[american institute of aeronautics and astronautics 46th aiaa/asme/sae/asee joint propulsion...

Development of Regression Formulas for CAMUI Type Hybrid Rockets as Functions of Local O/F

Harunori Nagata1, Shunsuke Hagiwara2, Yudai Kaneko3, Masashi Wakita4, Tsuyoshi Totani5

Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan

Tsutomu Uematsu6

Camuispaceworks Co. Ltd., Akabira, Hokkaido, 079-1101, Japan

Regression formulas for solid fuels in CAMUI type hybrid rockets were developed as functions of local O/F. The alternative fuel grain design used in this rocket consists of multiple stages of cylindrical fuel blocks with two ports. A fuel block in a CAMUI type grain has three burning surfaces, i.e., the upstream end face, port inner walls, and the downstream end face. A series of static firing tests by a laboratory model motor revealed controlling parameters to develop a regression formula for each burning surface. Some empirical constants in the regression formulas depend on local O/F. Based on these findings, regression formulas as functions of local O/F were developed for a 2500 N thrust class flight model motor. Obtained regression formulas contribute to obtain an optimal design of a grain configuration to minimize the weight of residual fuel mass and c* loss due to the O/F shift during firing.

Nomenclature

A = port sectional areaAt = nozzle throat area

a = empirical constantc = empirical constantc* = characteristic exhaust velocityc th

* = theoretical c*

D = characteristic lengthG p = mass flow density

H = block spacinghv = heat of gasification of the fuel

L = port circumference lengthL f = regression rate of upstream end faceLb = regression rate of downstream end face

l = empirical constantm = empirical constantmoxi = oxidizer mass flow densitym fuel = fuel mass flow density

Nu = Nusselt number

n = empirical constantO/F = oxidizer to fuel ratioPr = Prandtl numberpc = chamber pressureqtotal = total heat flux to the fuel surface

R = radius of an end facer p = port equivalent radiusr = linear regression rate

Re = Reynolds number St = Stanton numberSt 0 = Stanton number without blowingve = free stream velocityvb = velocity at the flameh = enthalpy difference of the gas between the

fuel surface and the flame = c* efficiency = viscosity = density of the fuel

1 Professor, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan, AIAA Member.2 Graduate student, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan3 Ph.D. student, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan4 Assistant professor, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan5 Associate professor, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8628, Japan6 President, Camuispaceworks Co. Ltd., 230-50, Kyowa, Akabira, Hokkaido, 079-1101, Japan

American Institute of Aeronautics and Astronautics1

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-7117

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I.IntroductionHE authors have developed CAMUI type hybrid rockets to realize an explosive-free small launch system 1. A main purpose is to reduce drastically the cost of sounding rocket experiments and launches of microsatellites to

LEO. A key idea is a new fuel grain design to accelerate the gasification rate of solid fuels and to increase the thrust. CAMUI comes from the abbreviation of the new combustion method of “cascaded multistage impinging-jet”. Figure 1 shows the basic idea of CAMUI type fuel grain2. By separating a conventional cylinder-shape solid fuel with a central port into multiple stages of cylinder blocks, end faces of all blocks burn concurrently. The combustion gas repeatedly collides with the solid fuel surface to accelerate the heat transfer to the fuel.

T

The solid fuel gasification rate is a major internal ballistics parameter of a hybrid rocket combustor, giving the fuel flow rate; m f= Ab r . In a conventional type fuel grain with a single port, the burning surface is the inner wall of the port and the regression rate is virtually uniform except a small part in the upstream3. A fuel block in a CAMUI type grain has three burning surfaces as Fig. 2 shows, i.e., the upstream end face, port inner walls, and the downstream end face. In each stage, regressions of these surfaces progress simultaneously with different regression rates one another. Also, regression rate varies with stages because of the variation of O/F, gas flow rate, and temperature with going downstream. Because of features listed above, predicting the progress of grain geometry and temporal variation of fuel flow rate are not easy. An optimal grain design aims at meeting two main objectives. One is to minimize the weight of residual fuel. A fuel grain is necessary to maintain its structure during firing. More specifically, an optimal design realizes an equal lifetime among stages. The other objective is to minimize c* loss due to O/F shift during firing. A possible approach is to design an optimal grain geometry based on a simplified regression model and an empirical regression formula for each burning surface. The simplified model assumes that the three burning surfaces, upstream and downstream end faces and port inner walls, regress uniformly and independently with each other, keeping edges between two faces a right angle. Previous research in Hokkaido University4 revealed controlling parameters to develop a regression formula for each burning surface. Another finding in the previous research was that some empirical constants in the regression formulas depend on local O/F. Accordingly, some empirical constants vary with stages. The main purpose of the present experimental study is to obtain regression formulas for CAMUI type hybrid rockets as functions of local O/F. Because the previous research was published in Japanese, the content of the paper will be introduced in detail for reader's convenience. Based on these findings, regression formulas as functions of local O/F was developed for a 2500 N thrust class flight model motor.

II. Firing tests with a laboratory model motor4

A. PropellantA combination of high-density polyethylene (HDPE) of 0.96 in specific weight and liquid oxygen was employed

as propellant. Figure 3 shows shape of a fuel block and a fuel spacer forming a grain. Outer diameter and axial length are 70 mm and 50 mm, respectively. Each fuel block has two axial ports with 15, 17, or 20 mm in diameter. Axes of the two ports are at 17.5 mm from the grain axis. Spacer rings with outer diameter of 70 mm, being the

same with that of fuel grains, keep the flow path of combustion gas between blocks. Inner diameter of spacer rings equals the sum of the distance between axes of two ports and the port diameter so the inner circle of a spacer ring is tangent to both ports. Axial length of spacers decides the initial block spacing to be 5 mm. A fuel grain consists of three stages of fuel blocks. A long spacer ring between the

American Institute of Aeronautics and Astronautics2Figure 3. Shape of a fuel spacer and a fuel block.

Figure 1. Schematic concept of CAMUI type hybrid rocket.

Upstreamend face

Downstreamend face

Inner wallof ports

Figure 2. Burning surfaces in a fuel block.

fuel grain and the nozzle keeps mixing area of 35 mm in length.

B. Laboratory model motorFigure 4 shows a schematic of the laboratory model motor. It mainly consists of a motor case, a combustion

chamber, and a nozzle. The combustion chamber is a copper tube of 5 mm in wall thickness and house a fuel grain, a graphite nozzle, and a positioner. The graphite nozzle is at the upstream of the positioner. Nozzle throat diameters were varied with firing tests to adjust chamber pressure. The clearance between the combustion chamber and the sidewall of the motor case served as a cooling water jacket. There are two pressure measurement ports at the downstream of the injector and the upstream of the nozzle to measure chamber pressure. Figure 5 describes details around the injector. A dummy block of 12 mm in axial length and a dummy spacer made of stainless steel were between the injector and the first stage fuel block. The clearance between the injector face and the upstream end face of the dummy block was 17 mm. Port diameters and the clearance between two ports are common to fuel blocks. It defines jet conditions impinging on the upstream end face of the uppermost fuel block. The injector is a stainless disc of 2.5 mm in thickness. It has two injector nozzles at an axisymmetric location with the same radial position 17.5 mm from the motor axis. Nozzle diameter was either 1.1, 1.4, or 1.9 mm. Because injector nozzles and dummy ports were in 90-degree staggered orientation with each other, liquid oxygen out of injector nozzles impinges on the upstream end face of the dummy block. This impingement would accelerate atomization of liquid oxygen.

Figure 6 shows outline of experimental apparatus. It mainly consists of a pressurization device using helium, a liquid oxygen (LOX) tank, and a motor. Inner volume of the liquid oxygen tank is 7.2 L. Of this volume, 5.3 L was liquid oxygen initially. The LOX line is wrapped in heat insulating material and cooled enough before each test. As a noteworthy feature in the LOX feeding, there is no valve in the liquid oxygen line. Before starting liquid oxygen feeding, evaporating oxygen gas (GOX) evacuates from the tank to the motor through the GOX line. This evacuation serves two purposes: One is to avoid self-pressurization of liquid oxygen. The other is to help ignition of an igniter fuel on the upstream end face of the uppermost fuel block. A nichrome wire ignites the igniter fuel by electrical heating. Ignition is easily detectable by viewing smoke out of the exhaust nozzle. A few seconds after ignition, a controller starts applying pressure on the LOX tank and close GOX line simultaneously to start feeding


Figure 4. Schematic view of the laboratory scale motor.

Figure 5. Details around the injector. Figure 6. Outline of experimental apparatus.

LOX into the motor. After prescribed firing duration, a valve relieves the pressure of the LOX tank to stop the feeding. Simultaneously, nitrogen gas purges the combustion chamber to stop firing quickly. Main measurement items during firing were combustion chamber pressure and LOX flow rate. Two differential pressure type flow meters, in the LOX tank and in the LOX line as Fig. 6 shows, measure oxygen flow rate. After each firing test, residual fuel grain was recovered from the combustion chamber to measure the weight and regression distribution.

Table 1 summarizes test conditions. From R32 to R35 were to find out the effect of block spacing on regression characteristics of upstream and downstream end faces. Clearance between the second and third stages of a fuel grain consisting of three stages varied from 5 mm to 50 mm, keeping all remaining spacing 5 mm. From R36 to R48 were to find out the effect of port diameter, LOX flow rate, and combustion chamber pressure on regression characteristics. Port diameter was either 15 mm, 17 mm, or 20 mm. LOX flow rate and chamber pressure varied from 40 g/s to 80 g/s and from 0.5 MPa to 2.0 MPa, respectively. Usually, a fuel grain consists of three stages of fuel blocks. To examine the effect of the number of stages, the fuel grain in R49 firing test had another 4th stage. Finally, R50 firing test was to examine the effect of port length on the regression characteristics of port inner walls. The grains consist of a single fuel block of 250 mm in axial length.

C. Regression characteristics in portsA regression rate of solid fuel is proportional to the heat flux to the fuel surface:

r=qtotal

hv(1)

Hybrid motors, including our CAMUI type, are characterized by a turbulent internal flow with dominant boundary layer effects. Therefore, heat transfer in hybrid combustors mainly arises from turbulent convection with minor contribution of radiation. If chemical reaction rate is virtually infinite comparing with species transfer rate and the flame has a zero thickness, a theoretical derivation gives the following relational expression5:

r= c 1−m

D1−m G pm St

St0 v e

vb hhv (2)


Table 1. Test conditions.

Evaluating all the constants in the equation experimentally is not easy. Therefore, many researchers use the following empirical expression:

a= c 1−m

D1−m StSt 0 v e

vb hhv (3)

r=aG pm (4)

Figure 7 shows port regression rate with various mass flow density. These data are from firing tests of R-36 to R-48. Port regression rate was defined as the difference of port radius before and after firing divided by firing duration. The following equation evaluates equivalent radius of a port expanding noncircularly during firing:

r p=2 AL (5)

Port contour L was viewed from the downstream end face. Therefore, the regression rate near the exit represents the port regression rate. In Fig. 7, port regression rate means the mean value of two ports for each stage. Mass flow density means the local gas flow rate divided by the mean port cross-sectional area before and after firing. Local gas flow rate includes the fuel flow rate being supplied by upstream fuel blocks. Therefore, local gas flow rate increases with going downstream. Three lines in the figure are results of least squares analysis using Eq. 4. Close agreements between plots and the line for each stage shows that the conventional empirical equation is applicable to the port regression rate of CAMUI type fuel grains. The mass flow density exponent m ranges from 0.64 for the third stage to 0.69 for the second stage, instead of the theoretical 0.8 for turbulent flow over a flat plate3. Chiaverini et al.6 reported a mass flow density exponent of 0.61 for HTPB fuel. They attributed the smaller exponent to the radiation effect. The mass flow density exponent becomes smaller under the influence of radiation than without radiation because of the reduced importance of convection. They also showed that the influence of radiation on regression rate is more pronounced at higher motor pressures. Wernimont and Heister 7 measured regression rates of a hydrogen peroxide/polyethylene hybrid rocket with various motor pressures and reported the mass flow density exponents of 0.78, 0.52, and 0.49 for motor pressures of 0.69, 1.38, and 2.76 MPa, respectively. Note that the mass flow density exponent decreases with the influence of radiation being pronounced. Our pressure exponents of 0.64 to 0.69 for motor pressures of 0.94 to 1.2 MPa, falling between 0.78 for 0.69 MPa and 0.52 for 1.38 MPa reported by Wernimont and Heister, are reasonable.

Mass flow density exponents for three stages agree closely among them. In contrast, the other empirical constant, a, varies widely with stages. The empirical constant increases with going downstream; 0.012, 0.015, and 0.026 for the first, second, and third stages, respectively. This increase is due to the variation of local O/F and thus local temperature. To equalize the effect of local O/F on regression rates for each stage, the authors made an effort to maintain local O/F at each stage with varying oxidizer flow rate by choosing appropriate combinations of oxidizer flow rate, port diameter, and the exhaust nozzle throat diameter. The following equation defines local O/F:

O /Fith=moxi

mfuel_1stmfuel_2nd・・・mfuel_ith (6)

Mean O/F of the first, second, and third stages were 13.4, 5.2, and 3.0, respectively. Corresponding adiabatic flame temperatures are 2510, 3350, and 3530 K, respectively8. This temperature increase is consistent with the increase of the empirical constant. The firing test with four blocks grain (R49) gave port regression rate of the fourth stage. The local O/F and the corresponding adiabatic temperature at this stage were 2.3 and 3510 K, respectively. Because adiabatic flame temperatures at the third and fourth stages are nearly identical, the port regression rate of the fourth stage is close to the line of the third stage as Fig. 7 shows.

Entrance region in each port showed greater regression because of thin boundary layer. As a result, regression rate in the entrance region strongly depends of the axial location. Because port length in a CAMUI type fuel grain is short comparing with conventional cases, port regression rates could depend on the axial length of the fuel block.


Figure 7. Regression rate of port inner wall.

The effect of port length on port regression rate was examined by the firing test R50. The fuel block in this firing test of 250 mm length was five times longer than the original cases of 50 mm. Port regression rates were measured in the same manner as original cases. That is, the regression rate near the exit represents the port regression rate. Mean local O/F near the exit was 4.8, which was close to the local O/F at the second stage in original cases. As Fig.7 shows, the port regression rate of R50 firing test was close to the line of the second stage. Accordingly, the axial length of 50 mm was long enough for a boundary layer to become enough developed.

D. Regression characteristics in end facesIn Eq. 3, the following equation gives port mass flow density as a function of Reynolds number:

Re=G p D ⇔ G p=

D

Re (7)

Substituting Eq. 7 into Eq. 3 gives

r= cD

Rem StSt0 ve

vb hhv (8)

The first half of the right-hand side, from c/ρ to Rem, represents convective heat transfer characteristics of the flow. Numerical values of c and m equals to these in the following equation giving Nusselt number in tube flow:

Nu=c Pr l Rem (9)In a jet impingement flow field, many researchers use the following equation to give Nusselt number9, 10:

Nu=c Pr l Rem HD

n

(10)

In this equation, Reynolds number Re is based on the jet diameter, corresponding to the diameter of the upstream port in the present case. Using Eq. 10 instead Eq. 9 leads to the following regression formula for upstream end faces:

L f =c 1−m

D1−m G pm H

D n

StSt0 ve

vb hh v =a G p

m HD

n

(11)

where a= c 1−m

D1−m StSt 0 ve

vb hhv (12)

Figure 8 shows measurement regions of regression distances for upstream and downstream end faces. Definitions of regression distance for the end faces are in the followings:Upstream end face: Project circles of the upstream ports with radius before and after firing. The definition of port radius is the same as those to obtain port regression rate (see Eq. 5). Line A, which is the line-symmetrical axis of the face, intersects with the circle of initial radius at points 2 and 3. Similarly, it intersects with the circle of final radius at points 1 and 4. Obtain mean regression distance along the segment from the center between points 1 and 2 to the center between 3 and 4. The value obtained in this manner agreed with the mean regression distance of the whole upstream end face within error of 5% in maximum and 2% on average.Downstream end face: Line B in Fig. 8 is obtained by rotating line A by π/6. The broken circle shows the location of a spacer wall before firing. Mean regression distance in two sectors formed by lines A and B and the broken circle was employed as the regression distance of the face.Definition of regression rate of a face is the regression distance divided by the firing duration. A laser displacement sensor (LK-080, KEYENCE) measured regression distance in measurement region at 0.2 mm intervals.


Initial diameter

Final diameter

1 2Measurement region

34

A Measurement region A B

Initial inner diameter

(a) Upstream face (b) Downstream faceFigure 8. Measurement region in end faces.

Although regression rate of upstream end face decrease with increasing block spacing, the effect was small in the present firing conditions. Firing tests from R32 to R35 gave the empirical exponent n to be -0.09. Because of the low dependence on H/D and small variation of block spacing in the present firing tests, the following regression formula was employed for upstream end faces, the effect of H/D being neglected:

L f =a G pm

(13)Figure 9 shows regression rate of upstream end faces with various port mass flow density. Firing tests from R36 to R48 provides these data. Because the jets impinging onto an upstream end face flow out of the upstream ports, port mass flow density of the upstream block was employed. For the first stage, port mass flow density means oxygen mass flow density in the ports of the dummy block. Three lines in the figure show results of least square analysis using Eq. 13. Because the local O/F at the upstream end face of the first block is far beyond the stoichiometric value and gas temperature should be low, the first stage shows significantly-small regression rate comparing with other stages. Empirical exponents m for the three stages were obtained to be 0.39, 0.47, and 0.53 for the first, second, and third stages, respectively. Laminar boundary layer theory gives the exponent to be 0.5. Donaldson et al.11 examined free jet impingement and compared their results to those predicted by laminar theory. They found that the heat transfer ratio (measured/laminar) is virtually independent on the Reynolds number. For laminar flow, the Nusselt number is proportional to the square root of the Reynolds number, giving the exponent of 0.5 in the present case. Therefore, the exponent of the Reynolds number, which is equal to the mass flow density exponent in the present case, did not depart much from the 0.5 power determined for laminar flow. The results of the second and third stages gave the exponents being close to 0.5. Correlation coefficients obtained by the least square analysis for these two stages were close to unity; 0.97 and 0.99 for the second and third stages, respectively. Consequently, the convective heat transfer mechanism Eq. 13 represents seems reasonable for these two stages. In contrast, the mass flow density exponent for the first stage was smaller than 0.5 with a low correlation coefficient of 0.87.

The mechanism of heat transfer to downstream end faces is less well understood. To obtain an empirical regression formula for downstream end faces, the authors considered three dominant parameters; block spacing, mass flow rate, and port diameter. Firing tests from R32 to R35 showed that the regression rate depends strongly on block spacing. Regression rate of downstream end faces decreased inversely with the 0.65th power of block spacing. To investigate the effect of port diameter, three firing tests with the same experimental conditions except port diameter were conducted (R38, R43, and R45). Despite virtually the same LOX flow rate and firing duration, these regression distributions did not agree with one another. Regression rate increased with the decrease of port diameter, showing that the effect of jet velocity or port mass flow density is not negligible. Therefore, in the present study, the authors chose port mass flow density and block clearance as parameters to give the following regression formula for downstream end faces:

Lb=a G pm H n (14)

Figure 10 shows regression rates of downstream end faces with various port diameter and mass flow rate. Because block clearance after firing fell within 20%, the effect of the variation of block clearance would be negligible.


Figure 10. Regression rate of downstream end face.

Figure 9. Regression rate of upstream end face.

Therefore, the following regression formula was employed to obtain the empirical exponent m:

Lb=a G pm (15)

Three lines are results of least square analysis using Eq. 15. Plots lied close to each line. Determination coefficients were 0.97, 0.99, and 0.94 for the first, second, and third stages, respectively. High determination coefficients being close to unity for the first and second stages show that the choice of port mass flow density as a parameter was reasonable for these firing conditions. For the third stage, the choice of port mass flow density as a parameter was not reasonable because no end face exists at the downstream of the third stage and the flow field is different from that of other stages. In contrast to port inner walls and upstream end faces, the mass flow density exponent varied with stages; 0.42, 0.63, and 0.40 for the first, second, and third stages, respectively. This variation may result from the difference of regression characteristics between the central area and near circumference, as discussed in detail later.

III.Firing tests with a flight model motor

A. CAMUI-250 motorThe dependence of regression formulas for CAMUI type fuels on local

O/F was summarized as follows. For port inner walls, the mass flow density exponents were around 0.67 and virtually independent of local O/F. These values were smaller than the theoretical 0.8 for turbulent flow over a flat plate due to the effect of radiation. For upstream end faces, the mass flow density exponent was around 0.5 except the uppermost stage, showing that jet impingement heat transfer was dominant. Again, the exponent was virtually independent of local O/F except the uppermost stage. Therefore, regression formulas for ports and upstream end faces would be as follows, the empirical constants a and a' being functions of local O/F:

r=a O /F G p0.67 (16)

L f =a O /F G p0.5H

D −0.09

(17)

In contrast, because the mass flow density exponent for downstream end faces varied with stages, another approach would be necessary to obtain a regression formula for downstream end faces as a function of local O/F.

Equations 16 and 17 were applied to a flight model motor. Figure 11 shows a schematic of a CAMUI-250 motor of 2500 N thrust class 12. The combustion chamber is 100 mm in inner diameter and 350 mm in length. This motor does not use any valve in the LOX line. There is a pair of outer and inner tubes in the LOX tank. A three-way valve (Launch Valve) connects a high-pressure helium tank to the LOX tank during the burning. Before supplying the LOX, the valve prevents pressure rising in the LOX tank by releasing gasified oxygen into the combustion chamber through the inner tube. A nichrome wire at the top of the fuel grain in the combustion chamber ignites the fuel by electrical heating. After the ignition, the launch valve closes the gas release line and opens the pressurizing line simultaneously. This operation decides the launch in a launch operation, which is the reason they apply the word “Launch Valve” to this valve. The orifice between the LOX tank and the combustion chamber is for the measurement of the LOX flow rate. The setup of static firing tests with this motor includes a nitrogen supply line to extinguish a fire promptly after prescribed firing duration, followed by recovering fuel blocks remaining after the firing test.

Figure 12 shows dimensions of a fuel block. A fuel grain consists of ten fuel blocks stacked longitudinally. The rim of 10 mm in height is to keep a space between blocks. Axial length of blocks varied from 20 mm to 35 mm depending on each axial regression rate, to realize an equal lifetime among them under a design condition. Figure 13 shows temporal variations of chamber pressure and LOX flow rate for five firing tests under the design condition with various firing duration.


Figure 11. CAMUI-250 motor.

100

75

50

Ø25

10L

Figure 12. Dimensions of a fuel block.

Time zero is when the launch valve changes the line to start supplying LOX into the combustion chamber. Although the data acquisition of chamber pressure for test-5 was not

successful, all histories clearly coincide with each other, showing good reproducibility.Because measuring fuel flow rate in a firing test of a hybrid rocket is not easy, the authors estimated the fuel

gasification rate from histories of LOX flow rate and chamber pressure by a reconstruction technique: The characteristic exhaust velocity, c*, is a function of propellant flow rate m p and chamber pressure pc:

c*=pc At

m p(18)

By using oxidizer to fuel ratio,

m p=m fuelmoxi=moxi

O /Fmoxi=moxi 1

O /F1 . (19)

Substituting Eq. 19 into Eq. 18,

c*=pc At

mo 1O /F

1 (20)

Also, a theoretical calculation provides c* also as a function of O/F and pc :cth

* = f O /F , pc (21)Using c* efficiency η leads to the following equation:

f O /F , pc =pc At

mo 1O /F

1 (22)

Unknown values in the above equation are η and O/F. The value of η was adjusted so that the calculated total fuel weight agrees with the experimental value.

Figure 14 shows temporal variation of the solid fuel mass in the combustion chamber. Solid line is the result by the reconstruction technique for test-07 and solid circles are fuel weight recovered after each firing test. Solid circles lie on the solid line, showing the reliability of the reconstruction technique. The result of the reconstruction technique for test-07 gave c* efficiency η of 0.980. Figures 15 and 16 show histories of propellant flow rates, c*, and O/F. The large fuel flow rate just after the start of LOX supply is because the fuel-rich combustion gas accumulated in the chamber burned at once. While the LOX flow rate kept almost constant value, the fuel flow rate decreased monotonically. As a result, O/F increased monotonically as Fig. 16 shows. With the combination of PE and LOX, c*

is at the maximum value of 1.82 km/s when O/F is around 2.2. As Fig. 16 shows, O/F keeps almost the optimum value until four seconds after the start of LOX feeding. The mass-averaged c* was 1.72 km/s, meaning that the loss due to the O/F shifting was about 3%.

B. Static firing testThree static firing tests were conducted with various LOX flow rates to obtain regression formulas as functions

of local O/F. Table 1 shows conditions of the three firing tests. Nitrogen gas flew into the combustion chamber to


2 4 6

1

2

0Time [s]

Mas

s [kg

]

Figure 14. Temporal variations of the mass of solid fuel.

2 4 6

1

2

3

0

0.5

1

1.5

0

Cham

ber p

ress

ure

[MPa

]

LOX

flow

rate

[kg/

s]

Time [s]

09 08 070605

Figure 13. Temporal variations of chamber pressure and LOX flow rate.

quench a fire quickly after prescribed firing duration. After a firing test, recover remaining fuel blocks to measure regression distance of burning surfaces. Regression distance of a burning surface divided by the firing duration gives the regression rate of the surface. The definition of regression distance of each burning surface is the same as before.

C. Regression formula for upstream end faceIn the regression formula for forward end faces, only a depends on local O/F. One can experimentally obtain a as

a function of local O/F, keeping n and m constant. Figure 17 shows variation of a with local O/F. Equation 17 was employed to calculate a for each LOX flow rate and stage. Unexpectedly, as Fig. 17 shows, a variations obtained by three different LOX flow rates did not agree one another, showing that the mass flow density exponent m of 0.5 is invalid in this case. Although the empirical exponent m may be different from that for the laboratory motor, if the assumption that m is independent of local O/F still holds, one can find out the empirical exponent according to the following procedure. Once a(O/F) have been obtained, one can obtain regression rate at a reference O/F from an observed data at any local O/F by the following equation:

r O /Fref =ra O/ Fref

a O /F(23)

Figure 18 (a) shows regression rates of upstream end faces at the reference O/F of 3 vs. mass flow density in the upstream port, giving the value of n as 0.75. Once n is obtained, one can obtain a as a function of local O/F as Fig.18 (b) shows. An iterative calculation is necessary to obtain these results. Judging from the high determination coefficient of 0.98, the assumption, m is independent of local O/F, would still hold. The exponent n of 0.75 shows that the heat transfer in the wall jet region rather than the stagnation region is dominant. Based on a simplified analysis, the Nusselt number is proportional to the Reynolds number to the 0.8th power at large distance from the stagnation point11. Hoogendoorn et al.13 obtained empirical correlations to determine the Nusselt number for the jet impingement flow field. In their empirical correlations, Nusselt number is proportional to the Reynolds number to the 0.5th power in the stagnation region and 0.75th power in the wall jet region. A possible cause of the disagreement in the empirical exponent between the laboratory model motor and the flight model motor is the difference of Reynolds number. Comparing the flight model motor with the laboratory model motor, mass flow densities were about twice greater. Initial port diameters were 1.25 to 1.67 times larger. Also, chamber pressure was 2.5 times greater. Accordingly, Reynolds number in the flight model motor was six to eight times greater than that in the laboratory model motor. Considering that the Nusselt number in the wall jet region increases more rapidly than that in the stagnation region with increasing Reynolds number, it is likely that the heat transfer in the wall jet region became dominant due to the increase of Reynolds number. Additional experimental research is necessary to confirm this hypothesis.

D. Regression formula for port inner wallThe empirical exponent 0.67 obtained by the laboratory scale motor for port inner walls was invalid in the flight

model motor either. Figure 19 shows the result of the iterative calculation. The exponent for port inner walls was 0.80, being equal to the theoretical 0.8 for turbulent flow over a flat plate. The cause of this disagreement is the short axial length of fuel blocks in the flight model motor. Because of the development of boundary layer, regression rate in the entrance region of ports strongly depends of the axial location. In the laboratory model motor, the axial length


1 2 3 4 5 6

1

2

3

4

5

0

1000

2000

0Time [s]

O/F

c* →

← O/F c* [m/s

]

Figure 16. Histories of c* and O/F.

1 2 3 4 5 6

200

400

600

800

0Time [s]

Flow

rate

[g/s

] LOX

Fuel

Figure 15. `Propellant flow rate histories.

of 50 mm was long enough for a boundary layer to become enough developed. The axial length to diameter ratio ranged 2.5 to 3.3. In the flight model motor, the axial length was 20 to 35 mm with the axial length to diameter ratio ranging 0.8 to 1.4. Because of the thin boundary layer, entrance region in ports shows greater regression. Figure 20 shows port regression rates at 17 mm downstream from the initial port entrance obtained by the firing tests of the laboratory model motor. Axial distance to diameter ratio ranges 0.85 to 1.1. Comparing with the regression rate near the exit (Fig. 7), the near entrance region shows higher regression rate. The empirical exponent was close to the result of 0.80 for the flight model motor. This result supports the short axial length of fuel blocks in the flight model motor as a cause of the disagreement of the empirical exponent between the laboratory model and flight model motors.

E. Regression formula for downstream end faceBecause the mass flow density exponent for downstream end faces depends on local O/F, another approach

would be necessary to obtain a regression formula as a function of local O/F. Figure 21 shows regression distributions of backward end faces after the firing test of No. 1. The reason m depends on local O/F is that the O/F dependence at the central part and the outer circumference are not the same. As Fig. 21 shows, the central area shows rather high regression rate, possibly due to the fountain flow hitting this area14, 15. Figure 22 shows a schematic of the flow field4. The circumference region is subjected to wall jets flowing parallel to the burning


200 400 600 800

1

2

3

4

5

0Mass flow density [kg/(m 2s)]

Fuel

regr

essi

on ra

te [m

m/s

]

r/(H/D)m

= aGprop

n = 0.75a = 0.028|r| = 0.98

LOX flow rate: 600 g/s: 400 g/s: 200 g/s

0.6

0.4

0.2

0

a

50403020100

O/F

LOX flow rate 600 g/s 400 g/s 200 g/s

(a) (b)

Figure 18. Empirical constants of regression formulas for forward end faces.

200 400 600 800

1

2

3

4

5


Fuel

regr

essi

on ra

te [m

m/s

]

r=aGpropn = 0.80a = 0.024|r| = 0.98


0.03

0.02

0.01

0

a

806040200O/F


(a) (b)

Figure 19. Empirical constants of regression formulas for port inner walls.

Figure 20. Regression rate at port entrance region.

100 200

0.5

1

1.5

0Propellant Mass Flux [kg/(m 2s)]

Fuel

Reg

ress

ion

Rate

[mm

/s]

1st

2nd

3rd

　　1st 2nd 3rdφ15φ17φ20

m=0.75

m=0.74

m=0.87

surface and a fountain flow impinges on the central part. Based on this flow field, Eq. 14 was employed to give the regression rate at the central area of backward end faces. This equation is valid if the jet Reynolds number of the fountain flow hitting this area is proportional to that of the jets out of the ports. For the circumference region, The

mass flow density in the upstream port is not suitable to account for the effect of the wall jets. To account for the effect of wall jets, mass flow density was defined by the area of a rectangle with width of grain radius and height of block spacing. That is, the following equation was employed as the regression formula for the circumference region:

Lb=a O /Fm prop

RH n

(24)

Figures 23 is the results for central parts and Fig 24 is for outer circumference of backward end faces. To cancel the effect of block spacing H on the regression of the central part, regression rate was divided by H -0.6 in Fig. 22(a). Although further study is necessary to clarify the mechanism of heat transfer to downstream end faces, high correlation coefficients of 0.97 (Fig. 23(a)) and 0.98 (Fig.24(a)) imply the availability of this treatment.

IV.ConclusionA series of static firing tests by a laboratory model motor provided regression formulas for CAMUI type hybrid

rockets. The alternative fuel grain design used in this rocket consists of multiple stages of cylindrical fuel blocks with two ports. Some of empirical constants in the formulas depend on local O/F and therefore vary with stages. Based on these findings, regression formulas as functions of local O/F were developed for a 2500 N thrust class flight model motor. The regression formula for port inner walls was obtained to be r=a O /FG p

m in which the empirical exponent n is common to all stages. The empirical exponent of 0.80 for the flight model motor was larger than that of around 0.67 for the laboratory model motor. The cause of this disagreement is the short axial length of fuel blocks in the flight model motor. The regression formula for upstream end faces was obtained to beL f =a O /FG p

m H /D n in which the empirical exponents m and n are common to all stages except the uppermost stage. The empirical exponent n of 0.5 obtained by the laboratory scale motor for upstream end faces was not valid in the flight model motor either. An iterative calculation estimated the value for the flight model motor to be 0.75. This value shows that the heat transfer in the wall jet region rather than the stagnation region is dominant. A possible


-40 -20 0 20 40

0

2

4

6Re

gres

sion

dep

th [m

m]

Distance from the grain axis [mm]

: 1st: 3rd: 6th: 9th

Figure 21. Regression distributions in backward end faces.

H

Figure 22. Schematic view of the flow field

between blocks.

200 400 600 800

2

4

6

8


Fuel

regr

essi

on ra

te [m

m/s

]

r/Hm=aGpropn = 0.78a = 0.45|r| = 0.97


0.03

0.02

0.01

0

a

50403020100

O/F


(a) (b)

Figure 23. Empirical constants of regression formulas for the central part of downstream end faces.

cause of the disagreement in the empirical exponent between the laboratory model motor and the flight model motor is the difference of Reynolds number. Based on limited knowledge, the regression formula for downstream end faces was decided to be Lb=a O /FG p

m H n O/F . Adding to the empirical constant a, the empirical exponent n also depends on local O/F. The variation of n with local O/F results from the difference of regression characteristics between the central area and near circumference. To account for this difference, individual regression formulas for the central area and near circumference were developed.

AcknowledgmentsThis research was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for

Scientific Research (B), 21360410, 2009.This research is supported by the Hybrid Rocket Research Working Group (HRrWG) of Institute of Space and

Astronautical Science, Japan Aerospace Exploration Agency. The authors thank members of HRrWG for their helpful discussion.

References

1Nagata, H. et al., "Development of CAMUI Hybrid Rocket to Create a Market for Small Rocket Experiments," Acta Astronautica, Vol. 59/1-5, 2006, pp. 253-258.

2Nagata, H., Okada, K., San'da, T., Akiba, R., Satori, S., Kudo, I., "New Fuel Configurations for Advanced Hybrid Rockets," 49th International Astronautical Congress, 1998, IAF-98-S.3.09.

3Chiaverini, M. J., Kuo, K. K. (ed.), Fundamentals of Hybrid Rocket Combustion and Propulsion, AIAA, 1st Edition, 2007, pp. 52-56

4Watanabe, M., Nagata, H., Totani, T., Kudo, I., “Numerical Simulation of the Flow Field in the Cascaded Multistage Impinging-jet (CAMUI) Hybrid Rocket,” Journal of the Japan Society for Aeronautical and Space Sciences, Vol. 53, No. 618, 2005, pp. 337-342 (in Japanese).

5Humble, R. et al., Space Propulsion Analysis and Design, 1st ed, McGraw-Hill Companies, Inc., New York, 1995, pp. 377.6Chiaverini, M. J., et al., “Regression Rate Behavior of Hybrid Rocket Solid Fuels,” Journal of Propulsion and Power, Vol.

16, No. 1, 2000, pp. 125-132.7Wernimont E. J. and Heister S. D., “Combustion Experiments in Hydrogen Peroxide/Polyethylene Hybrid Rocket with

Catalytic Ignition,” Journal of Propulsion and Power, Vol. 16, No. 2, 2000, pp.318-326.8Gordon, S. and McBridge, B. J., Computer Program for Calculation of Complex Chemical Equilibrium Composition and

Applications, NASA Reference Publications, 1311, 1994.9Viskanta, R., “Heat Transfer to Impinging Isothermal Gas and Flame Jets,” Experimental Thermal and Fluid Science, vol. 6,

No. 2, 1993, pp. 111-134.10Chander, S. and Ray, A., “Flame impingement heat transfer: A review,” Energy Conversion and Management, Vol. 46,

2005, pp. 2803–2837.11Donaldson, C. D., et al., “A Study of Free Jet Impingement, Part 2. Free Jet Turbulent Structure and Impingement Heat

Transfer,” Journal of Fluid Mechanics, Vol. 45, No. 3, 1971, pp. 477-512.12Nagata, H. et al., "Development and Flight Test of 250 kgf-class CAMUI Hybrid Rocket," Proceedings of 2007 JSASS-

KSAS Joint International Symposium on Aerospace Engineering, Kitakyushu, Japan, 2007, pp.304-307.


500 1000 1500

1

2

3

4

5

0

n = 0.75a = 0.028|r| = 0.98

r = a(mprop/(RH))n

Fuel

regr

essio

n ra

te [m

m/s

]

Mass flow density [kg/(m 2s)]


0.02

0.015

0.01

0.005

0

a

6050403020100

O/F


(a) (b)

Figure 23. Empirical constants of regression formulas for the outer circumference of downstream end faces.

13Hoogendoorn, C. J. et al., “Turbulent Heat Transfer on a Plane Surface in Impingement Round Premixed Flame Jets,” Proceedings of the Sixth International Heat Transfer Conference, Toronto, Vol. 4, 1978, pp. 1-19.

14Funazaki, K. et al., “Heat Transfer Characteristics of an Integrated Cooling Configuration for Ultra-High Temperature Turbine Blades: Experimental and Numerical Investigations,” ASME paper, 2001, 2001-GT-148.

15Cho, H. H. and Rhee, D. H., “Local Heat/Mass Transfer Measurement on the Effusion Plate in Impingement/Effusion Cooling Systems,” Journal of Turbomachinery, Vol. 123, 2001, pp. 601–606.


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