Roohollah TAHERINEZHAD, Gholamreza ZAREPOUR

Department of Mechanical Engineering, University of Guilan, Rasht 51665-315, Iran

KEYWORDS

Abstract In this paper, a novel pyrogenic pulser was designed both analytically and numerically and was evaluated with empirical tests.The motivation of this study was the need for active control of the aero acoustic pressure oscillations by injecting the secondary flow into the solid rocket motor.First, in brief, pyrotechnic and pyrogenic pulsers were introduced, and then analytical governing equations were presented in three transient, sinusoidal and Hercules methods. In order to understand the internal pressure of the pulsar and its plume length,the injection flow field was evaluated using the ANSYS-Fluent software with both k-ω SST and k-ε Realizable models both at ambient and motor pressure. After that, the design and manufacturing of the pulser hardware and the test process were described. Finally, analytical, numerical and experimental results were discussed.The results show that there is a good correlation between the transient analysis in theory and the numerical solution by the k-ω SST model and the empirical test data.In addition,pyrogenic pulsers design depends on various parameters of motor and pulser charge performance prediction.The quality of pulser charge bonding to its insulator and erosion of its throat path due to injection have an important role to obtain a desirable pulser mass flow rate and plume length.

1. Introduction

In the last seventy years, active control of aero acoustic pressure oscillations has been a serious challenge of designers in segmented large solid rocket motors.1,2Literatures have referred to two methods for active control of pressure oscillations including acoustic excitation using a loudspeaker and secondary injection of a pulsating fluid.3The loudspeaker method is suitable only to instabilities with relatively small amplitudes and therefore not be useful for suppression of pressure oscillations in solid rocket motors.4It seems that secondary injection of a pulsating fluid is the best method for active control of aero acoustic pressure oscillations in solid rocket motors.5Although secondary injection of both liquid and gaseous propellants has been used by other researchers,6but no injection of solid propellant has been used. Fig.1 indicates a scheme of motor chamber and a feedback controller with secondary fuel injection.7The secondary fluid should be injected with a pulser at a sufficient mass flow rate to influence the motor pressure oscillation.8

Fig.1 Scheme of active control of motor with secondary fuel injection7.

The pulsers can be divided into pyrotechnic and pyrogenic types, as shown in Fig.2.9In pyrotechnic pulsers, shown in Fig.2(a),a charge of granular pyrotechnic propellant utilizing black or red gunpowder is ignited by an initiator and pulser pressure overstresses a diaphragm. Pulser gases vent into the motor chamber, creating a blowing gas flow.10Fig.2 (b) indicates a pyrogenic pulser called‘‘PSpyroi-1”has been used for a liquid rocket motor. The initiator of this pulser is positioned behind the end of the propellant grain and its output ignites the output end of this grain without igniting the internal surface of the grain or thermally damaging the grain structure.11

The concentration of this paper is on design and evaluation of pyrogenic pulser due to its efficient and reliable energy release and sustained combustion within the required time limit,12which provides the necessary mass flow rate to active control of aero acoustic pressure oscillations in motor.In fact,in the pyrotechnic pulsers, the explosion of a pyrotechnic fuel occurs, and therefore the discharge outlet from the pulser is released in a fraction of milliseconds, which is not suitable for blowing and controlling motor pressure fluctuations, but in pyrogenic pulsers, with more time, it can be used in active control by secondary injection.

The oscillations are considered as longitudinal acoustic ones due to oscillation in the rear wall.13On the other hand,the combustion chamber can be considered as a closedclosed tube.14Although some researchers have described the wave propagation variable by the velocity potential of the gas particles,13it is easier to deal with the pressure, which is also the only variable usually measured when combustion instabilities occur.15The wave equation for pressure fluctuationp′（z，t） is:

The boundary condition is set on the gradient ofp′（z，t）:

Fig.2 Two kinds of pulsers9.

wherehandfaccommodate all influences of acoustic motions,mean flow, and combustion response, under conditions without external forcing. The functionshcandfcindicate volume and surface actions of acoustic modes control. For closedclosed chambers, the value offis zero.15So, the onedimensional wave equations can be solved in the motor axial direction using the separation of variables and Galerkin’s methods16:

and the value of ηn（t）is calculated from the solution of second order differential equation as below6:

When no surface control exists (fc=0), active control of aero acoustic pressure oscillation is done only with pulser volume control sourcehc, demonstrating the effect of secondary injection mass flow rate17:

2. Governing equations

2.1. Injection in transient state

The first term in Eq. (8) can be written as24:

The third term for isentropic injection flow in pulser may be expressed by25:

Fig.3 Analytical model for secondary injection in motor.

where charge density ρgiand empty space volume of pulserVfiare functions of time.On the other hand,empty space volume of pulserVfiis equal to total space volume of pulserVtisubtracting volume of pulser propellantVpi. So time gradient of empty space volume of pulser will be equal to27:

whereLpiis length of pulser propellant. Finally, governing equation for transient state of pulser chamber can be obtained as:

and after simplification:

where

Using the same method, the continuity equation in the motor can be written as:

and so the final equation for motor pressure variations can be obtained:

where

Eqs.(14)and(16)are nonlinear ordinary differential equations that can be solved by numerical analysis using fourthorder Runge-Kutta method that yields smaller error terms.28

2.2. Sinusoidal injection

The secondary injection can be assumed to be sinusoidal. For this purpose, the secondary mass flow rate is given by29:

whereBis a constant that depends on the total volume of the chamberVf, and the throat areaAt, as follows:

Differentiating the second term in Eq. (18) and setting it equal to zero, the maximum pressure perturbation due to secondary injection will be obtained:

2.3. Hercules-Aerojet analysis

Hercules and Aerojet companies have analyzed pyrotechnic pulsers. In Hercules analysis, the pulser chamber immediately aft of the rupture diaphragm/orifice assembly is treated as a classical shock tube, which forms at the orifice plate, travels through the motor mounting adapter (Fig.4), and expands in a quasi-spherical manner into the test chamber.30In Fig.4,Dvandpvare the diameter and pressure of pulser throat, respectively and δpis pressure difference in motor due to pulsation.The relationship between the throat pressure,pv, and internal pressure of the pulser,pci, is defined by pressure relation in isentropic flow with choked throat as31:

Based on Hercules analysis,pressure difference δpis defined as30:

where β=Dc/Dv,aci,γci,Ac,Lp,tcandgare a constant of proportionality, speed of sound,specific heat in the pulser,motor port area, pulser plume length, the time period of the motor first longitudinal mode and gravity constant, respectively.Using Eqs. (21)–(23), secondary injection mass flow rate can be obtained as:

Fig.4 Simplified schematic of Hercules-Aerojet pulser test setup.

2.4. Results of governing equations solution

Table 1 demonstrates input values of transient analysis of pulser and motor internal ballistic. In this study, active control design needs to have a minimum pulser plume length ofLp=570 mm in motor. To this end, pulser plume in ambient should be a minimum length ofLp=168 mm. In real, measurement of pulser plume length in motor is impossible and so authors decided to test and record pulser injection in ambient and then to compare the plume length pictures with ambient length of pulser plume calculation, both in analysis and ANSYS-Fluent. It seems that, if pulser length from ambient test is in accordance with theoretical calculations, then it is acceptable that pulser plume length in the motor can be equal to what is obtained from the theory.

Figs. 5–7 represent pulser and motor performance prediction in various injection analysis types during motor action times 0–1 s and 1.5–2.5 s. This time division has been decided due to motor pressure variations versus time. Fig.5 demonstrates that when pulser injects in ambient,its pressure is about 30 bar, but when injecting in motor with pressure about 40 bar, its pressure is higher than 40 bar and differs between 50 and 60 bar for transient analysis and 40–60 bar for sinusoidal injection type. On the other hand, transient pressure trace of pulser is the same as motor with a positive shift, but sinusoidal pressure trace differs.

Table 1 Input values of transient analysis of pulser and motor internal ballistic.

Fig.5 Pulser pressure prediction.

Fig.6 Motor pressure shift prediction due to pulser injection.

Fig.6 demonstrates that transient pulsing produces maximum gage pressure difference in motor relative to other methods. Fig.7 demonstrates that when pulser injects in ambient,its mass flow rate is about 0.015 kg/s, but when injecting in motor, its mass flow differs between 0.015 and 0.03 kg/s and its average is for transient analysis with the value of 0.02 kg/s.

Fig.7 Pulser mass flow rate prediction.

3. Numerical solution of pulser flow field

To help understand the behavior of pulsation fluid, 2D flow was solved using the computational fluid dynamics software‘‘ANSYS-Fluent”, due to its good capability and user friendliness.32Two turbulent models, thek-ε realizable and the shear stress transportk-ω SST, were used in this work to examine which one predicts the flow more closely to the measured values.33Solver was taken as density based and formulation as implicit, space as 2D and time as steady.8Solution initialization was done at first with hybrid method and then Full-Multi-Grid (FGM) was used.34For CFD analysis of the present wok, combustion was not considered.14The flow was assumed to be incompressible, hot,2D axisymmetric, viscous flow, ideal gas and uniform injection of fluid normal to boundary.35Under-relaxation factors including turbulence kinetic energy, dissipation rate, viscosity and courant number, were set as 0.8, 0.8, 1 and 10,respectively. Discretization equation including gradient, flow,turbulence kinetic energy and dissipations rate, were selected as least square cell based and second order up wind, respectively. The properties of gas including specific heat, thermal conductivity, viscosity and molecular weight were taken as 1901 J/(kg·K), 0.034 W/(m·K), 9×10-5kg/(m·s) and 28.23 kg/kmol, respectively.

3.1. Pulser injection in ambient

Fig.8 Pulsation flow field and it’s meshing.

Fig.8 represents the segmentation of pulsation flow field and mesh with 64,000 quadrilateral grids. Meshing field was divided to three sections 1,2 and 3 from pulser burning surface to the end of pulser throat, from pulser exhaust to the end of conical part and developed region of plume,respectively.Note that the origin of coordinate system is on pulser exhaust.Evaluation of grid resolution was done to obtain acceptable results in CFD including 21,000,41,000 and 64,000 grids.As shown in Fig.9, the difference of Mach number results between 21,000 and 41,000 grids is obvious with the maximum error of 93%,but when grid became finer to 64,000 grids, this difference nearly eliminated with the maximum error of 8.9%. Similar behavior was observed in other results like pressure and velocity. As shown in Fig.10,y+values from pulser throat beginning to pulser exhaust are in the range of 40–60. Because of using turbulent modelsk-ε realizable andk-ω SST, there is no need to very small meshing(y+＜4)near the pulser throat wall due to the use of wall function in velocity gradient calculation.8

Boundary condition was taken as mass flow inlet equal to 0.014 kg/s from pulser burning surface, temperature as 3200 K in pulser, initial gauge pressure as 0.82 bar and ambient temperature as 3200 K. Figs. 11–13 represent Mach number, temperature and velocity contours of pulser injection in ambient with two models ofk-ε realizable andk-ω SST.In all figures, effective length of contours was specified. As shown, contours length ofk-ω SST model is higher and more developed thank-ε realizable model. Therefore, it seems that in numerical approach done with ANSYS-Fluent,k-ω SST turbulent model gives a better answer thank-ε realizable model. In the future sections, this opinion will be confirmed in comparison with test results.

Fig.9 Evaluation of grid resolution on CFD results.

Fig.10 Evaluation of y+ results on pulser throat wall(Section 1).

Fig.11 Mach number contours of pulsation in ambient.

Fig.12 Temperature contours of pulsation in ambient.

Fig.13 Velocity contours of pulsation in ambient.

Fig.14 CFD Mach number results on pulser and motor axis due to pulsation in ambient.

Fig.14 represents Mach number variations through pulser and motor axis due to pulsation in ambient. As shown, Mach number in pulser throat reaches to one,increases to 4.5 in pulser exhaust, decreases to 0.067 atx=0.214 m and finally becomes constant. As shown in Fig.15, pressure decreases from about 37 bar on pulser burning surface to about 21 bar in pulser throat inlet and then to 15 bar in pulser exhaust. It is interesting that similar to Mach number, static pressure in pulser plume decreases to 0.836 bar inx=0.214 m and finally become constant.Really,it seems that effective plume length is up tox=0.214 m and thereafter ebbed.

3.2. Pulser injection in motor

The solid rocket motor used in this research, is 1:30 sub scale of shuttle boosters,which are geometrically,kinematically and dynamically similar to each other,36using Buckingham’s theorem.37Fig.16 shows 3D modeling and manufactured scheme for subscale motor with outside diameter 122 mm, length 1270 mm and throat diameter 45 mm. The case is made of 4130 steel with welded flanges and connection of segments is M6×30 bolts. For simplicity of manufacturing and time frugality, throat was made of Ta-Cu material.

Fig.15 CFD static pressure results on pulser and motor axis due to pulsation in ambient.

Fig.16 3D model of subscaled RSRM.

Shape of the thermal inhibitor between segments of propellant can be taken either rigid38or flexible.37In this project, it was assumed rigid with considering ablation in definite modeling time. Estimated values of the wally+value for this grid shows it less than 30 along the entire wall,indicating good resolution of the boundary layer.39To simulate pulsation flow in motor, exhaust flow from pulser and motor burning surfaces was solved in steady state with pulser mass flow rate of 0.021 kg/s. Fig.17 represents the temperature and velocity contours due to pulsation in motor. As shown, there is not a distinct boundary between them due to pulser and motor flows combination.Although the flow core length,in Fig.17(b),is tox=0.142–0.285 m,it seems that the effects of pulser injection on motor internal flow reach to positionx=0.57 m.

Fig.18 represents comparison between motor velocity contour with and without pulsation through motor axis, respectively. As shown, pulser injection changes the standing velocity contours in motor to conical at least tox=0.57 m.

According to Fig.19(a), Mach number starts with zero value on pulser burning surface and increases to one in pulser throat. Also Mach number with pulsation is a bit higher than without pulsation and this difference becomes lower through motor axis and zero in positionx=0.85 m.

Fig.19(b)shows that pressure value on pulser burning surface is about 62 bar and decreases to 44 bar in pulser throat.Detailed view, also, shows that pressure trace has a similar behavior of Mach number.

Fig.20 compares static pressure results of CFD between pulsation in motor and ambient.As shown,pressure difference in pulser chamber is about 25 bar with a similar behavior.After outflowing from pulser exhaust, although pressure trace of pulsation in motor follows the motor pressure, in ambient,plume pressure decreases to ambient pressure about 0.82 bar.

Fig.17 Results of pulsation flow filed solution in motor.

Fig.18 Motor velocity contours comparison with and without pulsation.

Fig.19 Mach number and static pressure comparison on motor axis with and without pulsation.

4. Pulser test

Fig.20 Static pressure comparison between pulsation in motor and ambient.

As obtained from the analytical calculations, to achieve the requirement of one second injection with a mass flow rate of 0.015 kg/s at 40 bar and 0.02 kg/s at 60 bar for pulsation in ambient and motor, respectively, pulser charges were made from pyrogenic solid propellant with the burning rate of 30 mm/s at mean pressure of 90 bar,obtained from strand burner,diameter of 23 mm and length of 30 mm.Necessity of end burning design leads to produce pulser propellant in PTFE tubes,as shown in Fig.21(a),to protect charge from side burning. After producing pyrogenic charge, it is placed in a steel case with a thread connection, as shown in Fig.21(b).

Fig.21 Pulser configuration.

Fig.22 Pulser connector.

Fig.23 Temporal pictures of pulsation in ambient.

All charged pulsers and motor igniter were installed on a steel connector, shown in Fig.22(a). The reason for such a design is the limitation in the dimensions of the motor and the need for installing the pulsers and igniter on the motor head end. The initiator used for any of the pulsers and the igniter,is a simple glow plug with two high-resistance bridge wires buried in the initiator charge,26installed in a minimum distance to the burning surfaces of pulser and igniter, as shown in Fig.22(b). When initiator fires, combustion products outflow of pulser path, stroke a closure and discharge to ambient or motor.The closure bonded to connector case with RTV and its role is to protect pulser pyrogenic charge from motor flame and undesirable ignition.

4.1. Pulser injection test in ambient

Fig.24 Pulser pressure due to pulsation in ambient.

In the first test, one pyrogenic pulser fired in ambient with delay time of 51 ms. Figs. 23 and 24 represent temporal pictures of pulsation plume that has been taken with a high speed camera and the pulser chamber pressure-time curve, respectively. As shown, pulser burning has a good behavior untilt=225 ms with a desired pressure of 30–35 bar. But thereafter, the pressure increases suddenly up to 157 bar and then decreases.

To evaluate pulser plume behavior and its pressure variations,the second test fired in an equivalent chamber.As shown in Fig.25, the equivalent chamber is an open-end tube with a length and diameter equal to the free grain motor’s volume,with the pulser connector installed on its head-end and four pressure sensors mounted on its external side.

Figs.26–28 represent temporal pictures of pulsation plume,pulser chamber pressure and ECP, respectively. As shown in Fig.26, the flow of the pulser out of equivalent chamber is nearly normal untilt=637 ms and thereafter, clearly,enlarged int=645 ms.

Fig.27 shows that the second test has a stable burning time tot=645 ms which is more than the first test. However,thereafter, the pressure increases suddenly up to 400 bar and then decreases. Data acquisition from pressure transducers on tube has been shown in Fig.28. Note that these are gage pressures relative to ambient pressure of 0.82 bar.

As shown in Fig.28(a), plume pressure level in P1 is closer to prediction and higher than other positions. On the other hand, pressure level in P2 and P3 is nearly similar but in P4 is lower. These differences have been shown in detailed view of Fig.28(b). Sinusoidal behavior of pulme pressures is due to reciprocating waves in the equivalent chamber tube.

Fig.25 Equivalent test chamber for identification of pulser plume in ambient.

Fig.26 Temporal pictures of pulsation in equivalent test chamber.

Fig.27 Pulser pressure due to pulsation in equivalent chamber.

4.2. Pulser injection test in motor

As shown in Fig.22(a), two pulsers were chosen to pulsate in motor. Fig.29 represents simultaneous demonstration of the pressure data acquisition from the motor and two the pulsers that were ignited att=0.25 s andt=1.7 s, respectively.

Using bisector rule,23burning rate of the first pulser is obtained astb=1.22 s and the second astb=1.27 s.Clearly,pulser pressure pattern due to pulsation in motor is similar to motor pressure curve with a positive shift, as referred in analytical calculation and since pulsation is finished,internal pressure of each pulser is matched with motor pressure. Pressure difference between two pulsers and motor, as shown in Fig.30, is about 8.9–12.7 bar and 6.2–8 bar with average of 10.8 bar and 7.1 bar, respectively.

To evaluate the repeatability of the pulsing test in the motor, a second motor test with one pulser was performed;the results are shown in Fig.31. According to the second test,the pulser mass flow rate is obtained and compared with theoretical calculations, as shown in Fig.32.

Fig.28 ECP due to pulser plume.

Fig.29 Simultaneous demonstration of pressure data acquisition from motor and two pulsers.

Fig.30 Pressure difference between two pulsers and motor.

5. Discussion

Fig.31 Simultaneous demonstration of pressure data acquisition from motor and one pulser.

Fig.32 Comparison of pulser mass flow rate between analysis and test.

In Eq. (13), it is clear that the discharge from the pulser is directly related to the motor burning discharge,the accumulation flow, and the discharge of the motor. On the other hand,the pulser and the motor mass flow are dependent on the internal pressure of each one, and therefore, mass flow will definitely affect the motor’s pressure. This description was added to the article text.

As shown in Table 2, a variation of pulser behavior was observed due to initiator performance, pulser charge burning sensitivity, delay time, sudden enhancement of pulser burning surface and throat diameter, and differences between pressure coefficientsaandn′, obtained from strand burner laboratory test and real static test.

Fig.33 represents pressure comparison of pulser test in ambient and equivalent chamber with transient analysis prediction. As shown, although pressure level of pulsation in equivalent chamber is lower than pulsation in ambient, action time is the opposite. The reason is that in the first test, throat diameter was 3 mm,as designed and manufactured,but in the second test,throat enhanced to about 3.5 mm due to effects ofthe first test hot combustion products. Note that connector was made of St-37 material.Also,decrement of the pulser test action time in ambient is due to sooner occurrence of sudden enhancement of burning surface relative to pulser test in equivalent chamber.Note that sudden enhancement of burning surface is due to faulty bonding of pulser propellant to its insulator tube. On the other hand, despite of pulser pressure prediction as neutral curve,test curves have progressive behavior due to cigarette burning nature.23

Table 2 Pulser identification results.

Fig.33 Pressure comparison of pulser test in ambient and equivalent chamber with prediction.

Fig.34 Non-dimensional comparison of pulser pressure in ambient, equivalent chamber and motor.

Fig.35 Comparison of motor and pulser pressure test data with prediction.

To solve sudden enhancement of pulser burning surface problem, adhesion processing of pulser charge to PTFE tube was revised.In addition,to avoid the problem of throat diameter,each pulser was tested in a separate position.Fig.34 represents non-dimensional comparison of pulser pressure in ambient, equivalent chamber and motor. As shown, the burning time of the pulsation in the motor have been improved to 1.22 s and 1.27 s, close to the time prediction of one second,and their curves behavior is nearly similar with no sudden enhancement.

As shown in Fig.30, difference between pressure levels of two pulsers is due to motor time that pulser fires. In the first and second pulser, motor pressure varies between 40–55 bar and 30–37 bar, respectively.

As shown in Fig.31, the internal pressure of the pulser is first encountered with a peal of 80 bar and then has its normal behavior. It seems that the presence of an initial peak in the pyrogenic pulser is inevitable. However, as shown in Fig.32,such a peak does not change much in the mass flow of the pulser, and the experimental mass flow is still within the theoretical prediction limit.

Fig.35 represents comparison of motor and two pulsers pressure test data with analytical prediction.As shown,pulsers pressure pattern in nearly similar to performance prediction with the maximum and mean error of 16% and 4%,respectively.

Although using transient solution of pulser plume is better and more accurate, steady state method was used due to author’s limitation on calculation space and this is a desirable approach used in some references.As noted later,pulser plume in ambient should have a minimum length ofLp=168 mm due to active control design with mass flow rate of 0.015 kg/s.

Fig.36 represents comparison of pulser plume calculation of CFD results withk-ω SST model and test plume. As shown, Mach and thereafter velocity plume length in nearly close to test plume luminous core with the error of 6.7% and 13.8%. Note that CFD has solved the pulser flow field in steady state whereas test is in transient state.

6. Conclusions

The innovation of this research is access to a pulser with pyrogenic charge for secondary injection in a solid rocket motor.In the previous studies, tests have been carried out with cold gas and at low pressures,but in the current research,the secondary injection was evaluated and tested for a real solid rocket motor. So it is claimed that the research is new in its kind and a step forward.

Fig.36 Pulser plume comparison between k-ω SST results and test.

The pulsers should be designed in such a way that,in addition to providing the required flow rate for the controller,they have a suitable plume length. Design, manufacture and test of a typical pyrogenic pulser were presented and discussed. Continuity, analytical equations for transient state with viewpoint of coupling between motor and pulser chambers were wrote and solved using numerical method of fourth-order Runge-Kutta and compared with two analytical methods, resulting a good agreement. The analytic relationships governing the design of the pulser provided a suitable method for predicting the flow and length of the pulser flame.Steady state solution of pulser flow field usingk-ω SST,especially in Mach contours,showed an acceptable point of view comparing with captured test plume. Comparison between analytical, CFD and test results showed that pulser pressure due to mass flow rate requirement of active control design can be estimated with a nearly good approximation.It should be considered that pyrogenic pulsers design depends on various parameters of motor and pulser charge performance prediction. The quality of pulser charge bonding to its insulator and erosion of pulser throat path due to injection play an important role in achieving a desirable pulser mass flow rate and plume length.The behavior of the pulser flame in the open air and the equivalent chamber and its comparison with the flame length of the flow solving was one of the interesting aspects of this project.