanger elements. It is rare that a single o]lmder is utilized by itself in such applications. The most common use of cyhnders are in a configuration that utilizes several of them in tandem, or in an organized fashion. The

* Assistant Professor, Aerospace Engineering, Texas A&M Universit), ** Associate Professor, Aerospace Engineering, Texas A&M University

0167-6105/90/$03.50 © 1990---Elsevier Science Publishers B.V.

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aerodynamic design considerations of a body in the wake of another bluff body in connection with the wind effects such as plural chimneys, smoke stacks, skyscrapers and oil p la t forms is of great importance.

Although cylinders in tandem have been investigated (Ishigai and Nishikawa, 1975), each new configuration due to a combination of more than one cylinder either in tandem or in parallel results in a complex flow field and wake interaction. Possibilities of different combinations and sizes as well as their utilities in the applied fluid dynamics and heat transfer area are endless. Extensive literature is available regarding measurements around and in the ,wake of a circular cylinder ranging from very low Reynolds number to very

h igh Reynolds number. Recent developments in the flow studies around cylinders from the wind engineering point of view has rekindled the interest in the low Reynolds number flows with simulated atmospheric boundary layers and at natural turbulence levels. Since the periodicity in the wake flow at sub critical Reynolds number can cause fatigue and vibration problem in a structure consisting of cylinders, it is obvious that a body in the wake of another body will experience more intense fluctuating wind loads and thus aggravating the problem.

Attention has been directed in the present experimental investigation to determine the flow field around some arrangements of cylinders in cross flow. Results are presented in the form of surface pressure distributions, turbulence intensity and velocity maps, and flow visualization photographs.

TEST PROGRAM

In order to study the near wake interaction of the cylinders spaced longitudinally and laterally in a cross flow, tests were initiated to determine the wake structure, turbulence intensities and velocity deficit. Tests were conducted in a 2'x3' boundary layer tunnel with a grid generated high free-stream turbulence in the order of 5% compared to undisturbed flow.

Model Geometry and Test Configurations.

Two of the cylinders consisted of standard PVC pipes of 3.5 in. outside diameter and 3 ft. long. The third cylinder was machined out of brass stock and fitted with a total of 36 surface pressure ports distributed around the cylinder circumference with even azimuthal spacing. These ports were fitted with 1/16 in. outside diameter stainless steel tubing. All models were foam filled and sealed with epoxy to prevent any leakage. Surface quality was ensured by maintaining a surface waviness of less than .0001% of the cylinder diameter.

Five configurations were tested at four different Reynolds numbers. The coordinate system and test configurations are shown in Fig. 1. The first two cylinders were positioned at a fixed distance from each other, and the third cylinder was placed at the center line at upto four diameters down-stream of the two cylinders.

Test Instrumentation

For each of the configurations tested wake surveys were conducted upto 5 diameters down stream, where each station is measured from x = 0. A pitot probe was used to obtain average velocity profiles, however, detailed measurements were made with a TSI split film sensor and a hot wire probe in conjunction with a TSI model IFA 200 dual channel hotwire/film

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anemometer system. The data was processed on an IBM personal computer with a TSI supplied software and a 12 bit A/D interface. The local turbulence intensity values were checked against the readings of an RMS voltmeter.

The velocity defidt was calculated from:- 1-ux/U

Where u× is the mean axial velocity in the wake, and U is the free stream velocity. Pressure coefficient of the third cylinder was calculated from:-

Cp = (p-P)/q

where p is the mean pressures measured from each of the 36 static pressure ports located 10 degrees apart, and P and q are the free-stream static and dynamic pressures respective!),.

Tunnel pressure gradient was held constant by applying suitable adjustments to the tunnel walls. Free-stream velocity was measured by pitot-static tube placed upstream of the model and was held constant within 2%. Before each test, the tunnel was allowed to run for at least 20 minutes to maintain a constant temperature environment for calibration of the hot film anemometry system. A thermo-couple was installed in the test section for temperature compensation of the hot film probe.

Flow Visualization

Flow visualization was carried out on a 1/8 in. thick, smooth fiberglass plate with curved leading edge. The plate was placed on the floor o f the tunnel and all of its sides were adhered to the tunnel walls to prevent plate flutter. The cylinders were mounted vertically. The Entire plate was painted with a mixture of tempra black powder and kerosene oil. The tunnel was then allowed to run for at-least 10 minutes during which a steady flow pattern was formed by the black pigment while the oil evaporated. The plate was later removed and photographed. ( A typical flow pattern is shown in figure x3.)

At higher Reynolds number some difficulties were encountered in getting an acceptable f lowpattern because the entire mixture of oil and powder would wash away from the plate due to the higher shear stress levels associated with the higher velocity gradients near the surface. This problem was remedied by increasing the pigment to oil ratio mixture.

RESULTS

Results of the flow visualization studies are shown in Figure 2. For all configurations, the primary separation line occurs just upstream of the primary horse-shoe vortex which is present due to the end wall. Without this end plate, this separation line would be a streamline with a stagnation point on the most forward position on the upstream cylinders. In all cases the flow appears to be symmetrical about the centerline of the two adjacent cylinders. This symmetry is maintained downstream as well as past the third cylinder. Care must be taken in interpreting these photographs due to the steady state nature of this experiment (time averaged flow visualization). There is a

~ ossibility that the wake may be oscillatory and somewhat skewed which can e deduced from a spectrum analysis of a hot wire signal only.

The space between the first two cylinders appears to be geometrically similar to tlaat of a nozzle throat through which the gap flow behaves like a two-dimensional jet discharging in to the wake. It is difficult for such a jet to maintain its discharging direction and is usually deflected towards the

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adjacent surface (cylinder itself) due to what is commonly known as the "Coanda" effect. The photographs show this effect very clearly (Figure 2a).

The effect on the downstream cylinder is quite pronounced as can be seen from Figure 3. The separated wake behind the aft cylinder appears to reattach at about one diameter downstream for all the configurations tested. The wake characteristic behind the downstream cylinder seems to be similar for all geometric spacings. However, the flow around the front cylinders appears to be less influenced by the presence of the aft cylinder when the spacing between the forward and the rear cylinders is larger than one tllameter.

Results of the wake velocity defect measurements for the 2 cylinders adjacent to each other (Fig. 3) show that the wake downstream appears to be slightly skewed downwards. This skewness was not apparent in the flow visuahzation studies. The turbulence intensities are minimum at the centerline and increase substantially behind each cylinder which coincides with the large velocity defect region. The addition of a downstream cylinder appears to have created a velocity defect profile similar to that of a bluff body wake, with an exponential decay from the outer edge to the centerline. Also the presence of the third cylinder at X/D = 1, appears to have restored the symmetry of the wake. With the third cylinder at X/D = 2, higher turbulence intensities and velocity deficits were measured. Peak turbulence intensity values dropped from 23 % for the low Reynolds number flow to 19 % for the high Reynolds number flow. The appearance of an organized flow structure at one diameter very quickly broke down into a wake like structure at 4 diameters down-stream.

Figure 8 shows the effect of Reynolds number on the pressure distribution of the third cylinder for the various configurations. A flat pressure region preceded by a decreasing pressure is considered to be a re~ion of flow separation. For all configurations, it appears that the azlmuthal location of separation is independent of Reynolds number but somewhat dependent on the longitudinal spacing. The regions of separation on the aft cylinder increases in size as the longitudinal distance is reduced. Pressure distribution also show a hi~her negative pressure for decreasing Reynolds number, but without sigrnficantly effecting the wake geometry.

REFERENCES

Ishigai, S. and Nishikawa, E., "Experimental Study of Gas Flow in Tube Banks with Tube Axes Normal to Flow, Part II" Bulletin of JSME, Vol.18 No.l19, 1975.

Roshko, A., "Experiments on the Flow Past Circular Cylinder in Cross-Flow at a very high Reynolds number," J. Fluid Mechanics, Vol. 10, No. 3, 1961.

Roshko, A., "Structure of Turbulent Shear Flows: A New Look," Dryden Research Lecture, AIAA Journal, Vol. 14, No. 10, Oct, 1976.

Schlichting, H., "Boundary Layer Theory," Sixth Edition, McGraw Hill, 1968. Naumann, A.; Marsbach, M.; and Kramer, C., "The Conditions of Separation and Vortex Formation Past Cylinders," AGARD CP-4, 1966.

McCroskey, W. J., "Introduction to Unsteady Aspects of Separation in Subsonic and Transonic Flow," AGARD CP-4, Part 1, 1965

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~Y C O N F I G U R A T I O N - A

X Cyl inder f I at Y/D = + 1 Cyl inder @ 2 at Y/D = - i

C O N F I G U R A T I O N - B

0 Cyl inder # 1 at Y/D = + 1 Cyl inder @ 2 at Y/D = - I Cyl inder # 3 at X/D = + i

C O N F I G U R A T I O N - C

Cyl inder # I at Y/D = + i Cyl inder # 2 at Y/D = - 1 Cyl inder # 3 at X/D = + 2

C O N F I G U R A T I O N - D

Cyl inder # I at Y/D = + 1 Cyl inder # 2 at Y/D = - i Cyl inder f 3 at X/D = + 3

C O N F I G U R A T I O N - E

Cyl inder # 1 at Y/D = + 1 Cyl inder # 2 at Y/D = - 1 Cyl inder # 3 at X/D = + 4

Figure 1 - Experimental Test Configuration.

(a) Configuration A

Figure 2 - End Plate Surface Flow Visualization, R.N = .15x10 6 .

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(b) Configuration B

(c) Configuration C

Figure 2 - Continued.

1101

(d) Configuration D

(e) Configuration E

Figure 2 - Concluded.

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Figure 3 . Wake Velocity De f ic i t and Turbulence Intensi ty Prof i les of Configuration - A.

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Figure 5. Wake Velocity Deficit and Turbulence Intensity Profiles of Configuration - C.

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Figure 6. Wake Velocity Deficit and Turbulence Intensity Profiles of Configuration - D.

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