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Wave motion in a cylindrical cavity due to localized heat addition Ram Prasad Mushini ME03B049 Guide: Prof K.Ramamurthi
When a heat source is placed inside the tube, energy is added to the standing wave. The heat augments the standing wave leading to loud sound. The assembly of the tube and the heat source is called Rijke tube. L>10D to ensure that the acoustic waves are one dimensional in nature In the present experiments L=160cm, D=10cm.
Literature review
Shekhar M Sarpotdar, N Ananthkrishnan and S D Sharma (Jan 2003). Construction of the Rijke tube Mechanism behind the thermo-acoustic phenomenon, 2 Problems of current industrial interest: 1. Rocket engine combustors 2.Jet engine combustors. K.R.Sreenivasan and S.Raghu (Sep 2000). 3π 1 1 lags by (approx.) Q u 8 Control of pressure oscillations by heat release
Konstantin Matveev (PH.D Thesis, California Institute of technology,Feb2003).
Used an electric heater in a horizontal tube and provided mean flow using a blower. Found out the stability boundary of the thermo-acoustic oscillation in the Rijke tube. Scope of the present work: Even though lot of work has been done on Rijke tube, the following are not clear: a) Critical conditions for which oscillations get excited. b) Factors by which the oscillations can be damped out. c) Frequencies of oscillations.
Experimental Set-up
The tube is mounted vertically on a stand. Mesh is the heating element. Bunsen burner is used to heat the mesh. The mesh is suspended by a wire passing over a pulley fixture at the upper end. A measuring scale is fitted to the frame of the pulley fixture.
Pulley
Wire
Rijke tube Scale
Pulley fixture and attachments
Hardware made
The burner height has been increased by 14cm by brazing. Heating element: 10 Wire meshes stacked and made into a tight unit Perforations were made on Mylar sheets. These sheets are folded and inserted inside the tube from the upper end so that the inner surface of the tube acts like a Rough surface. A horn of conical shape was made from a thick paper
Burner Brazing done here
Burner with increased height
A perforated sheet
Mike held at upper end
Measurement devices, Software used
Sigview was used for analysis on the recorded signal. K-type thermocouple Data Acquisition Unit (DAU) Mike A PCB sensor is used for the calibration purposes
Calibration of sound The microphone was calibrated against a standard. measured
A sinusoidal signal was generated using MATLAB For a few SPL’s, the data recorded from the mike and PCB sensor were compared. 1000 units on SIGVIEW correspond to 0.4 Pa
Experiments done
Experiments done with: i) Varying the initial mesh temperature and its position along the tube. ii) Varying the roughness of the pipe. iii) Placing an horn over tube.
Major Results
Growth of oscillations
Variation of temp. of mesh
Experiments were done by placing the mesh at L/4 position for which maximum amplitude of oscillations were obtained. Initial Temperature of mesh : 180 °C, 207 °C, 237 °C, 270 °C , 290 °C. The maximum pressure amplitude increases with the temperature initially fast and then saturates.
In all the results it is seen that the amplitude of the wave building up during the initial phase and decaying later. The amplitude of the wave written as: P = P0 eαt e iωt
αg
αd
:Growth constant(1/sec). :Decay constant(1/sec)
α g increases with increase in initial mesh temperature. α did not vary to any significant level with initial d
temperature of the mesh because in all the cases the inner surface remained unchanged.
The net growth α = α g + α d also increases. However, it is not linear. The net growth does not increase in proportion to the increase in the temperature driving the oscillation.
Harmonic content
FFT (Fast Fourier Transform) analysis is performed on the recorded sound signal. Frequencies are seen to be 109Hz,2x109Hz and 3x109Hz. The higher harmonics have decreasing amplitudes for all positions of mesh along the tube.
The fundamental frequency of 109Hz corresponds to the standing wave obtained with the tube open at both ends.
End correction =0.3D =0.3 x 10=3 cm
Effective length of the open-open tube (Leff ) = 160 + 3 = 163 cm c =2L eff
Fundamental frequency of the tube
= 101 Hz
The observed frequency however is higher at 109 Hz. This higher value is because of the higher temperature of air in the pipe.
T=207 °C
T=237 °C
T=270 °C
T=290 °C
Amplitude-Frequency spectra with different initial mesh temperatures
A sub-harmonic at 48 Hz is seen . Since the frequency of 48 Hz is about half the fundamental, it seems likely that 48 Hz comes from the open end partially acting as a closed end. Open end acting as a partially closed such a frequency is possible.
Varying the roughness of the The surface roughness of the pipe wall is varied and the pipe role of roughness has been analyzed.
Mylar sheets are folded and inserted inside the tube, so that the surface of the tube is smooth. When experiments were done with mesh at X=L/4,the SPL and the duration of sound remained almost same. Smoothening of walls does not change the SPL.
Mylar sheets covering the upper half
Rough surfaces were made by making perforations on the Mylar sheet. Three types of rough surfaces were used: i) Mylar sheet with 0.9 cm perforation height. ii) Mylar sheet with wedge like projections with asperity height of 1.9cm. iii) Sand paper BD-50. Experiments were done with the mesh at L/4 position and 207 °C For each type of Rough surface used the % of area covered were varied.
Mylar sheets with 0.9cm perforation
Top view after the sheets are inserted
Wedge like perforations with height 1.9 cm
Top view when perforated sheets were inserted
Top-view after the sand paper sheets are inserted
As the perforation height increased the Sound Pressure Level recorded decreased. As the % of area covered is increased, the SPL decreases. pressure amplitude vs.
Pressure amplitude (Pa)
height of perforations
16
12
Drop in pressure amplitude
8
4
0 0
12.5
25
% of surface covered
37.5
αg
decreases with increase in surface area covered and roughness α d increases with increase in surface area covered and roughness
Variation of growth constant
Variation of decay constant
The value α = α g + α d is the net growth because during the growth of wave motion damping is also present The net growth is seen to be nearly constant since in all the experiments the same driving force or temperature for driving the oscillations was employed.
Variation of net growth constant
Horn mounted at the upper A conical horn was made from thick paper and mounted end
on the upper end of the tube. No sound was produced by the tube. When a horn is introduced, the incident wave is radiated out and a standing wave formed is not formed.
Horn
Conclusions
Placement of a horn over the tube prevents pressure amplitudes being generated since a standing wave is no longer generated with the horn placed at the open end. A minimum temperature of 170°C is seen essential to trigger pressure oscillations in the tube considered when the wall surface is smooth. Introduction of surface roughness increase α d and keeping α same At higher values of heat release rates, additional frequency corresponding to upper end of the tube acting as a close end is seen.
When a heat source is placed inside the tube, energy is added to the standing wave. The heat augments the standing wave leading to loud sound. The assembly of the tube and the heat source is called Rijke tube. L>10D to ensure that the acoustic waves are one dimensional in nature In the present experiments L=160cm, D=10cm.
Literature review
Shekhar M Sarpotdar, N Ananthkrishnan and S D Sharma (Jan 2003). Construction of the Rijke tube Mechanism behind the thermo-acoustic phenomenon, 2 Problems of current industrial interest: 1. Rocket engine combustors 2.Jet engine combustors. K.R.Sreenivasan and S.Raghu (Sep 2000). 3π 1 1 lags by (approx.) Q u 8 Control of pressure oscillations by heat release
Konstantin Matveev (PH.D Thesis, California Institute of technology,Feb2003).
Used an electric heater in a horizontal tube and provided mean flow using a blower. Found out the stability boundary of the thermo-acoustic oscillation in the Rijke tube. Scope of the present work: Even though lot of work has been done on Rijke tube, the following are not clear: a) Critical conditions for which oscillations get excited. b) Factors by which the oscillations can be damped out. c) Frequencies of oscillations.
Experimental Set-up
The tube is mounted vertically on a stand. Mesh is the heating element. Bunsen burner is used to heat the mesh. The mesh is suspended by a wire passing over a pulley fixture at the upper end. A measuring scale is fitted to the frame of the pulley fixture.
Pulley
Wire
Rijke tube Scale
Pulley fixture and attachments
Hardware made
The burner height has been increased by 14cm by brazing. Heating element: 10 Wire meshes stacked and made into a tight unit Perforations were made on Mylar sheets. These sheets are folded and inserted inside the tube from the upper end so that the inner surface of the tube acts like a Rough surface. A horn of conical shape was made from a thick paper
Burner Brazing done here
Burner with increased height
A perforated sheet
Mike held at upper end
Measurement devices, Software used
Sigview was used for analysis on the recorded signal. K-type thermocouple Data Acquisition Unit (DAU) Mike A PCB sensor is used for the calibration purposes
Calibration of sound The microphone was calibrated against a standard. measured
A sinusoidal signal was generated using MATLAB For a few SPL’s, the data recorded from the mike and PCB sensor were compared. 1000 units on SIGVIEW correspond to 0.4 Pa
Experiments done
Experiments done with: i) Varying the initial mesh temperature and its position along the tube. ii) Varying the roughness of the pipe. iii) Placing an horn over tube.
Major Results
Growth of oscillations
Variation of temp. of mesh
Experiments were done by placing the mesh at L/4 position for which maximum amplitude of oscillations were obtained. Initial Temperature of mesh : 180 °C, 207 °C, 237 °C, 270 °C , 290 °C. The maximum pressure amplitude increases with the temperature initially fast and then saturates.
In all the results it is seen that the amplitude of the wave building up during the initial phase and decaying later. The amplitude of the wave written as: P = P0 eαt e iωt
αg
αd
:Growth constant(1/sec). :Decay constant(1/sec)
α g increases with increase in initial mesh temperature. α did not vary to any significant level with initial d
temperature of the mesh because in all the cases the inner surface remained unchanged.
The net growth α = α g + α d also increases. However, it is not linear. The net growth does not increase in proportion to the increase in the temperature driving the oscillation.
Harmonic content
FFT (Fast Fourier Transform) analysis is performed on the recorded sound signal. Frequencies are seen to be 109Hz,2x109Hz and 3x109Hz. The higher harmonics have decreasing amplitudes for all positions of mesh along the tube.
The fundamental frequency of 109Hz corresponds to the standing wave obtained with the tube open at both ends.
End correction =0.3D =0.3 x 10=3 cm
Effective length of the open-open tube (Leff ) = 160 + 3 = 163 cm c =2L eff
Fundamental frequency of the tube
= 101 Hz
The observed frequency however is higher at 109 Hz. This higher value is because of the higher temperature of air in the pipe.
T=207 °C
T=237 °C
T=270 °C
T=290 °C
Amplitude-Frequency spectra with different initial mesh temperatures
A sub-harmonic at 48 Hz is seen . Since the frequency of 48 Hz is about half the fundamental, it seems likely that 48 Hz comes from the open end partially acting as a closed end. Open end acting as a partially closed such a frequency is possible.
Varying the roughness of the The surface roughness of the pipe wall is varied and the pipe role of roughness has been analyzed.
Mylar sheets are folded and inserted inside the tube, so that the surface of the tube is smooth. When experiments were done with mesh at X=L/4,the SPL and the duration of sound remained almost same. Smoothening of walls does not change the SPL.
Mylar sheets covering the upper half
Rough surfaces were made by making perforations on the Mylar sheet. Three types of rough surfaces were used: i) Mylar sheet with 0.9 cm perforation height. ii) Mylar sheet with wedge like projections with asperity height of 1.9cm. iii) Sand paper BD-50. Experiments were done with the mesh at L/4 position and 207 °C For each type of Rough surface used the % of area covered were varied.
Mylar sheets with 0.9cm perforation
Top view after the sheets are inserted
Wedge like perforations with height 1.9 cm
Top view when perforated sheets were inserted
Top-view after the sand paper sheets are inserted
As the perforation height increased the Sound Pressure Level recorded decreased. As the % of area covered is increased, the SPL decreases. pressure amplitude vs.
Pressure amplitude (Pa)
height of perforations
16
12
Drop in pressure amplitude
8
4
0 0
12.5
25
% of surface covered
37.5
αg
decreases with increase in surface area covered and roughness α d increases with increase in surface area covered and roughness
Variation of growth constant
Variation of decay constant
The value α = α g + α d is the net growth because during the growth of wave motion damping is also present The net growth is seen to be nearly constant since in all the experiments the same driving force or temperature for driving the oscillations was employed.
Variation of net growth constant
Horn mounted at the upper A conical horn was made from thick paper and mounted end
on the upper end of the tube. No sound was produced by the tube. When a horn is introduced, the incident wave is radiated out and a standing wave formed is not formed.
Horn
Conclusions
Placement of a horn over the tube prevents pressure amplitudes being generated since a standing wave is no longer generated with the horn placed at the open end. A minimum temperature of 170°C is seen essential to trigger pressure oscillations in the tube considered when the wall surface is smooth. Introduction of surface roughness increase α d and keeping α same At higher values of heat release rates, additional frequency corresponding to upper end of the tube acting as a close end is seen.
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