Numerical studies for performance improvement of a variable geometry dual mode combustor by optimizing deflection angle

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Numerical studies for performance improvement of a variable geometry dual mode combustor by optimizing deflection angle

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Harbin Institute of Technology, 150001 Heilongjiang, People’s Republic of China

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Article history: Received 14 December 2016 Received in revised form 16 May 2017 Accepted 21 May 2017 Available online xxxx

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Shuo Feng, Juntao Chang ∗ , Yuanshi Zhang, Chenlin Zhang, Youyin Wang, Wen Bao

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Keywords: Variable geometry dual mode combustor Optimizing deflection angle Combustor performance

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As part of our efforts to study the effect of the deflection angle on combustor performance of a variable geometry dual mode combustor, the flow field characteristics and mechanisms of the combustor performance loss, which comprised of compression loss, combustion heat addition loss and expansion loss, were investigated in the variable geometry dual mode combustor numerically with a Mach number of 3, a divergence ratio of 1.76, a fuel equivalence ratio of 0.6, and a deflection angle ranging from 8◦ to 16◦ . Numerical results indicated that the total pressure recovery coefficient and combustion efficiency increased with the deflection angle and there was a maximum to be obtained at the deflection angle of 12◦ due to the interaction between the dominant shock resulted by combustion heat release and the additional shock caused by the wedge system. Irreversible entropy generation loss was analyzed specifically in this paper to clarify and describe the combustor performance loss for the variable geometry dual mode combustor. Moreover, thrust-to-drag ratio was utilized to assess the effect of the deflection angle on combustor performance. By taking into account the flow field characteristics and combustor performance characteristics, the high combustor performance of a variable geometry dual mode combustor can be improved by selecting and optimizing the deflection angle. © 2017 Elsevier Masson SAS. All rights reserved.

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1. Introduction

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Many different launch vehicle concepts have been proposed in the search for a space shuttle replacement [1–4]. Each of these vehicles promised to reduce costs and increase reliability over current launch vehicles. Low cost, reliability, flight safety and quick access to orbit are the aims pursued by space transportation industries. They can be operated over a wide range of flight Mach numbers if a multi-cycle propulsion system [5–7] is used. Huang et al. [8] studied the combustion characteristics of a rocked-based combined-cycle engine combustor numerically. Much work has been done on this particular aspect in recent years. Candon et al. [9] studied the effect of different configurations by three design parameters, namely, the streamwise injection position, injection total pressure, and injection angle, on thrust augmentation. Mahto et al. [10] studied the effect of the length-to-depth ratio and Mach number on the performance of a typical double cavity scramjet combustor. There was an optimal length-to-depth ratio of 7 for the performance of the double cavity. Zhang et al. [11] studied the ef-

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*

Corresponding author. E-mail addresses: [email protected] (S. Feng), [email protected] (J. Chang), [email protected] (Y. Zhang), [email protected] (C. Zhang), [email protected] (Y. Wang), [email protected] (W. Bao). http://dx.doi.org/10.1016/j.ast.2017.05.025 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.

fect of heat release on movement characteristic of shock train in an isolator by an unsteady numerical simulation. The shock train movement is classified into these stages by the pressure distribution or shock train location. Gerlinger et al. [12] improved the mixing enhancement in turbulent high speed flows by a favorably chosen strut geometry for dual mode combustor. Malsur et al. [13] studied the effect of the mixing and combustion behavior of ethylene fuel on the combustion performance through numerical simulation with a series of fuel equivalence ratios in a supersonic combustor. Roncioni et al. [14] studied the performance assessment of the aero-propulsive balance by different CFD-codes. The emission index of NO (nitrogen monoxide) could be drastically reduced by shifting the injector struts further downstream without compromising the combustion efficiency. Tian et al. [15] studied the effect of the thermal throat location on the performance of the dual mode scramjet. Kuamr et al. [16] studied complex-box algorithm method to optimize the position of fuel injection struts for maximizing thrust and combustion efficiency in a dual mode combustor. The results indicated that a change in the position of struts, one at the front and two struts at the back resulted in better maximum thrust and combustion efficiency. However, as previously mentioned, considering the operating boundary constrains of scramjet and required thrust, it is very difficult to operate in a wide flight Mach numbers for the scramjet combustor with fixed geometry.

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Nomenclature

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D F h1 h2 l r Ma p Pt s S irr T Tt

drag of total combustor, N thrust of total combustor, N vertical distance from wedge slider to upper wall of combustor, m height of isolator, m length of oblique shock train, m length of section II, m Mach number static pressure, Pa total pressure, Pa static entropy, J/K entropy per mass, J/kg K static temperature, K total temperature, K

T AFT x y Y

η ξ

σ ??

κ

adiabatic flame temperature, K axial distance from isolator entrance, m longitudinal distance of combustor, m species mass fractions combustion efficiency divergence ratio total pressure recovery coefficient fuel equivalence ratio thrust-to-drag ratio

Subscripts 0



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isolator entrance increment

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From a thermodynamic point of view, the extension of the flight Mach number range requires different divergent ratios for a combustor to balance the isolator–combustion interactions with engine safety operation. Indeed for a higher Mach number, it will be necessary to use less divergent ratio for a combustor to avoid the decrease in combustor performance. On the contrary, in order to extend the flight envelope to a lower Mach number, the divergence ratio of combustor must rise to accommodate large heat release. Optimum combustor performance is always influenced by the interactions between the combustor geometry and heat release for a wide range of flight Mach numbers. Several approaches have been proposed in the literature for fulfilling this required adaptation between combustor geometry and heat release. Since 1993, French and Russia have developed a variable geometry dual-mode ramjet called the Wide Range Ramjet (WRR) [17,18], following the concept of variable geometry in the scramjet flow path. Experimental and numerical studies have been conducted to design the WRR prototype and develop the system technology tests for several years. By comparing a fixed geometry combustor with the WRR, the performance of the fixed geometry combustor was obviously lower than the performance of WRR at a flight Mach number range from 1.5 to 3.5 because of the lack of a geometrical throat and the deficiency of lower divergence ratio. As the flight Mach number was increased, WRR still had a performance better than that of the fixed geometry combustor. The French program [19–21] carried a variable geometry dual-mode combustor, which globally rotates the cowl around an axis placed upstream of the minimum cross section area, and operates in the Mach number range from 2 to 8. For a low Mach number flight, the upstream part of the cowl was moved up to limit the divergence ratio of the combustor to a certain level. In the subsonic combustion mode, the combustor could be strongly diverging. When Mach number was increased, the divergence ratio of combustor was then progressively increased. In the supersonic combustion mode, the divergence ratio of combustor was then reduced for a Mach number of 8. These research results provided a good basis for an understanding the effect of different contributions on the aero-propulsive balance of a highly integrated hypersonic vehicle. An optimum combustor performance is always influenced by the interactions between the combustor geometry and heat release for a wide range of flight Mach numbers. The French and Russian proposed a variable geometry combustor by simply moving the engine cowl in the flight test program [22–25] taking place since 2003. A large part of technology development effort has been done in ground testing and then is dedicated to optimizing the combustor to deficiency ensure high performance. The modeling of the combustor was validated using basic experiment results taken

from literature. The supersonic combustion with cavity-strut injection [26] was investigated to improve the combustor performance in a model scramjet engine by studying the ignition schemes [27] and the fuel transport and mixing progress [28]. Avrashkov et al. [29] studied the gas-dynamic structure of the variable geometry dual mode combustor in detail. The results showed that tests of the variable geometry dual mode combustor of a wide-range ramjet engine had stable operation and the required performance over the entire model range of flight conditions. Based on French– Russian variable geometry dual mode combustor, Feng et al. [30] studied the effect of divergence ratio on flow field characteristics and mechanism of combustor performance loss. However, the effect of deflection angle on the flow field characteristics and combustor performance loss by using hydrocarbon fuel for the variable geometry dual mode combustor was not reported. Therefore, the French–Russian variable geometry dual mode combustor [29] was introduced to study the effect of deflection angle on flow field characteristics and the mechanism of combustor performance loss, including compression loss, combustion heat addition loss and expansion loss, with a Mach number of 3, a divergence ratio of 1.76, a fuel equivalence ratio of 0.6, and a deflection angle ranging from 8◦ to 16◦ . The effect of the deflection angle on the wall static pressure distribution, total pressure recovery coefficient, and combustion efficiency were investigated numerically for the variable geometry dual mode combustor with different deflection angles by taking into account the interaction between the dominant shock system caused by combustion heat release and the additional shock generated by the wedge slide system. Irreversible entropy loss analysis was utilized to study the mechanism of combustor performance loss for the variable geometry dual mode combustor. Moreover, the thrust-to-drag ratio was used to assess the combustor performance of the variable geometry dual mode combustor with different deflection angles. By taking into consideration the total pressure recovery coefficient, combustion efficiency, and thrust-to-drag ratio, the optimum deflection angle can be selected and obtained for the high performance of the variable geometry dual mode combustor with different deflection angles.

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2. Combustor model and computational fluid dynamic model

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2.1. Combustor setup

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The current set of numerical results was obtained using the variable geometry dual mode combustor model. A schematic of the variable geometry dual-mode combustor can be found in Fig. 1. The air entered the isolator segment of the combustor at a Mach

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Fig. 1. Schematic of variable geometry dual-mode combustor.

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Fig. 2. Schematic of operation sequence for the test facility.

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number of 3.0. The divergence ratio of the combustor was defined by h2 /h1 and was given as ξ = 1.76. The fuel equivalence ratio was given as ϕ = 0.6. The deflection angle of the combustor was varied from 8◦ to 16◦ to analyze the effect of the deflection angle on the combustor performance. The combustor had four sections (labeled as I, II, III and IV in Fig. 1). Section I was a constant cross section isolator and the struts were located at the central part of segment I. In order to minimize aerodynamic disturbance in the flow field and struts drag, a thin strut was employed with a blockage ratio of 3%. The combustor sections included a symmetric divergent section II, a constant section area III, and an inner nozzle section IV. When the combustor was operated under the ramjet mode in a low flight Mach number to avoid thermal blockage, the combustor was required to maintain a high divergence ratio to obtain good combustor performance. When the combustor was operated under the scramjet mode at a high flight Mach number, the divergence ratio was required to be small for obtaining good combustor performance. To measure the static pressure, a total of 28 pressure-tap ports are distributed on the center line of one side of the combustor wall. There are 28 pressure transducers mounted on the side wall of the combustor, which measure the pressure within the range of 0 ∼1 MPa with the maximum error of ±0.25% at the frequency of 0.5 kHz. The transducers are calibrated using least squares linear regression fits. All pressure values use to generate the calibration lines within 0.5% of the corresponding linear fit values. In order to improve ignition, the equivalence ratio during the ignition stage is set to ϕ = 0.5 and the fuel was injected only from the central strut. The detailed operation sequence of the system for a typical test is showing in the Fig. 2. Firstly, the pressure data acquisition starts

to run at t = 0. After a short period, the heated air flow enters the combustor through the two dimensional nozzle of the heater. Once a steady flow is established, the fuel injectors are turned on. Ignition then occurs at t 3 , this process usually lasts for 1.5 sec which ended at t 4 . Finally, a sustaining combustion heat release formed in the combustor for several seconds.

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2.2. Computational fluid dynamics model

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2.2.1. Numerical modeling In order to provide extra information for the flow field analysis of the variable geometry dual-mode combustor, the twodimensional model with computational fluid dynamics is employed to illustrate the effect of the deflection angle on combustor performance of the variable geometry dual mode combustor with a CFD commercial software FLUENT. A Navier–Stokes solver was provided to calculate the steady flow field surrounding the variable geometry dual-mode combustor model. The governing two-dimensional compressible Reynolds-averaged Navier–Stokes (RANS) equations were discretized using the finite volume framework. The advection term was discretized using the advection upstream splitting method (AUSM) scheme. The governing RANS equations of continuity, momentum and energy were coupled together using the density based solver. The coupled set of governing RANS equations were discretized in time using an implicit Euler scheme for steady-state simulation, thus time-marching proceeded until a steady-state solution was reached. In spatial discretization methods, a second order upwind scheme was used for the flow term, the turbulent kinetic energy term, and the specific dissipation rate term.

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Table 1 Reaction rates for the one-step mechanism [36]. Reaction

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Table 2 Species concentrations of air stream and hydrocarbon jet.

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Parameter of entrance

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The SST (shear stress transport) k–ω turbulence model is a hybrid of the standard k–ε and the k–ω models. The SST k–ω turbulence model can improve the ability to predict the flow separation better than the k–ε model by Bradshaw’s assumption [31]. Menter’s two-equation k–ω turbulence model SST was implemented with default closure coefficients [32]. However, it is also worth considering that RANS simulations are very sensitive to the values used for turbulent Schmidt and Prandtl numbers [33]. Hassan et al. [34] showed the resolved field to derive estimates for the turbulent Schmidt which was not constant with strong variations throughout the flow. Present work took the turbulent Schmidt number as 1.3 to obtain the best pressure profile. Smirnov et al. [35] performed a chemical kinetics mechanism on the acetylene with 11 reaction and 9 components. A modified k–omega turbulence model was used to simulate flame acceleration. In the calculations, single-step kinetics and finite-rate/eddy-dissipation were used to model the kerosene turbulence chemistry interaction kinetics. Rate data for the C12 H23 –O2 forward reaction mechanism had been adapted from Westbrook et al. [36] (see Table 1). This chemical mechanism already had a good agreement with that of rate data on the mixing and combustion characteristic of kerosene by Kumaran et al. [37]. The molecular formula of the hydrocarbon was assumed to be C12 H23 , and the supersonic freestream was composed of 21% O2 and 79% N2 . Then the chemical reaction equation for the hydrocarbon was

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C12 H23 + 17.5O2 → 12CO2 + 11.5H2 O

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The single chemical reaction rate expression [35] was usually expressed

R 1 = R exp(− E a / T )[fuel]α ( O 2 )β

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where R 1 was chemistry reaction rate, R was the pre-exponential collision frequency factor, E a was the activation energy, and ?? were the reaction rate coefficients.

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2.2.2. Boundary condition and initial conditions The boundary type of isolator entrance was chosen as a pressure-inlet. The static pressure, total pressure and total temperature of the isolator entrance were chosen to be 0.06 MPa, 1.68 MPa, and 1505 K, respectively. The boundary type of the injection was chosen as the mass-flow-inlet. The injector exit static pressure was at 1.1 MPa. The kerosene fuel was injected at 600 K from the fuel injection port. In general, the liquid hydrocarbon fuel required quick vaporization before mixing and the subsequent combustion. Their relatively long ignition delay times typically exceeded the residence time of the gas flow within combustor. The evaporation and diffusion of the liquid hydrocarbon droplets are a non-equilibrium progress. Tyurenkova et al. [38,39] investigated steady-state combustion of a liquid fuel droplet in the atmosphere of oxidizer under the condition of non-equilibrium evaporation from the surface. A mathematical simulation model was developed for non-equilibrium droplet evaporation by Dushin et al. [40]. Moreover, the evaporation kinetics were also an important parameter for modeling the evaporation. The evaporation kinetics were taken into account for studying the droplet evaporation mechanism and modeling the evaporation and ignition in the combustor by Betelin et al. [41]. The model applied both deterministic methods of continuous mechanics of multiphase flows to determine the

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mean values of parameters of the gaseous phase and stochastic methods to describe the evolution of polydispersed particles and fluctuations of parameters. However, the diffusivity was higher for the gaseous hydrocarbon fuel. In order to improve the mixing of the air-fuel and the stable combustion, more studies have demonstrated the investigation of supersonic combustion of gaseous hydrocarbon fuel by Kumaran et al. [37]. Thus, the kerosene was assumed as a gaseous in the paper. The air was modeled as a thermally perfect air and the fuel was modeled as a single-specie. Viscosity of the mixture was evaluated using the mass-weighted-mixing law. For the individual fluids in the mixture, these properties were evaluated using the Sutherland’s law and fifth-order polynomials in temperature. The ratio of specific heats is calculated by the temperature polynomial. Based on experiment results, the turbulent intensity of 10% is appropriate to the inlet of fully development of turbulence. The hydraulic diameter value (to estimate the turbulent length scale) at the entrance and the fuel injection ports were specified as 40 mm and 0.05 mm. All the variables of the supersonic flow at the combustor exit were determined from the interior of the domain by extrapolation. Non-slip and adiabatic wall conditions were employed for the solid boundary with standard wall functions. The species concentrations of air stream and hydrocarbon jet were shown in Table 2. Y O2 is the oxygen mass fraction in air. Y N2 is the nitrogen mass fraction in air. Y C12 H23 is the fuel kerosene mass fraction.

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2.2.3. Grid independence and validation The computational mesh was established using the ICEM software. The computational grids were optimized to capture the relevant physical and chemical features. Three computational grids of 0.32 million (coarse) nodes, 0.75 million (medium) nodes, and 1.1 million (fine) nodes were used to study the grid independence. The grids approaching the wall were distributed using geometric proportion way in order to capture the boundary layer. The height of the first cell center above the test-section floor was 0.01 mm. As shown in Fig. 3, the static pressure distribution was obtained from three computational grids. The detailed conclusion can be seen from good agreement between the curves of static pressures. The medium grids were used for the numerical simulations. The method of error estimates was from Smirnov et al. [42]. The numerical calculation error estimates were shown in Table 3.

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2.2.4. Numerical methods of validation In general, the wall pressure parameter is one of the most basic flow field parameters. The flow field parameters, for example, Mach number and temperature distribution can be obtained by the one-dimensional calculation based on the wall pressure data. Moreover, for the experimental validation of wall pressure measurements, much work has been done on the validation method. For example, Huang et al. [43] studied the interaction between the incident shock wave and the transverse by using the wall pressure validation method. Zhang et al. [44] studied the flow field characteristics and combustion modes classification for a strut/cavity dual-mode combustor by using the wall pressure validation method. Tian et al. [45] studied the effect of the air throttling on combustion mode formation and transition and also studied the combustion heat release by using the wall pressure validation method. Thus, the validation method may be reasonable for the

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Table 3 Numerical calculation error estimates. Allowable error 5% 5% 5%

Grid resolution 160 · 2000 250 · 3000 320 · 3450

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Reliability Rs = nmax /n

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Fig. 3. Certification of grids independence.

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Fig. 5. Effect of the deflection angle on wall static pressure distribution at φ = 0.6.

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entrance along the airflow direction and then reached the peak pressure as heat release increased. The wall pressure progressively decreased. By comparing numerical simulations with experimental results, the static pressure distributions remained almost coincident in the combustor.

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Fig. 4. Comparison of experimental and numerical static pressure distributions.

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3.1. Effect of deflection angle on wall pressure and Mach number distribution

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paper. For validation of numerical methods, two wall static pressure distributions by comparing numerical simulations with experimental results were obtained in Fig. 4. The current set of experimental results was obtained by the variable geometry dual-mode combustor with θ = 12◦ using the supersonic combustion research facility of Harbin Institute of Technology in China. The experimental results were represented using different symbols with different conditions. Numerical simulation results were represented by straight lines with different colors. The wall pressure distribution was obtained on the center line of side wall. It can be seen from Fig. 3 that the pressure increased from the vicinity of isolator

As shown in Fig. 5, for a given φ = 0.6 and ξ = 1.76, several typical wall static pressure distributions were obtained with different deflection angles for the variable geometry dual-mode combustor. It can be seen from Fig. 4 that the adverse pressure gradient is great enough that the pre-combustion shock train is formed in section I. With the increasing of the deflection angle, the length of the shock train gradually decreases in section I, until the minimum length of the shock train is reached at θ = 12◦ . Then with the further increase in the deflection angle, the length of the shock train begins to increase due to the rise in adverse pressure in section II. Moreover, as one can see from the figure, the static pressure of the combustor progressively rises due to the intense combustion when the deflection angle is increasing. The nature of the result is due to the interaction between the additional shock system generated by the wedge and the dominant shock system caused by combustion heat release. The maximum peak static pressure is reached at θ = 16◦ . As shown in Fig. 6, the axial distribution of mass-weighted average Mach number for the combustor was obtained with the different defection angles. The Mach number begins to decrease from supersonic to subsonic as the amount of heat release increases near the strut. The drop in Mach number is accompanied by an increase in static pressure. When the divergence ratio of the combustor is not sufficient to relieve the thermal occlusion resulting from the heat addition, the adverse pressure gradient of the isolator exit rises, which causes boundary layer separation in section I. Therefore, the Mach number abruptly decreases in section I and section II. The Mach number has a small change in section III due to the balance of the combustor geometry and heat release interactions. Moreover, it can be also seen from the Fig. 6 that intense

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Fig. 6. Mass-weighted average Mach number distribution for different deflection angles.

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combustion occurs when the deflection angle is increasing, and the Mach number is the smallest in the combustor with θ = 16◦ . It appears that a considerable increase in heat release is observed when an additional disturbance activates the dominant system of shocks due to the rise in deflection angle.

In order to further explain the flow field structures in the combustor, the Mach number contour shown in Fig. 7 reveal significant differences in flow separation and the pre-combustion oblique shock trains. It can be seen from Fig. 7a that both the speed of propagation and the downstream location, at which the shock train originates, depend strongly on the adverse pressure resulted by heat addition. The adverse pressure induces the boundary layer separation on the upper and lower wall. Boundary layer separation does occur in section I and section II. When the supersonic flow entering the combustor encounters the blockage caused by the separated flow near the wall, it forms an effective compression ramp from compression wavelets coalesce into the oblique shock waves. The oblique shock waves intersect and improve the refracted shock waves that bound a primary compression region. The shock refractions subsequently interact with the separated boundary layer and reflect into additional shock structures, which causes further thickening of the boundary. The resulting oblique shock train is located partially in section I and partially in section II in response to varying imposed back pressures. An oblique shock train adiabatically compresses the flow until its pressure is equal to the peak pressure in section II. It can also be seen from Fig. 7, when the deflection angle is gradually increasing from θ = 8◦ to θ = 12◦ , the effect of the thermal blockage becomes less up to θ = 12◦ in section II. It appears

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Fig. 7. Mach number contour for different deflection angle.

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12◦ , the total pressure loss begins to increase quickly. Moreover, it can be seen from Fig. 8 that the total pressure always decreases with increasing heating in section II and section III.

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Fig. 8. Mass-weight average total pressure recovery coefficient increment of combustor exit.

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that the dominant system of shocks caused by combustion heat release overcomes the additional shock system caused by the slight rise in deflection angle. The supersonic portions occurs in section II with θ = 12◦ . lc is a minimum to appear in section I. When the deflection angle is larger than 12◦ , the additional shock system caused by the slight rise in deflection angle dominants the combustion system. The combustion mode gradually transmits from supersonic to subsonic mode in section II. So l is added in an increase of the deflection angle in section I. As shown in Fig. 7f, lmax is seen at θ = 16◦ .

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3.2. Combustor performance loss mechanism

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3.2.1. Effect of deflection angle on total pressure recovery coefficient loss In general, the total pressure recovery coefficient associated with combustor performance loss of a combustor is always considered and analyzed with a total pressure recovery coefficient at θ = 16◦ as the reference value. The change in total pressure recovery coefficient can be calculated by dividing the total pressure recovery coefficient at θ = 16◦ . As shown in Fig. 8, the total pressure recovery coefficient of the combustor exit initially increases asymptotically with an increase in deflection angle, then reaches a maximum at θ = 12◦ , and finally decreases rapidly. This drop in total pressure recovery coefficient is accompanied by an irreversible entropy loss. Moreover, the total pressure recovery coefficient quickly falls off when the deflection angle is larger than 12◦ . The total pressure recovery coefficient for θ = 16◦ is 9% lower than that for θ = 12◦ . The detailed flow field information about total pressure contours are shown in Fig. 9. When the combustion begins near the strut, the total pressure decreases quickly associated with an increase in total temperature. Boundary layer separation does occur in section I and section II due to the increase in adverse pressure gradient. This causes in local thickening and separation of the viscous layer within the section I. It means that there is a high total pressure loss in section I and section II. The total pressure loss in section I is caused by friction in the down and upper wall. The total pressure loss in section II and section III is caused by combustion addition heat. la in section I is higher than lc . The total pressure in core region increases gradually with deflection angle up to θ = 12◦ and there is a maximum in section I with θ = 12◦ . With the further increase in deflection angle, l gradually increases. The total pressure in core region decreases by distinguishing contours label in total temperature. It means that the total pressure loss progressively decreases with the increase in deflection angle up to θ = 12◦ . And the total pressure loss is a minimum at θ = 12◦ . Then when the deflection angle is further increase to more than

3.2.2. Effect of deflection angle on combustion efficiency loss In order to obtain the combustion efficiency of the combustor with different deflection angles, the total temperature of the combustor exit is generally obtained by a mass-weighted average. The T −T combustion efficiency defined as η = T t − Tt0 . It is assumed that AFT t0 combustion occurs without either heat or work interaction with the surroundings, then the enthalpy of the final products will be the same as the initial reactants. The final equilibrium heat temperature is defined as the adiabatic flame temperature. The change in combustion efficiency can be calculated by dividing the combustion efficiency at θ = 16◦ . As shown in Fig. 10, the combustion efficiency begins to increase with the rise in defection angle, with a maximum at θ = 12◦ . When the deflection angle is larger than 12◦ , there is an obvious decrease in combustion efficiency. The equivalent heat addition by fuel combustion changes the static temperature and the flow velocity, and so is reflected in the increase in total temperature. It can also be seen from Fig. 10 that when the deflection angle is larger than 12◦ , the combustion efficiency of the combustor drops off abruptly, deflection angle has a great impact on combustion efficiency. For example, the combustion efficiency with θ = 12◦ is 8% larger than that at θ = 16◦ . The detailed flow field information about total temperature contours are shown in Fig. 11. The combustion release heat region includes section II and section III. When the combustion release heat begins near the strut, the total temperature increases quickly in section II. It can be seen from Fig. 11a that high temperature airflow propagates into the section I due to the increase in adverse pressure. The l in section I decreases with the increase in deflection angle, with a minimum up to θ = 12◦ . By comparison with θ = 12◦ , lc is obvious lower than la for θ = 8◦ .Then when the deflection angle is larger than θ = 12◦ , the l in section I increases. It appears that l f is obvious higher than lc . So the high temperature region increases with the increase in deflection angle more than 12◦ . Moreover, as shown in Fig. 11, rc in θ = 12◦ is 33.8% lower than ra for θ = 8◦ . It means that the atomization and evaporation of the fuel are mixed adequate with flow air in section II with θ = 8◦ . It contributes to combustion and greater high temperature regions in section II. When the deflection angle is higher than θ = 12◦ , the high temperature regions in section II obviously decreases by referring to the color label of total temperature.

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3.2.3. Effect of deflection angle on entropy loss Any entropy increase associated with total pressure decrease is considered as irreversibility. The entropy increase associated with irreversibility is an important performance parameter for combustor performance loss. The four sections of the variable geometry dual mode combustor have different combustor performance loss mechanisms. Boundary layer friction loss occurs in section I, combustion heat loss caused by heat addition occurs in section II and section III, and expansion loss occurs in section IV. As can be seen in Table 4, there is a cumulative entropy increase due to irreversibility in the four sections of the combustor. The entropy increase of section I is generated by friction and the oblique shock train due to boundary layer separation caused by heat addition. The entropy increase gradually decreases with the increase in deflection angle until the deflection angle up to 12◦ . There is a minimum at 12◦ in section I. And when the deflection angle is larger than 12◦ , the entropy increases. Similarly, the entropy loss also begins to decrease with increase in deflection angle in section II, until the minimum entropy is reached at 12◦ . However, there is a maximum entropy loss at θ = 12◦ in section III with the increase in deflection angle. When the deflection angle is larger than 12◦ ,

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Fig. 9. Total pressure contours for different deflection angles.

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slightly with the rise in deflection angle. Thus, as shown in Table 4, the total entropy loss of the combustor drops from θ = 8◦ , then reaches the minimum entropy loss at 12◦ , and when the deflection angle is higher than 12◦ , the total entropy loss increases. In order to further demonstrate the entropy increase loss predicted in detail, Fig. 12 shows the entropy contours with different deflection angles. As the combustion heat release is added near the strut, the supersonic flow begins to form a lower Mach number and higher static temperature caused by an increase in an adverse pressure gradient in section II. The adverse pressure gradient will lead to boundary layer separation and form an oblique shock train in section I. It can be seen from Fig. 12 that lc is obvious lower than la for θ = 8◦ in section I. It appears that the entropy loss decreases from θ = 8◦ , with a minimum up to θ = 12◦ . When the deflection angle is larger than θ = 12◦ , l in section I gradually increases. And the entropy increase rises with the further increase in deflection angle.

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3.3. Effect of deflection angle on thrust performance

the entropy loss begins to decrease, which indicates that the heat release of the combustion gradually decreases in section III. Moreover, the supersonic air flow expands and the freestream velocity increases in section IV. The entropy loss in section IV increases

In order to analyze the effect of the different deflection angle on thrust performance of the variable geometry dual-mode combustor, the thrust-to-drag ratio is defined as κ = DF . F is given by the one-dimensional wall pressure integral. D is comprised of the drag of wedge and the viscous friction of the total combustor and

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Fig. 10. Mass-weighted average combustion efficiency at the combustor exit versus deflection angle.

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Table 4 Entropy per mass of different combustor sections for different deflection angles.

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S irr (J/kg K)

θ = 8◦

θ = 11◦

θ = 12◦

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θ = 16◦

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section section section section Sum

201.0182 125.4959 93.5384 14.87 434.9225

137.5815 121.0079 149.0189 15.1692 422.7775

134.2444 120.0121 150.0227 15.34 419.6192

156.6946 120.9881 129.976 20.0913 427.75

171.3225 126.1273 124.8747 22.3041 444.6286

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4. Conclusions

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is obtained by numerical results. As shown in Fig. 13, κ begins to slightly rise with the increase in deflection angle, then reaches a maximum at θ = 12◦ . Finally, when the deflection angle exceeds 12◦ , κ abruptly drops due to the high drag caused by the wedge. It can also be seen from Fig. 13 that the thrust-to-drag of the combustor varies little when the deflection angle is less than 12◦ . However, there is an evident drop about the thrust-to-drag to be seen at θ = 16◦ . The thrust-to-drag at θ = 12◦ is 32.8% higher than that at θ = 16◦ . Very significantly, there is a better thrust-to-drag to be obtained at θ = 12◦ .

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A numerical simulation investigation to place to study flow field characteristics and combustor performance loss mechanisms for a variable geometry dual mode combustor. Initial conditions in-

cluded a Mach number of 3, a divergence ratio of 1.76, a fuel equivalence ratio of 0.6, and a deflection angle ranging from 8◦ to 16◦ . It can been concluded that the flow blockage in the variable geometry dual mode combustor is caused by both combustion heat addition and the intense shock systems generated by the deflection angle. Numerical results indicated that the wall static pressure increases gradually due to augmentation of blockage intensity with increase in deflection angle. Moreover, the total pressure recovery coefficient and combustion efficiency at the combustor exit increased with the increase in deflection angle and there was a maximum to be obtained at the deflection angle of 12◦ due to the interaction between the dominant shock system caused by combustion heat release and the additional shock generated by the deflection angle. When the deflection angle is larger than 12◦ , the total pressure recovery coefficient and combustion efficiency at the combustor exit progressively decreases.

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III, and expansion loss in section IV. For section I and section II of the combustor, the irreversible entropy loss decreases with deflection angle up to 12◦ , then gradually begins to rise with the further increase in deflection angle. There is a maximum entropy increase loss with deflection angle up to 12◦ in section III, and the entropy loss decreases for deflection angle larger than 12◦ . The overall irreversible entropy loss actually has a minimum for θ = 12◦ . The thrust-to-drag ratio is an important parameter for evaluating the performance of variable geometry dual mode combustor. The thrust-to-drag ratio is a maximum for a deflection angle of 12◦ . Therefore, it can be concluded by the above discussions that the deflection angle of 12◦ should be selected and further optimized to improve combustor performance for variable geometry dual mode combustor.

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Conflict of interest statement

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Fig. 13. Effect of deflection angle on thrust-to-drag ratio.

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None declared.

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Based on irreversible entropy increase analysis, the four sections of the variable geometry dual mode combustor had different combustor performance loss mechanisms, which is dominated by compression loss generated by the friction and the oblique shock train in section I, combustion heat addition loss in section II and

Acknowledgements

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This research work is supported by National Natural Science Foundation of China (Grants No. 91441204, and No. 51421063, and No. 51676204).

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