3.4 Results
3.4.5 Comparison with Measurements
In this section, the comparisons of some flow properties are made with the experimental data of Ramaprian and Haniu (1983) and Haniu and Ramaprian (1989).
As said earlier Ramaprian and Haniu (1983) and Haniu and Ramaprian (1989) have reported their experimental observations in the s–n coordinate system (Fig. 3.1). The component of the mean velocity along the jet streamline direction is termed as the streamwise velocity (us) and the component along the normal to the streamline is termed as the normal component velocity (vn). The upper part of the deflected jet (n/D
< 0) faces and mixes with the crossflow. This part of the jet is referred to as the outer portion and the other part of the jet (n/D > 0) is referred to as the inner portion of the jet.
In the present flow configuration, streamline curvature will have a stabilizing effect on turbulence in the lower shear layer (inner part of the jet) and a destabilizing effect in the upper shear layer of the jet (Bradshaw, 1969). Thus the shear stress, turbulence kinetic energy and jet spreading rate would be enhanced by the curvature correction in the outer shear layer relative to the unmodified model (standard k-ε model), while the reverse would occur in the lower shear layer.
Comparisons of the normalized streamwise component of the mean velocity are shown in Figs. 3.18 and 3.19 for R = 6 at different s/D locations. The peak value of the jet is higher near the jet discharge and it decreases in the downstream locations, where the spreading of the jet is more. It is observed that the jet is not symmetric about its axis unlike a jet in quiescent ambient.
Fig. 3.18: Comparison of mean streamwise velocity with the experimental data for R = 6, s/D = 4.94 and 9.68.
The curvature modification model should show an enhanced spreading rate in the outer part (n/D < 0) and reduced spreading rate in the inner part (n/D > 0) of the jet.
However due to the moving stream of the crossflow, the effects of curvature and co- flowing ambient counteract each other. Hence the spreading rate is not so distinguished in the outer part of the jet and the curvature modification model slightly over predicts compared to the standard k-ε model.
The improvement by the curvature modification model is seen in the inner part of the jet by a reduction of the spreading rate and more prominently at the edge of the
inner portion by showing a large negative velocity, thereby accurately predicting the recirculation below the jet.
Fig. 3.19: Comparison of mean streamwise velocity with the experimental data for R = 6, s/D = 18.86 and 28.12.
The maximum improvement by the curvature modification model over the standard k- ε model is approximately 20%.
Figs. 3.20 and 3.21 show a comparison of the normalized streamwise component of mean velocity for the value of R = 9 at different s/D locations. The value of peak velocity in this case is higher than for R = 6 as the jet is relatively stronger in this case. In this case also due to the effect of finite edge velocity the spreading rate is reduced in the outer part of the jet. The improvement by the curvature modification model in this case is less compared to the case with R = 6, because the flow experiences a small streamline curvature.
Fig. 3.20: Comparison of mean streamwise velocity with the experimental data for R = 9, s/D = 4.97 and 9.76.
Fig. 3.21: Comparison of mean streamwise velocity with the experimental data for R
= 9, s/D = 21.22 and 29.73.
Comparisons of the normal component of mean velocity (vn/vj)are shown in Figs.
3.22 and 3.23 for R = 6 at four different s/D locations. In the upper part of the jet the fluids show a positive component of velocity thus the making the motion upward and gradually the positive value decreases as one moves towards the jet centre. In the inner part of the jet all the fluid particles have a downward velocity. This is due to the recirculation below the jet. Thus it is observed that the recirculation determines these velocities rather than the jet turbulence. Another feature observable from Figs. 3.22 and 3.23 is that near the jet centre line in the inner part of the jet, the fluids show an upward motion making the fluids to move from the inner portion to the outer portion of the jet. Thus the entrainment rate is different at both portions of the jet. Moreover the spread of the jet at the upper and lower parts of the jet is not equal. It is more at the bottom part of the jet than that at the upper part. Due to unequal spread of the jet, profiles of the normal component of velocity show different trends at the upper and lower parts of the jet. Both the models predict the normal component of velocity well at first two downstream locations (s/D = 4.94 and 9.68), but at further downstream positions (s/D = 18.86 and 28.12) both the model show some difference of prediction from the experimental data. Comparatively the curvature modification model predicts better than the standard k-ε model especially in the inner part of the jet.
Fig. 3.22: Comparison of mean normal component velocity with the experimental data for R = 6, s/D = 4.94 and 9.68.
Fig. 3.23: Comparison of mean normal component velocity with the experimental data for R = 6, s/D = 18.86 and 28.12.
Comparisons of the normalized normal component profiles of the mean velocity are shown in Figs. 3.24 and 3.25 for jet with R = 9 at different s/D locations. In this case also due to recirculation, the n-component velocity has downward motion in the inner part of the jet. One significant difference observed in this case is that the variation of the n-component velocity with downward direction in the inner part of the jet is less compared to the case with R = 6. In case of jet with R = 6 the values of vertical velocity component reduce in the inner part of the jet and at far downstream locations (s/D = 18.86 and 28.12) the variation is more prominent. In the case of jet
with R = 9, the variation of velocity in the inner part of the jet is very small. In this case also the curvature modification model predicts better than the standard k-ε model in the inner portion of the jet.
Fig. 3.24: Comparison of mean normal component velocity with the experimental data for R = 9, s/D = 4.97 and 9.76.
Fig. 3.25: Comparison of mean normal component velocity with the experimental data for R = 9, s/D = 21.22 and 29.73.
Comparisons of the normalized turbulence shear stresses are shown in Figs. 3.26 and 3.27 for the jet with R = 6. The value of the shear stress decreases with the distance s/D. At low s/D values, i.e., near the jet slot the value of the shear stress is large at the inner portion of the jet whereas further downstream the value of shear stress in the upper part of the jet is more than that in the lower part. According to streamline curvature effect, there should be an enhancement of the shear stress in the upper part of the jet and reduction of shear stress in the lower part of the jet. This is observed in the present investigation. Due to the combined effect of the streamline
curvature and the edge velocity, the curvature modification model does not show adequate increase of shear stresses in the outer part of the jet, but it shows an appreciable reduction of the shear stress in the inner part of the jet compared to that predicted by the standard k-ε model.
Fig. 3.26: Comparison of turbulence shear stress with the experimental data for R = 6, s/D = 4.94 and 9.68.
Fig. 3.27: Comparison of turbulence shear stress with the experimental data for R = 6, s/D = 18.86 and 28.12.
The standard k-ε model over predicts the shear stresses especially in the inner part of the jet. Moreover the predictions of the positive and negative peak values of the stresses by the curvature modification model match better with the experimental data than those by the standard k-ε model.
Fig. 3.28: Comparison of turbulence shear stress with the experimental data for R = 9, s/D = 4.97 and 9.76.
Comparisons of the normalized turbulence shear stresses are shown in Figs. 3.28 and 3.29 for the jet with R = 9. The value of the shear stress in the near-filed of the jet is more than that in the case of jet with R = 6. In this case also the curvature modification model shows improvement in the prediction especially in the inner portion of the jet but fails to match the positive and negative peak values of the shear stresses. This is due to the fact that the flow field faces less streamline curvature effect than that in the case of R = 6.
Fig. 3.29: Comparison of turbulence shear stress with the experimental data for R = 9, s/D = 21.22 and 29.73.