# Investigations of transitional and turbulent shear flows using direct numerical simulations and large eddy simulations

We investigate the physical mechanisms and control of turbulent free shear and boundary layers flows. The governing equations of incompressible and compressible flows are numerically solved with sufficient spatial and temporal resolution to account for the dynamics and interactions of all significant scales of turbulence. The detailed information obtained from these simulations and the subsequent analyses will assist in the development of realistic physical models that explain the complex mechanics and phenomena associated with these turbulent shear flows. These include the instability and transition to turbulence, the formation of coherent flow structures and control of these phenomena. Thus, a better understanding of the complicated multi-scale turbulent flow physics leads to significantly optimised engineering designs in aviation, transportation, and power generation to reduce energy consumption and consequently to diminish carbon dioxide emissions## Area of science

Turbulent Flows Fluidisation and Fluid Mechanics Aerodynamics (excl. Hypersonic Aerodynamics)## Systems used

Magnus## Applications used

Home-developed massively parallel C/C++ and F90 codes with MPI and OpenMP with HDF5**Partner Institution:**Monash University |

**Project Code:**g75

The Challenge

Progress into the 21st century will be accompanied by new and complex challenges such as reduced availability and the ever-increasing cost of crude oil (energy security), climate change and its impact on the ecosystem (mandated reduction of CO2 emissions) and the development and training of a workforce capable of sustaining the technological needs of a global economy (sustainable standard of living). One important common factor in these challenges is the problem of complex multi-scale turbulent shear flows, which are prevalent in every aspect of life and contrary to popular belief is still an immature science, lacking fundamental understanding of the complex momentum and energy exchange mechanisms. This predicament is responsible for wasteful sub-optimal design in (i) energy production, (ii) energy conversion, (iii) transport platforms and (iv) manufacturing systems and high uncertainty in predictions of (i) environmental (oceans and atmospheric boundary layer) and (ii) urban flows (around cities and buildings). The goals of this project are to study the detailed physics of turbulent shear flows of two general canonical flows of:

1. Wall-bounded turbulent shear flows: A notably important turbulent flow encountered in everyday life is one where a fluid flows over a surface such as, when air flows over a car, a high-speed train, the wing of an aeroplane and the surface of the earth or water flows past the hull of a ship or the ocean floor. In each of these flows, a thin layer of fluid flow develops over the surface, known as a boundary layer. To illustrate the predominance of these wall-bounded flows, it is estimated that 25% of the energy worldwide used by industry and commerce is spent in moving fluids through pipes and canals, and in all forms of air and water transport systems, with about one-quarter of that energy dissipated by turbulence in the immediate vicinity of walls. In terms of a quantity of current topical interest, shear-dominated wall-bounded turbulence is directly responsible for about 5% of the CO2 dumped by mankind into the atmosphere. In many practical applications of interest such as the ones mentioned above, the boundary layer is characterised by chaotic seemingly random three-dimensional vortical motions known as turbulence, in this case, referred to as wall-bounded turbulence.

2. Turbulent Couette-Poiseuille flow: Turbulent Couette-Poiseuille (C-P) flow also falls under the classification of wall-bounded turbulent shear flows. As a classical model in turbulent research, C-P flow can be found in the space between two walls with relative motion, such as between the bottom of a moving vehicle and the road. The research focus on the C-P flow on the verge of separation, i.e., the bottom wall has zero mean wall shear stress. Flow in this typical situation is seldom studied. The classical theories obtained from attached flow, such as the law of the wall, cannot be applied to the flow on the verge of separation. This leads to limited references that are available to this research. Thus, basic properties will be addressed first and then investigate more specific research problems. The research problems include three parts: 1. Appropriate scaling of mean statistics and the scaling law in the C-P flow on the verge of separation. 2. The characterization and interaction between intense Reynolds stress and vortical structures. 3. Generation of the mean skin friction and its associated contributing factors.

3. Turbulent sub- and super-sonic jet flows: Turbulent jet flows fall under the more general classification of free turbulent shear flows, which are found in applications ranging from pharmaceutical drug delivery, manufacturing, material processing to combustion and propulsion. Our interest is specifically with high-speed flow associated with the under-expanded impinging jet (UIJ) which is a critical component in diverse processes ranging specifically from pharmaceutical systems, to novel manufacturing processes and aerospace propulsion applications. Under-expanded impinging jet flow is an inherently forced flow; this forcing being acoustic in nature, primarily driven via a feedback process that has its origin at the impingement surface. The nature of this “forced” flow is very poorly understood. This lack of understanding persists due to the fact that the typical “steady-state” case (i.e. the only one readily amenable to observation), has its own inbuilt forcing mechanism, in the form of the aforementioned acoustic feedback process. This inherent self-forcing means that the underlying “natural” stability of the jet cannot be directly inferred from the mean state of this “forced” flow. The lack of fundamental understanding regarding nature and stability characteristics of the UIJ makes prediction of these flows nearly impossible. Without predictive ability, dynamic control of the flow in its many diverse industrial applications is highly unreliable.

The research into these two broad areas is divided into four work-packages, work-package 1 – 3 are associated with research using direct numerical simulations (DNS) of wall-bounded turbulent shear flows, while work-package 4 is associated with research using DNS and large eddy simulations (LES) of turbulent supersonic jet flows

The Solution

This project studies the turbulent shear flows physics with a focus on efficiency improvements in transport systems and energy generation. To understand the physical mechanisms of these turbulent shear flows, direct numerical simulations (DNS) and large-eddy simulations (LES) are performed for both wall-bounded and free turbulent shear flows.

Work-package 1: DNS investigation of adverse pressure gradient turbulent boundary layer (APG-TBL)

-Analysis of the factors contributing to the skin friction

The investigation of the contributions of the viscous effects and the Reynolds shear stress to the mean skin friction and the role of the pressure gradient is performed. In this study, it is shown that the Reynolds stress remains the dominant contributor to the skin friction coefficient for all the pressure gradient cases. The positive contribution from the Reynolds shear stress is diminished by the negative contribution of the pressure gradient. Further analysis revealed that the dominant outer peak contribution to the mean skin friction is captured by the decomposition of Renard and Deck (2016) as well as by the formulation of Fukagata et al. (2002). The detailed investigation on this work is published in the special issue of the International Journal of Heat and Fluid Flow after invitation.

-Analysis of the uniform momentum zones (UMZs)

One of the many three dimensional coherent structures in wall-bounded flows are uniform momentum zones (UMZs), which are uneven regions in the flow with similar streamwise momentum and varying shape with time. The UMZs are separated from each other by layers which have high values of the local wall-normal gradient of the streamwise velocity with spanwise vorticity clustered along these boundaries. The interfaces between the UMZs are similar to a shear layer. The time persistence and spanwise extent of the UMZs are analyzed using a time-resolved direct numerical simulation of a zero pressure gradient turbulent boundary layer (ZPG TBL) at a friction Reynolds number of 1176. Probability density functions (PDFs) of the number of UMZs have been computed as a function of extent in the streamwise direction, confirming the previous result that a domain of 2 boundary layer thickness in the streamwise extent is the appropriate length scale to determine the UMZs in the ZPG TBL. This analysis was extended to the APG TBL and the findings are accepted for publication as a comprehensive paper in the Journal of Physics. The spanwise extent of the UMZs is found to be shorter than their streamwise extent regardless of the pressure gradient in the flow. In the ZPG-TBL flow, the majority of the UMZs have a spanwise extent of the order of one-tenth of a boundary layer thickness while for the APG-TBL, it is found to be on the order of one-hundredth of a boundary layer thickness. In the ZPG-TBL, the probability of finding 2 UMZs that persist over a time period of 2 integral time scales is around 50%. Similarly, for the APG-TBL, the probability of finding 2 UMZs with a time persistence of 0.4 integral time scale is over 50%. In the case of the ZPG-TBL, it is observed that some of the UMZs with higher persistence in time have higher streamwise momentum and are found to be closer to the free-stream in general. In contrast, for the APG TBL, UMZs with longer time persistence are found closer to the wall with lower streamwise momentum.

Analysis of the statistics and the Reynolds stress structures

The instantaneous velocity and pressure fields are generated and statistics are accumulated from the DNS of APG TBL. We use a modified far-field boundary condition to generate the required self-similar APG flow. The first-order statistics and two-point correlations of the zero pressure gradient TBL (ZPG TBL), the mild APG TBL and the strong APG TBL are presented in the International Journal of Heat and Fluid Flow and Journal of Fluid Mechanics. The investigation of the mean Reynolds stress profiles and instantaneous Reynolds stress structures in the self-similar APG-TBL at the verge of separation are presented in the Journal of Physics. In the APG TBL, we have shown that both of the peaks in the mean Reynolds stress and the production of turbulent kinetic energy move from the near-wall region out to a point consistent with the displacement thickness height. This is associated with a narrower distribution of the Reynolds stress and 1.6 times higher relative number of wall-detached negative Reynolds stress structures. The statistics of the DNS of the ZPG TBL, the mild APG TBL and the strong APG TBL are now available online in “https://bridges.monash.edu/articles/Statistics_of_Beta_0_1_39_Turbulent_Boundary_Layer_DNS/8790785”, which is a significant contribution to the research community.

Work-package 2: Data assimilation and the input of large scale experimental data into direct numerical simulations of wall-bounded turbulent flows as a means of reducing the required spatial extent and accelerating temporal convergence

– Limited near-wall inlet data assessment on the direct numerical simulation of turbulent channel flow

Direct numerical simulation (DNS) of turbulent flows requires a large computational domain and a long simulation time to capture and evolve the large-scale structures and attain a statistically stationary state. In contrast, experimental measurements can relatively easily capture the large-scale structures, but struggle to resolve the dissipative flow scales. This work-package aims to assimilate the large-scale experimental data into DNS to reduce the computational cost of high-fidelity DNS and enable the accurate computation of flows whose Reynolds numbers lie beyond the reach of present super-computing facilities. The spatial extent required for the DNS of a turbulent channel flow to recover turbulent fluctuations and energy when using experimental inlet data which is typically unable to capture fluctuations down to the viscous sub-layer or the smallest viscous scales (i.e. Kolmogorov scales) is investigated. Synthetic experimental fields from streamwise periodic channel flow are used as an inlet for a channel flow DNS with inlet-outlet boundary conditions. The effect of limited near-wall data at the inlet is examined by removing the near-wall energy and fluctuations in all but the zeroth Fourier mode. The influence of limited near-wall data on the convergence of mean and streamwise fluctuating velocity profiles is less significant when the fluctuations are removed at the inlet up to y+ = 5. However, the spanwise fluctuations are slightly weakened. The spanwise energy spectra suggest that at 1/16 of the domain length (x/h = π/4) the flow scales are recovered. When the fluctuations are removed up to y+ = 17 or greater, recovery of the full range of flow scales requires a domain larger than (x/h = 4π). The inlet without fluctuations up to y+ = 17 corresponds to the disruption of the near-wall peak and much of the near-wall cycle is removed for inlet without fluctuations up to y+ = 35. This suggests that despite maintaining the zero modes and hence the mean shear stress in the inlet, failing to capture the structure of the near-wall cycle results in a significant deficit in the production of turbulent kinetic energy which ultimately leads to a decrease in the turbulent fluctuation throughout the channel, until the near-wall cycle is re-established. The correlation between the inlet-fed DNS and baseline case indicates that the inlet-fed DNS while recovering the energy and statistics of the flows, is only able to maintain the same instantaneous structure of baseline when the near-wall peak is captured by the inlet. While this is not necessarily a requirement for the use of experimental data as an appropriate inlet to a DNS, it does indicate that maintaining the near-wall structure is important if one intends the flow to maintain the same evolution. This analysis is presented in the Journal of Physics. This investigation is extended to high Reynolds numbers.

Work-package 3: DNS investigation of turbulent Couette-Poiseuille flows on the verge of separation

– Analysis of scaling of the statistics and associated scaling laws:

The appropriate inner and outer scales are the most fundamental and necessary properties in the study of turbulence. The scales are related to the non-dimensionalization of data and the scaling law of the statistics. In proper scaling, the universality of data can be obtained. Otherwise, the data are case-based and lack of reference value. More importantly, it decides the way to present and interpret data correctly. In the DNS, the stable averaging scheme is used to compute the statistics, then we performed various small DNSs and interpolated the value of the pressure gradient to make the flow approaching the verge of separation. After that, three fully resolved DNSs with the correct value of the pressure gradient are performed to initiate the research. The classical works in attached wall-bounded turbulent flow indicated the proper inner scales are based on the mean skin friction on the wall (frictional scales). However, in the flow on the verge of separation, the classical inner scale becomes infinity. We found the scales based on the pressure gradient (pressure scales) are suitable for our case after many different inner scales were compared. Based on the pressure scales, we observed the scaling laws and proposed the division of the inner layer for the flow on the verge of separation. Primary results were presented in the 11th Australasian Heat and Mass Transfer Conference 2018 at Melbourne, Australia. Also, a manuscript of a journal paper is now in the review of co-authors and will be published.

– The characterization of intense Reynolds stress and vortical structures.

We implemented the numerical tool that enables the extraction of intense Reynolds stress structures and vortical structures by comparing the local value with its neighbouring points recursively. To identify vortical structures, the flow topology based on the invariants of the velocity gradient tensor is used in our analysis. The information of identified structures is collected to investigate their interactions and characterizations, such as location and intensity. Preliminary results were presented in International conferences. Further investigation is concluded in a paper that is in the review co-authors and will be published.

– Analysis of the contributions to the skin friction

Turbulent contribution to the skin friction generation is related to the behaviour of Reynolds structures, which is followed by the previous study regarding intense Reynolds stress. In this study, the co-spectrum of Reynolds shear stress will be analyzed to enable further observation in Fourier space. In the Fourier space, The field of Reynolds stress is decomposed into various sinusoidal functions with different wavelengths. Then the large-scale structures with specified wavelength can be filled out from the entire flow to study the large-scale contribution to the generation of the mean skin friction.

Work-package 4: DNS and LES of free and impinging jets

– Receptivity at the nozzle lip of supersonic under-expanded impinging jets:

Supersonic under-expanded impinging jets are classified as self-oscillatory flows. This is well-understood that in high-speed flows, the acoustic-hydrodynamic coupling is one of the main components influencing this oscillation behaviour which is considered an undesired behaviour in many engineering applications. The acoustic-hydrodynamic coupling occurs through the receptivity process at the sharp edge of the nozzle lip in the configuration of under-expanded supersonic jets. A receptivity analysis of internalisation of the acoustic waves at the nozzle lip into shear-layer instabilities performed as a part of this project. The transfer function at the nozzle lip, which receives the acoustic input and generates a hydrodynamic output in the form of a forced shear-layer instability was obtained.m It was observed that the transfer function is not only a function of the frequency but also the location of the source. The highest amplification was obtained for the source close to the infinite nozzle at an angle of 85 degree from the centreline of the nozzle and the lowest amplification was obtained when the source has a location with an angle less than 10 degree from the centreline of the jet (i.e. nearly in the shear layer). A more comprehensive manuscript is published in Journal of Fluid Mechanics where An illustration of the results appeared as the front cover of the Journal of Fluid Mechanics, volume 889. Motivated by this study the influence of nozzle lip thickness on the receptivity process is performed. It was found that increasing the nozzle lip thickness more than a jet diameter has insignificant influence on the receptivity characterised by a transfer function. A more comprehensive manuscript is under preparation to report these findings.

– Proper Orthogonal Decomposition analysis to unravel coherent structures in under-expanded supersonic impinging jets:

The recent experimental studies of the under-expanded supersonic jets performed by our team at LTRAC laboratory at Monash University shows the external geometry of the nozzle influences the globally dominant coherent structures in this flow. Motivated by these observations and to study the underpinning physics in more details (Numerical simulation provides three-dimensional primitive variables while the experiment is limited to few variables and to two-dimensional fields), the influence of the nozzle exit geometry on coherent structures is studied for the under-expanded supersonic jets with the nozzle to wall distance of 2 jet diameters and nozzle pressure ratio of 3.4 with three nozzle geometry of thin-lipped nozzle, infinite lipped nozzle and combination of thin-lipped and sound-absorbing foam. As the first stage of the data assimilation, Proper Orthogonal Decomposition was applied to these three cases to study the influence of external nozzle geometry on coherent structures. Consistent with experimental studies conducted at LTRAC laboratory, the external geometry of the nozzle has a strong impact on coherent structures as evidenced by the leading mode of each case.

The Outcome

Magnus, one of two Tier-1 high-performance computing and data research facilities in Australia, allowed Prof Soria and his research team to gain significant insights into fundamental physics of turbulent free shear and boundary layers flows. Already published work by Prof Soria and Dr Karami used high-fidelity simulations to unravel receptivity at the nozzle lip and proposed new ways to control instabilities in jet flows. Supercomputing facilities allowed Prof Soria and his team to gain significant insights into fundamental behaviours of large- and small-scale structures in boundary layer flows at the verge of separation to stage of being separated. The research team used the DNS to propose new ways to look at contributions of different turbulent structures into the friction coefficient. Considering the friction is the main mechanism of energy lost in many engineering applications, a minor reduction in friction could lead to a significant reduction in energy consumption and consequently to diminish emissions. The proposed decomposition of the friction coefficient allows characterising the structures which have high impact on the friction coefficient. Manipulating these structures has significant future impact on design improved, lower emissions engineering devices

List of Publications

Refereed Journal Articles (2019-2020)

1. Karami, S., Stegeman, P., Ooi, A., Theofilis, V. and Soria, J. “Receptivity characteristics of supersonic under-expanded impinging jets”, Journal of Fluid Mechanics (Journal Front Cover), 889: p. A27 (2020), doi: doi.org/10.1017/jfm.2020.63 [SNIP: 1.712, SJR: 1.591, FWCI: 1.51].

2. Senthil, S., Kitsios, V., Sekimoto, A., Atkinson, C., and Soria, J. “Analysis of the factors contributing to the skin friction coefficient in adverse pressure gradient turbulent boundary layers and their variation with the pressure gradient”, International Journal of Heat and Fluid Flow, 82: p. 108531(2020), doi:10.1016/j.ijheatfluidflow.2019.108531[SNIP: 0.981, SJR: 0.487] .

3. Senthil, S., Kitsios, V., Sekimoto, A., Atkinson, C., and Soria, J. “Analysis of the spanwise extent and time persistence of uniform momentum zones in zero pressure gradient and adverse pressure gradient turbulent boundary layers”, Journal of Physics: Conference Series, 1522 (2020), 012013.

4. Ezhilsabareesh, K., Atkinson, C., Lozano-Duran, A., Schmid, PJ., Jimenez, J., and Soria, J. “Effect of limited near-wall inlet data on the direct numerical simulation of turbulent channel flow”, Journal of Physics: Conference Series, 1522 (2020), 012019.

5. Karami, S., Stegeman, P., Ooi, A. and Soria, J. “High-order accurate Large Eddy Simulation of compressible viscous flow in cylindrical coordinate”, Computers & Fluids, 191: p. 104241(2019), doi:10.1016/j.compfluid.2019.104241[SNIP: 1.477, SJR: 0.999].