Pressure rising slope variation accompanying with combustion mode transition in a dual-mode combustor

Accepted Manuscript Pressure rising slope variation accompanying with combustion mode transition in a dual-mode combustor

Chenlin Zhang, Juntao Chang, Shuo Feng, Jicheng Ma, Junlong Zhang, Wen Bao

PII: DOI: Reference:

S1270-9638(16)30687-3 http://dx.doi.org/10.1016/j.ast.2017.05.034 AESCTE 4047

To appear in:

Aerospace Science and Technology

Received date: Revised date: Accepted date:

20 September 2016 15 May 2017 25 May 2017

Please cite this article in press as: C. Zhang et al., Pressure rising slope variation accompanying with combustion mode transition in a dual-mode combustor, Aerosp. Sci. Technol. (2017), http://dx.doi.org/10.1016/j.ast.2017.05.034

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Pressure rising slope variation accompanying with combustion mode transition in a dual-mode combustor Chenlin Zhang1, Juntao Chang2, Shuo Feng3, Jicheng Ma4, Junlong Zhang5, Wen Bao6 Harbin Institute of Technology, 150001 Heilongjiang, People’s Republic of China Abstract: Direct-connect experiment with equivalence ratio linear increasing in a dual-mode combustor with a strut is conducted at free stream Mach number of 2.0. Based on the pressure histories on side wall, pressure rising slope variation accompanying with combustion mode transition is found and discussed. The pressure rising has different slopes vary as equivalence ratio linearly increasing. Meanwhile, this characteristic of pressure slope variation leads to the change of combustor thrust. By analyzing the combustion heat release zone and the geometric configuration combustor, a typical simplified geometric model is proposed and studied by using numerical simulation. The phenomenon of the pressure rising slope variation is obtained and explained by the shock train movement in numerical simulation. In the process of shock train movement, a normal shock is established at thermal throat to make the airflow of throat position reach critical state, which could limit the mass flow rate of the supersonic mainstream. Further, inviscid and isentropic flow analysis is employed to illustrate the variation of pressure rising resulted from the occurrence of a normal shock wave. The analysis indicates that the cross-sectional area of mainstream is bounded by the subsonic boundary layer plays a key role

1 PhD Candidate, School of Energy Science and Engineering, [email protected]. 2 Professor, Academy of Fundamental and Interdisciplinary Sciences, [email protected]. (corresponding author) 3 PhD Candidate, School of Energy Science and Engineering, [email protected]. 4 PhD Candidate, School of Energy Science and Engineering, [email protected]. 5 PhD Candidate, School of Energy Science and Engineering, [email protected]. 6 Professor, School of Energy Science and Engineering, [email protected]. 1

to alter the pressure rising slope. Keyword: Scramjet; Direct-connect experiment; combustion mode; shock train

Nomenclature Ma =

Mach number

k

=

specific heat ratio

Φ

=

equivalence ratio

A

=

cross-sectional area

Cf

=

wall skin friction coefficient

D

=

hydraulic diameter

dw

=

wetted perimeter

R

=

gas constant

m

=

mass flow rate

T*

=

total temperature

P*

=

total pressure

λ

=

speed factor

p

=

static pressure

ccr

=

critical speed of sound

δ

=

root mean square

Hr

=

relative error

i

=

number of cross-sectional area in supersonic mainstream

2

I.

Introduction

Supersonic combustion ramjet (scramjet) is reckoned to be the most promising propulsive option for hypersonic flight of wide Mach number. In the range of flight Mach 4 to 8, the combustor needs to operate in different combustion modes, which have distinct characteristics of the operation, including pressure distribution, thrust, specific impulse [1-3]. Based on thermodynamic cycle, under low flight Mach number, the engine would present a better performance in a ramjet mode. By altering the cross-sectional area in combustor, the performance of the combustor operation also could be advanced [4, 5]. The incoming supersonic flow is compressed into subsonic by shock train in isolator [6], and it is effective to reduce the Rayleigh loss in combustor. For high Mach number incoming flow, large shock compression loss in isolator would restrain the performance of ramjet mode. In flight process of dual-mode scramjet, proper combustion mode is a critical factor to maintain the superior performance of supersonic combustion ramjet. On the other hand, in decelerated or accelerated process of scramjet, spanning different Mach number of incoming flow leads to combustion mode transition accompanying with some special phenomena (parameters sudden change, hysteresis loop) [7-8], which would cause a large change in both engine thrust and specific impulse, and may cause catastrophic damage during flight. In order to improve performance and stability of dual-mode scramjet in a wide flight Mach number, the mechanisms of those special phenomena in combustion mode need to be further investigated and clarified. Combustion mode is affected by many factors, which have been investigated in many papers. Masumoto [9] adjusted the total temperature from 1500K to 2400K to make ramjet mode transform to scramjet mode in a dual-mode combustor. Based on the HIFiRE-2 configuration and experiments, Yentsch [10] investigated the effect of free stream Mach number alteration and combustor configuration on the combustion mode. Le [11] and Rockwell [12] discussed combustion mode transition by means of changing the equivalence ratio and using vitiation air, respectively. Huang [13-15] investigated the inlet boundary conditions at the entrance of the isolator, injection strategy and jet-to-crossflow

3

effects on the combustion mode. The inlet boundary conditions at the entrance of the isolator and the jet-to-crossflow pressure ratio both have a substantial impact on the combustion mode transition. The separation zone would expand upstream with the increase of the jet-to-crossflow pressure ratio, and this is induced by the movement of the shock wave train in the isolator. In addition, boundary-layer suction [16], penetration depth of fuel [17] and wall temperature [18] also influences the combustion mode. In the cavity configuration, Micka [19] found that combustor exist two distinct combustion stabilization locations for different total temperature of the incoming flow. One was anchored at the leading edge of the cavity by heat release in the cavity shear layer and the other was stabilized a short distance downstream of the fuel injection jet in the jet-wake. Similarly, Wang [20, 21] indicated there are three combustion modes in the configuration with cavity acts as a flameholder by increasing cavity length or equivalence ratio, or decreasing distance between the fuel injection and the cavity. The influencing factors mentioned above have indicated that combustion mode is sensitive to boundary conditions, which would lead to complicating flow characteristics in different combustion modes and process of combustion mode transition. During the combustion mode transition, Fotia [22, 23] considered the behavior of combustion mode transition and found that there was a sudden change in the wall static pressure profile. The flame position that occurred as the downstream boundary condition was changed abruptly when the flow became unchoked. Additionally, he also showed the different interferograms of combustion mode in cavity configuration combustor, used the second law of thermodynamics analysis of isolator impulse theory to clarify the sudden change. Xiao [24] obtained that the pressure suddenly changes with the equivalence ratio increasing accompanying during the combustion mode transition process. For the strut configuration, Kouchi [25] captured the sudden thrust increase and classified combustion mode into weak mode and strong mode for a scramjet engine with strut by numerical simulation. As mentioned above, the sudden change originates from combustion mode transition has been covered by many 4

papers. This special phenomenon appears in different configurations of supersonic combustor. This paper found a pressure rising slope turning phenomenon accompanying with combustion mode transition by monitoring the pressure transducers in the experiment, which is distinct from the pressure sudden change. For the pressure rising slope alteration, the change of the pressure distribution profile and thrust would bring a serious of problems and challenges on the dual-mode scramjet operation in flight, especially for the control. It is made a detailed discussion and explanation for the special phenomenon of shock train movement in numerical simulation and the one-dimensional flow analysis.

II.

Experimental Setup

The experiment was completed using the direct-connected scramjet experiment system at the Harbin Institute of Technology, China. The high-pressure air as the air source was supplied by a vast chamber, which can ensure that the effective run time reaches about 1 min. Inlet airflow from air source can be heated to a total temperature of 1050K and a total pressure of 1.1MPa through the alcohol-air combustion in an air-heating system, which was located upstream of the supersonic nozzle. Additional oxygen is injected to maintain a 0.21 O 2 mole fractions in the heated products. A two-dimensional Laval nozzle with an exit area of 40mmu100mm was utilized to accelerate the heated air to Mach 2.0. A schematic of the combustor model was used in the current experiment is illustrated in Fig 1. The model has a constant width of 100mm includes an isolator and a combustor. The constant area isolator has a 40mmu100mm cross section. The isolator-combustor is a single side divergent configuration on the upper wall, which can be divided into six segments by the different divergent angles. The detail sizes are shown in Fig 1. Strut is located in the rear of the isolator at about 460mm in the direction of flow, as shown in Fig 2, that there are 42 holes with diameter of 0.6mm spreading over both sides and trailing edge of the strut. Kerosene fuel at room temperature is injected from the strut in the direction normal to the air flow direction and it can also serve as active cooling agent and effectively relieves the aerodynamic heating on the strut. 5

Fig 1 Schematic diagram of the isolator-combustor with strut

Fig 2 Three-dimensional schematic diagram of the strut To measure the static pressure, 41 pressure-tap ports are distributed on the center line of one side of the combustor wall. Each port is connected with a pressure transducer by hollow metal ducts, which could protect transducers from combustion. The pressure transducers range 0-1MPa and error 0.2% in full scale. Hollow metal ducts are 2.5mm diameter and 200mm length, which will decay the cutoff frequency of pressure measurements. To decrease this decay as much as possible, the hollow metal ducts were filled with kerosene. According to a conservative estimation, the cutoff frequency of the system is higher than 1.1 kHz, taking the speed of sound in kerosene as 1324 m/s. In the current experiments, the pressures on the side wall were sampled at 5 kHz during the whole test process.

Fig 3 Operation sequence of the experiments 6

The detailed operation sequence of the system for a typical test is illustrated in Fig 3. First, the pressure data and mass flow rate acquisition system start to run at t0. After the alcohol-air is ignited and release heat in the air-heating system, heated high-enthalpy airflow 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 in the combustor at t3, and processes of ignition lasted 0.5s, which ended at t4. Finally, a sustaining combustion heat release formed in the combustor for several seconds.

III. Results and Discussion A. A phenomenon of variation of pressure rising slope with equivalence ratio linear increasing in experiment Fig 4 is the equivalence ratio history of fuel which is injected from both sides of the strut in the experiment. Because of the requirement of strut ignition for the fuel, the initial equivalence ratio is set as Φ=0.25 to fulfill to ignite from 0s to 1s. The ignition could form a tranquil flame at the rear of the strut to maintain combustion stability in combustor. During the process of equivalence ratio increasing from 0.25 to 0.4, a slight overshoot is unavoidable at about 1s because the kerosene injection pressure needs to be sharply increased in the experiment. Subsequently, it is corrected quickly by relying on the system of closed-loop control, which includes turbine flow-meter, motor pump, and so on. To investigate the effect of linear increasing fuel on combustor mode, it is demanded that a relatively stable flow field should be established before the fuel is raised. This means there is absent of dynamic behavior of flow to interfere the initial flow field of fuel variation stage. Refer to the previous experience of experiments has been done in the last few years, keeping constant fuel continuously supplying at 1 second interval suffices to make the pressure distribution of combustor get to stability. Therefore, from 1s to 2s, the constant equivalence ratio Φ=0.4 is set to obtain a steady flow field before the fuel linearly increase. After 1.5s, the fluctuation of equivalence ratio originated from overshooting gradually attenuates and accompanies with the mass flow rate of fuel increasing. From 2s to 5.5s, the equivalence ratio 7

of fuel is altered from 0.4 to 0.9.

Fig 4 Equivalence ratio variation along with time in experiment Fig 5 is the pressure distribution of different moments from 2.0s (Φ=0.4) to 3.5s (Φ=0.614) in the isolator-combustor. The time interval between adjacent pressure distributions curves are 10 milliseconds. The five segments (I-V) have different divergence ratio is shown on top of the Fig 5. In the constant isolator, the segment I, the pressure distribution gradually is changed by the enhancing of combustion heat release and the leading edge of pressure distribution propagates toward to entrance of isolator from 400mm to 200mm in the direction of flow, which means the shock train in the isolator is pushed forward. With the equivalence ratio increasing, the pressure peak at about 600mm rises up to about 550KPa at 3.5s (Φ=0.614) in divergent segment II, where is the main combustion zone mentioned by Hu [26]. The divergent structure is also beneficial to accommodate more heat release and improve the combustor performance. In the second constant area segment III and second divergent segment IV, the pressure declines to near the environmental pressure. In general, this is the typical pressure distribution of the dual-mode combustor.

8

Fig 5 Pressure distributions along flow direction from 0mm to 1200mm in experiment

Fig 6 Pressure distributions along flow direction from 400mm to 800mm in experiment To investigate the pressure rising slope variation in the experiment, the part of Fig 5 from 400mm to 800mm in x-axis is enlarged. Just as shown in Fig 6, the typical pressure distribution 1 and 2 is denoted by the red line. In view of there is the same time interval at every adjacent pressure distribution, the sparse curve between the typical pressure distribution 1 and 2 indicates that the pressure rising slope in combustor is accelerated at the same equivalence ratio increment. From 2.0s (Φ=0.4) to 3.5s (Φ=0.614), the pressure rising experiences the slow-fast-slow process. Fig 7 is the pressure history monitored by the transducers from T13 to T18, which are distributed from 505mm to 705mm in the flow direction. According to Fig 4, the pressure history has a little lag comparing with equivalence ratio 9

variation and different pressure paths from T13 to T18 are similar in Fig (a). To investigate the pressure a path history in detail, typical pressure history of transducer T13 is showed in (b), which is located at 505mm in flow direction. Before 1s, the initial equivalence ratio Φ=0.25, which has fulfilled the ignition successfully, provides stable 310KPa pressure at T13 location. At 1s, with the Φ=0.25 is up to 0.4, the pressure is sharply boosted to 400KPa, the pressure overshoot may result from sudden increasing of heat release gradually remits until 1.675s. Comparing path of pressure history with path of equivalence ratio, there exists about 0.11s delay for the propagation process. In the period of Φ=0.4, pressure reaches a steady state between 1.675s and 2.36s. The relatively steady flow field is established under conditions of identical equivalence ratio. After 2.36s, the pressure at T13 starts to quickly rise at slope 1 of about constant 355KPa/s. It is just the region that is between typical pressure distribution 1 and 2 in Fig 6. Beyond 2.86s, the pressure rising slope1 converts to slope2 that is 74KPa/s, and the pressure variation rate decelerates obviously. The fuel equivalence ratio of linear increasing injected into combustor at a constant rate leads to two different constant slopes of pressure variation. And this change would cause other parameters change, such as specific impulse and thrust. Especially, because the location of pressure variation mainly occurs in divergent segment II, it could have a direct effect on the performance of combustor.

(a) Pressure variation histories at T13 to T18

10

(b) Pressure history of T13 Fig 7 Pressure variation histories at different transducers in experiment B. The characteristics about the process of pressure rising in mode transition To further investigate the combustor performance and parameter distribution in the experiment, solving the typical quasi-one-dimensional mass, momentum, and energy conservation equations based on a 1-D analysis approach is employed by reference paper [27]. In this paper, the 1-D model of the combustor is based on the following equations (1) (2) for Mach number Ma and total temperature T*DŽ A is the cross-sectional area of the combustor. The wall skin friction coefficient Cf was estimated by the Van Driest method [28]. The hydraulic diameter D is defined to be 4A/dw, where dw is the wetted perimeter of the duct.

dMa Ma

1 §  k  1 kMa 2  1 dT * Ma 2 dx º 2 · ª dA 1 Ma 4C f    ¨ ¸« 2 * Ma  1 © 2 2 T 2 D »¼ ¹¬ A

(1)

dT * T*

ª Ma 2  1 dp dA 1   k  1 Ma 2 1 dx º   4C f « » 2 2 1   k  1 Ma 2 ¬ kMa p A 2 D¼

(2)

11

(a) Pressure distributions at 2.36s and 2.86s

(b) Mach number distributions at 2.36s and 2.86s Fig 8 Pressure and Mach number distributions at 2.36s (Φ=0.451) and 2.86s (Φ=0.523) Fig 8 (a) is the pressure distribution at 2.36s and 2.86s, which are the turning point of pressure rising variation corresponding to Fig 7 (b). Between the two pressure curves there is the region of pressure rising variation at slope1. Fig 8 (b) is the one-dimensionally estimated Mach number distribution obtained by formula (1) and (2) in the flow direction. It can be seen obviously that Mach number distribution is above 1 at 2.36s, and Mach number distribution at some sections is below 1 at 2.86s. It is the special position point which is Mach number equals to 1 and is reckoned where is the thermal choking position, just as shown in Fig 8 (a). Choking point indicates the occurrence position of combustion mode transition. At 2.36s, thermal throat does not exist in the whole flow channel. The main stream passes through combustor at supersonic speed. With equivalence ratio increasing, the heat release leads to the state of flow 12

field changed. At 2.86s, two thermal choking points appear at about 580mm and 820mm, which means the airflow experiences combustion mode transition process. The pressure rising at slope1 indicates the transition process of combustion mode, or the occurrence of combustion mode transition would accompany with pressure rising change.

Fig 9 Thrust of isolator-combustor from 2s to 3.5s Fig 9 is the thrust of experiment from 2s to 3.5s. The thrust is available from experimental wall pressure integral. Along with the equivalence ratio increasing, the thrust is also added. At the stage of pressure rising at slope1, the thrust abruptly increases at about 2.49s (Φ=0.470), and the thrust increment is bigger. Subsequently, the thrust slope reduces because of the pressure rising gets slow at slope2. The alteration of thrust is undesirable in the operation of aircraft in reality. It would add the difficulty of aircraft control. C. Mechanism of pressure rising slope variation from numerical simulation

Fig 10 Schematic of numerical calculation model The isolator-combustor model has many diverse configurations and structures design, such as strut or cavity flameholder. The main factors influence on pressure distributions contain incoming flow condition, position of 13

combustion heat release and internal channel geometry profile of isolator-combustor model. For the experiment configuration with strut in this paper, the strut forms a mechanism throat, and downstream of strut is divergent segment. For combustor configuration with cavity, fuel injection from the upper wall forms a blockage which plays a role of throat, and downstream cavity acts as a role of the divergent section. In order to elucidate the mechanism of pressure rising slope variation, a common model is proposed and employed to numerical simulation. Fig 10 is the simplified model abstracted from common isolator-combustor configurations, including generalized throat which is the trigger of combustion mode transition and generalized divergent segment. In Fig 10, the model has a pair of fuel injection ports on side walls at 380mm in flow direction, and has a divergent segment, 200mm long, at 400mm. 1) Computational Fluid Dynamics Model and Validation of numerical methods For the two-dimension model, there are about 300000 structural grids created in the computational domain using the ICEM code. Most of them are set as 2u10-4m. The first layer of grids near the wall surface measure 1u10-5m could keep the typical value of Y+ below 3 for cells near the wall. Commercial computational fluid dynamics software Fluent was utilized to solve the 2-D compressible Reynolds-averaged Navier-Stokes equation with finite volume. And the associated boundary conditions were solved using a pressure-based, third-order MUSCL solver. A two-equation shear stress transport (SST) k-w model which was developed by Menter [29] was used to model the turbulence. The (SST) k-w turbulence model is suitable to solve the flow fields with adverse pressure gradients, especially for the transverse injection flow field. And it is more accurately for predicting the wall pressure distribution of the transverse injection [30-32]. Viscosity and specific heat of the mixture were 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, respectively. Steady flamelet model was used as the combustion model for our present work [33-34]. To account for compressibility of gas and varying pressure of the system, density, temperature, species mass fraction and enthalpy from the PDF tables is updated in every flow interaction. Given that the fast time scales of chemical reaction 14

flow is less than 1e-5s, and the time step size of the simulation was set to 1e-07 s to get a higher time accuracy. The inlet boundary conditions are set as same as the experiments. Non-slip and adiabatic wall conditions were employed for the solid boundary with standard wall functions. 10% of turbulence intensity and hydraulic diameter were considered to be appropriate as the boundary condition of turbulence. Different chemical reaction mechanisms of hydrogen have a significant effect on the numerical simulation results. Numerous experiments and simulation for H2/O2 have been conducted to investigate the kinetic mechanism. Different chemical kinetics reaction mechanisms also lead to different numerical simulation prediction results [35]. In present paper, the chemical reaction mechanism developed by Conaire et al. [36] which consists of 10 species and 19 reactions was used for our present work, which consists of 10 species and 19 reactions. This detailed kinetic mechanism could simulate the combustion of H2/O2 mixtures, over a wide range of temperature, pressures and equivalence ratios. Ignition delay times, flame speeds, and species composition data provide for a stringent test of the chemical kinetic mechanism. A sensitivity was carried out for the chemical reaction mechanism. Good agreement was observed between the model and the wide range of experiments simulated.

Fig 11 Schematic of DLR model used to validate numerical methods The scramjet at the Institute for Chemical Propulsion of the German Aerospace Center (DLR) was used as the simulation model to validate the numerical methods [33]. Many researchers use the physical model to validate the simulation method and investigate the supersonic combustion [37, 38]. Convergence monitoring compared the difference in the mass flow rate among the combustor inlet, outlet and fuel inlet, which was less than 1% of the injected fuel mass flow rate. The integrated values of fuel mass flow rate, static pressure, Mach number, and hydrogen mole 15

fraction at various x=constant planes downstream of the injection locations were all within 3% variations which a check on global fuel conservation.

Fig 12 Temperature distribution of cross section at 63mm location As shown in Fig 12, the structure grid, including the coarse grid, fine grid, and dense grid was specified as 5u10-4, 2u10-4 and 1u10-4 in the main coupling zone of turbulence and chemistry reaction, respectively. Good consistency can be seen between the flamelet method and experiment results. There is little difference of the temperature distributions from the three different quantitative grids. In comparison with Finite-Rate method, flamelet can be used to simulate the temperature field near the shear layer more accurately. Table 1 represents the difference between experimental data and simulation data from different grid sizes. δ and

Hr

are the root mean square and relative error of simulation data,

respectively. It is obvious that the mesh which own fine grid and dense grid has a good accuracy that the relative error is below 5%. So the fine grids were specified as 2u10-4 is employed in the model in this paper. Table 1 Validation of numerical method Difference between experiment and simulation data (K)

δ (K)

Hr

coarse grid

30.78

26.03

19.46

47.20

55.09

59.19

36.02

41.52

6.00%

fine grid

27.20

16.53

12.80

45.41

19.69

10.27

36.47

26.89

4.03%

dense grid

28.99

4.52

18.57

17.18

19.24

5.34

37.80

21.81

3.27%

16

Fig 13 Comparing of experimental and numerical shadow picture As shown in Fig 13, the locations of shock waves in the experiment and numerical simulation reach a good coherence. Shock wave 1 is the reflection wave reflecting on wall aroused by the incident shock wave that is compressed by a strut. Then, the shock wave 1 reflects on the shear layer between the fuel and main stream to produce the shock wave 2. The supersonic flow goes through the rear of the strut to expand and forms expansion wave 3. Similarly, expansion wave 4 is the reflection wave from the wall reflection. Additionally, in the combustion region, the CFD result captures the expansion of the shear layer aroused by the heat release. 2) Wall injection validation The numerical simulation model contains the wall injection on the two side walls, the wall injection validation and the influence of the turbulence model on the wall injection need to be validated. An experimental model from Spaid and Zukoski [39] is employed to validate the wall injection using (SST) k-w turbulence model. In the numerical simulation, the calculation model size and the relevant boundary conditions refers to the paper of Huang [38]. Injection static pressure is set as 53842Pa and Mach number of jet flow is kept 1. Fig 14 is the wall pressure distribution from experiment data and simulation results. The figure shows a good agreement between experiment and simulation. The numerical methods are fit for the jet-to-crossflow in this paper. 17

Fig 14 Wall pressure distribution validatoin using (SST) k-w turbulence model 3) Simulation Results and Discussion In the Fig 15, the pressure history at 360mm before the fuel injection port is shown in the simulation. Compare with Fig 7 (b), it is obvious that the pressure history of the two figures is similar to the variation of pressure rising. The simulation also contains two variations of pressure rising at slope3 and slope4, respectively. In period from 0.048s to 0.05636s, the slope3 of pressure rising is turned to be slope4 at 0.05s. Similar pressure history in the experiment and simulation denotes that the flow field of influencing pressure path variation is identical.

Fig 15 Pressure history path on low side wall at 360mm location To explain the phenomenon of pressure rising variation, Fig 16 is shown to present more details using simulation schlieren photographs from 0.0470s to 0.0525s. The heat release originates from fuel burning at 380mm forms the 18

subsonic zone along the walls behind the injection ports. Because heat release continuously leads to pressure increasing, the boundary layer at a divergent segment gradually thickens along the flow direction. Another aspect, from 0.04700s to 0.04900s, blockage of fuel injection induces the separation of boundary layer, and the separation region compresses incoming airflow to produce two shock waves, which is the leading edge of the shock train. Incident oblique shock waves interact near the center-axis, resulting in a pair of refracted shocks. The interaction of the refracted shock structure with the separated boundary layer reflects into compression waves structure and further thickens the boundary layer. Subsonic flow immediately downstream of the compression waves re-accelerates through the reduced core flow. Large pressure gradients in the core flow compared to the boundary layer push the boundary layer back toward the wall, resulting in transition to supersonic flow emphasized by the formation of an expansion fan. The interaction of the expansion fan with the boundary layer results in reflected compression shocks that merge into a single compression event. Subsequent interaction of these compression shocks with the boundary layer improves the thickness, with reflections merging into two oblique shock waves. The two oblique shock waves refract each other and reflect on boundary layer, and compare with other shock waves originate from compressing of fuel injection. This consists of a series of complicated shock wave structure, which constitutes the shock train under combustion heat release condition. In Fig 16, the leading edge of shock train passes through the position of 360mm at 0.0480s, and it makes the pressure rising sharply at the pressure monitor of 360mm location. At 0.0495s and 0.0500s, which are the turning point of pressure rising variation, the normal shock structure has formed at thermal throat resulting from fuel injection and combustion heat release. Corresponding to Fig 15, this normal shock structure would make pressure rising change. When a normal shock wave occurs at the thermal throat, the effect of which is similar to a typical throat of a converging-diverging nozzle. The appearance of normal shock wave indicates that the throat is critical state and the mass flow rate through the throat is limited in this state. After 0.0500s, the normal shock wave structure still exists and moves forward with the boundary layer. The critical state maintains to the upper limit of mass flow rate. Passing 19

through the normal shock, the relevant parameter of the core flow is altered and leads to a pair of symmetric Mach reflection wave occurs downstream at about 420mm in 0.0505s. Subsequently Mach reflection wave and regular reflection wave transform alternately. In the process of shock train movement, the interaction between shock wave and boundary layer is complicated and results in special characteristics. On the other hand, in this numerical simulation of two-dimensional flow, Mach number distribution along flow direction is complicated because of unsteady shock train movement, which is distinct from Mach number distribution obtained from one-dimensional flow analysis. The turning point of pressure increment variation occurs with normal shock at the thermal throat. It is seen as a sign that denotes the combustion mode transition.

Fig 16 Schlieren photographs of shock train movement As mentioned above, the appearance of normal shock train denotes the variation of pressure rising. It can be explained by using aerodynamics. In the Fig 17, some streamlines are shown at the background of temperature contour. The blockage of fuel injected at 380mm forms recirculation zone in the rear of injection ports, which provides the 20

necessary condition of stable combustion. In addition to this, a big pair of recirculation zones is produced at about 340mm. The high temperature gas is entrained from the combustion zone into the big recirculation zone. According to streamline distribution, it might be assumed that the main stream of supersonic passes through the isolator-combustor duct has little mass transfer with boundary layer of subsonic. Thus, a simplified model can be abstracted to be employed in one-dimensional flow analysis, just as Fig 18 shows. Fig 18 is Mach number distribution. By dealing with the figure, the red region is the main flow field with Mach number above 1, and other flow field is subsonic. Between the supersonic and subsonic region, the boundary is denoted by a bold black line. The subsonic zone of the boundary layer has the effect on restraining the supersonic flow boundary. Meanwhile, heat transfer from the boundary layer to the core flow is ignored.

Fig 17 Flow field streamline at 0.0500s

Fig 18 A boundary between supersonic and subsonic flow field at 0.0500s Based on conservation of mass, momentum, and energy in the core flow, formula (3) is given. And i represents the position of 1~4 cross sections resulting from the boundary layer thickness variation. K and q(λ) can be determined by k 21

and R. For the inviscid and isentropic flow, the parameters of 1~4 can be obtained when incoming flow conditions and cross-sectional areas are given. For the sake of simplicity, it is assumed that the areas in 2 and 3 are almost equal. It is worth noting that when the thermal throat of cross-sectional 4 forms the normal shock wave, some parameters will be restrained. And the supersonic upstream flow field is adjusted by the thickness of the boundary layer to balance pressure between supersonic main stream and subsonic boundary layer.

Kq (Oi ) Ai Pi* Kq(

­ °mi ° ° * ® Pi ° * °Ti ° ¯

T *i const

i 1, 2,3, 4

(3)

const

r 1

k § 2 · r 1 ¨ ¸ R © r 1 ¹

K

(4) 1

k  1 r11 § k  1 2 · k 1 q (O ) O ( ) ¨1  O ¸ 2 © k 1 ¹

(5)

Similar as the Fig 18, Fig 19 is the boundaries between supersonic and subsonic from 0.0480s to 0.0520s. The supersonic flow field (red region) constantly evolves to adjust the boundary and changes the cross-sectional area. Before the time of thermal throat formation, the position of throat locates at the cross section of injection ports, and the supersonic region after the cross section is converged. After 0.0500s, the position of choke (cross section 4) moves forward, and the profile of supersonic flow field transforms to divergent segment after cross section 4.

(a) A boundary between supersonic and subsonic flow field at 0.0480s

22

(b) A boundary between supersonic and subsonic flow field at 0.0490s

(c) A boundary between supersonic and subsonic flow field at 0.0510s

(d) A boundary between supersonic and subsonic flow field at 0.0520s Fig 19 Boundaries between supersonic and subsonic flow field at different moments Table 2 Ratio of cross-sectional area at different moments 0.0480s

0.0490s

0.0500s

0.0510s

0.520s

A1/A3

1.26

1.27

1.28

1.30

1.32

A3/A4

1.00

1.08

1.14

1.13

1.12

Table 2 shows the aero ratio of A1/A2 and A3/A4 measured from numerical simulation at different moments. Based on the parameters, the relationship with p3/P* from the inviscid and isentropic flow analysis at different times is shown in Fig 20. With variation of areas ratio, the p3 does not submit a linear variation. Different variation slope is separated by

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the red line in Fig 20. After the 0.0500s, the p3 variation path spans the red line to change the slope. This indicates that the pressure increment may be changed with the variation of cross-sectional areas and boundary layer thickness.

Fig 20 Effect of cross-sectional area changing on p3/P* Conclusions In this paper, the experimental and numerical investigation of supersonic combustion of equivalence ratio linear increasing is conducted at airflow of Mach number 2.0. For the experiment in a dual-mode combustor with strut, by monitoring the history of pressure transducer, a new phenomenon of pressure rising slope variation is found. With equivalence ratio increasing, the pressure distribution expansion variation experiences slow-fast-slow process. Based on the analysis of the one-dimensional Mach number, the occurrence of this phenomenon is accompanied with combustion mode transition. And this is different from the pressure sudden change in combustion mode transition process. The schlieren photograph of shock train movement in the numerical simulation shows that a normal shock wave appears at the thermal throat when the pressure rising slope variation. The thermal chock would restrain the mass flow rate of the main flow. Based on the flow field structure, an inviscid and isentropic flow analysis is employed and clarified the variation of pressure rising phenomenon. By the alteration of cross-sectional area in the mainstream, the pressure upstream of thermal throat is changed when the airflow reaches a critical condition in thermal throat. 24

Acknowledgments 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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