Design and Analysis of Air Intake Manifold for Formula Student Cars
Redesigning the Compressor Diffuser of a JetCat P90 Turbine to Improve Efficiency
1. 1
A Research Paper on Redesigning the Compressor
Diffuser of a JetCat P90 Turbine to Improve the
Efficiency
Authored by:
James Feldhacker
Nicholas Staikoff
Ryan Schwartzwalder
Frank Mitchell
Daniel Hoffmann
Michael Begovich
April 28, 2015
Supervisor: Professor Awatef Hamed, CEAS-Aerospace Eng & Eng Mech
Co-Supervisor: Professor Mark Turner, CEAS-Aerospace Eng & Eng Mech
University of Cincinnati
2600 Clifton Avenue
Cincinnati, OH 45221
3. 3
List of Tables and Figures
Table 1 - JetCat P-90RXI Parameters………………………………………………………......... 8
Table 2 - GasTurb Analysis Data……………………………………………………………...... 11
Table 3 - Station Numbering for the Compressor………………………………………………. 11
Table 4 - Compressor Flow Known and Assumed Conditions………………………………… 13
Table 5 - Vaned Diffuser Conditions…………………………………………………………… 14
Table 6 - Flow Calculations in the Compressor……………………………………………........ 17
Table 7 - Flow Calculations with Slip Factor Consideration………………………………….... 18
Table 8 - Mesh Statistics of Solution Domains…………………………………………………. 22
Table 9 - Computational Model Conditions……………………………………………….......... 23
Table 10 - Average Total Pressure Loss in Diffusers…………………………………………... 28
Table 11 - Loss Coefficient of Diffuser Designs……………………………………………….. 28
Table 12 - Static Pressure Coefficients of Designs……………………………………………... 28
Figure 1. Original diffuser……………………………………………………………………….. 6
Figure 2. JetCat P-90RXI Cutaway……………………………………………………………… 7
Figure 3. Vaneless space in diffuser…………………………………………………………....... 9
Figure 4. CAD geometry of original diffuser…………………………………………………… 10
Figure 5. Diffuser flow regimes (after Reneau et al. 1967)…………………………………….. 20
Figure 6. Redesigned diffuser design………………………………………………………….... 21
Figure 7. Solution domain and computational grid for the original (left) and redesigned (right)
diffuser………………………………………………………………………………………….. 21
Figure 8. Impeller exit velocity vector diagram……………………………………………........ 24
Figure 9. Total pressure carpet plots of the original diffuser vs. redesigned diffuser………….. 25
Figure 10. Total pressure carpet plot and streamline plots of original diffuser vs. redesigned
diffuser…………………………………………………………………………………………... 26
Figure 11. Total pressure at exit of the original diffuser (left) vs. redesigned diffuser (right)…. 26
Figure 12. Mach number carpet plots at midline of radial stator passage: original diffuser (left)
vs. redesigned diffuser
(right)............................................................................................................................................. 27
Figure 13. Yplus carpet plots for original (left) and redesigned (right) diffusers………………. 27
Figure 14. Area ratio vs length to width ratio for diffuser designs……………………………... 29
4. 4
Acknowledgements
We would like to extend our greatest appreciation to Dongyun Shin for providing us with the
foundation to analyze our designs in CFD. Without his help, we would not have been able to
complete the analysis on time.
We would also like to thank Professor Awatef Hamed, Professor Mark Turner, and Professor
Shaaban Abdallah for helping us with our project. Your insights were very helpful and
appreciated.
5. 5
Abstract
The objective of this senior design project was to increase the efficiency of the
centrifugal compressor within a JetCat P-90RXI gas turbine engine while it is operating at
military power. This is potentially achieved by redesigning the vaned diffuser within the
compressor. To achieve this, the inclination angle of the incoming flow to the first set of stators
was minimized and the number of stators on the vertical face of the diffuser was reduced from 15
to 12. Additionally, a splitter was added to the passage between the first set of stators to help
guide the flow. This helps to reduce blockage. Using CFD software, the redesigned diffuser had
a total pressure loss of 61,908 Pa while the original diffuser had a total pressure loss of 66,836 Pa
(7.4% improvement). The results supported the theoretical predictions summarized by Cumpsty
in his book “Compressor Aerodynamics” regarding minimizing the incidence angle of the
incoming flow on the first set of stators. The results also supported the extensive research by
NASA in their paper “High Efficiency Centrifugal Compressor for Rotorcraft Applications”.
However, the design is theoretical and does not meet the geometry constraints of the turbine
engine’s diffuser fastening locations.
6. 6
Part 1: Introduction
1.1 Project Objective
This report researches the possibility of improving the efficiency of the JetCat P90 gas
turbine engine by redesigning the diffuser of the compressor.
1.2 Operation of a Centrifugal Compressor
The main components of any gas turbine engine are the inlet, compressor, combustor,
turbine and nozzle. Within the aerospace field, two primary forms of compressors exist: axial
and centrifugal. This research focuses on the centrifugal compressor, which is used because it
significantly reduces the complexity and overall length of the engine. The objective of the
compressor is to increase the pressure of the flow before it goes into the combustor. If higher
pressure can be achieved, the greater the overall performance of the engine. Centrifugal
compressors can be broken into two components: the impeller and diffuser. The impeller
increases the flow velocity and changes the flow direction from axial to radial. The diffuser then
slows the flow down to increase the pressure going into the combustor, which allows for more
thrust to be created via combustion.
1.3 Constraints
The constraints of this project include geometry constraints of the JetCat P90 engine. The
diffuser is attached to the housing using screws. The locations of the screw holes constrain the
possible design choices of the new diffuser. Figure 1 shows the original diffuser and the screw
holes located on the front face of the diffuser.
Figure 1. Original diffuser.
7. 7
Part 2: Literature Review
2.1 Introduction
There are two readings that need to be brought to attention in order to create the best
design. One of these is the manual and datasheet for the JetCat P-90. This reading is important so
that the base performance of the engine can be documented, and so that improvements can then
be made. Another reference that was utilized was the book “Compressor Aerodynamics” by N.A
Cumpsty. This text offers information and content about vaned and vaneless diffusers, and how
these components work in relation to the rest of the compressor. It also provides detail on how to
optimize the vaned diffuser, and how to match the diffuser with an impeller.
2.2 JetCat P-90RXI Review
The Air Force will be providing the JetCat P-90 gas turbine engine. This model comes
with an “internal kerosene start, internal EGT sensor, internal solenoids, and internal fuel pump.
It has Bubble Detector Technology (all of the RXI models come with this), a single wiring
connection from the ECU to the engine. It has a lightweight ECU V10.0, along with a 2-cell
LiPo, or the 3-cell LiFe battery.” (2). Table 1 shows the various parameters of the JetCat P-
90RXI (2).
Figure 2. JetCat P-90RXI Cutaway.
8. 8
Table 1 - JetCat P-90RXI Parameters at Military Power
Parameter Value
Length 300 mm
Thrust 24 lbs. (105 N) @ 130,000 RPM
Weight ~3.12lbs (~1435 grams) (including starter)
Diameter 112 mm
RPM Range 35,000 - 125,000
Exhaust Gas Temperature 580°C-690°C (1076°F-1274°F)
Fuel Consumption 9 oz./min (33.75 lbs./hour) (at full power)
Fuel Jet A1
Lubrication ~5% synthetic turbine oil mixed in with the fuel
Maintenance Interval 25 hours
2.3 Compressor Aerodynamics Review
In Cumpsty’s book “Compressor Aerodynamics”, there is a section on vaneless and
vaned diffusers. In this section, it is said that one of the most crucial characteristics to account
for in the vaned diffuser is the blockage of the flow coming from the impeller to the first set of
vaned diffusers. Reducing the blockage in the vaned section will reduce the total pressure losses
that occur, and improve the efficiency of the diffuser (1).
The next topic discussed is the effect the incidence angle of the incoming flow has on the
performance of the diffuser (1). If the incidence angle is an extreme value, meaning it is too great
or too small, the diffuser vanes can experience stall. Stall is bad as the flow will separate from
the vanes and create more pressure loss. It is also recommend that determining the incidence of
the flow and matching the angle of the diffuser stators with it (1). The incidence angle can easily
be calculated with the mean radial and absolute tangential velocities out of the impeller.
The next area of concern in the text is the performance difference between vaneless and
vaned diffusers. In a vaneless diffuser, it is widely accepted that the diffusion process is less
efficient than that of a vaned diffuser. Another important design choice is the ratio of the vane
leading edge radius to the impeller tip radius (1). Since the efficiency of the diffusion process is
lower in the vaneless region, it is desirable to extend the leading edge of the stators toward the
tip (exit) of the impeller. Doing so makes better use of the area of diffusion.
9. 9
Part 3: Conceptual Design Selection
3.1 Optimizing Stator Blade Angles
Drawing from the literature, looking at the angles of the radial stators could yield a
potential area of improvement in the diffuser. If the original set of stator blades are not properly
angled for the incoming flow, blockage and pressure loss can occur. This would then cause a
drop in the efficiency of the compressor as a whole (1). It was estimated that this redesign option
would yield a 5% increase in the efficiency of the compressor if completed properly.
3.2 Optimizing Vaneless Section
Another idea that could have a significant potential impact on the efficiency is optimizing
the length of the radial stator blades, and more specifically the length of the vaneless section on
the diffuser. The most pressure loss occurs in the area between the impeller exit and vaned
diffuser entrance (1). By reducing this area, or optimizing how the flow moves through this area,
the efficiency of the compressor could potentially be increased. Figure 3 below provides a clear
image of the vaneless diffuser area, and where pressure rise and loss occur. This is helpful in
understanding where the pressure loss occurs in this section. Pressure loss occurs predominantly
in the vaneless and semi-vaneless spaces. Through this research it was found that this redesign
option is also capable of a 5% increase in the compressor efficiency.
Figure 3. Vaneless space in diffuser.
10. 10
Part 4: Analysis and Results
4.1 Original Diffuser CAD Design
For the initial CAD design of the diffuser, simple measurements and pictures in
SolidWorks were utilized to create the diffuser component. Pictures taken from the top and side
angles of the diffuser were uploaded into SolidWorks, and then traced to create an initial CAD
geometry. Using calipers, the diameters of the diffuser were also measured. Diameters of the
impeller outlet, diffuser inlet and outlet along with other diameters were then used to scale the
diffuser to the appropriate sizing. Figure 4 shows the CAD geometry that will be used for the
analysis. The angle displayed in the right picture is the angle of the first diffuser passage. This
angle is greater than the angle of the incoming flow shown in Figure 8 (alpha = 27.76°).
Figure 4. CAD geometry of original diffuser.
11. 11
4.2 GasTurb Analysis
GasTurb results for the JetCAT-P80 were found in the paper titled Modeling and
Simulation of an Aero Turbojet Engine with GasTurb by Jian-hua and Ying-yun of the Naval
University of Engineering. In this report the equations and calculations associated with running
GasTurb were stated. Table 2 below shows the GasTurb analysis data from the report.
Table 2 - GasTurb Analysis Data
Table 3 - Station Numbering for the Compressor
Compressor Station Number
Impeller Entrance 2
Impeller Exit 3
Vaned Diffuser Entrance 4
Vaned Radial Diffuser Exit 5
Axial Diffuser Exit 6
12. 12
Using the values in Table 2, a Matlab code was created to find the conditions at the
different points across the compressor. The creation of the code was a collaborative effort
between our group and the other diffuser group consisting of Thomas Caley, Cory Cantor, Brian
Heberling, Jacob Holden, and Eric Wesseling. The code has been provided in Appendix A. Table
3 describes the station numbers and their respective location in the compressor. The first steps
include assigning the values in Table 2 to variables, and finding the theoretical impeller
isentropic efficiency which is equal to 0.96 (1). Area calculations of the impeller and diffuser
were done next, which then lead to the calculations at station 2. For this station, initial values
were assumed and calculations for the values were then iterated until they converged. Using this
same process, the values at the exit of the impeller (station 3) and the exit of the radial diffuser
section (station 5) were calculated. The equations used are written below, and the tabulated
results are in Table 6.
13. 13
Table 4 – Compressor Flow Known and Assumed Conditions
Compressor FlowKnown and Assumed Conditions
Overall Conditions
Assumed
Overall Efficiency (η) 0.75
Impeller Efficiency (ηi) 0.9
Pressure Compression Ratio (PRcomp) 2.277
Known
Revolutions per Minute (RPM) 125000
Tip Radius (m) .02313178
Hub Radius (m) .0075565
Exit Radius (m) .033147
Blade Height at Exit (bd) .0049276
Mass Flow Rate (kg/s) .2376824
Impeller Entrance Conditions
Assumed
Total Pressure (Pa) 101325
Total Temperature (K) 294.44
Initial Values forIteration
Static Pressure (Pa) 101325
Static Temperature (K) 294.44
Mach Number 0.38745
Axial Velocity (m/s) 133.2676
Density (kg/m3
) 1.199
15. 15
𝐶 𝑟(𝑖) =
𝑝𝑐𝑟
𝜌3(𝑖)
𝐶3(𝑖) = √ 𝐶 𝑟(𝑖)2 + 𝐶𝑡2
𝑃3and 𝑇3 are set to 𝑃𝑡3 and 𝑇𝑡3, like for station 2
Second Set of Iterations: Find Conditions at Station 3 (Impeller Outlet)
𝑇3, 𝑃3, 𝜌3, 𝑀3 and 𝐶3 are all computed with the same iterative process as Station 2.
Conditionsat Station 4 (VanelessDiffusor Exit)
𝑃𝑡4 = 𝜂 𝑣𝑎𝑛𝑒𝑙𝑒𝑠𝑠 ∗ 𝑃𝑡3
𝑇𝑡4 = 𝑇𝑡3;
𝐶 𝑡4 = 𝑟𝑟 ∗ 𝐶 𝑡
𝐶𝑟4 = 0.9 ∗ 𝑟𝑟 ∗ 𝐶 𝑡
𝑇4 = 𝑇𝑡4 −
𝐶 𝑟4(𝑖)2
2 ∗ 𝐶 𝑝
−
𝐶 𝑡4(𝑖)2
2 ∗ 𝐶 𝑝
𝑃4 = 𝑃𝑡4(
𝑇4
𝑇𝑡4
)
𝛾
𝛾−1
𝑀4 =
𝐶4
√ 𝛾 ∗ 𝑅 ∗ 𝑇4(𝑒𝑛𝑑)
Third Set of Iterations: Find Conditionsat Station 4 (Impeller Outlet)
𝑇4(𝑖 + 1) = 𝑇𝑡4 −
𝐶𝑟4(𝑖)2
2 ∗ 𝐶 𝑝
−
𝐶 𝑡4(𝑖)2
2 ∗ 𝐶 𝑝
𝑃4(𝑖 + 1) = 𝑃𝑡4(
𝑇4(𝑖+ 1)
𝑇𝑡4
)
𝛾
𝛾−1
𝐶 𝑟4(𝑖 + 1) =
𝜌3( 𝑒𝑛𝑑)
𝜌4(𝑖)
∗ 𝑟𝑟 ∗ 𝐶 𝑟3(𝑒𝑛𝑑)
𝜌4 is computed with the same iterative process as Station 2.
Conditionsat Station 5 (Vaned DiffusorOutlet)
𝑃𝑡5 = 𝑃𝑡4 ∗ η 𝑣𝑑
𝑇𝑡5 = 𝑇𝑡4
𝑝𝑣5 =
𝑚̇
𝐴𝑣 𝑒𝑥𝑖𝑡
𝐶 𝑡5 = 𝐴𝐴 ∗ 𝐶 𝑡4
𝐶 𝑟5(𝑖) = 0.9 ∗ 𝐴𝐴 ∗ 𝐶 𝑟4(𝑒𝑛𝑑)
𝜌5(𝑖) = 𝜌4 (𝑒𝑛𝑑)
𝑇5 = 𝑇𝑡5 −
𝐶 𝑟5(𝑖)2
2 ∗ 𝐶 𝑝
−
𝐶5(𝑖)2
2 ∗ 𝐶 𝑝
16. 16
𝑃5 = 𝑃𝑡5(
𝑇5
𝑇𝑡5
)
𝛾
𝛾−1
𝑀5 =
𝐶5
√ 𝛾 ∗ 𝑅 ∗ 𝑇5(𝑒𝑛𝑑)
Third Set of Iterations: Find Conditionsat Station 5 (Vaned DiffusorOutlet)
𝑇5, 𝑃5, 𝜌5,and 𝐶 𝑟5 are all computed with the same iterative process as Station 4.
17. 17
Table 6 - Flow Calculation Results in the Compressor
Compressor Flow Conditions
ImpellerEntrance Conditions
StaticPressure (P2) 89365.47 Pa
StaticTemperature (T2) 284.06 K
Mach Number(M2) 0.427417
ImpellerExitConditions
StaticPressure (P3) 189602.96 Pa
StaticTemperature (T3) 361.61 K
Total Pressure (Pt3) 266362.91 Pa
Total Temperature (Tt3) 398.49 K
Mach Number(M3) 0.714125
VanelessDiffuserExitConditions
StaticPressure (P4) 198590.36 Pa
StaticTemperature (T4) 368.55 K
Total Pressure (Pt4) 261035.65 Pa
Total Temperature (Tt4) 398.49 K
Mach Number(M4) 0.637378
VanedRadial DiffuserExitConditions
StaticPressure (P5) 209169.32 Pa
StaticTemperature (T5) 380.72 K
Total Pressure (Pt5) 245373.51 Pa
Total Temperature (Tt5) 398.49 K
Mach Number(M5) 0.483047
Axial DiffuserExit Conditions
StaticPressure (P6) 224824.58 Pa
StaticTemperature (T6) 388.17 K
Total Pressure (Pt6) 230719.26 Pa
Total Temperature (Tt6) 391.06 K
Mach Number(M6) 0.19264
18. 18
As expected, Table 6 shows a rise in static pressure and temperature across all three
stations. The decrease in Mach number through the diffuser also supports the theoretical results
since decreasing the velocity of the flow raises the static pressure, which is the purpose of a
diffuser.
Something else to take into account with an impeller is the slip factor. The slip factor
effects the resulting exit velocity magnitude and direction. Table 7 shows the values for the flow
angles as it exits the impeller that were calculated for the slip factor. The values shown in Table
7 were then used to calculate the velocity components at the inlet of the diffuser. This velocity
triangle can be found in Figure 6.
Table 7 - Flow Calculations with Slip Factor Consideration
Angle alpha 27.76°
Angle beta 33.3°
19. 19
4.3 RedesignedDiffuser CAD Design
The diffuser was redesigned so that the angle of the first set of stators was equal to the
alpha angle of the incoming flow. As stated earlier, this should yield a zero degree incidence
angle and reduce the pressure losses and increase the efficiency. After analyzing this redesign, it
was noticed that significant turbulence occurred after the flow leaves the first stators.
Specifically, this turbulence occurred after the flow left the pressure side of the stator (left edge).
In order to smooth out the flow as it leaves this surface, the trailing edge was rounded with a 0.1”
fillet. This significantly reduced the turbulence and the results can be found in Figure 10.
The next design choice was to minimize the blockage. There are two different areas to
consider when discussing the blockage. These areas are the effective and geometric areas. The
effective area is simply the area that is seen by the flow, and that is used by the flow. The
geometric area is the physical area that the flow is passing through, which includes areas around
bends that the flow may not reach. The blockage that occurs in the diffuser is then the
relationship between these two areas, and is equivalent to 1 minus the effective area over the
geometric area. For this relationship to be optimal, the effective area should be as close as
possible to the geometric area. The original blockage value for the diffuser was 0.4076, while the
calculated blockage for the redesign yielded a value of 0.3538. This shows an overall drop in the
blockage, which is an ideal property of the redesign. If the blockage is too great, the greater the
boundary layer will be. Some boundary layer is required for the diffuser to work properly, but
too great of a boundary layer will result in losses while too small of a boundary layer will result
in swirl effects.
Next, the length to width ratios of the first diffuser passage of the original and redesign
diffusers were optimized. Sources found that an optimum length to width ratio is in the range of
2.5 to 6, and this is considered a standard in the field for an optimized diffuser vane. The length
to width ratio is important because a larger ratio value yields a larger pressure increase and
increases the overall stability. Both the original and redesign values fell within this range, with
values of 2.59375 and 2.8, respectively. The length to width ratio was increased and still
remained in the optimum range.
Finally, the area ratio of the first diffuser passage of the new diffuser design was
calculated. The area ratio of the redesigned diffuser is 1.2286 compared to 1.2258 of the original
diffuser. Using the area ratio and the length to width ratio, the design was checked against a chart
of diffuser flow regimes from Japikse’s book, “Introduction to Turbomachinery” (Figure 5). The
redesigned diffuser falls in the region of “no appreciable stall” which indicates that the diffuser
will function nearly ideally. Japikse explains that the flow regime of “no appreciable stall” is
“confined to geometries with small angles and area ratios.” In this case, the JetCat P-90 is a
small turbine engine and constrains the design to small area ratios.
The final design choice was to add a splitter in the passage between the first set of stators.
The splitter is used to help guide the flow through the passage which results in a less turbulent
flow. NASA states that vaned diffusers with splitters can increase the pressure recovery and
maintain total-to-static efficiency (6). The placement of the leading edge of the splitter was
determined by setting it sufficiently downstream of the throat to avoid high flow velocity at its
approach (6).
20. 20
Figure 5. Diffuser flow regimes (after Reneau et al. 1967).
The first attempt to change the angle of the first set of stators involved keeping the
original number of stators (15 stators). However, after running a simulation in CFX it was
discovered that this had a high degree of blockage because the effective area that the flow passed
through was much smaller than the original design. In order to improve the effective area and
minimize blockage, the number of first set stators was reduced from 15 to 12. The geometry of
the redesigned diffuser is shown in Figure 6. The angle in the figure to the right represents the
angle of the first diffuser passage and is equal to the angle of the incoming flow shown in Figure
8 (alpha = 27.76°).
Figure 6. Redesigned diffuser design.
21. 21
4.4 CFD Methodology
Computational fluid dynamics software was used to solve for the Navier-Stokes
equations and to calculate the total pressure loss of the diffuser designs. When discussing the
CFD software used is it important to note the various characteristics and variables that come into
play. These variables include the solution domain, computational grid, numerical scheme,
Courant-Freidrichs-Lewy condition, convergence criteria and turbulence. Below is an overview
of what each of these variables means in terms of the CFD analysis conducted, and how changes
in the variables involved can change the overall output of the software.
Solution Domain
The solution domain of any CFD code simply refers to the physical area in which
calculations are being solved for. This includes the dimensions of the area, along with the inlet
and outlet conditions of said area. Figure 7 shows the solution domain for the original and
redesigned diffuser.
Computational Grid
The computational grid refers to the size, shape and style of the grid utilized in the CFD
code to solve for specified flow conditions. Factors to consider when choosing a computational
grid include its orientation in the axial and radial directions, the use of a clustered or un-clustered
grid, the stretch ratio of the grid and the amount of points used across the entire grid. A clustered
grid refers to a grid which has more points in some areas than others, which is useful if a certain
area needs more detail than another. For this project, clustering was used at the inlet and along
the walls to better calculate the boundary layer properties. Specifically, 10 points along the
height of the inlet wall. The stretch ratio is defined as the distance between two neighbor cells,
and the change in this distance along the length of the grid. This means that a larger stretch factor
yields more room in between cells. For this project, a stretch ratio of 1.1 was used. Table 8
shows the number of nodes and elements used in the mesh for each design. Figure 7 shows the
solution domain and computational grid of the original and redesigned diffuser. The mesh was
created to yield a Yplus value less than 85.
Figure 7. Solution domain and computational grid for the original (left) and redesigned
(right) diffuser.
22. 22
Table 8 – Mesh Statistics of Solution Domains
Original Redesign
Numberof Nodes 312071 370075
Numberof Elements 908493 1098012
Numerical Scheme
The numerical scheme refers to the overall set up and characteristics of a certain project
being run in CFD. Properties that are included in this include the boundedness (limits the
predicted values to certain physical realistic bounds), the conservativeness (pertains to how the
laws of conservation are adhered to),
A numerical scheme can fall into one of three general categories: implicit, explicit or
conservative discretization. An implicit approach includes a numerical scheme in which the
solution of the entire grid is required for each time level. For a single time level, it is very
computationally expensive compared to the explicit approach but can often be used with much
larger intervals between time levels (i.e. much larger time steps). An explicit approach would
include a numerical scheme in which a single algebraic equation is used to evaluate each new
nodal variable at a single time step. The conservative discretization scheme is a numerical
scheme in which the discretization of the algebraic equation describing the transport processes
for a dependent variable is such that conservation of the associated extensive property is
mathematically assured. CFX uses an implicit numerical scheme.
Courant – Freidrichs – Lewy Condition (CFL)
In mathematics, and more specifically computational fluid dynamics, the CFL condition
specifies a needed condition for convergence while solving partial differential equations. It is
used in situations where the numerical analysis of explicit time integration schemes is needed.
This means that the solution of the equations in current time will be based on the solutions to the
corresponding equations from earlier in the iterative process. This iterative process utilizes small
steps and artificial time to solve for a given set of conditions. One of the most important
requirements of using this condition is to use the correct time step in the calculations. If the
incorrect time step is used, the simulation will produce incorrect results and not converge. In
CFX, the Courant number refers to the CFL number. For this project, the Courant number is
25.6573.
Convergence Criteria
An iterative process is used to converge specific variables to a certain point or value,
which can be labeled those points’ convergence criteria. This is the criterion by which a solution
is judged to determine if it is sufficiently converged. Convergence is normally dependent on
satisfaction of a number of such criteria. For the simulation in this project, the default RMS
convergence criteria in CFX was used (1e-4).
23. 23
Turbulence Model
The turbulence model encompasses sets of equations that determine the turbulent
transport terms, or Reynolds stresses, in the mean flow equations. For the simulations in this
project, the turbulence model used in CFX was “Medium (Intensity = 5%)”.
4.5 CFD Analysis
The diffuser designs were analyzed in the computational fluid design software CFX using
the flow conditions in Tables 6 and 7. Table 9 shows additional values and settings used to
model the flow in the diffuser. The exit static pressure value was taken from the Matlab code
discussed earlier. Additionally, the inlet flow profile used in the simulations was assumed to be
uniform. Realistically, the inlet flow profile is turbulent. Therefore, the simulations in this study
are only comparing the diffusing performance of each diffuser. The inlet velocity values for the
radial and theta directions were calculated using the velocity vector diagram in Figure 8.
Table 9 - Computational Model Conditions
CFD Parameters
Domain
Material AirIdeal Gas
Reference Pressure 1 atm
BuoyancyModel NonBuoyant
FluidModel
Heat Transfer Total Energy
FluidModel k-epsilon
Wall Function Scalable
InletVelocityComponents
Axial 0 m/s
Radial 133.0167212 m/s
Theta -252.7161518 m/s
InletBoundary Detail
Turbulence Medium(Intensity=5%)
Heat Transfer- Static Temperature 361.61 K
Exit Conditions
StaticPressure 224824.58 Pa
24. 24
Figure 8. Impeller exit velocity vector diagram.
Each design was analyzed over one stator section in order to decrease computation time.
Then the results were mapped over the whole domain of the diffuser to create an approximate
solution of the flow. Figure 9 shows the pressure contour of the two designs. Figure 10 shows the
pressure contour with a streamline plot overlay of the two designs. Figure 11 shows the total
pressure at outlet, and Figure 12 shows the Mach number carpet plots along the midline of the
passage.
25. 25
Figure 9. Total pressure carpet plots of the original diffuser (left) vs. redesigned diffuser
(right).
26. 26
Figure 10. Total pressure carpet plot and streamline plots of original diffuser (left) vs.
redesigned diffuser (right).
Figure 11. Total pressure at exit of the original diffuser (left) vs. redesigned diffuser (right).
27. 27
Figure 12. Mach number carpet plots at midline of radial stator passage: original diffuser
(left) vs. redesigned diffuser (right).
Figure 13. Yplus carpet plots for original (left) and redesigned (right) diffusers.
Looking at Figure 9, the effect of changing the angle of the first set of stators to equal the
alpha angle (zero incidence angle) results in a more even static pressure distribution in the first
stator section, and a higher static pressure in the second stator section. Figure 10 shows the
streamlines of the new design are much straighter as they enter the second set of stators which
suggests the flow is less turbulent. This is good for efficiency because it reduces the total
pressure loss. The most important indication that the redesigned diffuser increases the efficiency
of the compressor is shown in Figure 11. This figure shows the total pressure at the exit plane of
the diffuser. The total pressure at the exit of the redesigned diffuser appears to be much higher
than the original diffuser design. The values of the average total pressure at inlet and outlet, and
the resulting total pressure loss, is tabulated in Table 10. It is important to note that to increase
diffuser efficiency, it is desirable to minimize total pressure losses.
28. 28
Table 10 - Average Total Pressure Loss in Diffusers
Total Pressure Loss
Original Redesign
Total Pressure In(Pa) 331701 324911
Total Pressure Out(Pa) 264865 263003
Total Pressure Loss(Pa) 66836 61908
Decrease in Total Pressure Loss (%) 7.373271889
Table 11 – Loss Coefficient of Diffuser Designs
Loss Coefficient of Diffuser Designs
Original Redesign
Total Pressure In(Pa) 331701 324911
Total Pressure Out(Pa) 264865 263003
StaticPressure In(Pa) 199812 196146
𝜔̅ 0.50676 0.480783
𝜔̅ =
𝑃𝑡 𝑖𝑛 − 𝑃𝑡 𝑜𝑢𝑡
𝑃𝑡 𝑖𝑛 − 𝑃𝑠 𝑖𝑛
Table 12 – Static Pressure Coefficients of Designs
Pressure Coefficient
Original Redesign
Cp 0.53362 0.51433
29. 29
Figure 14. Area ratio vs length to width ratio for diffuser designs.
Looking at Table 10, the redesigned diffuser decreases the total pressure loss by 3%
compared to the original diffuser. However, the inlet flow profile used in the simulations was
uniform. Normally the inlet flow profile is turbulent. The actual losses will be higher because of
the actual non-uniform incoming velocity and total pressure profiles. Therefore, these results are
only a comparison of the diffusion performance of each design. Table 11 reiterates the total
pressure loss savings of the new device. The loss coefficient (𝜔̅) of the redesigned diffuser is
0.48 while the loss coefficient of the original diffuser is 0.51. A lower loss coefficient represents
a design with fewer losses.
Looking at Figure 14, the redesigned diffuser falls within the red area while the original
diffuser falls within the green area. The regions lie between pressure coefficient values of .5 and
.6 which supports the calculated pressure coefficient for the redesigned diffuser in Table 12 (cp =
.51433)
30. 30
Part 5: Conclusions and Recommendations
The purpose of this senior design project was to improve the efficiency of the compressor
in a JetCat P-90 turbine engine. Specifically, its efficiency while it was operating at military
power. Drawing from the work of Cumpsty, it was determined that the area of interest for the
redesigned diffuser was minimizing the incidence angle of the incoming flow on the first set of
stators and reducing the number of radial stators from 15 to 12 in order to minimize blockage. A
rounded edge was also added to the pressure side of the radial stators to minimize turbulence that
occurs after the flow leaves the first stators. Finally, a splitter was used in the flow passage
between the first set of stators. Using CFX to simulate both the original and redesigned diffusers
with identical mesh properties and solution models, the redesigned diffuser improved the
efficiency. Specifically, the original diffuser had a total pressure loss of 61,908 Pa while the
original diffuser had a total pressure loss of 66,836 Pa (7.4% improvement). Additionally, the
redesigned diffuser had a loss coefficient of 0.48 compared to 0.51 for the original diffuser.
However, the inlet flow profile used was uniform so this is simply a comparison of the diffuser
performance under the same circumstances. The results support the theoretical predictions from
the Cumpsty material as well as the NASA document. However, the design does not meet the
geometry constraints of the locations of the screw holes. Therefore, this design will only work in
a theoretical sense.
31. 31
References
1Cumptsy, N. A., Compressor Aerodynamics. Krieger Pub, Florida. 2004. Chap 7.
2JetCat P-90RXI. BVM Jets. 2014. Available from: http://www.bvmjets.com/Pages/p90rxi.htm
via the Internet. Accessed 11 Nov 2014.
3Frenk, Abraham PHD. A slip factor calculation in centrifugal impellers based on linear cascade
data. 2005. http://tx.technion.ac.il/~jetlab/6thsmp/frenk.pdf.
4Jian-hua Gao and Ying-yun Huang. Modeling and Simulation of an Aero Turbojet Engine with
GasTurb. Proceedings of the 2011 International Conference on Intelligence Science and
Information Engineering (ISIE '11). IEEE Computer Society, Washington, DC. 2011. p. 295-
298. http://dx.doi.org/10.1109/ISIE.2011.149
5Kalpakli, Athanasia. Experimental Study of Turbulent Flows Through Pipe Bend. Royal
Institute of Technology, 2012.
6Medic, Gorazd et. al. High Efficiency Centrifugal Compressor for Rotorcraft Applications.
NASA Glenn Research Center, Cleveland, OH. 2014.
7Japikse, David. Introduction to Turbomachinery. Oxford University Press. Oxford, NY. 1997. p.
8-21
32. 32
Appendix A: Flow Calculation Code
clc
clear all
close all
%Station 2 is the impeller inlet
%Station 3 is the impeller exit
%Station 4 is the radial diffuser exit
g = 9.81; %m/s^2
R = 287; % J/kg*K
gam = 1.4;
Tt2 = 294.44; %Kelvin
Pt2 = 101325; %Pascals
RPM = 125000; %Full Power
w = RPM*2*pi()/60; %Impeller radial Velocity
rt = .02313178; %tip radius in meters
rh = .0075565; %hub radius in meters
re = .033147; %exit radius in meters
bd = .0049276; %blade height at exit in meters
m = .2376824; %kg/s
u = w*re;
eta = .75; %Overall efficiency
PRcomp = 2.277; %Overall Compressor PR
% PRdiff = .975; %Estimated Diffuser PR
Cp = 1004.5; %Metric Units
Wimp = Cp*Tt2*(PRcomp^((gam-1)/gam)-1)/eta; %Impeller Work
A = pi()*(rt^2-rh^2);
pv = m/A;
%Just roll with it...
ei = .9; %Impeller Efficiency
PRimp = ((ei*Wimp)/(Cp*Tt2)+1)^(gam/(gam-1)); %Estimated Impeller PR
%Making assumptions about these efficiencies based off of Compressor
%Aerodynamics book
%% Inlet Conditions
i=1;
M(i)=.38745;
Ca(i)=133.2676;
rho(i)=1.199;
T2(i)= Tt2;
P2(i) = Pt2;
for i=1:20
T2(i+1) = Tt2-(Ca(i)^2)/(2*Cp);
P2(i+1) = Pt2*(T2(i+1)/Tt2)^(gam/(gam-1));
rho(i+1) = P2(i)/(R*T2(i+1));
Ca(i+1) = pv/rho(i+1);
M(i+1) = Ca(i+1)/sqrt(gam*R*T2(i+1));
i=i+1;
end
fprintf('Impeller entrance conditions: n')
33. 33
fprintf('Static Pressure 2 = %.2f Pa n', P2(end))
fprintf('Static Temperature 2 = %.2f K n', T2(end))
fprintf('Mach Number 2 = %.6f n n', M(end))
%% Impeller Exit Conditions
Tt3 = Wimp/Cp + Tt2;
Pt3 = PRimp*Pt2;
pcr = m/(2*pi()*re*bd);
Ct = Wimp/u;
i=1;
rho3(i) = Pt3/(R*Tt3);
Cr(i) = pcr/rho3(i);
T3(i) = Tt3;
P3(i) = Pt3;
C3(i) = sqrt(Cr(i)^2+Ct^2);
for i=1:20
T3(i+1) = Tt3-(C3(i)^2)/(2*Cp);
P3(i+1) = Pt3*(T3(i+1)/Tt3)^(gam/(gam-1));
rho3(i+1) = P3(i)/(R*T3(i+1));
Cr(i+1) = pcr/rho3(i+1);
C3(i+1) = sqrt(Cr(i+1)^2+Ct^2);
M3(i+1) = C3(i+1)/sqrt(gam*R*T3(i+1));
i=i+1;
end
C3u = Ct; %Cu or C theta component
alpha = acosd(C3u/C3(end));
wrel = sqrt(Cr(end)^2+(u-Ct)^2);%Relative Velocity component
beta = acosd((u-C3u)/wrel);
Mrel= wrel/sqrt(gam*R*T3(end));
fprintf('Impeller exit velocity triangles: n')
fprintf('Angle alpha is %.2f degrees n', alpha)
fprintf('Angle beta is %.2f degrees n', beta)
fprintf('Relative Mach Number 3 is %.4f n n', Mrel)
fprintf('Impeller exit conditions; n')
fprintf('Static Pressure 3 = %.2f Pa n', P3(end))
fprintf('Static Temperature 3 = %.2f K n', T3(end))
fprintf('Total Pressure 3 = %.2f Pa n', Pt3)
fprintf('Total Temperature 3 = %.2f K n', Tt3)
fprintf('Mach Number 3 = %.6f n n', M3(end))
%% Vaneless Diffuser
VanelessEf = .98;
Pt4 = VanelessEf*Pt3;
Tt4 = Tt3;
Avanedinlet =.00075; %.001469451
%diameter is 2.61 inches
pv4 = m/Avanedinlet; % rho*velocity, continuity
rr = .90629; %r3/r4 (radii)
i=1;
34. 34
Ct4 = rr*Ct; %C_Theta at vaneless exit
Cr4(i) = .9*rr*Cr(end); % radial velocity component
rho4(i) = rho3(end);
T4(i) = Tt4-((Cr4(i))^2/(2*Cp))-(Ct4^2/(2*Cp));
P4(i) = Pt4*((T4(i)/Tt4)^(gam/(gam-1)));
for i=1:20
T4(i+1) = Tt4-((Cr4(i))^2/(2*Cp))-(Ct4^2/(2*Cp));
P4(i+1) = Pt4*((T4(i+1)/Tt4)^(gam/(gam-1)));
rho4(i+1) = P4(i)/(R*T4(i+1));
Cr4(i+1) = (rho3(end)/rho4(i))*rr*Cr(end);
end
C4 = sqrt(Cr4(end)^2+Ct4^2);
M4 = C4/sqrt(gam*R*T4(end));
fprintf('Vaneless diffuser exit conditions: n')
fprintf('Static Pressure 4 = %.2f Pa n', P4(end))
fprintf('Static Temperature 4 = %.2f K n', T4(end))
fprintf('Total Pressure 4 = %.2f Pa n', Pt4)
fprintf('Total Temperature 4 = %.2f K n', Tt4)
fprintf('Mach Number 4 = %.6f n n', M4)
%% Vaned Radial Diffuser
%inlet diameter of 2.88 inches
%exit diameter of 3.83 inches
Vanedef = .94;
Avanedexit = .000919353; %.00121
Pt5 = Pt4*Vanedef;
Tt5 = Tt4; %Assumption adiabatic
pv5 = m/Avanedexit;
% AA = Avanedinlet/Avanedexit; %A4/A5 (Area ratio)
AA = .752;
i=1;
Ct5 = AA*Ct4; %C_Theta at vaneless exit
Cr5(i) = .9*AA*Cr4(end); % radial velocity component
rho5(i) = rho4(end);
T5(i) = Tt5-((Cr5(i))^2/(2*Cp))-(Ct5^2/(2*Cp));
P5(i) = Pt5*((T5(i)/Tt5)^(gam/(gam-1)));
for i=1:20
T5(i+1) = Tt5-((Cr5(i))^2/(2*Cp))-(Ct5^2/(2*Cp));
P5(i+1) = Pt5*((T5(i+1)/Tt5)^(gam/(gam-1)));
rho5(i+1) = P5(i)/(R*T5(i+1));
Cr5(i+1) = (rho4(end)/rho5(i))*AA*Cr(end);
end
C5 = sqrt(Cr5(end)^2+Ct5^2);
M5 = C5/sqrt(gam*R*T5(end));
fprintf('Vaned radial diffuser exit conditions: n')
fprintf('Static Pressure 5 = %.2f Pa n', P5(end))
fprintf('Static Temperature 5 = %.2f K n', T5(end))
35. 35
fprintf('Mach Number 5 = %.6f n', M5(end))
fprintf('Total Pressure 5 = %.2f Pa n', Pt5)
fprintf('Total Temperature 5 = %.2f K n n', Tt5)
%% Vaned Axial Diffuser
Pt6 = 33.463; %psi
Pt6 = Pt6*6894.75729; %Pascals
Tt6 = 703.90; %Rankine
Tt6 = Tt6*0.555555556; %Kelvin
rf1 = .097282/2; %meters
bh1 = .004826; %meters
rf2 = rf1+bh1;
Aed = pi()*(rf2^2-rf1^2); %meters squared
pv6 = m/Aed;
i=1;
M6(i)=M5(end);
C6(i)=C5(end);
rho6(i)=rho5(end);
T6(i)= Tt6;
P6(i) = Pt6;
for i=1:20
T6(i+1) = Tt6-(C6(i)^2)/(2*Cp);
P6(i+1) = Pt6*(T6(i+1)/Tt6)^(gam/(gam-1));
rho6(i+1) = P6(i)/(R*T6(i+1));
C6(i+1) = pv6/rho6(i+1);
M6(i+1) = C6(i+1)/sqrt(gam*R*T6(i+1));
i=i+1;
end
fprintf('Axial Diffuser exit conditions: n')
fprintf('Static Pressure 6 = %.2f Pa n', P6(end))
fprintf('Static Temperature 6 = %.2f K n', T6(end))
fprintf('Mach Number 6 = %.6f n', M6(end))
fprintf('Total Pressure 6 = %.2f Pa n', Pt6)
fprintf('Total Temperature 6 = %.2f K n n', Tt6)
etaaxial = Pt6/Pt5;
fprintf('Axial Diffuser Total Pressure efficiency = %.3f n n', etaaxial);
overall = etaaxial*Vanedef*VanelessEf*ei;
fprintf('Overall Total Pressure Efficiency = %.4f n', overall);
36. 36
Work Split & Lessons Learned
James Feldhacker
- Cumpsty summary (rough draft)
- CAD Model Creation
- original design
- proposed designs
- final design
- CFD Analysis
- CFD Post Processing
- Presentation
- Report writing
- CFD sections
- Miscellaneous revising
Before this project, I had never had experience with a research project that was this extensive.
Coming into the project, I had very little knowledge of turbomachinery and no experience with
CFD software. It was a significant challenge to become familiar enough with turbomachinery to
be able to perform an optimization research project on it. Most of our problems as a group came
from poor coordination. As the team leader I take that upon myself. Fortunately, we were able to
acknowledge this lack of coordination and were able to function more efficiently as a group for
the second semester of this project. Perhaps this is the most vital lesson learned; effective
teamwork. Finally, I learned how to use CFD software to a point where I can say that I am
comfortable modeling at an intermediate level.
37. 37
Nick Staikoff
- Created and compiled team presentations
- Cumpsty summary (wrote final draft)
- Assisted with Matlab coding
- CAD Modeling
- Assisted with conceptual designs
- Report Writing
- Introduction
- Assisted with Literature Review
- Conceptual Design Selection
- GasTurb Analysis Discussion
I feel that I gained a lot of useful knowledge and experience from being involved in this project.
Some of the most valuable things to me include an increased understanding and familiarity of
turbomachinery, learning how to use CFD, and increasing my skills and experience with
SolidWorks part designs and MATLAB coding.
Prior to this project, we had very limited exposure to turbomachinery. The only real experience
in this field that I had prior was my co-op experience, so this course greatly helped me
understand and apply first-hand the concepts and theory of designing a gas turbine engine. This
growth in turbomachinery knowledge is due in a large part to learning how to run CFD and
interpret the analysis. CFD is a vital aspect of designing a compressor, so I feel that I definitely
took some great knowledge away from working with it. Aside from running CFD, I was able to
improve my skills in SolidWorks and MATLAB skills by creating diffuser redesigns and helping
with the code to find flow properties.
38. 38
Ryan Schwartzwalder
- Slip Factor
- Cumpsty Summary
- Matlab Coding
- Blockage research
- Proposed Redesigns of Compressor
- Length to width ratio research and calculations
- Area ratio calculations
- Presentation
- CAD Modeling
- Conceptual Designs
- Proposed Designs
- Report Writing
- General Editing
- Abstract
- Literary Review Assistance
One of the biggest things I've learned in Engine Design is how the flow see the passage. This is a
big deal as it changes the effective area of the flow. Using the literature I was able to see how the
area ratio vs length over the width of the diffuser showed the stall ranges. The JETCAT P90 is a
small engine so the area ratio was small thus leading the redesign into the no appreciable stall
range. This was the ideal range for our redesign to be in as it shows there is very little stall in our
engine which would help the pressure recovery and total pressure loss.
Another thing I've learned from reading the literature is matching the incidence angle is not the
only thing that will help total pressure loss. When the incidence angles were matched on our
redesign the effective area decreased. This allowed for more blockage which hindered the
amount of flow going the diffuser. This lead to the redesign losing total pressure which is the
opposite of what a diffuser wants to do. The diffuser wants to limit the amount of loss for total
pressure. So matching only the incidence angle wouldn't help but also to decrease the vanes to
open up the passage. But opening the passage too much would cause stall so there is a fine
margin of the area ratio and the performance map helped us determine the best outcome.
Also meeting with James helped my knowledge of CFD. I now know the basics of CFD what a
good mesh looks like and what inflation layers do and put in initial conditions to run CFD. I was
able to learn some of the methodology built into the CFD code and how changing the CFL
number will help a solution based on the convergence of the model.
39. 39
Frank Mitchell
- Proposed Redesigns of Compressor
- Blockage research
- Cumpsty Summary
- Matlab Coding
- Length to width ratio research and calculations
- Area ratio research and calculations
- Slip Factor
- Presentation
- Report Writing
- General Editing and Review
In doing this senior project to increase the efficiency of a centrifugal compressor the most
interesting part for me has been boundary layers. Learning how they affect the flow in how
adapting them can help or hurt your efficiency. Figuring out different ways to make the boundary
layers as small as possible in order to cause the least amount of blockage to the flow has taken a
lot of research. However from all of this research it has been very interesting to see all the
creative ways engineers have come up with to reduce the boundary layer. Such as changing the
shape of the stators and reducing the number of stators all to allow as much flow through the
compressor as possible.
Daniel Hoffman
- Cumpsty Summary
- Research for valid References
- Proposed Redesigns of Compressor
- Length to width ratio research and calculations
- Area ratio research and calculations
- Boundary layer research
- Presentation
- Report Writing
- General Editing and Review
- Literature Review
- JetCat P-90RXI
- Compressor Aerodynamics
This project that I have taken upon presented different challenges and learning experiences.
Throughout these past few weeks I have had to become comfortable with the many different
tactics and theories on how to increase the efficiency of the centrifugal compressor. Working
with the compressor made me familiar with the workings and appreciate the importance of each
of its parts; particularly, with its two main (axial and centrifugal). I learned how to find ways to
keep the pressure loss at its minimum and how the impeller allows the flow to change direction
and convert to axial to radial flow. I learned how the diffuser also slows the flow down to
increase the pressure, and eventually allows more thrust to be created when the flow enters the
combustor. I learned about the factors to consider, such as vanes and incidence angles, and how
they can be optimized. This class made me really look into various conceptual designs for
increasing overall efficiency.
40. 40
Michael Begovich
- Research for Redesign Ideas
- Proposed Redesigns of Compressor
- Length to width ratio research
- Area ratio research
- Boundary layer research
- Presentation
- Report Writing
- General Editing and Review
- Equations and Assumptions
I learned that it can be difficult working with a team, and that effective teamwork greatly
increases the team’s performance. Prior to this project, I had little knowledge of turbomachinery
and was unfamiliar with CFD software. I take away from this project a much deeper
understanding of turbomachinery and am familiar enough with CFD to be able to execute
simulations at a beginner’s level.