Experiments on Very Large Structures in Fully

Experiments on Very Large Structures in Fully Developed Turbulent Pipe Flow Christoph Egbers, El-Sayed Zanoun, Emir Öngüner and Amir Shahirpour, Department of Aerodynamics and Fluid Mechanics (LAS), Brandenburg University of Technology (BTU), Germany, Email: [email protected], [email protected], [email protected], amir.shahirpour@btu-de Preliminary PIV measurements

Abstract Local turbulence properties in wall-bounded, i.e. pipe, channel and flat plate, flows are of equal importance in theory and engineering applications. The present project is, therefore, concerned with measurements of various scales of turbulent flow structures in pipe flows with thermal and optical probes for a wide range of Reynolds number. Identification of flow large scale motion (LSM) and very large scale structures/motions (VLSM) and their dynamics are to be investigated in details, i.e. to clarify uncertainties regarding their origin, nature, spatial and temporal evolution as well as their interactions with each other and with near-wall turbulence. The following open questions will be receiving answers from our running project.

Figure 5. Preliminary PIV measurements at Reb≈ 14×104 for streamwise (top) and crosssectional (right) configuration in CoLa-Pipe: snapshot of mean streamwise velocity

Preliminary measurements have been performed in collaboration with LaVision GmbH, in CoLa-Pipe at various Reynolds numbers with streamwise and cross-sectional configurations. For the streamwise PIV, a 2m section of the pipe was inspected with 4 cameras. Both measurements were carried out at X/D=90~100, to ensure a fully developed turbulence in the measured area.

Open Questions

HWA measurements - Are there convincing evidence proving the existence of VLSM at high Reynolds numbers or are they just experimental or numerical artifacts? - What would be the right method to define them, which properties would they have in terms of velocity, amplitude and length scales and how do they scale with Reynolds number and pipe geometry? - Are the near-wall turbulent structures and their regeneration mechanism universal? - How do the large scale motions contribute to turbulence properties and do they interact with the near-wall turbulence? - Are the LSM and VLSM geometrically self-similar as claimed by Townsend’s attached eddy hypothesis? - What is the inner peak value of streamwise turbulence intensity and does the appearance of an outer peak signal a fundamental change in turbulence characteristics at high Reynolds numbers?

Figure 2. Cooperation and Contribution

This project serves as a reference experiment (CoLaPipe) on turbulent pipe flows inside the SPP. The project is also benefiting from close collaborations and data exchange with potential partners (Figure 2). Collaboration inside EuHit - Turbulence Development at High Re in CoLaPipe, BTU with CNRS & Université du Havre, February- March 2016 - Spectral Scaling of Turbulence in CICLoPE, BTU with University of Bologna, June-July 2016 - Comparative 2D pipe flow experiment in CoLaPipe, BTU with University of Bologna and KTH Stockholm, January 2017 - High-Dynamic Range Measurements in CoLaPipe, BTU with University of Madrid Carlos III, University of Napoli and KTH Stockholm, March 2017

Premultiplied turbulent energy production measured at CoLaPipe is presented in Figure 6 for a range of Reynolds numbers. Since the area below the pre-multiplied profiles represents the overall energy production, it is observable, that at sufficiently high Reynolds numbers, it is the logarithmic region that contributes most to the bulk turbulence production. This turns out to be in good agreement with a similar study by Smits et al. (2010).

Working Packages (WP): WP BTU1: Facility Preparation and Instrumentation a) The existing data from streamwise and cross-sectional PIV and HWA measurements are to be exchanged with SPP partners b) Optimization of seeding process for the PIV at different Reynolds numbers, 6×104 ≤ Reb ≤106 for further streamwise non- intrusive PIV measurements c) Providing the new resulted streamwise PIV data to SPP partners WP BTU2: Cross-sectional PIV measurements and data transfer a) Intensive cross-sectional PIV (stereo and tomographic) measurements for 6×104 ≤ Reb ≤106 b) Providing the resulted PIV data to SPP partners

Figure 6. Premultiplied turbulent energy production

Figure 7 shows the pre-multiplied spectra (kxΦuu/ut2) for stream wise component of velocity, normalized by the shear velocity in the CICLoPE facility at R+=4800. When the pipe radius is used for scaling, a good collapse is observed at larger wave lengths for krR < 10, in particular for y/R < 0.3. The first peaks of spectra are considered as an evidence of the VLSMs which are originating at lower wavenumbers.

Figure 3. The Pipe Facility Suction pipe inner diameter =190 mm, Pipe length (L) =28 m, L/ Di147, Return pipe inner diameter =342 mm,

Pipe length (L) =28 m, L/ Di78,

Pipe surface roughness,  = 5 m,

in wall units, +  1,

Mean/bulk velocity  75 m/s,

Wall friction velocity  3 m/s

Mean-based Reynolds number, Rem  106,

Kármán number R+  1,8  1 04,

Viscous length scale  400 down to 20 m. Measuring techniques and control volumes: HWA, LDA, PIV, Pressure probes, Microphone,

Figure 1. a) Cross-sectional Stereo-PIV and b) TomographicPIV setup

WP BTU3: Simultaneous PIV measurements and data transfer a) Simultaneous PIV investigations (streamwise and crosssectional) with simultaneous laser sheet illumination for a double 2D domain reconstruction by BTU b) Providing the double 2D simultaneous PIV data to SPP partners WP BTU 4: Single and array HWA measurements a) Construction and implementation of multiple HWA module b) Comparison of multiple HWA measurements with PIV c) Providing the HWA array data to SPP partners to be compared with LES and DNS data WP BTU 5: Data analysis and Reporting a) Calculation of statistical properties, energy spectra & premultiplied spectra, 2D correlation functions b) Comparison of structures behavior between HWA measurements and PIV data c) Proper Orthogonal Decomposition (POD) of cross sectional and streamwise PIV data, to investigate the contribution of energetic modes to various turbulence properties d) Applying a Lagrangian Dynamic Mode Decomposition (LDMD) in a moving frame of reference on the streamwise PIV measurements (TUBerlin, J. Sesterhenn) e) Statistical analysis of HWA data and its comparative study with simulations carried out by SPP partners

Hot wire, l = 250 m, d = 1 m,

in wall units, l+ = (1 -50)

Hot wire, l = 1250 m, d = 5 m,

in wall units, l+ = (5 -250)

Figure 7. Premultiplied stream wise velocity spectra

Lagrangian DMD of the stream wise PIV data

Figure 4. Predicted ranges of turbulence length scale (Ɩc), from various pipe facilities vs. Kàrmàn number (R+).

CoLa-Pipe facility at BTU was designed to provide experimental data over a relatively wide range of high Reynolds numbers with high enough spatial resolution in comparison to other existing facilities. It is worth referring to McKeon and Sreenivasan (2007) statement that the greater urgency seems to be the ability to resolve all the turbulence scales, and not simply move towards ever increasing Re.

Bibliography König, F., Zanoun, E.-S., Öngüner, E., Egbers, Ch., “CoLaPipe - The New Cottbus Large Pipe Test Facility at BTU Cottbus”, Review of Scientific Instruments, Vol: 85, Issue: 7, July 2014 McKeon, B. J., and Sreenivasan, K. R., “Introduction: scaling and structure in high Reynolds number wall-bounded flows,” Phil .Trans. R. Soc. A (2007) 365, pp. 635–646, 2007. Talamelli, A., et al.. 2009 CICLoPE – “A response to the need for high Reynolds number experiments,” 41 021407, April 2009. Zanoun, E.-S., Kito, M., and Egbers, C., “A study on flow transition and development in Circular and Rectangular Ducts,” J. Fluids Engg. 131, 061204, June .2009 Öngüner, E., Zanoun, E.-S., König, F., Egbers, Ch., “Structure Investigation in Pipe Flow at High Reynolds Numbers”, Progress in Turbulence VI, Vol. 165, pp.217-220, Springer, 2016 Smits, A. J., McKeon B. J., Marusic, I.,“High Reynolds number wall turbulence”, Annu. Rev. Fluid Mech., 43, 353-375, 2010 Sesterhenn, J., Shahirpour, A., “A lagrangian dynamic mode decomposition”, under review for publication in the journal of Theoretical and Computational Fluid Dynamics

This project is funded inside the DFG-SPP (1881) "Turbulence & Superstructures" under grant no. EG100/24-1.

A Lagrangian Dynamic Mode Decomposition (LDMD) will be applied to the streamwise PIV data to follow the structures in a properly chosen frame of reference (in cooperation with TU-Berlin, J. Sesterhenn). As shown in Figure 8 for the solutions of a 1D KDVB equation, the latter will take place via a coordinate transformation from physical space into spatio-temporal space. The transformed snapshots will be decomposed using the standard DMD along τ. The dynamic modes being reconstructed in the spatio temporal space will be transformed back to physical space. The latter will represent a reduced order model of the system using only a few modes accommodating the structure with the dominant group velocity. Further Further details about the method are details the submitted t included in about the manuscript method are available in the manuscript submitted to the journal of Theoretical and Computational Fluid Dynamics. The results will be comparable with the Exact Coherent Structures captured and analyzed by Bremen Figure 8. Space time diagram for University (M. Avila). KDVB solutions

Publications Zanoun, E.-S., Öngüner, E., Egbers, Ch., Conventional Measuring Probes in the Walll-Layer Turbulent Subsonic Ducted Flows, Journal of Thermophysics & Aeromechanics, Vol:23, No:3, 2016 Selvam, K., Öngüner, E., Peixinho, J., Zanoun, E.-S., Egbers, C., Entrence Length for Fully Developed Turbulent Pipe Flow Using Wall Pressure, submitted to Journal of Fluid Mechanics, 2016 Öngüner, E., Zanoun, E.-S., Fiorini, T., Bellani, G., Shahirpour, A., Egbers, C., Talamelli, A., Wavenumber Dependenc of VeryLarge Scale Motions in CICLoPE at 4800 < Reτ < 37000, submitted to Progress in Turbulence VII, Springer Proceedings in Physics, 2016 Öngüner, E., Zanoun, E.-S., Egbers, C., Streamwise Auto-Correlation Analysis in Turbulent Pipe Flow Using Particle Image Velocimetry at high Reynolds Numbers, submitted to Progress in Turbulence VII, Springer Proceedings in Physics, 2016