This document summarizes research conducted by students at the University of Illinois to analyze jet engine thrust performance through computational fluid dynamics (CFD) simulation and physical testing. The students used CFD software to model the flow through nozzle designs for a JetCat P140-RX miniature turbine engine. Thrust values predicted by the CFD simulations closely matched manufacturer specifications. The students also designed and built a test stand to physically validate thrust measurements of the engine mounted on bearings between parallel rails. Further CFD simulations and nozzle designs were planned to more fully validate simulation results against physical performance data.

1. 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
𝑚𝑚̇ = 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
𝑣𝑣⃑
𝐹𝐹⃑
=
=
velocity of control volume in motion
net force due to stresses on control volume surface
1

2. 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� 𝑑𝑑𝑑𝑑
𝑆𝑆
= 0 (1)
𝜕𝜕
𝜕𝜕𝜕𝜕
� 𝜌𝜌𝑢𝑢�⃑ 𝑑𝑑𝑑𝑑
𝑉𝑉
+ � 𝑢𝑢�⃑𝜌𝜌(𝑢𝑢�⃑ − 𝑣𝑣⃑ ) ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑
𝑆𝑆
= − � 𝑝𝑝𝑛𝑛� 𝑑𝑑𝑑𝑑
𝑆𝑆
+ � 𝜌𝜌𝑓𝑓⃗ 𝑑𝑑𝑑𝑑
𝑉𝑉
+ 𝐹𝐹⃗ (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� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝑑𝑑
= 0 (3)
� 𝑢𝑢�⃑𝜌𝜌�𝑢𝑢�⃑ − 𝑣𝑣⃑�� ∙ 𝑛𝑛� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝑆𝑆
+ � 𝑝𝑝𝑛𝑛� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝑆𝑆
= 𝐹𝐹⃗ (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
2

3. 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.
𝑚𝑚̇ = 𝜌𝜌𝑢𝑢�⃑𝐴𝐴 (5)
𝑚𝑚̇ e = 𝑚𝑚̇ a + 𝑚𝑚̇ f = 𝑚𝑚̇ in + 𝑚𝑚̇ f (6)
𝑇𝑇�⃑ = 𝑚𝑚̇ e 𝑣𝑣e − 𝑚𝑚̇ in 𝑣𝑣in + (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
3

4. 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
4

5. 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
5

6. 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
6

7. 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
7

8. 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
𝑃𝑃𝑖𝑖 𝑖𝑖
𝑃𝑃𝑒𝑒
= �1 +
𝛾𝛾 − 1
2
𝑀𝑀2
�
𝛾𝛾
𝛾𝛾−1
(8)
𝑇𝑇𝑖𝑖 𝑖𝑖
𝑇𝑇𝑒𝑒
= 1 +
𝛾𝛾 − 1
2
𝑀𝑀2
(9)
𝑐𝑐 = �𝛾𝛾𝑅𝑅𝑎𝑎 𝑇𝑇 (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
8

9. 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
9

10. 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
10

11. 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
11

12. 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
12

13. 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.
13