Twin jets in cross-flow

Chemical Engineering Science 66 (2011) 2616–2626 Contents lists available at ScienceDirect Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces Twin jets in cross-flow V.S. Naik-Nimbalkar a, A.D. Suryawanshi a, A.W. Patwardhan a,n, I. Banerjee b, G. Padmakumar b, G. Vaidyanathan b a Department of Chemical Engineering, Institute of Chemical Technology, Matunga, Mumbai 400019, India Experimental Thermal Hydraulics Section, Separation Technology and Hydraulics Division, Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India b a r t i c l e i n f o a b s t r a c t Article history: Received 13 January 2011 Received in revised form 4 March 2011 Accepted 9 March 2011 Available online 16 March 2011 An experimental study and numerical investigation of thermal mixing are carried out on tandem twin jets in cross flow. Experiments were carried out for velocity ratios 1, 2 and 4 for 15 1C temperature difference between main pipe and jet fluid. Velocity and temperature fields are measured using Hot Film Anemometer (HFA). Three dimensional steady state Computational Fluid Dynamics (CFD) simulations have been carried out to predict the velocity and temperature fields. The predicted velocity and temperature fields are in good agreement with the experimental measurements. Temperature fluctuations have been predicted using temperature variance model. The effect of jet spacing for different velocity ratios is studied. For jet spacing equal to twice the jet diameter, both the jets influence each other. Increase in the jet spacing decreases the effect of jets on each other. & 2011 Elsevier Ltd. All rights reserved. Keywords: Mixing Heat transfer Fluid mechanics Turbulence CFD Temperature fluctuations 1. Introduction Jets in cross flow (JICF) are used in several engineering applications related to heat and mass transfer. Single, twin and multiple jets are introduced within the cross flow according to the aim of the handled application. Twin and multiple jet configurations are found in combustor wall cooling, cooling of gas turbine blades, etc. In these applications more than one jet is used to enhance the performance of each individual jet further downstream of its injection point. Similarly, we find these types of jets in the dispersion of hot liquid effluents into streams and rivers, which is relevant to water pollution. Also, mixing elements in static mixers and burners in the combustion units have rows of multiple jets issuing in the cross flow fluid. In literature several researchers have investigated single and multiple jets in cross flow configuration. The twin jet configuration is significantly less considered in spite of its great relevance. In fact, its understanding is likely to predict the effectiveness or ineffectiveness of multiple jet systems. The existing work on multiple jets focuses mainly on global characteristics such as jet trajectory, vorticity and circulation aspects of multiple jets in cross flow by varying number of jets in a row, or considering specific geometrical configurations of jets (Ziegler and Wooler, n Corresponding author. Tel.: þ91 22 33612018; fax: þ 91 22 33611020. E-mail address: aw.patwardhan@ictmumbai.edu.in (A.W. Patwardhan). 0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.03.018 1971; Makihata and Miyai, 1979; Isaac and Jakubowski, 1985; Kolar et al., 2003, 2006; Kolar and Savory, 2007; Radhouane et al., 2009). The scalar mixing characteristics such as concentration, temperature decay and temperature fluctuations that occur due to thermal mixing have not been studied. Scalar mixing studies are useful in solving design related issues. The present work addresses thermal mixing issues in dual jet systems. 2. Previous work The literature on the twin jets in cross flow (TJICF) is relatively scarce. It was first studied by Ziegler and Wooler (1971) by means of an analytical model for the flow of jets in cross flow. Different multiple jet configurations were investigated and the influence of an upstream jet on downstream jet was studied. The jet spacing was three times diameter of jet. The second jet trajectory was influenced by first jet as it was restricting the cross flow. The analytical model predictions matched well with the experimental data. Makihata and Miyai (1979) described the experiments and theoretical predictions of the trajectories of multiple buoyant and non-buoyant jets. They employed a finite difference method of analysis of momentum integral equation. The ratio of jet velocity to cross flow velocity was maintained in the range 1.2–10.6. The jets were emitted at an inclination angle of 451 and placed at a jet spacing of 0.8d. Their theoretical predictions of jet trajectories and V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 are illustrated by the flow visualization images. It showed that the trajectories in tandem cases are higher than for single jet case. Also dispersion aspects of twin jets were discussed using concentration measurements. Radhouane et al. (2009) studied the interaction of twin tandem in-line jets of variable temperature with cross flow. Particle image velocimetry (PIV) was carried out on twin jets with 3d jet spacing, 1.29 velocity ratio and jet inclination of 601 with horizontal plane. Numerical analysis was carried out using turbulent Reynolds stress model (RSM). They have studied the temperature distribution by tracking the evolution of the tangential shear stress component along the domain. They concluded that the initial stream wise inclination angle highly affects the thermal field that results from the interaction of twin tandem jets emitted within the cross flow. The main emphasis of the previous work was study of vorticity characteristics of tandem twin jet systems. For tandem twin jet systems, only few papers showed effect of upstream jet on second jet and vice versa. Also scalar mixing characteristics of twin jets in terms of concentration or temperature decay, temperature fluctuations that occur due to thermal mixing of hot twin jets in cooler cross flow were not addressed. These were the objectives of the present work. diffusion characteristics of multiple jets were in close agreement with the experimental data. Isaac and Jakubowski (1985) carried out wind tunnel experiments on different twin jet configurations. Hot wire anemometer was used for the velocity field measurements. The results showed flow similarities (mean velocity and turbulence parameters) between the single jet and tandem (in-line) twin jets in the downstream region of x/d410. Kolar et al. (2003) experimentally studied the vorticity distribution and turbulent vorticity transport associated with the TJICF. Velocity field measurements are carried out using hot wire anemometer. The vorticity transport features are visualized and interpreted in terms of turbulent vorticity fluxes. They have compared tandem and side by side twin jet arrangements (5d spacing between jets in both cases) in terms of vorticity distribution and jet penetration ability. They concluded that the above properties are strongly dependant on geometrical parameters like jet spacing and the angle between jet center to center connecting line. Ibrahim and Gutmark (2006) investigated the effect of velocity ratio ‘r’ on the dynamics of single and twin jet arrangement using particle image velocimetry (PIV). They have studied jet trajectories and penetration, deflection, mass entrainment, windward and leeward spread, decay rate and turbulent kinetic energy. In tandem setup, trajectory and penetration of the second jet are found to increase due to shielding effect of the upstream jet. Also, the presence of upstream jet hindered the entrainment characteristics of the second jet. The windward and leeward spread of the second jet was reduced by the presence of upstream jet. The reverse flow confined between the upstream jet and second jet was stronger than that of single jet and caused reduction in the size of reverse flow region downstream of the second jet. The peak turbulent kinetic energy value along the trajectory of the second jet was 20% smaller than that of first jet. They attributed the decrease in turbulent kinetic energy to the reduction in local interaction between cross flow and second jet. Kolar et al. (2006) investigated the vorticity distribution and overall circulation associated with the vortical structure of the TJICF. They have carried out wind tunnel experiments on single, tandem, side by side and oblique jet (second jet was in-line with upstream jet at 451) arrangements. Velocity field was measured with hot film anemometry. They found that the vortical structure of TJICF was similar to CVP (counter rotating vortex pair) of the single jet in cross flow. Kolar and Savory (2007) carried out velocity field analysis in wind tunnel experiments. The similarities and differences between the mean flow vortical features, vorticity and circulation associated with three basic jet arrangements – tandem, side by side and oblique – have been studied using hot wire anemometry. The comparison with single jet case was also carried out. The turbulent structures associated with the single and tandem jets 3. Cross flow type mixing experiments Figs. 1 and 2 show tandem twin jet test section and schematic diagram of experimental setup for cross flow experiments, respectively (Naik-Nimbalkar et al., 2010). The different locations of the second jet are 2 times jet diameter (2d), 4d and 6d from the center of the first jet as shown in Fig. 1. T-junction of both jets with cross flow pipe is constructed of acrylic pipes. Horizontal main pipe is of 0.05 m inner diameter and T-junction branch pipe is of 0.015 m inner diameter. Cold water enters from main pipe and hot water from the branch pipe. Velocity ratios of 1, 2 and 4 were maintained between branch pipe and main pipe flow. Table 1 shows the various experimental conditions maintained. Temperature difference of 15 1C is maintained between water from main pipe and jet with the help of temperature controllers connected to thermocouples. Velocity ratios of 1, 2 and 4 were maintained by adjusting flow-rate through main pipe and branch pipe. Magnetic turbine flow-meters are employed to monitor water flow-rate through main pipe and branch. The second branch pipe is adjustable to set up 2d, 4d and 6d spacing between centers of two jets. Velocity and temperature for both the branch pipes were maintained same for each test run. Velocities and temperatures at the main and branch pipes were confirmed to be at steady-state before each experiment was performed. Velocity and temperature measurements are carried out at four locations as shown in Fig. 1 using Hot-wire anemometer HFA measurement locations D 0.6m y Cold water in (303 K) 1 2 3 4 x 1st Jet Main pipe Branch Pipe (0.05m id, 1.2m long) (0.015m id) 2617 nd d 2d 4d 6d Hot water in (318 K) 2 Jet locations Branch Pipe (0.015m id) Fig. 1. Tandem twin jet test section for cross flow experiments. 2618 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 Temperature controllers Main pipe 0.05m diameter 1.2m length Water in (303K) TC1 To H1 To H2 To TC1 Thermocouple HFA measurement TC2 locations 1 2 3 4 Branch pipe 0.015 m diameter Water in (318K) To TC2 Thermocouples To Heat Exchanger Flow meter Flow meter From Heat Exchanger 318K 303K Heater H2 H1 Fig. 2. Schematic diagram of experimental setup for twin jet in cross flow experiments. Table 1 Experimental conditions for cross flow experiments. Velocity ratio, r ¼ Vh/Vc 1 2 4 Main pipe Branch pipe (Both jets) Diameter (m) Velocity ‘Vc’ (m/s) Temperature ‘Tc’ (K) Diameter (m) Velocity ‘Vh’ (m/s) Temperature ‘Th’ (K) 0.05 0.05 0.05 0.5 0.5 0.33 303 303 303 0.015 0.015 0.015 0.5 1 1.32 318 318 318 (Streamline Research Anemometer System 90N10 Frame, Dantec Dynamics Ltd., Denmark). HFA probe with support is mounted using leak proof Swagelok fittings to facilitate smooth vertical movement of probe. A constant temperature module (CTA) has been used for the measurement of local velocity in the system. The output of voltage versus time data was converted to velocity versus time data using calibration with non-intrusive flow velocity elucidates from Laser Doppler Anemometer (LDA, Dantec Dynamics Ltd., Denmark). A constant current module (CCA) has been used for the measurement of the local temperature in the system, which gives output as voltage versus time data. The voltage versus time data was converted to temperature versus time data with the help of calibration using thermometer. Dual (55R63) X-film type of fiber probe (quartz fiber probe covered by Ni thin film of thickness 0.1 mm, sensor diameter 70 mm, overall fiber length 3 mm, sensor length 1.25 mm) has been used along with the standard probe support provided with the system. At each measurement point, sampling time was 4 s and sampling rate was 1000 samples per second. At first, cross wire point of HFA probe is fixed at the measurement location. The flows through the main and branch pipe are started. The total outflow after mixing is passed though heat exchanger and sent back to cold water tank. After achieving steady state, HFA measurements were carried out for velocity and temperature. For each measurement point same procedure is repeated. Figs. 3 and 4 show experimental measurements of X-velocity and mean temperature respectively. 2d spacing twin jet measurements are compared with single jet in cross flow. Uncertainty analysis was carried out by repeating experiments for several times. There was þ/ 3% deviation in the measured values from mean value of all the measurements. Error bars show the possible range of variation in the experimental measurements in Figs. 3 and 4. From both the figures it is clear that the percentage error of 3% do not have any significant effect on velocity and temperature field measurements. Fig. 3 shows X-velocity distribution for 2d spacing twin jet at line 2 which is at 3d from first jet center. Line 2 is just after the entry of the second jet in cross flow. The single jet measurements were carried out by making first jet off and then the second jet was acting as single jet in cross flow. Fig. 3 shows X-velocity distribution for velocity ratio 4. For r ¼4, jet has fairly large momentum and it practically impinges on the opposite wall. For single jet case, the sudden change in velocity near the main pipe axis indicates the interaction point between jet fluid and main pipe fluid. For 2d twin jet case, this point is above the single jet case since the second jet penetrates more in the main pipe fluid due to shielding effect of the first jet. First jet 2619 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 0.5 m 0.4 m y Zone 1 0.05 m Zone 2 0.3 m Zone 3 x 0.015m Fig. 5. Computational domain for 3-D CFD simulations. ((x, y) ¼(0, 0)) shown in Fig. 5 is on the centerline of the main pipe above the 1st jet entry. Main pipe cold fluid flows downstream along x-direction and jet fluid enters perpendicular to main pipe axis along y-direction. To avoid entrance and exit effects, sufficient pipe length of 12D is maintained before and after 1st jet. The end effects have been studied for single jet in cross flow in our previous work Naik-Nimbalkar et al. (2010). The transport equations are as follows. Mass conservation equation Fig. 3. X-velocity distribution for 2d spacing twin jet on line 2 (3d) for r¼ 4 (m Single jet experiments, ~ Twin jet experiments). Momentum conservation equation ð2Þ 0.8 Energy conservation equation ! "  # @T @ W @T at þ t uj ¼ @xj @xj Prt @xj 0.6 0.4 Y / Rm ð1Þ       @ @P @ @ui @uj @  þ þ ðrui uj Þ ¼  m þ rui 0 uj 0 þ rg bðT T0 Þ @xj @xi @xj @xi @xj @xj 1 0.2 0 -0.2 @ðrui Þ ¼0 @xi 0 0.2 0.4 0.6 0.8 -0.4 1 3d y x -0.6 -0.8 d 2d 1Tm Normalized Fig. 4. Mean temperature distribution for 2d spacing twin jet on line 2 (3d) for r ¼4. Legend same as Fig. 3. obstructs the cross flow and due to this second jet was not confronted with the actual cross flow velocity. The negative X-velocity shows the recirculation zone near to the jet entry. Fig. 4 shows the mean temperature distribution and comparison of 2d twin jet case with single jet in cross flow. As the jet fluid was hot, normalized mean temperature varies from 1 to 0. The sudden variation of the mean temperature denotes the mixing region of jet and main pipe fluid as seen in Fig. 4. Peak of the mean temperature for 2d spacing twin jet case is higher than single jet case. This shows that due to shielding effect of first jet, second jet penetrates more in the cross flow. The detailed discussion of spacing effect on thermal mixing is continued along with numerical results in the results and discussion section. 4. CFD simulations Steady-state 3-dimensional CFD simulations were carried out on the domain shown in the Fig. 5. The co-ordinate system ð3Þ Along with these transport equations, scalar transport equation for temperature variance was solved to predict temperature fluctuation intensity. It was derived from basic thermal energy equation and given as pffiffiffiffiffiffiffi!2 ! " # !  @T 0 2 @ k2 @T 0 2 @T @ T 02 0 ui p þ CTT ¼ 2ui0 T 2eT 0 2a @xi @xi @xi e @xi @xi ð4Þ For solving temperature variance equation in CFD simulations, we have to model some terms as follows. The right hand terms are: molecular and turbulent diffusion, and gradient production, dissipation for temperature variance and molecular dissipation, respectively. We have eT 0 ¼ eT 02 ð5Þ Rk From gradient assumption of Fourier u0i T 0 ¼ at @T @xi ð6Þ Using all the above modeled terms and neglecting molecular dissipation, the temperature variance equation for steady state is, ! " # !2  @T02 @ k2 @T02 @T e ui ¼ p þCTT 2at 2 T02 ð7Þ @xi @xi @xi e @xi Rk The ability of temperature variance equation to predict temperature fluctuation depends largely on the modeling of the production and dissipation term. In previous literature, various mathematical models are proposed for the modeling of dissipation term. The detailed analysis of prediction of temperature fluctuations using different temperature variance models for single jet in cross flow is carried out by Naik-Nimbalkar et al. (2010). On the basis of that work, constant ‘R’ model (R¼2) is 2620 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 used to predict temperature fluctuations in the present case of twin jet in cross flow. The transport equations have been solved using the FLUENT software version 6.3.26 by Finite Volume Method. The standard k  e turbulence model was used. No slip and adiabatic condition was given to the wall. Boundary conditions at inlet for this model were mass flow inlet using the experimental conditions given in Table 1. The outlet boundary condition was outflow. The variation in density of working fluid due to temperature change was considered using the Boussinesq approximation and included as the last term in Eq. (2). ðrr0 Þg  r0 bðTT0 Þg ð8Þ The transport equations for momentum, k and e were discretized using second order upwind scheme and the transport equations for energy and T 02 were discretized using first order upwind scheme. The pressure values at the faces were interpolated using the standard scheme and the transport equations are solved using the SIMPLE algorithm. The equations were considered to be converged when the absolute values of the residuals were below 1  10  4. 5.2. CFD model predictions 5.2.1. Prediction of X-velocity Fig. 7 shows x-velocity contours for single jet and 2d, 4d, 6d twin jet cases. Figs. 8–10 and show X-velocity distribution and comparison of different twin jet cases with single jet in cross flow for velocity ratio 4. X-velocity is normalized by the main pipe velocity ‘Vc’. Fig. 8 shows X-velocity distribution for 2d spacing twin jet at line 2, which is at 3d from first jet center. Line 2 is just after the entry of the second jet in cross flow. For comparison the single jet measurements were carried out by making first jet off and then the second jet was acting as single jet in cross flow. Fig. 8 shows X-velocity distribution for velocity ratio 4. For r ¼4, jet has fairly large momentum and it practically impinges on the 5. Results and discussion 5.1. Grid independency Zone 2 in Fig. 5 was meshed with fine tetrahedral mesh of 2 mm (0.6 million), 1.5 mm (1.7 million) and 1.25 mm (1.92 million). Zones 1 and 3 were meshed with variable size tetrahedral mesh with size ratio of 1.2 and up to maximum size of 3 mm. Fig. 6 shows the CFD predictions of mean temperature on the measurement line 2, which is at 3d from the coordinate system as shown in Fig. 1. Mean temperature was normalized as TmNormalized ¼ ðTTc Þ ðTh Tc Þ ð9Þ From Fig. 6 it is clear that CFD predictions with 1.5 mm grid size in zone 2 shows good match with the experimental data. Further refinement of grid up to 1.25 mm in zone 2, does not show significant improvement. Thus, grid size of 1.5 mm was used in the zone 2. 1 0.8 3d y x 0.6 d 0.4 2d Y / Rm 0.2 0 -0.2 0 0.2 0.4 0.6 0.8 1 -0.4 -0.6 -0.8 -1 Tm Normalized Fig. 6. Grid independency: Mean temperature prediction for 2d spacing jet for r¼ 1 at line 2 (3d). (m Experiments, ?? CFD simulations: zone 2–1.25 mm, ——— CFD simulations: zone 2–1.5 mm, - - - - - - - CFD simulations: zone 2–2 mm). Fig. 7. X-velocity contours for r¼ 2. (a) Single jet, (b) 2d spacing twin jet, (c) 4d spacing twin jet and (d). 6d spacing twin jet. 2621 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 1 0.8 0.6 0.2 0 -1 -0.5-0.2 0 0.5 1 1.5 -0.4 2 2.5 3 3d y x -0.6 d -0.8 2d -1 X-velocity Normalized Fig. 8. X-velocity distribution for 2d spacing twin jet on line 2 (3d) for r ¼4 (m Single jet experiments, ~ Twin jet experiments, ——— Single jet CFD simulations, - - - - - - - Twin jet CFD simulations). 1 0.8 0.6 Y / Rm 0.4 0.2 0 -0.5 -0.2 0 0.5 1 1.5 2 2.5 3 5.5d -0.4 y x -0.6 d -0.8 4d -1 X-velocity Normalized Y / Rm Fig. 9. X-velocity distribution for 4d spacing twin jet on line 3 (5.5d) for r ¼4. Legend same as Fig. 8. 5.2.2. Prediction of mean temperature Figs. 11–13 and show the mean temperature distribution and comparison of different twin jet cases with single jet in cross flow. As the jet fluid was hot, normalized mean temperature varies from 1 to 0. The sudden variation of the mean temperature denotes the mixing region of jet and main pipe fluid as seen in Fig. 11. In the recirculation zone as described in Figs. 7(b) and 8, some of the cross flow fluid mixes with the jet fluid. So the mean temperature decreases in that zone. This has also happened in the case of 4d and 6d spacing cases as shown in Figs. 12 and 13. Peak of the mean temperature for 2d spacing twin jet case is higher than single jet case. This shows that due to shielding effect of first jet, second jet penetrates more in the cross flow. With increase in jet spacing, shielding effect decreases. So that the peak difference for the 4d and 6d spacing case decreases as shown in Figs. 12 and 13. In the twin jet cases, the thermal energy input from jet fluid is double compared to single jet case. For 4d and 6d cases, hot jet fluid mixes with the cross flow, which further interacts with the second jet. So that mean temperature values for twin jet cases are higher than single jet cases as shown in Figs. 11–13. In above cases CFD model predictions of X-velocity and mean temperature matches reasonably well with the experimental 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 -0.5 -0.2 0 0.5 1 1.5 2 2.5 3 8d -0.4 y Y / Rm Y / Rm 0.4 opposite wall. For single jet case, the sudden change in velocity near the main pipe axis indicates the interaction point between jet fluid and main pipe fluid. For 2d twin jet case, this point is above the single jet case since the second jet penetrates more in the main pipe fluid due to shielding effect of the first jet. First jet obstructs the cross flow and due to this second jet was not confronted with the actual cross flow velocity. The contour plot 7(b) portrays this interaction of 2d spacing twin jet with cross flow. The negative X-velocity shows the recirculation zone near to the jet entry. For the jet spacing of 4d and 6d, first jet gets fairly mixed with the cross flow fluid. So that the cross flow has recovered its momentum before interacting with the second jet. For r ¼4, the first jet mixing with cross flow is improved and cross flow totally overcome the shielding effect. Fig. 9 shows X-velocity distribution for r ¼4 at line 3 (5.5d). Due to decrease in shielding effect of first jet, the difference in the X-velocity distribution for single jet case and 4d spacing case decreases. For 6d spacing case, the shielding effect of first jet is almost removed as seen in Fig. 10. The contour plots 7(c) and (d) show the decrease in shielding effect of first jet with increase in the jet spacing. 0 -0.2 0 0.2 0.4 0.6 0.8 -0.4 -0.8 -1 x -0.6 -0.6 d d -0.8 6d X-velocityNormalized Fig. 10. X-velocity distribution for 6d spacing twin jet on line 4 (8d) for r ¼4. Legend same as Fig. 8. 3d y x 1 2d -1 TmeanNormalized Fig. 11. Mean temperature distribution for 2d spacing twin jet on line 2 (3d) for r¼ 4. Legend same as Fig. 8 2622 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 1 2 1.8 0.6 1.6 0.4 1.4 0.2 1.2 Y/rd Y / Rm 0.8 0 -0.2 0 0.2 0.4 0.6 0.8 1 0.8 5.5d -0.4 0.6 y x -0.6 0.4 0.2 d -0.8 1 0 4d 1- 0 TmeanNormalized Fig. 12. Mean temperature distribution for 4d spacing twin jet on line 3 (5.5d) for r¼ 4. Legend same as Fig. 8. 0.5 1 X/rd 1.5 2 1 0.9 1 0.8 0.8 0.7 0.6 Y/rd 0.6 0.4 0.5 0.4 Y/Rm 0.2 0.3 0 -0.2 0 0.2 0.2 0.4 0.6 0.8 1 -0.4 0 x 0 -0.6 -0.8 -1 0.1 8d y 0.2 0.4 0.6 0.8 1 X/rd d 6d TmeanNormalized Fig. 13. Mean temperature distribution for 6d spacing twin jet on line 4 (8d) for r¼ 4. Legend same as Fig. 8. measurements. This validated CFD model is used for the prediction of jet trajectory, centerline X-velocity decay, vorticity and temperature fluctuation intensity. 5.2.3. Prediction of jet trajectory Fig. 14 shows Comparison of jet trajectories for single and first jet of 2d, 4d, 6d spacing jets. The jet center is at (0, 0). For velocity ratio 2, first jet trajectories for all the cases are identical as seen in Fig. 10(a). Also trajectory data for r ¼3 given by Ibrahim and Gutmark (2006) is plotted in Fig. 14(a). In their case, first jet penetrates more in the cross flow fluid as shown in Fig. 14(a). They have attributed the impact on the first jet to the fact that the upward force of the restricted fluid between the two jets slows down the rate of deflection of the first jet. The jet diameter to main pipe diameter ratio in case of Ibrahim and Gutmark (2006) is 0.08. The mass of the jet fluid and its momentum was lower compared to main pipe fluid. So that it experiences the push from restricted fluid between two jets. In the cases studied in the present work, jet diameter to main pipe diameter ratio is 0.3. The mass of the jet fluid and its momentum is comparable to cross flow fluid. So that the effect on first jet similar to Ibrahim and Gutmark (2006) cannot be seen. Fig. 14. Comparison of jet trajectories for single and ‘first’ jet of 2d, 4d, 6d spacing jets. (a). For r ¼ 2 (m Ibrahim and Gutmark (2006) single jet experiments, r ¼3. ~ Ibrahim and Gutmark (2006) Twin jet experiments J ¼3.55d, r¼ 3. ——— Single jet CFD simulations. -  -  -  -  - 2d spacing twin jet CFD simulations. - - - - - - - 4d spacing twin jet CFD simulations. ??? 6d spacing twin jet CFD simulations). (b). For r ¼4 (——— Single jet CFD simulations. -  -  -  -  - 2d spacing twin jet CFD simulations. - - - - - - - 4d spacing twin jet CFD simulations. ??? 6d spacing twin jet CFD simulations). Interestingly in the present study as the velocity ratio increases to 4, trajectory of first jet for 2d spacing case is slightly lower than single, 4d and 6d spacing case as seen in Fig. 14(b). The second jet in 2d spacing case pulling the fluid behind it due to pressure difference and the first jet is close to that region. So that first jet slightly gets pulled by second jet and its trajectory gets lower. Figs. 16 and 17 show gage pressure contours. For 2d spacing case, Figs. 16(a) and 17(a) show negative gage pressure zone in between the two jets. The increase in velocity ratio results in the increase in low pressure zone as seen in Fig. 17(a) and the pulling of the first jet as seen in Fig. 14(b). As the jet spacing becomes 4d, first jet started mixing with cross flow and the cross flow fluid flowing around the first jet overcomes the low pressure zone. This can be seen from contour plot Figs. 16(b) and 17(b). In 2d twin jet case, first jet obstructs the cross flow fluid. Due to this, second jet gets shielded from the cross flow fluid and penetrates more in the main pipe as seen in Fig. 15. The shielding effect can be clearly seen in Fig. 15(a) for velocity ratio 2 and in Fig. 15(b) for velocity ratio 4. For 4d spacing case, second jet is at more downward distance. Now first jet started mixing with cross flow as seen in contour plot Fig. 7(c). Due to decrease in shielding V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 2623 400 2 1.8 100 1.6 1.4 -300 Y/rd 1.2 -600 1 0.8 -900 0.6 -1200 (pa) 0.4 0.2 0 400 0 0.5 1 X/rd 1.5 2 100 1 -300 0.9 0.8 -600 0.7 -900 Y/rd 0.6 0.5 -1200 (pa) 0.4 0.3 Fig. 16. Gage pressure contour for r¼ 2. (a) 2d spacing twin jet. (b) 4d spacing twin jet. 0.2 0.1 400 0 0 0.2 0.4 0.6 0.8 1 X/rd Fig. 15. Comparison of jet trajectories for single and ‘second’ jet of 2d, 4d, 6d spacing jets. (a) For r ¼2. Legend same as Fig. 14(a). (b) For r ¼4. Legend same as Fig. 14(b). 100 -300 -600 effect, second jet penetration becomes lower and its trajectory appears nearer to single jet case. For 6d spacing there is negligible shielding effect of first jet on second especially for r ¼4. Ibrahim and Gutmark (2006) observed the same shielding effect of first jet on second jet for the 3.55d spacing twin jet case as plotted in Fig. 15(a). From Figs. 14 and 15, it is clear that for jet spacing more than 4d, the above mentioned effects of twin jets on each other reduces. -900 -1200 (pa) 400 100 5.2.4. Centerline X-velocity decay Fig. 18 depicts the centerline X-velocity decay for r ¼2. The centerline X-velocity decay for single and first jet of twin jet cases is plotted in Fig. 18(a). For Ibrahim and Gutmark (2006) twin jet case, first jet decay is more than single jet. In the case of present study, first jet decay of 4d and 6d spacing case is similar to single jet case since the twin jet interaction with each other becomes lower. For 2d spacing case, the slight pulling by second jet and low pressure zone between two jets causes faster decay of first jet as seen in Fig. 18(a). For Ibrahim and Gutmark (2006) and present study, the second jet decays slowly than the single jet as seen in Fig. 18(b). Due to shielding effect of first jet on second, the second jet carries its momentum longer than single jet. So that its spreading is less and less amount of cross flow fluid can be entrained by it. As a result second jet decay is lower than single jet. -300 -600 -900 -1200 (pa) Fig. 17. Gage pressure contour for r¼ 4. (a) 2d spacing twin jet. (b) 4d spacing twin jet. 5.2.5. Prediction of vorticity The formation and decay of dominant vortical structure, the counter rotating vortex pair (CVP), is closely associated with the 2624 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 1 1 0.8 0.95 Y / rd X-velocity / Vhmax 0.9 0.85 0.6 0.4 0.8 0.75 0.2 0.7 0 0.65 0 0.2 0.6 0.4 0.6 0.8 1 X / rd 0 0.5 1 1.5 2 2.5 Fig. 19. Y-locations of peak vorticity regions for r¼ 4. (–m– Single jet, –~–2d spacing twin jet, –’– 4d spacing twin jet, –K– 6d spacing twin jet). Y/d 1 1 0.95 0.8 0.6 0.85 0.4 0.8 0.2 Y / Rm X-velocity / Vhmax 0.9 0.75 0.7 0 -0.2 0 0.1 0.2 0.3 -0.4 0.65 -0.6 0.6 -0.8 0 1 2 3 4 5 y x d 2d -1 Y/d 0.4 3d TrmsNormalized Fig. 18. Centerline X-velocity decay for r¼2. (a) For single and 1st jet of twin jet cases. Legend same as Fig. 14(a). (b) For single and 2nd jet of twin jet cases. Legend same as Fig. 14(b). 1 0.8 0.6 0.4 Y / Rm centerline turbulent vorticity transport across the plane of symmetry (Kolar et al., 2003). In the case of twin jets in cross flow, the vortical structure is naturally more complex than for a single jet in cross flow. The twin jet CVP is a result of merging process of the stronger CVP of first jet with slightly weaker CVP of a downstream shielded second jet. The second jet has higher transverse penetration ability and having a lifting effect on resulting CVP. In the case of twin jets, dominant vortical structures are formed downstream as a result of merging process of vortical structures associated with two single jets. Fig. 19 shows the center plane Y-locations of peak vorticity regions in the downstream direction for single and twin jet cases. Vorticity peaks for 2d spacing twin jets clearly show the shielding effect of first jet on second. Due to higher transverse penetration of second jet, vorticity peaks for 2d spacing twin jet case are higher than single jet case. Kolar et al. (2003, 2007) have observed the same trend of higher vorticity peak locations for twin jet case than single jet case. As a result of increase in jet spacing, there is decrease in shielding effect of first jet on second. For 4d spacing twin jet case, peak vorticity regions are nearer to those of single jet case. In case of 6d spacing twin jets, peak vorticity locations are almost similar to that of single jet case. This shows that the increase in jet spacing decreases the interaction between two jets. 0.2 0 -0.2 0 0.1 0.2 0.3 -0.4 y x -0.6 -0.8 0.4 3d d 2d -1 TrmsNormalized Fig. 20. Temperature fluctuation intensity distribution for 2d spacing twin jet on line 2 (3d). (a) For r ¼2 (m Single jet experiments, ~ Twin jet experiments, ——— Single jet CFD simulations, ??? Twin jet CFD simulations). (b) For r¼ 4 (m Single jet experiments, ~ Twin jet experiments, ——— Single jet CFD simulations, ??? Twin jet CFD simulations). 5.2.6. Prediction of temperature fluctuation intensity Figs. 20–22 illustrate the Trms distribution and comparison for single jet and 2d, 4d, 6d spacing twin jet case for r ¼2,4. Trms is 2625 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 1 0.8 0.6 Y / Rm 0.4 0.2 0 -0.2 0 0.1 0.2 0.3 0.4 8d -0.4 y x -0.6 d -0.8 6d -1 TrmsNormalized 1 1 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 -0.2 0 0.1 0.2 0.3 0.4 5.5d -0.4 Y / Rm Y / Rm 0.8 0 -0.2 0 0.1 0.2 0.3 8d -0.4 y y x -0.6 x -0.6 d -0.8 -0.8 4d -1 0.4 d 6d -1 TrmsNormalized TrmsNormalized Fig. 21. Temperature fluctuation intensity distribution for 4d spacing twin jet on line 3 (5.5d). (a) For r ¼2. Legend same as Fig. 20(a). (b) For r¼ 4. Legend same as Fig. 20(b). Fig. 22. Temperature fluctuation intensity distribution for 6d spacing twin jet on line 4 (8d). (a) For r¼2. Legend same as Fig. 20(a). (b) For r¼ 4. Legend same as Fig. 20(b). normalized by dividing it with temperature difference between jet fluid and main pipe fluid. 6. Conclusions TrmsNormalized ¼ Trms ðTh Tc Þ ð10Þ Fig. 20 shows temperature fluctuation intensity distribution for 2d spacing twin jet. Temperature fluctuations are higher in the mixing region of jet fluid and main pipe fluid. For velocity ratio 2, jet penetrates in the main pipe fluid and peak Trms is attained below main pipe axis as seen in Fig. 20(a). For higher velocity ratio of 4, peak Trms value is at the main pipe axis due to greater penetration of jet in the main pipe fluid as seen in Fig. 20(b). In both the cases peak for 2d twin jet case is at higher position than single jet due to higher second jet penetration in cross flow. As shown previously, the shielding effect of first jet decreases with increase in jet spacing. For 4d spacing case, the mixing of hot fluid from first jet causes increase in cross flow temperature. So the cross flow encountering with 2nd jet is at higher temperature as compared to single jet case. The local temperature fluctuations decreases due to reduction in temperature gradient between cross flow and 2nd jet. Due to this, peak temperature fluctuation intensity for twin jet case is less than single jet case as seen in Figs. 21(a) and (b). For 6d spacing case, same trend can be observed from Fig. 22(a). For higher velocity ratio of r¼4, shielding effect diminishes and the temperature fluctuations decreases as seen in Fig. 22(b)). Cross flow thermal mixing experiments were performed to investigate thermal mixing phenomenon in tandem twin jet systems. Fluid temperature and velocity measurements were carried out using Hot Film Anemometer modules, CCA and CTA respectively. Also three dimensional steady state CFD simulations were carried out to predict velocity and temperature field. Temperature fluctuation intensity was predicted using steady state CFD simulations by solving transport equation of temperature variance. The predicted mean velocities and temperatures are in good agreement with the measurements. The effect of jet spacing for different velocity ratios is studied by comparison with single jet case. For 2d spacing case, the first jet gets pulled by second jet in the downstream for higher velocity ratio of 4. Also, shielding effect of first jet on second jet results into higher penetration of second jet in cross flow. The X-velocity and mean temperature predictions, jet trajectory analysis, centerline velocity decay and vorticity clearly show the interaction between two jets. For jet spacing more than 4d, there is reduction in interaction between two jets. For higher velocity ratio and jet spacing of 6d, the interaction between two jets vanishes. The results obtained in the present work (both experimental and CFD simulations) enables calculation of jet spacing required between two adjacent jets in multiple jet systems issuing to a 2626 V.S. Naik-Nimbalkar et al. / Chemical Engineering Science 66 (2011) 2616–2626 cross flow. Study of temperature fluctuations occurred due to thermal mixing is useful in the case of design of mixing elements of the static mixers and burners in the combustion unit which had rows of multiple jets entering in the cross flow fluid. Nomenclature constant, 0.13 pecific heat of the fluid, J/kg K branch pipe diameter, m main pipe diameter, m jet spacing, m turbulent kinetic energy, m2/s2 molecular Prandtl number turbulent Prandtl number velocity ratio of branch pipe fluid velocity to main pipe fluid velocity R ratio of scalar fluctuation time scale to velocity fluctuation time scale ¼ eT 02 =eT 0 k radius of main pipe, m Rm T instantaneous temperature, K T , Tm mean temperature, K Trms root mean square of temperature fluctuations, K TmNormalized normalized mean temperature TrmsNormalized normalized r.m.s. temperature T 02 temperature variance, K2 Tc main pipe fluid temperature, K Th branch pipe fluid temperature, K instantaneous velocity, m/s ui ui time averaged mean velocity component, m/s u0i T 0 turbulent temperature fluxes u0i u0j Reynolds stresses m2/s2 Vc main pipe fluid velocity, m/s CTT cp d D J k Pr Prt r Vh Vhmax branch pipe fluid velocity, m/s maximum branch pipe fluid velocity, m/s Greek symbol e eT 0 r u a aT m turbulent kinetic energy dissipation rate, m2/s3 dissipation rate of temperature variance, K2/s fluid density, kg/m3 kinematic viscocity, m2/s molecular diffusivity of heat, m2/s turbulent diffusivity of heat, m2/s molecular viscosity, kg/m s References Ibrahim, I.M., Gutmark, E.J., 2006. Dynamics of single and twin circular jets in cross flow. In: Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. Isaac, K.M., Jakubowski, A.K., 1985. Experimental study of the interaction of multiple jets with a cross flow. AIAA J. 23 (11), 1679–1683. Kolar, V., Takao, H., Todoroki, T., Savory, E., Okamoto, S., Toy, N., 2003. Vorticity transport within twin jets in cross flow. Exp. Therm. Fluid Sci. 27, 563–571. Kolar, V., Savory, E., Takao, H., Todoroki, T., Okamoto, S., Toy, N., 2006. Vorticity and circulation aspects of twin jets in cross flow for an oblique nozzle arrangement. Proc. Inst. Mech. Eng. G. J. Aerosp. Eng. 220 (4), 247–252. Kolar, V., Savory, E., 2007. Dominant flow features of twin jets and plumes in cross flow. J. Wind. Eng. Ind. Aerodyn. 95, 1199–1215. Makihata, T., Miyai, Y., 1979. Trajectories of single and double jets injected into acrossflow of arbitrary velocity distribution. J. Fluids Eng. 101, 217–223. Naik-Nimbalkar, V.S., Patwardhan, A.W., Banerjee, I., Padmakumar, G., Vaidyanathan, G., 2010. Thermal mixing in T-junctions. Chem. Eng. Sci. 65, 5901–5911. Radhouane, A., Mahjoub, N., Mhiri, H., Palec, G.L., Bournot, P., 2009. Effect of two inline jets’ temperature on the turbulence they generate within a crossflow. Eng. Lett. 17 (3) EL_17_3_05. Ziegler, H., Wooler, P.T., 1971. Multiple jets exhausting into a crossflow. J. Aircraft 8 (6), 414–420.