Mechanisms of lobed jet mixing: About circularly alternating-lobe mixers

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.1 (1-19)

Aerospace Science and Technology ••• (••••) ••••••

1

Contents lists available at ScienceDirect

67 68

2 3

Aerospace Science and Technology

4

69 70 71

5

72

6

www.elsevier.com/locate/aescte

7

73

8

74

9

75

10

76

11 12 13

Mechanisms of lobed jet mixing: About circularly alternating-lobe mixers

16 17

81

School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China

83

82 84 85

19

a r t i c l e

i n f o

a b s t r a c t

86 87

21 22 23 24 25

Article history: Received 13 March 2019 Received in revised form 26 November 2019 Accepted 19 December 2019 Available online xxxx

26 27 28 29 30 31

79

Zhi-qiang Sheng ∗ , Jing-yuan Liu, Yu Yao, Yi-hua Xu

18 20

78 80

14 15

77

Keywords: Lobed jet mixing Transverse flow Streamwise vortices Heat and mass transfer Normal vortex ring

32 33 34 35 36 37 38 39 40 41 42

Two configurations of circularly arranged alternating-lobe nozzles were adopted to form lobed mixers with/without a mixing duct. The jet mixing of each mixer was numerically simulated with the unchanged initial conditions of the primary and secondary streams, except the altered initial velocity of the secondary stream. The jet-mixing mechanisms of the circularly alternating-lobe mixers were synthetically analysed by combining the evolution of the flow field structures and the process of heat and mass transfer in the mixing field. It is found that the transverse flow is usually caused by the lobed geometry, and the entrainment of the primary stream also plays a role in certain circumstances. There are two mechanisms for the deflection of the transverse flow at the lobe peaks and troughs. One of these mechanisms is to be suppressed to deflect the flow while the other is deflected by the reaction force and induction effect. The primary and secondary streams deflect to bring the transverse interval between them, and subsequently, the streamwise vortex core appears at the transverse interval. The deflected flow consistently “digging” in the radial and circumferential radiation increases the dimension of the streamwise vortices. The transverse flow velocity decreases and the direction becomes unstable leading to the breakdown of the streamwise vortices. The transverse flow brings the heat and mass transfer. Under the two mechanisms, the frontiers of the primary and secondary streams deflect. Initially, the primary and secondary streams flow around the streamwise vortex core. Subsequently, the mixed stream flows around the vortex core, and the mixing stream area gradually expands outward. The heat and mass transfer decrease in scale when the streamwise vortices break down. Because of the velocity gradient at the interface, shear instability occurs to generate the normal vortex ring. The heat and mass transfer pushes the interface, which leads to the stretch of the normal vortex ring. The mixing speed varies due to the heat and mass transfer. The velocity gradient decreases fast in the rapid mixing segment, where the normal vortex ring breaks first. © 2019 Elsevier Masson SAS. All rights reserved.

88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108

43

109

44

110

45

111 112

46 47

1. Introduction

48 49 50 51 52 53 54 55 56 57 58 59

Compared with the conventional jet outlet, the lobed jet outlet can greatly promote jet mixing. The lobed mixer is a device that uses the lobed jet outlet to promote jet mixing. In a turbofan engine, the lobed mixer was introduced to enhance the mixing of the core flow and fan flow for thrust augment and noise reduction [1–3], as well as infrared suppression [3–5]. In a turbofan engine with an afterburner, such as in AL-31F, the lobed mixer was mounted to mix the core flow and fan flow to make the afterburner combustion more uniform and to obtain a greater afterburning thrust. In the infrared suppressor of a helicopter, the lobed mixer was installed to pump ambient air for mixing with

60 61 62 63 64 65 66

*

Corresponding author. E-mail address: [email protected] (Z.-q. Sheng).

https://doi.org/10.1016/j.ast.2019.105660 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

engine exhaust gas, and as a result, suppress the infrared radiation [6–9]. The lobed mixer can be designed as a fuel nozzle to mix fuel and air to improve combustion efficiency and to reduce pollutant emissions [10–13]; therefore, in a scramjet combustor, it was devised for enhancing the mixing of fuel and supersonic air to improve combustion efficiency [14–19]. In a wind turbine, the lobed mixer can be employed to mix low- and high-speed air for more efficient utilization of low-grade wind energy [20]. In a heat pipe, the lobed mixer can be produced as an annular longitudinal vortex generator to enhance heat transfer [21]. In ventilation, the lobed mixer can be adopted to make the flow uniform and comfortable [22–24], and also to increase the air quantity; for example, a Riwa hairdryer, which comprises a circularly lobed nozzle. Scholars have conducted many researches on the jet-mixing mechanisms of lobed mixers. Anderson [25] and Povinelli [26] concluded that the main mechanism of lobed jet mixing is the inviscid streamwise vortices formatted downstream because of the trans-

113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.2 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

verse flow caused by the lobes. Paterson [27] pointed out that it is the large-scale transverse flow that dominates the mixing, which produces heat and momentum convection, and distorts the mixed interface to cause continuous radial and circumferential mixing. It was found that the greater the radial axial velocity ratio, the faster the mixing speed. Presz Jr. et al. [28] found that lobes with parallel sidewalls are more conducive to the generation of streamwise vortices. Werle et al. [29] observed the processes of forming, developing, and collapsing of the streamwise vortices. They pointed out that the formation of streamwise vortices is inviscid and found strong small-scale mixing in turbulent streamwise vortices. Skebe et al. [30] also concluded that mixing is mainly an inviscid process. The influence of the boundary layer is confined near the lobe’s surface, and the streamwise vortices are basically inviscid at the beginning; however, Eckerl et al. [31] pointed out that the transverse flow forms the streamwise vortices that only bring convection transport. The streamwise vortices break up to form turbulent mixing to make the flow field uniform. Therefore, the viscous effect is important. Ukeiley et al. [32] also found that the flow field became uniform after the break-up of the streamwise vortices. Elliott et al. [33] pointed out that the formation of the streamwise vortices and the increase of the initial interface area are the crucial factors promoting mixing, and the contribution of streamwise vortices increases with the increase of the primary streamto-secondary stream velocity ratio. The interaction between the streamwise vortices and the normal vortex ring will increase the thickness of the mixing layer. McCormick et al. [34] observed the periodic normal vortex structure. The streamwise vortices make the normal vortex structure deformation produce turbulent mixing. They and Yu et al. [35] found that before the complete dissipation of the streamwise vortices, the shear layer grew rapidly, and subsequently, the growth rate was lower than that of the shear layer, which only rolled up by the normal vortices. Glauser et al. [36] found that the shear layer is distorted by transverse flow at lobe peaks and troughs until fragmentation, which promotes the turbulent mixing. Tsui et al. [37] pointed out that mixing is mainly caused by the streamwise vortices, and the mixing intensity is related to the vorticity. The convection of the streamwise vortices makes the interface twisted and stretched. The streamwise and normal vortices increase the thickness of the interface and create turbulent diffusion. Waitz et al. [38] pointed out that the streamwise vortices increase the interface area and the local flow gradient. The convection scale of the streamwise vortices is far greater than that of the normal vortices, and the effect of streamwise vortices on mixing is comparative to the length of the tail edge. Yu et al. [39] pointed out that the stronger the streamwise vortex, the faster the mixing, and the streamwise vorticity is related to the lobe configuration. They suggested that the mixing of turbulent zones is not caused by the rupture of streamwise vortices, but rather by the action of positive turbulent energy sources. Belovich et al. [40] also reached the conclusion that the stronger the streamwise vortex, the faster the mixing. They pointed out that the interaction between the streamwise vortices and the normal vortex ring is important to promote mixing. In contrast to the interface area, as the velocity or the mixing distance increases, the contribution of the streamwise vortices increases. Yu et al. [41,42] also pointed out that the streamwise vortices are critical to the distortion and stretching of the normal vortex ring. They found that the streamwise vortices break into small-scale vortices, resulting in fine mixing. They suggested that the streamwise vortices play an important role in the formation of turbulent regions. Salman et al. [43] recommended that the strong interaction and distortion between adjacent streamwise vortices cause the rapid increase of downstream turbulent kinetic energy; however, Mao et al. [44] opined that the generation of turbulent kinetic energy is mainly attributed to the normal vortex ring.

O’Sullivan et al. [45] found that when the lobe penetration angle increased to more than 30◦ , because the low momentum flow filled the troughs, it was not beneficial to strengthen the streamwise vortices, and the flow began to separate at the troughs at 35◦ . When the penetration angle was less than 30◦ , the total pressure loss increment was mainly caused by the decrease of kinetic energy due to the formation of streamwise vortices. As the penetration angle continued to increase, the total pressure loss increment was mainly caused by the low velocity flow or the separation flow at the troughs. Abolfadl et al. [46] found that mixing increased with the penetration angle, reaching maximum at the penetration angle of 20◦ , and increased with the increase of the lobe height, reaching maximum when the lobe height was equal to the lobe width. Tew et al. [47] found that the efficiency of streamwise vortices decreases with the increase of the lobe height-to-width ratio, and a larger lobe height-to-width ratio enhances the streamwise vortices and leads to a greater total pressure loss. Mao et al. [48] found that the interaction of the adjacent streamwise vortices increased the total streamwise vorticity. The lobes with parallel sidewalls generated stronger streamwise vortices and therefore, have a better mixing performance. Koutmos et al. [49] found that the lobe valley of different penetration depths of the alternating-lobe nozzle produced streamwise vortices with different vorticity, sizes, and radial positions. Yu et al. [50] pointed out that scalloping can enhance the streamwise vortices and make them decay more rapidly. The transverse interaction between the adjacent streamwise vortices plays an important role in the collapse of the streamwise vortices. With the decrease of streamwise vortices, the mixing dominated by the streamwise vortices gradually becomes turbulent mixing. Jiang et al. [51] pointed out that the streamwise vortex breakdown of the axisymmetric lobed mixer occurs much earlier than that of the divider plate lobed mixer. Underwood et al. [52] found that the harmful effect from the heat release of the streamwise vortex mixing is less than that of shear layer mixing. Tew et al. [53] found that for the compressible condition, compared with the incompressible condition, the streamwise vortices have a longer time to extend the interface because the shear layer growth rate decreased. Lei et al. [54,55] and Wright et al. [56] studied the effect of an inlet whirl. It was found that the prerotation of the inside culvert flow strengthened the streamwise vortices and normal vortices, and accelerated their development, interaction, and dissipation, which obviously improve the mixing performance of the lobed mixer. Hu et al. [57–59] indicated that the interaction between the streamwise vortices and the normal vortex ring produces smallscale turbulence structures to accelerate the mixing. They found that, compared with a circular jet, the lobed jet has a shorter laminar flow area, a faster shear layer growth, a faster core flow attenuation, a smaller size of normal vortices, and an earlier appearance of small-scale turbulence structures. Hu et al. [60–63] also pointed out that the streamwise vortices flow downstream and break into smaller and weaker vortices, which not only enhance the large-scale mixing, but also accelerate the small-scale mixing. The normal vortex ring is twisted and fractured by the action of the streamwise vortices. The strong mixing caused by lobes is completed within a two times equivalent diameter, and the more downstream mixing mechanism is the same as a circular jet. Nastase et al. [64] pointed out that the shear of the streamwise vortices on the normal vortex ring makes the normal vortex ring discontinuous, and the development of streamwise vortices and their entrainment are not affected by the normal vortex ring. Brinkerhoff et al. [65] pointed out that the degree of interaction between streamwise vortices and normal vortices has a great influence on mixing. Small-scale turbulent structures rapidly dissipate the normal vortices and transform the downstream into turbulent mixing.

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.3 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

3

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12 13

Fig. 1. Geometry of a CALN with a duct.

78 79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102 103

37 38

Fig. 2. Schematic of a SwALN.

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

104 105

39

Wang et al. [66] and Feng et al. [67] asserted that the initial instability of fluid flowing through the lobe causes large-scale streamwise vortices. Wang et al. [66] pointed out that the evolution of large-scale streamwise vortices is accompanied by the development of normal vortices. The initial K–H instability has an important influence on the convection field. They believed that the secondary instability at the interface is the main cause of large-scale streamwise vortex breakdown. Feng et al. [67] pointed out that the large-scale coherent structure formed by the normal vortices continues to exist in the downstream and leads to the entrainment of the mixed layer, while the large-scale streamwise vortices bring convection transport. The large-scale streamwise vortices interact with the normal vortices and break into small-scale vortices, which significantly increase the interface area and ultimately promote mixing at the molecular level. Zhang et al. [68] pointed out that the streamwise vortices have complex three-dimensional characteristics and can promote mixing on a molecular scale. They found that there is an interface between the turbulent area and non-turbulent area, and there is severe turbulence entrainment at this interface. Feng et al. [67] and Zhang et al. [68] suggested that the T-shape vortex is the topological structure of the turbulent transition zone. The lobed jet-mixing mechanisms were investigated almost entirely from the fluid dynamics perspective; however, in previous investigations about the lobed jet mixing, it was concluded [69] that the large-scale mixing rate is related to the intensity of the heat and mass transfer (convective heat and mass transfer) at-

tainable in the streamwise vortices. In addition, the stretch and cut of the normal vortex ring are virtually determined by the heat and mass transfer and mixing process. It was propounded [70] that the side of the streamwise vortices, in which the primary and secondary streams come into contact, can be divided into three segments: windward, sideward, and leeward. Based on this, the heat and mass transfer processes were explored preliminarily. It was concluded [71] that the mixing is dominated by large-scale heat and mass transfer. It was suggested [71,72] that a high-performance lobed nozzle can be produced by optimizing the large-scale heat and mass transfer in the mixing process. It was also suggested [73] that a more reasonable mechanism for lobed jet mixing will be revealed when combined fluid dynamics and the heat and mass transfer are investigated. Differences in the fluid dynamics and heat and mass transfer with different constructional lobed mixers meant different mechanisms. Therefore, in the present study, two configurations of circularly arranged alternating-lobe nozzles were adopted to form lobed mixers with/without a mixing duct. By combining the evolution of flow field structures and the process of heat and mass transfer in the mixing field, the jet-mixing mechanisms of the circularly alternating-lobe mixers were synthetically analysed.

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128

2. Geometrical configurations

129 130

Fig. 1 shows the lobed mixer with a mixing duct. The lobed mixer without a mixing duct represents the mixer with only the

131 132

JID:AESCTE

4

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.4 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94 95

29 30

Fig. 3. Numerical simulation model.

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49

115

50

116

51

117

52

118

53

119

54

120

55

121

56

122

57

123

58

124

59

125

60

126

61

127

62

128

63

129 130

64 65 66

Fig. 4. Temperature and non-dimensional normal vorticity distributions for a splitter plate with a lobed trailing edge at the velocity ratios of 3:1 and 3:2 between the hot and cool streams. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.)

131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.5 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

5

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32 33

Fig. 5. 700-K temperature isosurfaces for the CALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

lobed nozzle. The lobed nozzle is a coplanar alternating-lobe nozzle (CALN). The nozzle has an annular inlet with an inner diameter of 210 mm and an outer diameter of 400 mm. The annular section passes through a rectifying cone with a length of 262.5 mm to change into a circular section. The outlet of the CALN is located 600 mm downstream from the inlet, and the outward lobe penetration angle is 12.1◦ . A diameter of the lobe peaks circle of 550 mm, a diameter of the shallow troughs circle of 293.7 mm, and a diameter of the deep troughs circle of 150 mm make an equivalent diameter of the outlet d = 400 mm. The mixing duct has an inlet of 100 mm before the nozzle outlet, and the outlet at 1050 mm downstream of the nozzle outlet, with a diameter D = 700 mm. Starting from the lobe peak of the normal lobe nozzle (NLN) in Fig. 2(a), a partial lobe trough and side wall was removed by the oblique cut of 40◦ , as shown in Fig. 2(b). Subsequently, the sword spoiler (sword deep trough) extended to oblique thrust towards the axis at the wide lobe trough. Finally, the sword alternatinglobe nozzle (SwALN), in Fig. 2(c), was obtained. For the SwALN, the outward lobe penetration angle, the diameter of the lobed peaks circle, the diameter of the shallow troughs circle, and the diameter of the deep troughs circle were consistent with those of the CALN, and the equivalent diameter of the outlet was similar to that of the CALN.

59 60

3. Numerical simulation method

61 62 63 64 65 66

99 100

34 35

98

Fig. 3(a) shows the numerical simulation domain. Fig. 3(b) shows the mesh model of the SwALN. The simulation domain was divided by unstructured meshes, as the geometries of the lobe mixers in this study were so complex that it is difficult to divide by structured meshes. Three layers of boundary layer meshes

were extrapolated from the wall, with a first-layer thickness of 0.05 mm. As indicated by the arrow in Fig. 3(a), the mesh refinement domain was set up in the region where the velocity and temperature change sharply, and the maximum value of the mesh edge length was 15 mm. The number of elements in the refinement domain was more than 20 million, and the number of elements outside the refinement domain was approximately 2.2 million. The FLUENT software was used, and the shear stress transport (SST) k–ω model, which was employed in many investigations about complex flows with large-scale vortices [74–78], was adopted in the numerical simulation. The pressure and velocity were coupled by the SIMPLE algorithm, and the discrete scheme was set to second order. A jet with a velocity of 125 m/s, temperature of 850 K, and turbulence intensity of 5% was set to the lobed nozzle inlet. The Reynolds order determined by the jet conditions and nozzle diameters was 2 × 106 . The far-field boundary conditions were the velocity inlet and pressure outlet, with a reference pressure of 101,325 Pa, temperature of 300 K, turbulence intensity of 5%, and far-field velocities of 0, 25, 50, and 75 m/s. The simulation results show that the maximum value of Y + is less than 2.5 at the far-field velocities of 0 and 25 m/s, less than 4 at a farfield velocity of 50 m/s, and less than 6.5 at a far-field velocity of 75 m/s. The maximum value of Y + is present in the leading edge of the mixing duct; the value of Y + in most other zones is close to 1.0. For a 1/6 model of the SwALN with a duct, the maximum size of the elements in the refinement domain was 14 mm. A threelayer boundary layer mesh with a first-layer thickness of 0.05 mm and a total thickness of 0.35 mm, a six-layer boundary layer mesh with a first-layer thickness of 0.025 mm and a total thickness of

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

6

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.6 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97 98

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Fig. 6. 700-K temperature isosurfaces for the SwALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

0.52 mm, and a twelve-layer boundary layer mesh with a firstlayer thickness of 0.02 mm and a total thickness of 2.04 mm were adopted. The numerical simulation shows that the results are almost the same, which illustrates that for the lobed jet mixing, the simulated accuracy of the shear layer between the primary and secondary streams depends mainly on the fineness of the downstream region meshes rather than on the number of layers of boundary layer meshes. Corresponding to the grid independence, the maximum value of the mesh edge length in the mesh refinement domain was determined [71–73]. For a six-lobe nozzle in [63], the simulation domain was divided by unstructured meshes. A mesh refinement domain was used. Three layers of boundary layer meshes were extrapolated from the wall. The SST k–ω model was adopted. The numerical simulation results when compared with Hu’s experimental results [63] showed that, the numerical simulation method adopted in this study can accurately simulate the jet mixing process of the six-lobe nozzle [71–73]. Additionally, the jet mixing of a splitter plate with a lobed trailing edge was simulated by adopting the SST k–ω model. The lobe height and width were 90 mm each, and the upper and lower lobe penetration angles were all 17.5◦ . The simulation domain was divided by unstructured meshes and a mesh refinement domain with a maximum mesh edge-length of 15 mm was used. Three layers of boundary layer meshes were extrapolated from the wall, with a first-layer thickness of 0.05 mm. A velocity of 60 m/s, temperature of 600 K, and turbulent intensity of 5% were assigned to the lower hot stream; and, velocities of 20 m/s and 40 m/s, temperature of 300 K, and turbulent intensity of 5% were assigned to the upper cool stream. Thus, velocity ratios of 3:1 and 3:2 were formed between the hot and cool streams. Fig. 4 depicts the simulated temperature and non-dimensional nor-

mal vorticity distributions. It can be seen that the simulated jet mixing process corresponds well with the physical reality. 4. Results and discussion

99 100 101 102 103 104 105 106

Figs. 5 and 6 show the 700-K temperature isosurfaces for the CALN and SwALN with/without a duct at different far-field velocities, respectively. To facilitate the analysis of the jet-mixing field of the alternating-lobe mixers, the primary stream in the mixing field is divided into the primary stream of the lobe peak channel, the primary stream between the deep and shallow troughs, and the primary stream in the core region. Correspondingly, the secondary stream is divided into the secondary stream of the deep-trough channel, the secondary stream of the shallow-trough channel, and the secondary stream outside the cycle of the lobe peaks. As compared in Figs. 5(a) and (d), and in Figs. 6(a) and (d), respectively, at a far-field velocity of 0 m/s, there is huge difference in the mixing process for a mixer with and without a duct. As compared in Figs. 5(b) and (e), and in Figs. 6(b) and (e), respectively, at a farfield velocity of 25 m/s, the mixing process is almost the same for a mixer with and without a duct, and it is also the same at the farfield velocities of 50 and 75 m/s. Therefore, it can be speculated that there are differences in the mixing mechanisms for a mixer with and without a duct at a far-field velocity of 0 m/s. When the far-field velocity increases to a certain value, such as 25 m/s, the mixing mechanism for a mixer with and without a duct is the same. Figs. 7, 8, and 10–13 show the distribution of the velocity vector, transverse velocity (un ), and axial velocity (u x = u) at 0.25d, 0.50d, and 1.0d (the x-direction distance of the cross-section from the nozzle outlet) for the CALN and SwALN without a duct at a

107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.7 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

7

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49

115

50 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

116

Fig. 7. Distribution of velocity vector for the CALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

51

far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s, respectively. Fig. 9 shows the local enlarged drawing of velocity vector distribution at 0.25d for the CALN at a far-field velocity of 0 m/s. The un is defined as follows:

un =



v2 + w2

(1)

where u, v, and w are the velocities in the x-, y-, and z-directions of the mixing stream, respectively. Figs. 7–13 show the distribution of the primary and secondary streams and reflect the mixing process with temperature distribution. In Figs. 7–9, the scaling factor of the velocity vector is consistent. The distribution of the transverse velocity in Figs. 10 and 11 and the distribution of the axial velocity in Figs. 12 and 13 are given with contour lines. Figs. 14–17

117

show the distributions of the non-dimensional streamwise vorticity and normal vorticity at 0.25d, 0.50d, 0.75d, and 1.0d for the CALN and SwALN with/without a duct at different far-field velocities, respectively. The non-dimensional streamwise vorticity ωx and normal vorticity ωn are defined as:

 ∂w ∂v ωx = − up ∂ y ∂z   2  2 ∂u D ∂u ∂ w ∂v ωn = − + − up ∂z ∂x ∂x ∂ y D



118 119 120 121 122 123 124

(2)

125 126 127

(3)

where D is the diameter of the duct, and u p is the initial velocity of the primary stream.

128 129 130 131 132

JID:AESCTE

8

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.8 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49

115

50 51

Fig. 8. Distribution of velocity vector for the SwALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

54 55

4.1. About the formation and evolution mechanism of the transverse flow

56 57 58 59 60 61 62 63 64 65 66

117 118

52 53

116

At a far-field velocity of 0 m/s, the high-speed primary stream will entrain the ambient secondary stream flow to downstream. In Figs. 7(a) and 8(a), for the lobed mixer without a duct, the secondary stream outside the circle of the lobe peaks flows radially inwards (see also Fig. 9(a)); while, for the lobed mixer with a duct, there is a small region outside the primary stream of the lobe peak channel where the secondary stream flows radially outwards (see also Fig. 9(b)). Figs. 12 and 13 also show that, for the lobed mixer without a duct, the 10-m/s axial velocity contour of the secondary stream moves radially outwards, while for the lobed mixer with

a duct, the 20-m/s axial velocity contour of the secondary stream has a radially inward shift. It is thus obvious that under the action of the primary-stream entrainment, due to the absence of the barrier of the duct for the lobed mixer without a duct, the secondary stream flows to the primary stream from upstream and around. It is then accelerated to flow downstream along with the primary stream. For the lobed mixer with a duct, the secondary stream can however only flow to the primary stream from the inlet between the duct and nozzle, and the velocity flow to downstream along with the primary stream is determined by the entrainment. Therefore, at a far-field velocity of 0 m/s, the transverse flow of the lobed mixer without a duct is caused by the joint action of the geometric structure of the lobed nozzle and the entrainment

119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.9 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

9

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97 98

32 33

Fig. 9. Local enlarged drawing of velocity vector distribution at 0.25d for the CALN at a far-field velocity of 0 m/s.

101

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

99 100

34

of the primary stream; while, the transverse flow of the lobed mixer with a duct is caused only by the geometric structure of the lobed nozzle. When the far-field velocity increases to that the secondary stream can supply the entrainment of the primary stream (for example, at a far-field velocity of 25 m/s), there is no difference in the transverse flow for a mixer both with and without a duct; because, the transverse flow is only caused by the geometric structure of the lobed nozzle. In Figs. 7 and 8, the primary streams of the lobe peak channel and between the deep and shallow troughs flow radially outwards; and, the secondary streams of the deep-trough and shallow-trough channels flow radially inwards. The transverse flow interaction near the secondary-stream frontier of the shallow-trough channel (see also Fig. 9(c)) is the same as the transverse flow interaction near the primary-stream frontier of the lobe peak channel for the lobed mixer without a duct at a far-field velocity of 0 m/s (see also Fig. 9(a)). The secondary-stream frontier of the shallow-trough channel is suppressed by the primary stream between the deep and shallow troughs (see also Fig. 9(c)). It is then deflected to both sides, penetrating the primary stream of the lobe peak channel from the side; thereafter, flowing radially outwards along with the primary stream, just like digging the primary stream on both sides. For the CALN, the difference of the transverse velocities between the transversal flow of the secondary stream of the shallow-trough channel and the transversal flow of the primary stream between the deep and shallow troughs is not significant (as in Fig. 10); hence, the movement of the suppression boundary is not obvious (as in Fig. 7). For the SwALN, the transverse velocity of the secondary stream of the shallow-trough channel is obviously less than that of the primary stream between the deep and shallow troughs (as in Fig. 11); thus, the suppression boundary moves to

the shallow-trough channel, decreasing as the far-field velocity increases (as in Fig. 8). Similarly, for the lobed mixer without a duct at a far-field velocity of 0 m/s, the primary-stream frontier of the lobe peak channel is suppressed by the secondary stream outside the cycle of the lobe peaks and deflected to both sides (see also Fig. 9(a)). It then penetrates the secondary stream outside the cycle of the lobe peaks from the side and flows radially inwards along with the secondary stream, just like digging the secondary stream on both sides. The transverse velocity of the primary stream of the lobe peak channel is far greater than that of the secondary stream outside the cycle of the lobe peaks (as in Figs. 10 and 11); therefore, the suppression boundary moves towards the outside of the cycle of the lobe peaks (as in Figs. 7 and 8). In addition, in Figs. 7 and 8, the transverse flow interaction near the secondary-stream frontier of the deep-trough channel (see also Fig. 9(d)) is the same as the transverse flow interaction near the primary-stream frontier of the lobe peak channel for the lobed mixer with a duct (see also Fig. 9(b)). The secondary-stream frontier of the deep-trough channel penetrates the primary stream of the core region and drives the primary stream in front to flow radially inwards. The primary stream between the deep and shallow troughs flows radially outwards and induces the primary stream behind it to flow to the region between the deep and shallow troughs. The secondary-stream frontier of the deep-trough channel pushes forward the primary stream; meanwhile, it experiences the reaction force from the primary stream, and both sides are induced by the primary stream, which flows to the region between the deep and shallow troughs. It is therefore deflected to both sides before flowing radially outwards along with the primary stream (see also Fig. 9(d)). Similarly, for the lobed mixer with a duct, the primary-stream frontier of the lobe peak channel pene-

102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

10

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.10 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Fig. 10. Distribution of transverse velocity (m/s) for the CALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

trates the secondary stream outside the cycle of the lobe peaks and drives the secondary stream in front to flow radially outwards. The secondary streams of the deep-trough and shallow-trough channels flow radially inwards and induce the secondary stream behind them to flow to the deep-trough and shallow-trough channels. The primary-stream frontier of the lobe peak channel pushes forward the secondary stream; meanwhile, it experiences the reaction force from the secondary stream, and both sides are induced by the secondary streams, which flow to the deep-trough and shallow-trough channels. It is therefore gradually deflected to both sides before flowing radially inwards along with the secondary streams (see also Fig. 9(b)). For the lobed mixer with a duct, with the increase of the far-field velocity, the depth of the secondary-stream frontier of the deep-trough channel penetrating the primary stream of the core region increases, while, the depth of the primary-stream

frontier of the lobe peak channel penetrating the secondary stream outside the cycle of the lobe peaks decreases. These show that the reaction forces on the secondary-stream frontier of the deeptrough channel and the primary-stream frontier of the lobe peak channel increased. Because the cross-sectional area of the core region is far less than that outside the cycle of the lobe peaks, the reaction force on the secondary-stream frontier of the deep-trough channel is far greater than that on the primary-stream frontier of the lobe peak channel. Therefore, the secondary-stream frontier of the deep-trough channel is swiftly deflected to both sides; however, the primary-stream frontier of the lobe peak channel is gradually deflected to both sides, and the deflection degree increases with the increase in the far-field velocity. In Fig. 10, for the CALN, the transverse velocity of the primary stream of the lobe peak channel is obviously larger than that of

115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.11 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

11

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Fig. 11. Distribution of transverse velocity (m/s) for the SwALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

the primary stream between the deep and shallow troughs; while, the difference between the transversal velocity of the secondary stream of the deep-trough channel and that of the secondary stream of the shallow-trough channel is smaller. The peak value of the transverse velocity of the secondary stream is close to that of the transverse velocity of the primary stream between the deep and shallow troughs. The SwALN was first obliquely cut off from the trough and sidewall, and subsequently, a sword spoiler extended from each wide trough. Thus, in Fig. 8, the primary stream flows around the sword spoiler. It then flows towards both sides and the core, so that the more secondary stream flows to the deep trough and flows towards both sides and the core along with the primary stream. In Fig. 11, the transverse velocity of the primary stream between the deep and shallow troughs and that of the secondary stream at the deep trough are therefore increased. The

peak values of the transverse velocity for the primary stream of the lobe peak channel, the primary stream between the deep and shallow troughs, and the secondary stream at the deep trough are similar. Generally, the transverse velocity of the primary and secondary streams will gradually reduce in the downstream, but for the SwALN, the deflection of the primary stream between the deep and shallow troughs effectively strengthens the deflection of the secondary stream of the shallow-trough channel (see Fig. 8). The transverse velocity of the secondary stream of the shallow-trough channel therefore increases slightly first, then decreases gradually (see Fig. 11). In fact, for the SwALN, the deflection of the secondary stream of the shallow-trough channel also promotes the deflection of the primary stream between the deep and shallow troughs. The primary stream is then entrained by the secondary stream of the deep-trough channel and flows radially inwards (see Fig. 8).

115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

12

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.12 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49 50 51 52 53

115

Fig. 12. Distribution of axial velocity (m/s) for the CALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

117

4.2. About the formation and evolution mechanism of the streamwise vortices

54 55 56 57 58 59 60 61 62 63 64 65 66

116

Due to the deflection of the radially outward flow of the primary stream and the radially inward flow of the secondary stream, the adjacent primary and secondary streams are connected end to end with transverse intervals present between them. The primary and secondary streams flow around the transverse interval, following which the vortex core appears at the transverse interval; thus, streamwise vortices form. In general, for the circular alternatinglobe nozzle, as the deep-trough and shallow-trough channels gradually shrink in the radial direction, the radially inward flow flank of the secondary stream of the deep-trough and shallow-trough channels cannot flow to the core region and the region between the deep and shallow troughs; but, it flows to the adjacent pri-

mary stream and is entrained and deflected by the primary stream to flow radially outwards. It is therefore easier to form a transverse interval near the lobe peak where the vortex core formed. As shown in Figs. 7(a) and 8(a), the vortex cores of the streamwise vortices off the side walls of the deep and shallow troughs of the CALN and SwALN are all located near the lobe peak. In Fig. 7, because of the narrow streamwise vortices off the side walls of the deep trough of the CALN, as the “digging” depth for the secondary-stream frontier of the deep-trough channel on the primary stream between the deep and shallow troughs increases, it is possible to have a transverse interval enough to form a vortex core near the deep trough. If the streamwise vortices off the side walls of the deep trough are not broken, then the streamwise vortices off the deep trough will be split out. From Figs. 7, 10, and 14, it can be speculated that when the far-field velocity is 50

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.13 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

13

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114 115

49 50

Fig. 13. Distribution of axial velocity (m/s) for the SwALN without a duct at a far-field velocity of 0 m/s and with a duct at the far-field velocities of 0, 25, and 50 m/s.

52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

116 117

51

or 75 m/s, the streamwise vortices off the deep trough of the CALN can be observed at 1.0d in a great probability. In Fig. 8, the primary stream flows around the sword spoiler of the SwALN, and then flows toward both sides and the core, while the secondary stream flows to the deep trough before flowing towards both sides and the core along with the primary stream. The transverse interval therefore appears very quickly on both sides of the root of the sword spoiler to form the strong streamwise vortices off the deep trough (see Fig. 15). However, for the SwALN without a duct at a far-field velocity of 0 m/s, due to the limited radial spacing, there is no forming of the streamwise vortices off the side walls of the deep trough. As shown in Figs. 7 and 8, the deflected flow will continue “digging” in the radial and circumferential radiation, thereby increasing

the radial and circumferential dimensions of the streamwise vortices. Because of the oblique cutting, the shallow-trough position of the SwALN is more forward, and the deflection of the secondary stream of the shallow-trough channel is induced by the deflection of the primary stream between the deep and shallow troughs. The circumferential dimension of the streamwise vortices off the side walls of the shallow trough is therefore increased faster near the shallow trough. If for the CALN the streamwise vortices off the deep trough can form, the circumferential dimension will also be larger at the radial inner side. Except for these, the circumferential dimensions of the other streamwise vortices are larger at the radial outer side. As shown in Figs. 10 and 11, the transverse velocity tends to decrease in the downstream. At a far-field velocity of 0 m/s, there

118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

14

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.14 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32 33

Fig. 14. Non-dimensional streamwise vorticity distributions for the CALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

99 100

34 35

98

are regions where the transverse velocity of the secondary stream is reduced to less than 4 m/s at 1.0d. For the lobed mixer with a duct, the transverse velocity of the secondary stream at these regions increases with the increase of the far-field velocity. As shown in Figs. 14 and 15, the streamwise vorticity is gradually reduced. At a far-field velocity of 0 m/s, the streamwise vorticity of the lobed mixer without a duct is smaller than that of the lobed mixer with a duct at the same region of the same cross-section. As the far-field velocity increases, the streamwise vorticity at the same region of 1.0d increases. Generally, scholars believe that the streamwise vorticity is reduced and then broken for the interaction with the normal vortex ring. This research suggests that when the transverse velocity is reduced to a certain value, the direction of transverse flow easily becomes unstable due to disturbance. The large-scale streamwise vortices break down due to instability of the transverse flow direction and reorganize to form multiple small-scale vortices. The transverse velocity of the radially inward flow of the secondary stream is small, while the transverse velocity of the adjacent radially outward flow of the primary stream is large. The transverse flow of the secondary stream is unstable due to the disturbance of the transverse flow of the primary stream. Thus, the large-scale streamwise vortices break into small-scale vortices, and the energy of the large vortices is also transmitted to the small vortices. According to the transverse velocity distribution of the primary and secondary streams shown in Figs. 10(c) and 11(c), it is speculated that at a far field velocity of 0 m/s, there is an earlier breakdown of the streamwise vortices for the lobed mixer with a duct than without a duct. For the lobed mixer with a duct, the transverse velocity of the secondary stream increases with the increase of the far-field velocity; thus, the streamwise vortex breakdown occurs at a more downstream position.

4.3. About the formation and evolution mechanism of the heat and mass transfer

101 102 103

The transverse flows of the primary and secondary streams and their interaction dominate the forming of the streamwise vortices and their evolution; they also create the heat and mass transfer. In Figs. 7 and 8, as the above analysis shows, the secondary-stream frontier of the shallow-trough channel is suppressed by the primary stream between the deep and shallow troughs and deflected to both sides. It penetrates the primary stream of the lobe peak channel from the side, and then flows radially outwards along with the primary stream (see also Fig. 9(c)). The secondary-stream frontier of the deep-trough channel pushes forward the primary stream. Meanwhile, it gets reaction force from the primary stream, and both sides are induced by the primary stream, which flows to the region between the deep and shallow troughs. It is therefore deflected to both sides and flows radially outwards along with the primary stream (see also Fig. 9(d)). For the lobed mixer without a duct at a far-field velocity of 0 m/s, the primary-stream frontier of the lobe peak channel is suppressed by the secondary stream outside the cycle of the lobe peaks and deflected to both sides. It penetrates the secondary stream outside the cycle of the lobe peaks from the side, and then flows radially inwards along with the secondary stream (see also Fig. 9(a)). For the lobed mixer with a duct, the primary-stream frontier of the lobe peak channel pushes forward the secondary stream. Meanwhile, it experiences the reaction force from the secondary stream, and both sides are induced by the secondary streams, which flow to the deep-trough and shallow-trough channels. It is therefore gradually deflected to both sides and flows radially inwards along with the secondary stream. The deflection degree increases with the increase of the far-field velocity (see also Fig. 9(b)).

104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.15 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

15

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32 33

Fig. 15. Non-dimensional streamwise vorticity distributions for the SwALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

99 100

34 35

98

In Fig. 7, for the CALN, the radially inward flow flank of the secondary stream of the deep-trough and shallow-trough channels cannot flow to the core region and the region between the deep and shallow troughs, but it flows to the adjacent primary stream and is entrained and deflected by the primary stream to flow radially outwards. This phenomenon is particularly evident in the deep-trough channel, while in the shallow-trough channel, with the increase of the circumferential dimension of the streamwise vortices, this phenomenon transits so that the secondary stream flows around the vortex core. Because the streamwise vortex core is located between the primary and secondary streams, as shown in Figs. 7 and 8, at first, the primary and secondary streams flow around the vortex core. With the heat and mass transfer and mixing of the primary and secondary streams, the mixed stream flows around the vortex core. The mixing stream area centred on the vortex core then gradually expands outwards. By contrasting forming/non-forming streamwise vortices off the deep trough for the CALN and forming/non-forming streamwise vortices off the side walls of the deep trough for the SwALN, it is presumed that when the large-scale streamwise vortices break into small-scale vortices, the heat and mass transfer process will change correspondingly around the vortex core and decrease the scale. At a far-field velocity of 0 m/s, as shown in Figs. 7 and 8, for the lobed mixer without a mixing duct, the primary-stream of the lobe peak channel is suppressed by the secondary stream and deflected to both sides, mixing with the secondary stream in this process (see also Fig. 9(a)). A lot of the mixed stream is entrained by the secondary stream to flow to the region between the deep and shallow troughs and the core region, and then mixes with the primary stream. However, for the lobed mixer with a mixing duct, only the flank of the primary stream of the lobe peak channel is gradually

deflected to both sides, and the mixing with the secondary stream produces less mixed stream (see also Fig. 9(b)). In addition, the mixed stream does not flow to the region between the deep and shallow troughs and the core region. Therefore, compared with the lobed mixer with a mixing duct, the lobed mixer without a mixing duct has a larger mixing rate for the primary stream of the lobe peak channel to be mixed near the lobe peak, and a smaller mixing rate for the primary stream to be mixed in the region between the deep and shallow troughs and the core region (Figs. 5 and 6). As shown in Figs. 14 and 15, the streamwise vortices in the lobed mixer without a mixing duct are however relatively weaker, especially for the streamwise vortices off the side walls. Thus, it is seen that there is no definite relationship between the streamwise vorticity and the mixing rate. The mixing rate of lobed jet mixing is determined by the heat and mass transfer. 4.4. About the formation and evolution mechanism of the normal vortex ring

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

Because of the velocity gradient at the interface, shear instability occurs that generates the normal vortices that form the normal vortex ring. The shape of the normal vortex ring and the distribution of the normal vorticity, as displayed by Figs. 16 and 17, are positively related to the shape of the interface between the primary and secondary streams and the velocity gradient at the interface shown in Figs. 12 and 13. In the mixing process, the normal vortex ring will be stretched and eventually broken. The real reason for the stretch and break is the heat and mass transfer, but not the streamwise vortices. It is impossible to give a complete and reasonable explanation for the stretch and break of the normal vortex ring only by the vortex motion or vorticity distribution of the streamwise vortices. This is because the profile change of

120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE

AID:105660 /FLA

16

[m5G; v1.261; Prn:3/01/2020; 11:06] P.16 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97 98

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Fig. 16. Non-dimensional normal vorticity distributions for the CALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

the interface is determined by the heat and mass transfer process (shown in Figs. 7 and 8), and the change of the velocity gradient is related to the local mixing speed; however, the local mixing speed is also closely related to the heat and mass transfer process. In Figs. 7 and 8, the secondary-stream frontier of the deepand shallow-trough channels and the primary-stream frontier of the lobe peak channel are deflected to both sides. Therefore, the interface is pushed to the primary stream side at downstream of the deep and shallow troughs; meanwhile, it is pushed to the secondary stream side at downstream of the lobe peaks. As shown in Fig. 13, for the SwALN, the mixing speed is very fast in the regions between the deep and shallow troughs and downstream of the side walls near the shallow trough, and the velocity gradient at these two regions decreases rapidly. Thus, as shown in Fig. 17, the normal vorticity decreases rapidly in the regions between the deep and shallow troughs and downstream of the side walls near the shallow trough. The normal vortex ring breaks earlier in these two regions. It is therefore clear that the heat and mass transfer pushes the interface, and the different mixing speed reduces the velocity gradient in varying degrees, which leads to the stretch of the normal vortex ring and the decrease of the normal vorticity. Finally, the normal vortex ring breaks at the rapid mixing segment of the interface.

59 60

5. Conclusions

61 62 63 64 65 66

In this research, two configurations of circularly arranged alternating-lobe nozzles were used to construct lobed mixers with/without a mixing duct. The jet mixing of each mixer was numerically simulated with the altered initial velocity of the secondary stream and the other initial conditions of the primary and

secondary streams unchanged. By combining the evolution of flow field structures and the process of heat and mass transfer in the mixing field, the jet-mixing mechanisms of the circular alternatinglobe mixers were synthetically analysed. The main conclusions are as follows: (1) About the formation and evolution mechanism of the transverse flow For the lobed mixer without a duct, when the far-field velocity is low, the transverse flow is caused by the joint action of the geometric structure of the lobed nozzle and the entrainment of the primary stream. When the far-field velocity increases to that the secondary stream can supply the entrainment of the primary stream, and for the lobed mixer with a duct, the transverse flow is only caused by the geometric structure of the lobed nozzle. There are two mechanisms for the deflection of transverse flow at the lobe peaks and lobe troughs, one of which is to be suppressed to deflect. The secondary-stream frontier (primary-stream frontier) is suppressed by the primary stream (secondary stream) and deflected to both sides. It penetrates the primary stream (secondary stream) on both sides, and then flows radially outwards (radially inwards) along with the primary stream (secondary stream). The other mechanism is deflected by the reaction force and induction effect. The secondary-stream frontier (primary-stream frontier) pushes forward the primary stream (secondary stream). It thus experiences the reaction force from the primary stream (secondary stream). Meanwhile, both sides of it are induced by the primary stream (secondary stream). It is therefore deflected to both sides (deflected to both sides gradually) before flowing radially outwards (radially inwards) along with the primary stream (secondary streams).

99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.17 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

17

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97 98

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Fig. 17. Non-dimensional normal vorticity distributions for the SwALN without a duct at the far-field velocities of 0 and 25 m/s ((d) and (e)) and with a duct at the far-field velocities of 0, 25, 50, and 75 m/s ((a), (b), (c), and (f)).

99 100 101

(2) About the formation and evolution mechanism of the streamwise vortices Because of the deflection of the primary and secondary streams, a transverse interval is present between them. The primary and secondary streams flow around the transverse interval. Therefore, the vortex core appears at the transverse interval, which means the streamwise vortices form. The deflected flow continues “digging” in the radial and circumferential radiation, thereby increasing the radial and circumferential dimensions of the streamwise vortices. When the transverse velocity is reduced to a certain value, the direction of transverse flow easily becomes unstable due to disturbance. Then, the large-scale streamwise vortices break down and reorganize to form small-scale vortices. (3) About the formation and evolution mechanism of the heat and mass transfer The transverse flows of the primary and secondary streams and their interaction bring the heat and mass transfer. Under the two mechanisms, the frontiers of the primary and secondary streams deflect at the lobe peaks and lobe troughs. After the formation of the streamwise vortex core, the primary and secondary streams flow around the vortex core. With the heat and mass transfer and mixing, the mixed stream flows around the vortex core, and then the mixing stream area gradually expands outward. When the large-scale streamwise vortices break into small-scale vortices, the heat and mass transfer process will change correspondingly around the vortex core and decrease the scale. (4) About the formation and evolution mechanism of the normal vortex ring Because of the velocity gradient at the interface, shear instability occurs to generate the normal vortex ring. The profile change of

the interface is determined by the heat and mass transfer process. The change of the velocity gradient is related to the local mixing speed. However, the local mixing speed is also closely related to the heat and mass transfer process. Thus, the heat and mass transfer push the interface, and the different mixing speed reduces the velocity gradient by varying degrees. These lead to the stretch of the normal vortex ring and the decrease of the normal vorticity. Finally, the normal vortex ring breaks at the rapid mixing segment of the interface.

102 103 104 105 106 107 108 109 110 111

Declaration of competing interest

112 113

This manuscript has not been published or presented elsewhere in part or in entirety, and is not under consideration by another journal. All the authors have approved the manuscript and agree with submission to your esteemed journal. There are no conflicts of interest to declare.

114 115 116 117 118 119

Acknowledgements

120 121

The authors gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China under Grants 11862016, 11562012, 51666012, and 51866010.

122 123 124 125

References

126 127

[1] W.M. Presz Jr., G. Reynolds, D. McCormick, Thrust augmentation using mixerejector-diffuser systems, AIAA Paper 1994-0020. [2] W.M. Presz Jr., G. Reynolds, C. Hunter, Thrust augmentation with mixer/ejector systems, AIAA Paper 2002-0230. [3] K.E. Acheson, E.C. Marques, M.D. Moore, A partial mixer nozzle for turbofan nacelles to provide significant jet mixing control, AIAA Paper 2011-3189.

128 129 130 131 132

JID:AESCTE

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.18 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

[4] Y. Shan, J.Z. Zhang, Numerical investigation of flow mixture enhancement and infrared radiation shield by lobed forced mixer, Appl. Therm. Eng. 29 (2009) 3687–3695. [5] L.W. Du, Y.H. Liu, T. Li, Numerical predictions of scarfing on performance of Sshaped nozzle with asymmetric lobe, J. Propuls. Power 31 (2) (2015) 604–618. [6] C.X. Pan, J.Z. Zhang, Y. Shan, Effects of exhaust temperature on helicopter infrared signature, Appl. Therm. Eng. 51 (2013) 529–538. [7] C.X. Pan, J.Z. Zhang, L.F. Ren, et al., Effects of rotor downwash on exhaust plume flow and helicopter infrared signature, Appl. Therm. Eng. 65 (2014) 135–149. [8] J.Z. Zhang, C.X. Pan, Y. Shan, Progress in helicopter infrared signature suppression, Chin. J. Aeronaut. 27 (2) (2014) 189–199. [9] C.X. Pan, Y. Shan, J.Z. Zhang, Parametric effects on internal aerodynamics of lobed mixer-ejector with curved mixing duct, J. Eng. Gas Turbines Power 136 (2014) 061504. [10] L.L. Smith, A.J. Majamaki, I.T. Lam, et al., Mixing enhancement in a lobed injector, Phys. Fluids 9 (3) (1997) 667–678. [11] J.H. Strickland, T. Selerland, A.R. Karagozian, Numerical simulations of a lobed fuel injector, Phys. Fluids 10 (11) (1998) 2950–2964. [12] A.J. Majamaki, O.I. Smith, A.R. Karagozian, Passive mixing control via lobed injectors in high-speed flow, AIAA J. 41 (4) (2003) 623–632. [13] M.G. Mitchell, O.I. Smith, A.R. Karagozian, Passive fuel-air mixing and emissions control via lobed injectors, AIAA J. 42 (1) (2004) 61–69. [14] M.F. Campuzano, T.Q. Dang, Numerical study of lobed-mixer fuel-injection strut in scramjet engine, AIAA Paper 1995-2449. [15] P. Gerlinger, P. Stoll, M. Kindler, et al., Numerical investigation of mixing and combustion enhancement in supersonic combustors by strut induced streamwise vorticity, Aerosp. Sci. Technol. 12 (2008) 159–168. [16] L.Y. Hou, B. Weigand, M. Banica, Effects of staged injection on supersonic mixing and combustion, Chin. J. Aeronaut. 24 (2011) 584–589. [17] C. Fureby, K. Nordin-Bates, K. Petterson, et al., A computational study of supersonic combustion in strut injector and hypermixer flow fields, Proc. Combust. Inst. 35 (2015) 2127–2135. [18] F.J. Förster, N.C. Dröske, M.N. Bühler, et al., Analysis of flame characteristics in a scramjet combustor with staged fuel injection using common path focusing schlieren and flame visualization, Combust. Flame 168 (2016) 204–215. [19] K. Makowka, N.C. Dröske, J.V. Wolfersdorf, et al., Hybrid RANS/LES of a supersonic combustor, Aerosp. Sci. Technol. 69 (2017) 563–573. [20] W.L. Han, P.G. Yan, W.J. Han, et al., Design of wind turbines with shroud and lobed ejectors for efficient utilization of low-grade wind energy, Energy 89 (2015) 687–701. [21] Y.Y. Tsui, S.W. Leu, Heat transfer enhancement by a multilobe vortex generator in internally finned tubes, Numer. Heat Transf., Part A 35 (1999) 553–566. [22] I. Nastase, A. Meslem, I. Vlad, et al., Lobed grilles for high mixing ventilation – an experimental analysis in a full scale model room, Build. Environ. 46 (2011) 547–555. [23] P. Bragança, K. Sodjavi, A. Meslem, et al., Airflow characteristics and thermal comfort generated by a multi-cone ceiling diffuser with and without inserted lobes, Build. Environ. 108 (2016) 143–158. [24] P. Bragança, K. Sodjavi, A. Meslem, et al., Passive control strategy for mixing ventilation in heating mode usinglobed insert, Energy Build. 133 (2016) 512–528. [25] B.H. Anderson, L.A. Povinelli, Factors which influence the behavior of turbofan forced mixer nozzles, NASA TM-81668, 1981. [26] L.A. Povinelli, B.H. Anderson, Investigation of mixing in a turbofan exhaust duct, part II: computer code application and verification, AIAA J. 22 (4) (1984) 518–525. [27] R.W. Paterson, Turbofan mixer nozzle flow field – a benchmark experimental study, J. Eng. Gas Turbines Power 106 (1984) 692–698. [28] W.M. Presz Jr., B.L. Morin, R.G. Gousy, Forced mixer lobes in ejector designs, J. Propuls. Power 4 (4) (1988) 350–355. [29] M.J. Werle, W.M. Presz Jr., R.W. Paterson, Flow structure in a periodic axial vortex array, AIAA Paper 1987-0610. [30] S.A. Skebe, R.W. Paterson, T.J. Barber, Experimental investigation of threedimensional forced mixer lobe flow fields, AIAA Paper 1988-3785. [31] W.A. Eckerle, H. Sheibani, J. Awad, Experimental measurement of the vortex development downstream of a lobed forced mixer, J. Eng. Gas Turbines Power 114 (1992) 63–71. [32] L. Ukeiley, M. Glauser, D. Wick, Downstream evolution of proper orthogonal decomposition eigenfunctions in a lobed mixer, AIAA J. 31 (8) (1993) 1392–1397. [33] J.K. Elliott, T.A. Manning, Y.J. Qiu, et al., Computational and experimental studies of flow in multi-lobed forced mixers, AIAA Paper 1992-3568. [34] D.C. McCormick, J.C. Bennett Jr., Vortical and turbulent structure of a lobed mixer free shear layer, AIAA J. 32 (9) (1994) 1852–1859. [35] S.C.M. Yu, T.H. Yip, Experimental investigation of two-stream mixing flows with streamwise and normal vorticity, Int. J. Heat Fluid Flow 18 (2) (1997) 253–261. [36] M.N. Glauser, L.S. Ukeiley, D.P. Wick, Investigation of turbulent flows via pseudo flow visualization, part II: lobed mixer, Exp. Therm. Fluid Sci. 13 (1996) 167–177. [37] Y.Y. Tsui, P.W. Wu, Investigation of the mixing flow structure in multilobe mixers, AIAA J. 34 (7) (1996) 1386–1391.

[38] I.A. Waitz, Y.J. Qiu, T.A. Manning, et al., Enhanced mixing with streamwise vorticity, Prog. Aerosp. Sci. 33 (1997) 323–351. [39] S.C.M. Yu, J.H. Yeo, J.K.L. Teh, Velocity measurements downstream of a lobedforced mixer with different trailing-edge configurations, J. Propuls. Power 11 (1) (1995) 87–97. [40] V.M. Belovich, M. Samimy, M.F. Reeder, Dual stream axisymmetric mixing in the presence of axial vorticity, J. Propuls. Power 12 (1) (1996) 178–185. [41] S.C.M. Yu, X.G. Xu, Turbulent mixing of coaxial nozzle flows with a centrallobed mixer, J. Propuls. Power 13 (4) (1997) 517–524. [42] S.C.M. Yu, X.G. Xu, Confined coaxial nozzle flow with central lobed mixer at different velocity ratios, AIAA J. 36 (3) (1998) 349–358. [43] H. Salman, J.J. McGuirk, G.J. Page, A numerical study of vortex interactions in lobed mixer flow fields, AIAA Paper 1999-3409. [44] R.H. Mao, S.C.M. Yu, L.P. Chua, Kelvin-Helmholtz and streamwise vortices in the near wake of a single-lobe forced mixer, Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 220 (2006) 279–298. [45] M.N. O’Sullivan, J.K. Krasnodebski, I.A. Waitz, et al., Computational study of viscous effects on lobed mixer flow features and performance, J. Propuls. Power 12 (3) (1996) 449–456. [46] M.A. Abolfadl, M.A. Metwally, A.M. El-Messiry, et al., Experimental investigation of lobed mixer performance, J. Propuls. Power 17 (5) (2001) 1109–1116. [47] D.E. Tew, B.S. Teeple, I.A. Waitz, Mixer-ejector noise-suppressor model, J. Propuls. Power 14 (6) (1998) 941–950. [48] R. Mao, S.C.M. Yu, T. Zhou, et al., On the vorticity characteristics of lobed-forced mixer at different configurations, Exp. Fluids 46 (2009) 1049–1066. [49] P. Koutmos, J.J. McGuirk, Velocity and turbulence characteristics of isothermal lobed mixer flows, J. Fluids Eng. 117 (1995) 633–638. [50] S.C.M. Yu, T.H. Yip, C.Y. Liu, Mixing characteristics of forced mixers with scalloped lobes, J. Propuls. Power 13 (2) (1997) 305–311. [51] L.Y. Jiang, I. Yimer, S. Manipurath, Flow-field of an axisymmetric lobed mixer, J. Therm. Sci. 13 (1) (2004) 40–45. [52] D.S. Underwood, I.A. Waitz, Effect of heat release on streamwise vorticity enhanced mixing, J. Propuls. Power 12 (4) (1996) 638–645. [53] D.E. Tew, J.C. Hermanson, I.A. Waitz, Impact of compressibility on mixing downstream of lobed mixers, AIAA J. 42 (11) (2002) 2393–2396. [54] Z.J. Lei, A. Mahallati, M. Cunningham, et al., Effects of core flow swirl on the flow characteristics of a scalloped forced mixer, J. Eng. Gas Turbines Power 134 (2012) 111201. [55] Z.J. Lei, Y.F. Zhang, Z.Z. Zhu, et al., Numerical research on the mixing mechanism of lobed mixer with inlet swirl in linear radial distribution, Proc. Inst. Mech. Eng. A, J. Power Energy 229 (3) (2015) 280–297. [56] A. Wright, Z.J. Lei, A. Mahallati, et al., Effects of scalloping on the mixing mechanisms of forced mixers with highly swirling core flow, J. Eng. Gas Turbines Power 135 (2013) 071202. [57] H. Hu, S.S. Wu, G.X. Shen, Experimental investigation on the jet mixing flows of lobed nozzles using laser induced fluorescence, AIAA Paper 1996-1937. [58] H. Hu, T. Kobayashi, T. Saga, et al., Particle image velocimetry and planar laserinduced fluorescence measurements on lobed jet mixing flows, Exp. Fluids 29 (7) (2000) 141–157. [59] H. Hu, T. Saga, T. Kobayashi, et al., Research on the vortical and turbulent structures in the lobed jet flow using laser induced fluorescence and particle image velocimetry techniques, Meas. Sci. Technol. 11 (2000) 698–711. [60] H. Hu, T. Saga, T. Kobayashi, et al., A study on a lobed jet mixing flow by using stereoscopic particle image velocimetry technique, Phys. Fluids 13 (11) (2001) 3425–3441. [61] H. Li, H. Hu, T. Kobayashi, et al., Wavelet multiresolution analysis of stereoscopic particle-image-velocimetry measurements in lobed jet, AIAA J. 40 (6) (2002) 1037–1046. [62] H. Hu, T. Saga, T. Kobayashi, et al., Mixing process in a lobed jet flow, AIAA J. 40 (7) (2002) 1339–1345. [63] H. Hu, T. Saga, T. Kobayashi, et al., Dual-plane stereoscopic PIV measurements in a lobed jet mixing flow, AIAA Paper 2005-0443. [64] I. Nastase, A. Meslem, Vortex dynamics and mass entrainment in turbulent lobed jets with and without lobe deflection angles, Exp. Fluids 48 (4) (2010) 693–714. [65] J.R. Brinkerhoff, H. Oria, M.I. Yaras, et al., Experimental and computational study of mixing mechanisms in an axisymmetric lobed mixer, J. Propuls. Power 29 (5) (2013) 1017–1030. [66] Q.C. Wang, Z.G. Wang, J. Lei, et al., Characteristics of mixing enhanced by streamwise vortices in supersonic flow, Appl. Phys. Lett. 103 (2013) 144102. [67] J.H. Feng, C.B. Shen, Q.C. Wang, Three-dimensional evolution of large-scale vortices in supersonic flow, Appl. Phys. Lett. 107 (2015) 254101. [68] D.D. Zhang, J.G. Tan, J.W. Hou, Structural and mixing characteristics influenced by streamwise vortices in supersonic flow, Appl. Phys. Lett. 110 (2017) 124101. [69] Z.Q. Sheng, S.C. Chen, Z. Wu, et al., High mixing effectiveness lobed nozzles and mixing mechanisms, Sci. China, Technol. Sci. 58 (7) (2015) 1218–1233. [70] Z.Q. Sheng, P.L. Huang, T. Zhao, et al., Configurations of lobed nozzles for high mixing effectiveness, Int. J. Heat Mass Transf. 91 (2015) 671–683. [71] Z.Q. Sheng, Jet mixing of lobed nozzles with spoilers located at lobe peaks, Appl. Therm. Eng. 119 (2017) 165–175.

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:AESCTE AID:105660 /FLA

[m5G; v1.261; Prn:3/01/2020; 11:06] P.19 (1-19)

Z.-q. Sheng et al. / Aerospace Science and Technology ••• (••••) ••••••

1 2 3 4 5 6 7 8 9

[72] Z.Q. Sheng, Z. Wu, J.Z. Ji, et al., Chevron spoiler to improve the performance of lobed ejector/mixer, Int. Commun. Heat Mass Transf. 77 (2016) 174–182. [73] Z.Q. Sheng, Y. Yao, Y.H. Xu, Suggestions on investigations of lobed jet mixing, Aerosp. Sci. Technol. 86 (2019) 415–429. [74] L.A. Kavurmacioglu, C.B. Senel, H. Maral, et al., Casing grooves to improve aerodynamic performance of a HP turbine blade, Aerosp. Sci. Technol. 76 (2018) 194–203. [75] K. Ananthakrishnan, M. Govardhan, Influence of fillet shapes on secondary flow field in a transonic axial flow turbine stage, Aerosp. Sci. Technol. 82–83 (2018) 425–437.

19

[76] A. Hassantabar, A. Najjaran, M. Farzaneh-Gord, Investigating the effect of engine speed and flight altitude on the performance of throttle body injection (TBI) system of a two-stroke air-powered engine, Aerosp. Sci. Technol. 86 (2019) 375–386. [77] S. Jiang, F. Chen, J.Y. Yu, et al., Treatment and optimization of casing and blade tip for aerodynamic control of tip leakage flow in a turbine cascade, Aerosp. Sci. Technol. 86 (2019) 704–713. [78] W. Cheng, Z.X. Wang, L. Zhou, et al., Infrared signature of serpentine nozzle with engine swirl, Aerosp. Sci. Technol. 86 (2019) 794–804.

67 68 69 70 71 72 73 74 75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94

29

95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49

115

50

116

51

117

52

118

53

119

54

120

55

121

56

122

57

123

58

124

59

125

60

126

61

127

62

128

63

129

64

130

65

131

66

132