# Preliminary Research on a High Thrust-to-Weight Ratio of Double-Sided Composite Impeller Microturbine Engine

Authors: Cheng Zhang; Bei Yang; Yun Wang; Gaoxing Tu
Journal: International Journal of Aerospace Engineering
 (2021)

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## Abstract

In some situations, the improvement of the thrust-to-weight ratio (TWR) of microturbine engines (MTEs) for energy-, economic-, and environment-related reasons can be achieved for military or civilian purposes. However, due to limitations of existing traditional MTE technology, it is difficult to meet the key requirements of small aircraft for high energy/power density and low-cost power, especially for long-endurance drone swarms. To address these problems, a novel compact concept of a high-TWR of MTE with a double-sided composite impeller (DSCI) is proposed in this research. First, the principle and structure of the concept are explained through theoretical analysis, and its potential advantages are discussed. Second, the DSCI is analyzed at the top level, and the design principle and important parameters are discussed. The DSCI and supporting jet engine are preliminarily designed. Then, their weight is estimated. Finally, theoretical analytical and numerical simulations are used to preliminarily research the performance parameters of DSCI jet engine at the design point, and the parameters are discussed. These calculations showed encouraging results, with all components of the DSCI jet engine meeting matching characteristics. Compared to the JetCat P500-PRO-GH, the DSCI jet engine has a 39.4% increase in TWR and a 36.82% decrease in specific fuel consumption (sfc). This study lays a foundation for the development of high energy/power density MTEs in the future.


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## Body

## 1. Introduction

Reference [1] presented the main trends of research into microturbine engines. Currently, the MTE is usually defined as an engine with a thrust less than 100 daN and mainly includes to military/civilian applications, such as the propulsion systems of small aircraft, the power of target missiles and cruise missiles, the portable energy of individual combat, and the auxiliary power unit (APU) of large aircraft [2–5]. The propulsion systems of this mechanical equipment have two important requirements, namely, long endurance and high energy/power density. As two important performance parameters, the thrust-to-weight ratio (TWR) and specific fuel consumption (sfc) are related to the two requirements. Several traditional techniques, such as increasing the overall pressure ratio (OPR), turbine inlet total temperature, and component efficiency, can improve the TWR and sfc. However, with the rapid development of aircraft performance, these parameters have recently faced technological limitations, and it is becoming less advantageous to increase the thermal efficiency and specific thrust for MTEs. However, reducing the weight of the structure, introducing impingement cooling technology, and using heat recovery technology are three appropriate methods for overcoming these limitations.The traditional gas generator consists of a single-stage centrifugal compressor, an annular combustor, and a single-stage axial turbine. Based on the innovative idea that a compact structure can reduce the weight of MTEs, United Technologies Corporation has developed compact MTEs with back-to-back single-stage centrifugal compressor and radial turbine, such as the TJ-50, TJ-90, and other products, which have significantly improvedTWR and are cost-effective [6]. References [7–10] demonstrate that the current research hot spot is the pursuit of compact structures and high energy/power density MTEs.From this perspective, using the idea of a compact structure and thermodynamic cycle fusion, along with metal additive manufacturing technology, a double-sided composite impeller (DSCI) and its application to the propulsion system are proposed. The DSCI consists of a double-sided centrifugal compressor and a hollow-tip turbine (turbine) as a potential solution for a high energy/power density MTE [11]. The turbine has the same number of blades as the centrifugal compressor.Aerodynamic and thermodynamic analyses of such a DSCI and its propulsion system were conducted to verify its potential in increasing theTWR and turbine inlet total temperature. The performance parameters of the DSCI jet engine and all component matching characteristics were numerically simulated and theoretically analyzed through the RANS-based CFD method. As a demonstration, a typical MTE was selected as the prototype and compared with the DSCI jet engine. This study is expected to provide the necessary technical basis for the development of high-TWR microturbine engine technology in the future.


## 2. Principle of the DSCI and Its Application to a High-TWR Propulsion System

### 2.1. Principle and Structure of the DSCI

Figure1 illustrates the structure of the DSCI. The DSCI consists of a double-sided centrifugal compressor driven by a hollow-tip turbine mounted at the double-sided centrifugal compressor tip. The hollow-tip turbine can achieve a positive circumferential velocity at a high spool speed. The two parts are attached to each other using a structural and aerodynamic design. The principle of the DSCI is shown in Figure 2 and is as follows. First, the centrifugal compressor breathes air from the atmosphere. Compressed air flows into the hollow-tip turbine inside and is further compressed using the principle of centrifugal supercharging. The high-pressure air is mixed with fuel in the reverse-flow annular combustor and combusted by a flame ignitor. Combusted hot gas expands in the hollow turbine guide and hollow-tip turbine outside, and the jet rotates at the hollow-tip turbine outlet. Rotary jet exhaust gives torque to the DSCI and supplies torque to the centrifugal compressor. The same process applies to the rear intake air. The blade numbers of the centrifugal compressor and the hollow-tip turbine must be the same to provide structural consistency and reliability.Figure 1
3D model of the DSCI rotor.Figure 2
Principle of the DSCI rotor.The DSCI rotor consists of a double-sided centrifugal compressor (two centrifugal compressors are fixed back-to-back), a hollow-tip turbine and two round hubs mounted at the double-sided centrifugal compressor tip, and a blade shroud located at the turbine tip. Through additive manufacturing technology, all parts of the DSCI rotor are manufactured in an integrated manner. The inside profile of the turbine is designed as a tubular diffuser structure. Additionally, the outside profile of the turbine maintains an axial turbine design.


### 2.2. Concept of the DSCI Jet Engine

DSCI jet engines are mainly applied to the power of missiles or target bombs. Figure3 depicts a preliminary jet propulsion system that adapts the DSCI. The propulsion system primarily consists of four components: (1) a starting component; (2) a rotating component; (3) a casing component; and (4) an inlet-exhaust component. Such a design has already been demonstrated in a Chinese patent [12].Figure 3
Structure of the DCSI jet engine.As mentioned, the principle of the DSCI rotor is systematically analyzed. However, the principle of other components can be clarified as follows (Figure4):
(1)
To spin up the DSCI rotor when the DSCI jet engine starts, the starting electric motor is connected to the DSCI by a magnetic clutch and main shaft. This motor can spin the DSCI up to 26,000 rpm. During spin up, the magnetic clutch transmits torque from the motor to the DSCI rotor. When spin up is completed, the clutch separates the motor and the DSCI rotor(2)
The high-pressure gas from inside the hollow-tip turbine is separated into two streams in the casing. The main part of the air directly flows into the reverse-flow annular combustor for stable combustion. The remaining air flows into the reverse-flow annular combustor after it exchanges heat with the high-temperature gas through the hollow turbine guide wall. This process prevents the reverse-flow annular combustor, prevents the turbine wall from overheating, and improves the life and reliability of the DSCI(3)
The DSCI jet engine uses a double fulcrum support method. The specific installation position requires that two bearings be installed to support the rotor components in the inlet guide vane.Figure 4
Principle of the DCSI jet engine [11].


### 2.3. Concept of the Gas-Driven Propeller DSCI Engine

The gas-driven propeller DSCI engine is a compact concept that further integrates a traditional turboprop engine with the DSCI jet engine and can be widely used to power expendable aircraft and drone swarms. Figure5 shows a gas-driven propeller system that integrates the DSCI. The system includes 5 components: (1) a starting component; (2) a rotating component I (DSCI); (3) a casing component; (4) an inlet-exhaust component; and (5) a rotating component II (gas-driven propeller). Such a design has already been demonstrated in a Chinese utility model patent [13]. For the concept of the gas-driven propeller DSCI engine, only a brief introduction is made here, and an in-depth study is not presented.Figure 5
Structure of the gas-driven propeller DSCI engine.There are many similarities in principle and structure between the gas-driven propeller DSCI engine and the DCSI jet engine, but there are also some differences, which are described as follows:(1)
The gas-driven propeller is also an aerodynamic component like a DSCI with three parts: the root turbine, the hub, and the propeller. The root turbine is radially connected with the propeller through the hub. Unlike the DSCI, the gas-driven propeller is not connected to the main shaft but is mounted to the nozzle through two sets of thrust bearings. This is a bit like a shaftless pump, as shown in Figure5(2)
To spin up the gas-driven propeller when the engine starts, the root turbine must be fixedly connected to the propeller through the hub. The root turbine is driven by the residual heat discharged from the DSCI rotor to provide power for the propeller. Meanwhile, owing to the torque balance, the root turbine plays a role similar to a reduction gearbox, namely, the aerodynamic reducer in Figure6 [14](3)
There are two rows of circumferential array rear intake pipes before and after the gas-driven propeller. The rear intake pipe, nozzle, and fairing cone are also integrated using additive manufacturing technology. Rear intake pipe I is located before the gas-driven propeller, which is located before rear intake pipe II as shown in Figure5. In addition to satisfying some of the rear intake conditions, rear intake pipe I also plays an important role as the turbine guide for driving the root turbine. The profile of rear intake pipe II is designed to be elliptical, which not only meets the rear intake condition requirements but also actively guides the airflow at the outlet of the root turbine(4)
The gas-driven propeller DSCI engine adopts three fulcrum support schemes. Bearings are provided on the inlet guide vane and the rear inlet guide vane to support rotor component I (DSCI). Two rows of thrust bearings are arranged at the front and rear under the hub of the gas-driven propeller, and they are seamlessly connected with the nozzle to support the gas-driven propeller.Figure 6
Principle of the gas-driven propeller DSCI engine.Through the preliminary analysis of the gas-driven propeller DSCI engine, the gas-driven propeller not only achieves power as a propulsion component but also replaces the reduction gearbox to achieve weight reduction as an aerodynamic reducer. Compared with the traditional shaft output power engine, there is not only a greater reduction in the axial size but also an obvious advantage in the structural weight. In addition, it is conducive to the reliability and starting characteristics of MTEs.As has been mentioned, compared with the traditional MTEs, the DSCI engine has the following characteristics:(1)
Since the axial size of the DSCI engine has been greatly reduced, the coaxiality and shock absorption are good(2)
The DSCI adopts compact structure and thermal fusion characteristics, which not only cool the turbine but also recover exhaust heat. On the other hand, the DSCI improves the thermal efficiency of MTEs and provides for potential development of low-cost, lightweight materials, or increasing the turbine inlet total temperature(3)
The DSCI engine has a compact structure, which reduces the structural weight and significantly improves theTWR/PWR(4)
The DSCI engine adopts the fulcrum support scheme to keep the bearing away from the high-temperature environment, which is beneficial for improving the life and reliability of the bearing(5)
With the help of additive manufacturing technology, installation of a DSCI jet engine can be more convenient, and a reduction in the number of parts can make the structure more reliable.


## 2.1. Principle and Structure of the DSCI

Figure1 illustrates the structure of the DSCI. The DSCI consists of a double-sided centrifugal compressor driven by a hollow-tip turbine mounted at the double-sided centrifugal compressor tip. The hollow-tip turbine can achieve a positive circumferential velocity at a high spool speed. The two parts are attached to each other using a structural and aerodynamic design. The principle of the DSCI is shown in Figure 2 and is as follows. First, the centrifugal compressor breathes air from the atmosphere. Compressed air flows into the hollow-tip turbine inside and is further compressed using the principle of centrifugal supercharging. The high-pressure air is mixed with fuel in the reverse-flow annular combustor and combusted by a flame ignitor. Combusted hot gas expands in the hollow turbine guide and hollow-tip turbine outside, and the jet rotates at the hollow-tip turbine outlet. Rotary jet exhaust gives torque to the DSCI and supplies torque to the centrifugal compressor. The same process applies to the rear intake air. The blade numbers of the centrifugal compressor and the hollow-tip turbine must be the same to provide structural consistency and reliability.Figure 1
3D model of the DSCI rotor.Figure 2
Principle of the DSCI rotor.The DSCI rotor consists of a double-sided centrifugal compressor (two centrifugal compressors are fixed back-to-back), a hollow-tip turbine and two round hubs mounted at the double-sided centrifugal compressor tip, and a blade shroud located at the turbine tip. Through additive manufacturing technology, all parts of the DSCI rotor are manufactured in an integrated manner. The inside profile of the turbine is designed as a tubular diffuser structure. Additionally, the outside profile of the turbine maintains an axial turbine design.


## 2.2. Concept of the DSCI Jet Engine

DSCI jet engines are mainly applied to the power of missiles or target bombs. Figure3 depicts a preliminary jet propulsion system that adapts the DSCI. The propulsion system primarily consists of four components: (1) a starting component; (2) a rotating component; (3) a casing component; and (4) an inlet-exhaust component. Such a design has already been demonstrated in a Chinese patent [12].Figure 3
Structure of the DCSI jet engine.As mentioned, the principle of the DSCI rotor is systematically analyzed. However, the principle of other components can be clarified as follows (Figure4):
(1)
To spin up the DSCI rotor when the DSCI jet engine starts, the starting electric motor is connected to the DSCI by a magnetic clutch and main shaft. This motor can spin the DSCI up to 26,000 rpm. During spin up, the magnetic clutch transmits torque from the motor to the DSCI rotor. When spin up is completed, the clutch separates the motor and the DSCI rotor(2)
The high-pressure gas from inside the hollow-tip turbine is separated into two streams in the casing. The main part of the air directly flows into the reverse-flow annular combustor for stable combustion. The remaining air flows into the reverse-flow annular combustor after it exchanges heat with the high-temperature gas through the hollow turbine guide wall. This process prevents the reverse-flow annular combustor, prevents the turbine wall from overheating, and improves the life and reliability of the DSCI(3)
The DSCI jet engine uses a double fulcrum support method. The specific installation position requires that two bearings be installed to support the rotor components in the inlet guide vane.Figure 4
Principle of the DCSI jet engine [11].


## 2.3. Concept of the Gas-Driven Propeller DSCI Engine

The gas-driven propeller DSCI engine is a compact concept that further integrates a traditional turboprop engine with the DSCI jet engine and can be widely used to power expendable aircraft and drone swarms. Figure5 shows a gas-driven propeller system that integrates the DSCI. The system includes 5 components: (1) a starting component; (2) a rotating component I (DSCI); (3) a casing component; (4) an inlet-exhaust component; and (5) a rotating component II (gas-driven propeller). Such a design has already been demonstrated in a Chinese utility model patent [13]. For the concept of the gas-driven propeller DSCI engine, only a brief introduction is made here, and an in-depth study is not presented.Figure 5
Structure of the gas-driven propeller DSCI engine.There are many similarities in principle and structure between the gas-driven propeller DSCI engine and the DCSI jet engine, but there are also some differences, which are described as follows:(1)
The gas-driven propeller is also an aerodynamic component like a DSCI with three parts: the root turbine, the hub, and the propeller. The root turbine is radially connected with the propeller through the hub. Unlike the DSCI, the gas-driven propeller is not connected to the main shaft but is mounted to the nozzle through two sets of thrust bearings. This is a bit like a shaftless pump, as shown in Figure5(2)
To spin up the gas-driven propeller when the engine starts, the root turbine must be fixedly connected to the propeller through the hub. The root turbine is driven by the residual heat discharged from the DSCI rotor to provide power for the propeller. Meanwhile, owing to the torque balance, the root turbine plays a role similar to a reduction gearbox, namely, the aerodynamic reducer in Figure6 [14](3)
There are two rows of circumferential array rear intake pipes before and after the gas-driven propeller. The rear intake pipe, nozzle, and fairing cone are also integrated using additive manufacturing technology. Rear intake pipe I is located before the gas-driven propeller, which is located before rear intake pipe II as shown in Figure5. In addition to satisfying some of the rear intake conditions, rear intake pipe I also plays an important role as the turbine guide for driving the root turbine. The profile of rear intake pipe II is designed to be elliptical, which not only meets the rear intake condition requirements but also actively guides the airflow at the outlet of the root turbine(4)
The gas-driven propeller DSCI engine adopts three fulcrum support schemes. Bearings are provided on the inlet guide vane and the rear inlet guide vane to support rotor component I (DSCI). Two rows of thrust bearings are arranged at the front and rear under the hub of the gas-driven propeller, and they are seamlessly connected with the nozzle to support the gas-driven propeller.Figure 6
Principle of the gas-driven propeller DSCI engine.Through the preliminary analysis of the gas-driven propeller DSCI engine, the gas-driven propeller not only achieves power as a propulsion component but also replaces the reduction gearbox to achieve weight reduction as an aerodynamic reducer. Compared with the traditional shaft output power engine, there is not only a greater reduction in the axial size but also an obvious advantage in the structural weight. In addition, it is conducive to the reliability and starting characteristics of MTEs.As has been mentioned, compared with the traditional MTEs, the DSCI engine has the following characteristics:(1)
Since the axial size of the DSCI engine has been greatly reduced, the coaxiality and shock absorption are good(2)
The DSCI adopts compact structure and thermal fusion characteristics, which not only cool the turbine but also recover exhaust heat. On the other hand, the DSCI improves the thermal efficiency of MTEs and provides for potential development of low-cost, lightweight materials, or increasing the turbine inlet total temperature(3)
The DSCI engine has a compact structure, which reduces the structural weight and significantly improves theTWR/PWR(4)
The DSCI engine adopts the fulcrum support scheme to keep the bearing away from the high-temperature environment, which is beneficial for improving the life and reliability of the bearing(5)
With the help of additive manufacturing technology, installation of a DSCI jet engine can be more convenient, and a reduction in the number of parts can make the structure more reliable.


## 3. Preliminary Design of the DSCI and Its Jet Engine

### 3.1. Preliminary Design Assumptions

To demonstrate the effects of DSCI, a preliminary design based on traditional MTEs. The first step for the preliminary design is to determine the top-level parameters of the DSCI jet engine. These parameters determine the performance of the DSCI jet engine and are used to guide the design of all components. According to thermodynamics theory, the performance parameters of the DSCI and its engine are approximately estimated if the following assumptions are introduced:(1)
For analysis convenience, the auxiliary impeller inlet conditions (the air breathed by centrifugal compressor through the rear intake pipe) are simplified to be the same as the main impeller inlet conditions(2)
Due to the complex structure of the reverse-flow annular combustor, it is simplified to an ideal state. The combustor outlet total temperatureTt4 is 1150 K. According to empirical coefficients and theoretical formulas, other cross-sectional parameters of the combustor can be obtained(3)
For analysis convenience, these parameters are set by default to be unchanged with static temperature: the air isentropic indexk is 1.4; the air constant R is 287; the gas isentropic index k′ is 1.33; and the gas constant R′ is 288(4)
To avoid introducing new problems, the hollow turbine guide is simplified to the turbine inlet absolute velocity boundary condition(5)
For analysis convenience, a convergent nozzle is used.From these top-level parameters for the DSCI jet engine, the design parameters of each component can be calculated, such as the mass flow rate, total pressure ratio and efficiency. First, in accordance with the top-level parameters listed in Table1, the aerodynamic parameters of the centrifugal compressor can be predictively calculated (considering the design size of a centrifugal compressor) [11]. Second, based on the top-level parameters listed in Table 2, the aerodynamic parameters of the turbine can be predictively calculated (considering double-sided centrifugal compressor power). Finally, with the help of these parameters, we can calculate the overall parameters of the DSCI and obtain its performance.Table 1
Top-level parameters of a 230 N microturbojet engine [11].
ParametersValueTotal pressure ratio3.6Mass flow (kg/s)0.45Turbine inlet total temperature (K)1023Rotating speed,n (r/min)100000Table 2
Top-level parameter parameters of Jet-Cat P500-PRO-GH.
ParametersValueDiameter (mm)178.6Length (mm)419Mass flow (kg/s)0.9Rotating speed (r/min)80000Total pressure ratio3.6Turbine outlet total temperature (K)1013Regarding thermodynamic analysis, Figure7 depicts the cross-section annotations of the DCSI jet engine.Figure 7
Cross-section annotations of the DCSI jet engine.


### 3.2. Preliminary Design Profiles of the DSCI Rotor

The design processes of the double-sided centrifugal compressor and the hollow-tip turbine are the same as those of other turbomachines, except the matching design process. These processes follow a preliminary design, throughflow design, 2D blading design, and 3D blading design [15]. Notably, the matching design process is necessary to meet the four matching balance conditions, as in the traditional gas generator shown in Figure 8 [16].
(1)
Rotation speed balance: it is known that the turbine and the double-sided centrifugal compressor are radially connected, so the conditions are naturally met(2)
Flow balance: the sum of double-sided centrifugal compressor air flow and combustion chamber fuel flow is equal to turbine gas flow. The DSCI engine flow is continuous(3)
Power balance: the power required by the double-sided centrifugal compressor is equal to the turbine output power multiplied by the mechanical efficiency(4)
Pressure balance: the pressures between each section should be linked to each other in the DSCI engine.Figure 8
Flow chart of operating conditions of the gas generator components.Since the hollow-tip turbine is mounted at the tip of the double-sided centrifugal compressor, the two parts are attached to each other using a structural and aerodynamic design. Several matching methods must be emphasized as follows:(1)
The number of blades of the double-sided centrifugal compressor and hollow-tip turbine must be equal (considering the feasibility of aerodynamics and rotor strength)(2)
As the diameter of the rotor increases at a given circumferential speed, the rotating speed should be reduced accordingly (the maximum circumferential speed of the rotor must be lower than 550 m/s)(3)
The turbine has a skewed blade to adapt the diameter changes from hub to shroud (considering the turning loss in the high-pressure air inside the turbine)(4)
The profiles of the turbine must adopt the design rules for blade transition sections (considering that the exit section of the double-sided centrifugal compressor is rectangular).Profiles of the DSCI are depicted in Figure9. In the preliminary design, since the turbine needs to meet the high load, the shape of the turbine must be designed as an impact turbine with a counterforce. On the other hand, the turbine is different from the conventional axial turbine in the transition section (defined from the hub to the 0.3 span). The inside profiles of the turbine adopt a similar tubular diffuser structure [17]. All the blades are stacked near the center of gravity, and the 3D structure of the double-sided centrifugal compressor and hollow-tip turbine can be seen in Figure 10.Figure 9
Section graphs of the DSCI (units: mm; 0% represents the hub; 100% indicates the tip). (a) Centrifugal compressor. (b) Hollow-tip turbine.
(a)(b)Figure 10
3D model of the DSCI.According to the above top-level parameters and assumptions, using the design parameters of the DSCI listed in Table3, the design performance of the DSCI jet engine can be calculated.Table 3
Design parameters of DSCI.
Design parametersValuesDouble-sided centrifugal compressorInside/outside the turbineπk∗/πT∗3.52.1/2.5ηk∗/ηT∗0.850.84/0.9n (104r/min)98Wa/Wg (kg/s)0.90.84/0.85r1 (mm)33.749.5r2 (mm)49.564Z5628ε (mm)0.10h(mm)——14.5β1k (°)——60β2k (°)5325cmax (mm)——24.6δ (mm)10.3


### 3.3. Preliminary Design of the DSCI Jet Engine

To facilitate the assessment of the structural weight with the DSCI jet engine, the engine model is preliminarily designed, as shown in Figure11. By evaluating the weight of each part in the engine, the DSCI jet engine weight can be predicted, as shown in Table 4.Figure 11
The structure of the DSCI jet engine.Table 4
Weight parameters of DSCI jet engine.
Part nameWeightG (kg)MaterialDSCI1.563GH93Main shaft0.027GH93Casing and combustor1.081NAS800Nozzle and rectifier cone0.625NAS800Starting dynamo0.787——Bearing0.01Babbitt metalFuel injection ring0.023NAS800Oil pump0.065——Oil filter0.02——Flame ignitor0.01——Inlet guide vane0.028SteelDSCI jet engine4.239——The preliminary design of the DSCI rotor and its supporting DSCI jet engine was carried out in the previous section, but the feasibility of DSCI and the performance parameters of the DSCI jet engine need to be verified. These topics will be discussed subsequently.


## 3.1. Preliminary Design Assumptions

To demonstrate the effects of DSCI, a preliminary design based on traditional MTEs. The first step for the preliminary design is to determine the top-level parameters of the DSCI jet engine. These parameters determine the performance of the DSCI jet engine and are used to guide the design of all components. According to thermodynamics theory, the performance parameters of the DSCI and its engine are approximately estimated if the following assumptions are introduced:(1)
For analysis convenience, the auxiliary impeller inlet conditions (the air breathed by centrifugal compressor through the rear intake pipe) are simplified to be the same as the main impeller inlet conditions(2)
Due to the complex structure of the reverse-flow annular combustor, it is simplified to an ideal state. The combustor outlet total temperatureTt4 is 1150 K. According to empirical coefficients and theoretical formulas, other cross-sectional parameters of the combustor can be obtained(3)
For analysis convenience, these parameters are set by default to be unchanged with static temperature: the air isentropic indexk is 1.4; the air constant R is 287; the gas isentropic index k′ is 1.33; and the gas constant R′ is 288(4)
To avoid introducing new problems, the hollow turbine guide is simplified to the turbine inlet absolute velocity boundary condition(5)
For analysis convenience, a convergent nozzle is used.From these top-level parameters for the DSCI jet engine, the design parameters of each component can be calculated, such as the mass flow rate, total pressure ratio and efficiency. First, in accordance with the top-level parameters listed in Table1, the aerodynamic parameters of the centrifugal compressor can be predictively calculated (considering the design size of a centrifugal compressor) [11]. Second, based on the top-level parameters listed in Table 2, the aerodynamic parameters of the turbine can be predictively calculated (considering double-sided centrifugal compressor power). Finally, with the help of these parameters, we can calculate the overall parameters of the DSCI and obtain its performance.Table 1
Top-level parameters of a 230 N microturbojet engine [11].
ParametersValueTotal pressure ratio3.6Mass flow (kg/s)0.45Turbine inlet total temperature (K)1023Rotating speed,n (r/min)100000Table 2
Top-level parameter parameters of Jet-Cat P500-PRO-GH.
ParametersValueDiameter (mm)178.6Length (mm)419Mass flow (kg/s)0.9Rotating speed (r/min)80000Total pressure ratio3.6Turbine outlet total temperature (K)1013Regarding thermodynamic analysis, Figure7 depicts the cross-section annotations of the DCSI jet engine.Figure 7
Cross-section annotations of the DCSI jet engine.


## 3.2. Preliminary Design Profiles of the DSCI Rotor

The design processes of the double-sided centrifugal compressor and the hollow-tip turbine are the same as those of other turbomachines, except the matching design process. These processes follow a preliminary design, throughflow design, 2D blading design, and 3D blading design [15]. Notably, the matching design process is necessary to meet the four matching balance conditions, as in the traditional gas generator shown in Figure 8 [16].
(1)
Rotation speed balance: it is known that the turbine and the double-sided centrifugal compressor are radially connected, so the conditions are naturally met(2)
Flow balance: the sum of double-sided centrifugal compressor air flow and combustion chamber fuel flow is equal to turbine gas flow. The DSCI engine flow is continuous(3)
Power balance: the power required by the double-sided centrifugal compressor is equal to the turbine output power multiplied by the mechanical efficiency(4)
Pressure balance: the pressures between each section should be linked to each other in the DSCI engine.Figure 8
Flow chart of operating conditions of the gas generator components.Since the hollow-tip turbine is mounted at the tip of the double-sided centrifugal compressor, the two parts are attached to each other using a structural and aerodynamic design. Several matching methods must be emphasized as follows:(1)
The number of blades of the double-sided centrifugal compressor and hollow-tip turbine must be equal (considering the feasibility of aerodynamics and rotor strength)(2)
As the diameter of the rotor increases at a given circumferential speed, the rotating speed should be reduced accordingly (the maximum circumferential speed of the rotor must be lower than 550 m/s)(3)
The turbine has a skewed blade to adapt the diameter changes from hub to shroud (considering the turning loss in the high-pressure air inside the turbine)(4)
The profiles of the turbine must adopt the design rules for blade transition sections (considering that the exit section of the double-sided centrifugal compressor is rectangular).Profiles of the DSCI are depicted in Figure9. In the preliminary design, since the turbine needs to meet the high load, the shape of the turbine must be designed as an impact turbine with a counterforce. On the other hand, the turbine is different from the conventional axial turbine in the transition section (defined from the hub to the 0.3 span). The inside profiles of the turbine adopt a similar tubular diffuser structure [17]. All the blades are stacked near the center of gravity, and the 3D structure of the double-sided centrifugal compressor and hollow-tip turbine can be seen in Figure 10.Figure 9
Section graphs of the DSCI (units: mm; 0% represents the hub; 100% indicates the tip). (a) Centrifugal compressor. (b) Hollow-tip turbine.
(a)(b)Figure 10
3D model of the DSCI.According to the above top-level parameters and assumptions, using the design parameters of the DSCI listed in Table3, the design performance of the DSCI jet engine can be calculated.Table 3
Design parameters of DSCI.
Design parametersValuesDouble-sided centrifugal compressorInside/outside the turbineπk∗/πT∗3.52.1/2.5ηk∗/ηT∗0.850.84/0.9n (104r/min)98Wa/Wg (kg/s)0.90.84/0.85r1 (mm)33.749.5r2 (mm)49.564Z5628ε (mm)0.10h(mm)——14.5β1k (°)——60β2k (°)5325cmax (mm)——24.6δ (mm)10.3


## 3.3. Preliminary Design of the DSCI Jet Engine

To facilitate the assessment of the structural weight with the DSCI jet engine, the engine model is preliminarily designed, as shown in Figure11. By evaluating the weight of each part in the engine, the DSCI jet engine weight can be predicted, as shown in Table 4.Figure 11
The structure of the DSCI jet engine.Table 4
Weight parameters of DSCI jet engine.
Part nameWeightG (kg)MaterialDSCI1.563GH93Main shaft0.027GH93Casing and combustor1.081NAS800Nozzle and rectifier cone0.625NAS800Starting dynamo0.787——Bearing0.01Babbitt metalFuel injection ring0.023NAS800Oil pump0.065——Oil filter0.02——Flame ignitor0.01——Inlet guide vane0.028SteelDSCI jet engine4.239——The preliminary design of the DSCI rotor and its supporting DSCI jet engine was carried out in the previous section, but the feasibility of DSCI and the performance parameters of the DSCI jet engine need to be verified. These topics will be discussed subsequently.


## 4. Thermodynamic Calculation and Analysis of the DSCI Jet Engine under Design Parameters

Currently, computational fluid dynamics (CFD) plays an important role in the aerodynamic design of turbomachines. To estimate the preliminary aerodynamic design of the DSCI, the DSCI rotor, an innovative and uncertain component, is certified through CFD and theoretical analysis. In addition, the performance parameters of the DSCI jet engine are also evaluated and compared with the JetCat P500-PRO-GH.


### 4.1. CFD Method

The ANSYS CFX commercial CFD software, including the meshing module ANSYS meshing and computing module CFX-TASCflow, was used for numerical simulation.The fluid domains of the DSCI inside, the turbine outside, and the solid domain of the turbine are meshed by ANSYS meshing. The turbine inside contains 1.44 million fluid domain grids, the turbine outside contains 3.09 million fluid domain grids, the turbine contains 2.75 million solid domain grids, and the double-sided centrifugal compressor contains 3.14 million fluid domain grids, as shown in Figure12. Through grid quality inspection, it is found that the maximum skewness is lower than 0.95 and that the average orthogonal quality is higher than 0.75, which indicates that these grids can be used for numerical simulation. Theoretically, the accuracy of a tetrahedral mesh (considering first-order elements) may be slightly lower when compared with a hexahedral mesh, but its self-adaptive mesh technology can be applied to any complex geometry and provide for mesh refinement of high stress gradient parts. The advantages of automatic grid encryption save cost and time.Figure 12
Each domain grid of the DSCI. (a) Outside the turbine fluid domain. (b) Inside the turbine fluid domain grids. (c) Turbine solid domain grids. (d) Double-sided centrifugal compressor grids.
(a)(b)(c)(d)A steady-state model and high-resolution discretization scheme were used for simulations. The discretized form of Reynolds Averaged Navier-Stokes (RANS) equations was iteratively solved for the DSCI. Since the SST model is used in turbomachinery, in most cases, it requiresY+ to be very small (Y+<2). Therefore, the layer mesh quality requirement of the SST model is higher than that of the k-epsilon model. Reference [18] demonstrated that when the computational grid number is very large, the k-epsilon model is used as the turbulence model in simulating turbomachinery in order to relax the demand on computer memory and raise the efficiency. The calculated residuals converge below 10-5.The boundary conditions are listed in Table5 and are as follows: the nonsliding solid wall treatment method is used, except the fluid-solid interface is set to exchange heat [19, 20]; the DSCI surfaces are set rotating, except that the shroud is a static boundary; the double-sided centrifugal compressor inlet total pressure Pt1 is 101325 Pa; the double-sided centrifugal compressor inlet total temperature Tt1 is 288 K; the turbine inside outlet static pressure P3 is 212783 Pa; the turbine outside inlet total temperature Tt4 is 1150 K; the turbine outside inlet axial velocity component Ca4B is 149.5 m/s; the turbine outside inlet circumferential velocity component Cτ4B is 590 m/s; and the turbine outside outlet static pressure P5 is 202650 Pa.Table 5
The fluid domain boundary conditions of the DSCI inside and outside.
Boundary conditionsFluid domainsFluid domain of DSCI insideFluid domain of DSCI outsideInletTotal temperature, Total pressureTotal temperature, velocity componentsOutletStatic pressureStatic pressureTurbulence5%5%Based on the property parameters of the GH93 material listed in Table6 [21], the missing data can be calculated using the least squares method in MATLAB.Table 6
Properties of the GH93 material.
Static temperature, Kλ (W m-1 K-1)Cp (J kg-1 K-1)Density (g cm-3)37312.774678.1947314.4449457315.9952067317.5454777318.9757287320.6460097322.32626107323.99652117325.83679127327.88706137330.06733147332.47760The grid independency is examined via increasing the node number until the evaluated design point performance of turbomachines is essentially no longer changed. As Figure13 shows, the calculated efficiency and total pressure ratio of DSCI and turbine have converged with 4.58 million and 5.84 million grids, respectively, which are considered to grid size effect independent. Otherwise mentioned, the computation model grid number in the later calculations is about 10.42 million, as shown in Figure 14 [22–25].Figure 13
Grid independence verification of turbomachines. (a) DSCI. (b) Turbine.
(a)(b)Figure 14
Calculation model of the DSCI.


### 4.2. CFD Results and Discussions

#### 4.2.1. Compression Process

First, Figure15 displays several contours of the double-sided centrifugal compressor under the design point. From left to right, there are the auxiliary impeller and the main impeller. In accordance with the centrifugal pressurization principle, the static pressure gradually increases from the inlet to the outlet of the meridian channel in the double-sided centrifugal compressor, as shown in Figures 15(a) and 15(b).Figure 15
Several contours of the double-sided centrifugal compressor. (a) Static pressure. (b) Total pressure in Stn frame. (c) Relative Mach number. (d) Static entropy.
(a)(b)(c)(d)Second, since the inside shape of turbine is asymmetrical along the mirror plane in Figures15(c) and 15(d), the flow field of main impeller is different from that of auxiliary impeller.Finally, because the leakage vortex caused by the angle-of-attack induces tip clearance flow and blade radial shear flow, there are more high entropy values (low-momentum air) in the tip area of the double-sided centrifugal compressor. When the leakage vortex is extreme, it spreads to the main flow area of the impeller, leading to impeller compression difficulties and reduced efficiency.Figures16–18 show the blade-to-blade planes of the double-sided centrifugal compressor under the design point. From left to right, there are the main impeller and the auxiliary impeller. As the blade height increases, the aerodynamic load of the blade increases, as shown in Figure 16. Due to the influence of the high adverse pressure gradient at the tip of the centrifugal compressor, the tip leakage vortex is easily induced, and in severe cases, the impeller will stall in advance. Figures 17 and 18 further confirm the above analysis. In Figure 17, it can be observed that the main impeller has produced some stall clusters at the 0.9 span.Figure 16
Blade-to-blade plane of double-sided centrifugal compressor for static pressure. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 17
Blade-to-blade planes of double-sided centrifugal compressor for relative Mach number. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 18
Blade-to-blade planes of double-sided centrifugal compressor for static entropy. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)In summary, due to the influence of the downstream inside turbine, in the main and auxiliary impellers of the same size, the main impeller is closer to the surge point, so the compression capacity of the main impeller is better, but the tip flow loss is greater.The double-sided centrifugal compressor is defined as the first stage compression section in Figure15.First, when these two flows exit the double-sided centrifugal compressor, they will mix with each other, thereby resulting in the loss of mixture. Because the total pressure ratio and isentropic efficiency of the main and auxiliary impellers are different from each other, the compression performance of the double-sided centrifugal compressor cannot be estimated. Since these two flows exit the double-sided centrifugal compressor and enter the inside of the turbine at the same time, the inlet section of the turbine inside can be used as the calculated outlet section of the double-sided centrifugal compressor. The first stage compression section total pressure ratioπc1∗ is 2.901, and its isentropic efficiency ηc1∗ is 0.8538 as calculated by the numerical simulation results and the following formulas:
(1)πc1∗=Pt2Pt1,(2)ηc1∗=πc1∗k−1/k−1Tt2/Tt1−1,where Pt1 refers to the double-sided centrifugal compressor inlet total pressure, Tt1 refers to the double-sided centrifugal compressor inlet total temperature, Pt2 refers to the turbine inside inlet total pressure, and Tt2 refers to the turbine inside inlet total pressure.Second, since the turbine is also rotating at the same speed as the double-sided centrifugal compressor, the high-pressure air is also compressed inside the turbine. For ease of expression, this process is defined as the internal channel diffusion of the hollow-tip turbine. The total pressure ratio of this processπc2∗ is 2.053, and the isentropic efficiency ηc2∗ is 0.7081 as calculated by CFD.Finally, the OPR of the compression processπk∗ is 5.957, and the overall isentropic efficiency ηk∗ is 0.7617 by formulas (3) and (4):
(3)πk∗=πc1∗πc2∗,(4)ηk∗=πk∗k−1/k−1Tt3/Tt1−1,where Tt3 refers to the outlet total temperature inside the turbine and Tt1 refers to the total temperature of the double-sided centrifugal compressor inlet.The isentropic efficiency of any single-stage compressor is generally higher than that of a multistage compressor. In this section, since there is convection heat transfer inside and outside the turbine,ηc2∗ is far below ηk∗. Specifically, the high-temperature gas outside the turbine transfers heat to the high-pressure air that is being compressed in the turbine, resulting in ηc2∗ being lower than the overall isentropic efficiency ηk∗.Based on the above analysis, Table7 displays the cross-sectional parameters of the compression process. The compressor power Wk is 252.6 kJ/kg and is calculated by
(5)Wk=kk−1RTt1πk∗k−1/k−1/ηk∗.Table 7
Parameters of each section during compression.
ParametersSection positionSection 1Section 2Section 3Total pressurePt (Pa)101325293984603569Total temperatureTt (K)288407.989539.455Air mass flowWa (kg/s)0.840.840.84Total pressure ratioπc∗2.9012.053Isentropic efficiencyηc∗0.85380.7081


#### 4.2.2. Combustion Process

To avoid introducing new problems and a large number of calculations, the traditional reverse-flow annular combustor was adopted. The fuel-air ratiofb is 0.017 at Tt3 and Tt4, and the combustor heat balance equation can be written as
(6)fb=it4−it3ξbHf−I4+it3,whereit4, it3, and I4 can all be determined with a look-up table and Hf is 42900 kJ/kg [26].The fuel mass flowmf is 0.014 kg/s, and the gas mass flow Wg is 0.854 kg/s as calculated by the formulas for the fuel-air ratio and gas mass flow:
(7)mf=Wafb,(8)Wg=Wa+mf.Notably, for the total pressure loss in the combustor, the total pressure recovery coefficientσb is empirically given as 0.98. The combustor outlet total pressure Pt4 is 591498 Pa, as calculated by
(9)Pt4=σbPt3.


#### 4.2.3. Expansion Process (outside the Turbine)

After analyzing the combustion process, the expansion process needs to be further studied. The profile design of the hollow-tip turbine is different from that of a traditional turbine, especially the transition section. Therefore, it is necessary to study the flow field and characteristics of the turbine.Figure19 illustrates the static pressure contours of the turbine. High-temperature gas pressure is released in the turbine rotor channel and then drives rotor acceleration. Because the turbine root is part of the transition section and the circumferential velocity is small, the pressure drop ratio is small at the blade root, regardless of differing blade height.Figure 19
Static pressure contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure20 shows the relative Mach number contours of the turbine. The high-temperature gas accelerates and depressurizes in the turbine rotor channel and then drives the DSCI rotor to rotate. The maximum relative Mach number appears at the throat of the turbine, which corresponds to the low-pressure area in Figure 19, indicating that the turbine throat outlet section is supersonic and generates a set of shock waves. This set of expansion shock waves hit the trailing edge of the suction surface of the adjacent turbine blades and interfere with the boundary layer, causing more serious loss of the boundary layer. As the height of the turbine blade increases, this phenomenon becomes more prominent.Figure 20
Relative Mach number contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure21 shows the static entropy contours of the turbine channel. The change in the angle-of-attack causes the phenomenon of separated flow or even back flow in the transition section, namely, the loss of turbine profiles. Comparing the different blade heights, the high entropy value of the turbine is mainly distributed near the trailing edge of the suction surface. This indicates that the supersonic velocity of the throat section of the turbine produces a set of expansion shock waves. These waves hit the trailing edge of the suction surface of the adjacent turbine and interfere with the boundary layer, causing a serious loss of the boundary layer.Figure 21
Static entropy contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Based on the above, the loss of turbine profiles and the shock wave boundary layer interference loss are the main reasons for the decrease of the turbine efficiency.Figure22 shows the relative velocity vector contours of the turbine. There is a certain deflection angle between the inlet relative flow angle and the inlet geometry angle at the turbine root, namely, a large positive angle-of-attack. This indicates that there is flow separation at the leading edge of the suction surface. However, as the height of the turbine increases, the tangential velocity also increases, and the corresponding relative flow angle also increases. The reduction of the positive angle-of-attack causes the flow separation at the leading edge to weaken. For this kind of problem, further optimization is possible by twisting the turbine root in the later stage.Figure 22
Relative velocity vector contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure23 shows the static pressure distribution of the turbine. The static pressure load difference between the pressure surface and the suction surface is small at the 0.1 span of the turbine, which further illustrates that the expansion of the turbine transition section is a poor function. As the leaf height increases, the expansion function is improved. At the turbine leading edge, the static pressure load on the suction side is greater than that on the pressure side, indicating that it is not appropriate to set a sharp front edge contour shape. In the later stage, general antiforce axial turbines can be considered.Figure 23
Static pressure distribution of turbine (0% represents the hub; 100% indicates the tip).Figure24(a) displays the static temperature contours of the DSCI wall. Although the cooling coefficient inside the turbine is close to 1 and the high-pressure gas has a good cooling effect on the turbine wall, there is a local high temperature at the trailing edge of the blade and the hub of the double-sided centrifugal compressor due to the heat conduction in the solid. Thus, the high local temperature may slightly affect the compression and structural strength of the DSCI, which needs to be further researched.Figure 24
Static temperature field contours. (a) Static temperature field contour of the DSCI. (b) Static temperature field contour the turbine outside.
(a)(b)Figure24(b) displays the static temperature contour outside the turbine wall. The maximum higher temperature is mainly distributed at the tip of the leading and trailing edges, and the cooling effect is evident at the middle and root in the turbine. This shows that the high-pressure gas flows along the root to the tip of the turbine inside and impulsively cools the turbine wall. On the other hand, since the outlet velocity of the throat of the turbine outside is high, the cooling effect is also good. The cooling effect is not evident far away from the high-pressure gas.In addition, the maximum temperature of the turbine wall is only 840.35 K, which is far below the maximum temperature limit of the GH93 of 1088 K. This means that it not only provides the potential for increasing the turbine inlet total temperature but also provides room for development for the use of low-temperature, low-cost, and lightweight materials, such as titanium alloys and high-entropy alloys. From the perspective of lightweight materials, this shows that the structural weight of the engine can be further reduced, which is conducive to the improvement ofTWR.First, based on the previous assumption, the hollow turbine guide is simplified to the absolute inlet velocity boundary condition of the turbine. On the other hand, there is a certain total pressure loss in the actual hollow turbine guide, which cannot be ignored. The total pressure recovery coefficient of the hollow turbine guideσ4B is 0.972, and the hollow turbine guide outlet total pressure Pt4B is 574703 Pa, as calculated by
(10)Pt4B=σ4BPt4.Second, the total pressure drop ratio of the turbineπT∗ is 2.532, and the isentropic efficiency ηT∗ is 0.9088 based on numerical simulation. The results show that a turbine with a blade shroud can avoid tip leakage to a certain extent and improve the isentropic efficiency.Based on the above analysis, Table8 shows the cross-sectional parameters of the expansion process. The turbine power WT is 249.74 kJ/kg and can be expressed as
(11)WT=k′k′−1R′Tt41−1πT∗k′−1/k′ηT∗.Table 8
Parameters of each section during the expansion process.
ParametersSection positionSection 4Section 4BSection 5Total pressurePt (Pa)591498574703227010Total temperatureTt (K)11501150934.731Gas flowWg (kg/s)0.8540.8540.854Total pressure drop ratioπT∗2.532Isentropic efficiencyηT∗0.9088Finally, the compressor powerPC is 212.2 kW, and the turbine power PT is 212.2 kW as calculated by formulas (12) and (13). This means that the turbine power can meet the compression needs of the DSCI.
(12)PC=WkWa,(13)PT=WTWgηm,where the mechanical efficiency ηm is 0.995.Through the previous calculations, all components met the matching characteristics in the gas generator. Indispensably, according to the outlet parameters of the turbine, the performance and economic indicators of the DSCI jet engine can be analyzed and compared with the JetCat P500-PRO-GH of the same radial size.First, the nozzle working status needs to be judged in the above hypothesis. Regarding the nozzle total pressure recovery coefficientσnz, considering the loss along the nozzle and the total pressure loss caused by the rear intake pipe to the rectification of the turbine exhaust gas, the empirical coefficient σnz is 0.95.Second, the critical pressure drop ratio of the nozzleπcr,nz is 1.947, and the available pressure drop ratio πus,nz is 2.128, as calculated by
(14)πcr,nz=1.85/σnz,(15)πus,nz=Pt5/PH,wherePH is 101325 Pa.Comparing the critical pressure drop ratio and available pressure drop ratio,πus,nz is greater than πcr,nz. This means that the nozzle is in a working supercritical state. Additionally, the gas is not fully expanded at the outlet of the nozzle, which is characterized by the local speed of sound at the outlet of the nozzle, and the outlet static pressure is greater than the outside atmospheric pressure.The outlet velocity of the nozzleC6 is 537.74 m/s as calculated by the following formula:
(16)C6=ϕnz2k′k′‐1R′Tt51‐1σnzPt5/P9k′−1/k′=ϕnz2k′k′+1R′Tt5,where the speed factor φnz is 0.97.In addition, the outlet cross-sectional area of the nozzleA6 is 3.05×10−3m2, as calculated by
(17)A6=WgTt6Km′Pt6qλ6,Since the flow process of the nozzle is an isentropic flow, the nozzle inlet total temperatureTt6 is equal to outlet total temperature Tt5; the nozzle outlet relative dense flow qλ6 is 1; and Km′ is 0.0397.The nozzle outlet static pressureP6 is 116535 Pa, as calculated by
(18)P6=Pt61+k′−1/2M62k′/k′−1,where the nozzle outlet Mach number M6 is 1.Through the parameters derived above, the performance and economic indicators of the DSCI jet engine can be calculated, as shown in the following formulas:The DSCI jet engine thrust can be expressed as(19)F=WgC6−WaV+P6−PHA6.The DSCI jet engine thrustF is 505.62 N when the flight speed V is 0.The DSCI jet engine specific thrust can be expressed as(20)Fs=FWa.The DSCI jet engine specific thrustFs is 601.93 (N s)/kg.The DSCI jet engine fuel consumption rate can be expressed as(21)sfc=3600mfF.The DSCI jet engine fuel consumption ratesfc is 9.54% [13].Table9 shows the important parameters of the DSCI jet engine and the JetCat P500-PRO-GH considering the design parameters. Compared to the JetCat P500-PRO-GH, the DSCI jet engine has a 34.37% reduction in axial size and a 13.49% reduction in weight due to its compact structure. Although there is a certain reduction in mass flow relative to the JetCat P500-PRO-GH, with the substantial increase in OPR (close to the optimal supercharging ratio) and turbo efficiency, the DSCI jet engine has a slightly higher in thrust than the JetCat engine. Additionally, the specific thrust increased by 10.11%.Table 9
Design point parameters of the DSCI jet engine and JetCat P500-PRO-GH.
ParametersEngine typeDSCI jet engineJetCat P500-PRO-GHDiameterd (mm)178178.6LengthL (mm)275419WeightG (g)42394900Mass flowWa (kg/s)0.840.9Maximum rotating speednmax (r/min)8000080000OPR5.9573.6Exhaust total temperatureTt5 (K)934.7311013Exhaust speedC6 (m/s)537.74551.67ThrustF (N)505.62492TWR12.178.73Maximum fuel consumption ratesfc (kg/(N h))0.09540.151Specific thrustFs (N s)/kg601.93546.67Under the combined effect of various parameters, theTWR of the DSCI jet engine is increased to 12.17, which is 39.4% higher than that of the JetCat P500-PRO-GH. In addition, the increased OPR is also close to the optimal economic pressure ratio. Coupled with the phenomenon of convective heat exchange inside and outside the turbine and the recovery of exhaust gas heat, the DSCI engine has a 36.82% reduction in sfc.Based on the above description, the DSCI jet engine has significant advantages in performance indicators and economic indicators in the same size radial engine, especially the potential to increase the turbine inlet total temperature and the complete expansion of the nozzle, which can make the DSCI jet engine performance higher.


## 4.1. CFD Method

The ANSYS CFX commercial CFD software, including the meshing module ANSYS meshing and computing module CFX-TASCflow, was used for numerical simulation.The fluid domains of the DSCI inside, the turbine outside, and the solid domain of the turbine are meshed by ANSYS meshing. The turbine inside contains 1.44 million fluid domain grids, the turbine outside contains 3.09 million fluid domain grids, the turbine contains 2.75 million solid domain grids, and the double-sided centrifugal compressor contains 3.14 million fluid domain grids, as shown in Figure12. Through grid quality inspection, it is found that the maximum skewness is lower than 0.95 and that the average orthogonal quality is higher than 0.75, which indicates that these grids can be used for numerical simulation. Theoretically, the accuracy of a tetrahedral mesh (considering first-order elements) may be slightly lower when compared with a hexahedral mesh, but its self-adaptive mesh technology can be applied to any complex geometry and provide for mesh refinement of high stress gradient parts. The advantages of automatic grid encryption save cost and time.Figure 12
Each domain grid of the DSCI. (a) Outside the turbine fluid domain. (b) Inside the turbine fluid domain grids. (c) Turbine solid domain grids. (d) Double-sided centrifugal compressor grids.
(a)(b)(c)(d)A steady-state model and high-resolution discretization scheme were used for simulations. The discretized form of Reynolds Averaged Navier-Stokes (RANS) equations was iteratively solved for the DSCI. Since the SST model is used in turbomachinery, in most cases, it requiresY+ to be very small (Y+<2). Therefore, the layer mesh quality requirement of the SST model is higher than that of the k-epsilon model. Reference [18] demonstrated that when the computational grid number is very large, the k-epsilon model is used as the turbulence model in simulating turbomachinery in order to relax the demand on computer memory and raise the efficiency. The calculated residuals converge below 10-5.The boundary conditions are listed in Table5 and are as follows: the nonsliding solid wall treatment method is used, except the fluid-solid interface is set to exchange heat [19, 20]; the DSCI surfaces are set rotating, except that the shroud is a static boundary; the double-sided centrifugal compressor inlet total pressure Pt1 is 101325 Pa; the double-sided centrifugal compressor inlet total temperature Tt1 is 288 K; the turbine inside outlet static pressure P3 is 212783 Pa; the turbine outside inlet total temperature Tt4 is 1150 K; the turbine outside inlet axial velocity component Ca4B is 149.5 m/s; the turbine outside inlet circumferential velocity component Cτ4B is 590 m/s; and the turbine outside outlet static pressure P5 is 202650 Pa.Table 5
The fluid domain boundary conditions of the DSCI inside and outside.
Boundary conditionsFluid domainsFluid domain of DSCI insideFluid domain of DSCI outsideInletTotal temperature, Total pressureTotal temperature, velocity componentsOutletStatic pressureStatic pressureTurbulence5%5%Based on the property parameters of the GH93 material listed in Table6 [21], the missing data can be calculated using the least squares method in MATLAB.Table 6
Properties of the GH93 material.
Static temperature, Kλ (W m-1 K-1)Cp (J kg-1 K-1)Density (g cm-3)37312.774678.1947314.4449457315.9952067317.5454777318.9757287320.6460097322.32626107323.99652117325.83679127327.88706137330.06733147332.47760The grid independency is examined via increasing the node number until the evaluated design point performance of turbomachines is essentially no longer changed. As Figure13 shows, the calculated efficiency and total pressure ratio of DSCI and turbine have converged with 4.58 million and 5.84 million grids, respectively, which are considered to grid size effect independent. Otherwise mentioned, the computation model grid number in the later calculations is about 10.42 million, as shown in Figure 14 [22–25].Figure 13
Grid independence verification of turbomachines. (a) DSCI. (b) Turbine.
(a)(b)Figure 14
Calculation model of the DSCI.


## 4.2. CFD Results and Discussions

### 4.2.1. Compression Process

First, Figure15 displays several contours of the double-sided centrifugal compressor under the design point. From left to right, there are the auxiliary impeller and the main impeller. In accordance with the centrifugal pressurization principle, the static pressure gradually increases from the inlet to the outlet of the meridian channel in the double-sided centrifugal compressor, as shown in Figures 15(a) and 15(b).Figure 15
Several contours of the double-sided centrifugal compressor. (a) Static pressure. (b) Total pressure in Stn frame. (c) Relative Mach number. (d) Static entropy.
(a)(b)(c)(d)Second, since the inside shape of turbine is asymmetrical along the mirror plane in Figures15(c) and 15(d), the flow field of main impeller is different from that of auxiliary impeller.Finally, because the leakage vortex caused by the angle-of-attack induces tip clearance flow and blade radial shear flow, there are more high entropy values (low-momentum air) in the tip area of the double-sided centrifugal compressor. When the leakage vortex is extreme, it spreads to the main flow area of the impeller, leading to impeller compression difficulties and reduced efficiency.Figures16–18 show the blade-to-blade planes of the double-sided centrifugal compressor under the design point. From left to right, there are the main impeller and the auxiliary impeller. As the blade height increases, the aerodynamic load of the blade increases, as shown in Figure 16. Due to the influence of the high adverse pressure gradient at the tip of the centrifugal compressor, the tip leakage vortex is easily induced, and in severe cases, the impeller will stall in advance. Figures 17 and 18 further confirm the above analysis. In Figure 17, it can be observed that the main impeller has produced some stall clusters at the 0.9 span.Figure 16
Blade-to-blade plane of double-sided centrifugal compressor for static pressure. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 17
Blade-to-blade planes of double-sided centrifugal compressor for relative Mach number. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 18
Blade-to-blade planes of double-sided centrifugal compressor for static entropy. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)In summary, due to the influence of the downstream inside turbine, in the main and auxiliary impellers of the same size, the main impeller is closer to the surge point, so the compression capacity of the main impeller is better, but the tip flow loss is greater.The double-sided centrifugal compressor is defined as the first stage compression section in Figure15.First, when these two flows exit the double-sided centrifugal compressor, they will mix with each other, thereby resulting in the loss of mixture. Because the total pressure ratio and isentropic efficiency of the main and auxiliary impellers are different from each other, the compression performance of the double-sided centrifugal compressor cannot be estimated. Since these two flows exit the double-sided centrifugal compressor and enter the inside of the turbine at the same time, the inlet section of the turbine inside can be used as the calculated outlet section of the double-sided centrifugal compressor. The first stage compression section total pressure ratioπc1∗ is 2.901, and its isentropic efficiency ηc1∗ is 0.8538 as calculated by the numerical simulation results and the following formulas:
(1)πc1∗=Pt2Pt1,(2)ηc1∗=πc1∗k−1/k−1Tt2/Tt1−1,where Pt1 refers to the double-sided centrifugal compressor inlet total pressure, Tt1 refers to the double-sided centrifugal compressor inlet total temperature, Pt2 refers to the turbine inside inlet total pressure, and Tt2 refers to the turbine inside inlet total pressure.Second, since the turbine is also rotating at the same speed as the double-sided centrifugal compressor, the high-pressure air is also compressed inside the turbine. For ease of expression, this process is defined as the internal channel diffusion of the hollow-tip turbine. The total pressure ratio of this processπc2∗ is 2.053, and the isentropic efficiency ηc2∗ is 0.7081 as calculated by CFD.Finally, the OPR of the compression processπk∗ is 5.957, and the overall isentropic efficiency ηk∗ is 0.7617 by formulas (3) and (4):
(3)πk∗=πc1∗πc2∗,(4)ηk∗=πk∗k−1/k−1Tt3/Tt1−1,where Tt3 refers to the outlet total temperature inside the turbine and Tt1 refers to the total temperature of the double-sided centrifugal compressor inlet.The isentropic efficiency of any single-stage compressor is generally higher than that of a multistage compressor. In this section, since there is convection heat transfer inside and outside the turbine,ηc2∗ is far below ηk∗. Specifically, the high-temperature gas outside the turbine transfers heat to the high-pressure air that is being compressed in the turbine, resulting in ηc2∗ being lower than the overall isentropic efficiency ηk∗.Based on the above analysis, Table7 displays the cross-sectional parameters of the compression process. The compressor power Wk is 252.6 kJ/kg and is calculated by
(5)Wk=kk−1RTt1πk∗k−1/k−1/ηk∗.Table 7
Parameters of each section during compression.
ParametersSection positionSection 1Section 2Section 3Total pressurePt (Pa)101325293984603569Total temperatureTt (K)288407.989539.455Air mass flowWa (kg/s)0.840.840.84Total pressure ratioπc∗2.9012.053Isentropic efficiencyηc∗0.85380.7081


### 4.2.2. Combustion Process

To avoid introducing new problems and a large number of calculations, the traditional reverse-flow annular combustor was adopted. The fuel-air ratiofb is 0.017 at Tt3 and Tt4, and the combustor heat balance equation can be written as
(6)fb=it4−it3ξbHf−I4+it3,whereit4, it3, and I4 can all be determined with a look-up table and Hf is 42900 kJ/kg [26].The fuel mass flowmf is 0.014 kg/s, and the gas mass flow Wg is 0.854 kg/s as calculated by the formulas for the fuel-air ratio and gas mass flow:
(7)mf=Wafb,(8)Wg=Wa+mf.Notably, for the total pressure loss in the combustor, the total pressure recovery coefficientσb is empirically given as 0.98. The combustor outlet total pressure Pt4 is 591498 Pa, as calculated by
(9)Pt4=σbPt3.


### 4.2.3. Expansion Process (outside the Turbine)

After analyzing the combustion process, the expansion process needs to be further studied. The profile design of the hollow-tip turbine is different from that of a traditional turbine, especially the transition section. Therefore, it is necessary to study the flow field and characteristics of the turbine.Figure19 illustrates the static pressure contours of the turbine. High-temperature gas pressure is released in the turbine rotor channel and then drives rotor acceleration. Because the turbine root is part of the transition section and the circumferential velocity is small, the pressure drop ratio is small at the blade root, regardless of differing blade height.Figure 19
Static pressure contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure20 shows the relative Mach number contours of the turbine. The high-temperature gas accelerates and depressurizes in the turbine rotor channel and then drives the DSCI rotor to rotate. The maximum relative Mach number appears at the throat of the turbine, which corresponds to the low-pressure area in Figure 19, indicating that the turbine throat outlet section is supersonic and generates a set of shock waves. This set of expansion shock waves hit the trailing edge of the suction surface of the adjacent turbine blades and interfere with the boundary layer, causing more serious loss of the boundary layer. As the height of the turbine blade increases, this phenomenon becomes more prominent.Figure 20
Relative Mach number contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure21 shows the static entropy contours of the turbine channel. The change in the angle-of-attack causes the phenomenon of separated flow or even back flow in the transition section, namely, the loss of turbine profiles. Comparing the different blade heights, the high entropy value of the turbine is mainly distributed near the trailing edge of the suction surface. This indicates that the supersonic velocity of the throat section of the turbine produces a set of expansion shock waves. These waves hit the trailing edge of the suction surface of the adjacent turbine and interfere with the boundary layer, causing a serious loss of the boundary layer.Figure 21
Static entropy contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Based on the above, the loss of turbine profiles and the shock wave boundary layer interference loss are the main reasons for the decrease of the turbine efficiency.Figure22 shows the relative velocity vector contours of the turbine. There is a certain deflection angle between the inlet relative flow angle and the inlet geometry angle at the turbine root, namely, a large positive angle-of-attack. This indicates that there is flow separation at the leading edge of the suction surface. However, as the height of the turbine increases, the tangential velocity also increases, and the corresponding relative flow angle also increases. The reduction of the positive angle-of-attack causes the flow separation at the leading edge to weaken. For this kind of problem, further optimization is possible by twisting the turbine root in the later stage.Figure 22
Relative velocity vector contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure23 shows the static pressure distribution of the turbine. The static pressure load difference between the pressure surface and the suction surface is small at the 0.1 span of the turbine, which further illustrates that the expansion of the turbine transition section is a poor function. As the leaf height increases, the expansion function is improved. At the turbine leading edge, the static pressure load on the suction side is greater than that on the pressure side, indicating that it is not appropriate to set a sharp front edge contour shape. In the later stage, general antiforce axial turbines can be considered.Figure 23
Static pressure distribution of turbine (0% represents the hub; 100% indicates the tip).Figure24(a) displays the static temperature contours of the DSCI wall. Although the cooling coefficient inside the turbine is close to 1 and the high-pressure gas has a good cooling effect on the turbine wall, there is a local high temperature at the trailing edge of the blade and the hub of the double-sided centrifugal compressor due to the heat conduction in the solid. Thus, the high local temperature may slightly affect the compression and structural strength of the DSCI, which needs to be further researched.Figure 24
Static temperature field contours. (a) Static temperature field contour of the DSCI. (b) Static temperature field contour the turbine outside.
(a)(b)Figure24(b) displays the static temperature contour outside the turbine wall. The maximum higher temperature is mainly distributed at the tip of the leading and trailing edges, and the cooling effect is evident at the middle and root in the turbine. This shows that the high-pressure gas flows along the root to the tip of the turbine inside and impulsively cools the turbine wall. On the other hand, since the outlet velocity of the throat of the turbine outside is high, the cooling effect is also good. The cooling effect is not evident far away from the high-pressure gas.In addition, the maximum temperature of the turbine wall is only 840.35 K, which is far below the maximum temperature limit of the GH93 of 1088 K. This means that it not only provides the potential for increasing the turbine inlet total temperature but also provides room for development for the use of low-temperature, low-cost, and lightweight materials, such as titanium alloys and high-entropy alloys. From the perspective of lightweight materials, this shows that the structural weight of the engine can be further reduced, which is conducive to the improvement ofTWR.First, based on the previous assumption, the hollow turbine guide is simplified to the absolute inlet velocity boundary condition of the turbine. On the other hand, there is a certain total pressure loss in the actual hollow turbine guide, which cannot be ignored. The total pressure recovery coefficient of the hollow turbine guideσ4B is 0.972, and the hollow turbine guide outlet total pressure Pt4B is 574703 Pa, as calculated by
(10)Pt4B=σ4BPt4.Second, the total pressure drop ratio of the turbineπT∗ is 2.532, and the isentropic efficiency ηT∗ is 0.9088 based on numerical simulation. The results show that a turbine with a blade shroud can avoid tip leakage to a certain extent and improve the isentropic efficiency.Based on the above analysis, Table8 shows the cross-sectional parameters of the expansion process. The turbine power WT is 249.74 kJ/kg and can be expressed as
(11)WT=k′k′−1R′Tt41−1πT∗k′−1/k′ηT∗.Table 8
Parameters of each section during the expansion process.
ParametersSection positionSection 4Section 4BSection 5Total pressurePt (Pa)591498574703227010Total temperatureTt (K)11501150934.731Gas flowWg (kg/s)0.8540.8540.854Total pressure drop ratioπT∗2.532Isentropic efficiencyηT∗0.9088Finally, the compressor powerPC is 212.2 kW, and the turbine power PT is 212.2 kW as calculated by formulas (12) and (13). This means that the turbine power can meet the compression needs of the DSCI.
(12)PC=WkWa,(13)PT=WTWgηm,where the mechanical efficiency ηm is 0.995.Through the previous calculations, all components met the matching characteristics in the gas generator. Indispensably, according to the outlet parameters of the turbine, the performance and economic indicators of the DSCI jet engine can be analyzed and compared with the JetCat P500-PRO-GH of the same radial size.First, the nozzle working status needs to be judged in the above hypothesis. Regarding the nozzle total pressure recovery coefficientσnz, considering the loss along the nozzle and the total pressure loss caused by the rear intake pipe to the rectification of the turbine exhaust gas, the empirical coefficient σnz is 0.95.Second, the critical pressure drop ratio of the nozzleπcr,nz is 1.947, and the available pressure drop ratio πus,nz is 2.128, as calculated by
(14)πcr,nz=1.85/σnz,(15)πus,nz=Pt5/PH,wherePH is 101325 Pa.Comparing the critical pressure drop ratio and available pressure drop ratio,πus,nz is greater than πcr,nz. This means that the nozzle is in a working supercritical state. Additionally, the gas is not fully expanded at the outlet of the nozzle, which is characterized by the local speed of sound at the outlet of the nozzle, and the outlet static pressure is greater than the outside atmospheric pressure.The outlet velocity of the nozzleC6 is 537.74 m/s as calculated by the following formula:
(16)C6=ϕnz2k′k′‐1R′Tt51‐1σnzPt5/P9k′−1/k′=ϕnz2k′k′+1R′Tt5,where the speed factor φnz is 0.97.In addition, the outlet cross-sectional area of the nozzleA6 is 3.05×10−3m2, as calculated by
(17)A6=WgTt6Km′Pt6qλ6,Since the flow process of the nozzle is an isentropic flow, the nozzle inlet total temperatureTt6 is equal to outlet total temperature Tt5; the nozzle outlet relative dense flow qλ6 is 1; and Km′ is 0.0397.The nozzle outlet static pressureP6 is 116535 Pa, as calculated by
(18)P6=Pt61+k′−1/2M62k′/k′−1,where the nozzle outlet Mach number M6 is 1.Through the parameters derived above, the performance and economic indicators of the DSCI jet engine can be calculated, as shown in the following formulas:The DSCI jet engine thrust can be expressed as(19)F=WgC6−WaV+P6−PHA6.The DSCI jet engine thrustF is 505.62 N when the flight speed V is 0.The DSCI jet engine specific thrust can be expressed as(20)Fs=FWa.The DSCI jet engine specific thrustFs is 601.93 (N s)/kg.The DSCI jet engine fuel consumption rate can be expressed as(21)sfc=3600mfF.The DSCI jet engine fuel consumption ratesfc is 9.54% [13].Table9 shows the important parameters of the DSCI jet engine and the JetCat P500-PRO-GH considering the design parameters. Compared to the JetCat P500-PRO-GH, the DSCI jet engine has a 34.37% reduction in axial size and a 13.49% reduction in weight due to its compact structure. Although there is a certain reduction in mass flow relative to the JetCat P500-PRO-GH, with the substantial increase in OPR (close to the optimal supercharging ratio) and turbo efficiency, the DSCI jet engine has a slightly higher in thrust than the JetCat engine. Additionally, the specific thrust increased by 10.11%.Table 9
Design point parameters of the DSCI jet engine and JetCat P500-PRO-GH.
ParametersEngine typeDSCI jet engineJetCat P500-PRO-GHDiameterd (mm)178178.6LengthL (mm)275419WeightG (g)42394900Mass flowWa (kg/s)0.840.9Maximum rotating speednmax (r/min)8000080000OPR5.9573.6Exhaust total temperatureTt5 (K)934.7311013Exhaust speedC6 (m/s)537.74551.67ThrustF (N)505.62492TWR12.178.73Maximum fuel consumption ratesfc (kg/(N h))0.09540.151Specific thrustFs (N s)/kg601.93546.67Under the combined effect of various parameters, theTWR of the DSCI jet engine is increased to 12.17, which is 39.4% higher than that of the JetCat P500-PRO-GH. In addition, the increased OPR is also close to the optimal economic pressure ratio. Coupled with the phenomenon of convective heat exchange inside and outside the turbine and the recovery of exhaust gas heat, the DSCI engine has a 36.82% reduction in sfc.Based on the above description, the DSCI jet engine has significant advantages in performance indicators and economic indicators in the same size radial engine, especially the potential to increase the turbine inlet total temperature and the complete expansion of the nozzle, which can make the DSCI jet engine performance higher.


## 4.2.1. Compression Process

First, Figure15 displays several contours of the double-sided centrifugal compressor under the design point. From left to right, there are the auxiliary impeller and the main impeller. In accordance with the centrifugal pressurization principle, the static pressure gradually increases from the inlet to the outlet of the meridian channel in the double-sided centrifugal compressor, as shown in Figures 15(a) and 15(b).Figure 15
Several contours of the double-sided centrifugal compressor. (a) Static pressure. (b) Total pressure in Stn frame. (c) Relative Mach number. (d) Static entropy.
(a)(b)(c)(d)Second, since the inside shape of turbine is asymmetrical along the mirror plane in Figures15(c) and 15(d), the flow field of main impeller is different from that of auxiliary impeller.Finally, because the leakage vortex caused by the angle-of-attack induces tip clearance flow and blade radial shear flow, there are more high entropy values (low-momentum air) in the tip area of the double-sided centrifugal compressor. When the leakage vortex is extreme, it spreads to the main flow area of the impeller, leading to impeller compression difficulties and reduced efficiency.Figures16–18 show the blade-to-blade planes of the double-sided centrifugal compressor under the design point. From left to right, there are the main impeller and the auxiliary impeller. As the blade height increases, the aerodynamic load of the blade increases, as shown in Figure 16. Due to the influence of the high adverse pressure gradient at the tip of the centrifugal compressor, the tip leakage vortex is easily induced, and in severe cases, the impeller will stall in advance. Figures 17 and 18 further confirm the above analysis. In Figure 17, it can be observed that the main impeller has produced some stall clusters at the 0.9 span.Figure 16
Blade-to-blade plane of double-sided centrifugal compressor for static pressure. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 17
Blade-to-blade planes of double-sided centrifugal compressor for relative Mach number. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)Figure 18
Blade-to-blade planes of double-sided centrifugal compressor for static entropy. (a) 0.1 span. (b) 0.5 span. (c) 0.9 span.
(a)(b)(c)In summary, due to the influence of the downstream inside turbine, in the main and auxiliary impellers of the same size, the main impeller is closer to the surge point, so the compression capacity of the main impeller is better, but the tip flow loss is greater.The double-sided centrifugal compressor is defined as the first stage compression section in Figure15.First, when these two flows exit the double-sided centrifugal compressor, they will mix with each other, thereby resulting in the loss of mixture. Because the total pressure ratio and isentropic efficiency of the main and auxiliary impellers are different from each other, the compression performance of the double-sided centrifugal compressor cannot be estimated. Since these two flows exit the double-sided centrifugal compressor and enter the inside of the turbine at the same time, the inlet section of the turbine inside can be used as the calculated outlet section of the double-sided centrifugal compressor. The first stage compression section total pressure ratioπc1∗ is 2.901, and its isentropic efficiency ηc1∗ is 0.8538 as calculated by the numerical simulation results and the following formulas:
(1)πc1∗=Pt2Pt1,(2)ηc1∗=πc1∗k−1/k−1Tt2/Tt1−1,where Pt1 refers to the double-sided centrifugal compressor inlet total pressure, Tt1 refers to the double-sided centrifugal compressor inlet total temperature, Pt2 refers to the turbine inside inlet total pressure, and Tt2 refers to the turbine inside inlet total pressure.Second, since the turbine is also rotating at the same speed as the double-sided centrifugal compressor, the high-pressure air is also compressed inside the turbine. For ease of expression, this process is defined as the internal channel diffusion of the hollow-tip turbine. The total pressure ratio of this processπc2∗ is 2.053, and the isentropic efficiency ηc2∗ is 0.7081 as calculated by CFD.Finally, the OPR of the compression processπk∗ is 5.957, and the overall isentropic efficiency ηk∗ is 0.7617 by formulas (3) and (4):
(3)πk∗=πc1∗πc2∗,(4)ηk∗=πk∗k−1/k−1Tt3/Tt1−1,where Tt3 refers to the outlet total temperature inside the turbine and Tt1 refers to the total temperature of the double-sided centrifugal compressor inlet.The isentropic efficiency of any single-stage compressor is generally higher than that of a multistage compressor. In this section, since there is convection heat transfer inside and outside the turbine,ηc2∗ is far below ηk∗. Specifically, the high-temperature gas outside the turbine transfers heat to the high-pressure air that is being compressed in the turbine, resulting in ηc2∗ being lower than the overall isentropic efficiency ηk∗.Based on the above analysis, Table7 displays the cross-sectional parameters of the compression process. The compressor power Wk is 252.6 kJ/kg and is calculated by
(5)Wk=kk−1RTt1πk∗k−1/k−1/ηk∗.Table 7
Parameters of each section during compression.
ParametersSection positionSection 1Section 2Section 3Total pressurePt (Pa)101325293984603569Total temperatureTt (K)288407.989539.455Air mass flowWa (kg/s)0.840.840.84Total pressure ratioπc∗2.9012.053Isentropic efficiencyηc∗0.85380.7081


## 4.2.2. Combustion Process

To avoid introducing new problems and a large number of calculations, the traditional reverse-flow annular combustor was adopted. The fuel-air ratiofb is 0.017 at Tt3 and Tt4, and the combustor heat balance equation can be written as
(6)fb=it4−it3ξbHf−I4+it3,whereit4, it3, and I4 can all be determined with a look-up table and Hf is 42900 kJ/kg [26].The fuel mass flowmf is 0.014 kg/s, and the gas mass flow Wg is 0.854 kg/s as calculated by the formulas for the fuel-air ratio and gas mass flow:
(7)mf=Wafb,(8)Wg=Wa+mf.Notably, for the total pressure loss in the combustor, the total pressure recovery coefficientσb is empirically given as 0.98. The combustor outlet total pressure Pt4 is 591498 Pa, as calculated by
(9)Pt4=σbPt3.


## 4.2.3. Expansion Process (outside the Turbine)

After analyzing the combustion process, the expansion process needs to be further studied. The profile design of the hollow-tip turbine is different from that of a traditional turbine, especially the transition section. Therefore, it is necessary to study the flow field and characteristics of the turbine.Figure19 illustrates the static pressure contours of the turbine. High-temperature gas pressure is released in the turbine rotor channel and then drives rotor acceleration. Because the turbine root is part of the transition section and the circumferential velocity is small, the pressure drop ratio is small at the blade root, regardless of differing blade height.Figure 19
Static pressure contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure20 shows the relative Mach number contours of the turbine. The high-temperature gas accelerates and depressurizes in the turbine rotor channel and then drives the DSCI rotor to rotate. The maximum relative Mach number appears at the throat of the turbine, which corresponds to the low-pressure area in Figure 19, indicating that the turbine throat outlet section is supersonic and generates a set of shock waves. This set of expansion shock waves hit the trailing edge of the suction surface of the adjacent turbine blades and interfere with the boundary layer, causing more serious loss of the boundary layer. As the height of the turbine blade increases, this phenomenon becomes more prominent.Figure 20
Relative Mach number contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure21 shows the static entropy contours of the turbine channel. The change in the angle-of-attack causes the phenomenon of separated flow or even back flow in the transition section, namely, the loss of turbine profiles. Comparing the different blade heights, the high entropy value of the turbine is mainly distributed near the trailing edge of the suction surface. This indicates that the supersonic velocity of the throat section of the turbine produces a set of expansion shock waves. These waves hit the trailing edge of the suction surface of the adjacent turbine and interfere with the boundary layer, causing a serious loss of the boundary layer.Figure 21
Static entropy contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Based on the above, the loss of turbine profiles and the shock wave boundary layer interference loss are the main reasons for the decrease of the turbine efficiency.Figure22 shows the relative velocity vector contours of the turbine. There is a certain deflection angle between the inlet relative flow angle and the inlet geometry angle at the turbine root, namely, a large positive angle-of-attack. This indicates that there is flow separation at the leading edge of the suction surface. However, as the height of the turbine increases, the tangential velocity also increases, and the corresponding relative flow angle also increases. The reduction of the positive angle-of-attack causes the flow separation at the leading edge to weaken. For this kind of problem, further optimization is possible by twisting the turbine root in the later stage.Figure 22
Relative velocity vector contours of turbine channel. (a) 0.1 span. (b) 0.3 span. (c) 0.5 span. (d) 0.7 span. (e) 0.9 span.
(a)(b)(c)(d)(e)Figure23 shows the static pressure distribution of the turbine. The static pressure load difference between the pressure surface and the suction surface is small at the 0.1 span of the turbine, which further illustrates that the expansion of the turbine transition section is a poor function. As the leaf height increases, the expansion function is improved. At the turbine leading edge, the static pressure load on the suction side is greater than that on the pressure side, indicating that it is not appropriate to set a sharp front edge contour shape. In the later stage, general antiforce axial turbines can be considered.Figure 23
Static pressure distribution of turbine (0% represents the hub; 100% indicates the tip).Figure24(a) displays the static temperature contours of the DSCI wall. Although the cooling coefficient inside the turbine is close to 1 and the high-pressure gas has a good cooling effect on the turbine wall, there is a local high temperature at the trailing edge of the blade and the hub of the double-sided centrifugal compressor due to the heat conduction in the solid. Thus, the high local temperature may slightly affect the compression and structural strength of the DSCI, which needs to be further researched.Figure 24
Static temperature field contours. (a) Static temperature field contour of the DSCI. (b) Static temperature field contour the turbine outside.
(a)(b)Figure24(b) displays the static temperature contour outside the turbine wall. The maximum higher temperature is mainly distributed at the tip of the leading and trailing edges, and the cooling effect is evident at the middle and root in the turbine. This shows that the high-pressure gas flows along the root to the tip of the turbine inside and impulsively cools the turbine wall. On the other hand, since the outlet velocity of the throat of the turbine outside is high, the cooling effect is also good. The cooling effect is not evident far away from the high-pressure gas.In addition, the maximum temperature of the turbine wall is only 840.35 K, which is far below the maximum temperature limit of the GH93 of 1088 K. This means that it not only provides the potential for increasing the turbine inlet total temperature but also provides room for development for the use of low-temperature, low-cost, and lightweight materials, such as titanium alloys and high-entropy alloys. From the perspective of lightweight materials, this shows that the structural weight of the engine can be further reduced, which is conducive to the improvement ofTWR.First, based on the previous assumption, the hollow turbine guide is simplified to the absolute inlet velocity boundary condition of the turbine. On the other hand, there is a certain total pressure loss in the actual hollow turbine guide, which cannot be ignored. The total pressure recovery coefficient of the hollow turbine guideσ4B is 0.972, and the hollow turbine guide outlet total pressure Pt4B is 574703 Pa, as calculated by
(10)Pt4B=σ4BPt4.Second, the total pressure drop ratio of the turbineπT∗ is 2.532, and the isentropic efficiency ηT∗ is 0.9088 based on numerical simulation. The results show that a turbine with a blade shroud can avoid tip leakage to a certain extent and improve the isentropic efficiency.Based on the above analysis, Table8 shows the cross-sectional parameters of the expansion process. The turbine power WT is 249.74 kJ/kg and can be expressed as
(11)WT=k′k′−1R′Tt41−1πT∗k′−1/k′ηT∗.Table 8
Parameters of each section during the expansion process.
ParametersSection positionSection 4Section 4BSection 5Total pressurePt (Pa)591498574703227010Total temperatureTt (K)11501150934.731Gas flowWg (kg/s)0.8540.8540.854Total pressure drop ratioπT∗2.532Isentropic efficiencyηT∗0.9088Finally, the compressor powerPC is 212.2 kW, and the turbine power PT is 212.2 kW as calculated by formulas (12) and (13). This means that the turbine power can meet the compression needs of the DSCI.
(12)PC=WkWa,(13)PT=WTWgηm,where the mechanical efficiency ηm is 0.995.Through the previous calculations, all components met the matching characteristics in the gas generator. Indispensably, according to the outlet parameters of the turbine, the performance and economic indicators of the DSCI jet engine can be analyzed and compared with the JetCat P500-PRO-GH of the same radial size.First, the nozzle working status needs to be judged in the above hypothesis. Regarding the nozzle total pressure recovery coefficientσnz, considering the loss along the nozzle and the total pressure loss caused by the rear intake pipe to the rectification of the turbine exhaust gas, the empirical coefficient σnz is 0.95.Second, the critical pressure drop ratio of the nozzleπcr,nz is 1.947, and the available pressure drop ratio πus,nz is 2.128, as calculated by
(14)πcr,nz=1.85/σnz,(15)πus,nz=Pt5/PH,wherePH is 101325 Pa.Comparing the critical pressure drop ratio and available pressure drop ratio,πus,nz is greater than πcr,nz. This means that the nozzle is in a working supercritical state. Additionally, the gas is not fully expanded at the outlet of the nozzle, which is characterized by the local speed of sound at the outlet of the nozzle, and the outlet static pressure is greater than the outside atmospheric pressure.The outlet velocity of the nozzleC6 is 537.74 m/s as calculated by the following formula:
(16)C6=ϕnz2k′k′‐1R′Tt51‐1σnzPt5/P9k′−1/k′=ϕnz2k′k′+1R′Tt5,where the speed factor φnz is 0.97.In addition, the outlet cross-sectional area of the nozzleA6 is 3.05×10−3m2, as calculated by
(17)A6=WgTt6Km′Pt6qλ6,Since the flow process of the nozzle is an isentropic flow, the nozzle inlet total temperatureTt6 is equal to outlet total temperature Tt5; the nozzle outlet relative dense flow qλ6 is 1; and Km′ is 0.0397.The nozzle outlet static pressureP6 is 116535 Pa, as calculated by
(18)P6=Pt61+k′−1/2M62k′/k′−1,where the nozzle outlet Mach number M6 is 1.Through the parameters derived above, the performance and economic indicators of the DSCI jet engine can be calculated, as shown in the following formulas:The DSCI jet engine thrust can be expressed as(19)F=WgC6−WaV+P6−PHA6.The DSCI jet engine thrustF is 505.62 N when the flight speed V is 0.The DSCI jet engine specific thrust can be expressed as(20)Fs=FWa.The DSCI jet engine specific thrustFs is 601.93 (N s)/kg.The DSCI jet engine fuel consumption rate can be expressed as(21)sfc=3600mfF.The DSCI jet engine fuel consumption ratesfc is 9.54% [13].Table9 shows the important parameters of the DSCI jet engine and the JetCat P500-PRO-GH considering the design parameters. Compared to the JetCat P500-PRO-GH, the DSCI jet engine has a 34.37% reduction in axial size and a 13.49% reduction in weight due to its compact structure. Although there is a certain reduction in mass flow relative to the JetCat P500-PRO-GH, with the substantial increase in OPR (close to the optimal supercharging ratio) and turbo efficiency, the DSCI jet engine has a slightly higher in thrust than the JetCat engine. Additionally, the specific thrust increased by 10.11%.Table 9
Design point parameters of the DSCI jet engine and JetCat P500-PRO-GH.
ParametersEngine typeDSCI jet engineJetCat P500-PRO-GHDiameterd (mm)178178.6LengthL (mm)275419WeightG (g)42394900Mass flowWa (kg/s)0.840.9Maximum rotating speednmax (r/min)8000080000OPR5.9573.6Exhaust total temperatureTt5 (K)934.7311013Exhaust speedC6 (m/s)537.74551.67ThrustF (N)505.62492TWR12.178.73Maximum fuel consumption ratesfc (kg/(N h))0.09540.151Specific thrustFs (N s)/kg601.93546.67Under the combined effect of various parameters, theTWR of the DSCI jet engine is increased to 12.17, which is 39.4% higher than that of the JetCat P500-PRO-GH. In addition, the increased OPR is also close to the optimal economic pressure ratio. Coupled with the phenomenon of convective heat exchange inside and outside the turbine and the recovery of exhaust gas heat, the DSCI engine has a 36.82% reduction in sfc.Based on the above description, the DSCI jet engine has significant advantages in performance indicators and economic indicators in the same size radial engine, especially the potential to increase the turbine inlet total temperature and the complete expansion of the nozzle, which can make the DSCI jet engine performance higher.


## 5. Conclusion

This research presents a conceptual design of DSCI for a high-TWR propulsion system. Through the work discussed above, the following conclusions can be drawn:
(1)
The DSCI engine includes the DSCI jet engine scheme and the gas-driven propeller DSCI engine scheme. In theory, compared with the traditional MTEs, the DSCI engine has good shock absorption and response characteristics. And its structural weight reduction and heat recovery provide imagination for MTE’s performance improvement. On the other hand, with the help of additive manufacturing technology, DSCI jet engine installation is more convenient and the structure is more reliable(2)
After satisfying four balance conditions and several assumptions, the turbine must adopt the design rules of skewed blades and transition sections. Preliminary design of the DCSI rotor, in which the profile of the turbine outside adopts a traditional turbine and the turbine inside adopts a tubular diffuser structure(3)
The thermal analysis of different processes shows that all components meet the matching characteristics of the gas generators at the design point. Among them, the OPR of the compression processπk∗ is 5.957, and the overall isentropic efficiency ηk∗ is 0.7617; the total pressure drop ratio of the turbine πT∗ is 2.532, and the isentropic efficiency ηT∗ is 0.9088. Notably, the cooling characteristics of the turbine, the high-pressure gas inside the turbine, and the high-temperature gas outside the turbine convectively exchange heat, so that the maximum temperature of the turbine drops to 840.35 K, which is much lower than the maximum temperature limit of the GH93 of 1088 K. These characteristics provide room for the development of an increased turbine inlet total temperature or the use of low-cost and lightweight materials such as titanium alloys. From the perspective of lightweight materials, this means that the structural weight can be further reduced, which is conducive to the improvement of DSCI jet engine TWR(4)
Compared to the JetCat P500-PRO-GH, the DSCI jet engine has a 34.37% reduction in axial size and a 13.49% reduction in weight. Due to structural weight reduction, highOPR, and exhaust heat recovery, the TWR is increased by 39.4%, and the sfc is reduced by 36.82%. So, the DSCI jet engine has significant advantages in performance indicators and economic indicators in the same size engine, especially the potential to increase the turbine inlet total temperature and the complete expansion of the nozzle, which can make the DSCI jet engine performance higher.



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*Source: 9931701-2021-12-01.xml*