Results and Discussion
4.2 New vortex flow patterns at H=12.5 mm
It is of interest to note in the flow visualization that two new vortex flow patterns appear when the jet-disk separation distance is reduced to 12.5 mm. More specifically, we observed radial rolls and moving circular waves in certain ranges of the jet Reynolds number and Rayleigh number. The top view flow photos taken at the midheight of the test section are presented in Figs. 4.29-4.42 for various Rej and Ra to illustrate these new vortex flow patterns. The results given in Fig. 4.29 for Ra=1,470 (ΔT=8°C) at Rej increased from 101 to 676 show that a few moving circular waves appear in the outer zone of the test section at the small Rej of 101. These waves are slightly deformed and do not possess axisymmetry. Besides, they move in the radial direction and their wave fronts are normal to the direction of the wall jet flow. Hence they are essentially the transverse waves. For an increase of Rej to 135 several radial rolls are induced, in addition to the weaker moving waves (Fig. 4.29(b)). Note that the radial rolls originate in the stagnation region of the impinging jet near the jet axis and grow in size in the radial direction. But the size of the induced radial rolls in the test section for the given Rej and Ra varies noticeably in the circumferential direction.
Some radial rolls are large than the other. As the jet Reynolds number is raised to 203 and high level, no moving waves and radial rolls are seen. Instead, the flow in the test section is dominated by the primary and secondary inertia-driven circular rolls (Figs.
4.29(c)-(j)).
To ascertain the conditions leading to the appearance of the new vortex flow structures, we repeat the above experiment for a smaller interval of the jet Reynolds number. The obtained top view flow photos are shown in Fig. 4.30 for Rej ranging from 27 to 149. The results indicate that the deformed moving waves prevail for Rej
as low as 27. As Rej is raised to 88 both the moving waves and radial rolls appear in
the test section (Fig. 4.30(j)).
Next, the results presented in Figs. 4.31-4.34 for slightly higher ΔT of 9°C and 10°C show that the moving waves and radial rolls appear in nearly the same range as that for ΔT=8°C. For a further raise of ΔT to 11°C the moving waves exist in a slightly smaller range of Rej (27 to 68). But the pattern characterized by the simultaneous presence of the radial rolls and moving waves, which is designated as
“the mixed roll-wave pattern”, prevails in a slightly wider range of Rej (101 to 135), as evident from Fig. 4.36. At the even higher ΔT of 12°C the range of Rej for the appearance of the moving waves is even smaller (27 to 61) and the mixed roll-wave pattern dominates in a wider Rej range (68 to 115). Note that for Rej ranging from 122 to 149 only the radial rolls appear and no moving waves are seen (Figs. 4.37 and 4.38).
For Rej larger than 149 the flow is dominated by the primary inertia-driven and buoyancy-driven rolls. For a still higher ΔT of 13°C the results in Figs. 4.39 and 4.40 indicate that the moving waves dominate for Rej ranging from 27 to 54 and the mixed pattern appears in a wider Rej range of 61 to 108. Besides, the radial rolls are prevalent for a wider range of Rej (115 to 149). As ΔT is raised to 14 °C Figs. 4.41 and 4.42 show that buoyancy roll prevails at low Rej and the moving waves only appear at Rej =27 to 41. For 47≦Rej ≦88 the mixed pattern dominates. And the radial rolls fill the test section for 95≦Rej ≦149.
Selected data for the measured time records of the non-dimensional air temperature are presented in Figs. 4.43-4.49 for various Rej and Ra at H=12.5 mm.
The results indicate that the air temperature also oscillates irregularly with time when the new vortex flow patterns dominate in the test section.
The result presented above clearly indicate that three new vortex flow patterns have been identified in the present study. These patterns include the vortex flow dominates by the pure moving circular waves, the pure radial rolls, and the
coexistence of the moving waves and radial rolls. The range of Rej and Ra for the appearance of these new vortex flow patterns are presented in flow regime maps given in Figs. 4.50 and 4.51 for H=12.5 mm.
The boundary separating the transversal waves and mixed roll-wave pattern can be correlated as
Ra= 3470-2.55*Rej1.5 (4.12) for 20<Rej<676 and 1,470<Ra<2,670
and the standard deviations is 8.4%.
Besides, the boundary between the mixed roll-wave pattern and radial rolls can be correlated as
Ra= 3770-1.14*Rej1.5 (4.13) for 20<Rej<676 and 1,470<Ra<2,670
and the standard deviations is 2.3%.
Then, the boundary separating the radial roll pattern and the pattern consisting of the primary inertia-driven roll and buoyancy-driven rolls can be correlated as
Ra= 4502-1.05*Rej1.5 (4.14) for 20<Rej<676 and 1,470<Ra<2,670
and the standard deviations is 2.5%.
Finally, the boundary separating the pattern including the primary inertia-driven roll and buoyancy-driven rolls and the pattern consisting of the primary inertia-driven roll, secondary inertia-driven roll, and buoyancy-driven rolls can be correlated as
Ra=-125+0.291*Rej1.5 (4.15) for 20<Rej<676 and 1,470<Ra<2,670
and the standard deviations is 14.1%.
Table 4.1 The characteristics of buoyancy-driven rolls
(a)
(b)
(c)
(d)
(e)
Fig.4.1 Steady side view flow photos taken at the cross plane θ=0∘& 180∘for various jet Reynolds numbers at Ra=0 (△T=0°C) for H=25.0mm.
Rej=372 (Qj=5.5slpm) Rej=406 (Qj=6slpm) Jet
θ=0° Heating plate θ=180°
Rej=338 (Qj=5slpm)
Rej=304 (Qj=4.5slpm)
Rej=270 (Qj=4slpm)
32
(f)
(g)
(h)
(i)
(j)
Fig.4.1 continued
Rej=203 (Qj=3slpm) Rej=237 (Qj=3.5slpm) Jet
θ=0° Heating plate θ=180°
Rej=169 (Qj=2.5slpm)
Rej=135 (Qj=2.0slpm)
Rej=101 (Qj=1.5slpm)
33
Fig.4.2 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various jet Reynolds numbers at Ra=2940 (△T=2°C)
Secondary inertia-driven roll
Buoyancy-driven rolls
Buoyancy-driven rolls
Buoyancy-driven rolls Buoyancy-driven rolls
Secondary inertia-driven roll
34
Fig.4.3 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various jet Reynolds numbers at Ra=4400 (△T=3°C)
Secondary inertia-driven roll
Buoyancy-driven rolls
Buoyancy-driven roll Buoyancy-driven rolls
Secondary inertia-driven roll Buoyancy-driven rolls
35
Fig.4.4 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various jet Reynolds numbers at Ra=5870 (△T=4°C)
Secondary inertia-driven roll
Buoyancy-driven rolls
Buoyancy-driven rolls Buoyancy-driven rolls
Buoyancy-driven rolls
36
Fig.4.5 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various jet Reynolds numbers at Ra=7340 (△T=5°C)
Secondary inertia-driven roll
Buoyancy-driven roll
Buoyancy-driven roll
Buoyancy-driven roll
Buoyancy-driven
37
(a) (b)
(c) (d)
(e) (f) Fig.4.6 Top view flow photos taken at midheight of the test section with Ra=2,940 (ΔT=2 )℃ &
H=25.0 mm for Rej= (a)101, (b) 135, (c) 203, (d) 270, (e) 338, and (f)406.
(a) (b)
(c) (d)
(e) (f)
Fig.4.7 Top view flow photos taken at midheight of the test section with Ra=4,400 (ΔT=3 )℃ & H=25.0 mm for Rej= (a)101, (b) 135, (c) 203, (d) 270, (e) 338, and (f)406.
40
(a) (b)
(c) (d)
(e) (f)
Fig.4.8 Top view flow photos taken at midheight of the test section with Ra=5,870 (ΔT=4 )℃ &
H=25.0mm for Rej= (a)101, (b) 135, (c) 203, (d) 270, (e) 338, and (f)406.
(a) (b)
(c) (d)
(e) (f)
Fig.4.9 Top view flow photos taken at midheight of the test section with Ra=7,340 (ΔT=5 )℃ & H=25.0 mm for Rej= (a)101, (b) 135, (c) 203, (d) 270, (e) 338, and (f)406.
.
Fig.4.10 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =1.5 (Rej=101 ) slpm for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
42
Fig.4.11 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =2 slpm (Rej=135 ) for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
43
Fig.4.12 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =3 slpm (Rej=203 ) for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
44
Fig.4.13 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =4 slpm (Rej=270 ) for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
45
Fig.4.14 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =5 slpm (Rej=338 ) for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
46
Fig.4.15 Side view flow photos taken at the cross plane θ=0∘& 180∘at statistical state for various ΔT at Qj =6 slpm (Rej=406 ) for H=25.0mm
θ=0° Heating plate θ=180°
Jet
Ra=0 (ΔT = 0 ˚ C)
Ra=2940 (ΔT = 2 ˚ C)
Ra=4400 (ΔT = 3 ˚ C)
Ra=5870 (ΔT = 4 ˚ C)
Ra=7340 (ΔT = 5 ˚ C)
47
Fig.4.16 Vortex flow evolution for H=25.0mm at Rej=101 (Qj=1.5 slpm)and Ra=2,940 (△T=2°C) illustrated by side view flow photos taken at the cross plane θ=0∘& 180∘.
t<0 s Jet
θ=0° Heating plate θ=180°
t = 2 s
t = 4 s
t = 6 s
t = 8 s
t = 10 s
48
Fig.4.16 Continued
Jet
θ=0° Heating plate θ=180°
t = 12 s
t = 16 s
t = 18 s
t = 20 s t = 14 s
t = 22s
49
Fig.4.16 Continued
Jet
θ=0° Heating plate θ=180°
t = 24 s
t = 26 s
t = 28 s
t = 30 s
t = 32 s
t = 34 s
50
Fig.4.16 Continued
Jet
θ=0° Heating plate θ=180°
t = 36 s
t = 38 s
t = 40 s
t = 42 s
t = 44 s
51
Fig.4.17 Vortex flow evolution for H=25.0mm at Rej=101 (Qj=1.5 slpm)and Ra=4,400 (△T=3°C) illustrated by side view flow photos taken at the cross plane θ=0∘& 180∘.
t<0 s Jet
θ=0° Heating plate θ=180°
t = 4 s
t = 8 s
t = 12 s
t = 20 s t = 16 s
52
Fig.4.17 Continued
t = 24 s Jet
θ=0° Heating plate θ=180°
t = 28 s
t = 32 s
t = 36 s
t = 40 s
53
Fig.4.17 Continued
Jet
θ=0° Heating plate θ=180°
t = 44 s
t = 48 s
t = 52 s
t =56 s
t = 60 s
54
Fig.4.17 Continued
Jet
θ=0° Heating plate θ=180°
t = 64 s
t = 68 s
t = 72 s
t = 76 s
t = 80 s
55
Fig.4.17 Continued
Jet
θ=0° Heating plate θ=180°
t = 84 s
t = 88 s
t = 92 s
t = 96 s
t = 100 s
56
Fig.4.17 Continued
Jet
θ=0° Heating plate θ=180°
t = 102 s
t = 104 s
t = 106 s
t = 108 s
57
Fig.4.18 Vortex flow evolution for H=25.0mm at Rej=101 (Qj=1.5 slpm)and Ra=5,870 (△T=4°C) illustrated by side view flow photos taken at the cross plane θ=0∘& 180∘.
t<0 s Jet
θ=0° Heating plate θ=180°
t = 2 s
t = 4 s
t = 6 s
t = 8 s
58
Fig.4.18 Continued
t = 10 s Jet
θ=0° Heating plate θ=180°
t = 12 s
t = 14 s
t = 16 s
t = 18 s
59
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 20 s
t = 22 s
t = 24 s
t = 26 s
t = 28 s
60
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 30 s
t = 32 s
t = 34 s
t = 36 s
t = 38 s
61
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 40 s
t = 42 s
t = 44 s
t = 46 s
t = 48 s
62
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 50 s
t = 52 s
t = 54 s
t = 56 s
t = 58 s
63
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 60 s
t = 62 s
t = 64 s
t = 66 s
t = 68 s
64
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 70 s
t = 72 s
t = 74 s
t = 76 s
t = 78 s
65
Fig.4.18 Continued
Jet
θ=0° Heating plate θ=180°
t = 80 s
t = 82 s
t = 84 s
66
Fig.4.19Vortex flow evolution for H=25.0mm at Rej=101 (Qj=1.5 slpm)and Ra=7,340 (△T=5°C) illustrated by side view flow photos taken at the cross plane θ=0∘& 180∘.
t<0 s Jet
θ=0° Heating plate θ=180°
t = 2 s
t = 4 s
t = 6 s
t = 8 s
67
Fig.4.19 Continued
t = 10 s Jet
θ=0° Heating plate θ=180°
t = 12 s
t = 14 s
t = 16 s
t = 18 s
68
Fig.4.19 Continued
Jet
θ=0° Heating plate θ=180°
t = 20 s
t = 22 s
t = 24 s
t = 25 s
t = 26 s
69
(a)
Fig..4.20 The time records of non-dimensional air temperature for Ra=2,940 (ΔT=2 )℃ ＆ H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.95 for
(a)
Fig.4.21 The time records of non-dimensional air temperature for Ra=4,400 (ΔT=3 )℃ ＆ H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.95 for Rej=
(a)
Fig.4.22 The time records of non-dimensional air temperature for Ra=5,870 (ΔT=4 )℃ ＆ H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.95 for Rej=
(a)
Fig.4.23 The time records of non-dimensional air temperature for Ra=7,340 (ΔT=5 )℃ & H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.95 for
(a)
Fig..4.24 The time records of non-dimensional air temperature for Ra=2,940 (ΔT=2 )℃ & H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.75 for
(a)
Fig.4.25 The time records of non-dimensional air temperature for Ra=4,400 (ΔT=3 )℃ & H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.75 for Rej=
(a)
Fig.4.26 The time records of non-dimensional air temperature for Ra=5,870 (ΔT=4 )℃ & H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.75 for Rej=
(a)
Fig.4.27 The time records of non-dimensional air temperature for Ra=7,340 (ΔT=5 )℃ & H=25.0 mm measured at selected locations on the vertical plane θ = 0˚ at Z = 0.5 and R = r/Rc = 0.75 for
Eq.(4.10)
Ra
Re
j100 200 300 400 500
0 4000 8000 12000