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Diameter and position effect determination of diaphragm on hybrid rocket motor
Acta Astronautica 126 (2016) 325–333
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Diameter and position effect determination of diaphragm on hybrid rocket motor Xingliang Sun, Hui Tian, Guobiao Cai n School of Astronautics, Beihang University, 100191, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2016 Received in revised form 25 April 2016 Accepted 27 April 2016 Available online 11 May 2016
This study is aimed to determine and better reveal the mixture enhancement and regression rate distribution of hybrid rocket motor with diaphragm by numerical approach. A numerical model based on the computational fluid dynamics software is built to simulate the flow and combustion inside the motor. Four firing tests of the motor, including one without diaphragm and three with diaphragm, are conducted on a standard experimental system and also used as a reference for numerical simulation, the consistency between the simulation and experiment demonstrates that the numerical approach is an effective method to study the diaphragm effect on the motor performance. The flow field characteristic and regression rate distribution inside the hybrid rocket motor are then calculated to analyze the effect of position and diameter of the diaphragm. The results indicate that the diaphragm almost have no effect on the regression rate before it. However, the regression rate after the diaphragm has a strong dependence on the position and diameter of the diaphragm. As the diameter decreases and the position moves backward, the regression rate increases larger and larger, this is mainly due to the augmentation of the eddy generated by the diaphragm, which enhances the heat feedback transferred to the grain surface. When the diameter of diaphragm located at middle of grain decreases from 50 mm to 20 mm, regression rate is increased from 0.30 mm/s to 0.57 mm/s. The use of the diaphragm does cause a combustion efficiency improvement; the maximum combustion efficiency is enhanced to 98.9% from lower than 90% of the motor with no diaphragm. The increasing amplitude displays a square relation with the diameter decrease, since the entrainment of the eddy make the reactants mix sufficiently to release more energy inside the motor. & 2016 IAA. Published by Elsevier Ltd. All rights reserved.
Keyword: Diaphragm effect Regression rate Combustion efficiency Hybrid rocket motor
1. Introduction The hybrid rocket motor utilizes liquid oxidant and solid fuel as the propellant. This characteristic makes the hybrid rocket motor distinct from the conventional solid or liquid rocket motor. The hybrid rocket motor has many advantages such as the capability of restart, thrust throttling, simplicity and safety. It has a broad range of applications including the sounding rocket, tactical missile and space engines [1–6]. However, due to the feature that the oxidant and solid fuel is stored separately, the combustion inside the motor belongs to the classical diffusion flame, the hybrid rocket motor suffers low regression rates and combustion efficiencies [7– 9]. These drawbacks have limited its widespread application. With great interests of the attractive feature and the amelioration of the drawbacks of the hybrid rocket motor, many efforts have been made to improve the low regression rate and low combustion n
Corresponding author. E-mail address: [email protected] (G. Cai).
http://dx.doi.org/10.1016/j.actaastro.2016.04.029 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved.
efficiency of the hybrid rocket motor [10–19]. The regression rate is a key parameter for the study and design of the hybrid rocket motor. Various experimental and theoretical methods have been proposed to enhance the low regression rate of the hybrid rocket motor. Risha and Evans [20–23] have studied the enhancement effect of the aluminum on the regression rate by series of firing tests, they found that the nanometer-sized aluminum has the highest enhancement on the regression rate, a 20% weight addition of aluminum can increase the regression rate by 40%. Yuasa et al. [24] have carried out some hybrid rocket motor firing tests with a swirl injector to study the effect of swirl strength on the regression rate, the results indicated that the average regression rate shows an increase up to 200% as swirl number increases. However, the higher regression rate is mainly localized near the inlet of fuel port, because the swirl strength is decreased with the increase of the axial distance. Knuth et al. [25] have designed a so-called vortex tube method, so that the swirl strength can reside significantly longer over the entire fuel port, this method consequently lead to a substantial
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Nomenclature Variables
A At Dd Dg Ea Ft G h Ld Lg λd λl ṁ ηc * pc ρ Q̇
Arrhenius pre-exponential constant Nozzle throat area Diaphragm port diameter Grain port diameter Activation energy Motor thrust Oxidizer flux Heat transfer coefficient Diaphragm axial distance Grain port length Ratio of diaphragm port diameter to grain port diameter Ratio of diaphragm axial distance to grain length Mass flow rate Combustion efficiency Chamber pressure Density Rate of heat transfer
increase in regression rate up to 150% compared to that without swirl. Karabeyoglu et al. [26] found and studied the higher regression rate of the paraffin fuel used for hybrid rocket motor, the test data showed that the regression rate is about 3 times higher than that of the HTPB fuel. But they also found the paraffin has a lower combustion efficiency. For the improvement of the low combustion efficiency of the hybrid rocket motor, one common method is to introduce a diaphragm inside the motor [27–29]. Both combustion efficiency and regression rate can be improved by the diaphragm, since that induces a large increase of the turbulence level in the combustion chamber and enhances the mixing of the propellants and the heat transfer to the grain surface. However, to the best of the authors’ knowledge, many studies about the effect of diaphragm is focused on the combustion efficiency. There has been few work done on the effect of the diaphragm parameters on the both regression rate and combustion efficiency, especially on the effect of the diaphragm position. So the numerical and experimental research on the influence of the one-hole diameter and axial position of the diaphragm to the regression rate and combustion efficiency is considerably meaningful. The paper is aimed to combine the numerical simulations and firing tests to study the effect of the diaphragm on the regression rate and combustion efficiency, and to better reveal the diaphragm effect and regression rate distribution by analyzing the internal flow field characteristics obtained by the established numerical model inside the motor. For this purpose, the work is carried out by following steps. First, an experimental hybrid rocket motor is designed to carry out firing tests with/without the diaphragm, and to provide references for the numerical results. Second, a numerical model is established to simulate the combustion and flow inside the hybrid rocket motor with the diaphragm. The numerical model is validated with the experimental data, and then series of simulation cases are defined to determinate the flow field parameters and regression rate distribution. Finally, the effect of position and diameter of the diaphragm on the regression rate and motor performance is analyzed and discussed.
r ṙ Ro t T after before conv end exp f g ini itf ox pyr rad sim s tot th
Grain port radial Regression rate Universal gas constant Test time Temperature subscripts: After the diaphragm Before the diaphragm Convection End of test Experiment Fuel Gas phase Initial Iteration Oxidizer Pyrolysis Radiation Simulation Surface total theoretical
2. Experimental setup 2.1. Motor configuration In order to carry out the firing tests of hybrid rocket motor with/without the diaphragm, the hybrid rocket motor components and the diaphragm are designed and manufactured. The physical composition of the motor is shown in Fig. 1. The motor is a reloadable system and is assembled by injection panel, pre-chamber, igniter, combustion chamber, aft-chamber and nozzle. The combustion chamber has an inner diameter of 100 mm and length of 500 mm, it has the capability of housing different combinations of the grain and diaphragm. In this study, the grain has an initial port diameter of 50 mm. The injection panel, igniter and nozzle is given out in Fig. 2. The nozzle has an expansion ratio of 2.96 with a nozzle throat diameter of 18 mm. The solid fuel is the grain with an initial grain port diameter of 50 mm and length of 500 mm. 2.2. Experimental schedules The experiment uses the polyethylene (PE) as the solid fuel and the liquid 90% hydrogen peroxide (90HP) as the oxidizer. The 90HP is ignited by an ignition motor, the structure chart of the ignition motor is shown in Fig. 3. The ignition motor is composed by ignition chamber and powder ring. To carry out firing tests, an electronic ignition signal is generated by the control system to start the ignition motor. The mass flow rate of the oxidizer is controlled by the venturi, so that it can be kept constant over the entire firing test. The diaphragm applies the silica phenolic resin material, considering it is often used as a high temperature resistant and
Fig. 1. Physical composition of hybrid rocket motor.
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Fig. 2. Injection panel and igniter and nozzle.
3.1. Governing equations The Navies–Stokes governing equations are applied to calculate the two dimensional, steady, viscous, compressible flow and combustion inside the hybrid rocket motor, given as follows:
∂ ∂ ∂ ⎛⎜ ∂Φ ⎞⎟ ∂ ⎛⎜ ∂Φ ⎟⎞ ΓΦ (ρuΦ) + rΓΦ (rρvΦ) = + + SΦ ∂x r ∂r ∂x ⎝ ∂x ⎠ r ∂r ⎝ ∂r ⎠
(1)
where SΦ is the source terms related to the mass, momentum, energy and species addition from the grain surface. Φ and Г are the general variables and diffusion coefficients, which are defined as follows: Fig. 3. Structure of ignition motor. Table 1 Firing test cases of the hybrid rocket motor. Case
Dd (mm)
Ld (mm)
λd
λl
F1 F2 F3 F4
– 36 36 36
– 115 245 345
1.0 0.72 0.72 0.72
– 0.23 0.49 0.69
ablation resistant material in aerospace engineering. The diaphragm has a thickness of 10 mm. The case parameters varied for tests are also detailed in Table 1. The Dd and L d are the diameter and axial position distance of the diaphragm, as shown in Fig. 4. The parameter λ d is the ratio of the diaphragm port diameter to grain port diameter Dd/Dg , which represents diameter effect of diaphragm. The parameter λl is the ratio of the diaphragm axial distance to the total grain length L d/L g , which represents the position effect of diaphragm. Simulations corresponding to the firing tests are also carried out to validate the numerical model.
⎧ ρ r /̇ Hc ⎫ ⎫ ⎧ 0 ⎧ 1⎫ ⎪ f ⎪ ⎪ μ+μ ⎪ ⎪ u⎪ ⎪ ⎪ 0 T ⎪ ⎪ ⎪ ⎪ ⎪ μ+μ ⎪ ⎪ ⎪ ̇ ̇ T ⎬ , Sϕ = ⎨ ρf rr /Hc ⎬ Φ = ⎨ v ⎬, Γ = ⎨ ⎪ h⎪ ⎪ μ + μ /Pr ⎪ ⎪ ⎪ h T ⎪ ⎪ ⎪ ⎪ ⎪ ρf rḣ f /Hc ⎪ ⎩Y⎭ ⎪ ⎪ ⎪ ⎪ ⎩ μ + μT /PrY ⎭ ⎩ ρf r /̇ Hc ⎭
(2)
where Hc is the height of the cell near the grain surface. 3.2. Turbulence model Considering the calculation of the mass and heat transfer near the grain surface belongs to the low Reynolds flow problem, the RNG turbulence model is adopted, since it can provide an analytically-derived expression for effective viscosity under low Reynolds number flow. The turbulence kinetic energy k and its rate of dissipation ε are calculated from the following transport equations:
∂ ∂ ∂ ⎛ ∂k ⎞ k ⎜ αk μeff ⎟ + Gk + Gb − ρε − 2ρε 2 ρk ) + ρkui ) = ( ( ∂t ∂xi ∂xj ⎝ ∂xj ⎠ a (3)
+ SK ∂ ε ∂ ∂ ⎛ ∂ε ⎞ ⎜ αk μeff ⎟ + C1ε ( Gk + C3ε Gb ) ρε) + ρεui ) = ( ( k ∂t ∂xi ∂xj ⎝ ∂xj ⎠
3. Numerical model The process of flow and combustion inside the hybrid rocket motor is simulated based on the secondary development tool (UDF) in a numerical calculation software FLUENT. The numerical model includes the following calculation modules.
− C2ε ρ
ε2 − Rε + Sε k
Where the constant parameters cμ = 0.0845, c1ε = 1.42, c2ε = 1.68
Fig. 4. Schedule drawing of motor with diaphragm.
(4) in
this
model
are
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3.3. Gas–solid coupling model For the hybrid rocket motor, the pyrolysis of the grain is caused by the heat transferred from the diffusion flame developed over the grain surface. The fuel gas is transported to the flame zone by convection and diffusion, and then subsequently mixes with the oxidizer. The two reactants combust in the diffusion flame and provide the heat to sustain further pyrolysis, which is the regression of the grain surface. To obtain the grain surface temperature and regression rate, the mass and energy transportation equation at the interface should be solved. At the grain surface, the energy balance equation is given by
Q̇ conv,in + Q̇ rad,in = Q̇ cond,out + Q̇ pyr,chg + Q̇ rad,out
(5)
Considering that there is no metal contained in the fuel in this study, the radiation could be safely ignored. Then
−λ g
∂T ∂y
= − λf g,itf
∂T ∂y
+ ( − ρg vhg − ρf rḣ f,itf ) f ,itf
(6)
The heat transferred into the solid fuel grain can be determined as
Fig. 5. Flow chart of numerical simulation.
∂T λf = ρf cp r ̇ ( Tf,itf − Tf,ini ) ∂y
(7)
The mass conservation equation in the fuel surface is given by
ρg vg = −ρf r ̇
(8)
Then, the simplified form of energy equation is
−λ g
∂T ∂y
(
= ρf r ̇ hc2h4, T f − hf ,ini g,itf
)
(9)
where hc2h4, Ts is the enthalpy of the C2H4 at temperature of the grain surface Tf , and hf, ini is the enthalpy of the fuel at the reference temperature (298.16 K). For the products of grain pyrolysis, many researchers have taken it as the entirely ethylene (C2H4), and experimental data also indicated that the major composition of the grain pyrolysis product is ethylene. The pyrolysis performances of the PE are shown by
⎛ Ea ⎞ ⎟ r ̇ = A exp ⎜ − R 0 Tf ⎠ ⎝
(10)
where, A = 2678.1 m/s and Ea = 2125.604 kJ/mol. When the Eqs. (9) and (10) are combined, both the Tf and r ̇ can be solved, this process is realized by UDF at the grain surface in form of boundary condition, other boundary conditions at the grain surface are treated as non-slip wall. The coupling relationship of UDF with internal flow field calculation is presented in Fig. 5. After the regression rate is calculated, the source terms of mass, momentum, energy and species can be determined and added into the computation domain by UDF. 3.4. Reaction model For the 90HP in the simulation, it is considered as a gaseous mixture of decomposition, which consists of 56.2% H2O and 43.8% O2 at a temperature of 1024 K, according to the thermodynamic calculation. Many efforts have been done to calculate the stable combustion flame in the stream of oxidizer, and a simplified reaction mechanism is generally considered as a fine description for combustion between C2H4 and 90HP [30–32]. The chemical reaction equations are presented as follows:
C2 H4 + 2O2 → 2CO + 2H2 O CO + 0.5O2 → CO2
(11)
The eddy dissipation model is applied to determine the reaction rate. It is suitable for the reaction when the mixing time of reactants is much longer than the reaction time, since the combustion process inside the hybrid rocket motor is dominated by the diffusion of the reactants. And the applicability of reaction model and simulation code has been certified by researches [33– 35]. In this model, the reaction rate is controlled by the turbulent mixing of fuel and oxidizer. The net rate of production of species i due to reaction r is given by expressions below:
Ri, r, ED = ν′i, r Mw, i Aρ
⎛ ⎞ ⎛ ⎞ ∑ YP ε YR ⎟ min ⎜ min ⎜ ⎟, B N P ⎜ R ⎝ ν′i, r Mw, R ⎠ κ ∑ j ν″j, r Mw, j ⎟⎠ ⎝
(12)
3.5. Simulation mesh and cases The mesh for the simulation is draw out from the different physical configuration of the motor with the diaphragm. The Fig. 6 presents a typical mesh for simulation. The diaphragm is located at the center of the grain and its diameter is 30 mm. The mesh near the diaphragm and wall surface are refined to size of 0.01 mm 0.01 mm, so that the y-plus is about 1 and the flow and heat transfer can be calculated accurately. To acquire a final numerical result, the convergence criteria are: (1) the residuals of all equations below 1E-4; (2) the result is invariant with iteration (variation less than 0.1%); and (3) at least 2000 iteration. To investigate the effect of position and diameter of diaphragm on the motor performance and regression rate distribution, the parameter λ d takes four levels of 0.4, 0.6, 0.8, 1.0 and the parameter λl takes four levels of 0.25, 0.5, 0.75 and 1.0. Considering the finiteness of the levels and the convenient of the numerical simulation, the simulation cases are organized by the complete orthogonal design and are given out in Table 2.
4. Results and discussion The regression rate and combustion efficiency of the hybrid rocket motor with different diaphragm parameters are determined
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Fig. 6. One typical mesh for simulation. Table 2 Definition of the simulation cases. Case C1
λd λl
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11 C12
1.0 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.4 0.4 / 0.25 0.5 0.75 1.0 0.25 0.5 0.75 1.0 0.25 0.5
C13
0.4 0.4 0.75 1.0
by firing tests and numerical simulation. The detailed results and flow field characteristics are discussed to better reveal the mixture enhancement of the diaphragm. 4.1. Experimental results 4.1.1. Original curves and figures Fig. 7 shows the typical experiment curves of the test case of F1, it includes the chamber pressure, motor thrust and oxidizer mass flow rate. During the motor operation, the oxidizer mass flow rate remains at a steady value, indicating that the oxidizer feeding system works well to meet the requirement of the test design. The chamber pressure has three peak value, corresponding A, B and C. A is caused by the ignition, B due to the combustion of the oxidizer injected into the motor, C results from the nitrogen purge, since its pressure is 3 MPa higher than the chamber pressure. Figs. 8 and 9 present the gain and diaphragm before and after the firing test. The port diameter of grain post segment after test is slightly larger than that of the grain front segment, it indicates that the grain after the diaphragm consumes more, this behavior is consistent with the numerical results. The diaphragm has a good structure integrity and plays an important part in mixing the reactants. The ablation is mainly due to the high temperature gas erosion. 4.1.2. Data analysis The experimental data of the four firing tests with/without the diaphragm is reported in Table 3. Also exhibited are the
Fig. 7. Experimental curves of the test case F1.
Fig. 8. Grain before and after the test.
Fig. 9. Diaphragm before and after the test.
corresponding simulation data as the references in this table. It can be note that the regression rate before and after the diaphragm meets well with the simulation data, the maximum error is lower than 5%. Chamber pressure errors between the firing tests and corresponding simulations are also less than 5%. The good agreement suggests that the accuracy of the established numerical simulation mode is accepted, it can be used to calculate regression rate and chamber pressure, which are need for the effect study of diaphragm on hybrid rocket motor. As seen in the Table 4, the using of the diaphragm does increase the regression rate after diaphragm and the combustion efficiency, especially when the diaphragm moves toward the end of the grain. This enhancement effect and regression rate distribution will be determined and analyzed by the results of the series of numerical simulation cases as planned above.
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Table 3 Data of the four firing tests case
F1 F2 F3 F4
Inlet
Before the diaphragm
After the diaphragm
ṁ o kg/s
̇ mm/s rexp
̇ mm/s rsim
Error %
̇ mm/s rexp
̇ mm/s rsim
Error %
Pc _ exp MPa
Pc _ sim MPa
Error %
0.375 0.380 0.381 0.381
0.403 0.404 0.409 0.396
0.408 0.395 0.406 0.410
1.24 2.22 0.73 3.53
0.409 0.529 0.547 0.555
0.412 0.542 0.559 0.562
1.68 2.38 2.25 1.21
1.97 2.17 2.33 2.21
1.94 2.13 2.29 2.17
1.52 1.87 1.71 1.81
Table 4 Data of the simulation cases. Case
ṁ o kg/s
r ̇before mm/s
̇ mm/s rafter
o/f
Pc MPa
C * m/s
ηc %
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13
0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13
0.262 0.251 0.257 0.260 0.262 0.251 0.257 0.260 0.262 0.251 0.257 0.260 0.262
0.262 0.306 0.314 0.318 0.320 0.395 0.405 0.410 0.413 0.566 0.581 0.588 0.592
3.32 3.04 3.11 3.24 3.43 2.47 2.68 2.99 3.45 1.82 2.12 2.61 3.47
1.043 1.049 1.048 1.045 1.040 1.059 1.056 1.050 1.040 1.075 1.061 1.058 1.039
1397.3 1438.1 1456.5 1477.7 1437.2 1404.4 1446.4 1487.5 1452.7 1326.3 1388.7 1479.2 1469.7
89.1 93.1 93.9 94.6 92.1 95.2 96.1 96.6 92.5 97.8 98.5 98.9 93.1
*
Fig. 10. Regression rate of the different axial position with λ d = 0.6 .
4.2. Regression rate behaviors 4.2.1. Diaphragm position effect The variation of regression rate with the axial position of the
Chamber pressure
diaphragm is shown in Fig. 10. In the figure, it can be easily noted that the regression rate is divided into two parts: the regression rates before the diaphragm is almost the same; but those after the diaphragm are changed obviously. For the former, the regression rate far from the front end of the diaphragm is unchanged by the diaphragm. However, the regression rate near the front end of the diaphragm is lower than that of before, the reason for this behavior can be figured out in Fig. 11. As seen that the existence of diaphragm makes the flame away from the grain surface, therefore, the total heat transferred to the grain surface is decreased and the regression rate is reduced. The regression rate behavior after the diaphragm is that: with the increase of the axial position, the regression rate increases rapidly enhanced to a peak value firstly and then decreases to a lower value, after which the regression rate raises monotonically with the increase of the axial position. This phenomenon can be explained by the combined effect of two causes: the strength of the eddy and the addition of the fuel mass flow rate. The generation of the eddy after the diaphragm enhances the heat transfer between the hot gas and the grain surface, so the regression rate can be increased. But the strength of the eddy decreases with the increase of the axial position of diaphragm, therefore, the regression rate decreases to a lower value. The dominant reason for the second increase of the regression rate is the large quantity addition of the fuel mass, which is caused by the higher regression rate at the upstream, since the regression rate has a positive correlation with the oxidizer mass flux for the hybrid rocket motor. In Fig. 10, it can be also figured out that the peak value of the regression rate after the diaphragm is becoming larger with the diaphragm backward movement. This results from the fact that the movement of diaphragm makes the eddy becoming larger, as provided by Fig. 12, and then the heat transfer and the regression rate are all enhanced. 4.2.2. Diaphragm diameter effect Fig. 13 presents the effect of the difference of diaphragm port diameter on the regression rate with the λl=0.5. The regression rate before the diaphragm almost has the same behavior, this indicates that the variation of the diaphragm port diameter have no influence on the flow and temperature fluid before the diaphragm, this can be easily draw out form Figs. 11 and 12. However, with the
Fig. 11. Temperature profiles of the cases C1 and C7.
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Fig. 12. Stream function of the cases C6 and C7 and C8.
4.3. 10. Combustion efficiency The combustion efficiency ηc* is defined by the ratio of simulation characteristic velocity C *sim to the theoretical one c*th . It is calculated as following equations.
C *sim =
ηc* =
Fig. 13. Regression rate behaviors of different port diameters with λl = 0.5.
decrease of the port diameter, the regression rate is increased, and the increasing amplitude is becoming larger, this is because that the decrease of the port diameter can augment the size of the eddy. With the port diameter decreases linearly, the gas velocity is changed in a square fashion, so the size of eddy also has a square fashion, as presented in Fig. 14. This results more heat transferred to the grain surface to enhance the regression rate. The regression rate after the diaphragm is enhanced from 0.30 mm/s to 0.57 mm/s.
Pc × At ṁ tot
c *sim c *th
(13)
(14)
4.3.1. Diaphragm position effect Fig. 15 illustrates the combustion efficiency of the different diaphragm position with the same diaphragm port diameter ( λ d = 0.4 ). The combustion efficiency of the based case (C1) is lower than 90%, however, when the diaphragm is used, the combustion efficiency is improved. The combustion efficiency increases until the diaphragm is located at the position of λl=0.75, beyond which the combustion efficiency is reduced, as the curve of C13 shown in the figure. The maximum value of combustion efficiency at λl=0.75 is 98.9%. It is due to that the size of the eddy is enlarged by the backward movement of the diaphragm, also as shown in Fig. 12, this augmentation mixes the reactants more sufficiently and then the effective combustion is achieved. It should be noted that the combustion efficiency of case C13 is less improved than other cases, but is still larger than that of basedcase C1. The behavior of case C13 can be easily comprehend by the fact that when the diaphragm is located at the end of the grain, the eddy merges with that generated by the aft-chamber to one eddy,
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Fig. 14. Stream function of the cases C3 and C7 and C11.
Fig. 15. Combustion efficiency of the different position with λ d = 0.4 .
so the enhancement is limited compared to the two eddies as appeared in other cases. 4.3.2. Diaphragm diameter effect The effect of the diaphragm diameter on combustion efficiency is given out in Fig. 16. With the decrease of the diaphragm port diameter, the combustion efficiency is increased, and the trend is becoming larger. It is believed that this behavior corresponds to the eddy changing bigger in square fashion with the port diameter changing in line fashion, as also have been discussed in Fig. 14. The larger of the eddy makes the propellant mix and combust more efficiently, and more energy is released inside the motor to improve the combustion efficiency. 5. Conclusion The objective of this paper is to better understand the effect of diaphragm, which is used as a mixture enhancing device inside
Fig. 16. Combustion efficiency of the different port diameter with λl = 0.4 .
hybrid rocket motor, on the motor performance by numerical simulations. In order to complete this study, four firing tests are carried out to verify the established numerical simulation model and provide some useful experimental data. Series of the numerical simulation cases are arranged to study the position and diameter of diaphragm on the regression rate and combustion efficiency. This paper studies the diaphragm effect on the regression rate and combustion efficiency of hybrid rocket motor. The main conclusions are presented as follows: 1) The experimental and numerical results demonstrate that the diaphragm has no effect on the regression rate before the diaphragm, but has a significant influence on the regression rate after the diaphragm. The regression rate is sensitive to the position and diameter of the diaphragm, with the backward of position and/or the decrease of the diameter, the regression rate can be increased outstandingly.
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2) The combustion efficiency really can be improved by the diaphragm, due to its mixture enhancement. The combustion efficiency of motor with no diaphragm is lower than 90%, when a diaphragm is located inside the motor, the combustion efficiency is greater than 92%, and the maximum value reaches 98.9%. 3) The diaphragm diameter has a square fashion effect on the increase of the combustion efficiency. With the diaphragm moving toward the end of grain, the amplitude is increased initially then reduced, in this study the peak value occurs around λl = 0.75.
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hybrid rocket fuel by helical grain configuration, Aerosp. Sci. Technol. (2007). [15] H. Tian, X. Sun, Y. Guo, et al., Combustion characteristics of hybrid rocket motor with segmented grain, Aerosp. Sci. Technol. 46 (1) (2015) 537–547. [16] C.P. Kumar, A. Kumar, Effect of diaphragms on regression rate in hybrid rocket motors, J. Propuls. Power 29 (3) (2013) 559–572. [17] N. Bellomo, M. Lazzarin, F. Barato, et al., Investigation of effect of diaphragms on the efficiency of hybrid rockets, J. Propuls. Power 30 (1) (2014) 175–185. [18] V.V. Tyurenkova., Non-equilibrium diffusion combustion of a fuel droplet, Acta Astronaut. 75 (2012) 78–84. [19] G. Gariani, F. Maggi, L. Galfetti, Numerical simulation of Htpb combustion in a 2D hybrid slab combustor, Acta Astronaut. 69 (5–6) (2011) 289–296. [20] B. Evans, N.A. Favorito, E. Boyer, et al., Characterization Nano-Sized Energetic Particle Enhancement of Solid-Fuel Burning Rates in an X-Ray Transparent Hybrid Rocket Engine, 2004-821, 2004. [21] G.A. Risha, B.J. Evans, E. Boyer, et al., Nano-Sized Aluminum- And Boron-Based Solid-Fuel Characterization in a Hybrid Rocket Engine, AIAA Paper 2003-4593, 2003. [22] G.A. Risha, E. Boyer, R.B. Wehrman, et al., Performance Comparison of HtpbBased Solid Fuels Containing Nano-Sized Energetic Powder in a Cylindrical Hybrid Rocket Motor, AIAA Paper 2002-3576, 2002. [23] G.A. Risha, A. Ulas, E. Boyer, et al., Combustion of Htpb-Based Solid Fuels Containing Nano-Sized Energetic Powder in a Hybrid Rocket Motor, AIAA Paper 2001-3535, 2001. [24] C.P. Kumar, A. Kumar, Effect of Swirl On the Regression Rate in Hybrid Rocket Motors, Aerosp. Sci. Technol. 29 (1) (2013) 92–99. [25] W.H. Knuth, D.J. Gramer, M.J. Chiaverini, et al., Development and Testing of a Vortex-Driven High-Regression Rate Hybrid Rocket Engine, AIAA Paper 19983507, 1998. [26] M.A. Karabeyoglu, B.J. Cantwell, D. Altman, Development and Testing of Paraffin-Based Hybrid Rocket Fuels, AIAA Paper 2001-4503, 2001. [27] M.F.F.B.M. Lazzarin, Cfd Simul. a Hybrid. Rocket. Mot. Liq. Inject. (2011) 2011–5537. [28] S. Kim, S. Kim, J. Lee, et al., Effect of Paraffin-Ldpe Blended Fuel in Hybrid Rocket Motor, AIAA Paper 2010-7031, 2010. [29] N. Bellomo, M. Lazzarin, F. Barato, Numerical Investigation of the Effect of a Diaphragm On the Performance of a Hybrid Rocket Motor, AIAA Paper 20107033, 2010. [30] V.V. Tyurenkova, M.N. Smirnova, Material combustion in oxidant flows: selfsimilar solutions, Acta Astronaut. 120 (2016) 129–137. [31] X. Pei, L. Hou, Numerical investigation on cavity structure of solid-fuel scramjet combustor, Acta Astronaut. 105 (2) (2014) 463–475. [32] N.N. Smirnov, V.V. Tyurenkova, M.N. Smirnova, Laminar diffusion flame propagation over thermally destructing material, Acta Astronaut. 109 (2015) 217–224. [33] C.P. Kumar, A. Kumar, Effect of swirl on the regression rate in hybrid rocket motors, Aerosp. Sci. Technol. 29 (1) (2013) 92–99. [34] H. Tian, X. Li, P. Zeng, et al., Numerical and experimental studies of the hybrid rocket motor with multi-port fuel grain, Acta Astronaut. 96 (2014) 261–268. [35] C.P. Kumar, A. Kumar, Effect of diaphragms on regression rate in hybrid rocket motors, J. Propuls. Power 29 (3) (2013) 559–572.
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Acta Astronautica journal homepage: www.elsevier.com/locate/aa
Diameter and position effect determination of diaphragm on hybrid rocket motor Xingliang Sun, Hui Tian, Guobiao Cai n School of Astronautics, Beihang University, 100191, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2016 Received in revised form 25 April 2016 Accepted 27 April 2016 Available online 11 May 2016
This study is aimed to determine and better reveal the mixture enhancement and regression rate distribution of hybrid rocket motor with diaphragm by numerical approach. A numerical model based on the computational fluid dynamics software is built to simulate the flow and combustion inside the motor. Four firing tests of the motor, including one without diaphragm and three with diaphragm, are conducted on a standard experimental system and also used as a reference for numerical simulation, the consistency between the simulation and experiment demonstrates that the numerical approach is an effective method to study the diaphragm effect on the motor performance. The flow field characteristic and regression rate distribution inside the hybrid rocket motor are then calculated to analyze the effect of position and diameter of the diaphragm. The results indicate that the diaphragm almost have no effect on the regression rate before it. However, the regression rate after the diaphragm has a strong dependence on the position and diameter of the diaphragm. As the diameter decreases and the position moves backward, the regression rate increases larger and larger, this is mainly due to the augmentation of the eddy generated by the diaphragm, which enhances the heat feedback transferred to the grain surface. When the diameter of diaphragm located at middle of grain decreases from 50 mm to 20 mm, regression rate is increased from 0.30 mm/s to 0.57 mm/s. The use of the diaphragm does cause a combustion efficiency improvement; the maximum combustion efficiency is enhanced to 98.9% from lower than 90% of the motor with no diaphragm. The increasing amplitude displays a square relation with the diameter decrease, since the entrainment of the eddy make the reactants mix sufficiently to release more energy inside the motor. & 2016 IAA. Published by Elsevier Ltd. All rights reserved.
Keyword: Diaphragm effect Regression rate Combustion efficiency Hybrid rocket motor
1. Introduction The hybrid rocket motor utilizes liquid oxidant and solid fuel as the propellant. This characteristic makes the hybrid rocket motor distinct from the conventional solid or liquid rocket motor. The hybrid rocket motor has many advantages such as the capability of restart, thrust throttling, simplicity and safety. It has a broad range of applications including the sounding rocket, tactical missile and space engines [1–6]. However, due to the feature that the oxidant and solid fuel is stored separately, the combustion inside the motor belongs to the classical diffusion flame, the hybrid rocket motor suffers low regression rates and combustion efficiencies [7– 9]. These drawbacks have limited its widespread application. With great interests of the attractive feature and the amelioration of the drawbacks of the hybrid rocket motor, many efforts have been made to improve the low regression rate and low combustion n
Corresponding author. E-mail address: [email protected] (G. Cai).
http://dx.doi.org/10.1016/j.actaastro.2016.04.029 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved.
efficiency of the hybrid rocket motor [10–19]. The regression rate is a key parameter for the study and design of the hybrid rocket motor. Various experimental and theoretical methods have been proposed to enhance the low regression rate of the hybrid rocket motor. Risha and Evans [20–23] have studied the enhancement effect of the aluminum on the regression rate by series of firing tests, they found that the nanometer-sized aluminum has the highest enhancement on the regression rate, a 20% weight addition of aluminum can increase the regression rate by 40%. Yuasa et al. [24] have carried out some hybrid rocket motor firing tests with a swirl injector to study the effect of swirl strength on the regression rate, the results indicated that the average regression rate shows an increase up to 200% as swirl number increases. However, the higher regression rate is mainly localized near the inlet of fuel port, because the swirl strength is decreased with the increase of the axial distance. Knuth et al. [25] have designed a so-called vortex tube method, so that the swirl strength can reside significantly longer over the entire fuel port, this method consequently lead to a substantial
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Nomenclature Variables
A At Dd Dg Ea Ft G h Ld Lg λd λl ṁ ηc * pc ρ Q̇
Arrhenius pre-exponential constant Nozzle throat area Diaphragm port diameter Grain port diameter Activation energy Motor thrust Oxidizer flux Heat transfer coefficient Diaphragm axial distance Grain port length Ratio of diaphragm port diameter to grain port diameter Ratio of diaphragm axial distance to grain length Mass flow rate Combustion efficiency Chamber pressure Density Rate of heat transfer
increase in regression rate up to 150% compared to that without swirl. Karabeyoglu et al. [26] found and studied the higher regression rate of the paraffin fuel used for hybrid rocket motor, the test data showed that the regression rate is about 3 times higher than that of the HTPB fuel. But they also found the paraffin has a lower combustion efficiency. For the improvement of the low combustion efficiency of the hybrid rocket motor, one common method is to introduce a diaphragm inside the motor [27–29]. Both combustion efficiency and regression rate can be improved by the diaphragm, since that induces a large increase of the turbulence level in the combustion chamber and enhances the mixing of the propellants and the heat transfer to the grain surface. However, to the best of the authors’ knowledge, many studies about the effect of diaphragm is focused on the combustion efficiency. There has been few work done on the effect of the diaphragm parameters on the both regression rate and combustion efficiency, especially on the effect of the diaphragm position. So the numerical and experimental research on the influence of the one-hole diameter and axial position of the diaphragm to the regression rate and combustion efficiency is considerably meaningful. The paper is aimed to combine the numerical simulations and firing tests to study the effect of the diaphragm on the regression rate and combustion efficiency, and to better reveal the diaphragm effect and regression rate distribution by analyzing the internal flow field characteristics obtained by the established numerical model inside the motor. For this purpose, the work is carried out by following steps. First, an experimental hybrid rocket motor is designed to carry out firing tests with/without the diaphragm, and to provide references for the numerical results. Second, a numerical model is established to simulate the combustion and flow inside the hybrid rocket motor with the diaphragm. The numerical model is validated with the experimental data, and then series of simulation cases are defined to determinate the flow field parameters and regression rate distribution. Finally, the effect of position and diameter of the diaphragm on the regression rate and motor performance is analyzed and discussed.
r ṙ Ro t T after before conv end exp f g ini itf ox pyr rad sim s tot th
Grain port radial Regression rate Universal gas constant Test time Temperature subscripts: After the diaphragm Before the diaphragm Convection End of test Experiment Fuel Gas phase Initial Iteration Oxidizer Pyrolysis Radiation Simulation Surface total theoretical
2. Experimental setup 2.1. Motor configuration In order to carry out the firing tests of hybrid rocket motor with/without the diaphragm, the hybrid rocket motor components and the diaphragm are designed and manufactured. The physical composition of the motor is shown in Fig. 1. The motor is a reloadable system and is assembled by injection panel, pre-chamber, igniter, combustion chamber, aft-chamber and nozzle. The combustion chamber has an inner diameter of 100 mm and length of 500 mm, it has the capability of housing different combinations of the grain and diaphragm. In this study, the grain has an initial port diameter of 50 mm. The injection panel, igniter and nozzle is given out in Fig. 2. The nozzle has an expansion ratio of 2.96 with a nozzle throat diameter of 18 mm. The solid fuel is the grain with an initial grain port diameter of 50 mm and length of 500 mm. 2.2. Experimental schedules The experiment uses the polyethylene (PE) as the solid fuel and the liquid 90% hydrogen peroxide (90HP) as the oxidizer. The 90HP is ignited by an ignition motor, the structure chart of the ignition motor is shown in Fig. 3. The ignition motor is composed by ignition chamber and powder ring. To carry out firing tests, an electronic ignition signal is generated by the control system to start the ignition motor. The mass flow rate of the oxidizer is controlled by the venturi, so that it can be kept constant over the entire firing test. The diaphragm applies the silica phenolic resin material, considering it is often used as a high temperature resistant and
Fig. 1. Physical composition of hybrid rocket motor.
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Fig. 2. Injection panel and igniter and nozzle.
3.1. Governing equations The Navies–Stokes governing equations are applied to calculate the two dimensional, steady, viscous, compressible flow and combustion inside the hybrid rocket motor, given as follows:
∂ ∂ ∂ ⎛⎜ ∂Φ ⎞⎟ ∂ ⎛⎜ ∂Φ ⎟⎞ ΓΦ (ρuΦ) + rΓΦ (rρvΦ) = + + SΦ ∂x r ∂r ∂x ⎝ ∂x ⎠ r ∂r ⎝ ∂r ⎠
(1)
where SΦ is the source terms related to the mass, momentum, energy and species addition from the grain surface. Φ and Г are the general variables and diffusion coefficients, which are defined as follows: Fig. 3. Structure of ignition motor. Table 1 Firing test cases of the hybrid rocket motor. Case
Dd (mm)
Ld (mm)
λd
λl
F1 F2 F3 F4
– 36 36 36
– 115 245 345
1.0 0.72 0.72 0.72
– 0.23 0.49 0.69
ablation resistant material in aerospace engineering. The diaphragm has a thickness of 10 mm. The case parameters varied for tests are also detailed in Table 1. The Dd and L d are the diameter and axial position distance of the diaphragm, as shown in Fig. 4. The parameter λ d is the ratio of the diaphragm port diameter to grain port diameter Dd/Dg , which represents diameter effect of diaphragm. The parameter λl is the ratio of the diaphragm axial distance to the total grain length L d/L g , which represents the position effect of diaphragm. Simulations corresponding to the firing tests are also carried out to validate the numerical model.
⎧ ρ r /̇ Hc ⎫ ⎫ ⎧ 0 ⎧ 1⎫ ⎪ f ⎪ ⎪ μ+μ ⎪ ⎪ u⎪ ⎪ ⎪ 0 T ⎪ ⎪ ⎪ ⎪ ⎪ μ+μ ⎪ ⎪ ⎪ ̇ ̇ T ⎬ , Sϕ = ⎨ ρf rr /Hc ⎬ Φ = ⎨ v ⎬, Γ = ⎨ ⎪ h⎪ ⎪ μ + μ /Pr ⎪ ⎪ ⎪ h T ⎪ ⎪ ⎪ ⎪ ⎪ ρf rḣ f /Hc ⎪ ⎩Y⎭ ⎪ ⎪ ⎪ ⎪ ⎩ μ + μT /PrY ⎭ ⎩ ρf r /̇ Hc ⎭
(2)
where Hc is the height of the cell near the grain surface. 3.2. Turbulence model Considering the calculation of the mass and heat transfer near the grain surface belongs to the low Reynolds flow problem, the RNG turbulence model is adopted, since it can provide an analytically-derived expression for effective viscosity under low Reynolds number flow. The turbulence kinetic energy k and its rate of dissipation ε are calculated from the following transport equations:
∂ ∂ ∂ ⎛ ∂k ⎞ k ⎜ αk μeff ⎟ + Gk + Gb − ρε − 2ρε 2 ρk ) + ρkui ) = ( ( ∂t ∂xi ∂xj ⎝ ∂xj ⎠ a (3)
+ SK ∂ ε ∂ ∂ ⎛ ∂ε ⎞ ⎜ αk μeff ⎟ + C1ε ( Gk + C3ε Gb ) ρε) + ρεui ) = ( ( k ∂t ∂xi ∂xj ⎝ ∂xj ⎠
3. Numerical model The process of flow and combustion inside the hybrid rocket motor is simulated based on the secondary development tool (UDF) in a numerical calculation software FLUENT. The numerical model includes the following calculation modules.
− C2ε ρ
ε2 − Rε + Sε k
Where the constant parameters cμ = 0.0845, c1ε = 1.42, c2ε = 1.68
Fig. 4. Schedule drawing of motor with diaphragm.
(4) in
this
model
are
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3.3. Gas–solid coupling model For the hybrid rocket motor, the pyrolysis of the grain is caused by the heat transferred from the diffusion flame developed over the grain surface. The fuel gas is transported to the flame zone by convection and diffusion, and then subsequently mixes with the oxidizer. The two reactants combust in the diffusion flame and provide the heat to sustain further pyrolysis, which is the regression of the grain surface. To obtain the grain surface temperature and regression rate, the mass and energy transportation equation at the interface should be solved. At the grain surface, the energy balance equation is given by
Q̇ conv,in + Q̇ rad,in = Q̇ cond,out + Q̇ pyr,chg + Q̇ rad,out
(5)
Considering that there is no metal contained in the fuel in this study, the radiation could be safely ignored. Then
−λ g
∂T ∂y
= − λf g,itf
∂T ∂y
+ ( − ρg vhg − ρf rḣ f,itf ) f ,itf
(6)
The heat transferred into the solid fuel grain can be determined as
Fig. 5. Flow chart of numerical simulation.
∂T λf = ρf cp r ̇ ( Tf,itf − Tf,ini ) ∂y
(7)
The mass conservation equation in the fuel surface is given by
ρg vg = −ρf r ̇
(8)
Then, the simplified form of energy equation is
−λ g
∂T ∂y
(
= ρf r ̇ hc2h4, T f − hf ,ini g,itf
)
(9)
where hc2h4, Ts is the enthalpy of the C2H4 at temperature of the grain surface Tf , and hf, ini is the enthalpy of the fuel at the reference temperature (298.16 K). For the products of grain pyrolysis, many researchers have taken it as the entirely ethylene (C2H4), and experimental data also indicated that the major composition of the grain pyrolysis product is ethylene. The pyrolysis performances of the PE are shown by
⎛ Ea ⎞ ⎟ r ̇ = A exp ⎜ − R 0 Tf ⎠ ⎝
(10)
where, A = 2678.1 m/s and Ea = 2125.604 kJ/mol. When the Eqs. (9) and (10) are combined, both the Tf and r ̇ can be solved, this process is realized by UDF at the grain surface in form of boundary condition, other boundary conditions at the grain surface are treated as non-slip wall. The coupling relationship of UDF with internal flow field calculation is presented in Fig. 5. After the regression rate is calculated, the source terms of mass, momentum, energy and species can be determined and added into the computation domain by UDF. 3.4. Reaction model For the 90HP in the simulation, it is considered as a gaseous mixture of decomposition, which consists of 56.2% H2O and 43.8% O2 at a temperature of 1024 K, according to the thermodynamic calculation. Many efforts have been done to calculate the stable combustion flame in the stream of oxidizer, and a simplified reaction mechanism is generally considered as a fine description for combustion between C2H4 and 90HP [30–32]. The chemical reaction equations are presented as follows:
C2 H4 + 2O2 → 2CO + 2H2 O CO + 0.5O2 → CO2
(11)
The eddy dissipation model is applied to determine the reaction rate. It is suitable for the reaction when the mixing time of reactants is much longer than the reaction time, since the combustion process inside the hybrid rocket motor is dominated by the diffusion of the reactants. And the applicability of reaction model and simulation code has been certified by researches [33– 35]. In this model, the reaction rate is controlled by the turbulent mixing of fuel and oxidizer. The net rate of production of species i due to reaction r is given by expressions below:
Ri, r, ED = ν′i, r Mw, i Aρ
⎛ ⎞ ⎛ ⎞ ∑ YP ε YR ⎟ min ⎜ min ⎜ ⎟, B N P ⎜ R ⎝ ν′i, r Mw, R ⎠ κ ∑ j ν″j, r Mw, j ⎟⎠ ⎝
(12)
3.5. Simulation mesh and cases The mesh for the simulation is draw out from the different physical configuration of the motor with the diaphragm. The Fig. 6 presents a typical mesh for simulation. The diaphragm is located at the center of the grain and its diameter is 30 mm. The mesh near the diaphragm and wall surface are refined to size of 0.01 mm 0.01 mm, so that the y-plus is about 1 and the flow and heat transfer can be calculated accurately. To acquire a final numerical result, the convergence criteria are: (1) the residuals of all equations below 1E-4; (2) the result is invariant with iteration (variation less than 0.1%); and (3) at least 2000 iteration. To investigate the effect of position and diameter of diaphragm on the motor performance and regression rate distribution, the parameter λ d takes four levels of 0.4, 0.6, 0.8, 1.0 and the parameter λl takes four levels of 0.25, 0.5, 0.75 and 1.0. Considering the finiteness of the levels and the convenient of the numerical simulation, the simulation cases are organized by the complete orthogonal design and are given out in Table 2.
4. Results and discussion The regression rate and combustion efficiency of the hybrid rocket motor with different diaphragm parameters are determined
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Fig. 6. One typical mesh for simulation. Table 2 Definition of the simulation cases. Case C1
λd λl
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11 C12
1.0 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.4 0.4 / 0.25 0.5 0.75 1.0 0.25 0.5 0.75 1.0 0.25 0.5
C13
0.4 0.4 0.75 1.0
by firing tests and numerical simulation. The detailed results and flow field characteristics are discussed to better reveal the mixture enhancement of the diaphragm. 4.1. Experimental results 4.1.1. Original curves and figures Fig. 7 shows the typical experiment curves of the test case of F1, it includes the chamber pressure, motor thrust and oxidizer mass flow rate. During the motor operation, the oxidizer mass flow rate remains at a steady value, indicating that the oxidizer feeding system works well to meet the requirement of the test design. The chamber pressure has three peak value, corresponding A, B and C. A is caused by the ignition, B due to the combustion of the oxidizer injected into the motor, C results from the nitrogen purge, since its pressure is 3 MPa higher than the chamber pressure. Figs. 8 and 9 present the gain and diaphragm before and after the firing test. The port diameter of grain post segment after test is slightly larger than that of the grain front segment, it indicates that the grain after the diaphragm consumes more, this behavior is consistent with the numerical results. The diaphragm has a good structure integrity and plays an important part in mixing the reactants. The ablation is mainly due to the high temperature gas erosion. 4.1.2. Data analysis The experimental data of the four firing tests with/without the diaphragm is reported in Table 3. Also exhibited are the
Fig. 7. Experimental curves of the test case F1.
Fig. 8. Grain before and after the test.
Fig. 9. Diaphragm before and after the test.
corresponding simulation data as the references in this table. It can be note that the regression rate before and after the diaphragm meets well with the simulation data, the maximum error is lower than 5%. Chamber pressure errors between the firing tests and corresponding simulations are also less than 5%. The good agreement suggests that the accuracy of the established numerical simulation mode is accepted, it can be used to calculate regression rate and chamber pressure, which are need for the effect study of diaphragm on hybrid rocket motor. As seen in the Table 4, the using of the diaphragm does increase the regression rate after diaphragm and the combustion efficiency, especially when the diaphragm moves toward the end of the grain. This enhancement effect and regression rate distribution will be determined and analyzed by the results of the series of numerical simulation cases as planned above.
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Table 3 Data of the four firing tests case
F1 F2 F3 F4
Inlet
Before the diaphragm
After the diaphragm
ṁ o kg/s
̇ mm/s rexp
̇ mm/s rsim
Error %
̇ mm/s rexp
̇ mm/s rsim
Error %
Pc _ exp MPa
Pc _ sim MPa
Error %
0.375 0.380 0.381 0.381
0.403 0.404 0.409 0.396
0.408 0.395 0.406 0.410
1.24 2.22 0.73 3.53
0.409 0.529 0.547 0.555
0.412 0.542 0.559 0.562
1.68 2.38 2.25 1.21
1.97 2.17 2.33 2.21
1.94 2.13 2.29 2.17
1.52 1.87 1.71 1.81
Table 4 Data of the simulation cases. Case
ṁ o kg/s
r ̇before mm/s
̇ mm/s rafter
o/f
Pc MPa
C * m/s
ηc %
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13
0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13
0.262 0.251 0.257 0.260 0.262 0.251 0.257 0.260 0.262 0.251 0.257 0.260 0.262
0.262 0.306 0.314 0.318 0.320 0.395 0.405 0.410 0.413 0.566 0.581 0.588 0.592
3.32 3.04 3.11 3.24 3.43 2.47 2.68 2.99 3.45 1.82 2.12 2.61 3.47
1.043 1.049 1.048 1.045 1.040 1.059 1.056 1.050 1.040 1.075 1.061 1.058 1.039
1397.3 1438.1 1456.5 1477.7 1437.2 1404.4 1446.4 1487.5 1452.7 1326.3 1388.7 1479.2 1469.7
89.1 93.1 93.9 94.6 92.1 95.2 96.1 96.6 92.5 97.8 98.5 98.9 93.1
*
Fig. 10. Regression rate of the different axial position with λ d = 0.6 .
4.2. Regression rate behaviors 4.2.1. Diaphragm position effect The variation of regression rate with the axial position of the
Chamber pressure
diaphragm is shown in Fig. 10. In the figure, it can be easily noted that the regression rate is divided into two parts: the regression rates before the diaphragm is almost the same; but those after the diaphragm are changed obviously. For the former, the regression rate far from the front end of the diaphragm is unchanged by the diaphragm. However, the regression rate near the front end of the diaphragm is lower than that of before, the reason for this behavior can be figured out in Fig. 11. As seen that the existence of diaphragm makes the flame away from the grain surface, therefore, the total heat transferred to the grain surface is decreased and the regression rate is reduced. The regression rate behavior after the diaphragm is that: with the increase of the axial position, the regression rate increases rapidly enhanced to a peak value firstly and then decreases to a lower value, after which the regression rate raises monotonically with the increase of the axial position. This phenomenon can be explained by the combined effect of two causes: the strength of the eddy and the addition of the fuel mass flow rate. The generation of the eddy after the diaphragm enhances the heat transfer between the hot gas and the grain surface, so the regression rate can be increased. But the strength of the eddy decreases with the increase of the axial position of diaphragm, therefore, the regression rate decreases to a lower value. The dominant reason for the second increase of the regression rate is the large quantity addition of the fuel mass, which is caused by the higher regression rate at the upstream, since the regression rate has a positive correlation with the oxidizer mass flux for the hybrid rocket motor. In Fig. 10, it can be also figured out that the peak value of the regression rate after the diaphragm is becoming larger with the diaphragm backward movement. This results from the fact that the movement of diaphragm makes the eddy becoming larger, as provided by Fig. 12, and then the heat transfer and the regression rate are all enhanced. 4.2.2. Diaphragm diameter effect Fig. 13 presents the effect of the difference of diaphragm port diameter on the regression rate with the λl=0.5. The regression rate before the diaphragm almost has the same behavior, this indicates that the variation of the diaphragm port diameter have no influence on the flow and temperature fluid before the diaphragm, this can be easily draw out form Figs. 11 and 12. However, with the
Fig. 11. Temperature profiles of the cases C1 and C7.
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Fig. 12. Stream function of the cases C6 and C7 and C8.
4.3. 10. Combustion efficiency The combustion efficiency ηc* is defined by the ratio of simulation characteristic velocity C *sim to the theoretical one c*th . It is calculated as following equations.
C *sim =
ηc* =
Fig. 13. Regression rate behaviors of different port diameters with λl = 0.5.
decrease of the port diameter, the regression rate is increased, and the increasing amplitude is becoming larger, this is because that the decrease of the port diameter can augment the size of the eddy. With the port diameter decreases linearly, the gas velocity is changed in a square fashion, so the size of eddy also has a square fashion, as presented in Fig. 14. This results more heat transferred to the grain surface to enhance the regression rate. The regression rate after the diaphragm is enhanced from 0.30 mm/s to 0.57 mm/s.
Pc × At ṁ tot
c *sim c *th
(13)
(14)
4.3.1. Diaphragm position effect Fig. 15 illustrates the combustion efficiency of the different diaphragm position with the same diaphragm port diameter ( λ d = 0.4 ). The combustion efficiency of the based case (C1) is lower than 90%, however, when the diaphragm is used, the combustion efficiency is improved. The combustion efficiency increases until the diaphragm is located at the position of λl=0.75, beyond which the combustion efficiency is reduced, as the curve of C13 shown in the figure. The maximum value of combustion efficiency at λl=0.75 is 98.9%. It is due to that the size of the eddy is enlarged by the backward movement of the diaphragm, also as shown in Fig. 12, this augmentation mixes the reactants more sufficiently and then the effective combustion is achieved. It should be noted that the combustion efficiency of case C13 is less improved than other cases, but is still larger than that of basedcase C1. The behavior of case C13 can be easily comprehend by the fact that when the diaphragm is located at the end of the grain, the eddy merges with that generated by the aft-chamber to one eddy,
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Fig. 14. Stream function of the cases C3 and C7 and C11.
Fig. 15. Combustion efficiency of the different position with λ d = 0.4 .
so the enhancement is limited compared to the two eddies as appeared in other cases. 4.3.2. Diaphragm diameter effect The effect of the diaphragm diameter on combustion efficiency is given out in Fig. 16. With the decrease of the diaphragm port diameter, the combustion efficiency is increased, and the trend is becoming larger. It is believed that this behavior corresponds to the eddy changing bigger in square fashion with the port diameter changing in line fashion, as also have been discussed in Fig. 14. The larger of the eddy makes the propellant mix and combust more efficiently, and more energy is released inside the motor to improve the combustion efficiency. 5. Conclusion The objective of this paper is to better understand the effect of diaphragm, which is used as a mixture enhancing device inside
Fig. 16. Combustion efficiency of the different port diameter with λl = 0.4 .
hybrid rocket motor, on the motor performance by numerical simulations. In order to complete this study, four firing tests are carried out to verify the established numerical simulation model and provide some useful experimental data. Series of the numerical simulation cases are arranged to study the position and diameter of diaphragm on the regression rate and combustion efficiency. This paper studies the diaphragm effect on the regression rate and combustion efficiency of hybrid rocket motor. The main conclusions are presented as follows: 1) The experimental and numerical results demonstrate that the diaphragm has no effect on the regression rate before the diaphragm, but has a significant influence on the regression rate after the diaphragm. The regression rate is sensitive to the position and diameter of the diaphragm, with the backward of position and/or the decrease of the diameter, the regression rate can be increased outstandingly.
X. Sun et al. / Acta Astronautica 126 (2016) 325–333
2) The combustion efficiency really can be improved by the diaphragm, due to its mixture enhancement. The combustion efficiency of motor with no diaphragm is lower than 90%, when a diaphragm is located inside the motor, the combustion efficiency is greater than 92%, and the maximum value reaches 98.9%. 3) The diaphragm diameter has a square fashion effect on the increase of the combustion efficiency. With the diaphragm moving toward the end of grain, the amplitude is increased initially then reduced, in this study the peak value occurs around λl = 0.75.
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