Filios A Etal_2001_direct And In-verse Design Calculations For A Settling Chamber And Contraction Arrangement

ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece Proceedings of First Nat. Conf. on Recent Advances in Mech. Eng. September 17-20, 2001, Patras, Greece

ANG1/P158 DIRECT AND INVERSE DESIGN CALCULATIONS FOR A SETTLING CHAMBER AND CONTRACTION ARRANGEMENT Andronicos E. Filios

Dionisios P. Margaris

University of Patras, Department of Mechanical and Aeronautical Engineering, Fluid Mechanics Lab., 26500 Patras, Hellas.

University of Patras, Department of Mechanical and Aeronautical Engineering, Fluid Mechanics Lab., 26500 Patras, Hellas.

Tel. & Fax: 061 997202, e-mail: [email protected]

Tel. & Fax: 061 997202, e-mail: [email protected]

Dimitrios G. Papanikas

Michalis Gr. Vrachopoulos

University of Patras, Department of Mechanical and Aeronautical Engineering, Fluid Mechanics Lab., 26500 Patras, Hellas.

TEI Chalkidos, Department of Mechanical Engin., Nirvana 29, 111 45 Patisia, Athens, Hellas. Tel. & Fax: 01 8324020, e-mail: [email protected]

Tel. & Fax: 061 997201, e-mail: [email protected]

wind tunnel fan, the corner guide vanes and the upstream walls are the main sources of the test section turbulence. A more than seventy years experience in wind tunnel design and testing proves that the settling chamber and contraction combination helps to accomplish the uniform low turbulence field in the test section. The degree of achievement of the required flow quality depends on the various flow manipulators (i.e. honeycomb, screens) installed in the settling chamber as well as on the area ratio and the shape of the contraction. Based on certain assumptions, various theories and empirical formulas have been proposed for computing the effect of flow manipulators and contraction on the intensity and uniformity of turbulent flow. Theoretical and experimental investigations regarding the effect both of screens and the contraction on the characteristics of the turbulent flow have been carried out from the decade of 30’s. The most representative studies regarding the effect of screens are those by Prandtl [1], Dryden and Schubauer [2], and Taylor and Batchelor [3]. The effect of contraction on turbulence was theoretically studied, by Prandtl [1], Taylor [4], Ribner and Tucker [5], and Batchelor and Proudman [6]. According to the reported studies, the quenching action of the screen on the turbulence velocity fluctuations is related to the magnitude of the screen resistance coefficient that depends on its porosity and the Reynolds number. In the case of few screens followed by a contraction with a medium area ratio, the comparison of measurements and calculations indicate a reasonable agreement. However, for several screens in series in

ABSTRACT The development of a calculation scheme that will serve as a flow quality predictor for various combinations of screens–contraction ratio and moreover it can be used for the correlation of experimental data with available theories, is discussed. The proposed calculation depends on application and it may be direct or inverse. The direct calculation refers to the prediction of the flow quality in the test section having defined the number and the mesh size of screens as well as the contraction ratio. The inverse calculation provides the optimum settling chamber configuration, i.e. number and porosity of screens, which in combination to the requested contraction ratio will insure the requested flow quality. The predictions are correlated with published measurements. KEYWORDS Wind tunnel, Settling chamber, Screens, Contraction. INTRODUCTION Despite of the rapid expansion in the area of the computational fluid dynamics, the wind tunnel remains an essential tool in engineering, both for model tests and basic research. The main aim when designing any wind tunnel is the production of a steady flow with spatial uniformity in the test section over a range of Reynolds number. This requirement can never be perfectly attained since there are always present small eddies of varying size and intensity which are collectively described as the turbulence of the air stream. The

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ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece

Screens have three main effects on the flow passing through them: i) reduction of mean velocity variation-leading to prevention of, or delay in, boundary layer separation; ii) reduction of turbulent fluctuations and iii) refraction of inclined flow – towards the local normal to the screen. The action of the screen is described in terms of two parameters: ks, the screen pressure-loss or drag coefficient and α, the deflection coefficient. The ks-coefficient is defined as the pressure loss across the screen divided by the dynamic pressure of the mean flow through the screen. The αcoefficient is defined as the ratio of the flow angle normal to the screen downstream to the flow angle normal to the screen upstream.

combination with a medium or high area ratio contraction the comparison indicates often a poor agreement and sometimes significant divergence. The choice of the optimum combination of screens with a required contraction ratio that is related to the tunnel energy ratio is a well-known problem to the subsonic wind tunnel designers. NOMENCLATURE c : Contraction ratio d : Screen’s wire diameter ft : Turbulence reduction factor due to screen ks : Screen’s pressure-loss coefficient λ : Width of square mesh screen A : Test section cross sectional area G1, G2 : Reduced resistance factors Red : Reynolds number based on wire diameter T : Turbulence level α : Screen’s deflection coefficient β : Porosity or open area of the screen λ : Factor for the increase of turbulence intensity in a contraction

Determination of ks and α Over the years, several expressions have been derived giving the pressure loss coefficient of a screen in terms of β, the porosity or open-area ratio of the screen and Red, the Reynolds number based on wire diameter. In the case of screens made of round wires, forming a square-mesh the porosity is (1 − d / λ)2 , where d is the wire diameter and λthe width of the square mesh. For the calculation of the pressureloss coefficient of a screen, Wieghardt [8] suggests the empirical formulae

SETTLING CHAMBER Screens have been used to improve flow quality in wind tunnels since 1930s. Firstly, Prandtl [1] gave a simple theory regarding the contribution of screens in improving the velocity distribution. Dryden and Schubauer [2] gave a physical explanation for the flow-manipulator role of the screen and they derived a simple theory for the reduction of turbulence intensity based on the assumption that the effect of a screen is partly to absorb the kinetic energy of turbulence. Taylor and Batchelor [3] produced a detailed analysis of the effect of screens on small disturbance. Their theory is linearized on the assumption that there is negligible natural decay of turbulence while the field is translated through the ‘region of influences’. Batcelor [7], on the assumption of isotropic turbulence far upstream, showed that the equations for the factors of reduction of turbulence intensity become relatively easy to compute. The suppression of turbulence can also be achieved by using honeycomb, which is more effective for removing swirl and lateral mean velocity variations. Its effect is demonstrated experimentally for lack of theoretical prediction. The maximum benefit from a honeycomb requires straight and uniform cells with optimum cell length to diameter ratio 7–10, without any critical dependence on their cross sectional shape. The use of the honeycomb is suggested for flow yaw angles less than 10o since greater yaw angles cause the ‘stall’ of the honeycomb cells resulting to a reduction of their effectiveness besides increasing the pressure losses. In the past, the honeycomb was used as a common flow manipulator upstream of the screens while in the modern wind tunnels rarely is in use and it is located downstream of a wide angle diffuser or a bellmouth inlet.

k s = C (1 − β)β −5 / 3 Re d −

1/ 3

(1)

The value of C-coefficient depends on Reynolds number and for a typical wind tunnel design, i.e. flow velocity in the settling chamber less than 10m/s and 60 < Red /β< 600, the value of C is 6. De Vahl [9] shows that for the lower Reynolds numbers the pressure-loss coefficient is equal to 2

ks = ko +

55,2  1 − 0,95β  55,2  + = Re d  0,95β  Re d

(2)

Equations (1) and (2) may be written as follows G1 =

ks

C (1 − β )β

−5 / 3

G 2 = k s − g 2 (β) =

=

ks 1 = g 1 (β) Re d 1 / 3

55,2 Re d

(3)

(4)

where G1 and G2 the reduced resistance factors depending only on Reynolds number as it is shown in Fig. 1. The functions g1(β) and g2(β) depends on screen characteristics as it is shown in Fig. 2. By definition, the deflection coefficient α can vary between 0 and 1. Extensive measurements and correlations on plane screens placed vertical to the airstream leads to the following semi-empirical relation [3] α=

2

1,1 1 + ks

(5)

ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece

coefficient α. Moreover, using potential flow theory and accounting for the boundary conditions on both sides of the screen they show that the axial turbulence reduction factor becomes (1+α-αks)/(1+α+ks). In Ref. 2, the energy change across the screen is equated to the difference between the upstream turbulent energy and the downstream turbulent energy. Since the turbulent velocity is proportional to the square root of the turbulent energy, the turbulent reduction factor becomes 1/(1+ks)0,5. A direct comparison of the turbulence reduction factors proposed by the above theories and the correlation with measurements is provided in Ref. 13. The experimental data presented in Refs. 2 and 12 seem to verify the theoretical decay law of Dryden and Schubauer. The installation of several screens in series results to a reduction of the incoming turbulence in each one by its turbulence factor. Therefore, the total turbulence reduction factor for a series of N-screens, each one having a pressure-loss coefficient ksi, is equal to the product of the individual reduction factors, i.e.

Reduced resistance factors G 1 and G2

0,6

0,5

0,4

0,3

G1

0,2

0,1

G2/10 0,0 10

100

1000

Red

N

Figure 1: Reduced resistance factors for screens.

ft =

∏ i =1

1,0

50

g1(β); C=6,5 g1(β); C=6,0 g1(β); C=5,5

0,9 0,8

30

0,5 0,4

20

Functions g 1 and g 2

Screen porosity, β

40

0,6

0,3 0,2

10

g2(β)

0,1 0,0

0 0,0

0,1

0,2

0,3

0,4

1 + k si

(6)

As seen from the above formulae, installing a sufficiently large number of screens can attain a low level of turbulence in the settling chamber. However, it must be kept in mind that beyond the screen, in addition to the turbulence passing through, there is also the turbulence created by the screen itself, the screen turbulence. The turbulence generated by the last screen determines the minimum attainable turbulence in the entrance of the wind tunnel contraction. With Red<60, screen turbulence is negligible and the largest contribution to the total turbulence is the acoustic turbulence. With Red>90, the contribution of the last screen in the turbulence intensity may be computed with acceptable accuracy from the formula proposed by Batchelor and Townsend [14].

β

0,7

1

CONTRACTION The contracting nozzle is placed upstream of the test section for two main reasons: a) It increases the flow mean velocity allowing the honeycomb and screens to be placed in the lower speed regions, thus reducing the pressure losses and the tunnel power factor. b) Both mean and fluctuating velocity variations are reduced to a smaller fraction of the average velocity at a given cross section. The most important single parameter in determining these effects is the contraction ratio. The theoretical studies by Prandtl [1], Taylor [4] and Batchelor and Proudman [6] imply that the contraction does exert a selective effect on the rms components of the fluctuating velocity, i.e. the longitudinal component is reduced while the lateral components are increased. On the assumption of isotropic turbulence and neglecting the decay of turbulence, Prandtl and Batchelor recommend the following λ-factors for the increase of the turbulence intensity

0,5

d/ l

Figure 2: Porosity functions for screens.

Effect of the screens in reducing flow irregularities In Ref. 1, Prandtl states that screens can be used to obtain a more uniform velocity distribution across the duct section and that a moderate velocity difference is approximately lowered by the factor 1/(1+ks). This factor has been extended to apply to turbulence reduction across a screen. Collar [10] using Bernoulli’s equation and assuming that the turbulent velocities are small compared to the mean velocity, shows that the reduction factor for rms u-component becomes equal to (2ks)/(2+ks). Taylor and Batchelor [11] utilizing the test data presented in Ref. 12, shows that the lateral turbulence reduction factor is approximately equal to deflection

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ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece

λP =

1 3c 2

+

2c or λ B = 3

ln(4c 3 − 1) 4c 2

+

c 2

code development, the existing alternatives are a) the method of Boerger [18] and b) the method of Cohen and Ritchie [19].

(7)

0,20

where c is the contraction ratio and subscripts ‘P’ and ‘B’ denote Prandtl’s and Batchelor’s theory respectively. Both equations show that the acceleration of the flow amplifies the turbulence intensity but the turbulence level is decreased due to the increase of the mean speed. The investigation carried out by klein and Ramjee [15] shows that the shape of the contraction does not have significant influence on the turbulence intensities at the exit of the contraction. The published theories defining the turbulence level reduction in contractions are limited for axisymmetric configurations and while they have been partially correlated with results from 2-D and 3-D geometries they also be applied herein.

1 x Μ18D

0,18

Turbulence level %

0,16

2 x Μ18D

0,14 0,12 0,10

3 x Μ18D

0,08 0,06 0,04

CALCULATIONS In the course of prediction the managing the flow quality in the test section of a subsonic wind tunnel, a calculation code is under development [16]. The code making use of published theories, empirical formulas and contraction design methods, except of the available correlations and direct comparisons it can be utilized as a tool in subsonic wind tunnel designers. The calculation may be direct or inverse. The direct mode of calculation regards the prediction of turbulence level in the test section having defined the screens into the settling chamber as well as the contraction ratio. The inverse mode of calculation targets to the optimum selection of screens and contraction ratio that meet the required specification of the turbulence level in the test section. The criterion of the optimum selection is the attainment of the lowest power factor for the wind tunnel with the shortest length for the settling chamber-contraction combination. For validation purposes, standard type of screens has been initially selected, where by ‘standard’ the availability of measurements is implied. An example of standard screens is shown in Table 1. The contraction wall shape depends on the availability of the design methods. In the present phase of the

0,02

Measurements [2]

0,00 1,0E+04

1,0E+05

1,0E+06

Re/m

Figure 3: Measured and predicted turbulence level in the test section of the NBS subsonic wind tunnel. 0,22 0,20

Measurements [2] 1 x M24D

0,18

Turbulence level %

0,16 1 x M20D

0,14 0,12 0,10

1 x M60D

0,08 0,06

3 x M20D + 3 x M24D

0,04

Table 1: Standard type of damping screens. Screen [17] Porosity Screen [2] Porosity M07M 0,6026 M18D 0,6436 M08M 0,6023 M20D 0,4354 M09M 0,5596 M24D 0,6715 M10M 0,5774 M60D 0,3355 M12M 0,5416 M13M 0,5476 M14M 0,5183 M16M 0,5070 Screen [13] Porosity M18M 0,4963 M03S 0,8854 M20M 0,4955 M07S 0,1578 M22M 0,4918 M19S 0,2009 M24M 0,4542 M27S 0,1458 M26M 0,4591 M35S 0,1210 M28M 0,4260 M03S 0,8854

0,02 0,00 1,0E+04

1,0E+05

1,0E+06

Re/m

Figure 4: Measured and predicted turbulence level in the test section of the NBS subsonic wind tunnel, for various screens and combinations of screens.

The direct mode of calculation is applied for the settling chamber-contraction combination of the National Bureau of Standards (NBS) subsonic wind tunnel due to the published test data in considerable detail [Ref. 2]. The cross sectional shape of the test section is octagonal with 4,5 ft width and the

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ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece

The aim of this preliminary investigation is the development and validation of a calculation tool that will be served as a flow quality predictor for various combinations of screens– contractions and moreover it can be used for the correlation of experimental data with available theories. The results of the considered test cases indicate: a) For a combination of maximum three screens and a contraction with an area ratio less than 10, the contribution of the last screen in the turbulence intensity may be omitted. The acceleration of the flow through the contraction affects the turbulence intensity variation that may be calculated applying Prandtl’s theory. b) When the number of the installed screens is greater than three, the contribution of the last screen in the turbulence intensity may be considered applying Batchelor-Townsend’s proposal. In that case and for a contraction ratio even greater than 10 the contraction contribution in the decrease of the turbulence level may be calculated applying Batchelor’s theory. c) The upstream flow structure can influence the performance of screens. Consequently the published dependence of the reduction factors on the pressure loss coefficient is not universal and may lead, for example, to unconservative estimates of the number of screens needed for given design. The present findings enlarge somewhat on the previous state of knowledge, primarily by focusing on the region immediately downstream of the screens and contraction. The information available on the effect of the wall shapes of a three-dimensional contraction is not sufficient to permit the exact computation of the turbulence levels to be expected in wind tunnels.

contraction ratio is 6,6. The cross sectional area (A) defines the reference length Lref=0,1A1/2 which is used along with the working section speed (U) for the definition of the Reynolds number. The predicted values of the turbulence level in the test section in direct comparison with measurements are shown in Figs. 3 and 4. In both cases no honeycomb is present in the settling chamber. Figure 3, presents plots of the turbulence level for one, two and three screens of the same mesh size. The reduction of the turbulence level due to the contraction effect is expressed through the Prandtl theory. Figure 4, shows plots of the turbulence level for single screens with various mesh sizes as well as for a tandem arrangement of six screens. In the calculation referring to the six screens combination, the Batchelor theory - regarding the turbulence level reduction due to the contraction - is applied. The incoming turbulence level at the entrance of the settling chamber is predicted by the polynomial Tin=a0+a1X+a2X2, where X is the Reynolds number per unit reference length and the ai-coefficients are determined through a correlation with available measurements. Table 2: Summary of the inverse calculation. Screens 3 x M20D + 3 x M24D 2 x M20D + 3 x M14D + 1 x M24D 1 x M08M + 5 x M07M + 2 x M24D 4 x M08M + 1x M07M + 3 x M24D

Contraction ratio

Predicted Total ks

Predicted T (%)

6,6

10,6958

0,0407

6,6

9,6035

0,0429

6,5

7,9706

0,0429

7,0

7,5169

0,0430

REFERENCES [1] Prandtl, L., 1933, "Attaining a steady air stream in wind tunnels", NACA T.M. No 726. [2] Dryden, H. L., and Schubauer, G. B., 1947, "The use of damping screens for the reduction of wind tunnel turbulence", J. Aeron. Science, Vol. 14. [3] Taylor, G.I., and Batchelor, G.K., 1949, "The effect of wire gauge on small disturbances in a uniform stream", Quart. Journal of Mech. and Applied Mathematics, Vol. II, pp. 1-29. [4] Taylor, G.I., 1935, "Turbulence in a contracting stream", Zeitschrift fur Angewandte Mathematik und Mechanik, Vol.15, pp. 91-96. [5] Ribner, H.S., and Tucker M., 1953, "Sprecturum of turbulence in a contracting stream", NACA TR 1113. [6] Batchelor, G.K., and Proudman, I., 1954, "The effect of rapid distortion of a fluid in turbulent motion", Quart. Journal of Applied Mathematics, Vol.7, pp. 83-103. [7] Batchelor, G.K., 1970, "The theory of homogenous turbulence", Cambridge Univ. Press, pp. 55-75. [8] Wieghardt, K.E.G., 1953, "On the resistance of screens", Aeron. Quarterly, Vol. 4.

The inverse design calculation is also applied in the previous considered settling chamber-contraction combination for validation purposes. Having as a requirement the turbulence level in the test section of the wind tunnel that is 0,04%, the calculation targets to the selection of the number along with the mesh size of the screens and the contraction ratio that is limited in the range 6 to 7. The predicted results for this exercise test case are summarized in Table 2. The first proposal corresponds to the considered arrangement while the last one may be considered the optimum alternative design. CONCLUSION Predictions of the flow quality in the test section of a subsonic wind tunnel have been conducted. Some design calculations were performed to study the effectiveness of screens in combination to the contraction for the turbulence management in the test section of a subsonic wind tunnel. Theories from the previous state of knowledge and suitable for design calculations are the background of the present work.

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ASME - GREEK SECTION, First Nat. Conf. on Recent Advances in Mech. Eng., September 17-20, 2001, Patras, Greece

[9] De Vahl, D.G., 1964, "The flow of air through wire screens", Hydraulics and Fluid Mechanics, Pergamon Press, pp. 191-212. [10] Collar, A.R., 1939, "The effects of a gauge on the velocity distribution in a uniform duct", A.R.C. R&M No. 1867. [11] Taylor, G.I., and Batchelor, G.K., 1949, "The effect of wire gauge on small disturbances in a uniform stream", Quart. Journal of Mech. and Applied Mathematics, Vol. II, pp. 1-29. [12] Schubauer, G. B., Spandenberg, W. G., and Klebanoff, P. S., 1950, "Aerodynamic characteristics of damping screens", NACA TM 2001. [13] Scheiman, J., and Brooks, J.D., 1981, "Comparison of experimental and theoretical turbulence reduction from screens, honeycomb, and honeycomb-screen combinations", J. Aircraft, Vol.18, No.8. [14] Kintse, I.O, 1963, "Turbulence", Moscow, Fizmatgiz. [15] Klein, A., and Ramjee, V., 1973, "Effect of contraction geometry on non-isotropic free stream turbulence", The Aeronautical Quarterly, Vol. 24, pp. 34-38. [16] Filios A.E., and Margaris D.P., 2000, "Floqua-code for the design of a settling chamber-contraction combination", Internal Report, Fluid Mech. Lab., University of Patras. [17] Mehta R. D., 1977, "The aerodynamic design of blower tunnels with wide-angle diffusers" Prog. Aerospace Sci., Vol. 18, pp 58-120. [18] Boerger, G.G., 1973, "Optimierung von windkanaldusen fur den unterschall bereich", Ruhr-Universitat, Bohum. [19] Cohen, M.J., and Ritchie, N.J.B., 1962, "Low speed three dimensional contraction design", J. Roy. Aero. Soc., 66, 231.

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