# Fractal forcing of axisymmetric turbulent jets; both fully developed and impulsively forced

Lead Research Organisation:
Imperial College London

Department Name: Dept of Aeronautics

### Abstract

In order to meet The Advisory Council for Aeronautics Research in Europe (ACARE) 's ambitious targets to reduce carbon dioxide, NOx and noise emissions by up to 90% in 2050 bold new flow solutions must be embraced by the aviation industry. One such flow solution is a fractal forced turbulent jet. A fractal is an object that is composed of identical geometrical shapes that are progressively smaller, and therefore appears to be similar regardless of the length scale at which one chooses to view it. Previous research on fractal generated turbulence has focused on homogeneous isotropic turbulence, and has shown an increase in turbulence intensity in comparison to turbulence generated by regular grids. This increase in turbulence intensity increases mixing, which can subsequently improve the efficiency of combustion. The pressure drop, and subsequent pressure recovery, has also been shown to be improved in the flow behind a fractal grid as opposed to a regular grid. A fractal forced jet thus has potential applications in jet flame combustion and propulsion nozzles, which are both integral components of a gas turbine engine. Similar geometry has also been shown to reduce the jet acoustic signature in modern aero-engines.

It has been observed that this fractal generated turbulence does not decay in the same manner as the universally accepted Richardson-Kolmogorov phenomenology, making it of great scientific interest. Unlike homogeneous isotropic turbulence, a jet is a free shear flow, in which there is a mean shear. This mean shear provides a mechanism by which energy can be transferred from the mean flow into turbulence. The fractal forcing in the jet is also applied directly to the shear layer, as opposed to a grid in which this forcing is applied to the bulk of the flow. This study will also examine the development of a turbulent flow over an elongated fractal boundary, the so-called "fractal rifle" case. This "fractal rifle" will also be modified to include a helical fractal pattern which will introduce swirl to the jet, which is known to stabilise jet flames in combustion applications. The flow physics of these types of fractal forced flows are not understood, which is a prerequisite for the adoption of such a promising device into industrial applications. This research thus seeks to use state of the art laser diagnostic techniques to observe these flow physics in the velocity field of a fractal forced turbulent jet. It will thus be possible to observe whether the turbulence generated by a fractal forced jet decays in the same non-equilibrium manner as that generated by a fractal grid. It will also determine whether there is a fundamental difference between a flow that is "impulsively" forced by a fractal geometry or allowed too develop along a fractal boundary and the axial length scale of the forcing at which this behaviour switches over.

It has been observed that this fractal generated turbulence does not decay in the same manner as the universally accepted Richardson-Kolmogorov phenomenology, making it of great scientific interest. Unlike homogeneous isotropic turbulence, a jet is a free shear flow, in which there is a mean shear. This mean shear provides a mechanism by which energy can be transferred from the mean flow into turbulence. The fractal forcing in the jet is also applied directly to the shear layer, as opposed to a grid in which this forcing is applied to the bulk of the flow. This study will also examine the development of a turbulent flow over an elongated fractal boundary, the so-called "fractal rifle" case. This "fractal rifle" will also be modified to include a helical fractal pattern which will introduce swirl to the jet, which is known to stabilise jet flames in combustion applications. The flow physics of these types of fractal forced flows are not understood, which is a prerequisite for the adoption of such a promising device into industrial applications. This research thus seeks to use state of the art laser diagnostic techniques to observe these flow physics in the velocity field of a fractal forced turbulent jet. It will thus be possible to observe whether the turbulence generated by a fractal forced jet decays in the same non-equilibrium manner as that generated by a fractal grid. It will also determine whether there is a fundamental difference between a flow that is "impulsively" forced by a fractal geometry or allowed too develop along a fractal boundary and the axial length scale of the forcing at which this behaviour switches over.

### Planned Impact

Aviation is responsible for carrying 2,500 million passengers annually and 35% by value of the world's trade, with these numbers set to increase in the coming years thereby increasing environmental threats posed by the industry, such as excessive noise generation and undesirable emissions. The Advisory Council for Aeronautics Research in Europe (ACARE) has published new targets for emissions for 2050 requiring a 75% reduction in CO2 emissions, 90% reduction in NOx emissions and 65% reduction in perceived noise emissions per passenger kilometre. The UK aerospace sector is the largest in Europe, worth £22 billion in 2009, and must continue to innovate by researching bold new flow solutions that can help to meet these targets. These must strive to ensure that the efficiency with which fuels are burned is increased whilst ensuring that the generation of undesired emissions is reduced, the energy that is used inefficiently in aerospace vehicles' propulsion is minimised and that the noise generated by these vehicles is also reduced. This grant application proposes a fractal forced turbulent jet as one such flow solution with industrial applications in increasing combustion and propulsion efficiency, and reducing the acoustic signature of jet propulsion. However, a thorough scientific understanding of this new flow solution is required before it can be implemented industrially.

The potential industrial benefits to this type of flow are numerous. The enhanced mixing generated by a fractal-forced jet offers a benefit to increasing the efficiency of turbulent combustion whilst at the same time reducing the production of soot and other undesired emissions. The combination of fractal forcing and swirl, which acts as a stabiliser for flames, in the "fractal corkscrew" in particular seems like an extremely promising development. Furthermore, when used as a propulsion nozzle there is potential to reduce the pressure drop, and therefore total energy loss whilst simultaneously reducing the noise generation in comparison to existing technology. It is hoped that this research will thus provide the scientific basis for the adoption of this technology into gas turbine engine applications, of which the UK is a world leader.

The Department of Aeronautics at Imperial College London has agreed to provide a DTA student on the condition of this grant application begin successful. This student will become experienced in the advanced laser diagnostic technique of tomographic PIV. It is an exceptionally powerful technique that is capable of producing fully three-dimensional data, without resorting to the use of Taylor's hypothesis [Taylor, 1938a,b] to create a pseudo spatio-temporal volume of data, at Reynolds numbers that are far in excess of any direct numerical simulation. The knowledge base to perform such advanced experiments is extremely limited in the UK. This student will thus become an extremely valuable asset to the future development of these techniques after the completion of his/her PhD, either in industry or academia.

The research that is the subject of this proposal seeks to gain a better understanding of the fundamental fluid mechanics of a fractal-forced jet. This will subsequently be built on with further research being directed at development of applications of this type of flow. One way in which this can be achieved is by leveraging the technology developed under EPSRC grant EP/K027379/1 "Developing Software for High- Order Simulation of Transient Compressible Flow Phenomena: Application to Design of Unmanned Aerial Vehicles". Dr. Vincent has developed a new direct numerical simulations (DNS) code to solve compressible flow cases with complex geometries on GPU architecture. Discussions have been initiated between OB and Dr. Vincent to use a fractal-forced jet flame as a test case for this code and to further develop a research proposal to investigate the utility of fractal geometry in combustion applications.

The potential industrial benefits to this type of flow are numerous. The enhanced mixing generated by a fractal-forced jet offers a benefit to increasing the efficiency of turbulent combustion whilst at the same time reducing the production of soot and other undesired emissions. The combination of fractal forcing and swirl, which acts as a stabiliser for flames, in the "fractal corkscrew" in particular seems like an extremely promising development. Furthermore, when used as a propulsion nozzle there is potential to reduce the pressure drop, and therefore total energy loss whilst simultaneously reducing the noise generation in comparison to existing technology. It is hoped that this research will thus provide the scientific basis for the adoption of this technology into gas turbine engine applications, of which the UK is a world leader.

The Department of Aeronautics at Imperial College London has agreed to provide a DTA student on the condition of this grant application begin successful. This student will become experienced in the advanced laser diagnostic technique of tomographic PIV. It is an exceptionally powerful technique that is capable of producing fully three-dimensional data, without resorting to the use of Taylor's hypothesis [Taylor, 1938a,b] to create a pseudo spatio-temporal volume of data, at Reynolds numbers that are far in excess of any direct numerical simulation. The knowledge base to perform such advanced experiments is extremely limited in the UK. This student will thus become an extremely valuable asset to the future development of these techniques after the completion of his/her PhD, either in industry or academia.

The research that is the subject of this proposal seeks to gain a better understanding of the fundamental fluid mechanics of a fractal-forced jet. This will subsequently be built on with further research being directed at development of applications of this type of flow. One way in which this can be achieved is by leveraging the technology developed under EPSRC grant EP/K027379/1 "Developing Software for High- Order Simulation of Transient Compressible Flow Phenomena: Application to Design of Unmanned Aerial Vehicles". Dr. Vincent has developed a new direct numerical simulations (DNS) code to solve compressible flow cases with complex geometries on GPU architecture. Discussions have been initiated between OB and Dr. Vincent to use a fractal-forced jet flame as a test case for this code and to further develop a research proposal to investigate the utility of fractal geometry in combustion applications.

### Publications

Beaumard P
(2019)

*The importance of non-normal contributions to velocity gradient tensor dynamics for spatially developing, inhomogeneous, turbulent flows*in Journal of Turbulence
Breda M
(2017)

*Progress in Turbulence VII*
Breda M
(2019)

*Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets*in Journal of Fluid Mechanics
Breda M
(2018)

*Effects of multiscale geometry on the large-scale coherent structures of an axisymmetric turbulent jet*in Journal of Visualization
Breda M
(2018)

*Influence of coherent structures on the evolution of an axisymmetric turbulent jet*in Physics of Fluids
Buxton O
(2015)

*Modulation of the velocity gradient tensor by concurrent large-scale velocity fluctuations in a turbulent mixing layer*in Journal of Fluid Mechanics
Buxton O
(2019)

*Importance of small-scale anisotropy in the turbulent/nonturbulent interface region of turbulent free shear flows*in Physical Review Fluids*Importance of small-scale anisotropy in the turbulent/nonturbulent interface region of turbulent free shear flows*in Physical Review Fluids

Buxton O
(2017)

*Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow*in Journal of Fluid Mechanics
Es-Sahli O
(2020)

*Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations*in Physics of FluidsDescription | The fractal geometry jet has proven to reduce the coherence in the jet and increase the entrainment performance. This reduction of coherence has potential benefits in jet noise reduction and a follow up proposal is planned. The increased entrainment performance has potential benefits in combustion applications. |

Exploitation Route | Jet noise reduction Improvement of combustion efficiency in jet flame combustion |

Sectors | Aerospace, Defence and Marine,Energy |

Description | Collaboration with Dr. Gerrit Elsinga |

Organisation | Delft University of Technology (TU Delft) |

Country | Netherlands |

Sector | Academic/University |

PI Contribution | I underwent a 2 week visit to acquire data and training using the technique of tomographic PIV (invented at TU Delft). The data acquired from this visit has led to a conference talk and will lead to the submission of at least one journal paper. |

Collaborator Contribution | Provided the infrastructure, equipment and expertise to train me and assist me in acquiring the data. |

Impact | One conference talk - disciplines = experimental fluid mechanics, turbulence physics |

Start Year | 2014 |

Description | Collaboration with Mohammed Afsar |

Organisation | University of Strathclyde |

Department | Human Resource Management |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | Mohammed and I are planning to exploit the properties of the fractal-forced jet to make reductions in jet noise and noise scattered from aerofoil trailing edges subjected to jet flow. |

Collaborator Contribution | Theoretical - Mohammed is able to estimate the noise scattering from my experimental data. |

Impact | No outputs as yet - we are working on a follow-up proposal |

Start Year | 2015 |