Combustion characteristics of a novel design of solid-fuel ramjet motor with swirl flow

Aerospace Science and Technology 92 (2019) 750–765

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Combustion characteristics of a novel design of solid-fuel ramjet motor with swirl flow Omer Musa a,b,∗ , Chen Xiong a , Li Weixuan a , Liao Wenhe a a b

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China Mechanical Engineering Department, Omdurman Islamic University, Omdurman, Sudan

a r t i c l e

i n f o

Article history: Received 31 October 2018 Received in revised form 12 June 2019 Accepted 1 July 2019 Available online 4 July 2019 Keywords: Solid fuel Ramjet CFD Combustion characteristics HDPE Propulsion

a b s t r a c t The coupling of high speed to wide range is the key problem in the military applications. Solid-fuel ramjet (SFRJ) has drawn much interest since the beginning of the last century which could be used to extend the range and speed of the missiles as in ramjet-powered missiles. Nevertheless, solid-fuel ramjet suffers from low regression rate of the solid fuel. To enhance the regression rate of the solid-fuel ramjet, in this paper, a new design is proposed and numerically investigated. The new design uses two solid fuels with keeping the simplicity in the design of the classic solid-fuel ramjet. For the simulations, an in-house CFD code has been developed to solve Reynolds-averaged Navier–Stokes equations of turbulent, reacting, unsteady, and swirl flow. Simulations are carried out for the proposed and classic designs with and without swirl flow. The results are compared with the classic design for the same configuration and flow conditions. It is shown that the new design has improved the regression rate, reactants mixing degree, and performance of SFRJ. The proposed design offered two diffusion flames at which the new flame started from the inlet of the combustion chamber in the swirl flow case and near to the combustor’s end for non-swirl case. © 2019 Elsevier Masson SAS. All rights reserved.

1. Introduction The most needed feature in the military applications is the combination of range and speed. Traditional rocket motors require carrying an oxidizer which makes the rocket heavier and then decreases its flight range. For the same size of a rocket motor, solidfuel ramjet (SFRJ) could fly for longer range with much higher speed; since it uses its forward motion to draw in the oxygen from the surrounding atmosphere and thus no need for carrying an oxidizer. Therefore, the larger fuel store allows SFRJ to sustain high speed during flight for longer range. The SFRJ is a simple air-breathing engine, in design, that contains no moving parts. Thus, the internal design of the SFRJ determines its performance. Nevertheless, the main disadvantage of the SFRJ is poor rate of fuel regression which is less than one mm/sec [1]. Meanwhile, in SFRJs design and operation, the key parameter is the rate of fuel regression which basically relies on the heat transferred into the solid fuel surface. This low regression rate increases oxidizer-to-fuel ( O / F ) ratio which leads to combustion instability,

*

Corresponding author at: School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China. E-mail address: [email protected] (O. Musa). https://doi.org/10.1016/j.ast.2019.07.003 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

nozzle erosion, erosive burning, and reduced motor duty cycles [2]. The classical design of SFRJ consists of systems shown in Fig. 1. Typically, the classical SFRJ uses a tubular solid fuel (tubular grain) as a combustion chamber where the solid fuel is regressing and reacting with incoming air depending on the flight conditions. However, the use of tubular grain in SFRJ has approved low regression rate since the diffusion combustion is self-controlled according to the flight conditions. Therefore, increasing the regression rate is aimed at many studies since the last century. Since then, approaches to increase fuel regression have considered different inner designs [3–6], fuel types [7–12], and also addition of swirl in the air intake system [1,13–17]. Earlier studies demonstrated higher regression rates with addition of swirl air flow [1,18–22]. On the other hand, the combustion process in the classical SFRJs is similar to that in the classical hybrid rocket motors (HRMs), in which the released fuel and oxidizer mix and react inside the solid fuel grain and then directed into the aft mixing chamber and the nozzle. Thus, approaches used for HRMs could help for SFRJs with keeping in mind that the SFRJ does not carry any oxidizer. Extensive studies of the use of complex configurations of solid fuels in hybrid rocket motors on the combustion characteristics and performance have been made and reported elsewhere [2,3, 23–32]. In open literature, few studies are available regarding different solid-fuel ramjet combustor’s designs. However, complex

O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

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Fig. 1. The classic design of solid-fuel ramjet engine.

configurations have been investigated extensively in hybrid rocket motors. Lee et al. [3] carried out experimental and numerical investigation in order to study the effect of both swirl injector and helical configuration of the grain (represented by a pitch number) on the enhancement of regression rate. They reported that a proper combination of helical configuration with large pitch number and a moderate inlet swirl can produce the condition for achieving the maximum regression rate. Kim et al. [30] have experimentally examined the combustion characteristics of the cylindrical multi-port grain of a hybrid rocket motor and showed the port number effects on the regression rate. They found that as the port number increases, the oxidizer/fuel ( O / F ) ratio in each grain shifts toward its optimum condition, besides, the regression rate is increased for three, four, and five ports with respect to the single port. Li et al. [29] performed numerical simulations on hybrid rocket motor with tube, star and wagon wheel grains. The results revealed that the average regression rates of the star and wagon wheel grains are much larger than that of the tube grain for the same flow condition. Tian et al. [25,27,28] conducted experimental and numerical investigation of the hybrid rocket motor with multi-port fuel, segmented, and helical grains. They demonstrated that the segmented grain configuration proves its ability to enhance the combustions efficiency and the regression rate of the hybrid rocket motor. Zhang et al. [26] numerically examined the tube and complex star swirl grains for hybrid rocket motor. They reported that the burning surface area is increased twice for star grain as well as the average regression rate is enhanced to about 60% for the same grain length. Whitmore et al. [2] stated that helical flows have significantly increased the local skin friction coefficient beside introducing a centrifugal component into the flow field which leads pushing flame zone closer to the wall surface and then increasing the flame diffusion efficiency. Therefore, helical ports serve to both increase the surface skin friction coefficient and simultaneously reduce the radial wall blowing effect that leads to a significant improvement of the overall regression rate. Recently, Ahn et al. [24] studied multiport design with optimum O / F ratio by adjusting the number of ports and diameter while decreasing the length. They reported that the use of simple cylindrical multiport design reduces the length-to-diameter ratio of the hybrid thruster and improves rocket combustion performance. Finally, Gong et al. [23] carried out an experimental and numerical study on combustion characteristics of the solid-fuel ramjet with star solid fuel. Their results revealed that star solid fuel exhibited higher space-averaged regression rate than that of the traditional single-port cylindrical solid fuel. Apparently, none of all previous studies, however, showed the optimum design of the solid fuel especially for solid-fuel ramjet motor that increases the regression rate. This motivates us to propose a novel design of the solid-fuel ramjet motor that works with a new combustion chamber in order to enhance the combustion characteristics, regression rate, and performance of solid-fuel ramjet motor. In this paper, we propose and examine a novel design of solidfuel ramjet’s combustion chamber with two solid fuel grains. In the proposed design, alongside the single-port cylindrical (tubular) grain, the combustion chamber contains additional rod solid fuel at the center of the tubular grain (see Fig. 2a). The idea is to enlarge

the solid fuel surface area contacting with incoming air to enhance the heat transfer into the solid fuel and then the regression rate. Moreover, this paper also investigates numerically the proposed SFRJ design using an in-house CFD code. The solver is written by FORTRAN with parallel computing to deal with the computational cost. The developed CFD code predicts the governing equations simultaneously by means of multi-block, finite volume method, structured, cell-centered, and density-based approach. 2. Numerical method 2.1. Governing equations of fluid domain The flow field considered is essentially three dimensional (3-D) for which all velocity and Reynolds stress components are included with regard to the simplifying condition of symmetry, whereas the flow is still angular symmetry (∂/∂θ = 0). Therefore, the 3-D Reynolds-average Navier-Stokes equations with angular symmetry condition in integral form, which are representing the conservation of mass, momentum, energy, and species equations, can be written as [33–35]:

∂ ∂t

˚

¨ Ud +



˚

=



¨



F · nx + G · n y ds −

s





Fv · nx + Gv · n y ds

s

(H + Hν ).εd + S

(1)



where n = nx i + n y j is the unit normal vector in outward direction of the boundary surface s, t is the time. The conservative vector U, convective flux vectors F, G, viscous flux vectors Fv , Gv , axisymmetric source terms H, Hν , and chemical reactions source term S are given by:

⎡

⎤

⎡

⎤

ρu ρv ρ ⎤ ⎢ ρ u2 + p ⎥ ⎢ ⎥ ρ vu ⎢ ρu ⎥ ⎢ ⎢ ⎥ ⎥ ⎥ ⎢ 2 ⎢ ⎢ ⎥ ⎥ ρ uv ⎥ ⎢ ρv ⎥ ⎢ ρv + p ⎥, U=⎢ G = , ⎥, F = ⎢ ⎢ ρu w ⎥ ⎢ ρvw ⎥ ⎢ ρw ⎥ ⎢ ⎢ ⎥ ⎥ ⎣ ρE ⎦ ⎣ (ρ E + p ) u ⎦ ⎣ (ρ E + p ) v ⎦ ρi ρi u ρi v ⎡

⎡

0

⎤

⎢ ⎥ τxx ⎢ ⎥ ⎢ ⎥ τxy ⎥, Fv = ⎢ ⎢ ⎥ τ xθ ⎢ ⎥ ⎣ u τxx + v τxy + w τxθ + q x ⎦ ⎡

ρ D i ∂∂cxi 0

⎤

⎢ ⎥ τ yx ⎢ ⎥ ⎢ ⎥ τ yy ⎢ ⎥, H = −1 Gv = ⎢ ⎥ τ yθ y ⎢ ⎥ ⎣ u τ yx + v τ y y + w τ y θ + q y ⎦

ρ D i ∂∂cyi

⎡

ρv ρ vu

⎤

⎢ ⎥ ⎢ ⎥ ⎢ ρ (v 2 − w 2) ⎥ ⎢ ⎥ ⎢ 2ρ v w ⎥ , ⎢ ⎥ ⎣ (ρ E + p ) v ⎦

ρi v

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O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

Fig. 2. The solid fuel ramjet being proposed and investigated.

⎡

0

⎤

⎡

sρ ⎢ ⎥ τ s yx ⎢ ρu ⎢ ⎥ ⎢ ⎥ τ 1⎢ s y y − τθ θ ⎢ ρ v ⎥, S = ⎢ Hν = ⎢ ⎥ 2τ y θ ⎢ sρ w y⎢ ⎢ ⎥ ⎣ s ⎣ u τ yx + v τ y y + w τ y θ + q y ⎦ ρE ∂ ci ρ Di ∂ y ω˙ i + sρi

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

• ε = 0 and w = 0 for two-dimensional plane flow in which x and y denote x and y in Cartesian coordinates system, respectively. • ε = 1 and w = 0 for axisymmetric flow in which x and y denote z and r in cylindrical coordinates system, respectively. • ε = 1 for axisymmetric swirl flow in which x and y denote z and r in cylindrical coordinates system, respectively. This technique is used to offer more flexibility to the developed code for which three solvers are combined in one code. And:

2



τxx = μ 2 3



 ∂u ∂u ∂ v v 2 ∂v v − − − − , τyy = μ 2 , ∂x ∂ y y 3 ∂y ∂x y



 ∂u ∂ v , + ∂y ∂x



 ∂v ∂w v τ y y − τθ θ = 2μ − , τxθ = μ , ∂y y ∂x

 w ∂w τ yθ = μ − , ∂y y

τxy = τ yx = μ

qx = k

∂T ∂ ci ∂T ∂ ci +ρ D i hi , qy = k +ρ D i hi , ∂x ∂x ∂y ∂x N

N

i =1

i =1

i=1→N where u, v, w, T , p, ρ , and E represent the axial, radial, tangential velocities, temperature, pressure, total density, and total energy per unit mass, respectively; sρ , sρ u , sρ v , sρ w , sρ E , and sρi are the mass, momentum, energy, and species source terms due to solid fuel pyrolysis and chemical reaction at the first cell in the fluid ˙i domain attached with the solid fuel, respectively. The variable ω is the mass production rate of species i due to chemical reactions, c i = ρi /ρ is the mass fraction, N is the number of species, τ is the shear stress, k is the thermal conductivity coefficient of the gases

O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

which is equal to the summation of its laminar kl and turbulent kt = C p (μt /Prt ) parts, and μ is the total effective viscosity which equals to the summation of laminar μl and turbulent μt viscosities. Prt is the turbulent Prandtl number. The laminar viscosity of the mixture is calculated using the following formula:

1/4 2

μli M i N N X j [1 + μli ( M j ) X i μli

μl = , φi = M φi 8(1 + i ) i =1

j =1

1 − Xi 1 − ci

(

μl Sc

+

μt Sc t

(3)

)

2

2

2

ρ E − ρ (u + v + w ) = 2

N i =1

ˆT

ρi (

C p i dT

+ h298 )− R u T i

N ρi i =1

298

Mi (4)

where h298 is the heat of formation at reference temperature i (298K ), and at high temperatures the specific heat at constant pressure C pi is estimated by: 2

3

4

C pi = (a1i + a2i T + a3i T + a4i T + a5i T ) R u

(5)

coefficients a ji ( j = 1, .., 5) are obtained from the chemical kinetics package [36] and R u is the universal gas constant. For thermally perfect gases the equation of state is given by:

p=

N ρi i =1

Mi

Ru T

(6)

For the mixture, the total density stant R = R u

N  i =1

ρ=

N  i =1

ρi , mixture gas con-

c i / M i , the specific heat C p =

ratio of total specific heats

γ = C p /(C p − R ).

N  i =1

c i C pi , and the

In this work, finite rate model is adopted to represent the chemical reaction processes. It should be noted that the turbulencechemistry interaction is neglected in this work. For I reactions, the reaction mechanism is presented by

v ik X i 

i =1

N

v ik X i , k = 1, ..., I

(7)

i =1

where v ik and v ik are stoichiometric coefficients. The rate of mass production of species N in I reactions is expressed as

ω˙ i = M i

I k =1

and

  ( v ik − v ik ) R f − R b

n

E a (J/mol)

C 2 H 4 + O 2 → 2C O + 2H 2

2.10E14

0

149779.2

2C O + O 2 → 2C O 2

3.48E11

2

84261.5

2H 2 + O 2 → 2H 2 O

3.00E20

-1

0.0

  N

 ρi v ik i =1

R b = r˙bk

Mi

  N

 ρi v ik i =1

Mi

⎛ .⎝

N ρj j =1

Mj

⎞L M C j⎠

,

⎞L M ⎛ N ρ j .⎝ C j⎠ j =1

Mj

where r˙ f k and r˙bk are the forward and backward reaction rate constants for each reaction, respectively; C j is the third-body efficiency; L M = 1 when there is the third-body ( M ) and L M = 0 elsewhere. Arrhenius formula (Eq. (9)) is utilized to determine reaction rate constants.

r˙k = A k T w nk exp [−( E a )k / R u T w ]

(8)

(9)

where A k is the pre-exponential factor, nk is the temperature exponent, E a is the activation energy, and T w is the solid-fluid interface wall temperature. In addition, Fourier’s equation is used to model the heat diffusion in the solid fuels; more details could found in our previous work regarding solid domain modeling [19]. 2.3. Solid-Fluid Interaction The solid fuel used for both proposed and classic designs, in this paper, is the high-density polyethylene (HDPE) grains. This paper assumes that the only pyrolysis product of the solid fuel is C 2 H 4 relied on the difficulty of having a precise chemical reaction model besides the very complex chemical reactions inside the solid-fuel ramjet. The reaction model of a 3-step gas-phase [37] is utilized in order to reduce the computing uncertainties since the 10-step model gives nearly similar results as 3-step model [37,38]. Thus, the gas-phase chemical reactions kinetic of HDPE [39] can be written as in Table 1. In order to model the solid fuel pyrolysis in the solid-fluid interface, the zeroth order (nk = 0) Arrhenius equation is used. The mass rate of fuel freed by pyrolysis is determined using:

˙ p = ρsol r˙ p = ρsol A sol exp [−( E a )sol / R u T w ] m

2.2. Finite rate model

N

A (cm3 /mol s)

R f = r˙ f k

with the laminar and turbulent Schmidt numbers are assumed constant S c = 0.5, S ct = 0.8, respectively. The total energy per unit volume is determined using Eq. (4) and then used to calculate the temperature using the Newton iteration method.

1

Chemical reaction

(2)

where μli , M i , and X i are the laminar viscosity, molecular weight, and mole fraction of species respectively. The mass diffusivity D i of species i in the mixture is given by

ρ Di =

Table 1 Chemistry model of ethylene.

]

Mj

753

(10)

The subscript “sol” denotes the solid fuel and the characteristics of HDPE are as follows: white color, density ρsol of 940 kg/m3 , thermal conductivity of 0.38 W/(m K), A sol of 8750 m/s, E asol of 130 KJ/mol [40,41]. The pyrolysis rate of HDPE due to heat transfer from fluid domain into the solid surface before combustion (gasification step) and during combustion must be considered as a source term affected on the fluid domain conservation equations. Therefore, the source terms added into the governing equations can be expressed as follows for a control volume:

• Mass equation: Since we assumed the only pyrolysis product is C 2 H 4 so the mass contributions from other species are neglected [42].

˙ p · Ab sρ = m where A b is burning area.

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O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

Table 2 Boundary conditions being used in the CFD code. Position

Boundary condition type

Inlet

Non-reflecting boundary condition with the Riemann invariant [43,44]

Inlet

For swirl cases, velocity profiles are given by the measurement data of Dellenback [45]

Inlet

Turbulence parameters’ equations at inlet are selected from [46]

Outlet

All axial gradients of flow quantities are set to zero

The axis

Axisymmetric boundary condition

Walls boundaries

No-slip adiabatic wall

Solid-fluid interface

The source terms due to the solid fuel pyrolysis are added to conservation laws

Solid-fluid interface

The direct coupling method for heat balance

The solid domain is modeled for heat diffusion by using the second-order central differences to discretize Fourier’s equation and explicit backward Euler approach for temporal discretization [51]. The direct coupling method is implemented to couple the solid and fluid domains besides adding the source terms into the fluid governing equations. Then, a multi-physics coupling code is developed using FORTRAN language and OpenMP (Open Multi-Processing) programming interface to share memory in parallel computers. The reliability and predictive capability of the developed code are verified and validated for different basic benchmark cases [52], including uncertainty and numerical errors, and for swirl cases [53]. Moreover, the combustion model for different turbulence models is validated as well [18,19,54]. 5. The new design of SFRJ

• Momentum equation: In this case, the change will happen only on y-direction which represents the burning surface direction.

sρ v = −ρsol r˙ p (˙r p ·

ρsol · A b ), ρ

sρ u = sρ w = 0

• Species equation: Only the mass of C 2 H 4 will be increased by:

˙ p · Ab · cC2 H 4 sC 2 H 4 = m where c C 2 H 4 denotes the mass fraction of C 2 H 4 in the total mass pyrolyzed which equals to unity. And for other species equal zeros, hence;

s O 2 = sC O = sC O 2 = s H 2 O = s H = 0

• Energy equation: sρ E =

1 2

r˙ p ·

ρsol ρ

2

ρsol r˙ p · A + h · (˙r p · ρsol · A b )

where h is the specific enthalpy due to pyrolysis. 3. Boundary conditions Table 2 reports the boundary conditions used in the work, more information could be found elsewhere [19]. To determine the wall temperature T w , the direct coupling method employs the energy balance as:

k

  ∂ T  ∂ T  = − k sol ∂ y  gas ∂ y solid

(11)

4. Numerical solution method and the code structure The aforementioned RANS equations have been solved by means of finite-volume method, cell-centered with structured grids, multi-block, and density-based approach. Whereas, AUSMPW+ [47] is selected to discretize the inviscid terms and enhanced by Van Albada [48] limiter function and the third-order upwindbiased MUSCL scheme [49], the second-order central differences for the viscous terms, Menter’s shear-stress transport (SST) turbulence model [50] for turbulence closure, and the LU-SGS implicit dual time-stepping algorithm [51] for temporal discretization. Finite rate model is employed to determine the chemical source terms. In this model, the flame is treated as laminar flame with neglecting the effect of turbulent fluctuating (turbulence-chemistry interaction), at which Arrhenius expression is used to determine the mean reaction rate. More details are available elsewhere [19].

The solid-fuel ramjet engine designed in this work is similar to the classic SFRJ (Fig. 1) with addition of a new solid fuel at the center of the combustor, as depicted in Fig. 2a. The new added solid fuel is in a rod shape configuration with a circular crosssection area. This design relied on the fact of increasing solid fuel surface area increases the heat transfer and hence the regression rate, besides, using the central oxidizer flow region with keeping the simplicity of the overall design. In classic SFRJs, the central oxidizer flows from the inlet till the outlet without contributing in the combustion process, however, the proposed design benefits from this region in the combustor at which the rod solid fuel is placed. Therefore, the combustion will take place on the inner surface of the tubular solid fuel alongside the outer surface of the rod solid fuel. Then, during the SFRJ flight, the tubular grain inner diameter will increase and the rod diameter will decrease. In order to examine the proposed design, numerical simulations are performed on the classic and proposed SFRJ. Swirl flow is also adopted for both designs to investigate its influences on the regression rate. Therefore, four different cases were simulated in which the classic design is simulated with and without swirl flow (cases 2 & 1, respectively) besides two cases of the proposed design with and without swirl are adopted as well (cases 4 & 3, respectively). The geometry and inlet flow conditions are the same for all cases except swirl and non-swirl cases. For non-swirl cases the swirl number equals to zero and for swirl cases equals to 0.6. At the inlet, the axial and swirl velocities profiles are given by the measurement data of Dellenback [45] and the total temperature is set to be 540 K and the mass flow rate is fixed at 0.6 kg/s. As presented in Fig. 2b, the ramjet has inlet inner diameter of 40 mm, grain port inner diameter of 70 mm, grain length of 300 mm. The diaphragm diameter is 62 mm and aft-mixing chamber diameter is 74 mm. The nozzle throat diameter is 36 mm and the exit nozzle diameter is 53 mm, the dimensions of which are based on a typical experimental test engine. The mesh comprised of a multi-block 2-D structured grids with total mesh number 104982 cells and the first cell height from the wall is 10−6 m which gives y + ≈ 1. The rod is 20 mm diameter and 303 mm in length, more information about the numerical procedure is available in [19,54]. 6. Results and discussion This section provides the numerical results obtained through the developed solver for the aforementioned cases 1-4. Two cases (case 1 & 2) were considered for the classic design of the solid-fuel ramjet with and without swirling flow and other two cases (case 3 & 4) for the proposed design for swirl and non-swirl flows. Swirl flow is used in this study to demonstrate its effect on enhancing

O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

755

Fig. 3. Radial profiles of normalized axial and tangential velocities at different locations inside the SFRJ’s combustor for classic and proposed designs.

the regression rate and performance of the designed SFRJ as has been done in our previous works for classic SFRJ [19,21]. At first, in order to deeply analyze the flow inside the SFRJ, the profiles were taken at twelve locations along the axial direction inside the combustion chamber and nine locations in aftmixing chamber. Each profile represents the flow feature in the radial direction starting from the chamber centerline towards the chamber’s wall. The velocities shown in this section are nondimensionalized by the maximum axial velocity at the inlet (U O ) and the radial lengths by the inner port radius ( R ). 6.1. Combustion chamber 6.1.1. Flow field Predicted axial and tangential velocities radial profiles for reacting flow with and without swirl for the proposed and classic designs of SFRJ at twelve axial locations are shown in Fig. 3a and 3b, respectively. Swirl cases exhibit large value of axial velocity radial gradient which is indicative of high turbulence energy generation in a strong shear layer. Because of the centrifugal force, the axial velocity profiles are bifurcating, yielding a low velocity zone along the combustor axis in classic design and rod fuel surface in the proposed design. At the first location (0.01 m), if we compare the profiles of classic design for swirl and non-swirl flow we can see that the maximum velocity occurs at the centerline for non-swirl case, approximately at r / R = 0.56 for the swirl case, as well as, at rod surface (r / R = 0.28) for non-swirl case and at r / R = 0.60 for swirl case for proposed design as shown in Fig. 3a. This means the new recirculation zone is appeared in swirl cases

for both designs which will enhance the mixing degree of the reactants and increases the reactants residence time. The same is observed at the outer surface of the rod solid fuel in the proposed design at which the swirl case showed a recirculation zone starting for the chamber’s inlet and decaying towards axial direction. Corner recirculation zone appears for all four cases near the inner surface of the tubular solid fuel (r / R = 1) which is good to see in dump combustors for combustion stabilization. The flow separation behind the step creates the corner recirculation zone which will start to decay while moving further downstream the combustor. The corner recirculation zone completely vanishes due to the flow reattachment to the combustor wall at the reattachment point. The other eleven locations presented similar trend except the last four locations for the proposed design without swirl at which the axial velocity displayed low values at outer surface of the rod solid fuel. This might be occurred due to the pyrolyzed solid fuel or the flow at aft-mixing chamber whereas a new recirculation region is generated just after the rod solid fuel. For the proposed design, the maximum velocity moves towards the inner surface of the tubular solid fuel when the flow progresses downstream for other locations. This will significantly increase the heat transfer into the solid fuel surface and then increases the regression rate as can be seen in Figs. 4 and 7. In Fig. 3b, tangential velocity profiles display solid-bodyrotation behavior (W /U O = 0 at r / R = 0) at the centerline for classic design and at the rod surface for the proposed design. Obviously, the tangential velocity increases the magnitude velocity and hence increases the velocity gradient at the tubular solid fuel

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O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

Fig. 4. Temperature radial profiles and contours for the classic and proposed designs.

inner surface, for swirl cases. At the first location (x = 0.01 m), the maximum tangential velocity is occurred for all cases and decays as the flow progresses axially (downstream). For the proposed and classic designs, the radial profiles and contours of temperature are shown in Fig. 4a - 4c, respectively. The first profile (x = 0.01 m) illustrates rapid increase of inlet temperature to its maximum, at approximately r / R = 0.61 for classic design and r / R = 0.64 for proposed design, for non-swirl cases ( S = 0.0) (see Fig. 4a). Whilst, at the ninth axial position (x = 0.24 m), the maximum temperature (the flame) moves towards the solid fuel surface (r / R = 1.0), besides, the proposed design displayed a new peak as approximately, r / R = 0.51. This means a new diffusion flame has been created near to the rod solid fuel as a result of solid fuel pyrolysis due to heat transfer. Therefore, the proposed design offered two diffusion flames for non-swirl case starting from x = 0.24 location on. The similar is observed for the proposed design with swirl flow at which the second flame is started from the second position x = 0.02 m, as can be seen clearly from temperature contours (Fig. 4b and 4c) and the second profile (x = 0.02 m). Whereas the second peak is located at r / R = 0.5 and goes further close to the inner surface till merged

with the first flame approximately at x = 0.16 m. For each swirl case, the maximum temperature along the axial positions occurred at its reattachment point. Further, it takes place between the positions 0.06 m and 0.08 m for classic design with swirl flow, and between 0.02 m and 0.03 m for the proposed design with swirl flow. This also indicates that the new design decreases the corner recirculation zone. Contours visualization of temperature for non-swirl cases of the proposed and classic designs (Upper and lower half, respectively, in each figure) and for swirl cases are presented in Fig. 4b and 4c, respectively. Comparing lower and upper halves in Fig. 4b, one can see that the flame position is located further close to the wall in the case of new design compared with classic design for the non-swirl flow. Furthermore, a new flame is observed in the proposed design near to the rod solid fuel surface and merged with the first flame at the aft-mixing chamber. This causes higher heat flux into the fuel inner surface of the tubular solid fuel and outer surface of the rod solid fuel; hence a higher regression rate could be achieved. For swirl cases (Fig. 4c), the same behavior as nonswirl cases is observed but the new flame started from the inlet of the combustion chamber due to the effect of swirl flow. This

O. Musa et al. / Aerospace Science and Technology 92 (2019) 750–765

makes the two flames to merge inside the combustor and significantly increases the heat transfer into both solid fuels. It becomes

Fig. 5. The local heat flux transferred to the solid fuel surface.

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evident that the heat transferred into the solid fuels for the proposed design is somewhat stronger that the classic design; therefore, the proposed design improves the heat transfer process inside the combustion chamber. 6.1.2. The rate of regression It is well-known that the main parameter affecting on the SFRJ performance is the solid fuel regression rate which is basically occurs due to chemical decomposition depending on the heat transferred into the fuel surface. As the magnitude of velocity in the combustion chamber is enhanced due to swirl, therefore, the heat and mass transport at the solid surface is increased as well due to the large gradients of the velocity at the solid fuel surface, as presented in Fig. 5. Whereas, the heat transferred into the solid fuel surface for all cases is illustrated. Moreover, because of the flow recirculation the local heat flux increases rapidly in the recirculation zone till reaches its maximum at the reattachment point, for non-swirl case - classic design, thereafter, decreases next the reattachment point. On the other hand, the same tendency is noticed for both designs but with higher rates for swirl cases. Though, for the proposed design without swirl, the heat flux increases again near to the combustor outlet and gives a new trend. This is because the flow behavior at

Fig. 6. Axial distribution of local regression rate for the proposed design without swirl flow along (a) the tubular and (b) rod solid fuels’ surfaces at different time intervals.

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Fig. 7. Regression rates along axial direction for the proposed and the classic designs.

Fig. 8. C 2 H 4 mass fraction contours of the proposed (upper half) and the classic design (lower half).

this region alongside the second flame effects. One can conclude, however, that the proposed design exhibits higher heat transfer than the classic design for both unswirled and swirled cases. The ignition process is achieved by using hot gas flowing together with the incoming air into the combustor. The ignition gas flows with 0.4 kg/s, total temperature of 2500 K and contains N 2 , H 2 O , and C O 2 . The ignition gas is produced through combustion of double-based propellant and only the gas components are considered in the model. After 0.35 second the ignition gas has stopped and only the incoming air flow is continued. Normally, ignition delay time includes; heating (gasification) time delay, mixing time delay, and chemical processes time delay; but mixing time is very small and can be ignored. Fig. 6a shows the local regression rates of inner surface of the tubular solid fuel. We divided the total combustion process to three zones; time before ignition (Z1), time after ignition (Z2), and time of sustained combustion (Z3). The gasification is started in Z1 (0-0.18 s) and the ignition is happened between Z1 and Z2 (0.18-0.19 s) since

the regression rate has increased suddenly due to the ignition heat transferred into fuel surface. At Z2 (0.19-0.34 s), same trend of the regression rate is observed at higher values due to the ignition gases. At 0.35 s, the ignition gases are stopped then the regression rate is dropped and sustained combustion and regression rate is achieved in Z3 (0.36-0.44), these results are consistent with Ref. [55]. Fig. 6b presents the local regression rates for outer surface of the rod solid fuel. As can be seen, the pyrolysis starts from the end of the combustor (0.3 m) due to the effect of incoming air jet. As time progresses the pyrolysis moves toward the inlet till the distance 0.17 m. Since the heat transferred into the solid fuel surface governs the local regression rate, the same tendency of heat fluxes is observed for the regression rate at the solid fuel surface. Whereas, the rate of fuel regression grows speedily in the corner recirculation region until attains its maximum at the reattachment point then decreases progressively next the reattachment point, as shown in Fig. 7a. However, the proposed design without swirl displayed ad-

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ditional maximum peak of regression rate close to the combustor’s end due to the high rate of heat transferred to tubular solid fuel surface from the second flame. The second flame, which is generated because of the fuel released from the rod solid fuel, pushes the first flame, which is generated because of the fuel released

from tubular solid fuel, close to the inner surface of the tubular grain. That leads to increase the rate of heat transport into the inner surface of the tubular grain from the first flame and then the regression rate at this region. The behavior does not observe in the proposed design with swirl because of the two flames merged inside the combustor and become one flame, but for non-swirl case the two flames merged in the aft-mixing chamber, as can be seen clearly from temperature contours (Fig. 4b and 4c). Moreover, the proposed design decreases the inlet and port cross-section areas and then increases the mass flux which is defined as the ratio of the air mass flow rate to the cross-section area of the combustor (Eq. (12)). Increase of mass flux decreases the corner recirculation zone and increases local regression rate. Thus, for the same configuration as the classic SFRJ, the proposed design gives higher mass flux and then enhances the regression rate.

˙ a/ A p Ga = m

Fig. 9. The average regression rate of HDPE for all cases.

759

(12)

˙ a are grain cross-section area and the mass flow where A p and m rate, respectively. The solid fuel regression rate at the outer surface of the rod solid fuel is investigated as well. As depicted in Fig. 7b, the regression rate trend for the rod grain is presented at which the regression rate for both cases is significantly higher than the inner surface regression almost ten times (also see Fig. 8). Therefore, the amount of the fuel released is much higher in the proposed

Fig. 10. Radial profiles of the reactants at different locations inside the SFRJ’s combustor for classic and proposed designs.

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Fig. 11. Radial profiles of the products at different locations inside the SFRJ’s combustor for classic and proposed designs.

design compared with the same configuration of classic SFRJ, as shown in Fig. 8 for C 2 H 4 mass fraction. It is obvious, from Fig. 7b, that the solid fuel starts to pyrolysis from the combustor’s inlet (between 0 − 0.05 m) for swirl case and near to the combustor’s end (between 0.15 − 0.2 m) for non-swirl case. Average regression rate for all cases is given in Fig. 9 at which, the proposed SFRJ cases (cases 3 and 4) exhibited higher average regression rate than the classic SFRJ cases (cases 1 and 2) for non-swirl and swirl flow, respectively. 6.1.3. Species distribution The reactants and combustion products concentrations are analyzed inside the combustion chamber through radial profiles at twelve axial locations as depicted in Figs. 10 and 11. The C 2 H 4 is assumed to be the only pyrolysis product of the high-density polyethylene (HDPE). As can be seen from Fig. 10b that, for all cases in the corner recirculation zone and along the surface, the oxygen concentration decreases to a very low value. Despite the enhancement of the oxygen concentration due to the swirl effect near to the wall, however, yet no oxygen near the wall in fuel-rich zone, as can be seen in Fig. 10a and 10b. In the proposed design with swirl, the oxygen content is consumed at location of 0.16 m and there is no oxygen in other positions. This is due to the higher rate of C 2 H 4 released from both solid fuels as displayed in Fig. 11a. The non-swirl case indicated similar behavior especially at last four positions. Thus, the proposed design implies that the oxygen content is consumed inside the combustor for the both cases with and without swirl then the regression rate is pretty enough as required.

Because of the high flow recirculation, the products profiles (Fig. 11a and 11b) demonstrated maximum values in the corner recirculation zone, while for other axial positions, the profiles are increased when approaching to the grain’s surfaces. On the other hand, for all cases, the combustion at the surface of the tubular grain is not much different. This is because the stinginess of the oxygen at the wall for both designs. However, swirl flow demonstrated better mixing away the inner surface especially for the proposed design. In spite of that the classic design shows week mixing at the combustor’s core except close to the end. Whilst all the oxygen content is consumed for the proposed design. As it is shown in Figs. 10 and 11, for the classic design cases, no combustion products are found at the middle of radial distance and over the combustor. Meanwhile, unless the last three axial locations, the gases’ composition nearly corresponds to that of air. However, the proposed design implies interesting profiles since it uses two solid fuels which improve the reactants mixing degree and then consume the oxygen content. 6.2. Aft-mixing chamber Aft-mixing chamber is utilized in SFRJ motor to enhance the reactants’ residence time, the reactants’ mixing degree, creating a new recirculation zone to enhance the flame stability and then improves the combustion efficiency and the motor performance. The diaphragm is used to separate the aft-chamber and the combustor. In the proposed design, a new part is added into the diaphragm which the rear of the rod solid fuel. This directly will create a new recirculation region behind the rod grain alongside the corner re-

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Fig. 12. Radial profiles of axial and tangential velocities at different axial positions in the aft-chamber for all cases.

circulation zone which is clearly shown in Fig. 12a. In this figure, the proposed design demonstrated, for swirl and non-swirl cases, a very low values of axial velocity at the centerline of the aftchamber in the first three locations (x = 0.313 − 0.333m) which means a new recirculation region is formed. This will enhance the flames’ stabilization as illustrated in Fig. 13; whereas the temperature profiles are uniform for the proposed design throughout the aft-chamber. The tangential velocity is not much different by using a new design thereby its effect can reach the nozzle which might be affected negatively on the thrust coefficient and the nozzle [56, 57] (see Fig. 12b). Moreover, the reactants concentrations profiles at aft-chamber are also presented (Fig. 14). A very high amount of fuel (C 2 H 4 ) is observed in aft-chamber for the proposed design cases (see Fig. 14a). This is because the oxygen is consumed inside the combustor and the higher amount of fuel released from the solid fuels (tubular and rod), as depicted in Fig. 14b, whereas no oxygen observed for the proposed design cases unlike the classic design cases. Therefore, new oxygen is needed to fully benefit from using

this design by adding bypass air into aft-chamber. In addition, contour visualization of mass fraction of oxygen supports this discussion. Contours visualization of oxygen mass fraction for non-swirl cases of the proposed and classic designs (Upper and lower half, respectively, in each figure) and for swirl cases are presented in Fig. 15a and 15b, respectively. Whereas, the oxygen in the central flow cannot mix with the fuel sufficiently and spurts out from the nozzle directly for the classic design; when compare upper and lower halves in Fig. 15a. The insufficient combustion of the fuel is the main reason of the low combustion efficiency of solid-fuel ramjet motor. With the proposed design, the central oxidizer flow is almost consumed inside the combustor. In Fig. 15b, swirl cases, for both classic and proposed designs, showed similar behavior as non-swirl cases but the oxygen is fully consumed inside the combustor for the proposed design. The carbon dioxide mass fractions are also visualized in Fig. 16 for all cases which support the discussion above and shows that the proposed design gives uniform distribution of C O 2 especially at aft-chamber.

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Fig. 13. Temperature radial profiles at different axial positions in the aft-chamber for all cases.

Fig. 14. The reactants radial profiles at different axial positions in the aft-chamber for all cases.

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Fig. 15. Oxygen mass fraction contours of the proposed (upper half) and the classic designs (lower half).

Fig. 16. Carbon dioxide mass fraction contours of the proposed (upper half) and the classic designs (lower half).

6.3. Performance The impact of the proposed design on ramjet performance is also examined. The performance’s parameters such as the specific impulse, thrust, characteristic velocity, and air-fuel ratio are calculated and displayed in Fig. 17 for all cases. For both designs, swirl cases showed; decrease in air-fuel ratio, a slight enhancement in characteristic velocity, a significant increase of thrust. Further, the proposed design decreases air-fuel ratio, enhances characteristic velocity and the thrust for both swirl and non-swirl cases. In spite of that the proposed design; however, negatively influences on the specific impulse at which it is slightly dropped. This is also observed for classic design when using swirl flow. The reason behind that might be the totally consuming the oxygen content in the proposed design besides much higher regression rate. Thus, if added a new air into the aft-chamber, a good impact of using the

proposed design on specific impulse can be achieved. Because of increasing the oxygen content and thrust then increases the specific impulse. In mathematics, from Eq. (15), the specific impulse is function of thrust and fuel mass flow rate, thus, increasing the thrust increases the specific impulse while increasing fuel mass flow rate decreases the specific impulse. Since the proposed design increases the fuel mass flow rate (regression rate) thus the specific impulse is decreased despite increasing the thrust with lower rate. Therefore, adding new air (bypass air) into the aft-chamber could increase the thrust significantly and then enhances the specific impulse. The performance parameters are calculated by:

⎫

˙ a /m ˙f A/ F = m ⎬ ˙ f = A s r¯˙ρ f m ⎭ A s = 2π (d p /2) L g

(13)

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Declaration of Competing Interest The authors declare no conflict of interest. Acknowledgements This work has been financially supported by the Jiangsu Postdoctoral Research Foundation, grant number AD41872. References

Fig. 17. Performance of the proposed and classic designs for all cases.

⎫

˙ e ve − m ˙ a va = m ˙ e c F c∗ − m ˙ a va ⎬ F =m ˙a +m ˙f ˙e =m m ⎭ ˙e c ∗ = p 0 A t /m

(14)

˙f I sp = F /m

(15)

The parameters are defined elsewhere [21]. 7. Conclusions In this work, a new solid-fuel ramjet motor was designed with two solid fuels; the tubular grain as in the classical SFRJs alongside a rod grain which placed at the centerline of the combustion chamber. The new design was examined numerically with an inhouse code for swirl and non-swirl flows. FORTRAN language was used to write the CFD code with parallel computing in order to reduce the time cost. The solver was verified and validated using several test cases which approved its reliability and the predictive capability. The results were compared with the classic SFRJ with the same flow conditions and configurations. The most obvious findings to emerge from this study are;

• It is found that the proposed design has improved the local re-

• •

• • •

gression rate and increased the amount of solid fuel inside the motor for the same size compared to the classical solid-fuel ramjet. A new diffusion flame has been created near to the rod solid fuel as a result of solid fuel pyrolysis due to heat transfer. Therefore, the proposed design offered two diffusion flames. For the proposed design with swirl, the two flames merged inside the combustor and became one flame, but for non-swirl case the two flames merged in the aft-mixing chamber. This significantly increases the heat transfer into both solid fuels, thus, the proposed design improves the heat transfer process inside the combustion chamber. The amount of the fuel released is much higher in the proposed design compared with the same configuration of classic SFRJ. The new design creates a new central recirculation region in the aft-mixing chamber while decreases the corner recirculation region in the combustor. For both designs, swirl cases showed; a decrease in air-fuel ratio, a slight enhancement in characteristic velocity, a significant increase of thrust. Furthermore, the proposed design decreases air-fuel ratio, enhances the thrust and characteristic velocity for both swirl and non-swirl cases.

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