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Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions
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Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions Vishnu Hariharan a, Ratna Kishore Velamati a,*, C. Prathap b a
Department of Mechanical Engineering, Amrita School of Engineering, Ettimadai Campus, Amrita Vishwa Vidyapeetham, Amrita University, Coimbatore, India b Department of Aerospace Engineering, Indian Institute of Space Technology, Valiamala, Trivandrum, India
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abstract
Article history:
The present work numerically investigated the effect of variation in the inlet Mach number
Received 15 June 2015
and stagnation temperature on the mixing of fuel with the oxidizer and the subsequent
Received in revised form
stabilization of a flame in a combustor at supersonic conditions. Dimensions of the studied
20 January 2016
combustor were taken from literature. It had a 10 wedge located at the top wall of the
Accepted 9 February 2016
combustor. The combustor was modeled and analyzed using ANSYS FLUENT software.
Available online xxx
Three-dimensional, compressible, reacting flow calculations with a detailed chemistry model were performed. Turbulence was modeled using SST k-u model. Necessary grid
Keywords:
refinement was done to capture the incident oblique shock formed at the 10 wedge.
Hydrogen
Hydrogen was injected through the fuel inlet port. The computations were performed for
Scramjet
Mach numbers of 2.0, 2.5 and 3.0 at the combustor inlet for a combustion inlet stagnation
Supersonic combustion
temperature of 1500 K. Later, the combustor inlet Mach number was kept constant at 2.5
Oblique shock
and the combustor inlet stagnation temperature was varied as follows: 1500 K, 1700 K, and 1900 K. The results indicated that as the combustor inlet Mach number increased, the location of incidence of the oblique shock shifted to the downstream of the fuel inlet and it resulted in the better mixing of the fuel with cross flow stream of air and led to better degree of combustion of hydrogen. The contours of mole fraction of OH radical and hydrogen also corroborated the improvement in the mixing of fuel with the cross flow air and the subsequent flame stabilization at higher Mach numbers. The flow pattern, mixing of fuel with air and flame stabilization was not affected significantly till 1700 K whereas for 1900 K, combustion of hydrogen was more uniform. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Hypersonic air breathing propulsion systems have a significant role in both the military and civilian applications. A
significant amount of high-speed combustion research has been directed towards the design of the scramjet combustor due to emerging interest in hypersonic flights. The combustion and mixing timescales in a supersonic combustion are of the order of few milliseconds [1e3]. Hence, the duration
* Corresponding author. E-mail addresses: [email protected], [email protected] (R.K. Velamati). http://dx.doi.org/10.1016/j.ijhydene.2016.02.054 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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available for complete combustion is very short. The intake air conditions drastically change with altitudes and for a ramjet flying in a flight regime of Mach number (Ma) 6e8; the combustor inlet Ma is expected to be in the range of 2e3 [1]. Therefore, it is important to study the effect of variation in the inlet Mach number on the mixing of fuel with air and subsequent combustion process in this flight regime. To overcome the inherent problem of fuel-oxidizer mixing, variety of fuel injection strategies and flame holding methods had been proposed by earlier studies. The injection strategy in a supersonic combustor aims to increase the surface contact between the fuel and air and thus promote better mixing [4,5]. Also, different fuel injector geometries such as circular, elliptic and rectangular [6,7] had been tried and tested in supersonic combustors to enhance the mixing of fuel and air. The various fuel injection strategies that had been studied are transverse injection [6,8,9], angled injection [10] and parallel injection [11,12] of fuel into the air. Transverse injection of fuel results in a strong bow shock. It leads to boundary layer separation. It also results in a larger stagnation pressure drop across the combustor. For parallel high speed streams, improved techniques for mixing enhancement were required due to their limited mixing capabilities. This can be obtained either by shock waves [13,14] or by creation of stream wise vortices [15,16]. Ali et al. [13] numerically studied the interaction between the oblique shock wave and the transversal fuel injection and its effect on the fuel-air mixing and subsequent combustion. Their inlet conditions were: Ma ¼ 2.5 and stagnation pressure ¼ 0.5 MPa. Their results suggested that the mixing of hydrogen with air occurs at a lower rate in the absence of an oblique shock. They introduced a wedge and generated an oblique shock. The oblique shock increased the length of recirculation zone and augmented the mixing of hydrogen and air significantly. Mai et al. [17] studied the interaction between the incident shock wave and the transversal fuel jet flow and its effect on fuel-air mixing and combustion using NO-PLIF and PIV measurements. They performed measurements for the following inlet conditions: Mach number ¼ 2.5, stagnation pressure ¼ 0.5 MPa, stagnation temperature ¼ 567e756 K. They concluded that the effect of the oblique shock when introduced downstream of injection slot results in expansion of recirculation region in comparison with no oblique shock. This enhanced mixing was due to the increase in the residence time of fuel with the oxidizer. Nakamura et al. [18] numerically investigated the transverse injection of hydrogen fuel into the cross flow stream of air in the presence of an incident shock wave. Their study showed that the incident shock wave at the downstream of the fuel injection slot acted as a flame holder even at lower air stream stagnation temperatures. Apart from the challenge of mixing of fuel with air, flame holding and flame stability are also equally important for sustained supersonic combustion. Flame holding in supersonic combustor has been achieved using struts [7,11,19,20], pylon [21], ramp [22], backward facing step [23], cavity [4,5,8,24,25] or combinations of abovementioned methods [23,25]. It is widely reported that flame holding using cavity has provided better sustained combustion and minimal stagnation pressure losses [4,5,8,24,25]. Wang et al. [26] investigated the combustion characteristics in a supersonic
combustor with a cavity where the hydrogen was injected upstream of cavity. It was found that stable combustion could not be obtained without a cavity. Jeong et al. [10] studied the influence of variation of stagnation enthalpies on the combustion in a cavity based combustor. They varied the combustor inlet stagnation pressure from 92 to 11 kPa, temperature from 899 to 1700 K, enthalpy from 3.82 to 6.45 MJ/kg and Mach number from 3.7 to 4. Their study concluded that the ignition delay time increased with decrease of total enthalpy and a combination of low total enthalpy and high equivalence ratio led to thermal choking. The angled injection upstream of the cavity allows the cavity to act as a flame holder. Strut based fuel injection scheme injects the fuel into the core of the supersonic flow stream and enhances mixing and combustion efficiency. Kumar et al. [11] performed the optimization of fuel injection struts for maximizing the combustion efficiency and augmenting the thrust. Their combustor inlet Mach number was 2.0. Their combustor inlet stagnation temperature and pressure were 1700 K and 3.91 bar. Kuang et al. [16] investigated the mixing of fuel with air by measuring the fuel distribution using PLIF technique at Mach numbers of 2 and 3. They studied the effects of wedge angle, strut length and shape of base of strut on the mixing of fuel and air. They found that struts with larger wedge angle and shorter root length showed better mixing performance. Grady et al. [25] numerically and experimentally studied the supersonic air flow over a ramped wall cavity with an upstream strut at an inlet Mach 2. Based on their measurement and numerical results, they reported that the inclusion of an upstream strut increased cavity recirculation and promoted mixing of fuel with air. Three-dimensional numerical simulations of the supersonic hydrogen combustion in a model combustor were performed by Kumaran and Babu [23]. Hydrogen fuel was injected from the strut as well as wall injection ports into the air. Three injection schemes, namely, strut, staged (i.e., strut and wall) and wall were studied in this work. Their inlet operating conditions were: Mach number ¼ 2.5, stagnation temperature ¼ 1500 K and stagnation pressure ¼ 1 MPa. They reported that the SST k-u model predicted the mixing of fuel with air and flow separation phenomenon better than the Spalart-Allmaras turbulence model. Kumaran and Babu [27] studied the effect of single and multi-step reaction chemistry models. Their study showed that the detailed chemistry model predicted the reacting flow pattern better than single step chemistry. They used laminar finite rate model to model the combustion. They also mentioned that the single step chemistry model was capable enough to predict the overall performance parameters of the combustor with less computational cost than comparing to detailed chemistry model. Based on the existing literature, it is very clear that the presence of incident shock enhances mixing and improves flame stability. Also, the detailed chemistry model predicted the reacting flow much better than the single step reaction chemistry. To the best of the author's knowledge, most of the existing numerical studies available on supersonic combustor were for specific inlet conditions only. Hence, it is important to analyze the effects of variation of the combustor inlet conditions on the mixing pattern and combustion efficiency. The objective of the present work is to investigate the
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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interaction between the incident shock wave and the transverse fuel injection and its effect on combustion at different combustor inlet thermodynamic and flow conditions. The combustor design in the present work was adapted from Mai et al. [17] and Ali et al. [13] respectively. In the present work, the combustor inlet Mach number was varied from 2.0 to 3.0 which corresponds to the lower limit of hypersonic flight Mach number regime [1] at inlet stagnation conditions of 1500 K and 5 bar. Also, at a constant combustor inlet Mach number of 2.5 and stagnation pressure of 5 bar, the inlet stagnation temperature was varied from 1500 K to 1900 K.
Computational details Physical model The dimensions of the model combustor considered in the present work is identical to that of Mai et al. [17]. The physical combustor considered, has a channel of 120 30 20 mm3 with a rectangular injection slot of 100 0.25 mm2 that is located 45 mm from the leading edge of the bottom wall as shown in Fig. 1. The bottom injection surface is at an angle þ2 relative to the direction of supersonic airflow. Shock is generated from a wedge with an angle of 10 at the upper wall of the combustor. The origin of the coordinate system is at the center of the injection slot and the positive direction on the x axis represents the downstream region.
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detailed mechanism consists of 9 species (N2, O2, H2, H2O, OH, O, H, HO2, and H2O2) and 37 reactions. Thermal and multicomponent diffusion has been taken into consideration. All the numerical simulations are carried out using the ANSYS FLUENT Software [29].
Computational grid Due to the symmetry, the computation required only one half of the combustor region to be modeled for computational analysis. A three-dimensional structured grid has been generated using GAMBIT. The generated computational grid on symmetry plane is shown in Fig. 2. The grid was clustered near the fuel injection locations and walls. This grid clustering was to resolve the shock occurring near the fuel injection and the boundary layer on the wall. Further, the density of the grid has been relaxed near the combustor entry and exit regions. Initially, the numerical solution was obtained on a base mesh with 374520 cells. The grid was adapted based on gradients of static pressure to resolve the shock which resulted in about 580,000 cells. It was further adapted based on gradient of fuel mass fraction which gave about 790,000 cells. The resulting centerline static pressure distribution for the above mentioned three different grid densities are shown in Fig. 3, does not vary much. Maximum error obtained in the static pressure distribution between the medium and fine grid simulations is within 2.2%. This implies that the final adapted grid of 790,000 cells was accurate enough to capture the essential flow features.
Governing equations Boundary conditions Three-dimensional, compressible and turbulent averaged NaviereStokes equations are solved along with species conservation equations. Turbulence is modeled using two equation SST k-u model. The governing equations of a compressible turbulent flow can be written using timeaveraged Reynolds averaged quantities. They are derived by decomposing the dependent variables in the conservation equation into time-mean and fluctuating components and then averaging the entire equation. The ideal gas law is employed for the estimation of density. A finite rate detailed chemistry model [28] has been used in this present study. The
At the inlet of the combustor, static pressure, stagnation pressure, stagnation temperature and species mole fractions are specified. Static pressure is specified at the exit with an appropriate back pressure. The combustor top and bottom walls are adiabatic with non-slip wall boundary condition. The combustor inlet stagnation pressure was kept constant at 0.5 MPa. Then, the combustor inlet Mach number was varied as 2.0, 2.5 and 3.0 at a stagnation temperature of 1500 K. Also, the combustor inlet stagnation temperature was varied from 1500 K to 1900 K at a inlet Mach number of 2.5. Hydrogen-
Fig. 1 e Geometry of physical model. Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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Fig. 2 e Grid geometry of the model combustor.
Fig. 3 e Grid Independence study for the model combustor. air mixture with an equivalence ratio of 4 was injected from the slot at sonic condition. The stagnation pressure and temperature for slot injection is 1.2 MPa and 300 K respectively and it was kept constant for all the studied conditions.
Solution methodology Initially, the courant number to determine the time step was set as 0.5 for initial few iterations and then, increased up to about 0.6 to achieve steady state solution. Convection diffusion terms were discretized using Total variation Diminishing Method with MUSCL limiter and second order central difference schemes respectively. Specific heat, viscosity and mass diffusivity of the mixture, are evaluated using mixing law, mass weighted mixing law and kinetic theory laws respectively. Turbulent Prandtl and Schmidt numbers were taken to be 0.9 and 0.5 respectively.
pressure (wall static pressure relative to the free stream static pressure) is plotted against non-dimensional distance from leading edge in Fig. 4. Fig. 4 also shows the measured pressure distribution at the bottom wall obtained from Aso et al. [30]. The present predicted results show good agreement with the literature experimental data. The pressure and the flow fields at the symmetry plane were also compared. The nondimensional separation length obtained from the measurements of Aso et al. [30] (0.0897 mm) was compared with the present predictions (0.0915 mm) obtained using SST-k u model. The error is within ±2.06%. The separation length, variation of pressure with the shock structure including bow shock, barrel shock, and separation shock were well predicted. The transverse fuel jet issuing from the slot resulted in a barrel shock and it acts as an obstacle to the supersonic flow. This forms a strong jet induced detached bow shock. Consequently, due to presence of this detached bow shock, an adverse pressure gradient is created and resulted in the separation of the upstream wall boundary layer. The boundary layer separation from the near the fuel injection slot resulted in more fuel being drawn into the recirculation region due to of the presence of counter rotating vortices. The formation of counter rotating vortices in the flow field increased the residence time of fuel in the recirculation zone. In case of hot mainstream flow, the recirculation region encourages auto-ignition. The under expanded jet from the injection slot suddenly accelerates and expands to main flow
Validation of numerical model Validation of numerical model was done against the experimental results of Aso et al. [30]. A channel with dimension 500 150 170 mm and a slot of 100 1 mm has been used. The slot is located 330 mm from the inlet of the bottom plane. The supersonic combustor inlet conditions were as follows: Ma ¼ 3.75, stagnation temperature ¼ 299 K and stagnation pressure ¼ 1.2 MPa. Nitrogen was injected from the slot at sonic condition. The stagnation temperature was kept at 250 K. The stagnation pressure ratio of nitrogen to the main flow was kept at 0.31. The non-dimensional wall static
Fig. 4 e Comparison of Pressure distribution at bottom wall, experimental results of Aso et al. [30] with the obtained numerical result.
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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and results in reduced pressure as shown in Fig. 4. The surface pressure is normalized by upstream undistributed wall pressure.
Results and discussion After the validation, numerical studies are performed to study the effects of inlet conditions on supersonic combustion in a three dimensional model supersonic combustor. The specifications of the combustor are explained in section 2.1. Initially, the effect of Mach number is studied by varying it as 2, 2.5 and 3 at constant stagnation temperature of 1500 K. The effect of change in inlet stagnation temperature from 1500 K to 1900 K at an inlet Mach number 2.5 is also studied. The combustion efficiency is calculated as follows: hcomb ¼
TO;exit TO;inlet TO;max TO;inlet
100
Where, the total temperature at combustor exit isTO;exit ,TO;inlet is total temperature at the combustor inlet and TO;max is the maximum total temperature inside the combustor.
Effect of inlet mach number Three dimensional model of combustor explained in section 2.1 was numerically simulated with inlet Mach of 2, 2.5 and 3.0 at a stagnation temperature of 1500 K. In all the cases, an oblique shock was generated using a wedge with an angle of 10 located at the top wall of the combustor. The wedge was positioned at 20 mm downstream of combustor inlet. The Mach number distributions along the symmetric plane for different inlet Mach numbers were shown in Fig. 5. In Fig. 5, the oblique shock generated by the wedge is indicated by a line OB and separation shock is indicated by line SS. The transverse injection of fuel into the supersonic main flow leads to the formation of a strong bow shock which results in boundary layer separation upstream of the shock and results in separation shock. The location of leading edge of separation shock remains nearly same for all the studied inlet Mach numbers. The size of recirculation zone formed upstream of fuel injector due to separation shock increased with increase in inlet Mach number. The oblique shock formed at the wedge interacts with the separation shock. The oblique shock wave angles for Ma 2.0, 2.5 and 3.0 obtained from present simulations showed good agreement with the values obtained from theoretical, one dimensional oblique shock wave angle as tabulated in Table 1. For inlet Mach number of 2, the interaction of the separation shock and oblique shock leads to a formation of normal shock. The normal shock decelerates the supersonic flow to subsonic conditions. A large stagnation pressure drop is noted across the normal shock. As the flow proceeds, it becomes supersonic. At Mach 2.0, the oblique shock formed incident in the bottom wall of the combustor upstream of the fuel injector and affecting only the recirculation zone upstream of the fuel injector. The recirculation zone downstream of fuel injector remains unaffected and it is same as that of no incident shock as observed from Fig. 5(a) and also by Ali et al. [13]. The effect of oblique shock on mixing of air and fuel and subsequently
Fig. 5 e Contours of Velocity for Mach number 2.0, 2.5, 3.0 on the symmetry plane with an oblique incident shock.
on combustion can be understood by looking into mole fraction distributions of hydrogen and OH which will be discussed in the later part of this section. Fig. 5(b) and (c) shows that the normal shock is not formed for Ma 2.5 and 3.0. At Mach 2.5, the oblique shock crosses the axis of transverse injection and it incident at X ¼ 2.7 mm downstream of the fuel injection slot. So, the transverse fuel jet is disturbed by the oblique shock. This results in better mixing of fuel with air at the edge (leading or trailing) of fuel jet. When Mach number is increased to 3.0, incident location of the oblique shock on the combustor wall moves further downstream at X ¼ 10.1 mm. The penetration depth of the fuel jet is higher for inlet Mach 3.0 when compared with inlet Mach 2.5. This is mainly because the oblique shock does not intercept the fuel jet for inlet Ma 3.0. This augments mixing of fuel and air at the downstream of the incident location of oblique shock as observed by Nakamura et al. [18]. The above observations are also evident when their combustion efficiency is calculated. The combustion efficiency is found to be higher for Mach 2.0 (40.12%) when compared with Mach 2.0 (30.31%) and Mach 3.0 (35.82%).
Table 1 e Comparison with theoretical shock wave angle for various inlet Mach numbers. Boundary conditions Mach 2.0 Mach 2.5 Mach 3.0
Theoretical shock wave angle
Numerical shock wave angle
39.3 30.1 27.35
38.3 29.3 26.2
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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Fig. 7 e Contours of OH mole fraction for Mach number 2.0, 2.5, 3.0 with an oblique incident shock. Fig. 6 e Contours of mole fraction of hydrogen for Mach number 2.0, 2.5, 3.0 with an oblique incident shock.
Figs. 6 and 7 shows the contours of mole fraction of hydrogen and OH for different inlet Mach numbers. The contours are presented with X-section planes starting from X ¼ 5 mm to X ¼ 55 mm for every 10 mm. The mole fraction of H2 are presented with lower cut-off limit of 0.06 (10% of inlet mole fraction) and OH mole fraction are presented with lower cut-off limit of 0.07 (maximum OH mole fraction was 0.3). The dispersion of the fuel into the mainstream flow can be comprehended from the contours of mole fraction of hydrogen. OH contours show the location of reaction zone. Fig. 8 shows the contours of static pressure on the symmetric plane along with OH mole fractions at various X-section planes. The contours of mole fraction of H2 show that the penetration depth of fuel increased with increase in inlet Mach number in the studied combustor. At inlet Mach number of 2.0, the mixing of fuel and air is not proper, as it is evident from Fig. 6(a), that the mole fraction of H2 is about 0.25 even at X ¼ 35 mm. The entrainment of air into the recirculation zone downstream of fuel injection slot is restricted due to high pressure as indicated in Fig. 8(a). This could also be verified in the contours of mole fraction of OH where at X ¼ 35 mm plane, the mole fraction of OH was very low along the symmetric plane (core of downstream section of transverse jet) indicating that the combustion intensity is minimum. For inlet Mach number of 2.5, air-fuel mixing has improved significantly resulting in better combustion as the mole fraction of H2 is less than 0.1 beyond X ¼ 25 mm. A negative static pressure is observed in the downstream of the fuel injection due to incident shock as seen in Fig. 8(b). This leads to bigger downstream recirculation zone resulting in better air entrainment and also increases the residence time of fuel in the air having a positive impact on combustion phenomenon. Also, OH
contours in Fig. 7(b) show that until X ¼ 25 mm, the combustion intensity is less in the downstream core and beyond X ¼ 25 mm OH mole fraction in the core is uniform and high indicating better combustion. For inlet Mach 3.0, fuel jet disperses more as oblique shock incidents at downstream of the fuel injection. The incident shock forces the fuel to disperse into the upstream of the fuel injection slot. Fig. 6(c) clearly shows that air-fuel mixing is not as good as that with Ma ¼ 2.0. Also, flame holding and combustion is not proper as OH mole fraction behind transverse fuel jet is not uniform even at X ¼ 25 mm as seen in Fig. 7(c). After understanding the effects of inlet Mach number on the mixing of fuel with air and subsequent combustion, an attempt was made to understand the variation in the inlet stagnation temperatures at a constant inlet Mach number. Simulations were performed for the following inlet conditions: Mach 2.5 and inlet stagnation temperatures of 1500 K, 1700 K and 1900 K. The contours of Mach number for the above said inlet conditions were illustrated in Fig. 9 at the symmetry plane. With increase in inlet stagnation temperature, the location of the incidence of the oblique shock moves slightly downstream from X ¼ 3.75 to X ¼ 10.2 mm. The size of recirculation zone upstream of fuel injection slot is similar for inlet stagnation temperature of 1500 K and 1700 K. At an inlet stagnation temperature of 1900 K, the separation shock starts only at X ¼ 30 mm which leads to a shorter recirculation zone upstream of fuel injection slot. Also, it leads to a change in the incidence point of oblique shock. Figs. 10 and 11 show the contours of mole fraction of hydrogen and OH for various inlet stagnation temperatures of 1500 K, 1700 K and 1900 K at an inlet Mach number of 2.5. The contours are presents with Xsection planes starting from X ¼ 5 mm to X ¼ 55 mm for every 10 mm similar to that of Figs. 5 and 6. It is worth reminding
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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Fig. 8 e Contours of static pressure profile in the symmetric plane and OH mole fraction for Mach number 2.0, 2.5 at stagnation temperature 1500 K.
that X ¼ 0 mm corresponds to the center of fuel injection. Hence, the calculated combustion efficiency for inlet stagnation temperature 1500 K is higher (40.12%) compared to 1700 K (34.87%) and 1900 K (24.05%) The contours of mole fraction of
hydrogen fuel mole fraction, clearly show the fuel jet penetration, dispersion and mixing of fuel-air due the interaction with the oblique shock. The OH mole fraction contours illustrate the combustion intensity and stability of the flame.
Fig. 9 e Contours of Mach number for stagnation temperature 1500 K, 1700 K, 1900 K at Mach 2.5 on the symmetry plane with an oblique incident shock.
Fig. 10 e Contours of mole fraction of hydrogen for Mach number 2.5 at stagnation temperature 1500 K, 1700 K, 1900 K on the symmetry plane with an oblique incident shock.
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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This affects the recirculation zone upstream of fuel injection slot. The normal shock is not observed for Ma ¼ 2.5 and 3.0. 2. The location of incidence of oblique shock on the bottom wall of the combustor moves downstream of the fuel injection slot with increase in Mach number. This helps in better mixing of fuel and air. The fuel dispersion into the main air flow stream is also increased at higher Mach number. Combustion was not uniform for Ma ¼ 3.0 which is shown by the OH mole fraction distribution 3. The location of the oblique shock moves slightly downstream at an inlet stagnation temperature of 1900 K. The contours of mole fraction of OH at inlet stagnation temperatures of 1500 K and 1700 K are similar indicating that the combustion is not affected by inlet stagnation temperature. The hydrogen disperses rapidly into the main flow supersonic airstream for stagnation temperature 1900 K. At this condition the OH mole fraction is uniform indicating better combustion Fig. 11 e Contours of OH mole fraction at stagnation temperature 1500 K, 1700 K and 1900 K at inlet Mach 2.5 on the symmetry plane with an oblique incident shock.
As, it can be seen in Fig. 10 (a) and (b), the mixing pattern of fuel with air for inlet stagnation conditions of 1500 K and 1700 K is almost same. It can be further indicated from the contours of mole fraction of OH shown in Fig. 11 (a) and (b). The above discussion clearly point out that the mixing pattern and the subsequent combustion was not significantly affected during the variation of inlet stagnation temperature from 1500 K to 1700 K. The contours of mole fraction of hydrogen shown in Fig. 10 (c) indicates shorter penetration depth. It leads to slow mixing of fuel with air than comparing to other stagnation temperatures. The oblique shock makes the fuel jet to disperse both into the upstream and the downstream regions of the injection slot. With increase of stagnation temperature to 1900 K, OH mole fraction is almost uniform at X ¼ 35 mm indicating the better combustion only due to high inlet stagnation temperature.
Conclusions The effect of the incidence of oblique shock with variation of inlet conditions like stagnation temperature and Mach number has been studied for a model supersonic combustor. The oblique shock was formed at the leading edge of a wedge with an angle of 10 . The oblique shock causes an augmentation of the recirculation zone when it incident on the bottom wall of the combustor downstream of the injector. The following conclusions are made, 1. The oblique shock wave angle measured with respect to top wall decreased from 38.3 to 26.2 with increase in inlet Mach number from 2.0 to 3.0. The numerically obtained shock wave angles are close to theoretical values. A normal shock is observed for inlet Mach number 2.0.
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combustion scramjet flight experiments. In: AIAA paper, 7034; 2003. Gerlinger P, Stoll P, Kindler M, Schneider F, Aigner M. Numerical investigation of mixing and combustion enhancement in supersonic combustors by strut induced streamwise vorticity. Aerosp Sci Technol 2008;12:159e68. Hsu K-Y, Carter CD, Gruber MR, Tam C-J. Mixing study of strut injectors in supersonic flows. In: 45th AIAA/ASME/SAE/ ASEE Joint propulsion Conference & Exhibit, Denver, Co; 2009. p. 2e5. Mai T, Sakimitsu Y, Nakamura H, Ogami Y, Kudo T, Kobayashi H. Effect of the incident shock wave interacting with transversal jet flow on the mixing and combustion. Proc Combust Inst 2011;33:2335e42. Nakamura H, Sato N, Kobayashi H, Masuya G. Effect of the location of an incident shock wave on combustion and flow field of wall fuel-injection. Trans Jpn Soc Aeronaut. Space Sci 2008;51:170e5. Ground C, Vergine F, Maddalena L, Viti V. Experimental and numerical investigation of the flow characteristics of a strut injector for scramjets. In: AIAA 2014-3217; 2014. Bao W, Yang Q, Chang J, Zong Y, Hu J. Dynamic characteristics of combustion mode transitions in a strutbased scramjet combustor model. J Propuls Power 2013;29:1244e8. Vergine F, Maddalena L, Miller V, Gamba M. Supersonic combustion and flame-holding characteristics of pylon injected hydrogen in a Mach 2.4 high enthalpy flow. In: AIAA paper, 333; 2012.
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€ nig R, Theisen D, Fink R, Lachner R, Kappler G, Rist D, et al. [22] Ho Experimental investigation of a SCRAMJET model combustor with injection through a swept ramp using laser-induced fluorescence with tunable excimer lasers. In: Symposium (International) on combustion, Elsevier; 1996. p. 2949e56. [23] Kumaran K, Babu V. A comparison of the numerical predictions of the supersonic combustion of hydrogen using the SA and SST k-w models. Prog Comput Fluid Dyn 2008;8:475. [24] Baurl R, Gruber M. A study of recessed cavity flow-fields for supersonic combustion application. In: AIAA paper 98e0938. Washington, DC: American Institute of Aeronautics and Astronautics, Inc.; 1998. [25] Grady N, Pitz RW, Carter CD, Hsu K-Y, Godke C, Menon S. Supersonic flow over a ramped-wall cavity flame holder with an upstream strut. J Propuls Power 2012;28:982e90. [26] Wang H, Wang Z, Sun M, Wu H. Combustion modes of hydrogen jet combustion in a cavity-based supersonic combustor. Int J Hydrogen Energy 2013;38:12078e89. [27] Kumaran K, Babu V. Investigation of the effect of chemistry models on the numerical predictions of the supersonic combustion of hydrogen. Combust Flame 2009;156:826e41. [28] Li J, Zhao Z, Kazakov A, Dryer FL. An updated comprehensive kinetic model of hydrogen combustion. Int J Chem Kinet 2004;36:566e75. [29] FLUENT 6.3 user's guide, Fluent documentation. 2006. [30] Aso S, Okuyama S. Experimental study on mixing phenomena in supersonic flows with slot injection. In: AIAA, 91-0016; 1991. p. 3e16.
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Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions Vishnu Hariharan a, Ratna Kishore Velamati a,*, C. Prathap b a
Department of Mechanical Engineering, Amrita School of Engineering, Ettimadai Campus, Amrita Vishwa Vidyapeetham, Amrita University, Coimbatore, India b Department of Aerospace Engineering, Indian Institute of Space Technology, Valiamala, Trivandrum, India
article info
abstract
Article history:
The present work numerically investigated the effect of variation in the inlet Mach number
Received 15 June 2015
and stagnation temperature on the mixing of fuel with the oxidizer and the subsequent
Received in revised form
stabilization of a flame in a combustor at supersonic conditions. Dimensions of the studied
20 January 2016
combustor were taken from literature. It had a 10 wedge located at the top wall of the
Accepted 9 February 2016
combustor. The combustor was modeled and analyzed using ANSYS FLUENT software.
Available online xxx
Three-dimensional, compressible, reacting flow calculations with a detailed chemistry model were performed. Turbulence was modeled using SST k-u model. Necessary grid
Keywords:
refinement was done to capture the incident oblique shock formed at the 10 wedge.
Hydrogen
Hydrogen was injected through the fuel inlet port. The computations were performed for
Scramjet
Mach numbers of 2.0, 2.5 and 3.0 at the combustor inlet for a combustion inlet stagnation
Supersonic combustion
temperature of 1500 K. Later, the combustor inlet Mach number was kept constant at 2.5
Oblique shock
and the combustor inlet stagnation temperature was varied as follows: 1500 K, 1700 K, and 1900 K. The results indicated that as the combustor inlet Mach number increased, the location of incidence of the oblique shock shifted to the downstream of the fuel inlet and it resulted in the better mixing of the fuel with cross flow stream of air and led to better degree of combustion of hydrogen. The contours of mole fraction of OH radical and hydrogen also corroborated the improvement in the mixing of fuel with the cross flow air and the subsequent flame stabilization at higher Mach numbers. The flow pattern, mixing of fuel with air and flame stabilization was not affected significantly till 1700 K whereas for 1900 K, combustion of hydrogen was more uniform. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Hypersonic air breathing propulsion systems have a significant role in both the military and civilian applications. A
significant amount of high-speed combustion research has been directed towards the design of the scramjet combustor due to emerging interest in hypersonic flights. The combustion and mixing timescales in a supersonic combustion are of the order of few milliseconds [1e3]. Hence, the duration
* Corresponding author. E-mail addresses: [email protected], [email protected] (R.K. Velamati). http://dx.doi.org/10.1016/j.ijhydene.2016.02.054 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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available for complete combustion is very short. The intake air conditions drastically change with altitudes and for a ramjet flying in a flight regime of Mach number (Ma) 6e8; the combustor inlet Ma is expected to be in the range of 2e3 [1]. Therefore, it is important to study the effect of variation in the inlet Mach number on the mixing of fuel with air and subsequent combustion process in this flight regime. To overcome the inherent problem of fuel-oxidizer mixing, variety of fuel injection strategies and flame holding methods had been proposed by earlier studies. The injection strategy in a supersonic combustor aims to increase the surface contact between the fuel and air and thus promote better mixing [4,5]. Also, different fuel injector geometries such as circular, elliptic and rectangular [6,7] had been tried and tested in supersonic combustors to enhance the mixing of fuel and air. The various fuel injection strategies that had been studied are transverse injection [6,8,9], angled injection [10] and parallel injection [11,12] of fuel into the air. Transverse injection of fuel results in a strong bow shock. It leads to boundary layer separation. It also results in a larger stagnation pressure drop across the combustor. For parallel high speed streams, improved techniques for mixing enhancement were required due to their limited mixing capabilities. This can be obtained either by shock waves [13,14] or by creation of stream wise vortices [15,16]. Ali et al. [13] numerically studied the interaction between the oblique shock wave and the transversal fuel injection and its effect on the fuel-air mixing and subsequent combustion. Their inlet conditions were: Ma ¼ 2.5 and stagnation pressure ¼ 0.5 MPa. Their results suggested that the mixing of hydrogen with air occurs at a lower rate in the absence of an oblique shock. They introduced a wedge and generated an oblique shock. The oblique shock increased the length of recirculation zone and augmented the mixing of hydrogen and air significantly. Mai et al. [17] studied the interaction between the incident shock wave and the transversal fuel jet flow and its effect on fuel-air mixing and combustion using NO-PLIF and PIV measurements. They performed measurements for the following inlet conditions: Mach number ¼ 2.5, stagnation pressure ¼ 0.5 MPa, stagnation temperature ¼ 567e756 K. They concluded that the effect of the oblique shock when introduced downstream of injection slot results in expansion of recirculation region in comparison with no oblique shock. This enhanced mixing was due to the increase in the residence time of fuel with the oxidizer. Nakamura et al. [18] numerically investigated the transverse injection of hydrogen fuel into the cross flow stream of air in the presence of an incident shock wave. Their study showed that the incident shock wave at the downstream of the fuel injection slot acted as a flame holder even at lower air stream stagnation temperatures. Apart from the challenge of mixing of fuel with air, flame holding and flame stability are also equally important for sustained supersonic combustion. Flame holding in supersonic combustor has been achieved using struts [7,11,19,20], pylon [21], ramp [22], backward facing step [23], cavity [4,5,8,24,25] or combinations of abovementioned methods [23,25]. It is widely reported that flame holding using cavity has provided better sustained combustion and minimal stagnation pressure losses [4,5,8,24,25]. Wang et al. [26] investigated the combustion characteristics in a supersonic
combustor with a cavity where the hydrogen was injected upstream of cavity. It was found that stable combustion could not be obtained without a cavity. Jeong et al. [10] studied the influence of variation of stagnation enthalpies on the combustion in a cavity based combustor. They varied the combustor inlet stagnation pressure from 92 to 11 kPa, temperature from 899 to 1700 K, enthalpy from 3.82 to 6.45 MJ/kg and Mach number from 3.7 to 4. Their study concluded that the ignition delay time increased with decrease of total enthalpy and a combination of low total enthalpy and high equivalence ratio led to thermal choking. The angled injection upstream of the cavity allows the cavity to act as a flame holder. Strut based fuel injection scheme injects the fuel into the core of the supersonic flow stream and enhances mixing and combustion efficiency. Kumar et al. [11] performed the optimization of fuel injection struts for maximizing the combustion efficiency and augmenting the thrust. Their combustor inlet Mach number was 2.0. Their combustor inlet stagnation temperature and pressure were 1700 K and 3.91 bar. Kuang et al. [16] investigated the mixing of fuel with air by measuring the fuel distribution using PLIF technique at Mach numbers of 2 and 3. They studied the effects of wedge angle, strut length and shape of base of strut on the mixing of fuel and air. They found that struts with larger wedge angle and shorter root length showed better mixing performance. Grady et al. [25] numerically and experimentally studied the supersonic air flow over a ramped wall cavity with an upstream strut at an inlet Mach 2. Based on their measurement and numerical results, they reported that the inclusion of an upstream strut increased cavity recirculation and promoted mixing of fuel with air. Three-dimensional numerical simulations of the supersonic hydrogen combustion in a model combustor were performed by Kumaran and Babu [23]. Hydrogen fuel was injected from the strut as well as wall injection ports into the air. Three injection schemes, namely, strut, staged (i.e., strut and wall) and wall were studied in this work. Their inlet operating conditions were: Mach number ¼ 2.5, stagnation temperature ¼ 1500 K and stagnation pressure ¼ 1 MPa. They reported that the SST k-u model predicted the mixing of fuel with air and flow separation phenomenon better than the Spalart-Allmaras turbulence model. Kumaran and Babu [27] studied the effect of single and multi-step reaction chemistry models. Their study showed that the detailed chemistry model predicted the reacting flow pattern better than single step chemistry. They used laminar finite rate model to model the combustion. They also mentioned that the single step chemistry model was capable enough to predict the overall performance parameters of the combustor with less computational cost than comparing to detailed chemistry model. Based on the existing literature, it is very clear that the presence of incident shock enhances mixing and improves flame stability. Also, the detailed chemistry model predicted the reacting flow much better than the single step reaction chemistry. To the best of the author's knowledge, most of the existing numerical studies available on supersonic combustor were for specific inlet conditions only. Hence, it is important to analyze the effects of variation of the combustor inlet conditions on the mixing pattern and combustion efficiency. The objective of the present work is to investigate the
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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interaction between the incident shock wave and the transverse fuel injection and its effect on combustion at different combustor inlet thermodynamic and flow conditions. The combustor design in the present work was adapted from Mai et al. [17] and Ali et al. [13] respectively. In the present work, the combustor inlet Mach number was varied from 2.0 to 3.0 which corresponds to the lower limit of hypersonic flight Mach number regime [1] at inlet stagnation conditions of 1500 K and 5 bar. Also, at a constant combustor inlet Mach number of 2.5 and stagnation pressure of 5 bar, the inlet stagnation temperature was varied from 1500 K to 1900 K.
Computational details Physical model The dimensions of the model combustor considered in the present work is identical to that of Mai et al. [17]. The physical combustor considered, has a channel of 120 30 20 mm3 with a rectangular injection slot of 100 0.25 mm2 that is located 45 mm from the leading edge of the bottom wall as shown in Fig. 1. The bottom injection surface is at an angle þ2 relative to the direction of supersonic airflow. Shock is generated from a wedge with an angle of 10 at the upper wall of the combustor. The origin of the coordinate system is at the center of the injection slot and the positive direction on the x axis represents the downstream region.
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detailed mechanism consists of 9 species (N2, O2, H2, H2O, OH, O, H, HO2, and H2O2) and 37 reactions. Thermal and multicomponent diffusion has been taken into consideration. All the numerical simulations are carried out using the ANSYS FLUENT Software [29].
Computational grid Due to the symmetry, the computation required only one half of the combustor region to be modeled for computational analysis. A three-dimensional structured grid has been generated using GAMBIT. The generated computational grid on symmetry plane is shown in Fig. 2. The grid was clustered near the fuel injection locations and walls. This grid clustering was to resolve the shock occurring near the fuel injection and the boundary layer on the wall. Further, the density of the grid has been relaxed near the combustor entry and exit regions. Initially, the numerical solution was obtained on a base mesh with 374520 cells. The grid was adapted based on gradients of static pressure to resolve the shock which resulted in about 580,000 cells. It was further adapted based on gradient of fuel mass fraction which gave about 790,000 cells. The resulting centerline static pressure distribution for the above mentioned three different grid densities are shown in Fig. 3, does not vary much. Maximum error obtained in the static pressure distribution between the medium and fine grid simulations is within 2.2%. This implies that the final adapted grid of 790,000 cells was accurate enough to capture the essential flow features.
Governing equations Boundary conditions Three-dimensional, compressible and turbulent averaged NaviereStokes equations are solved along with species conservation equations. Turbulence is modeled using two equation SST k-u model. The governing equations of a compressible turbulent flow can be written using timeaveraged Reynolds averaged quantities. They are derived by decomposing the dependent variables in the conservation equation into time-mean and fluctuating components and then averaging the entire equation. The ideal gas law is employed for the estimation of density. A finite rate detailed chemistry model [28] has been used in this present study. The
At the inlet of the combustor, static pressure, stagnation pressure, stagnation temperature and species mole fractions are specified. Static pressure is specified at the exit with an appropriate back pressure. The combustor top and bottom walls are adiabatic with non-slip wall boundary condition. The combustor inlet stagnation pressure was kept constant at 0.5 MPa. Then, the combustor inlet Mach number was varied as 2.0, 2.5 and 3.0 at a stagnation temperature of 1500 K. Also, the combustor inlet stagnation temperature was varied from 1500 K to 1900 K at a inlet Mach number of 2.5. Hydrogen-
Fig. 1 e Geometry of physical model. Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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Fig. 2 e Grid geometry of the model combustor.
Fig. 3 e Grid Independence study for the model combustor. air mixture with an equivalence ratio of 4 was injected from the slot at sonic condition. The stagnation pressure and temperature for slot injection is 1.2 MPa and 300 K respectively and it was kept constant for all the studied conditions.
Solution methodology Initially, the courant number to determine the time step was set as 0.5 for initial few iterations and then, increased up to about 0.6 to achieve steady state solution. Convection diffusion terms were discretized using Total variation Diminishing Method with MUSCL limiter and second order central difference schemes respectively. Specific heat, viscosity and mass diffusivity of the mixture, are evaluated using mixing law, mass weighted mixing law and kinetic theory laws respectively. Turbulent Prandtl and Schmidt numbers were taken to be 0.9 and 0.5 respectively.
pressure (wall static pressure relative to the free stream static pressure) is plotted against non-dimensional distance from leading edge in Fig. 4. Fig. 4 also shows the measured pressure distribution at the bottom wall obtained from Aso et al. [30]. The present predicted results show good agreement with the literature experimental data. The pressure and the flow fields at the symmetry plane were also compared. The nondimensional separation length obtained from the measurements of Aso et al. [30] (0.0897 mm) was compared with the present predictions (0.0915 mm) obtained using SST-k u model. The error is within ±2.06%. The separation length, variation of pressure with the shock structure including bow shock, barrel shock, and separation shock were well predicted. The transverse fuel jet issuing from the slot resulted in a barrel shock and it acts as an obstacle to the supersonic flow. This forms a strong jet induced detached bow shock. Consequently, due to presence of this detached bow shock, an adverse pressure gradient is created and resulted in the separation of the upstream wall boundary layer. The boundary layer separation from the near the fuel injection slot resulted in more fuel being drawn into the recirculation region due to of the presence of counter rotating vortices. The formation of counter rotating vortices in the flow field increased the residence time of fuel in the recirculation zone. In case of hot mainstream flow, the recirculation region encourages auto-ignition. The under expanded jet from the injection slot suddenly accelerates and expands to main flow
Validation of numerical model Validation of numerical model was done against the experimental results of Aso et al. [30]. A channel with dimension 500 150 170 mm and a slot of 100 1 mm has been used. The slot is located 330 mm from the inlet of the bottom plane. The supersonic combustor inlet conditions were as follows: Ma ¼ 3.75, stagnation temperature ¼ 299 K and stagnation pressure ¼ 1.2 MPa. Nitrogen was injected from the slot at sonic condition. The stagnation temperature was kept at 250 K. The stagnation pressure ratio of nitrogen to the main flow was kept at 0.31. The non-dimensional wall static
Fig. 4 e Comparison of Pressure distribution at bottom wall, experimental results of Aso et al. [30] with the obtained numerical result.
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and results in reduced pressure as shown in Fig. 4. The surface pressure is normalized by upstream undistributed wall pressure.
Results and discussion After the validation, numerical studies are performed to study the effects of inlet conditions on supersonic combustion in a three dimensional model supersonic combustor. The specifications of the combustor are explained in section 2.1. Initially, the effect of Mach number is studied by varying it as 2, 2.5 and 3 at constant stagnation temperature of 1500 K. The effect of change in inlet stagnation temperature from 1500 K to 1900 K at an inlet Mach number 2.5 is also studied. The combustion efficiency is calculated as follows: hcomb ¼
TO;exit TO;inlet TO;max TO;inlet
100
Where, the total temperature at combustor exit isTO;exit ,TO;inlet is total temperature at the combustor inlet and TO;max is the maximum total temperature inside the combustor.
Effect of inlet mach number Three dimensional model of combustor explained in section 2.1 was numerically simulated with inlet Mach of 2, 2.5 and 3.0 at a stagnation temperature of 1500 K. In all the cases, an oblique shock was generated using a wedge with an angle of 10 located at the top wall of the combustor. The wedge was positioned at 20 mm downstream of combustor inlet. The Mach number distributions along the symmetric plane for different inlet Mach numbers were shown in Fig. 5. In Fig. 5, the oblique shock generated by the wedge is indicated by a line OB and separation shock is indicated by line SS. The transverse injection of fuel into the supersonic main flow leads to the formation of a strong bow shock which results in boundary layer separation upstream of the shock and results in separation shock. The location of leading edge of separation shock remains nearly same for all the studied inlet Mach numbers. The size of recirculation zone formed upstream of fuel injector due to separation shock increased with increase in inlet Mach number. The oblique shock formed at the wedge interacts with the separation shock. The oblique shock wave angles for Ma 2.0, 2.5 and 3.0 obtained from present simulations showed good agreement with the values obtained from theoretical, one dimensional oblique shock wave angle as tabulated in Table 1. For inlet Mach number of 2, the interaction of the separation shock and oblique shock leads to a formation of normal shock. The normal shock decelerates the supersonic flow to subsonic conditions. A large stagnation pressure drop is noted across the normal shock. As the flow proceeds, it becomes supersonic. At Mach 2.0, the oblique shock formed incident in the bottom wall of the combustor upstream of the fuel injector and affecting only the recirculation zone upstream of the fuel injector. The recirculation zone downstream of fuel injector remains unaffected and it is same as that of no incident shock as observed from Fig. 5(a) and also by Ali et al. [13]. The effect of oblique shock on mixing of air and fuel and subsequently
Fig. 5 e Contours of Velocity for Mach number 2.0, 2.5, 3.0 on the symmetry plane with an oblique incident shock.
on combustion can be understood by looking into mole fraction distributions of hydrogen and OH which will be discussed in the later part of this section. Fig. 5(b) and (c) shows that the normal shock is not formed for Ma 2.5 and 3.0. At Mach 2.5, the oblique shock crosses the axis of transverse injection and it incident at X ¼ 2.7 mm downstream of the fuel injection slot. So, the transverse fuel jet is disturbed by the oblique shock. This results in better mixing of fuel with air at the edge (leading or trailing) of fuel jet. When Mach number is increased to 3.0, incident location of the oblique shock on the combustor wall moves further downstream at X ¼ 10.1 mm. The penetration depth of the fuel jet is higher for inlet Mach 3.0 when compared with inlet Mach 2.5. This is mainly because the oblique shock does not intercept the fuel jet for inlet Ma 3.0. This augments mixing of fuel and air at the downstream of the incident location of oblique shock as observed by Nakamura et al. [18]. The above observations are also evident when their combustion efficiency is calculated. The combustion efficiency is found to be higher for Mach 2.0 (40.12%) when compared with Mach 2.0 (30.31%) and Mach 3.0 (35.82%).
Table 1 e Comparison with theoretical shock wave angle for various inlet Mach numbers. Boundary conditions Mach 2.0 Mach 2.5 Mach 3.0
Theoretical shock wave angle
Numerical shock wave angle
39.3 30.1 27.35
38.3 29.3 26.2
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Fig. 7 e Contours of OH mole fraction for Mach number 2.0, 2.5, 3.0 with an oblique incident shock. Fig. 6 e Contours of mole fraction of hydrogen for Mach number 2.0, 2.5, 3.0 with an oblique incident shock.
Figs. 6 and 7 shows the contours of mole fraction of hydrogen and OH for different inlet Mach numbers. The contours are presented with X-section planes starting from X ¼ 5 mm to X ¼ 55 mm for every 10 mm. The mole fraction of H2 are presented with lower cut-off limit of 0.06 (10% of inlet mole fraction) and OH mole fraction are presented with lower cut-off limit of 0.07 (maximum OH mole fraction was 0.3). The dispersion of the fuel into the mainstream flow can be comprehended from the contours of mole fraction of hydrogen. OH contours show the location of reaction zone. Fig. 8 shows the contours of static pressure on the symmetric plane along with OH mole fractions at various X-section planes. The contours of mole fraction of H2 show that the penetration depth of fuel increased with increase in inlet Mach number in the studied combustor. At inlet Mach number of 2.0, the mixing of fuel and air is not proper, as it is evident from Fig. 6(a), that the mole fraction of H2 is about 0.25 even at X ¼ 35 mm. The entrainment of air into the recirculation zone downstream of fuel injection slot is restricted due to high pressure as indicated in Fig. 8(a). This could also be verified in the contours of mole fraction of OH where at X ¼ 35 mm plane, the mole fraction of OH was very low along the symmetric plane (core of downstream section of transverse jet) indicating that the combustion intensity is minimum. For inlet Mach number of 2.5, air-fuel mixing has improved significantly resulting in better combustion as the mole fraction of H2 is less than 0.1 beyond X ¼ 25 mm. A negative static pressure is observed in the downstream of the fuel injection due to incident shock as seen in Fig. 8(b). This leads to bigger downstream recirculation zone resulting in better air entrainment and also increases the residence time of fuel in the air having a positive impact on combustion phenomenon. Also, OH
contours in Fig. 7(b) show that until X ¼ 25 mm, the combustion intensity is less in the downstream core and beyond X ¼ 25 mm OH mole fraction in the core is uniform and high indicating better combustion. For inlet Mach 3.0, fuel jet disperses more as oblique shock incidents at downstream of the fuel injection. The incident shock forces the fuel to disperse into the upstream of the fuel injection slot. Fig. 6(c) clearly shows that air-fuel mixing is not as good as that with Ma ¼ 2.0. Also, flame holding and combustion is not proper as OH mole fraction behind transverse fuel jet is not uniform even at X ¼ 25 mm as seen in Fig. 7(c). After understanding the effects of inlet Mach number on the mixing of fuel with air and subsequent combustion, an attempt was made to understand the variation in the inlet stagnation temperatures at a constant inlet Mach number. Simulations were performed for the following inlet conditions: Mach 2.5 and inlet stagnation temperatures of 1500 K, 1700 K and 1900 K. The contours of Mach number for the above said inlet conditions were illustrated in Fig. 9 at the symmetry plane. With increase in inlet stagnation temperature, the location of the incidence of the oblique shock moves slightly downstream from X ¼ 3.75 to X ¼ 10.2 mm. The size of recirculation zone upstream of fuel injection slot is similar for inlet stagnation temperature of 1500 K and 1700 K. At an inlet stagnation temperature of 1900 K, the separation shock starts only at X ¼ 30 mm which leads to a shorter recirculation zone upstream of fuel injection slot. Also, it leads to a change in the incidence point of oblique shock. Figs. 10 and 11 show the contours of mole fraction of hydrogen and OH for various inlet stagnation temperatures of 1500 K, 1700 K and 1900 K at an inlet Mach number of 2.5. The contours are presents with Xsection planes starting from X ¼ 5 mm to X ¼ 55 mm for every 10 mm similar to that of Figs. 5 and 6. It is worth reminding
Please cite this article in press as: Hariharan V, et al., Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.02.054
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Fig. 8 e Contours of static pressure profile in the symmetric plane and OH mole fraction for Mach number 2.0, 2.5 at stagnation temperature 1500 K.
that X ¼ 0 mm corresponds to the center of fuel injection. Hence, the calculated combustion efficiency for inlet stagnation temperature 1500 K is higher (40.12%) compared to 1700 K (34.87%) and 1900 K (24.05%) The contours of mole fraction of
hydrogen fuel mole fraction, clearly show the fuel jet penetration, dispersion and mixing of fuel-air due the interaction with the oblique shock. The OH mole fraction contours illustrate the combustion intensity and stability of the flame.
Fig. 9 e Contours of Mach number for stagnation temperature 1500 K, 1700 K, 1900 K at Mach 2.5 on the symmetry plane with an oblique incident shock.
Fig. 10 e Contours of mole fraction of hydrogen for Mach number 2.5 at stagnation temperature 1500 K, 1700 K, 1900 K on the symmetry plane with an oblique incident shock.
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This affects the recirculation zone upstream of fuel injection slot. The normal shock is not observed for Ma ¼ 2.5 and 3.0. 2. The location of incidence of oblique shock on the bottom wall of the combustor moves downstream of the fuel injection slot with increase in Mach number. This helps in better mixing of fuel and air. The fuel dispersion into the main air flow stream is also increased at higher Mach number. Combustion was not uniform for Ma ¼ 3.0 which is shown by the OH mole fraction distribution 3. The location of the oblique shock moves slightly downstream at an inlet stagnation temperature of 1900 K. The contours of mole fraction of OH at inlet stagnation temperatures of 1500 K and 1700 K are similar indicating that the combustion is not affected by inlet stagnation temperature. The hydrogen disperses rapidly into the main flow supersonic airstream for stagnation temperature 1900 K. At this condition the OH mole fraction is uniform indicating better combustion Fig. 11 e Contours of OH mole fraction at stagnation temperature 1500 K, 1700 K and 1900 K at inlet Mach 2.5 on the symmetry plane with an oblique incident shock.
As, it can be seen in Fig. 10 (a) and (b), the mixing pattern of fuel with air for inlet stagnation conditions of 1500 K and 1700 K is almost same. It can be further indicated from the contours of mole fraction of OH shown in Fig. 11 (a) and (b). The above discussion clearly point out that the mixing pattern and the subsequent combustion was not significantly affected during the variation of inlet stagnation temperature from 1500 K to 1700 K. The contours of mole fraction of hydrogen shown in Fig. 10 (c) indicates shorter penetration depth. It leads to slow mixing of fuel with air than comparing to other stagnation temperatures. The oblique shock makes the fuel jet to disperse both into the upstream and the downstream regions of the injection slot. With increase of stagnation temperature to 1900 K, OH mole fraction is almost uniform at X ¼ 35 mm indicating the better combustion only due to high inlet stagnation temperature.
Conclusions The effect of the incidence of oblique shock with variation of inlet conditions like stagnation temperature and Mach number has been studied for a model supersonic combustor. The oblique shock was formed at the leading edge of a wedge with an angle of 10 . The oblique shock causes an augmentation of the recirculation zone when it incident on the bottom wall of the combustor downstream of the injector. The following conclusions are made, 1. The oblique shock wave angle measured with respect to top wall decreased from 38.3 to 26.2 with increase in inlet Mach number from 2.0 to 3.0. The numerically obtained shock wave angles are close to theoretical values. A normal shock is observed for inlet Mach number 2.0.
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