Evaluation of the relationship between the

Our reference: AESCTE 4936

P-authorquery-v14

AUTHOR QUERY FORM Journal: AESCTE

Please e-mail your responses and any corrections to:

Article Number: 4936

E-mail: [email protected]

Dear Author, Please check your proof carefully and mark all corrections at the appropriate place in the proof. It is crucial that you NOT make direct edits to the PDF using the editing tools as doing so could lead us to overlook your desired changes. Rather, please request corrections by using the tools in the Comment pane to annotate the PDF and call out the changes you would like to see. To ensure fast publication of your paper please return your corrections within 48 hours. For correction or revision of any artwork, please consult http://www.elsevier.com/artworkinstructions Any queries or remarks that have arisen during the processing of your manuscript are listed below and highlighted by flags in the proof.

Location in article Q1

Query / Remark: Click on the Q link to find the query’s location in text Please insert your reply or correction at the corresponding line in the proof

Your article is registered as a regular item and is being processed for inclusion in a regular issue of the journal. If this is NOT correct and your article belongs to a Special Issue/Collection please contact immediately prior to returning your corrections. (p. 1/ line 1)

Q2

The author names have been tagged as given names and surnames (surnames are highlighted in teal color). Please confirm if they have been identified correctly and are presented in the desired order. (p. 1/ line 17)

Q3

IMPORTANT!!! Please note that your MS Word manuscript was converted to LaTeX in the appropriate Journal layout and style. Therefore, the final proof might have some flaws. Kindly please check your proof carefully in this regard. (p. 1/ line 45)

Q4, Q5, Q6, Q7

Please check: comma in subscript: "u^\{,\}". Shouldn’t there be used "\prime " instead? (p. 2/ line 97,103,107,124)

Q8

Figure(s) will appear in black and white in print and in color on the web. The figure(s) contains references to color or the colors are mentioned in the main text. Based on this, the explanatory text about the interpretation of the colors has been added. Please check, and correct if necessary. (p. 4/ line 66)

Q9

Please provide a grant number for the sponsor NSERC (if available) and include this number into the main text where appropriate. (p. 12/ line 85)

Q10

Please provide a conflict of interest statement. If there is no conflict of interest, state that. (p. 12/ line 90)

Q11

Reference(s) given here were noted in the reference list but are missing from the text - please position each reference in the text or delete it from the list: [17]. (p. 12/ line 94)

Q12

Please check if sponsor names have been identified correctly and correct if necessary. (p. 14/ line 4)

Please check this box or indicate your approval if you have no corrections to make to the PDF file

Thank you for your assistance.

Page 1 of 1

JID:AESCTE AID:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.1 (1-13)

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

1Q1

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 14 15 16 17Q2 18 19 20

Evaluation of the relationship between the aerothermodynamic process and operational parameters in the high-pressure turbine of an aircraft engine Trung Hieu Nguyen a,∗ , Tri Phuong Nguyen b,∗ , Francois Garnier a TFT Laboratory, Ecole de Technologie Superieure (ETS), Montréal, H3C 1K3, Quebec, Canada b University of Montreal (UdeM), Montreal, H3C 3J7, Quebec, Canada

25 26 27 28 29 30 31 32

79 80 81 82 83 85 86 87

a r t i c l e

i n f o

88

a b s t r a c t

89

23 24

78

84

a

21 22

77

Article history: Received 8 August 2017 Received in revised form 25 November 2018 Accepted 2 January 2019 Available online xxxx Keywords: High-pressure turbine Aerothermodynamic process Operational parameters Aircraft engine

33 34 35 36

Gaining a full understanding of the aerothermodynamic (AT) process in the high-pressure turbine of an aircraft engine is a complex task. The data in the literature on this topic are very limited, particularly that on tridimensional simulation. We report herein, for the first time, the designs, computer simulations, tridimensional calculations of the interactions of AT parameters under various operation conditions (takeoff, cruise) of an aircraft engine by using a refined mesh system containing approximately 6 million polyhedrons and more than 1 million interactions to solve equations in a high-pressure turbine (HPT). Our research provides, for the first time, an overview of high-resolution topographic images of the distribution of AT parameters in multi-row turbomachinery. Our calculations indicate that the relationship between these parameters was convoluted and depended on each operating condition. For example, our findings show that the thermal boundary conditions and rotor speeds strongly affected the flow temperatures (14%) and flow velocity (31%). On the other hand, the cooling system appeared not to affect AT parameters. The temperature nonuniformities in the turbine in the axial and radial directions were also observed. © 2019 Elsevier Masson SAS. All rights reserved.

90 91 92 93 94 95 96 97 98 99 100 101 102

37

103

38

104

39

105 106

40 41

1. Introduction

42 43 44 45Q3 46 47 48 49 50 51 52 53 54 55 56 57 58

Gas-turbine engines have been widely used in the air-transport industry for many years. Understanding the aerothermodynamic process within such engines (combustor, turbine, and nozzle) stands out as an important issue. This knowledge helps aircraft airlines and manufacturers determine the performance of gasturbine engines, ensure flight safety, reduce maintenance costs, and extend aircraft lifetime. Additionally, studying accurately the aerothermodynamic parameters can also decrease losses, increase efficiency, and reduce fuel consumption. In this context, many researchers have attempted to investigate the aerothermodynamic process in the combustor and nozzle [1–6], studies focusing on turbine components are very scarce. This is mainly due to the lack of a comprehensive picture of the aerothermodynamic process, which is indispensable in order to approximate the various actual engine operating conditions in performing research.

59 60 61 62 63 64 65 66

*

Corresponding authors. E-mail addresses: [email protected] (T.H. Nguyen), [email protected] (P.N. Tri). https://doi.org/10.1016/j.ast.2019.01.011 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

In fact, the literature contains barely any research on AT evolution in turbines generally and high-pressure turbines (HPTs) specifically. The complexities of the AT process in the HPT are related to the 3D design of complex blade profiles, the simulation of the movement of one row (rotor) to the other (stator) (multi-rows), the influences of different operating conditions and the effect of the cooling system at the rotor blade on the flow. Other challenges relate to the computational cost of 3D calculations, requiring powerful supercomputers to calculate and simulate the complex flow in the HPT. Producing a 3D design of rotor and stator blades for highpressure turbine (HPT) remains a challenge due to the complexity of HPT blade profiles [7]. Demeulenaere [8] developed a 3D design of turbomachinery including the fundamental turbine geometry parameters such as hub and shroud radius, chord length, chord ratio, blade pitch, and flow inlet and outlet angles, which were starting to come into use for 3D designs. While the final blade was designed for an optimized pressure distribution, numerical simulation of all the flow was not carried out. With respect to turbine numerical modeling, Rose et al. [9] used the 2D URANS method to study the thermodynamics in an axial turbine. They showed the transformation of wakes and their interactions with the rotor blades. Nevertheless, the multi-rows

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:4936 /FLA

1 2 3 4 5 6 7 8 9 10

[m5G; v1.250; Prn:9/01/2019; 16:40] P.2 (1-13)

T.H. Nguyen et al. / Aerospace Science and Technology ••• (••••) •••–•••

2

Abbreviations HPT CFD LE TE TKE

High-pressure turbine Computational fluid dynamics Leading edge Trailing edge Turbulent kinetic energy

11

Symbols

12

R Radius C Length of chord S Blade pitch S /C Chord ratio T , T total Temperature, Total temperature T inlet , T outlet Temperature at the HPT inlet/outlet

13 14 15 16 17 18

67

Nomenclature

68 69

P , P static , P total Pressure, Static pressure, Total pressure P inlet , P outlet Pressure at the HPT inlet/outlet V , V inlet , V outlet Velocity, Velocity at the HPT inlet/outlet ζ Enthalpy-loss coefficient η Cooling effectiveness Temperature of the hot-gas stream Tg Rotor-blade temperature Tm Cooling-air temperature Tc δ Radial displacement of streak temperature Temperature of isovalue T iso Rotational speed Axial velocity Wz φ Flow coefficient Temperature at tip surface T tip Temperature at hub surface T hud

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

19

86

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

(stator–rotor) and their interactions, the effect of 3D geometry on the flow, and the influence of operating conditions on the flow were not discussed. Lampart et al. [10] used the RANS approach to produce a numerical simulation of 3D flow in axial turbomachinery, explaining the transformation and distribution of flow parameters in the turbine. The blade profile was also modified to increase flow efficiency. The models were, however, limited to simulating multirows (stator–rotor) with only three stator and rotor blades (quite small in comparison to the actual number of blades in a turbine engine). Moreover, the influence of the cooling system and the effect of operating conditions on flow were not considered. Yilmaz et al. [11] evaluated the relationship between exhaustgas temperature and operation parameters in CFM-56 engines at two different power settings—including cruise and takeoff—using experimental data. They varied operation parameters—such as rotational speed, boundary temperature, and fuel flow—and studied their effect on exhaust-gas temperature. Wei et al. (APEX) [12, 13] also conducted experiments to measure gas-engine emissions and exhaust-gas temperature as functions of operating conditions. None of this research broached the intra-engine aerothermodynamic process. Herein, we introduce new insights about the 3D design of HPTs (high-pressure turbines) and 3D numerical evolution of aerothermodynamic parameters for multi-row turbines (stator– rotor) as functions of operational parameters in takeoff and cruise of CFM-56 engines, which are widely used in airliners, examples being the Boeing 737 and the Airbus A320 and Airbus A340 families. The effects of boundary temperatures, rotation speeds, and cooling systems on the flow behavior and nonuniformities of the thermal field were calculated and simulated with the RANS turbulence-modeling strategy. The RANS approach used herein is an optimized option to study multi-row turbomachinery as well as both the stationary- and rotating-blade rows. In order to achieve our goals, our design process was as follows: (1) The HPT design of the gas turbine was performed with the BLADE GEN module; (2) STAR-CCM+ (CD-ADAPCO) software was used to simulate the aerothermodynamic process and estimate the influences of different operating conditions on the aerothermodynamic parameters; and (3) the results are analyzed with an in-house MATLAB routine, and compared with that reported in the literature.

2. Aerothermodynamic modeling

87 88

2.1. Governing equations

89 90

The governing equations of the RANS approach in STAR-CCM+ are described below in three dimensions (x, y , z):

91 92 93

∂ ∂ρ + (ρ U j ) = 0 ∂t ∂xj

(1)

∂ ∂p ∂ ∂ρUi + (ρ U i U j ) = − + τi j − ρ u ,i u ,j + S M ∂t ∂xj ∂ xi ∂xj

(2)

∂ ∂ ρ htot ∂ p − + (ρ U j htot ) ∂t ∂t ∂xj ∂T ∂ ∂ , , λ + U j τi j − ρ u i u j + U j S M = ∂xj ∂xj ∂xj

94 95 96 97Q4 98 99 100 101

(3)

102 103Q5 104

where, in a Cartesian coordinate system, each velocity component u i can be replaced with the sum of a mean and fluctuating compo, nent u i = U i + u i ; τ is the molecular stress tensor (including both normal and shear components of the stress); htot is total enthalpy and related to the static enthalpy h( T , p ) by

105 106 107Q6 108 109 110

htot = h +

1 2

U 2j

(4)

and S M = ( S M x , S M y , S M z ) is the source term of the rotor speed. For an N b blade rotor, the rotor-source term to be added to the discretized momentum equation is:

SM =

112 113

− →

− →

111

N b ϕ 2π

114 115 116 117

− → (− F )

(5)

where ϕ is the distance that a blade would travel while travers-

− →

ing a control volume and F is the instantaneous force acting on that control volume, which depends on the velocity field. The source term is averaged over 2π to account for the fact that the , , rotor has been modeled [14]. The term ∂∂x (U j (τi j − ρ u i u j )) reprej

sents the work due to viscous stresses, referred to as the viscous work term, and is negligible. The term U j S M represents the work due to external momentum sources (source term of rotor speed), and these two terms are currently neglected [15,16]. In this work, the k− ε model is used and introduces two new variables into the system of equations. STAR-CCM+ solves the turbulent kinetic energy and epsilon equations in the following form:

118 119 120 121 122 123 124Q7 125 126 127 128 129 130 131 132


[m5G; v1.250; Prn:9/01/2019; 16:40] P.3 (1-13)


3

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 93

27 28 29

Fig. 1. Fluid domain structure of (a) one stator and two rotor blades, (b) complete HPT structure, (c) mesh structure of periodic surfaces, and (d) appreciation of bad elements to improve mesh quality.

30 31 32

∂ ∂ ∂(ρ k) + (ρ U j k) = ∂t ∂xj ∂xj

33 34 35 36 37 38 39 40 41 42

∂ ∂ ∂(ρε ) + (ρ U j ε ) = ∂t ∂xj ∂xj

μt ∂ ε μ+ σε ∂ x j

ε

+ (C ε1 P k − C ε2 ρε + C ε1 P εb ) k

(6)

(7)

where P k is the turbulence production due to viscous forces; P kb represents the influence of the buoyancy forces; C ε1 , C ε2 , σk , and σε are constants (C ε1 = 1.45, C ε2 = 1.9, σk = 1.0, and σε = 1.3); and μt is a turbulent viscosity. 2.2. Aerothermodynamic modeling

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

and rotor-blade profile (see Fig. 1a). The number of HPT stator and rotor blades in a CFM56 engine is 43 and 83, respectively. Then, assembling the stator and rotor provided for obtaining the complete HPT structure, as shown in Fig. 1b.

97 98 99 100 101

43 44

95 96

μt ∂ k + P k − ρε + P kb μ+ σk ∂ x j

94

2.2.1. HPT design Our study focused on the CFM56 engine, which is among the most popular aircraft engines and has been simulated and tested by several researchers [12,13,18,19]. This paper also took advantage of the findings of past studies to build a high-pressure turbine (HPT) in a CFM56 engine using the BLADE GEN design module. First, the general rotor- and stator-geometry parameters were built. Then, the blade surface was constructed. The main rotor angles (horizontal angle of the blade profile: beta and vertical angle of the blade profile: theta) were implemented. Defining the blade geometry depends on blade thickness as a function of blade position. The length (C ) and the chord ratio (S /C ) (S is the blade pitch) were set to 46.069 and 2.396, respectively. The general dimension at two cylindrical surfaces (hub and shroud), leading edge (LE), and trailing edge (TE) were also implemented: R LE-Hub = 254 mm, R LE-Shroud = 360 mm, and R TE-Shroud = 360 mm (where R is a radius). Based on these dimensions, the rotor-blade profile was identified. This process was repeated for the stator, with R LE-Hub = 254 mm, R LE-Shroud = 356 mm, and R TE-Shroud = 360 mm; chord length C = 71.713; and the chord ratio S /C = 0.518. This information was used to obtain the stator-

2.2.2. Computational fluid dynamics (CFD) Unstructured meshes are especially suitable for complex geometries, such as turbine blades [7,20]. This approach has several advantages over structured meshing for the current applications, including automation and the ability to concentrate the mesh points in the region of the blades. To simplify computations or reduce blade passage numbers, circumferentially periodic boundary conditions are applied at the domain faces coincident with neglected adjacent blades [21,22] (see Fig. 1c). For multi-row turbomachinery, a mixture of sliding and mixing planes can be used to increase accuracy and reduce computational cost [23]. Herein, the outlet of the stator-blade fluid domain, associated with the rotor-blade inlet, was coupled (called the “mixing plane”). The stator/rotor interactions were accounted for though the exchange of averaged aerothermodynamic parameters. Studies [24–26] have shown that the mesh quality affected both the efficiency and accuracy of the computational-fluid-dynamic (CFD) solution. Meshes with distorted elements have rendered computation more difficult and less accurate. To achieve a highquality mesh system, we determined surface smoothing, uniform size, and transferring angles of the elements in accordance with recent publications [27,28]. Then, the distortion elements in the mesh were identified. The mesh system was modified and remeshed to improve its quality, as shown in Fig. 1d. Lastly, approximately 6 million polyhedral unstructured mesh types were used. The number was chosen based on the mesh study in three different mesh systems involved 2, 6, or 10 million meshes. The 6 million and 10 million meshes yielded similar CFD results that were slightly different from those obtained with 2 million meshes (data not shown).

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:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.4 (1-13)


4

1 2 3 4 5 6 7

Table 1 Initial aerothermodynamic conditions. Parameter

Value

Parameter

Value

Pstatic (kPa) Ptotal (kPa) Ttotal (K) Rotor speed (rpm)

3.092 3.113 1341 8500

Velocity (m/s) Turbulence intensity Turbulent length scale (m)

100 0.10 0.01

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

The CFD calculations reported in this paper were performed on a stage stator–rotor domain; the computations were made with an implicit solver and a coupled flow model to solve the RANS equations. The coupled flow model solved the conservation equations for mass, momentum, and energy, simultaneously. One advantage of this formulation is its robustness for solving flows with dominant source terms, such as rotation [29,30]. These calculations involve the use the high-resolution (secondorder) advection scheme. Table 1 provides the initial values of temperature, pressure, velocity, and turbulence rates at the stator inlet and rotor speed. The type of wall treatment implemented herein was proposed by Coull [7] and Goldstein [31]: the walls were considered adiabatic, with no heat transfer to the fluid near the walls. The velocity components were zero at the walls (non-slip condition).

25 26

3. Results and discussion

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

In our study, all the simulations were produced with different operating conditions. The boundary conditions (Table 1) are used in section 3.1. In section 3.2, we present the influences of thermal-field changes for two cases of the operating function on the HPT flow (takeoff and cruise) that had large different temperature values at the boundary condition (1554 K at the HPT inlet for takeoff and 1341 K for cruise) [11,32,33]. Section 3.3 discusses the effect of rotor speed during operating cruise. Two different rotor speeds were computed: 8500 rpm, corresponding to a normal operating-cruise rate, and 15,183 rpm, which is the maximum operating speed of the turbine [1,34]. In section 3.4, the rotor-blade cooling temperature depends on engine type and rotor-blade materials [35,36]. We obtained results for simulated internal cooling for three cases: (1) an adiabatic blade boundary condition; (2) a wall temperature of 870 K, corresponding to a blade material consisting of titanium-based alloys; and (3) the wall set at 990 K, corresponding to a blade material consisting of nickel-based alloys. Section 3.5 discusses the complexities of nonuniformities in the thermal-field distribution under the effects of 3D spatial turbineblade profiles, operating conditions, and radial and axial spacing in the turbine. For every simulation, more than one million iterations, according to the HPT positions, were used to solve the equations, resulting in high resolution for both time and space. The acceleration

factor of calculation convergence was chosen as 0.2 (it can be set from 0 (slow but stable) to 1 (fast but least stable)). The stopping criterion of satisfaction was 10−6 .

67 68 69 70

3.1. Aerothermodynamic calculation results

71 72

Fig. 2 shows the temperature and pressure evolutions in the HPT. Both the temperature and pressure decreased from the turbine inlet to outlet, which can be directly linked to temperature and pressure losses in the turbine. There are some typical sources of losses in turbines: profile losses, shock losses, tip-leakage losses, endwall losses, and cooling loss. The profile losses occurred principally at the stator and rotor TEs. In the rotor, the trailing vortex mixing with rotational speed produces a complex flow and contributes to rotor losses [37]. Shock loss was pronounced at the leading edge blade of the stator and rotor; this was particularly true of pressure evolution (Fig. 2b). Tip-leakage losses concerned the clearance between the blade tip and casing; with the unshrouded blade our study, tip leakage was negligible. Given the same behavior of profile losses in the HPT, the endwall losses concentrated primarily at the rotor TE. As for cooling loss, a simplified cooling modeling was used in which the wall temperatures were changed to simulate internal cooling. The related effect is discussed in detail in section 3.4. The cooling losses herein resulted mainly from the modification of the transition near the boundary layer. Nevertheless, the decreases in temperature and pressure are directly linked to five main types of loss. In many instances, however, it is difficult to distinguish between them because of their interaction and mixing. Many papers on loss source [38–44] have expressed turbine losses in terms of loss coefficients. The authors studied the loss coefficients with various loss prediction methods, but the total losses were always calculated as follows:

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

ζ = ζ i

(8)

102

In the stator:

ζ N = ζpr, N + ζsh, N + ζtl, N + ζew, N + ζco, N

103

(9)

104 105

In the rotor:

ζ R = ζpr, R + ζsh, R + ζtl, R + ζew, R + ζco, R

101

106

(10)

where ζ is the enthalpy loss coefficient; ζi is the component loss coefficient; ζ N , ζpr, N , ζsh, N , ζtl, N , ζew, N , and ζco, N are the stator loss coefficient, stator-profile loss coefficient, stator-shock loss coefficient, stator-tip-leakage loss coefficient, stator-endwall loss coefficient, and stator-cooling-loss coefficient, respectively; and ζ R , ζpr, R , ζsh, R , ζtl, R , ζew, R , and ζco, R are the rotor loss coefficient, rotor-profile loss coefficient, rotor-shock loss coefficient, rotor-tipleakage loss coefficient, rotor-endwall loss coefficient, and rotorcooling-loss coefficient, respectively.

107 108 109 110 111 112 113 114 115 116 117

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

130 131

65 66Q8

Fig. 2. Temperature and pressure evolutions in the HPT. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

132


[m5G; v1.250; Prn:9/01/2019; 16:40] P.5 (1-13)


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 85

19 20

Fig. 3. Temperature, pressure, and velocity evolution from the combustor outlet to the HPT outlet.

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

Fig. 4. Temperature evolution in two cases of initial temperature: cruise (13,41 K) (a) and takeoff (1554.5 K) (b) at the 50% of the span.

101

36

102

37

103

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. 3 shows the temperature, pressure, and velocity 1D evolution behind the combustor. These normalized flow parameters were calculated based on an average on a 2D cylindrical surface of the HPT, at 50% span. The temperature dropped from 1341 K at the HPT inlet to 963 K at the HPT outlet. Similarly, the pressure passing on the stator–rotor fell from 3113.2 kPa to 625.1 kPa. The velocity increased from 100 m/s to 668 m/s at the “mixing plane” and then decreased to 462 m/s at the HPT outlet. The tendency of flow parameters observed in our work appears quite consistent with past experiments reported by the NASA Lewis Research Center [35,46,47] and other research on the aerodynamic evolution in turbomachinery [1,34,48]. The T outlet / T inlet value in our simulation was 0.72 (compared to 0.65 in the references); the P outlet / P inlet was 0.28 (compared to 0.2 in the references); and the V outlet / V inlet was 3.57 (compared to 3.33 in the references). A slight difference in these values might be due to differences in the blade profile used in the simulation and the real geometry used in the experiments for the different types of engine in the CFM56 family. This directly impacts loss values (especially profile losses) and aerothermodynamic transformation, involving changes in flow-parameter values, including T outlet / T inlet , P outlet / P inlet , and V outlet / V inlet . As a consequence, the velocity gradient was positive in the stator and negative in the rotor, while the temperature and pressure gradients were negative throughout the HPT. The increased stator velocity could be explained by static enthalpy of temperature converting into kinetic energy. So, in the stator, the fluid accelerated while the temperature decreased in the rotation direction. The fluid’s ki-

netic energy was converted into blade kinetic energy associated with the decreased flow velocity in the rotor [45].

104 105 106

3.2. Influence of the initial temperature field at cruise and takeoff

107

Fig. 4 presents the temperature evolutions with two initial temperatures: cruise (1341 K) (a) and takeoff (1554.5 K) (b) at the 50% span. In this figure, the temperature gradient evolutions are quite similar. The vortex was mainly concentrated in two turbine zones around the leading and trailing edges of the blades. The horseshoe vortex and small leading-edge corner vortices appeared at the leading edges and formed the wake into lumps of flow, which entered the stator and rotor passage. The passage vortex occurred strongly past the stator and rotor trailing edges, especially after the rotor trailing edges, enhanced by the additional effects of the moving rotor. The vortex production in this calculation was in line with that reported in the literature [49–53]. With respect to temperature, after the initial temperature increase, the temperature fell from 1554 K to a minimum of 969 K in takeoff, compared to rapidly dropping from 1341 K to 843 K in cruise. Fig. 5 presents the distribution of temperature values and temperature evolution gradient. It shows that the takeoff temperatures were always higher than that in cruise, which can be explained by the increased initial temperature, directly causing the increase in enthalpy. This led to an increased temperature field throughout the HPT, as shown in Fig. 5c. If the temperature at the HPT inlet significantly affects the thermal field, it seems to have no significant impact on the pressure field (Fig. 6). This figure clarifies that the pressure difference in

109

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

JID:AESCTE

6

AID:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.6 (1-13)


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 95

29 30

Fig. 5. Temperature distributions (a, b) and temperature variations (c) in two cases of initial temperature: cruise (1341 K) and takeoff (1554.5 K).

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

116 117

51 52

Fig. 6. Pressure variations as a function of position in two cases of initial temperature: cruise (1341 K) and takeoff (1554.5 K).

54 55

both cases, which occurred around the rotor blades, is negligible

56

(about 3%). On the other hand, the temperature change strongly

57

affected the velocity field (Fig. 7). The velocity differences in both

58

cases were concentrated at the mixing plane and turbine outlet,

59

where there were many vortices. The greatest difference in veloc-

60

ity was about 11.5% at the turbine outlet. Fig. 7 also shows that

61 62

118 119

53

the velocity at takeoff was always greater than in cruise because

63

of the temperature increase resulting in increased static enthalpy,

64

thereby accelerating the transfer of static enthalpy into kinetic en-

65

ergy. This increased the value of the velocity field. For the same

66

reason, the increased kinetic energy increased the turbulent kinetic

energy (TKE) in takeoff. As shown in Fig. 8, the TKE gradients in both cases were quite similar and only their values were different.

120 121 122 123

3.3. Influence of rotor speed in two cases: operating cruise and maximum rotor speed

124 125 126

Figs. 9 to 11 show the temperature, pressure, and velocity distribution in the stator and rotor at two different rotor speeds: 8500 rpm, corresponding to a normal operating-cruise rate, and 15,183 rpm, corresponding to a turbine maximum operational speed. The flow-parameter values were homogeneously distributed from the stator inlet to the trailing edges (TEs) of the stator

127 128 129 130 131 132


[m5G; v1.250; Prn:9/01/2019; 16:40] P.7 (1-13)


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 85

19 20

Fig. 7. Velocity variations as a function of position in two cases of initial temperature: cruise (1341 K) and takeoff (1554.5 K).

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 99

33 34

Fig. 8. Evolution of turbulent kinetic energy (TKE) in two cases of initial temperature: cruise (1341 K) and takeoff (1554 K).

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

130 131

65 66

Fig. 9. Temperature distributions (a, b) and temperature variations (c) in two cases of rotor speed: 8500 rpm and maximum 15,183 rpm.

132

JID:AESCTE

8

AID:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.8 (1-13)


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 96

30 31

Fig. 10. Pressure distributions (a, b) and pressure variations (c) in two cases of rotor speed: 8500 rpm and maximum 15,183 rpm.

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

126 127

61 62

Fig. 11. Velocity distributions (a, b) and velocity variations (c) in two cases of rotor speed: 8500 rpm and maximum 15183 rpm.

64 65 66

128 129

63

blades in both cases. Flow-parameter differences, however, appeared downstream from the stator-blade TEs to the turbine outlet. The rotor flow in this area seems to have had a tendency to be

compressed. As a result, there were fewer fluctuations of temperature, pressure, and velocity values in the rotor than at operating cruise. The flow-parameter values did not differ ahead of the

130 131 132


[m5G; v1.250; Prn:9/01/2019; 16:40] P.9 (1-13)


9

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75 76

10

Fig. 12. Temperature of rotor-blade surfaces in two cases: (a) no cooling and (b) cooling at 870 K.

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

78

stator-blade TEs in either case. The effect of this change ahead of the stator-blade TEs was negligible. Although the effect of the rotor-speed source term on each flow parameter (temperature, pressure and velocity) varied, it was remarkable that the rotor speeds had little effect on pressure and temperature (Figs. 9c and 10c). The temperature and pressure differences occurred principally around the mixing plane and rotor blade corresponding to the interactions of the stator and rotor regions, the vortex around rotor blades, and the pressure differential between the pressure and suction sides. The maximum temperature difference was 4.3% at the rotor blades and the maximum pressure differential in both cases was 22.6% at the mixing plane. The temperature and pressure differences at the turbine outlet were 1% and 0.4%, respectively. On the other hand, rotor speed had a greater impact on the velocity field than the temperature or pressure field (Fig. 11c). This figure shows that the velocity differences began appearing behind the stator-blade TEs and at the turbine outlet with a maximum value of about 31.2%. The rotorspeed’s mechanism of action on velocity is complex and can be explained in two ways. First, the increase in rotor speed raised the relative velocity and then increased the absolute velocity, while the axial velocity remained almost constant in the rotor. Second, the increased rotor speed engendered vortices in the rotor, increasing losses around the rotor blades, leading to the decrease in absolute velocity in the rotor. Therefore, the velocity in the case of maximum rotor speed was not always higher than that in operating cruise, as shown in Fig. 11c. Consequently, rotor speed has a direct relationship with rotor blade kinetic energy and significantly influenced the kinetic energy of flow and the velocity field. In contrast, the rotor-blade kinetic energy weakly influenced the static enthalpy and pressure. That can be explained by the fact that the conversion of static enthalpy into kinetic energy of flow occurred almost in one direction (see section 3.1). In the reverse direction, the conversion of kinetic energy to static enthalpy was quite small and, consequently, rotor speed had a trivial effect on temperature and pressure. 3.4. Effect of rotor-blade cooling

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

77

Rotor-blade cooling is necessary to achieve high intra-engine performance engine and to protect rotor-blade material. The rotorblade cooling temperature depends on engine type and rotor-blade materials [35,36]. We report here the results obtained for three cases of simulated internal cooling: (1) an adiabatic blade boundary condition; (2) the wall temperature set at 870 K, corresponding to a blade material consisting of titanium-based alloys; and (3) the wall set at 990 K, corresponding to a blade material consisting of nickel-based alloys Fig. 12 shows the temperature of rotor-blade surfaces for two cases without and with cooling at 870 K. As described above, the blade-surface temperature without cooling is too high and can reach up to around 1200 K. Our study used cooling at 870 K to protect the blade material. Fig. 13 presents the temperature distribution in the HPT for these cases. Fig. 13a shows that cooling reduced the zone of high

temperatures above 1150 K was reduced and that the zone of lower temperatures around 900 K increased. Fig. 13b shows the same tendency, meaning that a decrease of the high-temperature area was observed, occurring at the same time as the increase of the lower-temperature zone in both cases (870 K and 900 K). Thus, the cooling system tended to decrease the static enthalpy around the rotor blades and then cause a decrease in the total static enthalpy in the HPT. The low-temperature area around the rotor blades was maintained (called “film cooling”) to protect rotor-blade material. Figs. 14 and 15 provide more details about the effect of cooling on flow (temperature and pressure variations with and without cooling at 870 K. The temperature difference in these two cases appeared primarily at the rotor-blade leading edge and then extended to the turbine outlet because the cooling system only affects rotor blades. The maximum difference of temperature in these two cases was about 1.7% at the middle of the rotor blades and about 0.7% at the HPT outlet. Fig. 15 shows that the pressure distribution in both cases was very similar and was in good agreement with that reported in a recent publication [48]. It should be noted that the difference in velocity values in these two cases was negligible. In other words, cooling appears to have had greater effect on temperature than on pressure and velocity. Let us return to the effects of the cooling system on the temperature field. This phenomenon depends on differences between the rotor-surface temperature and the temperature of the hot-gas stream. Past studies [54–56] and experiments reported by Leach et al. [35] demonstrated that cooling effectiveness was defined as:

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

η=

T g − Tm T g − Tc

108

(11)

where T g is the temperature of the hot-gas stream, T m the rotorblade surface (temperature of the metal), and T c the cooling-air temperature. While the temperature of the hot-gas stream (T g ) only depends on engine type and operating functions, the cooling system can be influenced by rotor-blade temperature and material (relation of T m and T c ). Compared to the change of initial temperature discussed in section 3.2, in the both cases, the changes in initial temperature and cooling behaved similarly with global temperature evolution, although initial temperature factor appears to have had a larger impact than cooling process. Nevertheless, the cooling system had a strict relationship with initial temperature in the turbine. Table 2 summarizes the maximum values of the various flowparameters as well as the differences in these parameters at the turbine outlet (calculated in sections 3.2, 3.3, and 3.4). Research on the temperature field HPTs is important in order to gain understanding of turbine operating functions and the intraengine chemical reactions because temperature is a major factor affecting chemical transformation processes. The 3D distribution of the thermal field is complex and nonuniform. The following paragraph presents thermal-field nonuniformities.

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:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.10 (1-13)


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

Fig. 13. Cooling effect on temperature field.

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

124 125

59 60 61 62 63

Fig. 14. Temperature variations as a function of position in two cases: cooling with rotor-blade temperature at 870 K and without cooling.

3.5. Nonuniformities in the thermal field distribution in the spatial HPT

64 65 66

Fig. 16 presents the thermal-field distribution based on isothermal values for four typical zones: (a) 1341 K–1200 K; (b) 1200 K–

1100 K; (c) 1100 K–1000 K; and (d) 1000 K–843 K. Each zone

126 127 128 129

herein is presented with 8 different isothermal values to clearly

130

show the temperature value. The temperature decreased through-

131

out the turbine (Fig. 16a–d), which can be explained by the losses

132


[m5G; v1.250; Prn:9/01/2019; 16:40] P.11 (1-13)


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

Fig. 15. Pressure variations as a function of position in two cases: cooling with rotor-blade temperature at 870 K and without cooling.

22 23 24 25 26 27 28 29 30

86 87

21

88

Table 2 Effects of initial temperature change, rotor-speed change, and cooling system.

89 90

Parameters

DiTmax

DiT-outlet

Dipmax

Dip-outlet

Divmax

Div-outlet

91

Initial temperature (1341 K–1554.5 K) Rotor-speed change (8500 rpm–15183 rpm) Cooling system (870 K – no cooling)

14.2%

13.4%

3.2%

0.3%

11.5%

11.5%

92

4.3%

1%

22.6%

0.4%

31.2%

31.2%

1.7%

0.7%

0.4

0.3%

1.1%

1.1%

93 94 95 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

Fig. 16. Isovalues of the thermic field in the turbine in four zones: (a) 1341 K–1200 K; (b) 1200 K–1100 K; (c) 1100 K–1000 K; and (d) 1000 K–843 K.

58 59 60 61 62 63 64 65 66

122 123

57

(see section 3.1); the temperature around the rotor blades was high, ranging from 1050 K to 1250 K, as mentioned above (section 3.4). Besides, the thermal-field distribution in the turbine was not uniform. Temperature nonuniformities were observed in the stator and especially in the rotor in both the axial and radial directions. The temperature nonuniformities in the axial direction led to a temperature decrease (section 3.1) and the nonuniformities in the radial direction were directly linked to the wakes

from the stator, moving rotor blades, and nonuniform inlet temperature or inlet-temperature distortion at the rotor inlet. In our research, we calculated and simulated the thermal field in both parts of the turbine (stator and rotor). These calculations were much more complex than that realized only for one stator or rotor row. The rotor-inlet temperature was directly linked to the stator-outlet temperature results via the “hub” and was nonuniform.

124 125 126 127 128 129 130 131 132

JID:AESCTE

AID:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.12 (1-13)


12

had little effect. This factor had a slight impact on the temperature around the rotor-blade surface with a value of about 1.7%. This research also highlights the temperature nonuniformities in the turbine in the axial and radial directions. The results show a temperature difference of about 28.2% between the HPT outlet and inlet in the axial direction. In the radial direction, this value was lower (12.5%) on the hub and tip surfaces. This paper is a continuation and extension of earlier research conducted by the author and coworkers to study the interactions of aerothermodynamic and chemical processes in HPTs. This paper contributes useful information and new insights to better understand the aerothermodynamic process and the operating functions of HPTs. The findings can be applied to various aircraft engines and helps to optimize compressor and turbine design for the next generation of aircraft engines.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Funding

17 19

Fig. 17. Simple predicted model (Eq. (12)) of the temperature isovalue line along the rotor pressure surface.

20 21 22 23 24 25 26 27 28 29 30 31 32

Fig. 16a–b shows that the maximum surface temperature on the pressure side was higher than the average gas temperature on the suction side. Butler et al. [57] and Kerrebrock et al. [58] have already accounted for this phenomenon as being the separation tendency of hot and cold gases in the turbine rotor. Thus, we concentrated on the material on the pressure side of the rotor blade for its protection. Fig. 16 reveals that the distribution of isothermal values was complex. Nevertheless, based on past studies [57–59], the line of isothermal values along the rotor pressure surface can be predicted as follows:

33

d2 δ

34

d2 z

=

1 R

T iso T0

1 ( R )2 = −1 2 R W z ( z)

T iso T0

−1

1

φ2

(12)

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

where, δ is the radial displacement of isothermal values in comparison with mean surface streamline [59] (as shown in Fig. 17); z is the axial axis or the rotational axis; R is the radius; T iso is the isothermal value; T 0 is the fluid static temperature; is the rotational speed; W z is the axial velocity on the blade pressure Wz surface; and φ = is the familiar nondimensional flow coeffiR cient. Equation (12) reveals that the displacement scaled linearly with streak temperature and at the low flow coefficient, there was more influence on the radial displacement that for the high flow coefficient. Therefore, the distribution of isothermal values in the rotor was as a function of many variables: radius, streak temperature, rotor speed, and axial velocity. Fig. 16 provides more details about the thermal-field nonuniformities: the temperature decreased about 28.2% from 1341 K at the HPT inlet to 963 K at the HPT outlet (T outlet / T inlet = 0.72) in the axial direction. In the radial direction, the temperature increased from 1050 K at the hub surface to 1200 K at the tip surface; the maximum difference between these two surfaces was calculated at about 12.5% and T tip / T hud = 1.14.

55 56

4. Conclusions

57 58 59 60 61 62 63 64 65 66

68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

16 18

67

The 3D design of an HPT, tridimensional computed calculations and modeling on the aerothermodynamic evolution, the influence of operational parameters on the aerothermodynamic process, and the nonuniformities of the thermic field in the HPT were investigated. The thermal boundary condition strongly affected the flow temperature; the maximum temperature difference between takeoff and cruise processes was about 14.2%, while the rotor speed significantly affected the flow velocity. Additionally, the cooling system

83 84

This work was financially supported by the National Science and Engineering Research Council (NSERC) of Canada.

85Q9 86 87

Conflict of interest statement

88 89

None declared.

90Q10 91

Uncited references

92 93

[17]

94Q11 95

References

96 97

[1] S.P. Lukachko, et al., Engine design and operational impacts on particulate matter precursor emissions, J. Eng. Gas Turbines Power 130 (2) (2008) 021505. [2] A.M. Starik, et al., Impact of operating regime on aviation engine emissions: modeling study, J. Propuls. Power 29 (3) (2013) 709–717. [3] J. Bisson, et al., Numerical prediction of gaseous aerosol precursors and particles in an aircraft engine, J. Propuls. Power (2016) 1–11. [4] C. Dhatchanamoorthy, et al., Study and performance analysis of gas turbine combustion chamber and improving combustion efficiency by using ceramic composite material coating, Int. J. Mech. Eng. Robot. Res. 4 (1) (2015) 195. [5] C.P. Mark, A. Selwyn, Design and Analysis of Annular Combustion Chamber of a Low Bypass Turbofan Engine in a Jet Trainer Aircraft, Propulsion and Power Research, 2016. ´ ´ ˙ nski, J. Seczyk, ˛ P. Wolanski, Influence of compression ratio on combus[6] T. Leza tion, turbulence, swirls into model combustion chamber of SI engines, J. KONES (2015) 22. [7] J.D. Coull, N.R. Atkins, H.P. Hodson, Winglets for improved aerothermal performance of high pressure turbines, J. Turbomach. 136 (9) (2014) 091007. [8] A. Demeulenaere, R. Van den Braembussche, Three-dimensional inverse method for turbomachinery blading design, in: ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers, 1996. [9] M. Rose, P. Schüpbach, M. Mansour, The thermodynamics of wake blade interaction in axial flow turbines: combined experimental and computational study, J. Turbomach. 135 (3) (2013) 031015. [10] P. Lampart, S. Yershov, A. Rusanov, Increasing flow efficiency of high-pressure and low-pressure steam turbine stages from numerical optimization of 3D blading, Eng. Optim. 37 (2) (2005) 145–166. [11] I˙ . Yılmaz, Evaluation of the relationship between exhaust gas temperature and operational parameters in CFM56-7B engines, Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 223 (4) (2009) 433–440. [12] C. Wey, et al., Aircraft Particle Emissions Experiment (APEX), NASA Glen Research Center TM-2006-214382, Cleveland, OH, 2006. [13] C.C. Wey, et al., Overview on the aircraft particle emissions experiment, J. Propuls. Power 23 (5) (2007) 898–905. [14] K. Guntupalli, Development, Validation and Verification of the Momentum Source Model for Discrete Rotor Blades, Thesis, Iowa State University, 2011. [15] H.-P. Kersken, et al., Time-linearized and time-accurate 3D RANS methods for aeroelastic analysis in turbomachinery, J. Turbomach. 134 (5) (2012) 051024. [16] E. Pomraning, K. Richards, P. Senecal, Modeling Turbulent Combustion Using a RANS Model, Detailed Chemistry, and Adaptive Mesh Refinement, 2014, SAE Technical Paper. [17] A.J. Lew, G.C. Buscaglia, P.M. Carrica, A note on the numerical treatment of the k-epsilon turbulence model, Int. J. Comput. Fluid Dyn. 14 (3) (2001) 201–209.

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


[m5G; v1.250; Prn:9/01/2019; 16:40] P.13 (1-13)


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

[18] T.J. Grindle, F.W. Burcham Jr, Engine Damage to a NASA DC-8-72 Airplane from a High-Altitude Encounter with a Diffuse Volcanic Ash Cloud, National Aeronautics and Space Administration, Dryden Flight Research Center, Edwards, California, 2003, 93523-0273, NASA/TM-2003-212030. [19] T. Nijdam, R.v. Gestel, Service Experience with Single Crystal Superalloys for High Pressure Turbine Shrouds, National Aerospace Laboratory NLR, 2011, NLRTP-2011-547. [20] K.C. Hall, et al., Harmonic balance methods applied to computational fluid dynamics problems, Int. J. Comput. Fluid Dyn. 27 (2) (2013) 52–67. [21] J.I. Erdos, E. Alzner, W. McNally, Numerical solution of periodic transonic flow through a fan stage, AIAA J. 15 (11) (1977) 1559–1568. [22] G. Gerolymos, G. Michon, J. Neubauer, Analysis and application of chorochronic periodicity in turbomachinery rotor/stator interaction computations, J. Propuls. Power 18 (6) (2002) 1139–1152. [23] F. Montomoli, H. Hodson, L. Lapworth, RANS–URANS in axial compressor, a design methodology, Proc. Inst. Mech. Eng. A, J. Power Energy 225 (3) (2011) 363–374. [24] L.A. Freitag, On combining Laplacian and optimization-based mesh smoothing techniques, in: ASME Applied Mechachics Division-Publication-AMD, vol. 220, 1997, pp. 37–44. [25] M. Batdorf, L.A. Freitag, C. Ollivier-Gooch, Computational study of the effect of unstructured mesh quality on solution efficiency, in: Proc. 13th AIAA Computational Fluid Dynamics Conf., 1997. [26] R.V. Garimella, M.J. Shashkov, P.M. Knupp, Triangular and quadrilateral surface mesh quality optimization using local parametrization, Comput. Methods Appl. Mech. Eng. 193 (9) (2004) 913–928. [27] Y. Zhang, C. Bajaj, Adaptive and quality quadrilateral/hexahedral meshing from volumetric data, Comput. Methods Appl. Mech. Eng. 195 (9) (2006) 942–960. [28] Y. Zhang, C. Bajaj, B.-S. Sohn, 3D finite element meshing from imaging data, Comput. Methods Appl. Mech. Eng. 194 (48) (2005) 5083–5106. [29] N.H. Brummell, N.E. Hurlburt, J. Toomre, Turbulent compressible convection with rotation. II. Mean flows and differential rotation, Astrophys. J. 493 (2) (1998) 955. [30] J.N.r. Sørensen, W.Z. Shen, Numerical modeling of wind turbine wakes, J. Fluids Eng. 124 (2) (2002) 393–399. [31] M.a.J.R.H. Goldstein, Boundary Conditions for the Diffusion Solution of Coupled Conduction-Radiation Problems, in NASA Technical Note, NASA TN D-4618. [32] S.A. Shakariyants, Generic Methods for Aero-Engine Exhaust Emission Prediction, PhD thesis, Faculty of Mechanical, Maritime and Materials Engineering, TU, Delft, Netherland, 2008. [33] U.C.A. Authority, Aircraft engine emissions individual datasheets, ICAO Aircraft Engine Emissions Databank at http://www.caa.co.uk, 2006. [34] A.M. Starik, et al., Modeling of sulfur gases and chemiions in aircraft engines, Aerosp. Sci. Technol. 6 (1) (2002) 63–81. [35] K. Leach, Energy Efficient Engine High-Pressure Turbine Component Rig Performance Test Report, 1983, NASA Report No. CR-168189. [36] R. Dewangan, et al., Gas turbines blades – a critical review of failure on first and second stages, Int. J. Mech. Eng. Robot. Res. 4 (1) (2015) 216. [37] N. Anton, W. Wiberg, Aerodynamic Design of a Gas Turbine Rotor Blade for the KTH Test Turbine, 2013, ISRN LUTMDN/TMHP-13/5284-SE. [38] S. Moustapha, S. Kacker, B. Tremblay, An improved incidence losses prediction method for turbine airfoils, J. Turbomach. 112 (2) (1990) 267–276. [39] J. Denton, N. Cumpsty, Loss Mechanisms in Turbomachines, 1987, ImechE Paper, No. C260/87. [40] T. Schobieri, M. Abouelkheir, Row-by-row off-design performance calculation method for turbines, J. Propuls. Power 8 (4) (1992) 823–828.

13

[41] M. Okan, D. Gregory-Smith, A simple method for estimating secondary losses in turbines at the preliminary design stage, in: ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, 1992. [42] M. Yaras, S. Sjolander, Prediction of tip-leakage losses in axial turbines, in: ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, 1990. [43] S. De Cecco, M. Yaras, S. Sjolander, Measurements of the tip-leakage flow in a turbine cascade with large clearances, in: ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, 1995. [44] M. Wehner, et al., Measurement and prediction of tip leakage losses in an axialflow transonic turbine, in: ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, American Society of Mechanical Engineers, 1997. [45] S. Hutton, Introduction to the theory of flow machines, J. Fluid Mech. 28 (04) (1967) 824–826, By A. Betz, Pergamon 1966, 281 pp. 75s. Fluid Mechanics of Turbomachinery. By S.L. Dixon, Pergamon, 1966, 213 pp. 25s. Axial Flow Turbines. By J.H. Horlock, Butterworth, 1966, 275 pp. 97s. 6d. [46] L. Timko, Energy Efficient Engine High Pressure Turbine Component Test Performance Report, 1984, NASA Report No. CR-168289. [47] E. Halila, D. Lenahan, T. Thomas, Energy Efficient Engine High Pressure Turbine Test Hardware Detailed Design Report, 1982, NASA Report No. CR-167955. [48] S.P. Lukachko, et al., Production of sulfate aerosol precursors in the turbine and exhaust nozzle of an aircraft engine, J. Geophys. Res., Atmos. 103 (D13) (1998) 16159–16174. [49] P. Marchal, C. Sieverding, Secondary flows within turbomachinery bladings, in: AGARD Secondary Flows in Turbomachines, vol. 20, 1977 (SEE N 78-11083 02-07). [50] L. Langston, Crossflows in a turbine cascade passage, J. Eng. Power 102 (4) (1980) 866–874. [51] C. Sieverding, Recent progress in the understanding of basic aspects of secondary flows in turbine blade passages, J. Eng. Gas Turbines Power 107 (2) (1985) 248–257. [52] T. Sonoda, Experimental investigation on spatial development of streamwise vortices in a turbine inlet guide vane cascade, in: ASME 1985 International Gas Turbine Conference and Exhibit, American Society of Mechanical Engineers, 1985. [53] R.J. Goldstein, R.A. Spores, Turbulent transport on the endwall in the region between adjacent turbine blades, J. Heat Transf. 110 (4a) (1988) 862–869. [54] J.E. Albert, D.G. Bogard, F. Cunha, Adiabatic and overall effectiveness for a film cooled blade, in: ASME Turbo Expo 2004: Power for Land, Sea, and Air, American Society of Mechanical Engineers, 2004. [55] J.E. Albert, D.G. Bogard, Measurements of adiabatic film and overall cooling effectiveness on a turbine vane pressure side with a trench, J. Turbomach. 135 (5) (2013) 051007. [56] S. Ito, R. Goldstein, E. Eckert, Film cooling of a gas turbine blade, J. Eng. Power 100 (3) (1978) 476–481. [57] T. Butler, et al., Redistribution of an inlet temperature distortion in an axial flow turbine stage, J. Propuls. Power 5 (1) (1989) 64–71. [58] J.L. Kerrebrock, A. Mikolajczak, Intra-stator transport of rotor wakes and its effect on compressor performance, J. Eng. Power 92 (4) (1970) 359–368. [59] T. Shang, A.H. Epstein, Analysis of hot streak effects on turbine rotor heat load, J. Turbomach. 119 (3) (1997) 544–553.

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

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

JID:AESCTE

AID:4936 /FLA

[m5G; v1.250; Prn:9/01/2019; 16:40] P.14 (1-13)

Sponsor names

1 2 3 4Q12 5

Do not correct this page. Please mark corrections to sponsor names and grant numbers in the main text.

NSERC, country=Canada, grants=

67 68 69 70 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

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