Exerimental Setu High Seed Camera PCO.dimax, 1 bit Resolution: 1008x1000 ixels @ 4500 fs Resolution: 000x000 ixels @ 1400 fs High Reetition Rate Laser Photonics DM60-57 Nd:YLF Maximum ulse rate - 10 khz Pulse energy: 60mJ at 1KHz Tracer Particles -- Hollow glass sheres, 8-1m Dimensions of Cavity Cavity width (L): 38.1mm Cavity deth (H): 30.0mm Free Stream Seed in Exeriment Flow Direction Leading Edge Cavity Wall Field of View (55 mm) Trailing Edge H=30.0 mm L=38.1 mm 1.15m/s Reynolds Number Re=37,700 (based on cavity width) Image size: 5x5 mm Vector Sacing: 0. mm Interrogation window size: 0.4X0.4 mm
Flow Field of View H=30.0 mm Mean Velocity and Pressure (Ue=1.15 m/s) Based on an average of 10,000 realizations u / Ue v / Ue L=38.1 mm U V Mean Velocity and Pressure C mean C rms
Reynolds Stress Distributions u U e v U e 0.06 0.0 uv U e Flow Field of View H=30.0 mm L=38.1 mm Other turbulence statistics obtained from measurements (not sown here): Pressure-velocity correlations; Pressure-strain correlations. Results of sectrum analysis of flow quantities also obtained and are in agreement with theory and our other exerimental data for this same flow.
Samle Raw Data: Characteristic Flow Phenomena Vortex Shearing and Aearance/ Disaearance of Low Pressure at Corner Samle movie: Characteristic Flow Phenomena Swirling Strength ci Click to launch the movie Pressure Coefficient C Streamline: u u c, taking u c as 0.5U e
Characteristic Flow Phenomena Vortex Break U and Aearance/ Disaearance of Corner Pressure Peaks Samle movie: Characteristic Flow Phenomena Swirling Strength ci Click to launch the movie Pressure Coefficient C Streamline: u u c, taking u c as 0.5U e
Characteristic Flow Phenomena Deformation of a Shear Layer Vortex Due to the High Shear in the Corner Samle movie: Characteristic Flow Phenomena Swirling Strength ci Click to launch the movie u/ y Streamline: u u c, taking u c as 0.5U e
Samle Flow Patterns downwash downwash downwash
Samle Flow Patterns downwash downwash downwash
Samle Flow Patterns
Relationshi between Vortex Location and Pressure Peaks around Corner Eddy ustream downwash Eddy close to corner Note: Aearance/ Disaearance of ressure eaks is consistent with our cavitation observation
Conditional Samling Results v /Ue C Eddy ustream Eddy ustream v /Ue C Eddy close to corner Eddy close to corner
Vorticity Generation on the Wall Vorticity on to of the trailing corner comes from two sources: Vorticity transorted from ustream; Vorticity generated locally due to ressure gradient. z v Vorticity fluxes into the control volume are examined. Moment when large eddies ustream zl U e Vorticity flux from ustream Vorticity flux generated locally Vorticity flux into the control volume through this surface reresents local roduction Conclusion: The local roduction of vorticity is eriodic, and significant, esecially when large eddies are ustream away from the trailing corner.
Vorticity Generation on the Wall Lighthill (1963) ointed out that vorticity flux is directly related to ressure gradient at the wall: 1 x wall z x z v Correlation between the local vorticity flux and the local ressure gradient is examined. wall zl U e Local vorticity flux Correlation value between dc/dx and local vorticity flux: 0.50.
The acoustic analogy relates the acoustic ressure to quantities obtainable from measurements or comutation (Curle 1955; Ffowcs Williams and Hawkings 1969; Howe 004, 003; Lighthill 195). The Lighthill (195) acoustic equation: The Lighthill analogy does not include solid boundaries. Curle (1955) overcomes this limitation by formulating an analogy for non-moving solid bodies: Sakar and Hussaini (1993) suggests that temoral derivatives of the source term are referable to satial derivatives. Thus, the equation is modified to (Lasson et al., 004): Neglecting the volume integral and viscous contributions (Lasson et al., 004), the surface-generated acoustic ressure field can be estimated by (Koschatzky et al. 010; Haigermoser, 009) Ji and Wang (010), using LES, shows that a forward ste is a stronger source than a backward facing ste in regions located close to the ste corner. V S j i j i ds r n x a dv r T x x a t ) ( 4 1 ) ( 4 1 ), ( y y x V S j i j i j i j i ds r t r a n l dv T r l l t T r a l l t T r a l l t ) ( 1 4 1 ) ( 3 3 4 1 ), ( 3 y y x S a r t j i ds r r a t n l t ) ( 4 1 ), ( y x j i j i i a u u T where x x T x a t Estimate of Acoustic Pressure from Time Resolved PIV Data
Samle Instantaneous Acoustic and Hydrodynamic Pressure Fields Click to launch the movie Acoustic Radiation from Corner Pressure Coefficient
Power Sectra of Sound at Selected Locations SPL 0log10 ( rms / ref ) FFT length: 048 (5 sets) Resolution of frequency:.hz ref 0Pascal SPL(dB) Origin of sectral eaks: 4.4 0 Hz large scale recirculation in cavity (estimated) 11, 18, 6, 33, 40, 48 Hz large eddies in the shear layer (fl/u c =(n±0.5), n=1,,3, Martin et al. 1975) 97.4 Hz interaction of secondary structures within a large eddy (observations)
SPL ref 0log10( 0Pascal rms / ref ) 1 4 S front Breakdown of Contributions l i n j t /(a r) ds(y) tr / a 1 4 S front l i n j / r tr / a ds(y) Vertical, forward wall contribution Horizontal to corner contribution
Effect of Shedding Vortex Frequency on Wall Pressure Sectrum (Point Measurements) 0.006 0.006 0.005 0.005 0.004 0.003 Effect of Shedding Vortex Frequency on Wall Pressure Sectrum 0.004 0.003 0.00 0.00 0.001 0.001 Flow Direction P, U Cavity Wall 0 1 10 100 1000 10000 Frequency (Hz) Ue=5m/s Trailing Edge fl fw U e Location of Pressure Transducer 1.8 1.6 1.4 1. 1 0.8 0.6 0.4 0. fl 1 0.5 n Ue 4 0 1 10 100 1000 10000 Frequency (Hz) Ue=10m/s Ue=5m/s Theory Ue=10m/s fl c 1 n U U 4 e c Take 0. 5 e U e (Martin et al, 1975; Blake, 1986) L=38.1 mm 0 0 1 3 4 n
Velocity and Pressure Sectra Flow Field of View Location A, sd of u H=30.0 mm L=38.1 mm Location A, sd of Location A, sd of v
Velocity and Pressure Sectra Flow Field of View Location B, sd of u H=30.0 mm Velocity and Pressure Sectra L=38.1 mm Location B, sd of Location B, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location C, sd of u H=30.0 mm L=38.1 mm Location C, sd of Location C, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location D, sd of u H=30.0 mm L=38.1 mm Location D, sd of Location D, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location E, sd of u H=30.0 mm L=38.1 mm Location E, sd of Location E, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location F, sd of u H=30.0 mm L=38.1 mm Location F, sd of Location F, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location G, sd of u H=30.0 mm L=38.1 mm Location G, sd of Location G, sd of v
Velocity and Pressure Sectra Flow Field of View Velocity and Pressure Sectra Location H, sd of u H=30.0 mm L=38.1 mm Location H, sd of Location H, sd of v
Flow Field of View H=30.0 mm Pressure-Velocity Correlations L=38.1 mm u 3 U e v 3 U e Both < u > < v > change sign around the corner Hooer and Musgrove (1997) also reorted strong negative correlation between fluctuating ressure and streamwise velocity comonent in a develoed ie flow using a cobra (4-hole) robe.
Trile Velocity Correlations u U 3 3 / e uv U 3 / e Comared with the ressure velocity correlations, it can seen that the ressurevelocity correlation model u 0.uu u i is not valid. i k k u v 3 / U e v U 3 3 / e
R 11 Pressure-Rate-of-Strain Tensor u L x 3 U e R v L y 3 U e 3 Production L U e R ii is of the same order of magnitude as TKE roduction rate. Clear evidence of inter comonent energy transfer.
Conclusions Time resolved satial ressure measurements have been conducted in an oen cavity shear layer, with an emhasis on the flow cavity trailing corner interactions. The large shear layer eddies are deformed and break u in the corner, eriodically feeding vorticity to the boundary layers on the corner walls. There are two equally imortant vortcity sources above the cavity corner Advected shear layer vorticity; Vorticity generated at the wall, due to local ressure gradients. Local roduction of vorticity is eriodic, and occurs mostly when the large eddies are located away from the corner. Imingement of the vortex induces flow on the corner eriodically and eliminates the ressure eaks on both sides of the corner.