Optimal Bass Reflex Loudspeaker Port Design Andri Bezzola | Samsung Research America | Audio Lab 2019/10/03 2019 COMSOL Conference | Boston, MA | 10/03/2019 | Andri Bezzola
Optimal Bass Reflex Loudspeaker Port Design
Andri Bezzola | Samsung Research America | Audio Lab2019/10/03
2019 COMSOL Conference | Boston, MA | 10/03/2019 | Andri Bezzola
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Loudspeaker Ports
• Mass of air in port and compliance of air in enclosure form a resonator
• Bass reflex (vented) can be abstracted to a 2-Mass-Spring-Damper System
• Excursion of the diaphragm is reduced compared to a sealed box with same SPL
• Nonlinear distortions are reduced
Displacement (mm)
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Turbulence, Vortex Shedding, and Port Noise
• At high output, air in port tube can become turbulent
• Flow separation and vortex shedding occurs
• Experience tells us that continuously flared port tubes sound better
• How much flare is optimal?
• Fully turbulent models are numerically expensive and impractical as design tools
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Flow Separation and Vortex Shedding
𝑢𝜕𝑢
𝜕𝑠= −
1
𝑝
𝑑𝑝
𝑑𝑠+ 𝜈
𝜕2𝑢
𝜕𝑦2
Stream-wise momentum equation:
• Adverse pressure gradient when 𝑑𝑝
𝑑𝑠> 0
• 𝑢 can become zero or negative
• Flow separation leads to vortex shedding
• Impulse-like excitation of air in port tube
• Excitation of port eigenfrequencies
𝑓𝑝1 =
𝑐
𝜆≈
𝑐
2𝐿
Effect of flow separation:
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Old Research Revisited
• Which port profile has the lowest propensity to generate turbulence, flow separation, and vortex shedding?
• Simulated 4 port geometries from Rapoport and Devantier [1]
Velocity Contours
[1] Rapoport, Z. and Devantier, A., “Analysis and Modeling of the Bi-Directional Fluid Flow in Loudspeaker Ports,” in Audio Engineering Society Convention 117, San Francisco, (2004)
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Hypothesis
“The best sounding port has the lowest
propensity for flow separation.
Flow separation is minimal when the
particle velocity contours at port exit have
minimal curvature.”
Plan for Verification of Hypothesis
• Design ‘optimal’ ports of different 𝐿/𝐷0aspect ratios
• Construct slightly under- and over-flared ports
• Maintain tuning frequency for all ports
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• Near-field hemi-anechoic measurements
• Measure noise induced by ports
• Correlation with hypothesis and simulation?
Simulation Measurement
• Near-field recordings
• Double-blind playback through high-end headphones
1. Rating of sound quality
2. How much louder can optimal ports play?
• Correlation with hypothesis, simulation, and measurements?
Blind Listening Tests
Simulation Setup
• Axisymmetric
• Acoustic-structure interaction
• Electrical circuit model for loudspeaker driver
• 3 optimization routines
1. Find box volume for 40 Hz tuning
2. Find optimal flare rate
3. Find slightly over- and under-flared profiles with same 40 Hz tuning
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PML
PML
Enclosure
Port
Driver 1 Driver 2
Internal Wall
Mounting Baffle
Port Exit Flange
Simulation Results
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59 mm 61 mm57 mm Straight with blends
Straight no blends
3:1(L = 180 mm)
4:1(L = 240 mm)
Measurements
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• Hemi-anechoic (2𝜋) chamber
• 2 x 10-inch woofers
• Near-field measurement with G.R.A.S 46 AM microphone
• Signal: Multi-sine from 20 Hz to 80 Hz for 3:1 ports, 40 Hz sine for 4:1 ports
Measurement Results3:1 Ports
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Measurement Results4:1 Ports
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Double-Blind Listening Tests
• 3 different sound files with fundamental at 40 Hz
– Kick drum
– Whale drum
– Bass guitar
• Recorded at 4, 20, 40, 60 V
• Playback through headphones, normalized for loudness
• Preference scale 0-100
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• Whale drum signal
• Reference is 59 mm port at 52 V
• Adjust drive level until port noise is equally objectionable
Preference Test Method of Adjustment Test
Whale drum examples at 52 V:
59 mm 61 mm57 mm Straight with blends
Straight no blends
Listening Test Results
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Preference Test Method of Adjustment Test
Conclusions
• Optimal amount of flare is now predictable!
• Acoustic simulations are fast and amenable for optimization
• Simulations, measurements, and listening tests correlate and validate the hypothesis:
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“The best sounding port has the lowest propensity
for flow separation.
Flow separation is minimal when the particle velocity
contours at port exit have minimal curvature.”
• Optimally flared ports can be played >10 dB louder than straight ports!
• Optimally flared ports can be played >1 dB louder than slightly under- or over-flared ports
Thank you!
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Andri Bezzola
https://www.linkedin.com/in/andribezzola/
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Listening Test Results
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Preference Test Method of Adjustment Test
Different PortsPort 57 mm 59 mm 61 mm
Straight w/ blends
Straight no blends
57 mm 59 mm 61 mm
Aspect Ratio 3:1 3:1 3:1 3:1 3:1 4:1 4:1 4:1
Length [mm] 180 180 180 180 180 240 240 240
Dc [mm] 57 59 61 69 69 57 59 61
De [mm] 177 117 97 69 69 150 126 102
Rb [mm] 8.4 8.4 8.4 8.4 - 10.1 10.1 10.1
Vbox [L] 30.6 30.6 30.6 30.6 30.6 24.6 24.6 24.6
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