How To Make A Slit Type Pintle Injector To Be Used In A Rocket Engine.

A slit type pintle injector is the most suitable injector to be used in a throttle able liquid rocket engine. Radial flow from the pintle is similar to spokes of the wheel. This radial flow of liquid hits the axial flow from the annular opening and atomizes the propellants in a rocket engine.This high speed impingement of fuel and oxidizer  at an angle of 90 degree is the working principle of a Slit type pintle injector. Slit type pintle injector is the injector used in SpaceX Merlin Engines.

Radial and axial flow from a slit type pintle injector for liquid rocket engine

This radial and axial flow hitting each other at 90 degree creates the spray in slit type pintle injector.

Spray from a slit type pintle injector for a liquid rocket engine.

Spray quality of a pintle injector can be controlled by the differential pressure between two inlets.

Its design is simple and fabrication can be finished within one week. Procedure for design and fabrication of a slit type injector for a liquid rocket engine is mentioned below. A slit type pintle injector can be designed with just 5 simple steps.

• STEP 1-Select the thrust and propellants of the rocket engine-5000N, RP1-LOX 
• STEP 2 -Combustion chamber pressure – 15 Bar
• STEP 3- Fix the optimum mixture ratio of the rocket engine
• STEP 4- Find out the Flame temperature, molar mass, specific heat ratio and characteristic velocity of the exhaust gases in the rocket combustion chamber using NASA CEA application.
• STEP 5-Calculate the mass flow rate of fuel, oxidizer and the pintle injector exit area required to achieve this mass flow rate.

A pintle injector can be fabricated using the following procedure.

1. Select the outer diameter of the pintle
2. Select fuel centered or oxidizer centered configuration.
3. Divide the circumference of the pintle into equal number of holes equidistant from each other. 
4. Divide the discharge area into the number of holes to be made on the pintle.
5. Now the holes can be split into two rows, a primary row and a secondary row. 
6. Select the diameter of the holes and the distance between these holes.
7. Outer diameter of the annular gap can be calculated by oxidizer discharge are=Pi(R*R-r*r), where r and R corresponds to inner and outer radius of the annular gap.

Table below shows the different parameters of a 5000N engine calculated using Pintle Design Software.

Pressure (Atm)	Optimum Mixture Ratio	C.F	Area of throat (mm2)	Mass flow rate Kg/s	Area of Fuel discharge(mm2)	Area of Oxidizer discharge(mm2)	Annular gap (mm)	Pintle opening (mm)
10	2.11	1.27	39.21	2.19	46.01	81.22	0.7	1.29
15	2.15	1.36	24.39	2.04	42.2	76.27	0.65	1.21
20	2.17	1.42	17.53	1.95	40.09	73.12	0.61	1.16
25	2.2	1.46	13.62	1.89	38.49	71.17	0.59	1.13
30	2.21	1.5	11.1	1.87	37.86	70.32	0.58	1.11

A sample calculation for 5000 N engine is given below

• Let the outer diameter of pintle be 13.1 mm. So the circumference of the pintle is 41.15 mm
• We take fuel centered approach indicating fuel is supplied through the slit holes in the pintle.
• From the table above, area required for fuel discharge is 42.2 mm2. This area should be divided for two rows so each row gets 21.1 mm2. 
• Now small holes totalling to an area of 21.1 mm2 should be separated equidistantly through out the circumference of the pintle.
• Select the diameter of the holes and the distance between these holes.The number of holes possible=pintle circumference/(Single hole diameter+Distance between holes).
• let diameter be 0.55 mm and distance between holes be 1 mm. So number of holes possible is 27.22. If remainder comes, accommodate that remainder equally in the spacing between the holes. So 0.22/2 can be accommodated in spacing. So spacing between holes becomes 1.008mm.
• Now second row holes below the first row should be placed in such a way to fill the gap created by the first row of pintle holes. Just keep the second row holes in the centre of gap in primary row.
• Now annular gap for oxidizer discharge need to be fixed. Oxidizer discharge area is 76.27 mm2. The lesser the sheet thickness the more good will be the resulting spray. The annular gap area should be 76.27mm2. Radius of outer circle of the annular gap=square root of {(Oxidizer discharge are/Pi)+r*r}=8.196 mm. Annular gap=outside radius(R)-inside radius(r)=8.196-6.55=1.64 mm.

Material suitable for Slit type pintle injector is stainless steel(SS304) due to its strength and heat resistance. 

1. Buy one long bit of stainless steel having a damter of 60 mm or above as per the combustion chamber size. 
   
   
   
   

   

   3 parts of a slit type pintle injector, a base plate, pintle and an annular disc.

   
   
   
   
   
   
   
   
2. Now drill four holes in the outer circumference for fastening.
3. Cut the long bit into two equal pieces. One for attaching pintle and other for creating the annular gap.It is better to drill holes for bolts before cutting the metal to avoid mismatch of drilled holes.



Making pintle in a lathe machine.

4. Take one bit, drill a hole in the center of bit and make a thread in the hole for the pintle to be screwed in. The other end of the bit is the inlet to the pintle.
5. Take the other bit and drill an inside hole of diameter 16.392 mm to match the annular gap of 1.64 mm. Drill a suitable hole perpendicular to the circumference of the bit till it reaches the centre hole.This is the inlet for the annular gap flow.



Pintle and base plate after lathe operation.

6. Now take a stainless tube pipe and turn it to 13.1 mm diameter in size.Or drill a hole inside another bit of necessary length and make the outer diameter 13.1 mm. One side of the pintle need a outside thread matching the inside thread of the first bit and the other end should be closed in the shape of a dome.
7. Now use EDM machine to drill the 27 holes of 0.55 mm diameter holes in the circumference of the pintle.



Slit type pintle screwed inside into the base plate.

8. Screw in the pintle to the base bit, take the second bit and match it with the first bit holes and bolt it tight using stainless steel bolts. 
9. Connect the fuel and oxidizer  to the respective inlets and pressurize the system using nitrogen gas cylinders.
10. Open the tank valves and enjoy testing the injector at different conditions. You have made the same injector that is used in SpaceX Merline engines that power Falcon 9 rockets. 

    

    Assembled slit type pintle injector. Inlets to the annular discharge is given from left and right sides for even water discharge from the annular gap.

Spray-important questions answered

• What is a spray? A spray is defined as a flow of individual liquid droplets evolving in a surrounding gaseous medium. Each droplet has its own diameter and velocity and may collide and coalesce with other droplets. 

• How do you characterize the spray?  The most significant spray characteristics are the drop-size distribution, the drop-velocity distribution, the density (number of droplets per unit volume), the spatial distribution (local volume fraction), and drop temperature.

• What is drop size distribution?  It is an information about the drop sizes and the  number of droplets corresponding to that size in a spray. It is just a graph of count V/s size. From the below mentioned graph, it is evident that droplets in the size range of 16 to 55 micro meters cover the majority portion of the spray. 

• What are the instruments for measuring drop size distribution?One of the most common measurement techniques is Phase Doppler Anemometer (PDA), interferometric laser imaging for droplet sizing (ILIDS) with glare-points technique (GPT), 

• What is velocity distribution in sprays? It is analogous to drop size distribution. It is an information about the velocity of the droplets at different locations. The figure below shows a typical Velocity distribution data for a spray. You can see that the velocity of the droplets near the center line is higher than the droplets near the spray boundary.

• What is the density of the spray? It is the number of droplets per unit volume.7

• What is D32/Sauter Mean Diameter? Sauter Mean Diameter (expressed as SMD, d₃₂ ) is an average of particle size. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. In other words it the diameter of a drop having the same volume/surface area ratio as the entire spray.
  

• What are the spray characteristics diameters apart form SMD? Arithmetic Mean Diameter (D10)-The average of the diameters of all the droplets in the spray sample.

Volume Mean Diameter (D30)- It is the diameter of a droplet whose volume, if multiplied by the total number of droplets, will equal the total volume of the sample.

Sauter Mean Diameter (D32)-  It is the diameter of a droplet whose ratio of volume to surface area is equal to that of the complete spray sample.

Mass (Volume) Median Diameter (DV0.5)/MMD- It is the diameter which divides the mass (or volume) of the spray into two equal halves. Thus 1/2 of the total mass is made up of droplets with diameters smaller than this number and the other half with diameters that are larger.

- DV0.1 would represent the diameter of which 10% of droplets are smaller than and DV0.9 would represent the diameter that 90% of droplets are smaller than

• What is Ohnesorge number?

This number is used initially to account for the influence of viscosity drop break up. The Ohnesorge number is a dimensionless constant to describe the tendency of a drop to either stay together or fly apart by comparing viscous forces with inertial and surface tension forces.

Larger Ohnesorge numbers indicates the profound influence of viscosity.
 To account for the liquid viscosity in droplet formation, the appropriate non-dimensional number is the Ohnesorge number which represents the ratio of internal viscosity dissipation to the surface tension energy. The Ohnesorge number may be written in terms of the square root of the Weber number divided by the Reynolds number. The Ohnesorge number is sometimes also referred to as stability number, viscosity number, Laplace number, or Z number. It is independent on the velocity and therefore only adequate to describe droplet ejection in conjunction with the Weber number. The lower the Ohnesorge number the weaker are the friction losses due to viscous forces. This means that most of the inserted energy converts into surface tension energy, i. e. a droplet can be formed. The higher the Ohnesorge number the more dominant is the internal viscous dissipation. This means that most of the inserted energy converts into internal viscous dissipation.

•  What is Webber Number?

It is the ratio of disruptive aerodynamic forces to consolidating surface tension forces.  Higher the Webber Number higher the deforming external pressure forces and represents greater tendency to breakup.

We = ρ v² l / σ                                             Where:We = Weber number (dimensionless)ρ = density of fluid (kg/m³, lb/ft³)v = velocity of fluid (m/s, ft/s)l = characteristic length (m, ft)σ = surface tension (N/m)

• What is critical Webber Number?

It the Webber Number at which the aerodynamics forces equals to surface tension forces.
We_crit = 8/C_d
                Where C_d=Drag co-efficient. 

FABRICATION AND TESTING OF A PINTLE INJECTOR

The material chosen for the fabrication of pintle injector is SS-304. The Injector is made of two parts. the outer body and the inner pintle. The pintle is screwed inside the outer body so that the pintle opening distance can be varied for the different experiments.

Figure 6 .2-D drawing of the injector with dimensions in millimeter.

In the outer body of the injector. two inlets are placed diametrically opposite to each other. The diameter of these inlets are 5 mm each. One inlet leads to the outer annular gap and the second one to the center of the injector. The pintle angle is 25°.

Figure 7. Different views of the injector

Figure 8. Sectional view of the outer body 

The spray images from the injector is given below:

Atomization was seen insufficient for the combustion of liquid kerosene and Liquid Oxygen. For kerosene to burn, the mean drop size should be less than 30 to 50 microns.

The challenge with the injector was to achieve the proper propellant distribution through the annular orifice.

Pintle opening (mm)	Pressure (Kg/cm2)	Time (s)	Flow rate Kg/s	Area of Discharge (mm2)	Velocity (m/s)	Reynolds Nu	Webber nu
0.55	1.5	10	0.132	30.549	4.31	2360.438	140.003
0.63	1.5	7.6	0.156	34.992	4.46	2798.799	171.837
0.95	1.5	9.5	0.172	52.766	3.25	3079.86	137.991
1.33	1.5	9.8	0.185	73.873	2.51	3324.432	114.841
1.6	1.5	9.8	0.189	88.869	2.13	3397.698	99.716
1.89	1.5	7.9	0.197	104.977	1.88	3544.577	91.872

The diamter of pintle minimum opening was 8.84 mm. Pintle was screwed to the first part. Some leak was seen in testing.

Annular gap data is given below:

The spray from a  pintle injector with water and air can be seen below:

Radial flow can be seen below: 

 Another thing to notice is the material selection, the material chosen was stainless steel. However welding stainless steel need TIG welding and it was very difficult to find compared to oxyacetylene. It required traveling and extra cost for welding. If the material can be welded with oxyacetylene it would have been time saver. More details of the spray tests will be updated soon.