Thrust Measurement of R/C Scale Jet Engine Using CFD and Validation

Kevin Burns, William Yoshida, David Liljewall, Michael Vershaw, Je Won Hong, Ovini Silva University of Illinois at Urbana Champaign Aerospace Engineering Department, Urbana, IL, 61801

Indronil Ghosh University of Illinois at Urbana Champaign Physics Department, Urbana, IL, 61801

and

Bradley Rafferty University of Illinois at Urbana Champaign Mechanical Engineering Department, Urbana, IL, 61801

A turbojet engine is a complex and precisely engineered device that relies on multiple stages of machine-fluid interaction before ultimately producing the desired output thrust. The engine's internal hardware - fan, compressor, combustor, turbine, and mixer - would never achieve this propulsive force if not for a nozzle that dictates the thrust level. This research paper details the efforts and findings of the AIAA JetCat Engine Technical Project Group of University of Illinois at Urbana Champaign in its endeavor to analyze the effects of nozzle design on the thrust performance of model jet engines through computational fluid dynamics software. To test the validity of the computational fluid dynamics (CFD) results, the measured thrust is compared to manufacturer product specifications. For further validation of physical performance, the JetCat P140-RX Miniature Turbine Engine is to be mounted to two pillow block bearings riding two parallel rails to allow unhindered, uniaxial movement and to provide an accurate thrust reading via spring loading scales. The team also has designed three nozzles for the engine on computer aided design (CAD) software to compare them against each other as well as data from the stock nozzle, specifically peak thrust and various flow characteristics. The purpose of these efforts is to gain valuable experience in research, computational fluid dynamics, properly controlled testing, and hands-on work with a miniature jet engine.

Nomenclature

𝐴𝐴 = cross-sectional area c = speed of sound in air 𝛾𝛾 = specific heat ratio dS = differential surface area element dy = differential in terms of y dz = differential in terms of z �̇�𝑚 = mass flow rate M = Mach number 𝑛𝑛� = normal unit vector p = pressure 𝑃𝑃 = pressure 𝜌𝜌 = density of substance R = specific gas constant 𝑇𝑇�⃑ = thrust 𝑢𝑢�⃑ = velocity of flow �⃑�𝑣 �⃑�𝐹

==

velocity of control volume in motion net force due to stresses on control volume surface

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Subscripts a = air e = exit in = inlet f = fuel

I. Introduction CFD is a useful engineering tool that allows the estimation of performance parameters and validation of a certain

device that is a subject to testing. Two dimensional flow analysis of an exhaust nozzle is an important example of

computer-based simulation which requires understanding of: physical theory and phenomena of incompressible and

compressible flow, ideal gas theory, and control of proper meshing techniques and appropriate boundary conditions.

The AIAA Student Chapter at the University of Illinois Urbana Champaign focuses on the validation of its small-

scale jet engine utilizing both computer simulation and hardware test using a test stand designed and built by a group

of students. According to CFD results, theoretical estimation of the JetCat P140-RX engine thrust closely matches

the specification of the manufacturer within 1% error, although the sophistication of our physical validation is not

yet finalized. Further validation is to be carried out using an electronic force sensor installed on the engine test stand

while running the engine at different throttle levels.

II. Theoretical Background and Calculation Set-Up General thrust of a turbo-machine follows conservation of mass and momentum, in which the following

equations are valid. Equation (1) and Equation (2) are the conservation of mass and momentum, respectively.1

𝜕𝜕𝜕𝜕𝜕𝜕�𝜌𝜌 𝑑𝑑𝑑𝑑

𝑉𝑉

+ �𝜌𝜌𝑢𝑢�⃑ ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑𝑆𝑆

= 0 (1)

𝜕𝜕𝜕𝜕𝜕𝜕�𝜌𝜌𝑢𝑢�⃑ 𝑑𝑑𝑑𝑑

𝑉𝑉

+ �𝑢𝑢�⃑ 𝜌𝜌(𝑢𝑢�⃑ − �⃑�𝑣 ) ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑𝑆𝑆

= −�𝑝𝑝𝑛𝑛� 𝑑𝑑𝑑𝑑𝑆𝑆

+ �𝜌𝜌𝑓𝑓 𝑑𝑑𝑑𝑑𝑉𝑉

+ �⃗�𝐹 (2)

Assumption of steady flow, stationary control volume and constant pressure acting on the cross-sectional area

reduces the conservation of mass and conservation of

momentum equations to the following.

� 𝜌𝜌𝑢𝑢�⃑ ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 0 (3)

�𝑢𝑢�⃑ 𝜌𝜌�𝑢𝑢�⃑ − �⃑�𝑣 �� ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑆𝑆

+ �𝑝𝑝𝑛𝑛� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑆𝑆

= �⃗�𝐹 (4)

Equations (3) and (4) constitute the analytical

expressions by which thrust is calculated. A turbojet

engine consists of an air inlet, a compressor, combustion

chamber, turbine blades and a nozzle exit as shown in Figure 1. Our simplification of the jet engine subject to testing

is based on the assumption that it consists of an inlet and outlet with a pressure drop due to the combustion process.

Figure 1. Diagram of Jet Engine in Axial Cut

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This simplification results in a general thrust equation with known parameters at the inlet and outlet. Mass and

momentum conservation express the mass flow rate at the nozzle exit and the resultant thrust as follows.

�̇�𝑚 = 𝜌𝜌𝑢𝑢�⃑ 𝐴𝐴 (5)

�̇�𝑚e = �̇�𝑚a + �̇�𝑚f = �̇�𝑚in + �̇�𝑚f (6)

𝑇𝑇�⃑ = �̇�𝑚e𝑣𝑣e − �̇�𝑚in𝑣𝑣in + (𝑃𝑃e − 𝑃𝑃0)𝐴𝐴e (7)

With known quantities specified by the manufacturer of the engine and by CFD results, the thrust of the device

may be estimated using the above expressions. The estimated thrust is to be compared to the manufacturer

specifications to validate our results.

The JetCat P140-RX R/C scale jet engine is known for its simplicity of operation, its stability, and its relatively

low fuel consumption rate. The simple nozzle geometry and assembly feature also serve as a perfect test subject for

3D CAD programming, nozzle design manipulation, and 2D CFD analysis. From the cross-sectional cut of JetCat

engine shown in Figure 2 below, it is reasonable to make the assumption of a simplified jet engine with

componentry as shown in Figure 1.

III. CFD Simulation Using ANSYS Fluent

A. Nozzle Measurement and Geometry Set-Up

for CFD

ANSYS Fluent is the CFD simulation tool of

choice due to its simple user interface and powerful

meshing ability in 2D flow analysis.3 ANSYS Fluent

is capable of importing the simple geometry of a simulation

subject into its Workbench Modeler and accepting the subject as

a surface in which a fluid of choice can be physically simulated

by assigning boundary conditions for inlet type, outlet type and a

wall section. To properly design the nozzle geometry, the engine

nozzle is disassembled and its dimensions are measured. Based on dimensions tabulated in Table 1, the nozzle is

modeled using Creo Parametric 3.0 and its cross-sectional geometry is imported to ANSYS Workbench. The nozzle

geometry in 3D CAD model format is shown in Figure 3, and its cross-section that was implemented in ANSYS

Workbench is shown in Figure 4.

Figure 2. Diagram of cut-view of JetCat engine2

Table 1. JetCat P140-RX Nozzle Dimension

Dimension Type Measurement (mm) Inlet Diameter 360

Outlet Diameter 361 Wall Thickness 1.5

Length 560

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Figure 3. JetCat P140-RX Nozzle in 3D CAD model Format Figure 4. Cross-sectional nozzle sketch

B. ANSYS Modeler Set-Up4

2D nozzle flow simulation on ANSYS is set up as a nozzle-to-chamber configuration in order to observe the

flow characteristics past the exit area of the nozzle. The chamber dimensions are 47.5X100mm, as shown in Figure

5. The surface created from the sketch is divided into 14 different sections to allow more precise meshing at the

nozzle wall and chamber wall boundaries. The nozzle has the rising point at the coordinate of 260mm from y-axis

with offset of 7.5mm, combined with a curvature that connects two lines drawn toward inlet and outlet each.

Figure 5. ANSYS Workbench modeler geometry implementation of JetCat nozzle and a chamber

C. Mesh Set-Up

Meshing the simulation subject properly is one of the most critical stages in any CFD analysis. Improper

meshing can cause the simulation result to not converge properly and significant discrepancies will arise when

compared to the accepted values, e.g. manufacturer specifications. For the nozzle simulation, the mesh size is set to

2.5e-1mm for all sections from the model sketch. It is important to properly assign the inlet, outlet, wall and axial

boundaries. Below in Figure 6 is the resultant mesh.

JetCat Nozzle Chamber

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Figure 6. Meshing of the nozzle and the chamber

D. Boundary Conditions and Simulation Model

According to the manufacturer specifications (see Table A of the Appendix), the JetCat P140-RX has a pressure

ratio of 3.2 at its maximum throttle. For our purposes, we assume that the pressure inside the testing chamber is

equal to atmospheric pressure and its temperature is room temperature. The specifications also state that the

maximum temperature of the gas flow from JetCat nozzle reaches 950K. Ideal gas and laminar flow with energy

equation are utilized for this particular 2D flow analysis. The axis-symmetric option is checked to mirror the

simulation result as a full nozzle and chamber combined. Below in Table 2 are the boundary conditions used for this

simulation.

Table 2. Boundary conditions for 2D flow simulation

Component Boundary Type Variables

Temperature (K) Pressure (kPa)

Nozzle Inlet Pressure-Inlet 950 324.24

Nozzle Outlet Pressure-Outlet 300 101.33

An example of the inlet boundary condition set-up interface is shown in Figure 7.

Figure 7. Boundary condition set-up interface of ANSYS Fluent 15.0

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The numbers of iterations is set to 250 and the meshing technique is also iterated and modified accordingly to

ensure reasonable simulation results. The calculation process on ANSYS Fluent interface is shown in Figure 8.

Figure 8. Iteration and calculation interface of ANSYS Fluent 15.0

E. Result and Thrust Calculation

The result of 2D flow analysis for the JetCat engine nozzle is exported in the form of a contour plot. The

velocity, pressure, and temperature contour plots are shown in Figures 9, 10, and 11, respectively.

Figure 9. Flow velocity contour of the JetCat nozzle and chamber

Figure 10. Flow pressure contour of the JetCat nozzle and chamber

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Figure 11. Flow temperature contour of the JetCat nozzle and chamber

Flow velocity, pressure, and temperature on the nozzle axis are plotted as shown in Figure 12, 13 and 14. The

three quantities are plotted on the domain of the axial coordinate of the nozzle to represent inlet, internal and exit

flow characteristics. The simulated parameters at the nozzle exit are used for theoretical calculation of the nozzle

thrust in the next section using equations previously stated in Section II of this report.

Figure 12. Gas flow velocity along JetCat nozzle axis

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Figure 13. Gas flow pressure along JetCat nozzle axis

Figure 14. Gas flow temperature along JetCat nozzle axis

IV. Validation of Simulation and Theoretical Calculation

Based on the assumptions of steady, one-dimensional, isentropic flow of an ideal gas, the following expressions

of pressure ratio and temperature ratio are derived and utilized.6

𝑃𝑃𝑖𝑖𝑖𝑖𝑃𝑃𝑒𝑒

= �1 +𝛾𝛾 − 1

2 𝑀𝑀2�𝛾𝛾

𝛾𝛾−1 (8)

𝑇𝑇𝑖𝑖𝑖𝑖𝑇𝑇𝑒𝑒

= 1 +𝛾𝛾 − 1

2 𝑀𝑀2 (9)

𝑐𝑐 = �𝛾𝛾𝑅𝑅𝑎𝑎𝑇𝑇 (10)

The simulations results of ANSYS Fluent 15.0 for pressure, gas flow velocity, and temperature at the nozzle’s

inlet and outlet are tabulated below.

Table 3. Boundary conditions for 2D flow simulation

Nozzle Part Quantity Type

Gas Flow Velocity (m/s) Temperature (K) Pressure (kPa)

Inlet 145.95 940.63 309.69

Outlet 400.20 876.50 217.72

The Mach number of the gas flow at the nozzle exit is 0.6745, and 𝛾𝛾 is 1.369 as per equation (9). Calculating

theoretical gas pressure at the outlet yields 290.57 kPa, which generates an error of 6.2% in comparison to the

results of the simulation. The error is likely due to the simplification of the engine model as constant pressure along

its inlet/outlet cross-section, which is not true for a viscous flow model. This error is quite reasonable and small

enough to validate the theoretical calculations.

The inlet quantities of the engine are calculated by referencing manufacturer’s specification, which state the

JetCat P140-RX has an air mass flow rate of 0.35kg/s at the intake. The diameter of the inlet is listed in Section III,

subsection A as 360 mm, from which the area is calculated as 0.1018 m3. In using Equation (5) and taking air

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density in room temperature (300 K) as 1.184 kg/m3, the inlet flow velocity is calculated to be 2.9 m/s. By adding

0.0073 kg/s of fuel consumption rate at maximum throttle of the engine, thrust is calculated to be 141.98N. JetCat

P140-RX has the maximum thrust of 142 N according to the specification, which is a mere 0.014% error.5

The engine specifications list the maximum gas exhaust velocity as 1461 km/h, or 405.83m/s. The simulated

result of 400.2 m/s is only 1.39% different. Therefore, our ANSYS Fluent CFD results are valid and quite accurate

for this simple converging nozzle performance analysis.

V. Physical Validation and Nozzle Design Variation

The customized test stand is constructed using two linear rails and sliding pillow block bearings with minimal

friction to attempt to created unhindered uniaxial motion for the physical testing of the engine. Mounting brackets,

which are sold separately by JetCat, are installed on the engine body and the engine is attached to the bearings via

two laser-cut, wooden adapter plates as shown in Figure 15. To halt the motion of the engine-bearing assembly at

the end of the rails, two blocks of square aluminum rod are cut and bolted to the test stand at the end of the rails as

shown in Figure 16.

Figure 15. Pillow block bearings, rails and JetCat P140-RX assembly on the test stand

Figure 16. Stoppers installed at the end of the test rails

The overall assembly of a physical test configuration is shown below in Figure 17.

wooden adapter plate

mounting bracket

pillow block bearing

rail

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Figure 17. Assembly of JetCat P140-RX engine testing stand

The initial plan was to employ an electronic force sensor, however spring load scales were substituted for this

purpose due to hardware issues. Two manual spring load scales are connected to a metal spacer installed on each

pillow block and are rigidly attached to the stand. This thrust measurement technique is not as accurate as the

electronic alternative, and so slight discrepancies arise when compared to the simulation results and the

manufacturer’s specifications. Testing is conducted in 10-minute intervals and consists of ignition, low throttle, max

throttle, idle, and finally a cooling process. A total of three runs are conducted with thrust and temperature readings

recorded. Temperature is measured via a temperature sensor that is installed by the manufacturer within the nozzle.

Table 4. Physical test results of the JetCat P140-RX

Trial Number Temperature (°C) Thrust on Scale 1 (N) Thrust on Scale 2 (N) Total Thrust (N)

1 725 69.0 67.0 136.0

2 731 70.0 69.0 139.0

3 727 69.0 68.0 137.0

Average 727.67 69.3 68.0 137.3

Likely sources of error are: friction between the metal rails and pillow block bearings, inexact alignment of

JetCat engine along the desired axial direction of motion, and spring load scale friction. Despite these sources of

error, the calculated error is still well within reason.

VI. Conclusion

In our efforts we were able to successfully analyze, both numerically and physically, the thrust output by the

miniature jet engine. Our simulations were refined to the point of error within a nominal 6% or less when compared

to manufacturer specifications, and in this refinement process we learned the importance and intricacy of iteration

and convergence to a desired solution. Additionally, our physical testing confirmed the accuracy of our simulations

and theoretical calculations and agrees well with expected values. Our physical testing could be improved by the

successful implementation of an electronic force sensor for more accurate readings, as well as by employing a

stable, one-rail testing rig to reduce the amount of friction in the system. We are now prepared to manufacture our

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own nozzle and compare it against our current findings. In all, we are very satisfied with the knowledge we have

gained regarding CFD analysis, design for manufacturability, and physical testing implementations.

VII. Future Plans

Our next step for the project is to manufacture one of the nozzles we designed. The models below in Figures 18 and

19 are examples of nozzle geometry variations we have designed that will be analyzed in ANSYS, and one of which

will be sent to the metal shop to be manufactured. Figure 20 shows the jet engine fitted with a 3D-printed nozzle for

dimensional analysis purposes. This is the nozzle design we plan to manufacture out of solid aluminum. We will

also explore 3D CFD analysis in order to expand on the 2D analysis we have established.

Figure 18. Nozzle design with concave-up curvature Figure 19. Nozzle design with straight line geometry

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Figure 20. 3D-printed nozzle design

Appendix

A. Manufacturer Specification of JetCat R/C Scale Jet Engines3 Type P20-SX P60-SE P100-RX P80-SE P140-RX P180-RX P200-SX Idle Rpm (1/min) 80000 50000 40000 35000 32000 32000 33000 MaxRpm (1/min) 245000 165000 152000 125000 125000 125000 112000 Idle thrust (N) 0,3 1 1,9 3 6 7 9 max thrust (N) 24 63 100 97 142 175 230 EGT (°C) 480-690 480-730 510-730 510-700 520-749 520-750 480-750 pressure ratio 1,5 2 2,3 2,4 3,2 3,6 3,7 massflow (kg/s) 0,0516 0,16 0,24 0,25 0,35 0,38 0,45 Exhaustgas velocity(km/h) 1674 1418 1500 1397 1461 1658 1840 Power output (thrust) (kW) 5,6 12,4 20,8 18,8 28,8 40,3 58,8 Fuel consumption @maxRpm (ml/min) 90 230 360 340 550 625 730 Fuel consumption @idle (ml/min) 12 70 60 95 110 122 129 Fuel consumption @idle (kg/min) 0,01 0,056 0,048 0,076 0,088 0,098 0,103 Fuel consumption @maxRpm (kg/min) 0,072 0,184 0,288 0,272 0,44 0,5 0,584 specific fuel consumption @ maxRpm (kg/Nh) 0,18 0,175 0,173 0,168 0,186 0,171 0,152 weight (g) 350 830 1050 1360 1580 1595 2560 diameter 60 83 97 112 112 112 132 lenght (incl. Starter) (m m ) 180 245 240 290 293 297 355

B. Pressure Simulation Values from ANSYS Fluent 15.0 X [ m ] Y [ m ] Z [ m ] Pressure [ Pa ]

-5.00E-03 0.00E+00 0.00E+00 3.07E+05

1.78E-03 0.00E+00 0.00E+00 3.10E+05

8.56E-03 0.00E+00 0.00E+00 3.12E+05

1.53E-02 0.00E+00 0.00E+00 3.12E+05

2.21E-02 0.00E+00 0.00E+00 3.12E+05

2.89E-02 0.00E+00 0.00E+00 3.10E+05

3.57E-02 0.00E+00 0.00E+00 3.03E+05

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4.24E-02 0.00E+00 0.00E+00 2.88E+05

4.92E-02 0.00E+00 0.00E+00 2.60E+05

5.60E-02 0.00E+00 0.00E+00 2.18E+05

C. Temperature Simulation Values from ANSYS Fluent 15.0 X [ m ] Y [ m ] Z [ m ] Temperature [ K ]

-5.00E-03 0.00E+00 0.00E+00 9.39E+02

1.78E-03 0.00E+00 0.00E+00 9.41E+02

8.56E-03 0.00E+00 0.00E+00 9.42E+02

1.53E-02 0.00E+00 0.00E+00 9.42E+02

2.21E-02 0.00E+00 0.00E+00 9.42E+02

2.89E-02 0.00E+00 0.00E+00 9.41E+02

3.57E-02 0.00E+00 0.00E+00 9.36E+02

4.24E-02 0.00E+00 0.00E+00 9.26E+02

4.92E-02 0.00E+00 0.00E+00 9.07E+02

D. Gas Flow Velocity Simulation Values from ANSYS Fluent 15.0 X [ m ] Y [ m ] Z [ m ] Velocity [ m /s ]

-5.00E-03 0.00E+00 0.00E+00 1.49E+02

1.78E-03 0.00E+00 0.00E+00 1.46E+02

8.56E-03 0.00E+00 0.00E+00 1.47E+02

1.53E-02 0.00E+00 0.00E+00 1.52E+02

2.21E-02 0.00E+00 0.00E+00 1.63E+02

2.89E-02 0.00E+00 0.00E+00 1.80E+02

3.57E-02 0.00E+00 0.00E+00 2.09E+02

4.24E-02 0.00E+00 0.00E+00 2.55E+02

4.92E-02 0.00E+00 0.00E+00 3.20E+02

5.60E-02 0.00E+00 0.00E+00 4.00E+02

Acknowledgments The authors thank Rodney L. Burton of University of Illinois at Urbana Champaign Aerospace Engineering

department, the professor Emeritus for advising us and reviewing the overall contents and validity of test process, Greg S. Milner and Lee A. Booher of Aerospace Engineering department machine shop for their generosity regarding hardware components for test stand assembly and manufacturing knowledge for the nozzle, Kevin Lee and Brian S. Woodard of Aerospace Engineering department for CFD simulation instructions.

References 1 John D. Anderson, Fundamentals of Aerodynamics, 5th ed. US: McGraw-Hill, 2010. 2 Jacob A. Baranski, John L. Hoke, Paul J. Litke, and Frederick R. Schauer, "Preliminary Characterization of Bio-

fuels using a Small Scale Gas Turbine Engine," 49th AIAA Aerospace Sciences Meeting, January 2011. 3 JetCat, "JetCat RX Turbines with V10 ECU," JetCat GmbH, Staufen im Breisgau, Technical Manual. 4 GANDIKOTA B.V. KISHORE and Kaparthy Akash, "CFD Analysis of a Rocket Nozzle with one Inlet at Mach

0.6," Aeronautical Engineering, Malla Reddy College of Engineering and Technology, Hyderabad, Project Report. 5 Gerald Hagemann, Richard Schwane, Philippe Reijasse, and Joseph Ruf, "Plug Nozzles: Assessment of Prediction

Methods for Flow Features and Engine Performance," 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit , 2002.

6 Jerry M. Seitzman. (2001) Isentropic Flow with Area Change. PDF.

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