Home Physical Sciences Research on optimization of combustor liner structure based on arc-shaped slot hole
Article Open Access

Research on optimization of combustor liner structure based on arc-shaped slot hole

  • Zhenpeng He , Tao Huang EMAIL logo , Zhenxing Bao , Ziyi Lei , Baoshen Zhang , Gui Luo and Meng Cai
Published/Copyright: August 21, 2024
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 22 Issue 1

Abstract

The flow and heat transfer characteristics of the fluid in the combustor were investigated using numerical simulation in this study. The physical properties of the cooling airflow were fully utilized, and the structure of the combustor was improved. Film hole with novel structure (arc-shaped slot hole) was proposed and compared with cylindrical hole. The optimization schemes for the combustor liner structure were established, in the meanwhile, the influence of different inclinations and slot depths on the temperature distribution of the combustor liner wall was investigated. Compared with the original structure, the average temperature of the target cooling zones in these optimized schemes are reduced by a minimum of 15.12% (227.1 K) and a maximum of 20.65% (351.6 K). A new assessment model (weighted average temperature assessment model) was proposed to provide an effective assessment of the overall cooling effect. The following conclusions were arrived at: high temperature in localized areas is an important reason for the damage of combustor liner wall. Compared to cylindrical hole, the cooling performance of arc-shaped slot hole is better. When the hole type is the same, the larger inclination has higher jet height than the smaller inclination, and the cooling effect is worse. Increasing the slot depth h can improve the cooling efficiency.

Keywords: combustor liner; slot depth; average temperature; cooling efficiency

Nomenclature

D

diameter of the hole

DO

discrete ordinates

DPM

discrete phase model

F j

momentum exchange source term

f

mixed fraction

G k

turbulent kinetic energy

h

depth of slot

m f

mass flow rate of fuel

P

chemometric oil/gas ratio

P t,in

inlet total pressure

QAR

quick access recorder

r

the radius

S h

energy exchange source term

S m

mass exchange source term

T c

coolant temperature

T m

mainstream temperature

T t,in

inlet total temperature

T w

wall temperature

T *

weighted average temperature

µ t

turbulent viscosity

θ

half cone angle for fuel injection

α

inclination angle of the hole

η

cooling effectiveness

1 Introduction

There are complex physical phenomena inside the combustor, and the process of fluid flow and heat transfer inside is very complex. Fuel reacts with air in the combustor in a combustion reaction, which provides the aero-engine with its source of power [1]. Therefore, the combustor is an important part of the aero-engine and affects the working condition of the aero-engine. With the continuous advancement of new generation aero-engine development technology, the working temperature inside the combustor is constantly increasing. This also leads to the phenomenon of damage on the combustor liner becoming increasingly prominent [2]. In order to protect the combustor liner wall, a variety of cooling technologies are used in the combustor. Among them, the film cooling technique can effectively protect the wall by generating cooling film [3,4,5], which is suitable for application in the structural optimization design of combustor liner.

Currently, many scholars have conducted a lot of research on the physical properties of film cooling technology, especially the flow and heat transfer characteristics. In addition to the improved design of the hole shape [6,7], the additional slot structure at the outlet of the cooling hole can provide a good enhancement for the cooling performance [8,9,10]. After the cooling airflow flows out of the film hole, diffusion occurs under the action of the slot structure, which tends to form a wider film coverage on the wall surface. Zhang et al. [11] used numerical simulations to investigate the effect of forward expansion angle on the flow field, temperature field, and cooling effect downstream of the film hole. The results show that increasing the forward expansion angle leads to a reduction in the momentum of the cooling jets, which improves the film cooling efficiency in both the forward and lateral directions. Kanani et al. [12] conducted a numerical simulation study on the effect of blowing rate and film hole structure on cooling performance. During the course of the study, it was found that the shape of the film hole has a great influence on the cooling performance. Du et al. [13] investigated the effect of slots on the cooling performance of the turbine end wall by numerical simulation. It is concluded that the effect of slot depth on the cooling properties of the end wall all behave differently at different slot widths. Wang et al. [14] investigated the film cooling characteristics of fluted holes using transient liquid crystal measurements. Zhang and Wang [15] used orthogonal simulations to investigate the film cooling performance of a cross-slope trough. The presence of cross-slope slot was found to inhibit the formation of anti-kidney vortices, which in turn enhances the cooling performance. Liu et al. [16] investigated the effect of inclination angle of cylindrical hole on cooling efficiency. The conclusion is that increasing the angle reduces the overall cooling effect. Zhang et al. [17] investigated the cooling performance of end-wall discrete holes at five jet angles, 20°, 25°, 30°, 35°, and 40°, and found that the smaller the jet angle, the higher the film cooling efficiency. Dai et al. [18] added small cooling holes on the combustor liner wall and used numerical simulation to study the cooling effect of the four hole types, and concluded that the slit holes had the best cooling performance. Li and Yang [19] investigated the cooling performance of the reflux combustor and designed optimization schemes with different inclination angles and different hole types combined with each other. The result shows that the smaller the inclination is, it is more favorable to improve the cooling effect.

Studies on the effect of the hole structure on the cooling performance had focused heavily on simplified models and turbine blades, with fewer studies on the cooling hole in the combustor liner wall. The research on the physical properties of film cooling holes mainly focuses on simplified models and turbine blades, while there is less research on the cooling holes on the combustor liner wall. In addition, the combustion process occurring in the combustor is very complex, accompanied by complex airflow and heat transfer. The airflow coming out of the cooling hole is not only used to form film to protect the walls, but may also be involved in the combustion reaction. Therefore, it is important to carry out research on the film cooling technology on the combustor liner wall. Considering the above, in this research, the heat transfer mechanism of combustor liner was investigated through numerical simulation. The optimization study of the combustor structure was carried out based on the heat transfer mechanism. Arc-shaped slot holes were designed and the effect of different inclinations and slot depths on the cooling effect on the combustor liner wall was investigated. During the research process, a weighted average temperature assessment model was proposed, which could provide an effective assessment for the overall cooling effect.

2 Configuration and numerical setup

2.1 Computational model

The study object of this research is a certain type of aero-engine, which is mainly used in civil aircraft, as shown in Figure 1. Its combustor, located between the compressor and the turbine, is annular and geometrically periodic. It mainly consists of inner casing, outer casing, combustor liner, fuel nozzle, primary holes, dilution holes, film cooling holes, and other parts.

Figure 1 Annular combustor.
Figure 1

Annular combustor.

The annular combustor contains 20 swirlers, each with a fuel nozzle mounted on the head. In order to save computational resources and improve computational efficiency, the combustor was divided into 20 equal parts, and the 1/20 model was taken for the study. At the same time, the structures that do not affect the mainflow field, heat transfer, and combustion processes were simplified. The physical model of 1/20 of the combustor is shown in Figure 2.

Figure 2 Physical model of the 1/20 combustor.
Figure 2

Physical model of the 1/20 combustor.

It can be structurally divided into four parts: the outer casing, the inner casing, the swirler, and the combustor liner. The swirler is located at the head of the combustor liner. Combustor liner can be categorized into inner liner and outer liner. The combustor outer liner has one row of primary holes, one row of dilution holes, and five rows of film cooling holes. In addition to one row of primary holes and one row of dilution holes on the combustor inner liner, there are three rows of film cooling holes and one row of impingement cooling holes. The film cooling holes are shown in the blue box in Figure 2, and the impingement cooling holes are shown in the purple round box.

It can be divided into five zones according to its working principle: inlet, combustor head, primary combustion zone, complementary combustion zone, and outlet. The high-pressure air from the pressurizer enters through the combustor inlet and flows through the head of the combustor liner before splitting into three streams of airflow. Two streams of air flow into the inner ring cavity and outer ring cavity of the combustor liner, part of which enters the inside of combustor liner through the primary holes, dilution holes and cooling holes, and the remaining air flows out through the outlet. There is also a stream of air flowing through the swirler, which passes through primary swirler and secondary swirler, and finally forms a high-speed rotating airflow inside the combustor. The fuel is ejected at the head of the combustor liner and reacts with air in the primary combustion zone, and the incompletely burned fuel will be burned completely in the complementary combustion zone. After the combustion reaction, the high temperature gas will flow out of the outlet into the high-pressure turbine.

Figure 3 shows the processing of the model. Figure 3(a) indicates the positions of the combustor outer liner and inner liner. Figure 3(b) shows a 1/20 model of the combustor liner. Figure 3(c) shows the processed computational domain

Figure 3 Processing of model: (a) combustor outer and inner liner; (b) combustor liner; and (c) computational domain.
Figure 3

Processing of model: (a) combustor outer and inner liner; (b) combustor liner; and (c) computational domain.

2.2 Grid division and independent verification

Figure 4 shows the division of the grid. In this research, Fluent-meshing was used to construct the grid. The combustor liner wall is the key research area, and local densification is carried out on the combustor inner and outer liners. The body of influence (BOI) region in Figure 4(a) is the encrypted region of the grid. Adjusting the grid size of the encrypted area, five different numbers of grids were divided. They are 2.34 million, 3.74 million, 5.54 million, 7.63 million, and 10.17 million. The division of three representative grids is shown in Figure 4(b)–(d), and the main difference between them is that the BOI region has grids of different densities. Figure 5 shows the time consumed by these calculations and the highest temperature obtained. Considering the computational requirements and the time consumed, a grid of 5.54 million was chosen for the computational study in this research.

Figure 4 Division of the grid: (a) computational domain and BOI region; (b) division of the 3.74 million grid; (c) division of the 5.54 million grid; and (d) division of the 7.63 million grid.
Figure 4

Division of the grid: (a) computational domain and BOI region; (b) division of the 3.74 million grid; (c) division of the 5.54 million grid; and (d) division of the 7.63 million grid.

Figure 5 Grid-independent verification.
Figure 5

Grid-independent verification.

Figure 4(c) is the schematic diagram of grid division for 5.54 million. The target grid size of the locally encrypted area is set to 0.8 mm, with a growth rate of 1.2. Using poly-hexcore to fill the volume mesh, the peel layer is set to 1, the minimum cell length is set to 0.2 mm, and the maximum cell length is set to 3.2 mm. The minimum size of the surface mesh is set to 0.01 mm, and its maximum size is set to 3.2 mm with a growth rate of 1.2.

2.3 Boundary conditions and control equations

The combustion and heat transfer process of fuel with air follows the equations of conservation of mass, conservation of momentum, and conservation of energy, as shown below:

(1) ∂ ∂ x i ( ρ u i ) = S m ,

(2) ∂ ∂ t ( ρ u i ) + ∂ ∂ x j ( ρ u i u j ) = − ∂ P ∂ x j + ∂ ∂ x i ( τ i j − ρ u ′ i u ′ j ¯ ) + F j ,

(3) ∂ ∂ t ( ρ c p T ) + ∂ ∂ x i ( ρ c p u i T ) = ∂ ∂ x i ( λ ∂ T ∂ x i ) + S h ,

where S m is the mass exchange source term, F j is the momentum exchange source term, and S h is the energy exchange source term.

Very complex gas flows were involved in the combustion process, and the Realizable k–ε model can well simulate rotating shear flows, free flows containing jets and mixtures, and other complex flows, so this model was chosen as the turbulence model in this research [20]. The transport equations for k and ε in the Realizable k–ε model are as follows:

(4) ∂ ( ρ k ) ∂ t + ∂ ( ρ k u i ) ∂ x i = ∂ ∂ x j μ + μ t σ k ∂ k ∂ x j + G k − ρ ε ,

(5) ∂ ( ρ ε ) ∂ t + ∂ ( ρ ε u i ) ∂ x i = ∂ ∂ x j μ + μ t σ ε ∂ ε ∂ x j + ρ C 1 E ε − ρ C 2 ε 2 k + v ε ,

where µ t is the turbulent viscosity and G k is the turbulent kinetic energy due to the mean velocity gradient. C 1 and C 2 are constants. σ k and σ ε , respectively, are the turbulent Prandtl numbers for k and ε.

According to the data of quick access recorder, take-off stage is the maximum operating stage of the combustor. This research focused on the cooling problem of the combustor liner wall; therefore, the take-off condition was used as the basis for boundary condition setting. The detailed computational boundary conditions are shown in Table 1.

Table 1

Computation boundary conditions

Boundary condition Value
Inlet total pressure P t,in (kPa) 2,920
Inlet total temperature T t,in (K) 807.86
Mass flow rate of fuel m f (kg/s) 0.0529
Half cone angle for fuel injection θ (degree) 45
Chemometric oil/gas ratio P 0.068

The discrete phase model (DPM) was used for simulation and the cone nozzle model was chosen to simulate the fuel injection, with C12H23 as the alternative component of the fuel. The wall model was set to be a solid wall without slip, and the standard wall function was used in this research to deal with the near-wall region. A discrete ordinate radiation model was used to simulate the high temperature radiative heat transfer process and the transfer of thermal radiation follows Eq. (6).

(6) d I ( r → , s → ) d s + ( a + σ s ) I ( r → , s → ) = a n 2 σ T 4 π + σ s 4 π ∫ 0 4 π I ( r → , s → ′ ) Φ ( s → ⋅ s → ′ ) d Ω ′ ,

where r → is the position vector, s → is the direction vector, s → ′ is the scattering vector, s is the path length, a is the absorption coefficient, n is the refractive index, σ s is the scattering coefficient, σ is the Boltzmann’s constant, I is the radiation intensity, Φ is the phase function, and Ω′ is the steradian angle.

The SIMPLEC algorithm was used to couple the pressure and velocity terms, with the PRESTO! scheme chosen for pressure and the second-order upwind scheme chosen for momentum, turbulent kinetic energy, and turbulent dissipation rate for iteration. The convergence criteria for the calculations were residual curve values below 10−6 for the energy equation and below 10−3 for the remaining equations.

3 Calculation results and discussion about the original structure

3.1 Model validation

This research used the same model validation method as Dai et al. [18] and Li and Yang [19]. This research analyzed the temperature distribution characteristics of the combustor liner obtained through numerical simulation and compared it with the actual crack damage on the combustor liner.

Figure 6 shows the temperature distribution on the combustor liner and the actual crack damage. The left side is the combustor inner liner, and the right side is the combustor outer liner. The upper side shows the actual crack damage, and the lower side shows the temperature distribution on the combustor liner. There are six significant high-temperature zones (I, II, III, IV, V, and VI) in the temperature distribution on the combustor liner, as shown by the black dashed box. Compared with III and VI, the temperatures in I, II, IV, and V are significantly higher. I and IV are located in the primary combustion zone where the combustion reaction is most intense, and the high temperature phenomenon is most obvious. The high temperature phenomenon of II and V is weaker than that of I and IV. They are located in the complementary combustion zone, which has a weaker combustion reaction than the primary combustion zone. The combustion reaction between fuel and air mainly occurs in the primary combustion zone and complementary combustion zone. The combustion reaction occurring in the area behind the dilution holes is very weak, and the high temperature phenomenon on III and VI is the least obvious. Comparing the actual crack damage with the high temperature zones on the combustor liner, the results show that their positions are consistent, which verifies the rationality and accuracy of the model.

Figure 6 Temperature distribution of combustor liner wall and location of actual damage.
Figure 6

Temperature distribution of combustor liner wall and location of actual damage.

3.2 Velocity field

Figure 7 shows the distribution of velocity vectors in the center section. After the airflow enters the combustor, two vortices are formed at the head of the ring cavity, as shown at a. The vortex at a stabilizes the flow field into the outer and inner ring cavities. The red box in Figure 7 shows the velocity vector distribution of 50% leaf height section of the secondary swirler blade, whose inner and outer rings are two streams of airflow, and the swirler will process the airflow into the primary swirl shown in the orange box and the secondary swirl shown in the blue box. The two swirls interact with the air entering through the primary holes to form two vortices at the primary combustion zone c. Atomization and evaporation of fuel occurs at b, and combustion reactions occur in the primary combustion zone. The two vortices formed at c can stabilize the combustion process of the fuel.

Figure 7 Distribution of velocity vectors in the center section: (a) two vortices are formed at the head of the ring cavity; (b) atomization and evaporation of fuel; and (c) two vortices at the primary combustion zone.
Figure 7

Distribution of velocity vectors in the center section: (a) two vortices are formed at the head of the ring cavity; (b) atomization and evaporation of fuel; and (c) two vortices at the primary combustion zone.

3.3 Heat transfer mechanism of combustor liner

Figure 8 shows the temperature distribution of the central section. Fuel and air undergo intense combustion reactions in the primary combustion zone, releasing a large amount of heat. The temperature in the primary combustion zone is very high, with a peak temperature of 2609.9 K. Compared with the primary combustion zone, the combustion reaction in the complementary combustion zone is weaker and the temperature is lower. The red box in Figure 6 shows a local area on the combustor liner that contains film holes. Taking this area as an example, by studying the interaction between the cooling film and the mainstream gas, the heat transfer mechanism of the airflow near the combustor liner wall is analyzed. The blue arrow indicates the flow direction of cooling airflow, while the red arrow indicates the flow direction of mainstream gas. Under the action of the film holes, the cooling airflow in the ring cavity enters the interior of the combustor liner in the direction close to the surface of combustor liner wall. Under the action of mainstream gas, the cooling airflow forms a cooling film attached to the combustor liner wall. This cooling film not only serves to cool the combustor liner wall, but also provides a certain degree of isolation between the mainstream gas and the combustor liner wall. Observe the temperature distribution near the combustor liner wall. The area near the film hole outlet is a blue low-temperature area, and as the distance from the film hole increases, a green area with a higher temperature than the blue area gradually appears. Yellow and red high-temperature areas appear in the area far from the film hole. These yellow and red high-temperature areas are mainly distributed at the combustor liner skirt, and the area they are located in is considered a risk area. As shown in the red dashed box in Figure 8, these risk areas are far from the film hole outlet, have deep contact with the high-temperature mainstream. This is because as the distance from the film hole outlet increases, the thickness of the cooling film continuously decreases, and the cooling effect gradually weakens. In the combustor liner skirt, the cooling effect of the cooling film is the weakest, so there are high-temperature zones in the local area, which poses a risk of crack damage to the combustor liner wall.

Figure 8 Distribution of temperature in the central section.
Figure 8

Distribution of temperature in the central section.

Figure 9 shows the wall temperature distribution on different localized sections of the combustor liner. Figure 9(M) and (N) shows the locations of the localized cross sections of the combustor inner and outer liners. As shown in Figure 9(a) and (b), the cooling airflow from the inner annular cavity enters the primary combustion zone through the primary holes, and the entry of the low-temperature airflow has a cooling effect on the entrance of the primary hole. The high temperature gas near the wall is mixed with the cooling airflow and the temperature is reduced. Therefore, the closer the area is to the cooling holes, the better the cooling effect is, and the further the area is from the cooling holes, the weaker the cooling effect is. At the same time, when the airflow enters the combustor liner through the primary holes and the dilution holes, some of the cooling film will be dispersed. As a result, the temperature of the airflow near the left wall of the primary hole is low, and the temperature on the right side is high, which becomes more significant as the distance from the cooling hole increases. The case of the outer liner is similar to that of the inner liner, as shown in Figure 9(c) and (d).

Figure 9 Temperature distribution of different local sections: (M–N) the locations of the localized cross sections of the combustor inner and outer liners; (a-l) temperature distribution of different local sections.
Figure 9

Temperature distribution of different local sections: (M–N) the locations of the localized cross sections of the combustor inner and outer liners; (a-l) temperature distribution of different local sections.

Figure 9(e) and (f) shows the temperature distribution of the primary holes of the inner and outer liners located at the center section as shown in Figure 8. The primary holes shown in the two figures have smaller radial dimensions compared to Figure 9(a) and (c), and the airflow from the inner and outer annular cavities enters through the primary holes to participate in the combustion, and the temperature of the gas decreases in the vicinity of the primary holes, and there are localized high temperature zones at the end away from the cooling holes. Compared to Figure 9(a) and (c), the temperature is higher on both sides of the primary hole outlet located in the center section. The reason is that they are positioned close to the fuel nozzle, where the fuel is more concentrated and closer to the combustion core of the primary combustion zone. The primary holes at the periodic interface are far away from the combustion core zone, relatively distant from the fuel nozzle, and the degree of combustion reaction is relatively weak.

Figure 9(g) and (h) shows the temperature distribution of the inner and outer liner dilution holes at the 1/3 circumferential section of the computational model. The airflow of inner and outer annular cavities enters the cavity through the dilution holes, and the temperature is lower at the end near the cooling holes, and there are high temperature zones at the corresponding combustor liner skirt. Compared with Figure 9(b) and (d), its high temperature phenomenon is more significant. Since its position is closer to the center section, the fuel concentration is denser and the combustion reaction is more intense.

Figure 9(i) and (j) shows the temperature distribution of localized horizontal cross sections in the primary combustion zone of the combustor inner and outer liners. The left primary hole is close to the center section and the right primary hole is close to the periodic interface. The wall temperature of the inner liner is low, and the airflow from both sides into the cavity takes some of the heat away near the inlet. The temperature of the gas near the inner liner wall increases with the distance from the wall, because the cooling film near the wall plays a role in mixing and cooling, as the distance increases, its cooling effect is gradually weakened. At the same distance, the temperature rise is higher on the left side than on the right side, and the closer to the center cross section, the more intense the combustion reaction is and the more the heat released is. The situation is similar at the complementary combustion zone, as in Figure 9(k) and (l).

4 Optimization schemes

Zones of the combustor liner wall away from the film cooling holes have a weaker degree of cooling film coverage and higher wall temperature. In order to protect the combustor liner wall, additional film cooling holes are added on localized zones prone to high temperature. The addition of cooling holes reduces the amount of air involved in combustion, but appropriately reduces the risk of thermal damage to the combustor and enhances the life of the combustor. When the volume of inlet air is constant, the problem of wall cooling and combustion efficiency will be a compromise optimization problem and will be the focus of subsequent research. The focus of this research mainly revolves around the cooling of the combustor liner, and later research can be done to effectively cool the combustor liner by optimizing the air intake in the case of ensuring combustion. The six walls located at the primary combustion zone and the complementary combustion zone were used as the target cooling zones, as shown in Figure 10.

Figure 10 Locations of target cooling zones and additional cooling holes.
Figure 10

Locations of target cooling zones and additional cooling holes.

Figure 10 illustrates the structural design scheme of the additional cooling holes. Film cooling holes have been added to the walls at six locations to allow outside cooling air to enter the inside of the combustor liner through the cooling holes, which can cool zones of the wall that are prone to high temperature. The locations of the additional cooling holes are shown in the black dashed boxes in (Aʹ)–(Fʹ) of Figure 10.

As shown in Figure 11, an arc-shaped slot hole is proposed. It is augmented with an arc-shaped slot at the outlet of the cylindrical hole. The diameter of the hole D is 1.0 mm. The distance between the front and rear ends of the slot and the ends of the hole outlet is the same, both are 0.5 mm. The downstream end of the outlet has a curved structure with a radius of curvature r = 0.5 mm. A total of three different slot depths of h = 0.6 mm, h = 0.8 mm, and h = 1 mm were used for comparative study with cylindrical hole. Combining the two inclination angles of α = 30° and α = 60°, eight group optimized schemes of cooling structure were established. In these optimized schemes, the center position of the inlet cross section of the cooling hole is kept constant in order to improve the reliability of the comparison.

Figure 11 Design schemes of cooling structure.
Figure 11

Design schemes of cooling structure.

5 Calculation results and discussion about the optimization schemes

5.1 Feasibility

Figure 12 shows the maximum gas temperature in the combustor and the average temperature at the outlet of the combustor corresponding to the eight group schemes. Calculation results show that the maximum gas temperature of the eight group schemes are not much different from the corresponding temperature of the original structure, which is 2609.9 K. The highest gas temperatures of Case1 and Case6 are 2607.5 and 2608.9 K, which are only 2.4 and 1.0 K different from the original structure. In order to effectively express the magnitude of the decrease in average outlet temperature, the difference between the average outlet temperature of the optimized scheme and the average outlet temperature of the original structure is calculated. Then divide this difference by the average outlet temperature of the original structure, and the ratio obtained is used to represent the magnitude of the decrease. The purple markings in Figure 12 represent the reduction amplitude of the corresponding scheme. Compared to the original structure, all of these optimized schemes have some reduction in the average outlet temperature, but the reduction is small.

Figure 12 Comparison of the calculation results of the optimized schemes with the original structure.
Figure 12

Comparison of the calculation results of the optimized schemes with the original structure.

Therefore, it is considered that the normal operating process of the combustor in these optimized schemes has not been changed excessively and these optimized schemes are feasible.

5.2 Wall temperature

The wall temperature distribution of the combustor inner and outer liners for the eight cases are shown in Figures 13 and 14. The temperature distribution of the wall at six places has been greatly improved compared with the original structure, especially at the wall of the primary combustion zone, and the cooling effect is obvious.

Figure 13 Temperature distribution of the combustor inner liner.
Figure 13

Temperature distribution of the combustor inner liner.

Figure 14 Temperature distribution of the combustor outer liner.
Figure 14

Temperature distribution of the combustor outer liner.

At both 30° and 60° inclination angles, the wall low-temperature zone of case with the arc-shaped slot is more widely distributed than that of the cylindrical hole, and the cooling effect after the addition of the slot structure is significantly better. When the hole type and slot depth are the same, the wall cooling of α = 30° is significantly better than that of α = 60°. When the outlet structures are both slots, the distribution of the low-temperature zone located at the hole outlet downstream is compared. Case4 is greater than Case3, and Case2 is the smallest. When the inclination angle is 30°, the low-temperature zone located downstream of the hole outlet is most widely distributed in Case8 and least in Case6. The results show that as the slot depth h increases, the distribution of low-temperature zone located downstream of the hole outlet becomes wider and the cooling effect is better. Case with an inclination of 30° cylindrical hole has a wider distribution of wall low-temperature zones than case with a combination of 60° inclination and 1 mm slot depth. It shows that the inclination angle and the slot depth all have an important influence on the cooling effect, and both of them should be considered comprehensively in the process of structural design.

The target cooling zones contain many walls, and the number of schemes is large. When comparative analyses are performed between schemes, all walls need to be considered at the same time. Moreover, the selection of the best scheme from a large number of schemes still requires an assessment for its overall cooling effect. This results in a heavy workload and makes it difficult to efficiently select the best scheme.

In order to solve the above problems, a method for comprehensively evaluating the cooling effectiveness of all walls was designed. A calculation assessment model of weighted average temperature was proposed along the following lines: the average temperature of each wall in these optimized schemes is produced with the wall area of the corresponding original structure, and finally six values will be obtained because there are six walls. These six values are summed and then the ratio to the total wall area is found. The resulting value is the weighted average temperature. The value of weighted average temperature can effectively assess the overall cooling effect of the cooling structure on the combustor liner wall. This can be expressed as follows:

(7) T ⁎ = ∑ i n T i ¯ ⋅ S i ∑ i = 1 n S i ,

where T * is the weighted average temperature, i is the serial number of the corresponding wall, T i ¯ is the average temperature of the corresponding wall, and S i is the area of the corresponding original structural wall.

This formula differs from the area-averaged temperature. Since the structure size of the additional holes is very small in relation to the combustor liner wall, and the change in the wall area is small, no recalculation is carried out, and the wall area of the original structure is used for calculation.

Comparisons between the eight cases were made according to the weighted average temperature values, as shown in the table below.

Table 2 shows the weighted average temperatures of the different cases, and the results show that Case8 has the lowest value of weighted average temperature and it has the best overall cooling effect. The average temperature of the target cooling zones in Case8 is compared with the original structure, as shown in Table 3.

Table 2

Weighted average temperatures for different cases

Case Weighted average temperature (K)
Case1 1347.0
Case2 1344.8
Case3 1336.2
Case4 1332.2
Case5 1325.1
Case6 1281.8
Case7 1278.5
Case8 1268.2
Table 3

Comparison of average temperatures in target cooling zones

Target cooling zone Average temperature of the original structure (K) Average temperature of Case8 (K) Temperature decrease value (K) Reduction amplitude (%)
Wall-1 1645.2 1323.5 321.7 19.55
Wall-2 1306.8 1041.8 265.0 20.27
Wall-3 1547.3 1293.5 253.8 16.40
Wall-4 1702.6 1351.0 351.6 20.65
Wall-5 1595.1 1287.9 307.2 19.26
Wall-6 1502.1 1275.0 227.1 15.12

As can be seen in Table 3, the average wall temperatures at all six locations in Case8 are reduced compared to the original structure. Wall-1 and Wall-4, which are located in the primary combustion zone, are the ones with the largest temperature reduction values, with average temperature reductions of 321.7 and 351.6 K, respectively. Wall-2 and Wall-5, which are located in the middle area between the primary holes and the dilution holes, were reduced by 265.0 and 307.2 K, respectively. Wall-3 and Wall-6, which are located in the complementary combustion zone, have the lowest temperature reductions of 253.8 and 227.1 K. The cooling effect of the cooling structure decreases step by step from the primary combustion zone to the complementary combustion zone. This results in a reasonable temperature distribution on the combustor liner wall and improves the overall cooling performance. The average temperatures of the target cooling zones in these optimization schemes are reduced by a minimum of 15.12% (227.1 K) and a maximum of 20.65% (351.6 K).

5.3 Cooling efficiency

Define the film cooling efficiency η according to Eq. (8):

(8) η = T m − T w T m − T c ,

where T m is the mainstream gas temperature, T w is the wall gas temperature, and T c is the cooling airflow temperature.

The study focuses on the cooling effect of the wall, so T w is the maximum temperature of the corresponding wall.

The cooling effectiveness of the additional cooling structures are compared, as shown in Figure 15. The results show that the arc-shaped slot holes are able to increase the cooling effectiveness in the flow and spreading directions compared to the cylindrical holes at both inclinations, which is more significant at 30° inclination. The overall cooling efficiency is low when α = 60°, and the increase in the slot depth has no significant effect on the cooling performance. The overall cooling efficiency is high when α = 30°, the cooling efficiency improvement in the flow and spread directions is significant with the increase in h. When α is small, the slot depth has an important effect on the cooling performance, and increasing h can play a significant role in improving the cooling efficiency. The cooling airflow appears to be deflected, and the direction of the deflection is shown by the red arrow. The cooling holes shown in the red box in Figure 15 are located in the center section, and they are offset to a small degree because they are subjected to the combined effect of airflow from both sides. Therefore it is taken for analyzing and studying as shown in Figure 16.

Figure 15 Distribution of cooling efficiency.
Figure 15

Distribution of cooling efficiency.

Figure 16 Temperature distribution and cooling airflow jet pathlines.
Figure 16

Temperature distribution and cooling airflow jet pathlines.

5.4 Cooling mechanism

Figure 16 shows the temperature distribution and cooling airflow jet pathlines. The results show that the cooling airflow has a lower jet height and the film covers a larger area on the wall with better cooling performance for a small incidence angle. The orange box in Figure 16 shows the arc-shaped slot structure in Case8, which is structurally different from the cylindrical hole in three main zones (as shown in 1, 2, and 3 in the figure). 1 is located at the upstream slot corner at the outlet end of the hole. After the high-temperature mainstream passes through 1, part of the airflow will flow into the slot corner to interact with the cooling airflow. This process increases the action degree of the mainstream on the cooling airflow and inhibits the growth of the cooling airflow jet height.

The slot corner at the downstream end of the arc-shaped slot is located at 2, and part of the cooling airflow enters 2 after flowing out of the hole outlet, forming a vortex structure at the slot corner. It effectively reduces the kinetic energy of the airflow, inhibits the formation of kidney-shaped vortices, reduces the penetration of the cooling airflow jet into the mainstream, and improves the cooling efficiency of the flow direction. The slot corner at 2 hinders part of the cooling airflow in the flow direction, so that lateral diffusion occurs to both sides, which improves the cooling efficiency in the lateral direction. Increasing the slot depth h, causes more cooling airflow to enter the slot corner, which creates a stronger vortex and reduces the momentum of more cooling airflow, resulting in more efficient cooling in the flow direction. At the same time, the amount of airflow that undergoes lateral diffusion to both sides is increased, and the lateral cooling efficiency becomes higher.

Where the cooling airflow passes through the curved section at the downstream end of the arc-shaped slot (as shown in 3), the Coanda effect is produced. The Coanda effect allows more cooling airflow to adhere to the wall, effectively enhancing the cooling effect. When the angle of inclination is small, the jet height of the cooling airflow is lower and more airflow acts on the slot corner at 2. The vortex formed attenuates the momentum of more cooling airflow, allowing more airflow to spread laterally. Therefore, the improvement in cooling performance is more significant by increasing the slot depth h in the case of small inclination than in the case of large inclination.

A comparison of the cooling efficiency between the different schemes is shown in Figure 17. In order to accurately and efficiently analyze the cooling effect of the eight optimization schemes. Cooling efficiencies were analyzed in the flow direction within 5 mm (S = 5D) of the hole outlet. S denotes the distance from the downstream end of the cooling hole outlet. The color indicates the angle and the shape of the dot indicates the hole type. Red color indicates inclination angle α = 60°, blue color indicates inclination angle α = 30°. Circle indicates cylindrical hole, square indicates arc-shaped slot hole with h = 0.6 mm, square triangle indicates arc-shaped slot hole with h = 0.8 mm, and inverted triangle indicates arc-shaped slot hole with h = 1.0 mm. Observing the distribution characteristics of the dots, the red dots are located to the left of the blue dots, except for the dots at S = 0 mm. It can be inferred that the cooling effect of the film hole with larger inclination angle is poor. This is also caused by the fact that the larger inclination angle increases the height of the jet as shown in Figure 16.

Figure 17 A comparison of the cooling efficiency between the different schemes.
Figure 17

A comparison of the cooling efficiency between the different schemes.

In order to effectively differentiate the distribution characteristics between dots, some areas are zoomed in, as shown by the purple boxes in Figure 17. Observing all the red dots, except for the dots at S = 0 mm, the circular dots are located on the leftmost side, the square dots are located on the right side of the circular dots, the triangular dots are located on the right side of the square dots, and the inverted triangle dots are located on the rightmost side. When S = 2.0 mm, Case1 has the lowest cooling efficiency, η case1 = 0.3561. Case2 has a higher cooling efficiency than Case1, η case2 = 0.4559. Case3 has a lower cooling efficiency than Case4, η case3 = 0.4694, η case4 = 0.4789. Like the red dots, the blue dots also have the same distribution characteristics. When S = 2.0 mm, Case5 has the lowest cooling efficiency, η case5 = 0.5300. Case6 has a higher cooling efficiency than Case5, η case6 = 0.6443. Case8 has the highest cooling efficiency, followed by Case7, η case7 = 0.6852, and η case8 = 0.6928. It can be inferred that the cooling performance of arc-shaped slot hole is better than that of cylindrical hole. As the slot depth h increases, the cooling efficiency gradually improves. This is consistent with the conclusion drawn from Figure 16.

6 Conclusion

In this research, the flow and heat transfer characteristics of the fluid inside the combustor of an aero-engine were investigated using numerical simulation. The physical properties of the film hole were fully utilized to improve the combustor liner structure. A new assessment model (weighted average temperature assessment model) was proposed for cooling effect evaluation. Some conclusions are given as below:

1) As the distance from the film cooling holes increases, the film cooling effect is weakened, and it is easy to form localized high-temperature zones. The presence of these localized high-temperature zones can easily lead to crack damage on the combustor liner wall. Additional cooling holes on the combustor liner wall can reduce the wall temperature in these high-temperature zones. The average temperature of the target cooling zones in these optimized schemes are reduced by a minimum of 15.12% (227.1 K) and a maximum of 20.65% (351.6 K).

2) Arc-shaped slot hole can increase the action degree of the high temperature mainstream on the cooling airflow, and inhibit the formation of kidney-shaped vortices. The airflow forms a vortex at the slot corner, and this vortex attenuates the kinetic energy of the cooling airflow and enhances the cooling efficiency of the flow direction. The slot corner allows part of the cooling airflow to flow to both sides, enhancing the cooling efficiency in the lateral direction. The airflow at the slot’s curved structure creates Coanda effect, which causes more cooling airflow to adhere to the wall and improves the cooling effect. In summary, the arc-shaped slot hole provides better cooling effect compared to the cylindrical hole.

3) T*(Case1) = 1347.0 K, T*(Case5) = 1325.1 K. The cooling effect of α = 30° is better than that of α = 60° when the hole type is cylindrical hole. T*(Case2) = 1344.8 K, T*(Case6) = 1281.8 K. The cooling effect of Case6 is better than that of Case2. In addition, T*(Case3) > T*(Case7), T*(Case4) > T*(Case8), when the hole type is arc-shaped slot hole, the cooling effect of α = 30° is better than α = 60°. In summary, when the hole type is the same, the larger inclination has higher jet height than the smaller inclination, and the cooling effect is worse.

4) The increase in the slot depth h will have a greater attenuation effect on the kinetic energy of the cooling airflow, which can effectively inhibit the formation of the kidney-shaped vortex and improve the coverage degree of the cooling airflow on the wall. When S = 2.0 mm, η case2(0.4559) < η case3(0.4694) < η case4(0.4789) and η case6(0.6443) < η case7(0.6852) < η case8(0.6928). The increase in the slot depth h plays a significant role in improving the cooling efficiency downstream of the film hole outlet.

Acknowledgments

The authors acknowledge the support by Engineering Technology Training Center at Civil Aviation University of China.

  1. Funding information: This research is financially supported by the Key Project of Natural Science of the Basic Research Funds of the Central Universities (3122023045), the General Program of Tianjin Natural Science Foundation (23JCYBJC00110), Experimental Technology Innovation Fund Project of Civil Aviation University of China (*2021CXJJ25), and the Special Funds Project of the Basic Research Funds of the Central Universities (3122022040), for which the authors would like to express their gratitude.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The data generated or analyzed during this study are included in this published article.

References

[1] Salpingidou C, Vlahostergios Z, Misirlis D, Donnerhack S, Flouros M, Goulas A, et al. Thermodynamic analysis of recuperative gas turbines and aero engines. Appl Therm Eng. 2017;124:250–60.Search in Google Scholar

[2] Yang Q, Ran JH, Li MJ, Lin F. Experimental study on load characteristics of dual fuel combustor of gas turbine. J Propuls Technol. 2022;43(4):392–400.Search in Google Scholar

[3] Li XY, Ren J, Jiang HD. Influence of different film cooling arrangements on endwall cooling. Int J Heat Mass Transf. 2016;102:348–59.Search in Google Scholar

[4] Lee KD, Kim KY. Performance evaluation of a novel film-cooling hole. J Heat Transf-Trans ASME. 2012;134(10):101702.Search in Google Scholar

[5] Halder P, Samad A, Kim JH, Kim KY. Film-cooling characteristics of upstream ramp enhanced turbine blade surface cooling. Heat Transf Res. 2017;48(11):969–84.Search in Google Scholar

[6] Zhang JZ, Zhang SC, Wang CH, Tan XW. Recent advances in film cooling enhancement: a review. Chin J Aeronautics. 2020;33(4):1119–36.Search in Google Scholar

[7] Elnady T, Hassan I, Kadem L, Lucas T. Cooling effectiveness of shaped film holes for leading edge. Exp Therm Fluid Sci. 2013;44:649–61.Search in Google Scholar

[8] Oguntade HI, Andrews GE, Burns AD, Ingham DB, Pourkashanian M. Improved trench film cooling with shaped trench outlets. J Turbomachinery-Transactions ASME. 2013;135(2):021009.Search in Google Scholar

[9] Feng HK, Wang CH, Fan FS, Zhang JZ. Optimization research of film cooling structures with cratered cylindrical hole. J Propuls Technol. 2019;40(5):1099–106.Search in Google Scholar

[10] Zhang W, Zhou S, Wu Z, Li GC, Kou ZH. Film cooling mechanism of combined hole and Saw-tooth slot. Int J Turbo Jet-Engines. 2019;36(4):425–33.Search in Google Scholar

[11] Zhang B, Lin LB, Li JQ, Zhang NR, Ji HH. Effect of forward expansion angle on film cooling characteristics of shaped holes. Open Phys. 2020;18(1):302–14.Search in Google Scholar

[12] Kanani H, Shams M, Ebrahimi R, Ahmadian T. Numerical simulation of film cooling effectiveness on a flat plate. Int J Numer Methods Fluids. 2008;56(8):1329–36.Search in Google Scholar

[13] Du K, Li ZG, Li J. Effects of trenched film hole configurations on the endwall film cooling and suction side phantom cooling. J Therm Sci. 2019;28(5):905–14.Search in Google Scholar

[14] Wang ZW, Zhu HR, Zhang ZW, Meng QK. Effect of trench hole depth and momentum flux ratio on film cooling characteristics. J Aerosp Power. 2012;27(11):2455–61.Search in Google Scholar

[15] Zhang L, Wang C. Orthogonal simulation of effects of different transverse declining slot structures on film cooling. J Propuls Technol. 2016;37(5):922–9.Search in Google Scholar

[16] Liu CL, Xie G, Zhu HR. Experimental research on the effect of hole-inclined angle on the film cooling characteristics under high mainstream turbulence intensity. J Xi’an Jiaotong Univ. 2018;52(1):47–53.Search in Google Scholar

[17] Zhang WX, Liu ZS, Yang X, Liu Z, Feng ZP. Effects of mass flow ratio and film hole orientation angle on turbine endwall film cooling characteristics. J Xi’an Jiaotong Univ. 2021;55(4):107–15.Search in Google Scholar

[18] Dai HW, Zhang JH, Ren YY, Liu NH, Lin JW. Effect of cooling hole configurations on combustion and heat transfer in an aero-engine combustor. Appl Therm Eng. 2021;182:115664.Search in Google Scholar

[19] Li WP, Yang LJ. Research and analysis of cooling performance of combustion liner in a reverse-flow combustor. Acta Aeronaut et Astronaut Sin. 2023;44(9):127326.Search in Google Scholar

[20] He X. Performance analysis and structure optimization design of multi-point direct combustion chamber. Tianjin: Civil Aviation University of China. 2020.Search in Google Scholar
Received: 2024-01-22
Revised: 2024-05-05
Accepted: 2024-07-23
Published Online: 2024-08-21

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
  3. Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
  4. High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
  5. Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
  6. Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
  7. Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
  8. The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
  9. Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
  10. A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
  11. Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
  12. Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
  13. Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
  14. Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
  15. Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
  16. Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
  17. Chaotic control problem of BEC system based on Hartree–Fock mean field theory
  18. Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
  19. Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
  20. Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
  21. Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
  22. Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
  23. Model of conversion of flow from confined to unconfined aquifers with stochastic approach
  24. Study of fractional variable-order lymphatic filariasis infection model
  25. Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
  26. Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
  27. Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
  28. Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
  29. Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
  30. Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
  31. Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
  32. A two-stage framework for predicting the remaining useful life of bearings
  33. Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
  34. Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
  35. Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
  36. In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
  37. Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
  38. Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
  39. A comparative analysis of shielding effectiveness in glass and concrete containers
  40. Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
  41. Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
  42. Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
  43. Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
  44. Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
  45. Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
  49. Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
  55. Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
  56. An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
  57. CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
  58. Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
  59. A short report on a probability-based interpretation of quantum mechanics
  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
  62. Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
  64. A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
  65. Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
  66. Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
  67. Thermal analysis of extended surfaces using deep neural networks
  68. Steady-state thermodynamic process in multilayered heterogeneous cylinder
  69. Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
  70. Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
  71. Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
  72. The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
  74. Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
  77. Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
  79. Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
  81. New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
  82. Physical aspects of quantile residual lifetime sequence
  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
  91. New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
  93. Inflation and the principle of equivalence
  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
  97. Photon balance in the fiber laser model
  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
https://doi.org/10.1515/phys-2024-0072
Keywords for this article
combustor liner; slot depth; average temperature; cooling efficiency
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
  3. Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
  4. High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
  5. Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
  6. Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
  7. Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
  8. The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
  9. Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
  10. A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
  11. Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
  12. Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
  13. Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
  14. Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
  15. Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
  16. Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
  17. Chaotic control problem of BEC system based on Hartree–Fock mean field theory
  18. Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
  19. Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
  20. Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
  21. Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
  22. Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
  23. Model of conversion of flow from confined to unconfined aquifers with stochastic approach
  24. Study of fractional variable-order lymphatic filariasis infection model
  25. Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
  26. Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
  27. Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
  28. Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
  29. Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
  30. Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
  31. Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
  32. A two-stage framework for predicting the remaining useful life of bearings
  33. Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
  34. Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
  35. Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
  36. In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
  37. Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
  38. Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
  39. A comparative analysis of shielding effectiveness in glass and concrete containers
  40. Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
  41. Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
  42. Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
  43. Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
  44. Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
  45. Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
  49. Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
  55. Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
  56. An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
  57. CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
  58. Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
  59. A short report on a probability-based interpretation of quantum mechanics
  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
  62. Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
  64. A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
  65. Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
  66. Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
  67. Thermal analysis of extended surfaces using deep neural networks
  68. Steady-state thermodynamic process in multilayered heterogeneous cylinder
  69. Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
  70. Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
  71. Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
  72. The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
  74. Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
  77. Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
  79. Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
  81. New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
  82. Physical aspects of quantile residual lifetime sequence
  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
  91. New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
  93. Inflation and the principle of equivalence
  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
  97. Photon balance in the fiber laser model
  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 15.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2024-0072/html
Scroll to top button