** **

** **

**Experimental
Investigation of Characteristics of a Double-Base Swirl Injector in a Liquid
Rocket Propellant Engine**

** **

^{1*}Fathollah OMMI, ^{2}Koros
NEKOFAR, ^{1}Amir KARGAR, and ^{1}Ehsan MOVAHED

^{1,*}*Mech.Eng**.**Dep., **Tarbiat** **Modares** **University**, **Tehran**, **Iran*

^{2}*Islamic **Azad** **University** of Tafresh, **Tafresh**, **Iran*

E-mails: ^{*}fommi@modares.ac.ir, nekofar@yahoo.com, emovahed@yahoo.com, karegar@yahoo.com

(* Corresponding author)

* *

* *

**Abstract**

In this work the fundamentals of swirl injector calculation is investigated and new design procedure is proposed. The design method for double-base liquid-liquid injectors is presented based on this theory and experimental results. Then special conditions related to double-based liquid-liquid injectors are studied and the corresponding results are applied in design manipulation. The behaviour of injector in various performing conditions is studied, and the design procedure is presented based on obtained results. A computer code for designing the injector is proposed. Based on this code, four injectors are manufactured. A specialized laboratory was setup for the measurement of macroscopic spray characteristics under different pressure such as homogeneous droplet distribution, spray angle, swirl effect. Finally, through PDA cold test, the microscopic characteristics of injectors spray are also obtained and measured. The results, which will be explained in detail, are satisfactory.

**Keywords**

Swirl Injector, Double-Base Injector, Macroscopic and Microscopic Characteristics, Atomization, PDA Laboratory

Introduction

The double-based liquid-liquid injectors have many advantages making them applicable in aerospace industries. Fuel and oxidizer can be mixed more efficiently in such injectors, creating an ideal combustion condition and reducing the probability of combustion instability. Since fuel and oxidizer are both exhausted from one injector, without any increase in the diameter of injector plate, a higher discharge rate of fuel and oxidizer can be obtained. In the same way with a fixed discharge rate, it is possible to decrease combustion chamber diameter, and have a stronger thrust. This, in turn, gives higher pressure in the combustion chamber.

The injector has been designed in a way that the fluid may swirl around its axis. The swirl effect's advantages include producing micro-diameter droplets and desirable spray angle, which provide the perfect combustion condition.

In the following design procedure, the governing equations for an ideal fluid are solved and the results are corrected using correction factors based on experimental data. The rules used in the swirl injector theory are based on the principles of mass, angular momentum, energy conservation (Bernoulli's Equation), maximum flow rate and minimum energy laws.

Figure1 shows a schematic of a swirl injector in which *d _{Bx},
L_{Bx}* and

*Figure 1.** Double base- swirl
injector cross section [1]*

** **

The geometrical parameter of a swirl injector has an important role in the design procedure and is defined bellow [1]:

_{} (1)

Where *r _{c}*

According to the conservation of angular momentum principle,
parameter *M* is constant.

_{} (2)

The swirl force of the fluid increases as it passes through the injector. Due to this force, a hollow cylinder shape flow forms at the exit of the injector, this is filled by air. The cross section area of this flow is equal to:

_{} (3)

Where, *r _{m}*

_{} (4)

According to the maximum mass flow rate principle, for an
optimal amount of *φ _{c}* the discharge rate of the injector
becomes maximum. The injector flow rate is equal to:

(5)

In which, µ is called discharge rate coefficient which is a
function of *A* and *φ _{c}*. According to the explanations
given above and the principal of maximum discharge rate, d

*The Friction Effect on the Flow*

When the fluid passes through the entrance whole and reaches to swirl chamber, a pressure drop is formed in fluid that is equal to:

_{} (6)

Where, ζ_{Bx} is the drop coefficient of
entrance hole and is obtained from experimental tests. Figure2 shows the variation
diagram of ζ_{Bx} as a function of Reynolds number, which is
defined as the following:

_{} (7)

*Figure 2**. Diagram of the amount
of input channel resistance ξ _{BX} and Reynolds number Re[1]*

** **

When the fluid enters to swirl chamber from entrance hole,
it contracts in a way that the average radius of rotation increases and changes
from *R* to *R*_{є}. A coefficient named є is defined
here and is found from experimental tests as follows:

_{} (8)

Figure3, presents the variation of *є* versus 1/*B*,
where_{}.
Using the coefficient є, the injector geometrical characteristic can be
calculated from:

_{} (9)

*Figure 3**. Relationship of amount
of transformation input current ε and 1/B*

There is a loss of energy inside the swirl chamber due to
the friction between the fluid and the wall. The amount of friction is obtained
using the friction coefficient ג_{k} which
is obtained from figure 4. The parameter *θ* is defined that shows
the amount of the friction effects and is equal to [1]:

_{} (10)

where, *R _{k}*
is the radius of swirl chamber.

A hydraulic jump occurs because of an abrupt change in flow
path slop, just after the nozzle entrance cone. This in turns causes an energy
loss in entrance channel (Δ*Bx*), swirl chamber.

*Figure 4.** Relationship between
value of friction and the input Reynolds number [1] *

*1) Experimental relation, 2) Theoretical
relations*

The shape of spray is a cone with an angle, which its calculated value is corrected using the following correction factor:

_{} (11)

Where *α _{EXP}*

*Figure 5.** Relationship of spray
cone relative angle α with θ set*

*Swirl Injector Design Procedure*

The swirl injector should provide the necessary discharge rate of the fluid under a definite spray cone angle and the pressure difference. It is also recommended to have minimum energy drop, in order to face with minimum reduce of exit flow velocity and injection quality.

As mentioned before the total amount of θ determines
the effect of friction and the smaller value of θ show the smaller effects
of fluid viscosity on the injector hydraulics. For low viscosity liquids such
as gasoline, oil and water, the suitable range of injector expansion coefficient
(_{})
recommend within 1.25≤*C _{c}*≤5. In this state as spray,
cone angle is larger; the size of

In most injectors, 2 to 3 canals will be sufficient to make
the symmetric spray cone. When the number of canals becomes more than three, no
considerable change is made in the quality of fuel distribution; however, the
injector structure becomes more complex and its precision becomes less. In open
injectors (low amounts of *C _{c}*) the loss of energy reveals
itself in input canals; thus, it is necessary to take

The hydraulic design of a simple swirl injector includes determining dimensions of nozzle, swirl chamber and input canals. The initial data consists of the cone angle of spray, discharge rate, pressure difference of injector, and the entrance angle to nozzle, number of holes to the swirl chamber, density and fluid viscosity. The design stages could be described as below:

1.
Determine the values of *ψ, n, C _{c}, V, ρ, G,
ΔPФ,*

2. Considering
*α _{0}*=0.85 as the first approximation from its range of
variation,

_{} (12)

3. Obtaining the values
of *A _{D1}*

*Figure 6**. Relationship of
discharge coefficient and nozzle contraction coefficient and spray angle to the
geometric characteristic of injector [2]*

4.
Determine the value of *μ _{1}* using Figure6.

5. Obtain the injector nozzle diameter from the following equation:

_{} (13)

6.
Determine the swirl radius *R*_{l}, using chosen value of *C _{c}*
and

_{} (14)

7. Calculating the entrance channel diameter using the following relation:

_{} (15)

*ε _{0}* = 0.8 as the first
approximation.

8. Calculating the flow Reynolds number [4]:

_{} (16)

9. Determine the friction coefficient using Figure4.

10. Calculate the injector equivalent characteristic length using [5]:

_{} (17)

where_{}and _{}

11. Obtaining the value of α1 using Figure5.

12.
Determine *μ _{θ1}* and

13. Calculate the first approximation of spray cone angle [6]:

_{} (18)

14. Calculate the total energy loss in injector using Figure2:

_{} (19)

15-
Calculating Δ*BX _{l}*

_{} (20)

16.
Calculating Δ*k*_{l }by the following equation [7]:

_{} (21)

17.
Selecting an appropriate value for nozzle resistance coefficient (*ξ _{c}*)
in the range of 0.11 and 0.16 [1].

18.
Obtaining *φ _{c}* using Figure 6 and considering

19.
Calculating *ΔC _{l}* using the

_{} (22)

20. Obtaining a first approximate value for_{} [8]:

_{} (23)

21.
Calculating the coefficient of transformation, *ε _{l}*, via
Figure3.

22.
Updating the values of *ε _{1}, μ_{p1}* and

23.
Considering the value of *α _{2}* and using Figure6 the values
of

24.
Calculating *μ _{2}*

_{} (24)

25. Calculating the nozzle injector diameter using the following formula:

_{} (25)

26.
Obtaining the swirl radius by: *R _{2}*=

27. Calculating the inlet channel diameter using the following expression [9]:

_{} 26)

Where,
n is determined before and the amount of *λ _{k1}, C_{k1}*
and

28. Reynolds number is calculated [10]:

_{} (27)

29. The friction coefficient is determined using Figure5.

30. Obtaining the injector equivalent characteristic using:

_{} (28)

Where_{}and _{}

31. Determining
the amounts of *μ _{θ2}* and

32.
Obtaining the value of *α _{2}* by using Figure5.

33. By
using formula_{}, the magnitude of the spray cone angle
in second approximation is obtained.

34. Calculating the energy loss coefficient using the same procedure in the first stage.

35. The discharge coefficient in second approximation is obtained from following relations:

_{} (29)

36.
Obtaining the value of *ε _{2}* using the values of

37.
Comparing the calculated values of *ε _{2}, α_{p2}*
and

38.
After calculation of *d _{c}*,

_{}

Then the nozzle length (*L _{c}*), inlet channel
length (

39. The proposed procedure has an extensive application and its results are precise within ±10%.

*The Double-Base Swirl Injector Calculation Results*

Figure7 shows a double-base injector. In this injector, fuel
and oxidizer are mixed outside the nozzle. The injector parameters should be
selected in a way that the fuel and oxidizer spray cones do not cut each other
near nozzle outlet. *α _{f}* and α

*Figure 7**. Double-base external
mixing injector [2]*

Considering an ideal fluid and same pressure difference for fuel and oxidizer paths, the following expressions are derived for these types of injectors:

_{} (30)

in
which, _{},
_{}_{ }are
oxidizer and fuel densities, respectively.

The oxidizer to fuel mass flow rate ratio is:

_{} (31)

Where, *m _{Ф0}* and

m_{f}=m_{f}0+m_{f}_{F}=_{} (32)

in
which _{}.
Considering the law of angular momentum conservation one may write:

_{} (33)

_{} (34)

_{} (35)

According to the aforementioned relations, the geometric characteristic of a double-based swirl injector could be written as:

_{} (36)

Expression for *μ _{Ф}*,

_{} (37)

in
which _{} and
*m** _{f}* is the
passage efficiency or total discharge rate coefficient and

Depending on the value of_{}, some corrections in
discharge coefficient might be necessary. The relationship between experimental
and theoretical discharge rate coefficient (*μ _{Ф} *&

*Figure 8**. Correction factor of
coefficient flow versus swirl radius*

Based on the presented design procedure, a computer code is developed, which performs the design and necessary calculations of different dimensions of injector. This program designs injector based on design data and calculates its dimensions. To design a double-base injector, the data of internal and external nozzle should be input in the program separately to obtain its geometry. However, as mentioned, the radius of external nozzle should be more than the external radius of nozzle in the inner injector. At the same time, the spray cone angle of inner injector should be more than outer injector, therefore both spray cones would contact to each other after discharging form injector. According to the design condition, the internal nozzle must inject flow of 20cc/sec in defined pressure of 10 bars. The external nozzle must also inject 120cc/sec in four bars. The spray angles for the internal and external nozzles obtained 85° and 75° respectively.

*Manufacturing the Injectors*

Four injectors are manufactured based on design calculations. The double-based swirl injector has three parts including internal nozzle, external nozzle and lid. Brass metal was chosen due to its special characteristics for accurate machining and minute drilling. Detailed drawings of internal and external nozzle are shown in figure 9&10. These three parts are brazed and assembled precisely as shown in figure 11.

*Figure 9.** Manufacturing Diagram
of the Internal Nozzle *

*Figure 10.** Manufacturing Diagram
External Nozzle*

* *

*Figure 11**. Assembled and
disassembled of a Manufactured Injector*

* Hydrodynamic Test Laboratory*

To check the quality of the manufactured injectors, a
preliminary laboratory set-up is needed. This set-up will measure the
macroscopic characteristics of injectors spray such as homogeneous spray
distribution, spray angle and swirl effect on the spray formation under different
pressure. This test rig was set up with the following parts as, Injector Stand,
Pressurized Liquid Tanks, High Pressure Nitrogen Capsule, Manometer and
Regulator, Radial and Sectional Collector, Stroboscope and High Speed Camera. The
liquid emitted by the injectors are collected in two different collectors made
of flexi glass material as shown in figures 12&13. The level of fluid in
the radial and sectional collectors display spray distribution quality in r and
*θ* direction respectively. Sectional collector divided into six 60°
section and the radial one divided into three co-centric cylinders.
Furthermore, a high-speed camera is used to capture the spray cone angle and atomized spray
distribution of both internal and external nozzle.

*Figure 12, 13.** Radial (Left) and
Angular (right) Collector*

Test Results of Injectors

*Flow-Pressure
Test*

This test is conducted to measure the flow changes under different working pressure for both internal and external nozzle. Figures 14&15 present the results of the experimental flow for a specific set of design conditions.

*Figure 14.** Flow rate of internal
nozzle (cc/s) versus pressure (bar)*

*Figure15**. Flow rate of external nozzle
(cc/sec) versus pressure (bar)*

** **

*Spray
Angle Test*

To show the spray formation of internal and external nozzle clearly a stroboscope and a high-speed camera are used. Figure 16 displays the spray circulation of injector. As fluid pressure increases from zero to ten bars, the spray cone gradually opens to become fully developed as seen in figure17.

*Figure 16**. Spray Formation Stages
with Regarding to Fluid Swirl*

*Figure 17**. Fully Opened Spray
Cone Under design condition (P _{f}=10, *

** **

In figures 18 and 19 the spray
cone angle of both internal and external nozzle are approximately 70° and 80°
respectively under design condition (*P _{o}*=4,

*Figure 18**. Spray cone angle of
internal nozzle*

* *

*Figure 19.** Spray cone angle of
external nozzle *

*Spray
symmetry and homogeneity test*

Sectional and radial collectors are used to check the symmetry of the fluid spray. To obtain a symmetrical distribution of injection, the machining and drilling processes must be precise and accurate. Figures 20 and 21, shows the spray distribution in each compartment of the collector.

*Figure 20.** Spray distribution of
the injector in each 60° section*

* *

*Figure 21.** Spray distribution of
the injector in each cylinder*

* *

*Microscopic
Spray Droplet Test*

Using PDPA laser laboratory, the microscopic characteristics of the injector spray have been identified. This instrument works with Doppler frequency difference phenomenon. As shown in figure 22 phase Doppler particle analyzing system consists of a laser light source, optical arrangements, a transmitter, and a data acquisition system. The visualization system used in this experiment consists of a laser source, lenses and mirrors, a high-pressure spray chamber, and CCD camera.

*Figure 22. **Phase Doppler analysis
system*

* *

According to figure 23 mounting the injector on the
apparatus and setting the fluid tanks pressure on the design condition droplet
normal velocity (m/s) and SMD (Micron) distribution at 100mm
downstream, for *P _{o}*=4 and

*Figure 23**. View of laser beams
emitted to the spray*

*Figure 24.** Velocity (m/s)
distribution of Spray in a normal plan*

*Figure 25**. SMD (Micron)
distribution of Spray in a normal plan*

Conclusion

A theoretical design procedure for double-base liquid-liquid swirl injectors is described. A computer code is developed for the proposed method and the results are compared with experimental data. According to design calculations, four swirl injectors have been manufactured precisely. To check the quality of the injectors, a preliminary laboratory was set up to measure the macroscopic characteristics of sprays such as spray angle, distribution quality. In order to obtain microscopic characteristics such as droplets velocities and SMD PDA laser laboratory was used. Experimental results show that the manufactured injectors based on the design procedure are flawless.

References

1. Ditiakin, E.F., Koliachko, L.F., Noikov, B.V., Yagodkin, V.E., "Fluids Spray", Moscow, 1977.

2. Vasiliov, A.P., Koderaftsov, B.M., Korbatinkov, B.D., Ablintsky, A.M., Polyayov, B.M. Palvian, B.Y., "Principles of Theory and Calculations of Liquid Fuel Jet", Moscow, 1993.

3.
Rammurthi, K., Tharakan, J., "Experimental
Study of Liquid Sheets Formed in Coaxial Swirl Injectors", *J. of Propulsion
and Power*, VOL.11, №6, 1995.

4.
Sivakumar, D., Raghunandan, B.N., "Jet
Interaction in Liquid-Liquid Coaxial Injectors", *J. of Fluid engineering*,
VOL.118, June 1996.

5. Sutton, G. P., "Rocket Propulsion Elements", John Wiley & Sons, Fifth Ed, 1986.

6. Huzel, D.K., Huang, D.H., "Design of Liquid Propellant Rocket Engineering", NASA, Second Ed, 1971.

7. Barrerf, M., "Rocket Propulsion", Paris, 1959

8.
Chuech, S.G., "Numerical Simulation of No
swirling and Swirli3ng Annular Liquid Jets", *AIAA J*., VOL 31, №6,
June 1993.

9. Shames, E. Herman, "Mechanics of Fluids", fourth Printing 1988, McGraw-Hill.

10.
Bazarov, V.G., Yang, V., "Liquid-Propellant
Rocket Engine Injector Dynamics", *J. of Propulsion and Power*, VOL.
14, №5, 1998.

11.
Jeng, S.m., Jog, M.A., Benjamin M.A., "Computational
and Experimental Study of Liquid Sheet Emanationg from Simplex Fuel
Nozzel", *ALAA Journal*, Vol. 36, №2, 1998.

12.
Parlange, J.Y., "A Theory of
Water-Bells", *J. of Fluid Mechanics*, VOL. 29, Part 2, 1967.

13. Ghafourian, A., Mahalingam, S., Dindi, H., Daily, J.W., "A Review of Atomization in Liquid Rocket Engines", AIAA Paper 91-0283.

14. Sankar, S.V., Wang, G., Rudoff, R.C., Isakovic, A., Bachalo W.D., "Characterization of Coaxial Rocket Injector Sprays Under High Pressure Environments", ATTA Paper, 1991.

15. Fischer, U., Valinejad, A., "Tables and Standards of Design and Machinery", Taban, Iran, 2005.