ASSESSMENT OF ANISOTROPY IN THE NEAR FIELD OF A RECTANGULAR TURBULENT JET

Transcription

1 TUR-3 ExHFT-7 8 June 03 July 009, Krakow, Poland ASSESSMENT OF ANISOTROPY IN THE NEAR FIELD OF A RECTANGULAR TURBULENT JET Α. Cavo 1, G. Lemonis, T. Panidis 1, * 1 Laboratory of Applied Thermodynamics, University of Patras, Patras, Greece Hellenic Aerospace Industry S.A., Schimatari, Greece ABSTRACT. The anisotropy in the near field of a rectangular turbulent jet with aspect ratio 6 is experimentally assessed. The presented data were obtained using an in-house constructed 1-sensor hot wire probe consisting of three closely separated orthogonal 4-hot wire velocity arrays. Measurements have been conducted in a jet with Reynolds number Re D = 1000 at distances from the nozzle exit, x/d =1, 3, 6 and 11, where D is the width of the nozzle. The results of the present study indicate that the direct production of turbulent energy by the mean shear leads to a strong anisotropy in the fluctuating fields for 0<x/D<11. Moreover, it is clear that the large scales have not relaxed to isotropy in spite of the absence of the mean shear at the centreline of the jet. Keywords: Rectangular jet, turbulent jet, mixing layers, plane jet, free jet INTRODUCTION A rectangular turbulent jet has many practical applications in aerospace, in mechanical and chemical engineering. There were many experimental investigations in jets issuing from rectangular nozzles which have enhanced our understanding of the underlying physics of these flows mainly from information on the velocity field (Krothapalli et al. 1981, Sfeir 1979, Sforza & Stasi 1979, Grinstein 001, etc). It has been well documented from many researchers that aspect ratio of the nozzle and initial conditions at the jet exit play an essential role in the distribution of the rectangular jets properties, especially in the near field (Quinn 199, Lazanova & Stankov 1998, Deo et al. 007, etc). The intention of this work is to assess the anisotropy in the near field of a rectangular turbulent jet an issue not extensively covered in current literature, due to inherent difficulties in measuring the relevant characteristic properties. A unique attribute of the present study is that the spatial derivatives in all three directions of the three components of the fluctuating velocity field have been directly measured using a 1-sensor hot wire anemometry probe. The performance of the 1-sensor probe in the near field of a rectangular turbulent jet has been assessed by Cavo et al. (007) in comparison with corresponding measurements with an X-wire probe and other experimental and numerical studies. EXPERIMENTAL ARRANGEMENT The jet exits from a rectangular nozzle with length L=300 mm and width D=50 mm (Figure 1). The aspect ratio is AR=L/D=6. The experiment was conducted at a Reynolds number Re = U 0 D/ν = 1000, where U 0 is the exit velocity from the nozzle and ν is the air s kinematic viscosity at environmental temperature (3 C). The streamwise turbulence intensity distribution at * Corresponding author: Prof. T. Panidis Phone: , Fax: address: panidis@mech.upatras.gr 85

2 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland X D Y 1 3 L Z Figure 1 Jet nozzle and coordinate system the nozzle exit was uniform and had a constant value of about 1%, except in the boundary layers adjacent to the nozzle lips, where the maximum value was about %. The initial boundary layers developed on the nozzle lips are characterised as laminar (Cavo et al. 007). The 1-sensor probe manufacturing, probe calibration and data reduction techniques rely upon previous work of Lemonis (1995), and have been further improved and refined at the Laboratory of Applied Thermodynamics of the University of Patras. The probe composing of three 4-wire arrays (Figure ) measures simultaneously the three-dimensional velocity vector components at the centroids of the three arrays on a cross plane of the flow field. Spatial velocity derivatives are estimated using a forward difference scheme of first order accuracy. Streamwise velocity derivatives are estimated using Taylor s frozen turbulence hypothesis. Details regarding the design and operation of the 1-sensor probe as well as the experimental facility, used in the present experiment can be found in Cavo et al. (007) Long prong Short prong tube teflon insulation epoxy prong 45 0 ~ Figure. Schematic diagram showing the 1-sensor probe front view and a 45 inclined hot-wire with supporting prongs

3 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland Figure 3. Flow visualization of a rectangular jet in the near field region EXPERIMENTAL RESULTS The behaviour of the planar jet due to the merging of the mixing layers is consistent with the eventual breakdown of the structures generated from the rollup and pairing of spanwise vortices ( 0 x / D 4 5) to strongly three-dimensional turbulence. Figure 3 shows a characteristic flow visualization image of the rectangular jet in the near field region. Rockwell & Niccolls (197) results, as well as the present visualization, indicate that near the nozzle exit the large-scale structures in the flow field are predominately symmetric for flat exit profiles. When the shear layers interact downstream, these structures reorganize into an asymmetric configuration in the fully developed region of the jet. Measurements of the present study have been conducted in the jet at distances from the nozzle exit, x/d =1, 3, 6 and 11. Experimental results based on measurements with the 1 wire and the X wire probe are compared with several experimental and computational (DNS) data of other investigations on plane jets (Browne et al. 1983, 1984, Everitt and Robins 1978, Gutmark and Wygnanski 1976, Ramaprian and Chandrasekhara 1985, Stanley et al. 00), rectangular jet (Quinn 199) and two stream mixing layer (Bell and Mehta 1990, Spencer and Jones 1971, Wygnanski and Fiedler 1970) of various Reynolds numbers. Mean velocity-vorticity field The mean streamwise velocity, U, profiles normalized by the centreline velocity, U c, at different stations are shown in Figure 4, in comparison with corresponding measurements of the X-wire probe (Cavo et al. 007) and experimental results of other investigators. The velocity at the exit plane of the nozzle presented an almost top hat profile as evidenced by x/d=1 measurements. Further downstream the profiles assume a bell shaped distribution and are in agreement with corresponding profiles of Quinn (199) and Browne et al. (1984). The presented results at x/d=6 and 11 indicate that planar jet similarity as far as the mean velocity distributions are concerned may be claimed at least for a limited range, within the two dimensional region of rectangular jets. In rectangular jets downstream derivatives of mean velocity components are expected to be small compared to cross-stream derivatives, x<< y. Under these conditions, the dominant mean vorticity component Ω z = V x U y can be estimated approximately as U y and a reasonable estimate of Ω z may be obtained by differentiating the distribution U(y). 87

4 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland U / U C AR=6 x/d=1 X-wire AR=6 x/d=1 1-wire AR=6 x/d=6 X-wire AR=6 x/d=6 1-wire AR=5 x/d=5 Quinn (199) AR=10 x/d=5 Quinn (199) AR=0 x/d=7 Browne et al. (1984) U / U C AR=6 X-wire AR=6 1-wire AR=5 x/d=1.6 Quinn (199) AR=10 x/d=1.6 Quinn (199) 0, 0, 0,5 1,5,0,5 0,5 1,5,0,5 y / y c y / y c Figure 4. Mean streamwise velocity profiles (x/d=1, 3, 6, 11) Figure 5 depicts lateral profiles of mean spanwise vorticity, Ω z, at different locations downstream (Cavo et al. 007). Two kinds of estimates are presented. Based on the above analysis Ω z is first estimated calculating the U y derivative, differentiating U(y) curve measured with the X wire. The second Ω z estimate is obtained by averaging the time series of local instantaneous spanwise vorticity results of the 1-wire probe. Close to the nozzle exit high values of vorticity are observed in the shear layers developing between the jet and the ambient fluid, whereas doesnsteam measurements indicate the diffusion of vorticity from the shear layers towards the centre and the edges of the jet. Turbulent velocity-vorticity field Figure 6 shows measurements of the root mean square (rms) values of the three fluctuating velocity and vorticity components at x/d=1, 3, 6, 11. The profiles have been normalized with U 0 and U 0 /D respectively. These results demonstrate the growth of velocity-vorticity fluctuations in the potential core region (x/d=1, 3) within the shear layer due to rollup and pairing of spanwise vortices. The lateral distributions of the velocity-vorticity components are significantly changed downstream by the interaction of the shear layers. This change is associated with the growth of fluctuations around x/d=3 differetiating U=f(y) 1-wire vorticity mean Ω z y c / U C 0, -0, 0,5 1,5-0,,0 0,5 1,5,0 3,0,5,0 1,5 0,5 x/d=1-0,5 0,5 1,5,0 y/y c 0, 0, -0, 0,5 1,5,0 y/y c x/d=6 88 Figure 5. Mean spanwise vorticity distributions (x/d=1, 3, 6, 11)

5 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland w'/u 0 v'/u 0 u'/u 0 0,5 0,15 0, , 1, 1,4 1,6 0,5 0,15 0, , 1, 1,4 1,6 0,5 x/d=1 x/d=3 x/d=6 0,15 8 0, , 1, 1,4 1,6 y/y c 0 0,5 1,5 ω'z D/U 0 ω'y D/U 0 ω'x D/U x/d=1 x/d=3 x/d= ,5 1, ,5 1,5 10 y/y c Figure 6. Measured rms value of the three fluctuating velocity-vorticity components the axis area and with decrease of rms values within the shear layers (x/d=6, 11). This behaviour is characterized by the turbulence diffusion from shear layers towards the centre and edges of the jet. It seems that areas with low or high levels of velocity turbulence are associated with corresponding levels of vorticity turbulence respectively. Assessment of anisotropy The normal Reynolds stresses anisotropy levels at y/y c 1 in the near field region of the rectangular jet are shown in Table 1 compared to available experimental and numerical (DNS) data. The direct production of energy by the mean shear at x/d=1 seems to lead to a strong anisotropy in the fluctuating field in this region of the jet, amplifying the vv q component. As expected this anisotropy is reduced downstream and jet development seems to be characterized by a redistribution of energy between the three directions probably due to pairing, which is the main mechanism of the evolution of the shear layer (Grinstein 001). This process results in the augmentation of the other two normal stresses at the expense of the vv component, which eventually becomes less than the isotropic value. Differences with Stanley et al. (00) results should probably be attributed to the different initial and boundary conditions whereas all other results on plane jets depicted in table 1 have been obtained in the full development region. On the jet centreline at (Table ) the streamwise component is higher than the isotropic level while the lateral and spanwise components are below this level. It is clear that the large scales have not relaxed to isotropy in spite of the absence of mean shear at the centreline. As shown in Table, the present results are in a good agreement with the experimental results of Gutmark & Wygnanski (1976) and Browne et al. (1983) for fully developed jets. Table 3 lists the normal velocity derivative variances on the centreline as well as in the high-shear regions. While DNS results are very close to the isotropic value, the deviations of the present results from it are significant. The different values between the two cases should be attributed to the different stage of the flow development, since the results of Stanley et al. (00) indicate that at the jet has reached full development. As stated in their work the large scales of the flow relax slowly to isotropy in the absence of mean shear at the centreline whereas the small scales 89

6 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland Table 1 Comparison of the jet turbulence intensities for y/y c 1 in the near filed region at x/d=1, 3, 6 and 11 with several experimental and computational (DNS) data of other researchers (x/d>30 characterises the full development region) Source Position uu q vv q ww q uv q Present study Stanley et al (00) (DNS) Wygnanski & Fiedler (1970) Spencer & Jones (1971) Bell & Mehta (1990) Gutmark & Wygnanski (1976) Ramaprian & Chandrasekhara (1985) x/d=1 x/d=3 x/d=6 x/d= x/d> x/d> x/d> x/d> x/d>30 y/y c 1 y/y c assumes q = (3 )( u + v ) Table Comparison of the jet turbulence intensities for y/y c =0 in the near filed region at with several experimental and computational (DNS) data of other researchers (x/d>30 characterises the full development region) Source Position uu q vv q ww q 1-wire DNS Stanley (00) Gutmark & Wygnanski (1976) x/d> Ramaprian & Chandr. (1985) x/d> Everit & Robins (1978) x/d> Browne et al. (1983) x/d> assumes ( ) q = 3 ( u + v ) 90

7 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland Table 3 Normal-derivative variances in the near filed region at ( u/ x) ( v/ y) ( ε /15 v) ( ε /15 v) ( w/ z) ( ε /15 v) Isotropic Value Present work y/y c 1 y/y c = Stanley et al. (00) y/y c 1 y/y c = adjust quite rapidly. The results of the present work indicate that the jet has not reached the full development region in accordance with experimental results of previous studies indicating that full development of planar jets is attained at distances x/d> The development of rectangular jet in the near field after the interaction of the shear layers which occurs beyond the tip of the jet potential core, similar to that of a plane jet, is controlled by largescale coherent vortical structures which are characterized by their persistence. On the other hand, vortices in the full development region have lost most of their energy. Consequently it is expected that the near field region will be characterized by anisotropy whereas the flow may relax towards isotropic attributes in the fully developed region. Table 4 shows the variance of the cross-derivative terms at, where the same differences between the two investigations are observed. This behaviour is attributed also to the different initial and boundary conditions of the two studies. As is well known jet development in the near field is expected to be influenced mainly by aspect ratio and factors such as jet exit formation, Reynolds number and room turbulence (Cavo et al. 007). Table 4 Cross-derivative variances in the near filed region at ( u/ y) ( u/ x) ( u/ z) ( u/ x) ( v/ x) ( v/ y) ( v/ z) ( v/ y) ( w/ x) ( w/ z) ( w/ y) ( w/ z) Isotropic Value Present work y/y c y/y c = Stanley et al. (00) y/y c 1 y/y c =

8 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 8 June 03 July 009, Krakow, Poland CONCLUSIONS The anisotropy in the near field of the turbulent rectangular jet of aspect ratio 6, at Re=1000 has been illustrated and discussed in detail. The results obtained with a 1 sensor hot wire probe indicate that the formation and development of large-scale vortices in the shear layers of the rectangular jet lead to the anisotropy of the flow. A strong advantage of the current results in comparison with other studies is that the spatial derivatives of the three components of the fluctuating velocity field in all three directions have been directly measured. REFERENCES 1. Bell, J. H. and Mehta, R. D., Development of a two-stream mixing layer from tripped and untripped boundary layers, AIAA J., Vol. 8, pp , Browne L. W. B., Antonia R. A, Rayagopalan S., Chambers, A. J., Interaction region of a two dimensional turbulent plane jet in still air, In structure of complex turbulent shear flow (ed. R. Dumas & L. Fulachier), Springer, pp , Browne, L. W. B., Antonia, R. A., Chambers, A. J., The interaction region of turbulent plane jet, J Fluid Mech., Vol. 149, pp , Cavo, A., Lemonis, G., Panidis, Th., Performance of a 1-sensor vorticity probe in the near field of a rectangular turbulent jet, Exp. in Fluids, Vol 43, pp 17-30, Deo, R. C., Mi, J., Nathan, G. J., The influence of the nozzle aspect ratio on the plane jets, Exp. Therm. and Fluid Sci., Vol. 31, pp , Everitt, K. W. and Robins, A. G., The development and structure of turbulent plane jets, J. Fluid Mech., Vol. 88, pp 91-1, Gutmark, E. and Wygnaski, I., The planar turbulent jet, J. Fluid Mech., Vol. 73, pp , Grinstein, F., Vortex dynamics and entrainment in rectangular free jets, J. Fluid Mech., Vol. 437, pp , Krothapalli, A., Baganoff, D., Karamacheti, K., On the mixing of a rectangular jet, J. Fluid Mech., Vol. 107, pp 01-0, Lozanova, M. and Stankov, P., Experimental investigation on the similarity of a 3D rectangular turbulent jet, Exp. in Fluids, Vol. 4, pp , Lemonis G. C., An experimental study of the vector fields of velocity and vorticity in turbulent flows, PhD Thesis, Swiss Federal Institute of Technology, Zurich, Quinn, W. R., Turbulent free jet flows issuing from sharp-edged rectangular slots, The influence of slot aspect ratio, Exp. Thermal Fluid Sci., Vol. 5, pp 03-15, Ramaprian, B. R. and Chandrasekhara, M. S., LDA measurements in plane turbulent jets, Trans. ASME: J. Fluids. Engng., Vol. 107, pp 64-71, Rockwell, D. O. and Niccols, W. O., Natural breakdown of planar jets, Trans. ASM, J. Basic Engng., Vol. 94, pp , Sfeir, A. A., Investigation of three-dimensional turbulent rectangular jets, AIAA J., Vol. 17(10), pp , Sforza, P. M and Stasi, W., Heated three-dimensional turbulent jets, ASME, J. Heat Mass Transfer, Vol. 101, pp , Spencer, B. W. and Jones, B. G., Statistical investigation of presure and velocity fields in the turbulent two mixing layer, AIAA Paper, pp , Stanley, S. A., Sarkar, S., Mellado, J. P., A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation, J Fluid Mech., Vol. 450, pp , Wygnanski, I. and Fiedler, H. E., The two-dimensional mixing region, J. Fluid Mech., Vol. 41, pp ,