Costa, Melissa

Frederick, Robert

Hulka, James

Lineberry, David

Unruh, Evan

Venters, James

Woods, Jessica

NASA Technical Reports Server

Uncertainty Analysis of Experimental Discharge 
Coefficients in Additively Manufactured Liquid 
Injector Elements 
August 19, 2019
James Venters
Undergraduate Research Assistant
University of Alabama in Huntsville
Propulsion Research Center
Co-Authors
Melissa Costa, Evan Unruh, David Lineberry, and Robert Frederick
University of Alabama in Huntsville
Jessica Woods
NASA Marshall Space Flight Center
James Hulka
Jacobs
https://ntrs.nasa.gov/search.jsp?R=20190030455 2019-09-26T18:56:27+00:00Z
Outline
• Introduction
• Facility Overview
• Approach
• Test Matrix
• Hardware Description
• Procedure
• Analysis Methodology
• Uncertainty Results
• Individual Test Articles
• Common Design Variant Across all Manufacturers
• All Design Variants for each Manufacturer
• Design Variant Prediction Interval
• Conclusion
2
Additive Manufacturing
Additive Rocket Engine Components
• Advantages
• Mass Reduction
• Part count reduction
• Reduced assembly time
• Reduced manufacturing costs
• Reduced lead time
• Challenges
• Still a maturing technology
• Small geometric features and 
passages/Large scale parts
• Manufacturing imperfections
• Several successful test programs with 
AM parts.  
3
Hot-fire testing of an Aerojet Rocketdyne RL 10C-X 
prototype engine with 3-D printed core components.  
[1]
Subscale Integral injector 
manufactured with SLM. [2]
1. “3-D Printed RL10C-X Prototype Rocket Engine Soars Through Initial Round of Testing,” Aerojet Rocketdyne Press Release, 
www.rocket.com/article/3-d-printed-rl10c-x-prototype-rocket-engine-soars-through-initial-round-testing, 2019.
2. Soller, S. et. al., “Design and Testing of Liquid Propellant Injectors for Additive Manufacturing,”  7th European Conference for Aerospace Sciences, 
2017.
3. Gradl, P., et. al. “Additive Manufacturing of Liquid Rocket Engine Combustion Devices: A Summary of Process Developments and Hot-Fire Testing 
Results,” 54th AIAA/SAE/ASE Joint Propulsion Conference, 2018.
SLM produced integrated nozzle 
film coolant ring designed and tested 
at NASA. [3]
Objective
• Assess the manufacturer-to-manufacturer variability in flow 
discharge coefficients of identical parts with small flow passages. 
Scope:
• Investigate two internal geometries: 
• 1) Radial-Fed Annulus
• 2) Cavitating Venturi
• Investigate subtractive (baseline) and additive manufacturing (11 
vendors) .
• Cold flow (water) parts over relevant operating regimes
• Perform detailed measurement uncertainty analysis
• Determine  and compare differences in discharge coefficients among 
the manufacturing methods 
4
Facility Overview
PRC Injector Spray Facility 
Non-Reactive, cold flow environments for the 
study of injectors and injection processes in liquid 
injection devices.  
• Pressurized Spray Chamber
• 18” Internal Diameter x 72” Tall
• 500 psig Max Pressure
• Four - 6” Diameter Optical Access Ports
• Atmospheric Spray Bench
• Flow Bench
• Liquid simulant flow rates up to 2 lbm/s (water 
and water based solutions) 
• Gas flow rates up to 1 lb/s (Nitrogen/Compressed 
Air)
• Optical Diagnostic Access:  
• High Speed or Standard Video
• Laser Diagnostics (PIV, PDPA)
• Common DAQ system
• High Speed 1Ms/s
• Integrated adjustable Low Pass Filtering
• Temperature/Static Pressure  (1000Hz) 5
Injector Specifications
• 11 Manufacturers using SLM printers
• 4 Design Variants on the same build plate
• 45 Injectors
• Operating Conditions
• Atmospheric Back Pressure
• Flow Geometry 1
• 75 psig to 550 psig
• 0.5 lb/s to 1.6 lb/s
• Flow Geometry 2
• 50 psig to 1550 psig
• 0.05 lb/s to 0.3 lb/s
6
Flow Geometry 1: Flow Geometry 2:
Radially-Fed Annulus Cavitating Venturi
Design Variant
Radial Hole ID
# of Radial 
Holes
Annulus ID Annulus OD Flow Duct ID Venturi ID
(% of Baseline) (% of Baseline) (% of Baseline) (% of Baseline) (% of Baseline)
1 100 168 100 100 100 100
2 100 168 111.2 100 100 105.3
3 115.8 168 107.5 111.9 100 110.5
4 157.9 67 103.7 100 100 115.8
Baseline 100 168 100 100 100 100
Test Setup
7
 
P
P
P
Pressure 
Supply
Water Tank
0.26" Venturi
0.01" Venturi
DP 
Transducer
Sample 
Holder/
Manifold
Upstream
Pressure
Geo. 1
Upstream
Pressure
Geo. 2
Catch 
Basin
Vent
• Venturis shared common DP Transducer
• Venturi manually selected based on Flow 
rate
• Pressures measured at 1000Hz and 
averaged over 7 seconds of steady state 
flow
Venturis
8
Venturi Calibration
𝐶𝐶𝑑𝑑 = 𝑚𝑚𝑡𝑡2𝜌𝜌∆𝑃𝑃1
𝜋𝜋𝑑𝑑𝑡𝑡
24 2 − 1𝜋𝜋𝑑𝑑124 2
9
Establish single Discharge Coefficient, Cd, 
for each venturi
• In-line, end-to-end calibration
• Timed collection at steady flow
• 18 setpoints (0.10 venturi)
• 12 setpoints (0.26 venturi)
m = mass of collected water
t = collection time
dt = venturi throat diameter
d1 = venturi inlet diameter
ρ = density
ΔP = ventrui pressure drop 
(inlet to throat)
𝜎𝜎 = standard deviation
𝑡𝑡𝛼𝛼,𝜈𝜈= student t distribution
Calculate Setpoint Discharge 
Coefficient (Cd vent)
Calculate Setpoint Discharge 
Coefficient Uncertainty
(UCd vent)
Calculate Average Cd and 
mean Cd Uncertainty for 
Venturi
𝑈𝑈𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠 = 𝐵𝐵𝐶𝐶𝑑𝑑_sp 2 + 1.96𝜎𝜎𝐶𝐶𝑑𝑑_sp𝑁𝑁𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 2
𝐵𝐵𝐶𝐶𝑑𝑑_sp = 𝜕𝜕𝐶𝐶𝑑𝑑𝜕𝜕𝑚𝑚 𝐵𝐵𝑠𝑠 2 + 𝜕𝜕𝐶𝐶𝑑𝑑𝜕𝜕𝑡𝑡 𝐵𝐵𝑡𝑡 2 + 𝜕𝜕𝐶𝐶𝑑𝑑𝜕𝜕𝜌𝜌 𝐵𝐵𝜌𝜌 2 + 𝜕𝜕𝐶𝐶𝑑𝑑𝜕𝜕𝜕𝑃𝑃𝐵𝐵𝛥𝛥𝛥𝛥 2
𝑈𝑈𝐶𝐶𝑑𝑑 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 = � 𝑈𝑈𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 ∗ 𝜎𝜎𝐶𝐶𝑑𝑑 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2
Systematic Uncertainties (B)
𝐶𝐶𝑑𝑑_𝑣𝑣𝑠𝑠𝑠𝑠𝑡𝑡 = 1𝑁𝑁�𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠
Venturi Calibration
0.100” venturi
Cd = 1.015
Ucd = 2.7%
0.02 Lb/s to 0.3 Lb/s
10
0.260” venturi
Cd = 0.984
Ucd = 4.6%
0.1 Lb/s to 2.1 Lb/s
Larger uncertainty at low mass 
flow due to low  ΔP
Testing Procedure
11
Load injector into housing
Set system pressure to 
lowest setpoint
Wait for steady state flow
Trigger Labview
Take data for 7 seconds
Set system pressure for next 
setpoint
Flow Geometry 1 
Design Variant 1
12
• Noted “Clustering”:  4 groups  
• Wide range of mass flow variation at given inlet pressure
• 2 significantly lower performing test articles
• Discontinuous trend for Manufacturer 11
Flow Geometry 1 
Design Variant 1
13
• Linear trends with square root of pressure
Individual Test Article Analysis
14
Calculate mass flow (?̇?𝑚) at 
each setpoint
Calculate mass flow 
Uncertainty at each setpoint
(𝑈𝑈ṁ𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣 )
Calculate Cd for injector at 
each setpoint (𝐶𝐶𝑑𝑑)
ṁ = 𝜋𝜋4 𝐶𝐶𝑑𝑑 𝑣𝑣𝑠𝑠𝑠𝑠𝑡𝑡 𝑑𝑑𝑡𝑡2 2𝜌𝜌𝜕𝑃𝑃
�1 − (𝑑𝑑𝑡𝑡4
𝑑𝑑1
4
𝑈𝑈ṁ𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣 = 𝜕𝜕ṁ𝜕𝜕𝐶𝐶𝑑𝑑 𝑣𝑣𝑠𝑠𝑠𝑠𝑡𝑡 𝑈𝑈𝐶𝐶𝑑𝑑 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 2 + 𝜕𝜕ṁ𝜕𝜕𝜌𝜌 𝑈𝑈𝜌𝜌 2 + 𝜕𝜕ṁ𝜕𝜕𝜕𝑃𝑃𝑈𝑈𝛥𝛥𝛥𝛥 2 + 1.96𝜎𝜎ṁ𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑁𝑁ṁ𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣
2
𝐶𝐶𝑑𝑑 = ṁ
𝐴𝐴𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡 )2𝜌𝜌(𝑃𝑃𝑠𝑠𝑠𝑠 − 𝑃𝑃𝑐𝑐𝑠𝑠𝑣𝑣
?̇?𝑚 = mass flow rate
dt = venturi throat diameter
d1 = venturi inlet diameter
ρ = density
ΔP = ventrui pressure drop 
(inlet to throat)
𝐶𝐶𝑑𝑑 𝑣𝑣𝑠𝑠𝑠𝑠𝑡𝑡= venturi discharge coefficient
𝑃𝑃𝑠𝑠𝑠𝑠 = inlet pressure
𝑃𝑃𝑐𝑐𝑠𝑠𝑣𝑣 = vapor pressure
Calculate Cd for injector 
Uncertainty at each setpoint
(𝑈𝑈𝐶𝐶𝑑𝑑 _sp) 𝑈𝑈𝐶𝐶𝑑𝑑 _sp = 𝜕𝜕𝐶𝐶𝑑𝑑 𝑠𝑠𝑠𝑠𝑖𝑖𝜕𝜕ṁ 𝑈𝑈ṁ 2 + 𝜕𝜕𝐶𝐶𝑑𝑑 𝑠𝑠𝑠𝑠𝑖𝑖𝜕𝜕𝜌𝜌 𝐵𝐵𝜌𝜌 2 + 𝜕𝜕𝐶𝐶𝑑𝑑 𝑠𝑠𝑠𝑠𝑖𝑖𝜕𝜕𝑃𝑃𝑠𝑠𝑠𝑠 𝐵𝐵𝛥𝛥𝑠𝑠𝑣𝑣 2 + 1.96𝜎𝜎𝐶𝐶𝑑𝑑𝑁𝑁𝐶𝐶𝑑𝑑 2
𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 = � 𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 𝜎𝜎𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2
Calculate Average Cd and 
mean Cd Uncertainty for 
each test article
𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠𝑖𝑖 = 1𝑁𝑁�𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠
𝑃𝑃𝑠𝑠𝑠𝑠 = inlet pressure
𝑃𝑃𝑐𝑐𝑠𝑠𝑣𝑣 = vapor pressure
Flow Geometry 1 
Design Variant 1
15
Test Article with 
discontinuous 
mass flow trend
Test Articles with 
significantly lower 
mass flow rates
• Uncertainty ranged from 3% to 6% for 9 of the test articles
• 12%-53% Uncertainty for 3 of the test articles
Flow Geometry 2
Design Variant 1
16
Uncertainty Range:  4%-13%
Common Design Variant Across 
all Manufacturers
17
Calculate average Cd for all 
manufactures for a given 
design variant and flow path
𝐶𝐶𝑑𝑑 = 1𝑁𝑁�𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠𝑖𝑖
𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 = � 𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 𝜎𝜎𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2
Calculate uncertainty of 
average Cd for all 
manufactures for a given 
design variant and flow path
• Geometry 1 uncertainty ranged from 10% to 14%
• Geometry 2 uncertainty ranged from 6% to 10%
Results by Manufacturer
18
Calculate average Cd for all 
design variants for a given 
manufacturer and flow path
𝐶𝐶𝑑𝑑 = 1𝑁𝑁�𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠𝑖𝑖
Calculate uncertainty of 
average Cd for all design 
variants for a given 
manufacturer and flow path
𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 = � 𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 𝜎𝜎𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2
Normalize injector Cd for 
both flow paths 𝐶𝐶𝑑𝑑 𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠 = 𝐶𝐶𝑑𝑑 𝑠𝑠𝑠𝑠𝑖𝑖𝐶𝐶𝑑𝑑 𝑏𝑏𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Results by Manufacturer
19
• Flow geometry 1
• 10 manufacturers ranged from 7%-30%
• 1 manufacturer was 61 %
• Flow geometry 2
• 9 manufacturers ranged from 4%-10%
• 1 manufacturer was 61 %
Normalized Results by 
Manufacturer
20
Predictive Interval Analysis
21
Calculate average Cd for all 
manufacturers for a given 
flow path and geometry 
Calculate uncertainty of 
average Cd for all 
manufacturers for a given 
flow path and geometry 
Calculate the predicted Cd 
for a new injector from the 
same population
𝐶𝐶𝑑𝑑 = 1𝑁𝑁�𝐶𝐶𝑑𝑑_𝑠𝑠𝑠𝑠𝑖𝑖
𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 = � 𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 𝜎𝜎𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠𝑣𝑣𝑣𝑣𝑁𝑁𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 2
𝐶𝐶𝑑𝑑𝛥𝛥𝑡𝑡𝑠𝑠𝑑𝑑𝑠𝑠𝑐𝑐𝑡𝑡𝑠𝑠𝑑𝑑 = 𝐶𝐶𝑑𝑑 ± 𝑈𝑈95 1 + 1𝑛𝑛
Calculate the prediction 
interval for the new injector
𝑈𝑈95 = � 𝑈𝑈𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖𝑁𝑁 2 + 𝑡𝑡𝛼𝛼,𝜈𝜈 𝜎𝜎𝐶𝐶𝑑𝑑 𝑠𝑠𝑣𝑣𝑖𝑖 2
Flow Geometry 1 
Design Variant 1
22
Flow Geometry 2 
Design Variant 1
23
Conclusion
• Flow Geometry1:
• The mean CD of all injectors was 0.16
• Significant mean CD variability depending on the 
manufacturer
• Additive CD’s generally lower than subtractive baseline
• Flow Geometry 2:
• The mean CD of all injectors was 0.80
• Significant mean CD variability depending on the 
manufacturer
• Additive CD’s generally lower than subtractive baseline
• Differences among CD of all injectors are generally 
well beyond the uncertainty bars of the CD results. 
• Manufacturer is more important than slight changes in 
geometry
24


Uncertainty Analysis of Experimental Discharge Coefficients in Additively Manufactured Liquid Injector Elements

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