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Experimental study of drag coefficient of multistrand wires using single normal hot-wire anemometer probe
Author’s Accepted Manuscript Experimental study of drag coefficient of multistrand wires using single normal hot-wire anemometer probe M.A. Ardekani, F. Farhani, A. Nourmohammadi www.elsevier.com/locate/flowmeasinst
PII: DOI: Reference:
S0955-5986(16)30085-1 http://dx.doi.org/10.1016/j.flowmeasinst.2016.07.009 JFMI1231
To appear in: Flow Measurement and Instrumentation Received date: 28 November 2014 Revised date: 26 June 2016 Accepted date: 25 July 2016 Cite this article as: M.A. Ardekani, F. Farhani and A. Nourmohammadi, Experimental study of drag coefficient of multistrand wires using single normal hot-wire anemometer probe, Flow Measurement and Instrumentation, http://dx.doi.org/10.1016/j.flowmeasinst.2016.07.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental Study of Drag Coefficient of Multistrand Wires Using Single Normal Hot-Wire Anemometer Probe
M.A. Ardekani*, F. Farhani, A. Nourmohammadi
Department of Mechanical Engineering, Iranian Research Organization for Science and Technology (IROST), Tehran, Iran *Corresponding author. Department of Mechanical Engineering, Iranian Research Organization for Science and Technology (IROST), P.O. Box 15815 – 3538, Tehran, Iran. Tel./Fax: (0098)56276632. [email protected] (M.A. Ardekani)
Abstract In a vertical wind tunnel, used for testing of aircraft and helicopters spin and simulation of skydiving, a protective net made of multistrand wires is installed below the flight chamber to prevent the fall of the test models or skydivers to the ground. The drag due to the protective net is significant, which results in pressure drop and subsequent increase in the required power to attain a desired speed in the tunnel. This paper presents the results of an experimental study of drag coefficient of multistrand wires, using (i) a single normal hot-wire anemometer probe (HWA), (ii) a pitot tube, which measures the total pressure downstream of the multistrand wires. Initially, the non-dimensional distance, X/D, at which HWA measurements can be used to determine the drag coefficient of the multistrand wires with acceptable accuracy, was obtained by considering flow velocity profile and turbulence intensity, downstream of a cylindrical rod of diameter D. The distance was determined to be X/D > 30, where X is the distance along the test section downstream of the cylindrical rod. Results of pitot tube and HWA measurements are in good agreement. These results show that at Reynolds number, Re = 2000, drag coefficient of the multistrand wires is greater than the cylindrical rod by approximately 16%. However, the difference in the drag coefficients 1
decreases with increase in Re; the two values approaching each other and attaining an almost equal value at Re = 10000.
Keywords: Cylindrical rod, Drag coefficient, Hot-wire anemometer, Multistrand wires,
Turbulence intensity, Wake survey method
Nomenclature Latin symbols CD CDm CDT d D L Ps,e Ps,w Re U , ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ W W/D X X/D Y Y/D Greek symbols
Coefficient of drag The momentum difference component of the coefficient of drag The Reynolds stress component of the coefficient of drag Wire diameter Cylindrical rod diameter Characteristic Length Static pressure upstream of cylindrical rod Static pressure of wake dynamic pressure Reynolds number X- direction velocity Free stream streamwise velocity Components of velocity fluctuation Mean of squared fluctuations in X, Y, Z directions Width of wake region Non-dimensional width of wake region Distance along wake (X-direction) Non-dimensional distance along wake Distance perpendicular to wake (Y-direction) Non-dimensional distance perpendicular to wake Shear stress Dynamic Viscosity Density
Subscripts Free Stream Value at the inlet Abbreviations 2
HWA IROST 1.
Hot-Wire Anemometer, Hot Wire Anemometry Iranian Research Organization for Science and Technology
Introduction
Vertical wind tunnels are used for testing of aircraft and helicopters spin and simulation of the free fall of skydivers. In such a wind tunnel, a protective net made of typically 5 cm mesh of multistrand wires of 2 to 3 mm diameter, is installed below the flight chamber to prevent the fall of skydivers or test models to the ground. The small mesh size of the protective net and the maximum dynamic pressure, which occurs at the flight chamber of the wind tunnel, produce a large pressure drop of about 20 to 30% of the total pressure drop at this section [1], resulting in increased power requirement to attain a desired speed in the tunnel. Therefore, it is necessary to consider this pressure drop in the design of vertical wind tunnels. For this purpose, drag coefficient of the multistrand wires that make up the protective net should be determined from the pressure measurements downstream of the wires. The multistrand wires are typically 2 to 3 mm in diameter, which makes it difficult to use the model surface pressure distribution or balance methods to determine the drag coefficient of the wires. Consequently, the preferred option will be to use the wake survey method [2]. In this method, flow velocity and turbulence intensity downstream of the test model must be measured. Van Dam [3] took into account Reynolds stress and applied continuum and conservation of linear momentum equations to a control volume of the test model to present the following equation for the drag coefficient: p s,e p s,w y U CD d 2 q L U
U 1 U
y 1 y d L q xx d L
(1)
The quantity xx can be expressed as the summation of viscous and Reynolds stresses as given below:
3
U 2 xx 2 .V u2 2U ' u ' u2 x 3
(2)
The first and second terms in Eq. (2) present the viscous stress and the Reynolds stress, respectively. In case of flow over flat plates, the flow condition can be considered as turbulent at Reynolds numbers, Re > 105. However, in the present investigation, due to the large velocity fluctuations for bluff bodies under study, the conditions can be considered turbulent even at low Re values. Moreover, because of the high ratio of Reynolds stress to viscous stress, the first term in Eq. (2) may be neglected. Additionally, density fluctuations of incompressible flows are negligible, and hence, can be neglected. Therefore, on substitution of the reduced form of Eq. (2) in Eq. (1), the rephrased form of Eq. (1) is obtained as Eq. (3): p s,e p s,w y U d 2 C D L q U
U 1 U
y u2 y d 2 d L U 2 L
(3)
In Eq. (3), the first, second and third integrals represent the pressure difference, momentum difference and the Reynolds stress, respectively. Since it is difficult to measure the static pressure in the wake region, Goldstein [4] considered the static pressure in this region as three-dimensional turbulence (in the form of Eq. (4)). On the basis of Goldstein analysis, the static pressure can be obtained from the measurement of velocity fluctuations. Consequently, the formulation in the form of Eq. (5) can be written for CD:
ps ,e ps, w q , q U wU
CD 2
U 1 U
1 (u '2 v2 w2 ) 2
y d L w
v 2 w 2 u ' 2 U 2
y d L
(4)
(5)
If either Eq. (1) or Eq. (3) is used in the measurements, the static and dynamic pressures must be simultaneously measured. On the other hand, if Eq. (5) is applied, three dimensional hotwire probes will be needed for the flow measurements. However, three-dimensional hot-wire 4
probes cannot be used because of their large dimensions compared to the dimensions of the wake region of the multistrand wires or cylindrical rods, which are about 2 to 3 mm in diameter [5]. If turbulence in the wake region is assumed to be homogenous , Eq. (5) can be simplified, which makes it possible to use a single normal hot-wire anemometer probe for making measurements with acceptable accuracy. Therefore, for measurement of the momentum difference using a single normal hot-wire anemometer probe, it is important to determine the appropriate distance (X/D) from the model, where the homogenous turbulence condition holds, i.e., the shear stress is a minimum and flow turbulence could be considered to be almost homogenous
being of the
same order). Flow downstream of small diameter cylindrical rods has been studied by other researchers [57]. For example, Lu et al. [6] used wake survey method and applied Eq. (5) to study the drag coefficient of cylindrical rod with a highly turbulent three-dimensional wake region. Using pitot tube and hot-wire anemometers (HWA), they measured dynamic pressure and components of flow velocity fluctuations and obtained the drag force over the cylindrical rod. At close distances from the cylinder, contribution of the Reynolds stress component is higher; however, the effect decreases with increase in the distance at downstream. Antonia and Rajagopalan [7] used X-probe hot-wire anemometer to study the drag coefficient over a cylindrical rod at up to 60D (where D is the cylindrical rod diameter) and Reynolds number of 56000. At distance X/D = 5, the Reynolds stress term constitutes about 22% of the total drag coefficient; decreasing with increase in the distance downstream of the cylinder, so that at X/D = 20, this term accounts for only 5% of the total drag coefficient. Dutta et al. [8] examined the properties of the wake of a square cylinder as a function of its orientation to the incoming flow. They considered three Reynolds numbers and three different orientations in their experiments and characterized the wake in terms of drag
5
coefficient, Strouhal number, velocity profiles, and the velocity fluctuations. In another experimental study, Kurian and Fransson [9] characterized the turbulence by means of energy spectra, characteristic turbulence length scales, energy dissipation, and kinetic energy decay rate, behind a set of grids with the feature of having roughly the same solidity but different mesh and bar widths. This procedure was used to vary the turbulence characteristic length scales while keeping the same turbulence intensity. They performed measurements using hotwire X-probes oriented in both directions, obtaining data about all three directional velocity components. Small single-wire probes were also used for faster frequency response. In the present work, drag coefficient of multistrand wires was determined from measurement data using a single HWA probe. Moreover, the drag coefficient of multistrand wires of 10 mm diameter was also determined using a pitot tube of 1.2 mm diameter to measure the total pressure downstream of the wires. Initially, flow velocity profile and turbulence intensity downstream of a cylindrical rod of diameter D were used to obtain the non-dimensional distance, X/D, at which single HWA probe measurements can be used to determine the drag coefficient of the multistrand wires with acceptable accuracy. Consequently, at Reynolds numbers of interest, drag coefficients of the multistrand wires and the cylindrical rods were measured and the results were compared. In addition, results for the drag coefficient of the multistrand wires obtained from the single HWA probe and pitot tube measurements were compared.
2.
Experimental Method
All experiments using a closed circuit wind tunnel were carried out at Iranian Research Organization for Science and Technology (IROST). Figure 1 shows the experimental wind tunnel, which is 2 m long with a 60 cm × 60 cm test section. Flow velocity is controlled by varying the speed of a fan in the range of 2 to 28 m/s. In order to obtain adequate airflow, 4
6
mesh screens are installed in the wind tunnel settling chamber, of which, one is placed before and the remaining three are placed after the honey comb. A hot-wire anemometer (HWA) (Fara Sanjesh Saba Co., Iran) was used to measure the flow velocity profile and turbulence intensity downstream of the multistrand wires and the cylindrical rods. The hot-wire probe is of single normal (SN) type with a sensor made of 5µm tungsten wire. The HWA and its probe have a cutoff frequency of 16 kHz. The measurement data is transferred to a PC via a 12 bit A/D data acquisition card for further processing and analysis using dedicated software (Flow Ware). The probe is moved in the wind tunnel using a traverse mechanism of 0.01 mm accuracy. In addition, a pitot tube of 1.2 mm diameter has been used for the measurement of total pressure in the wake of multistrand wires of 10 mm diameter. Details of the equipment used in this study are presented as following:
Pressure transducer: Model: DC005NDC4, Honeywell, Pressure Range: ± 5.0 in H2o, Temperature compensated over 0°C to 50°C
The length of the filament of hot-wire probe: 1.25 mm
The overheat ratio ((Rw-Ra)/Ra): 0.8. Here, Ra and Rw are the H.W. sensor resistance at ambient and operating temperatures, respectively.
Moreover, the laboratory ambient temperature was about 28 ºC, which was kept constant during the experiments. Initially, HWA measurements were used to determine the drag coefficients of cylindrical rods of 3 and 10 mm diameters, and the results were compared with corresponding values reported in the open literature [10]. Consequently, flow downstream of the multistrand wires was measured at Reynolds numbers of interest. Table 1 presents the characteristics of the multistrand wires and the cylindrical rods used in the experiments at different flow velocities. Figure 2 shows a specimen of multistrand wires, 3 mm in diameter, made of seven strands of wire of 1 mm diameter.
7
The main sources of measurements uncertainty associated with the determination of drag coefficient are the uncertainty pertaining to the measurement of instantaneous velocities and the uncertainty related to the positioning of the hot-wire probe. Assuming a Gaussian distribution and a coverage factor of 2, the total uncertainty (%) is obtained as follows [11]:
Uncertainty in velocity measurements (U > 2.5 m/s) using pitot tube and pressure transducer: 0.006
Uncertainty due to the traverse mechanism: 0.003
Uncertainty due to the A/D board resolution for 12 bit and 10 volts: 0.0007
Uncertainty due to ambient temperature variations: 0.002 from Ref. [12]
Uncertainty in spline curve fitting: 0.004
From above, the total uncertainty in velocity measurement using HWA is determined to be 1.57%.
3.
Results and Discussion
The experiments were conducted at different Reynolds numbers. The minimum and maximum Reynolds numbers pertaining to the cylindrical rods experiments were 1570 and 10470, and the corresponding drag coefficients at these Reynolds numbers were 0.96 and 1.2, respectively (see Fig. 3). In order to measure the momentum difference term, it is necessary to measure velocity at the wake region of the cylindrical rod. Figure 4 shows the nondimensional velocity distribution (U/U ) downstream of the cylindrical rod versus the nondimensional distance perpendicular to the wake region (Y/D), at X/D = 2, 10, 20, 30 and Re = 1570. At X/D = 2, two phenomena take place in the flow, namely velocity deficiency and velocity overflow (velocity higher than the free stream velocity) [5]. With increase in the distance at
8
downstream, the velocity deficiency decreases and the overflow phenomenon disappears; however, the width of the wake region increases. Figure 5 depicts the variations of the minimum non-dimensional velocity (Umin/U ) downstream of the cylindrical rod at various X/D values and different Reynolds numbers. As shown, velocity deficiency close to the cylindrical rod is large; however, it reduces with increase in the distance downstream of the cylindrical rod. At X/D = 8, the minimum velocity at the wake region is about 82% of the corresponding free stream velocity, remaining almost constant with further increase in the distance. It is worth mentioning that at distances X/D ≤ 4, the velocity profile exhibits overflow. In addition, width of the wake region plays an important role in the measurement of the momentum difference term (see Eq. (3)). Distribution of the non-dimensional width of the wake region for the cylindrical rod (the ratio W/D) at different Reynolds numbers is depicted in Fig. 6. As shown, the ratio W/D increases with increase in X/D. At X/D = 2, width of the wake region shows a steep slope, after which, the increasing trend continues, albeit with a more gentle (gradual) slope. In addition, it was observed that W/D increases with increase in Reynolds number, which may lead to a probable increase in drag coefficient. Another term in Eq. (3), which is important for the determination of drag coefficient by the wake survey method, is the Reynolds stress term. On the basis of Eq. (3), the Reynolds stress term produces a reducing effect on the drag coefficient. However, according to Eq. (5), where the pressure difference at the wake region is expressed in terms of turbulence intensity, it will be necessary to measure the turbulence intensity in three-dimensions. In that case, according to Eq. (5), the consideration of Reynolds stress will result in more realistic determination of drag coefficient. Provided the turbulence intensity downstream of the cylindrical rod is homogenous, a one-dimensional probe can be used to measure the turbulence intensity and the pressure difference, and Reynolds stress terms can then be expressed by Eq. (4) using the
9
Goldstein assumptions [4]. Turbulence intensity distribution at various X/D values and Re = 1570 is shown in Fig. 7. The turbulence intensity (Tu) is obtained from the relation, √̅̅̅̅̅
. As seen, close to the cylindrical rod, the turbulence intensity is high, showing an increase of up to 30%. At very short distances from the cylindrical rod (for example at X/D = 2), the turbulence intensity at the center of the wake region is not maximum. However, with increase in the distance (for example at X/D = 10), the turbulence intensity attains its maximum value at the center of the wake region, showing a decreasing trend. Figure 8 depicts the distribution of the maximum flow turbulence, downstream of the cylindrical rod at different Reynolds numbers. As shown, turbulence intensity close to the cylindrical rod is high at about 35% and decreases sharply with increase in X/D for up to X/D = 20, reaching values of 10 to 13%. On further increase in X/D, the slope becomes more gentle, and at X/D = 35, turbulence intensity reaches values of 8 to 11%. It is to be noted that the maximum turbulence intensity is dependent on Reynolds number, and the above increase in turbulence intensity from 8% to 11% is due to the increase in Reynolds number from 1570 to 10470. Figure 9 presents the relative numbers of the momentum difference term, CDm/CD, on the basis of the distance downstream of the cylindrical rod at different Reynolds numbers. As shown, at distances close to the cylindrical rod (X/D < 5), the drag coefficient due to the momentum difference term in Eq. (5) is low; with less than 50% contribution to the total drag coefficient. However, with increase in X/D, the drag coefficient increases, and at X/D = 20, its contribution to the total drag coefficient increases to about 82%. On further increase in X/D, the increasing slope of the drag coefficient due to the momentum difference term becomes gentler. However, its increasing trend continues, such that at X/D = 35, the drag coefficient attains a value close to 93% of the total drag coefficient. As shown in Fig. 9, the ratio CDm/CD is dependent on Reynolds number. For example, at X/D = 35, the ratio attains a value of 97% 10
at Re = 1570, and at Re = 10470, this value reaches 95%, which clearly indicates the dependency of variations of CD on Reynolds number, which corresponds to the values in Fig. 3 and Table 1. The relative numbers of Reynolds stress term (CDT/CD), which present the distribution of the drag coefficient due to the Reynolds stress term downstream of the cylindrical rod, is shown in Fig. 10 for different Reynolds numbers. At low X/D values, Reynolds stress is high, decreasing with increase in X/D. The slope of this decrement is gentle up to X/D = 20, after which, the decreasing trend continues, albeit at a lower rate. In addition, with increase in Reynolds number, the drag coefficient due to Reynolds stress term is increased. It is worth mentioning that at low X/D values, the flow turbulence is not homogenous [7], while the turbulence at higher X/D values is assumed to be homogenous. Figure 11 shows the results obtained from the application of Eq. (5), which is the summation of drag coefficients due to the momentum difference and Reynolds stress terms. As shown, at low X/D values, the drag coefficient is much lower than the corresponding value obtained from Fig. 3; approaching the value in Fig. 3 with increase in X/D value. Deviation of the measured data from the literature data [10] for the cylindrical rod at different Reynolds numbers against the non-dimensional measurement location (X/D) is shown in Fig. 12. The deviations are due to the use of a single normal HWA probe instead of a 3dimensional HWA probe for the determination of drag behind bluff bodies. If the measurement is carried out at X/D = 2, the deviation of about 45 to 60% is incurred. This shows that flow turbulence is not homogenous in this zone, and therefore, it is not possible to use a one-dimensional hot-wire probe. Deviation in measurements decreases with increase in distance, such that at X/D = 20, the deviation is reduced to 10 to 15% and at X/D = 35, the corresponding deviation is about 1 to 4%. Under this condition, the flow turbulence can be assumed to be homogenous. Considering Fig. 8, it can be concluded that when the turbulence
11
intensity is about 10% or lower, Deviation in measured data also will be lower than 10%. Therefore, to use a one-dimensional hot-wire probe for obtaining accurate data for the determination of the drag coefficient of the multistrand wires, the measurements should be performed at X/D > 30. In order to determine the drag coefficient, the total pressure in the wake of multistrand wires of 10 mm diameter was also measured using a pitot tube. Figure 13 shows the variations of Pt Ps , e q
on the basis of Y/D at Re=2665 and Re=10380, where Pt is the total pressure, Ps,e is
the static pressure outside the wake region, and
is dynamic pressure in the free stream.
The figure shows the effect of static pressure in the determination of drag coefficient (refer to Eq. (3)). Drag coefficients of cylindrical rods determined from HWA measurements and application of Eq. (5), and drag coefficients of the multistrand wires determined from HWA measurements, application of Eq. (5), and the measurements using the pitot tube are shown in Fig. 14. In addition, for comparison purpose, variations of drag coefficient for cylindrical rod versus Reynolds number from Ref. [10] have been included in this figure. As shown for the multistrand wires, results of the measurement data from pitot tube and HWA are in good agreement. The drag coefficient of cylindrical rod, Fig. 3 from Ref. [10], at Re = 1000 is about 1 and decreases slightly with increase in Reynolds number up to 2500. Then, it acquires an increasing trend, reaching a value of 1.2 at Re = 10000. Subsequently, it attains a constant value of 1.2 up to Re = 2 × 105 (see Fig. 3). The measurement data pertaining to the cylindrical rod are close to the values reported for cylindrical rods in Ref. [10], showing a similar trend. In addition, as shown in Fig. 14, drag coefficient values for the multistrand wires are higher than those of the cylindrical rods, being almost constant for Reynolds numbers between 2000 and 10000. At Re = 2000, drag coefficient of the multistrand wires is
12
higher than that of the cylindrical rod by about 23%. This difference decreases with increase in Reynolds number, so for Re > 10000, drag coefficient values for the multistrand wires and the cylindrical rods are almost similar. Considering Ref. [13], the critical Reynolds number (Reynolds number at which the flow changes from laminar to turbulent separation) decreases with increase in turbulence intensity of the free flow. In addition, the roughness of the cylindrical rod surface also causes a reduction in the critical Reynolds number. As shown in Fig. 3, for Re>105, there is a steep fall in the CD of the cylindrical rod due to the creation of transient boundary layer, which delays the flow separation point and reduces the width of the wake behind the cylinder. Moreover, drag coefficient depends on the angle of separation of the flow from the cylindrical rod surface, so that for Re > 10000, the flow separation angle is larger compared to the range 2000 < Re < 10000. Comparing the roughness of the surfaces of the multistrand wire and the cylindrical rod, it can be concluded that the drag coefficients of the two are equivalent at higher Reynolds numbers. Figure 15 shows the flow velocity distribution for cylindrical rod at X/D = 30 and Re = 1570 and Re = 10470. As shown, the velocity deficiency is higher at Re = 10470. In addition, the width of wake region is slightly bigger than the case of Re = 1570. Figure 16 shows the flow velocity distribution for the multistrand wires at X/D = 30 and Re = 1570 and Re = 10470. As shown, the width of wake region and the flow velocity deficiency are similar for the multistrand wire at Re = 1570 and Re = 10470. Therefore, it may be concluded that the drag coefficients of the multistrand wires at Re = 1570 and Re = 10470 are nearly constant. In view of the aforementioned discussion, it is evident that the drag coefficient of the multistrand wires at Re = 1570 is higher than that of the cylindrical rod by about 16%. At Re = 10470, the drag coefficients of the multistrand wires and the cylindrical rod are similar.
13
4.
Conclusions
In this work, drag coefficient of multistrand wires, used in the construction of protective nets of vertical wind tunnels, was investigated. Two methods were applied: (i) measurement of flow velocity distribution and turbulence intensity downstream of wires using a single normal hot-wire anemometer probe, (ii) measurement of total pressure in the wake of the multistrand wires of 10 mm diameter using a pitot tube. Moreover, the wake survey method was used in this study. Results obtained by the two methods are in good agreement. Other conclusions drawn from this study are:
Use of a single normal hot-wire anemometer probe for the measurement of drag is only valid under homogenous turbulence conditions. Moreover, at a reduced turbulence intensity, the homogeneity assumption becomes more accurate, and hence, a single normal hot-wire anemometer probe can be used for the measurements with acceptable accuracy.
Deviation of the measured data from the literature data [10] at distances X/D ≤ 5 is about 40 to 45%. At X/D = 20, depending on Re number, the error is about 10 to 15%, and at X/D = 35, the error is reduced to less than 4%. At distances farther than X/D = 35, the maximum turbulence intensity is found to be about 10%.
As shown in Fig. 3, with increase in Re number in the range of 2 x 105 to 5 x 105, drag coefficient, CD, is reduced. Similarly, in the above range of Re, the use of roughness on cylindrical rod will reduce the drag coefficient. In this case, roughness can be considered as an artificial increase in the Reynolds number.
In the range 2000 < Re < 10000, which is of interest in vertical wind tunnel protective net application, the roughness of the multistrand wires artificially increases Re by shifting it further to the right as shown in Fig. 3. However, contrary to the cylindrical
14
rod, in this case due to the larger roughness of the multistrand wires (about 16%), this artificial increase in Re increases the drag coefficient of the multistrand wires. This explains the higher observed values of drag coefficient of the multistrand wires in the investigated range of Reynolds numbers.
At Re = 2000, drag coefficient of the multistrand wires is greater than the cylindrical rod by approximately 16%. However, this difference decreases with increase in Reynolds number; the two values approaching each other and attaining an almost equal value at Re = 10000.
References
[1]
Barlow, J.B., Rae, W.H. and Pope, A., 1999. Low Speed Wind Tunnel Testing, Wiley-Interscience Publication. John Wiley and Sons, Inc.
[2]
Ardekani, M.A., 2009. Low Speed Wind Tunnel (In Persian), Khajeh Nasir Technical University Publications, Tehran, Iran.
15
[3]
Van Dam, C.P., 1999. Recent Experience with diffrent methods of drag prediction, Progress in Aerospace Sciences, 35(8), pp. 751-798.
[4]
Goldstein, S., 1936. A Note on the Measurement of Total Head and Static Pressure in a Turbulent Stream., Proceedings of the Royal Society of London, Series A, 155, pp. 570-575.
[5]
Ardekani, M.A., 2009. Hot-wire Calibration using vortex shedding, Measurement, 42, pp. 722-729.
[6]
Lu, B. and Bragg, M., 2002. Experimental Investigation of the Wake Survey Method for a Bluff Body With a Highly Turbulent Wake, 20th AIAA Applied Aerodynamics Conference.
[7]
Antonia, R.A. and Rajagopalan, S., 1990. Determination of Drag of a Circular Cylinder, AIAA Journal, 28, pp. 1833-1834.
[8]
Dutta, S., Muralidhar, K. and Panigrahi, P.K., 2003. Influence of the orientation of a square cylinder on the wake properties, Experiments in Fluids, 34(1), pp. 16-23.
[9]
Kurian, T. and Fransson, J.H.M., 2009. Grid-generated turbulence revisited, Fluid Dyn. Res, 41(2).
[10]
Schlichting, H. and Gersten, K., 2000. Boundary-Layer Theory, 9th German Edition, Publisher Springer-Verlag Berlin Heidelberg.
[11]
Jorgensen, F.F, 2002. How to measure turbulence with hot-wire anemometer – a practical guide, DANTECH DYNAMICS Info., Publication No. 9040U6151.
[12]
Ardekani, M.A and Farhani, F., 2009. "Experimental Study on Response of Hot-Wire and Cylinderical Hot Film Anemometers Operating Under Varying Fluid Temperatures", Flow Measurement and Instrumentation 20, pp. 174-179.
16
[13]
Zdravkovich, M.M., 1990. Conceptual Overview of Laminar and Turbulent Flows Past Smooth and Rough Circular Cylinders, International Colliquimn on Bluff Body Aerodynamics and Applications, Kyoto, Japan.
Figures Captions Fig. 1: The closed circuit experimental wind tunnel. Fig. 2: A specimen of the multistrand wire used in the experiments. Fig. 3: Drag coefficient vs. Reynolds number for cylindrical rod [10]. Fig. 4: Non-dimensional velocity distribution at various distances downstream of cylindrical rod at Reynolds number of 1570. Fig. 5: Variations of the minimum non-dimensional velocity downstream of the cylindrical rod at different Reynolds numbers. Fig. 6: Distribution of the non-dimensional width of the cylindrical rod’s wake region at different Reynolds numbers. Fig. 7: Distribution of the turbulence intensity at various distances, downstream of cylindrical rod at Reynolds number of 1570. Fig. 8: Distribution of the maximum airflow turbulence intensity downstream of the cylindrical rod at different Reynolds numbers. Fig. 9: Relative numbers of momentum difference term (CDm/CD) on the basis of distance downstream of the cylindrical rod (X/D) at different Reynolds numbers. Fig. 10: Relative numbers of Reynolds stress term (CDT/CD) on the basis of distance downstream of the cylindrical rod (X/D) at different Reynolds numbers. Fig. 11: Distribution of the drag coefficient at various distances downstream of the cylindrical rod at different Reynolds numbers. Fig. 12: Deviation of measured data from literature data [10] for cylindrical rod at different Reynolds numbers.
17
Fig. 13: Variations of non-dimensional pressure (
) on basis of Y/D at two Reynolds
numbers. Fig. 14: Distribution of the drag coefficient for the tested multistrand wires and cylindrical rods vs. Reynolds number. Fig. 15: Flow velocity distribution for cylindrical rod: at distance X/D = 30, Re = 1570 and 10470. Fig. 16: Flow velocity distribution for multistrand wires: at distance X/D = 30, Re = 1570 and 10470.
Table 1: Multistrand wires and cylindrical rods used in the experiments at different flow velocities Sl.
Test specimen
No.
Diameter
Flow velocity
Reynolds
Drag Coefficient
(mm)
(m/s)
number
(from Fig. 3)
1
Multistrand wire
3
10
1570
-
2
Multistrand wire
3
15
2356
-
3
Multistrand wire
3
20
3140
-
4
Multistrand wire
10
3
1570
-
5
Multistrand wire
10
4.5
2356
-
6
Multistrand wire
10
6
3140
-
7
Cylindrical rod
3
10
1570
0.96
8
Cylindrical rod
3
15
2356
0.97
9
Cylindrical rod
3
20
3140
0.98
10
Cylindrical rod
10
10
5235
1.05
11
Cylindrical rod
10
15
7853
1.12
12
Cylindrical rod
10
20
10470
1.20
Highlights
The wake survey method was used for measuring drag of multistrand wires.
The non-dimensional distance for acceptable measurement error was X/D > 30. 18
Multistrand wires have higher drag than cylindrical rods at 1570 ≤ Re ≤ 10000.
Drag of cylindrical rod and multistrand wires is almost equal at Re ≥ 10000.
Results can be used for making protective wire nets of acceptable drag.
19
20
21
22
23
24
25
PII: DOI: Reference:
S0955-5986(16)30085-1 http://dx.doi.org/10.1016/j.flowmeasinst.2016.07.009 JFMI1231
To appear in: Flow Measurement and Instrumentation Received date: 28 November 2014 Revised date: 26 June 2016 Accepted date: 25 July 2016 Cite this article as: M.A. Ardekani, F. Farhani and A. Nourmohammadi, Experimental study of drag coefficient of multistrand wires using single normal hot-wire anemometer probe, Flow Measurement and Instrumentation, http://dx.doi.org/10.1016/j.flowmeasinst.2016.07.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental Study of Drag Coefficient of Multistrand Wires Using Single Normal Hot-Wire Anemometer Probe
M.A. Ardekani*, F. Farhani, A. Nourmohammadi
Department of Mechanical Engineering, Iranian Research Organization for Science and Technology (IROST), Tehran, Iran *Corresponding author. Department of Mechanical Engineering, Iranian Research Organization for Science and Technology (IROST), P.O. Box 15815 – 3538, Tehran, Iran. Tel./Fax: (0098)56276632. [email protected] (M.A. Ardekani)
Abstract In a vertical wind tunnel, used for testing of aircraft and helicopters spin and simulation of skydiving, a protective net made of multistrand wires is installed below the flight chamber to prevent the fall of the test models or skydivers to the ground. The drag due to the protective net is significant, which results in pressure drop and subsequent increase in the required power to attain a desired speed in the tunnel. This paper presents the results of an experimental study of drag coefficient of multistrand wires, using (i) a single normal hot-wire anemometer probe (HWA), (ii) a pitot tube, which measures the total pressure downstream of the multistrand wires. Initially, the non-dimensional distance, X/D, at which HWA measurements can be used to determine the drag coefficient of the multistrand wires with acceptable accuracy, was obtained by considering flow velocity profile and turbulence intensity, downstream of a cylindrical rod of diameter D. The distance was determined to be X/D > 30, where X is the distance along the test section downstream of the cylindrical rod. Results of pitot tube and HWA measurements are in good agreement. These results show that at Reynolds number, Re = 2000, drag coefficient of the multistrand wires is greater than the cylindrical rod by approximately 16%. However, the difference in the drag coefficients 1
decreases with increase in Re; the two values approaching each other and attaining an almost equal value at Re = 10000.
Keywords: Cylindrical rod, Drag coefficient, Hot-wire anemometer, Multistrand wires,
Turbulence intensity, Wake survey method
Nomenclature Latin symbols CD CDm CDT d D L Ps,e Ps,w Re U , ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ W W/D X X/D Y Y/D Greek symbols
Coefficient of drag The momentum difference component of the coefficient of drag The Reynolds stress component of the coefficient of drag Wire diameter Cylindrical rod diameter Characteristic Length Static pressure upstream of cylindrical rod Static pressure of wake dynamic pressure Reynolds number X- direction velocity Free stream streamwise velocity Components of velocity fluctuation Mean of squared fluctuations in X, Y, Z directions Width of wake region Non-dimensional width of wake region Distance along wake (X-direction) Non-dimensional distance along wake Distance perpendicular to wake (Y-direction) Non-dimensional distance perpendicular to wake Shear stress Dynamic Viscosity Density
Subscripts Free Stream Value at the inlet Abbreviations 2
HWA IROST 1.
Hot-Wire Anemometer, Hot Wire Anemometry Iranian Research Organization for Science and Technology
Introduction
Vertical wind tunnels are used for testing of aircraft and helicopters spin and simulation of the free fall of skydivers. In such a wind tunnel, a protective net made of typically 5 cm mesh of multistrand wires of 2 to 3 mm diameter, is installed below the flight chamber to prevent the fall of skydivers or test models to the ground. The small mesh size of the protective net and the maximum dynamic pressure, which occurs at the flight chamber of the wind tunnel, produce a large pressure drop of about 20 to 30% of the total pressure drop at this section [1], resulting in increased power requirement to attain a desired speed in the tunnel. Therefore, it is necessary to consider this pressure drop in the design of vertical wind tunnels. For this purpose, drag coefficient of the multistrand wires that make up the protective net should be determined from the pressure measurements downstream of the wires. The multistrand wires are typically 2 to 3 mm in diameter, which makes it difficult to use the model surface pressure distribution or balance methods to determine the drag coefficient of the wires. Consequently, the preferred option will be to use the wake survey method [2]. In this method, flow velocity and turbulence intensity downstream of the test model must be measured. Van Dam [3] took into account Reynolds stress and applied continuum and conservation of linear momentum equations to a control volume of the test model to present the following equation for the drag coefficient: p s,e p s,w y U CD d 2 q L U
U 1 U
y 1 y d L q xx d L
(1)
The quantity xx can be expressed as the summation of viscous and Reynolds stresses as given below:
3
U 2 xx 2 .V u2 2U ' u ' u2 x 3
(2)
The first and second terms in Eq. (2) present the viscous stress and the Reynolds stress, respectively. In case of flow over flat plates, the flow condition can be considered as turbulent at Reynolds numbers, Re > 105. However, in the present investigation, due to the large velocity fluctuations for bluff bodies under study, the conditions can be considered turbulent even at low Re values. Moreover, because of the high ratio of Reynolds stress to viscous stress, the first term in Eq. (2) may be neglected. Additionally, density fluctuations of incompressible flows are negligible, and hence, can be neglected. Therefore, on substitution of the reduced form of Eq. (2) in Eq. (1), the rephrased form of Eq. (1) is obtained as Eq. (3): p s,e p s,w y U d 2 C D L q U
U 1 U
y u2 y d 2 d L U 2 L
(3)
In Eq. (3), the first, second and third integrals represent the pressure difference, momentum difference and the Reynolds stress, respectively. Since it is difficult to measure the static pressure in the wake region, Goldstein [4] considered the static pressure in this region as three-dimensional turbulence (in the form of Eq. (4)). On the basis of Goldstein analysis, the static pressure can be obtained from the measurement of velocity fluctuations. Consequently, the formulation in the form of Eq. (5) can be written for CD:
ps ,e ps, w q , q U wU
CD 2
U 1 U
1 (u '2 v2 w2 ) 2
y d L w
v 2 w 2 u ' 2 U 2
y d L
(4)
(5)
If either Eq. (1) or Eq. (3) is used in the measurements, the static and dynamic pressures must be simultaneously measured. On the other hand, if Eq. (5) is applied, three dimensional hotwire probes will be needed for the flow measurements. However, three-dimensional hot-wire 4
probes cannot be used because of their large dimensions compared to the dimensions of the wake region of the multistrand wires or cylindrical rods, which are about 2 to 3 mm in diameter [5]. If turbulence in the wake region is assumed to be homogenous , Eq. (5) can be simplified, which makes it possible to use a single normal hot-wire anemometer probe for making measurements with acceptable accuracy. Therefore, for measurement of the momentum difference using a single normal hot-wire anemometer probe, it is important to determine the appropriate distance (X/D) from the model, where the homogenous turbulence condition holds, i.e., the shear stress is a minimum and flow turbulence could be considered to be almost homogenous
being of the
same order). Flow downstream of small diameter cylindrical rods has been studied by other researchers [57]. For example, Lu et al. [6] used wake survey method and applied Eq. (5) to study the drag coefficient of cylindrical rod with a highly turbulent three-dimensional wake region. Using pitot tube and hot-wire anemometers (HWA), they measured dynamic pressure and components of flow velocity fluctuations and obtained the drag force over the cylindrical rod. At close distances from the cylinder, contribution of the Reynolds stress component is higher; however, the effect decreases with increase in the distance at downstream. Antonia and Rajagopalan [7] used X-probe hot-wire anemometer to study the drag coefficient over a cylindrical rod at up to 60D (where D is the cylindrical rod diameter) and Reynolds number of 56000. At distance X/D = 5, the Reynolds stress term constitutes about 22% of the total drag coefficient; decreasing with increase in the distance downstream of the cylinder, so that at X/D = 20, this term accounts for only 5% of the total drag coefficient. Dutta et al. [8] examined the properties of the wake of a square cylinder as a function of its orientation to the incoming flow. They considered three Reynolds numbers and three different orientations in their experiments and characterized the wake in terms of drag
5
coefficient, Strouhal number, velocity profiles, and the velocity fluctuations. In another experimental study, Kurian and Fransson [9] characterized the turbulence by means of energy spectra, characteristic turbulence length scales, energy dissipation, and kinetic energy decay rate, behind a set of grids with the feature of having roughly the same solidity but different mesh and bar widths. This procedure was used to vary the turbulence characteristic length scales while keeping the same turbulence intensity. They performed measurements using hotwire X-probes oriented in both directions, obtaining data about all three directional velocity components. Small single-wire probes were also used for faster frequency response. In the present work, drag coefficient of multistrand wires was determined from measurement data using a single HWA probe. Moreover, the drag coefficient of multistrand wires of 10 mm diameter was also determined using a pitot tube of 1.2 mm diameter to measure the total pressure downstream of the wires. Initially, flow velocity profile and turbulence intensity downstream of a cylindrical rod of diameter D were used to obtain the non-dimensional distance, X/D, at which single HWA probe measurements can be used to determine the drag coefficient of the multistrand wires with acceptable accuracy. Consequently, at Reynolds numbers of interest, drag coefficients of the multistrand wires and the cylindrical rods were measured and the results were compared. In addition, results for the drag coefficient of the multistrand wires obtained from the single HWA probe and pitot tube measurements were compared.
2.
Experimental Method
All experiments using a closed circuit wind tunnel were carried out at Iranian Research Organization for Science and Technology (IROST). Figure 1 shows the experimental wind tunnel, which is 2 m long with a 60 cm × 60 cm test section. Flow velocity is controlled by varying the speed of a fan in the range of 2 to 28 m/s. In order to obtain adequate airflow, 4
6
mesh screens are installed in the wind tunnel settling chamber, of which, one is placed before and the remaining three are placed after the honey comb. A hot-wire anemometer (HWA) (Fara Sanjesh Saba Co., Iran) was used to measure the flow velocity profile and turbulence intensity downstream of the multistrand wires and the cylindrical rods. The hot-wire probe is of single normal (SN) type with a sensor made of 5µm tungsten wire. The HWA and its probe have a cutoff frequency of 16 kHz. The measurement data is transferred to a PC via a 12 bit A/D data acquisition card for further processing and analysis using dedicated software (Flow Ware). The probe is moved in the wind tunnel using a traverse mechanism of 0.01 mm accuracy. In addition, a pitot tube of 1.2 mm diameter has been used for the measurement of total pressure in the wake of multistrand wires of 10 mm diameter. Details of the equipment used in this study are presented as following:
Pressure transducer: Model: DC005NDC4, Honeywell, Pressure Range: ± 5.0 in H2o, Temperature compensated over 0°C to 50°C
The length of the filament of hot-wire probe: 1.25 mm
The overheat ratio ((Rw-Ra)/Ra): 0.8. Here, Ra and Rw are the H.W. sensor resistance at ambient and operating temperatures, respectively.
Moreover, the laboratory ambient temperature was about 28 ºC, which was kept constant during the experiments. Initially, HWA measurements were used to determine the drag coefficients of cylindrical rods of 3 and 10 mm diameters, and the results were compared with corresponding values reported in the open literature [10]. Consequently, flow downstream of the multistrand wires was measured at Reynolds numbers of interest. Table 1 presents the characteristics of the multistrand wires and the cylindrical rods used in the experiments at different flow velocities. Figure 2 shows a specimen of multistrand wires, 3 mm in diameter, made of seven strands of wire of 1 mm diameter.
7
The main sources of measurements uncertainty associated with the determination of drag coefficient are the uncertainty pertaining to the measurement of instantaneous velocities and the uncertainty related to the positioning of the hot-wire probe. Assuming a Gaussian distribution and a coverage factor of 2, the total uncertainty (%) is obtained as follows [11]:
Uncertainty in velocity measurements (U > 2.5 m/s) using pitot tube and pressure transducer: 0.006
Uncertainty due to the traverse mechanism: 0.003
Uncertainty due to the A/D board resolution for 12 bit and 10 volts: 0.0007
Uncertainty due to ambient temperature variations: 0.002 from Ref. [12]
Uncertainty in spline curve fitting: 0.004
From above, the total uncertainty in velocity measurement using HWA is determined to be 1.57%.
3.
Results and Discussion
The experiments were conducted at different Reynolds numbers. The minimum and maximum Reynolds numbers pertaining to the cylindrical rods experiments were 1570 and 10470, and the corresponding drag coefficients at these Reynolds numbers were 0.96 and 1.2, respectively (see Fig. 3). In order to measure the momentum difference term, it is necessary to measure velocity at the wake region of the cylindrical rod. Figure 4 shows the nondimensional velocity distribution (U/U ) downstream of the cylindrical rod versus the nondimensional distance perpendicular to the wake region (Y/D), at X/D = 2, 10, 20, 30 and Re = 1570. At X/D = 2, two phenomena take place in the flow, namely velocity deficiency and velocity overflow (velocity higher than the free stream velocity) [5]. With increase in the distance at
8
downstream, the velocity deficiency decreases and the overflow phenomenon disappears; however, the width of the wake region increases. Figure 5 depicts the variations of the minimum non-dimensional velocity (Umin/U ) downstream of the cylindrical rod at various X/D values and different Reynolds numbers. As shown, velocity deficiency close to the cylindrical rod is large; however, it reduces with increase in the distance downstream of the cylindrical rod. At X/D = 8, the minimum velocity at the wake region is about 82% of the corresponding free stream velocity, remaining almost constant with further increase in the distance. It is worth mentioning that at distances X/D ≤ 4, the velocity profile exhibits overflow. In addition, width of the wake region plays an important role in the measurement of the momentum difference term (see Eq. (3)). Distribution of the non-dimensional width of the wake region for the cylindrical rod (the ratio W/D) at different Reynolds numbers is depicted in Fig. 6. As shown, the ratio W/D increases with increase in X/D. At X/D = 2, width of the wake region shows a steep slope, after which, the increasing trend continues, albeit with a more gentle (gradual) slope. In addition, it was observed that W/D increases with increase in Reynolds number, which may lead to a probable increase in drag coefficient. Another term in Eq. (3), which is important for the determination of drag coefficient by the wake survey method, is the Reynolds stress term. On the basis of Eq. (3), the Reynolds stress term produces a reducing effect on the drag coefficient. However, according to Eq. (5), where the pressure difference at the wake region is expressed in terms of turbulence intensity, it will be necessary to measure the turbulence intensity in three-dimensions. In that case, according to Eq. (5), the consideration of Reynolds stress will result in more realistic determination of drag coefficient. Provided the turbulence intensity downstream of the cylindrical rod is homogenous, a one-dimensional probe can be used to measure the turbulence intensity and the pressure difference, and Reynolds stress terms can then be expressed by Eq. (4) using the
9
Goldstein assumptions [4]. Turbulence intensity distribution at various X/D values and Re = 1570 is shown in Fig. 7. The turbulence intensity (Tu) is obtained from the relation, √̅̅̅̅̅
. As seen, close to the cylindrical rod, the turbulence intensity is high, showing an increase of up to 30%. At very short distances from the cylindrical rod (for example at X/D = 2), the turbulence intensity at the center of the wake region is not maximum. However, with increase in the distance (for example at X/D = 10), the turbulence intensity attains its maximum value at the center of the wake region, showing a decreasing trend. Figure 8 depicts the distribution of the maximum flow turbulence, downstream of the cylindrical rod at different Reynolds numbers. As shown, turbulence intensity close to the cylindrical rod is high at about 35% and decreases sharply with increase in X/D for up to X/D = 20, reaching values of 10 to 13%. On further increase in X/D, the slope becomes more gentle, and at X/D = 35, turbulence intensity reaches values of 8 to 11%. It is to be noted that the maximum turbulence intensity is dependent on Reynolds number, and the above increase in turbulence intensity from 8% to 11% is due to the increase in Reynolds number from 1570 to 10470. Figure 9 presents the relative numbers of the momentum difference term, CDm/CD, on the basis of the distance downstream of the cylindrical rod at different Reynolds numbers. As shown, at distances close to the cylindrical rod (X/D < 5), the drag coefficient due to the momentum difference term in Eq. (5) is low; with less than 50% contribution to the total drag coefficient. However, with increase in X/D, the drag coefficient increases, and at X/D = 20, its contribution to the total drag coefficient increases to about 82%. On further increase in X/D, the increasing slope of the drag coefficient due to the momentum difference term becomes gentler. However, its increasing trend continues, such that at X/D = 35, the drag coefficient attains a value close to 93% of the total drag coefficient. As shown in Fig. 9, the ratio CDm/CD is dependent on Reynolds number. For example, at X/D = 35, the ratio attains a value of 97% 10
at Re = 1570, and at Re = 10470, this value reaches 95%, which clearly indicates the dependency of variations of CD on Reynolds number, which corresponds to the values in Fig. 3 and Table 1. The relative numbers of Reynolds stress term (CDT/CD), which present the distribution of the drag coefficient due to the Reynolds stress term downstream of the cylindrical rod, is shown in Fig. 10 for different Reynolds numbers. At low X/D values, Reynolds stress is high, decreasing with increase in X/D. The slope of this decrement is gentle up to X/D = 20, after which, the decreasing trend continues, albeit at a lower rate. In addition, with increase in Reynolds number, the drag coefficient due to Reynolds stress term is increased. It is worth mentioning that at low X/D values, the flow turbulence is not homogenous [7], while the turbulence at higher X/D values is assumed to be homogenous. Figure 11 shows the results obtained from the application of Eq. (5), which is the summation of drag coefficients due to the momentum difference and Reynolds stress terms. As shown, at low X/D values, the drag coefficient is much lower than the corresponding value obtained from Fig. 3; approaching the value in Fig. 3 with increase in X/D value. Deviation of the measured data from the literature data [10] for the cylindrical rod at different Reynolds numbers against the non-dimensional measurement location (X/D) is shown in Fig. 12. The deviations are due to the use of a single normal HWA probe instead of a 3dimensional HWA probe for the determination of drag behind bluff bodies. If the measurement is carried out at X/D = 2, the deviation of about 45 to 60% is incurred. This shows that flow turbulence is not homogenous in this zone, and therefore, it is not possible to use a one-dimensional hot-wire probe. Deviation in measurements decreases with increase in distance, such that at X/D = 20, the deviation is reduced to 10 to 15% and at X/D = 35, the corresponding deviation is about 1 to 4%. Under this condition, the flow turbulence can be assumed to be homogenous. Considering Fig. 8, it can be concluded that when the turbulence
11
intensity is about 10% or lower, Deviation in measured data also will be lower than 10%. Therefore, to use a one-dimensional hot-wire probe for obtaining accurate data for the determination of the drag coefficient of the multistrand wires, the measurements should be performed at X/D > 30. In order to determine the drag coefficient, the total pressure in the wake of multistrand wires of 10 mm diameter was also measured using a pitot tube. Figure 13 shows the variations of Pt Ps , e q
on the basis of Y/D at Re=2665 and Re=10380, where Pt is the total pressure, Ps,e is
the static pressure outside the wake region, and
is dynamic pressure in the free stream.
The figure shows the effect of static pressure in the determination of drag coefficient (refer to Eq. (3)). Drag coefficients of cylindrical rods determined from HWA measurements and application of Eq. (5), and drag coefficients of the multistrand wires determined from HWA measurements, application of Eq. (5), and the measurements using the pitot tube are shown in Fig. 14. In addition, for comparison purpose, variations of drag coefficient for cylindrical rod versus Reynolds number from Ref. [10] have been included in this figure. As shown for the multistrand wires, results of the measurement data from pitot tube and HWA are in good agreement. The drag coefficient of cylindrical rod, Fig. 3 from Ref. [10], at Re = 1000 is about 1 and decreases slightly with increase in Reynolds number up to 2500. Then, it acquires an increasing trend, reaching a value of 1.2 at Re = 10000. Subsequently, it attains a constant value of 1.2 up to Re = 2 × 105 (see Fig. 3). The measurement data pertaining to the cylindrical rod are close to the values reported for cylindrical rods in Ref. [10], showing a similar trend. In addition, as shown in Fig. 14, drag coefficient values for the multistrand wires are higher than those of the cylindrical rods, being almost constant for Reynolds numbers between 2000 and 10000. At Re = 2000, drag coefficient of the multistrand wires is
12
higher than that of the cylindrical rod by about 23%. This difference decreases with increase in Reynolds number, so for Re > 10000, drag coefficient values for the multistrand wires and the cylindrical rods are almost similar. Considering Ref. [13], the critical Reynolds number (Reynolds number at which the flow changes from laminar to turbulent separation) decreases with increase in turbulence intensity of the free flow. In addition, the roughness of the cylindrical rod surface also causes a reduction in the critical Reynolds number. As shown in Fig. 3, for Re>105, there is a steep fall in the CD of the cylindrical rod due to the creation of transient boundary layer, which delays the flow separation point and reduces the width of the wake behind the cylinder. Moreover, drag coefficient depends on the angle of separation of the flow from the cylindrical rod surface, so that for Re > 10000, the flow separation angle is larger compared to the range 2000 < Re < 10000. Comparing the roughness of the surfaces of the multistrand wire and the cylindrical rod, it can be concluded that the drag coefficients of the two are equivalent at higher Reynolds numbers. Figure 15 shows the flow velocity distribution for cylindrical rod at X/D = 30 and Re = 1570 and Re = 10470. As shown, the velocity deficiency is higher at Re = 10470. In addition, the width of wake region is slightly bigger than the case of Re = 1570. Figure 16 shows the flow velocity distribution for the multistrand wires at X/D = 30 and Re = 1570 and Re = 10470. As shown, the width of wake region and the flow velocity deficiency are similar for the multistrand wire at Re = 1570 and Re = 10470. Therefore, it may be concluded that the drag coefficients of the multistrand wires at Re = 1570 and Re = 10470 are nearly constant. In view of the aforementioned discussion, it is evident that the drag coefficient of the multistrand wires at Re = 1570 is higher than that of the cylindrical rod by about 16%. At Re = 10470, the drag coefficients of the multistrand wires and the cylindrical rod are similar.
13
4.
Conclusions
In this work, drag coefficient of multistrand wires, used in the construction of protective nets of vertical wind tunnels, was investigated. Two methods were applied: (i) measurement of flow velocity distribution and turbulence intensity downstream of wires using a single normal hot-wire anemometer probe, (ii) measurement of total pressure in the wake of the multistrand wires of 10 mm diameter using a pitot tube. Moreover, the wake survey method was used in this study. Results obtained by the two methods are in good agreement. Other conclusions drawn from this study are:
Use of a single normal hot-wire anemometer probe for the measurement of drag is only valid under homogenous turbulence conditions. Moreover, at a reduced turbulence intensity, the homogeneity assumption becomes more accurate, and hence, a single normal hot-wire anemometer probe can be used for the measurements with acceptable accuracy.
Deviation of the measured data from the literature data [10] at distances X/D ≤ 5 is about 40 to 45%. At X/D = 20, depending on Re number, the error is about 10 to 15%, and at X/D = 35, the error is reduced to less than 4%. At distances farther than X/D = 35, the maximum turbulence intensity is found to be about 10%.
As shown in Fig. 3, with increase in Re number in the range of 2 x 105 to 5 x 105, drag coefficient, CD, is reduced. Similarly, in the above range of Re, the use of roughness on cylindrical rod will reduce the drag coefficient. In this case, roughness can be considered as an artificial increase in the Reynolds number.
In the range 2000 < Re < 10000, which is of interest in vertical wind tunnel protective net application, the roughness of the multistrand wires artificially increases Re by shifting it further to the right as shown in Fig. 3. However, contrary to the cylindrical
14
rod, in this case due to the larger roughness of the multistrand wires (about 16%), this artificial increase in Re increases the drag coefficient of the multistrand wires. This explains the higher observed values of drag coefficient of the multistrand wires in the investigated range of Reynolds numbers.
At Re = 2000, drag coefficient of the multistrand wires is greater than the cylindrical rod by approximately 16%. However, this difference decreases with increase in Reynolds number; the two values approaching each other and attaining an almost equal value at Re = 10000.
References
[1]
Barlow, J.B., Rae, W.H. and Pope, A., 1999. Low Speed Wind Tunnel Testing, Wiley-Interscience Publication. John Wiley and Sons, Inc.
[2]
Ardekani, M.A., 2009. Low Speed Wind Tunnel (In Persian), Khajeh Nasir Technical University Publications, Tehran, Iran.
15
[3]
Van Dam, C.P., 1999. Recent Experience with diffrent methods of drag prediction, Progress in Aerospace Sciences, 35(8), pp. 751-798.
[4]
Goldstein, S., 1936. A Note on the Measurement of Total Head and Static Pressure in a Turbulent Stream., Proceedings of the Royal Society of London, Series A, 155, pp. 570-575.
[5]
Ardekani, M.A., 2009. Hot-wire Calibration using vortex shedding, Measurement, 42, pp. 722-729.
[6]
Lu, B. and Bragg, M., 2002. Experimental Investigation of the Wake Survey Method for a Bluff Body With a Highly Turbulent Wake, 20th AIAA Applied Aerodynamics Conference.
[7]
Antonia, R.A. and Rajagopalan, S., 1990. Determination of Drag of a Circular Cylinder, AIAA Journal, 28, pp. 1833-1834.
[8]
Dutta, S., Muralidhar, K. and Panigrahi, P.K., 2003. Influence of the orientation of a square cylinder on the wake properties, Experiments in Fluids, 34(1), pp. 16-23.
[9]
Kurian, T. and Fransson, J.H.M., 2009. Grid-generated turbulence revisited, Fluid Dyn. Res, 41(2).
[10]
Schlichting, H. and Gersten, K., 2000. Boundary-Layer Theory, 9th German Edition, Publisher Springer-Verlag Berlin Heidelberg.
[11]
Jorgensen, F.F, 2002. How to measure turbulence with hot-wire anemometer – a practical guide, DANTECH DYNAMICS Info., Publication No. 9040U6151.
[12]
Ardekani, M.A and Farhani, F., 2009. "Experimental Study on Response of Hot-Wire and Cylinderical Hot Film Anemometers Operating Under Varying Fluid Temperatures", Flow Measurement and Instrumentation 20, pp. 174-179.
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[13]
Zdravkovich, M.M., 1990. Conceptual Overview of Laminar and Turbulent Flows Past Smooth and Rough Circular Cylinders, International Colliquimn on Bluff Body Aerodynamics and Applications, Kyoto, Japan.
Figures Captions Fig. 1: The closed circuit experimental wind tunnel. Fig. 2: A specimen of the multistrand wire used in the experiments. Fig. 3: Drag coefficient vs. Reynolds number for cylindrical rod [10]. Fig. 4: Non-dimensional velocity distribution at various distances downstream of cylindrical rod at Reynolds number of 1570. Fig. 5: Variations of the minimum non-dimensional velocity downstream of the cylindrical rod at different Reynolds numbers. Fig. 6: Distribution of the non-dimensional width of the cylindrical rod’s wake region at different Reynolds numbers. Fig. 7: Distribution of the turbulence intensity at various distances, downstream of cylindrical rod at Reynolds number of 1570. Fig. 8: Distribution of the maximum airflow turbulence intensity downstream of the cylindrical rod at different Reynolds numbers. Fig. 9: Relative numbers of momentum difference term (CDm/CD) on the basis of distance downstream of the cylindrical rod (X/D) at different Reynolds numbers. Fig. 10: Relative numbers of Reynolds stress term (CDT/CD) on the basis of distance downstream of the cylindrical rod (X/D) at different Reynolds numbers. Fig. 11: Distribution of the drag coefficient at various distances downstream of the cylindrical rod at different Reynolds numbers. Fig. 12: Deviation of measured data from literature data [10] for cylindrical rod at different Reynolds numbers.
17
Fig. 13: Variations of non-dimensional pressure (
) on basis of Y/D at two Reynolds
numbers. Fig. 14: Distribution of the drag coefficient for the tested multistrand wires and cylindrical rods vs. Reynolds number. Fig. 15: Flow velocity distribution for cylindrical rod: at distance X/D = 30, Re = 1570 and 10470. Fig. 16: Flow velocity distribution for multistrand wires: at distance X/D = 30, Re = 1570 and 10470.
Table 1: Multistrand wires and cylindrical rods used in the experiments at different flow velocities Sl.
Test specimen
No.
Diameter
Flow velocity
Reynolds
Drag Coefficient
(mm)
(m/s)
number
(from Fig. 3)
1
Multistrand wire
3
10
1570
-
2
Multistrand wire
3
15
2356
-
3
Multistrand wire
3
20
3140
-
4
Multistrand wire
10
3
1570
-
5
Multistrand wire
10
4.5
2356
-
6
Multistrand wire
10
6
3140
-
7
Cylindrical rod
3
10
1570
0.96
8
Cylindrical rod
3
15
2356
0.97
9
Cylindrical rod
3
20
3140
0.98
10
Cylindrical rod
10
10
5235
1.05
11
Cylindrical rod
10
15
7853
1.12
12
Cylindrical rod
10
20
10470
1.20
Highlights
The wake survey method was used for measuring drag of multistrand wires.
The non-dimensional distance for acceptable measurement error was X/D > 30. 18
Multistrand wires have higher drag than cylindrical rods at 1570 ≤ Re ≤ 10000.
Drag of cylindrical rod and multistrand wires is almost equal at Re ≥ 10000.
Results can be used for making protective wire nets of acceptable drag.
19
20
21
22
23
24
25