GB2520553A

GB2520553A - Determination of turbulence in a fluid

Info

Publication number: GB2520553A
Application number: GB1320795.6A
Authority: GB
Inventors: Thomas Henry Clark
Original assignee: OCEAN ARRAY SYSTEMS Ltd
Current assignee: OCEAN ARRAY SYSTEMS Ltd
Priority date: 2013-11-26
Filing date: 2013-11-26
Publication date: 2015-05-27
Anticipated expiration: 2033-11-26
Also published as: GB201320795D0; GB2520553B

Abstract

A method for approximating or modelling turbulence in a fluid flow e.g. for a marine or wind turbine comprises: determining at least one profile of the flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and using the signature(s) to perform a deconvolution of the profile, in order to determine, for each selected eddy type, a probability density function as a function of the size and/or strength parameters. This method may be used in a unit for controlling or designing turbines such as marine turbines. The use of simplified eddy profiles improves computational efficiency.

Description

Determination of turbulence in a fluid The Invention relates to systems and methods to determine turbulence in a fluid and its effect on energy generation devices.

It is known that tidal and atmospheric flows comprise boundary layers, i.e. a region of fluid close to a solid surläce (or similar wall). Boundary layers in geographic flows of such large scale are almost invariably turbulent. Additional turbulence Is generated by features and roughness In the bathymetry or landscape.

Unlike the laboratory, where tools such as Particle Image Velocimetry (Ply), Particle Tracking (P110 and Dye Visualisation (DV) aie readily used to investigate the spatial characteristics of turbulence (e.g. in water or wind tunnels), measurement devices for the marine environment are more limited in capability. Typically, measurement devices are point instaiments (e.g. marine Laser/Acoustic Doppler Anemometers (1DM) and Mlcrostructure Profilers), or have a measurement domain limited to a line (e.g. Acoustic Doppler Current Profilers, ADCP). Many methods are affected by water quality, thus requiring seeding or partlcul.ates in the flow to work effectively.

Some attempts have been made to utilise Ply for planar measures in marine and atmospheric flows, but the extent of the plane and the optical constraInts significantly restrict the spatial extents over which the technique is available. The quality of the seeding, and therefore the accuracy and robustness of the technique, cannot be easily controlled.

As a result, most or all measurements of turbulence in marine and atmospheric flows have a highly limited spatial extent, I.e. a point or a line, and limited spatial resolution. Many measurements have no dIrectIonalIty or limited dimenslonality, i.e. measure a speed or a dIssipation rate, rather than a velocity vector, or measure fewer than three components of a velocity vector.

Further problems are caused by the long timescales required to converge on turbulent statistics, especIally For large scale turbulence. This is exacerbated by noise, and the time to converge on turbulent quantities greatly exceeds the time to converge on a mean flow distribution. In the case of tidal flows, this is can become terminal, since the mean flow is constantly changing, rapidly enough that the time period required to converge on turbulent statistical quantities for large eddy structures exceeds any time over which the mean flow could be considered constant, and this by orders of magnItude. This results in poor convergence ol'turbulent spectra at the large scales.

Acoustic Doppler Current Profilers GADCP) have some ability to measure turbulence. However, their application may be impaired by insuFficient spatial resolution, high noise levels. ;ncomplete data and a constantly changing tidal flow (i.e. the measurement time period is implicitly too short to achieve statistical convergence of turbulence metrics, especially high order indices). Noise can be accounted for to some degree (using assumpt;ons of isotropy, as described in the article Method for Identification of Doppler Noise Levels In Turbulent Flow Measurements DedIcated to Tidal Energy.

by Richard J.B. Thomson J., Polagye B. and Bard J.. European Wave and Tidal Energy Conference 2013), but a problem called haystacking' Q.e. poor convergence of the spectrum (or large and/or slow motions) remains: in reference to ADCP data, bulk tidal motion (considered colloquially to be the mean) is incorporated into or otherwise distorts turbulence data.

However, the Issue of turbulence, along with wave propagation, meteorological effects and many other (typically unsteady) fluid flow and environmental effects impact the generation of power from wind turbines, tidal stream turbines and wave energy converters.

These issues must all be considered at the assessment, design and analysis stages of building power plants. The presence of unsteadiness in the flow affects mean and Instantaneous energy yield. as well as through-life dynamic loading on structural, mechanIcal and electrical components.

Due to the large range of scales involved (from geographic to sub-mm scales of turbulence), the computational effort required to simulate turbulence in geographic flows is currently prohibitive, as is tne effort which would be required to survey (for bathymetry/landscape) and to establish inflow conditions for a computational domain.

Attempts to computationafly simulate turbines or other energy generation devices within geographic flows complicates matters further -any attempts to model effects of turbulence must be modified to take Into account the energy sink represented by the device as well as accounting for the local change in turbulent characteristics caused by the device. Moreover, to ascertain accurate performance of the device, fine scales of turbulence must be Incorporated Into the simulation In order that separation characteristics and skin friction quantities are accurately computed. To understand dynamics of the device, the computation must be time resolved and the nature of turbulence at the inlet prohibits the use of symmetry in reduction of computational effort.

In the wind engineering community, attempts to tackle turbulence have relied predominantly on point measurements (at a proposed hub height) or line measurements using masts on which to mount instruments. A series of masts is often used to understand spatial variation of turbulence and wind speed over proposed sites. Such measurements can be used to generate turbulent spectra. Similarly, spectra in the marine environment can be pmduced from ADCP and other anemometer data. Due to the limitations of instrumentation discussed above, produced spectra may only be partial, i.e. not resoMng parts of the spectrum at both upper and lower ends, or suffer from haystacking.

In analysis of turbines, low-order computational techniques such as Blade Element Momentum (BEM) and Actuator Disk (AD) approaches have been used. In some cases, Lifting Line, Lifting Surface, Free Vortex, and Surface Panel methods have been used to provide Improved integrity with respect to BEM and AD approaches. These methods provide considerably improved computational speed conipared to fully viscous Computational Fluid Dynamics (CFD) approaches, such as ReynoldsAveraged Navier Stokes (RANS) and Large Eddy Sirnuiatbn (LES). However these approaches are less generalisable in terms of the geornetdes that can be analysed easily.

Most cornputtonal anayses use uniform inflows to sirnplfty the problem. Mean boundary layer proliles are also often used at the inlet of a computational doman to represenL a changing mean inflow with heiaht.

Fully vscous CFD modeling (RANS, LES and variants) often use simple parameterised models to reflect the effect of turbulence a typical twoparameter model may assume a representative turbulent lengthscale and intensity. This reflects dissipation of energy due to turbulence, but does not compute unsteady dynamics.

Aspects of the invention address or at east ameliorate at least one of the above issues.

In one aspect, the invention provides a method for approximating at least one quantity representative of turbulence in a marine flow, comprising a unit: determining at least one profile of the marine flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and using at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function as a function of the at least one size parameter and/or the strength parameter.

The profile may be a mean profile.

The method may further comprise the unit performing a convolution of the at least one probability density function with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the marine flow. The method may further comprise the unit outputting the at least one probability density function and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a control unit configured to control an operation of an array of at least one device adapted to convert kinetic energy of the turbulent marine into electrical energy. The method may further comprise the unit outputting the at least one probability density function and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a design unit configured to perform a design of at least one device adapted to be placed in the marine flow.

The selected eddytype may comprise at least one of the following: type A, and/ortype B, and/ortype C, and/or a single line element, and/or a ring.

The method may further comprise the unit receiving simulation data and/or measurement data in order to determine the mean profile, and determining the mean profile using at least one of the following: an analytical solution, an analytical fit to unconverged measurement data, and/or a converged average of raw measurement data.

Where a mean flow of the marine flow over a first time window associated with turbulent motions in the liquid is below a predetermined threshold, the method may further comprise the unit applying a filtered value or using data over a second time window narrower than the first time window, so as to generate a mean flow of the marine flow. The method may further comprise the unit performing the approximating one or more times.

In another aspect, the invention provides a method for approximating at least one quantity representative of turbulence in a fluid flow interacting with at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy, comprising a unit determining at least one profile of the fluid flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; using at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function as a function of the at least one size parameter and/or the strength parameter; and outputting the determined at least one probability density function to a simulation unit configured to simulate, in a simulation domain, a behaviour of the turbulent fluid flow interacting with at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy for design or operation purposes.

The profile may be a mean profile.

The method may further comprise the unit performing a convolution of the at least one probability density function with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the fluid flow; and outputting the determined turbulent spectra and/or Reynolds stress distributions of the fluid flow to the simulation unit.

The method may further comprise the unit generating a distribution field of the selected at least one eddy type, oriented in the streamwise direction of the fluid flow; determining a velocity u(x,y,z,t) induced by the generated distribution field, at at least one control point (x,y,z) at an instant t, by implementing a Biot-Savart law; and advecting the generated distribution field through the simulation domain in the flow direction overtime.

The method may further comprise the unit outputting the determined probability density function and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit configured to use at least one of the following models: a Free Vortex Model, a Lifting Line and/or Surface Analysis, a Panel model, and/or a Blade Element Momentum Model. The method according may further comprise the unit outputting the turbulent spectra and/or the Reynolds stress distributions of the fluid flow to the simulation unit configured to use Synthetic Eddy Methods, for finite volume and particle based Computational Fluid Dynamics analyses, such as Large Eddy Simulation and Smoothed Particle Hydrodynamics.

The method may further comprising the unit outputting the determined probability density function and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit forming a control unit configured to control an operation of an array of at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy and/or the simulation unit forming a design unit configured to perform a design of at least one device adapted to be placed in the fluid flow.

The method may further comprise the unit distributing the at least one eddy type randomly in the streamwise direction and in the cross-stream direction; and/or according to a predetermined distribution function. The method may further comprise the unit maintaining the eddy type constant overtime, or modifying the eddy type as a result of a self-influence and/or an influence of at least one device placed in the turbulent fluid flow and/or at least a wake.

The method may further comprise: at least one module of the unit performing the deconvolution; at least one module of the unit determining at least one quantity representative of the turbulence in the flow; and a reconciliation module reconciling outputs of the modules.

The method may further comprise an optimisation module implementing Machine Learning and/or Artificial Intelligence to the reconciliation module. The reconciliation module may implement a Projection Onto Convex Sets, POCS, algorithm.

The unit may perform the approximating one or more times.

In another aspect, the invention provides a unit for approximating at least one quantity representative of turbulence in a marine flow, configured to: determine at least one profile of the marine flow; select at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determine a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and use at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function as a function of the at least one size parameter and/or the strength parameter.

The profile may be a mean profile.

The unit may be configured to perform a convolution of the at least one probability density function with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the marine flow. The unit may be configured to output the at least one probability density function and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a control unit configured to control an operation of an array of at least one device adapted to convert kinetic energy of the turbulent marine into electrical energy. The unit may be configured to output the at least one probability density function and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a design unit configured to perform a design of at least one device adapted to be placed in the marine flow.

The selected eddy type comprises at least one of the following: type A, and/or type B, and/or type C, and/or a single line element, and/or a ring.

The unit may be configured to: receive simulation data and/or measurement data in order to determine the mean profile, and determine the mean profile using at least one of the following: an analytical solution, an analytical fit to unconverged measurement data, and/or a converged average of raw measurement data.

Where a mean flow of the marine flow over a first time window associated with turbulent motions in the liquid is below a predetermined threshold, the unit may be configured to apply a filtered value or use data over a second time window narrower than the first time window, so as to generate a mean flow of the marine flow.

The unit may be configured to perform the approximating one or more times.

In another aspect, the invention provides a unit for approximating at least one quantity representative of turbulence in a fluid flow interacting with at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy, configured to: determine at least one profile of the fluid flow; select at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determine a velocity signature and/or a turbulent intensity signature, for each selected eddy type; use at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function as a function of the at least one size parameter and/or the strength parameter; and output the determined at least one probability density function to a simulation unit configured to simulate, in a simulation domain, a behaviour of the turbulent fluid flow interacting with at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy for design or operation purposes.

The profile may be a mean profile. The unit may be configured to: perform a convolution of the at least one probability density function with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the fluid flow; and output the determined turbulent spectra and/or Reynolds stress distributions of the fluid flow to the simulation unit. The unit may be configured to: generate a distribution field of the selected at least one eddy type, oriented in the streamwise direction of the fluid flow; determine a velocity u(x,y,z,t) induced by the generated distribution field, at at least one control point (x,y,z) at an instant t, by implementing a Biot-Savart law; and advect the generated distribution field through the simulation domain in the flow direction over time. The unit may be configured to output the determined probability density function and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit configured to use at least one of the following models: a Free Vortex Model, a Lifting Line and/or Surface Analysis, a Panel model, and/or a Blade Element Momentum Model. The unit may be configured to output the turbulent spectra and/or the Reynolds stress distributions of the fluid flow to the simulation unit configured to use Synthetic Eddy Methods, for finite volume and particle based Computational Fluid Dynamics analyses, such as Large Eddy Simulation and Smoothed Particle Hydrodynamics.

The unit may be configured to output the determined probability density function and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit forming a control unit configured to control an operation of an array of at least one device adapted to convert kinetic energy of the turbulent fluid flow into electrical energy and/or the simulation unit forming a design unit configured to perform a design of at least one device adapted to be placed in the fluid flow.

The unit may be configured to distribute the at least one eddy type randomly in the streamwise direction and in the cross-stream direction; and/or according to a predetermined distribution function.

The unit may be configured to maintain the eddy type constant overtime, or modify the eddy type as a result of a self-influence and/or an influence of at least one device placed in the turbulent fluid flow and/or at least a wake.

The unit may further comprise: at least one module configured to perform the deconvolution; at least one module configured to determine at least one quantity representative of the turbulence in the flow; and a reconciliation module configured to reconcile outputs of the modules.

The unit may 1irther comprise an optimisation module configured to implement Machine Learning and/or Artificial Intelligence to the reconciliation module. The reconciliation module may be configured to implement a Projection Onto Convex Sets, POCS, algorithm.

The unit may be configured to perform the approximating one or more times.

The unit may be implemented at least partially as software or firmware and/or at least partially in a physical casing.

Aspects of the invention extend to computer program products such as computer readable storage media having instructions stored thereon which are operable to program a programmable processor to carry out a method as described in the aspects and possibilities set out above or recited in the claims and/or to program a suitably adapted computer to provide the system recited in any of the claims.

The invention has numerous advantages over the prior art.

The invention may be apphed to both tidal and atmospheric turbulent flows comprising boundary layers of large scale (e.g., geographic).

The invention does not need although may beneficially utilise input data from measurement tools such as Particle Image Velodmetry (PIV), Particle Tracking (PTV) and Dye Visualisation (DV). and may use measurement devices, such as point instruments (e.g. manne Laser/Acoustic Doppler Anemometers (LDAs) and Microstructure Profilers) or instruments having a measurement domain limited to a line (e.g. Acoustic Doppler Current Profilers, ADCP) and other anemometer data.

in combination with e.g., ADCP5, the invention may have the advantage of deriving turbulent quantities From the profile, e.g., the mean profile, mean flow profiles converging more rapidly than turbulence metrics. The invention may thus overcome the haystacking problem of the pnor art. may improve overall convergence and may be far less vulnerable to noise in the measurement data.

The invention may enable simulation of turbulence in geographic flows, with an acceptable computational effort. The invention may provide convergence of turbulent spectra at the large scales, and is not affected by haystacklng. The Invention may be used In combination with computational techniques such as Blade Element Momentum (BEM), Actuator Disk (AD), Lifting Une, Lifting Surface. Free Vortex, Surface Panel, Computational Fluid Dynamics (CED), such as Reynolds-Averaged Navier Stokes (RANS) and Large Eddy Simulation (LES). The invention may thus be used to aid selection of an inlet condition for a higher order CFD process, in a smaller number of high order simulations, where it is computationally expensive but allows independent validation of some of the scenario cases run to improve confidence in the lower order simulation technique.

The invention may thus enable taking into account the issue of turbulence, along with wave propagation, meteorological effects and many other (typically unsteady) fluid flow and environmental effects, e.g., the generation or power From wind turbines, tidal stream turbines and wave energy converters. As a result, the invention may be applied in the fields of wind and tidal power engIneering for assessment of available resource, energy yield and structural loading characteristics.

The invention may also thus enable taking into account the issue of turbulence, along with wave propagation, meteorological effects and many other (typically unsteady) fluid flow and environmental effects, at the assessment, design and analysis stages of building power plants. As a result, the invention may be applIed to computational simulation of aerodynamIc and/or hydrodynamic loading on structures and/or devices present In a turbulent flow.

The invention may thus enable taking into account the presence of unsteadiness in the flow and how it affects mean and instantaneous energy yield, as well as through-life dynamic loading on structural, mechanical and electrical components.

The invention may thus have the advantages of Coherent Structural Modeling (CSM) in marine turbulence.

The invention may be integrated to many measurement data, in order to provide net improvement in accuracy, robustness or representation of physical behaviour in post* processed results.

The invention may reveal dynamics of the fluid flow for a period of time, but may also be applied to multiple or many scenarios In order to ascertain statistics related to hydrodynamic loads, load dIstributions, generated power and other performance variables, thanks to its computational efficiency. This many-run' use can therefore be used to ascertain peak loadIngs in normal usage and under extreme environmental loading scenarios, useful in certification processes and specification of component strength and design. The many-run use can also be used to ascertain lifetimes of componentry Qcnowledge of load spectra allows lifetime and fatigue studies to be carried out), useful In financial modeling as well as cost/value engineering of devices. The many-mn use can also be used to provide predictions of the energy yield of potential and existing turbine arrays which take site turbulence into account.

Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings in whicfl: Figure 1 schematIcally illustrates an example method according to the disclosure; Figure 2 schematically illustrates an example unit implementing a method according to the disclosure; -10 -Figure 3 schematically iflustrates an example boundary layer with wafl and a mean flow profile; Figure 4 schematicafly illustrates fidds of realistk:aHy shaped and representative eddies, Figure 5 schematically fliustrates an example of a probabiltty density function, as a function of the strength parameter and/or the size parameter: Figure 8 schemaficafly iflustrates an example representative hairpin vortex with strength and size parameters; and Figure 7 schematically illustrates a field of eddies advecting through a turbine disc. showing nduction ot velocity at control points on a turbine blade.

In a ol the Figures, similar pals are referied to by like numerical references.

Overview of a unit and a rnthod Figures 1 and 2 schematically illustrate a unit I configured to approximate at least one quanhty representative of turbulence in a tuid, e g. a liquid such as a marine ulow in one non-limiting exampe. As described in more detail below, the quantity may be a shape. and/or a size, and/or a strength and/or a distribution of the turbulence, represented by at least one type of coherent structure, relërred to below as an eddy type.

The unit I is thus mainly configured to: determine, in 31 0, a profile, preferably the mean prohl e, ol low quantities in the fluid; especiaHy the mean velocity profile: select, in 811 at east one eddy type. preferably two eddy types, representative of the turbulence, utilizing experience arid available validation data such as visualisations or measurements to select the shape types: determrne, in 812. a turbulent quantity signature, such as a velocity signature (sucri as a velocity defect signature) and/or a turbulent intensity signature (usually both), for each selected eddy type; and perform. in 313. a deconvolution of the determined signatures from the profile(s).

preferably the mean prcfi!e( , determined in 810, in order to determine, for each selected eddy type.

at least one probabil!ty density hinction 41 as a function or the strength parameter and;or' the size parameters. In -813 the unit uses at east one determined signature to perform the deconvolution of the profile. eg. a mean profile, such as the mean velocity profiie.

Figure 3 schematically illustrates a boundary layer determined in 310.

-11 -As known to the skilled in the art, the boundary layer is a region of fluid flow adjacent to a solid (or relatively solid) surface. As explained in the introductory part, atmospheric and tidal flows contain large scale boundary layers, with land (or the sea surface) acting as the boundary (in atmospheric flows) and a seabed 11 acting as the boundary in marine flows. in many flows, especially geographic ones, the Reynolds Numbers of boundary layers are large enough for the boundary layer to be turbulent -le. be comprised of a profile, e.g., a mean flow profile, 12 varying with distance from the boundary and a superimposed component that fluctuates In time due to turbulent eddies.

In $10, in order to determine e.g., the mean velocity profile, the unit I may be configured to receive simulation data or measurement data. As explained in greater detail below, the measurement data may be provided by measurement devices. such as point instruments (e.g. marine Laser/Acoustic Doppler Anemometers Q..DAs) and Microstructure Profilers) or instnirnents having a measurement domain limited to a line (e.g. Acoustic Doppler Current Profliers, ADCP) and other anemometer data.

In order to determine e.g., the mean velocity profile from the simulation data or measurement data, the unit I may be further configured to use at least one of the following: an analytical solution, an analytical fit to un-converged (noisy) measurement data, and/or a converged average of raw measurement data.

In $10, in embodiments where a mean flow of the fluid over a first time window (e.g. the time span of measurement data over many tidal cycles) is not representative of the mean flow (e.g. for marine use wliere mean flow over a long period of time is close to zero), the unit I may be further configured to apply a filtered value (such as a windowed average or value filtered using a Kalman filler) in order to use data over a second time window narrower than the first to be representative of a mean flow. This Is the case e.g. for marine use in order to perform decomposition (or turbulence at a given point In the tidal cycle. For example, a windowed average may be applied to measurement data over a timescale at least as long as that associated with the turbulent motions (over the second window) but shorter than the a recorded full tidal cycle (the first window) to get a representative mean flow as a function of time throughout the tidal cycle, in the absence of short timescale turbulent motion. As already stated, alternatively data must be taken over a sufficiently large number of tidal cycles that average flows for an entire cycle can be produced.

In $11 * the unit 1 selects at least one eddy type representative of the turbulence, utilizing experience and available validation data such as visualisations or measurements including the mean profile to select the shape types.

The InventIon takes advantage oF tne fact that turDulence in boundary layers 12, as shown in Figure 3. comprIses coherent structures, as shown In Figures 4 and 6, especIally haIrpin vortices' 33 (so called due to the appearance of a common eddy type). Figure 4 shows a field of turbulent eddies 33 -12-having complex shapes In a flow. The field of coherent structures 33 may preferably be simplIfied by a field of analogs or representative structures 32, It Is appreciated that the simplified representative structures 32 may be used for computational efficiency by the unit 1, compared to more complex structures 33.

To represent the coherent structures present in turbulence, at least one type of representative structure (eddy type) is used. Each eddy type comprises: at least one straight or arcuate line vortex element 321, 322: a strength parameter 23 Q.e. K. representative of the cIrculatIon as known to the skilled In the art); and at least one geometric parameter 22 determining the size, orientation to the flow direction, orientation to the boundary, and location in the wall-normal direction of the line vortex element(s).

Figure 8 shows an example eddy type known as a hairpin or delta vortex comprising: four line vortex elements 321, 322 each having strength parameter 23 Qs. circulation K); a single geometric parameter 22; two parallel straight lines 321. separated by a distance 21 related to size parameter 22 (e.g. IS times distance parameter h), and oriented in the mean flow direction 31; and two inclined straight lines 322, from an end of the lines 321 and joining at a tip 323 The tip 323 Is located at a height and/or size parameter 22 (i.e. height h) from a plane formed by the two parallel straight lines 321 * and at a downstream distance equal to the size parameter 22 from the end of the lines 321.

Figure 4 shows a field of representative eddies 32 in a flow, all eddies having the same type with a distribution 41 of sizes 22 and strengths 23.

The use of the complex coherent structures 33, and/or their representative structures 32, by the unit I to perform analyses of turbulence may be reterred to as Coherent Structural Modeling (CSM), and the selection of the eddy types by the unit I in $11 may use observation. characterisatlon of structures from experimental data and/or use a technIque known by the skilled in the art from the articles: On the mechanism of wall turbulence", by Petty A E. and Chong M. S., J. Fluid Mech. (1982), Vol 119, which illustrates the concept of the horse-shoe, hairpin or A' vortex 34, and -13 -shows that these models give a connection between the mean velocity distribution, the broadband turbulence intensity distributions and the turbulence spectra; and "A wall-wake model for the turbulence structure of boundary layers, Part 1: Extension of the attached eddy hypothesis" and "A wall-wake model for the turbulence structure of boundary layers, Part 2: Further experimental support', by Perry A. E. and Marusic I.. J. Fluid Mech. (1995), Vol 298, which illustrate the eddy hypothesis wherein two eddy types, representative of the turbulence, enable determination of all the components of the Reynolds stresses. The first type may be referred to as type-A and shown in fIgure 8 may be interpreted as giving a wall structure'. The second type may be referred to as type-B and may give a wake structure', lithe above mean velocity formulation is accepted, once the eddy geometries are fixed for the two eddy types, all Reynolds stresses and associated spectra contributed from the attached eddies can be computed without any further empirical constants. This is done by using the momentum equation and certain convolution Integrals (or the sIgnature of Individual vortices).

The eddy types may be of type A, B and C as known to those skilled in the art or other types according to requirements for a particular flow (e.g. horizontal line vortices oriented In the cross stream direction to account for shear layers in the flow). Eddy types may be attached' to the boundary wall 11 (Le. have one or more ends of the vortex elements e.g. 321. 322 touching the boundary) or some distance from it (unattached'). Distance of unattached eddies from the wall can vary with the eddy size parameter(s) which is typically the case with type A eddies 34 and Type B eddies as known to those skilled in the art, but may vary with an additional geometric parameter for other eddy types.

In some embodiments, the unit may be configured to select at least one of the following eddy types: A, B. C, single line elements, or rings in order to account for features not necessarily appearing in laboratory or analytical studies of turbulence e.g., shear layers caused by therTnocllnes or density gradients in marine flows or additional structural content resulting from wave breaking.

Preferably, the unit 1 is configured to determine at least the strength and/or size distributions 41 for flelds 32 of each eddy type such as Type A' 34. Thus in 812, the unit deternnes a velocity defect signature and a turbulent intensity signature, for each selected eddy shape type.

In $12 the determination of the velocity signature (e.g., the velocIty defect signature) and/or the turbulent intensity signature Is performed with respect to a wall 11 normal distance, non-dimensionalised by an eddy characteristic size, for each eddy type selected. Eddy signatures (i.e. deficit functions and/or turbulent intensity functions) descnbe (for an eddy of particular type having -14 -unit characteristc size and strength) the contribution of an individual eddy structure to turbulent intensity, spectra and vebcity deficit thstribuUons of a flow containing that single eddy at unit size.

In addition to the presence of a boundary layer wa 11 (e.g., the seabed), the free surface also reqtures considerafion when computing velocity and/or intensity signatures for madne applications.

In 513. the unit I periorms a deconvolution of the determined signatures, in order to determine, for each selected eddy type, at least one probabiiity density funchon 41 as a function of the strength parameter and/or the geometric parameter(s) e.g. size 22, as shown in Figure 5.

In $14. the unit 1 may perform convolution of at east one probabihty density function 41 with the eddy signatures for eddies of unit parameter value. This convolution of individual signatures with PDFs 41 of at least one parameter for an entire l.eld of stnctures 32 allows determination ot fuU turbulent spectra and Reynolds stress distributions in a fluid containing the field o structures 32 whose parernetens are distributed accorthng to the PDFs 41.

In some embodin]ents. for vaUdation purposes, turbulent spectra derived using this technique car. be validated against turbulent spectra directly calcuiated from unsteady flow measurements. Unit

Figure 1 sian schematically iliustrates an exemplary unit 1 further compdsing at least one nodule 123 configured to determine at least one quantity reoresentative of a turbulent stream of fluid.

To advantage, the unit 1 further compnses a reconciliation module 5 configured to reconc!ie the at least one determination of the at least one module 120 and the at least one approximation of the at least one unit 1 according to the disclosure, e.g. performed by at least one dedicated module 110.

The unit 1. and particularly the at east one module 120. may thus he used to advantage where data (such as measurement data) integrity is sufficient to he reliable for parts of the spectrum (i.e a range of scales) or for parts of the spatial domain for which dta is required. or where data contains aspects of behaviour of the fluid not encompassed by the OSM model (e.g. internal wave breaking) implemented e.g., by the module 110 of the unit 1. This part of the data from the module 120 is thus taken into account by in the unit 1, and the OSM model may he applied by the modue 110 of the unit 1 for other parts, and then taken into account by in Erie unit I. An optimisation module 51 may be conligured to implement Machine Learning and/or Artificial Intelligence to the reconciliation module 5. The module 5 may implement reconciliation or a weighting framework, such as Projection Onto Convex Sets (P005).

-15 -It will be aupreciated that one possible advantage of data reconciation is to provide data conditioning and/or postprocesshiq rooted in physical knowlec:ge of the fluid flow characteristics. This is equivalent to denoising or fiRering results, but with a filter selected on the basis of direct observations of the turbulent structure al play in the measurement, as opposed to an arbitrarily selected filter (e.g. gaussian smoothing). Within this framework, results can be based strongly on measurement data by the unit 1 (such as coming from at least one module 120 and/or sensor 20) where it is valid, whilst.

results depending on data outside avad measurement range (e.g. outside the band limit or spatial resolution, of the measurement natrument or sensor 20. or in locations such as ciose to the free surface where data inteqrty is frequently poor due to wave interaction) to be ascertained by the unit 1 using the more robust and tess noisy mean flow data from the module 110 of the unit 1. Similarly results can he based strongly on measurement data from at east one module 120 and/or sensor 20 ir' regions where the OSM module 110 of the unit 1 does not appropriately rnodei [he physics in play.

such as part of a domain suect to internal wave breaking or a reg;on ol the spectrum where a particular bathymetric feature causes a spike hut more strongly on CSM behaviour from the module 1 5 110 of the unit 1 elsewhere where the model is more valid In enibodirnents involving at east two modules 110 or at east two modules 120; the module 5 allows reconciliation of multiple instruments operating in adjacent, overlapping or separate parts of the spectrum or domain. Data from each instrument can be reconciled into a single results set valid across a wider range, based on CSM adjusted and weighted according to confidences by the module 5.

It wilt be appreciated that the at least one module 120 and/or the at least one module 110 and/or the reconcihation module 5 may be implemented at least partiatly as software or firmware. Sonic functionalitres of the at least one module 120 and/or the at least one modue 110 and/or the reconciliation module S may thus be performed interchangeably, or at least partialty merged Additionally or alternatively the at least one module 120 and/or the at lea;t one unit 110 and/or the reconciliation module 5 may be implemented at east partially in a physical casing.

Overview of applications As shown also in Figure 1, the unit I may output tho results to a simulation unit, such as: a control unit 300 conlioured to control an operation of an array of at least one device 3 adapted to convert kinetic energy of the turbulent fluid into etectrical energy (such as wind turbines, tidat stream turbines and wave energy converter's); and/or a design unit 101 configureo to perform a design of at least one device 3 adapted to be placed in the turbuient fiuid (such as wind turbines, tidal stream turbines and wave energy converters) -16 -a simulation unIt 102 configured to simulate a behaviour of the turbulent fluid.

It is thus appreciated that in examples and as explained below, a representation of turbulence in the fluid (e.g., comprising coherent structures 34 as shown in Figure 5) whose strength.. distribution.

shape and size is determined by the unit 1 using very preferably a CSM, can he used H a hydrodynarn!o or aerodynamic model, such as computational simulation (e.g. fl calibration of turbulence modeis for Computational Flud Dynamics packages) and/or experimental verification of aero/hydrodynamic performance of energy generation devices such as wind and tidal turbines. The strength. distribution., shape and size of the coherent structures 34 may comprise the turbuient 1 0 spectra and the Reynolds Stresses, The unit I may be configured to output the turbulent spectra and We Reynolds stress distributions of the stream to a simulation unit 102 conligured to use at least one of the following models known to those skiued in the art a Free Vortex Model: a Lifting Line and/or Surface Anaysis, a Panel model.

arid/or a Blade Element Momenti.im Model, arid/or Synthetic Eddy Methods (as described e.g.. in the article "A New Divergence Free Synthetic Eddy Method or the Reproduction of Inlet Flow Conditions for LES", by Poietto R., Craft T. and Revell A.; Flow Turbulence Cornhust (2013) 9i:519-539), to produce inlet conditions representing the actual measured turbulence at a site: suitabe for finite volume and particle based Computational Fluid Dynamics analyses. such as Large Eddy Simulation (LES) and Smoothed Particle Hydrodynamics.

As shown in Figures 2, 4 and 6, ri examples in SI 5 the unit I may be conhgured to: generate a distribution held ol the selected at east two eddy types (e.g. Type A eddies 34).

oriented in the streamwise direction 31 of the fluid; determine a velocfty u(x,y,z,t) 51. induced by the generated distribution field, at at least one control point (X:Y:Z) 53 at an instant t. by implementing a Biot-Savart law as known to those skilled in the art; and advect the generated distribu ion field through the simulation domain in the flow direction 31 over time.

The unit I may be conhigured to distribute the at east two eddy types randomly n the streamwise direction 31 and in the cross-stream direction and/or according to a predetermined distrihutior: function.

In examples where the unit 1 0-1 and/or 102 is conhigured to using a Blade Element Momeniurn (BEM) Model or a Free Vortex Model (FVM), the control points 53 may be located on a blade 52 oF a device -17- 3. such as a turbine, or elsewhere (e.g. control points of a wake sheet or other elements In the simulation), at a point in time t.

The unit I may maintain the eddy types 32 and/or 33 constant over time, or modify the eddy types as a result of a self-influence and/or an influence of at least one device 3 placed in the turbulent fluid and/or wakes.

Examples of applications It is known that ADCPs are capable in measuring mean flow profiles (hence Current Profilers) and an ACP output dataset typically consists of a set ol mean flow profiles, as expected at different points throughout the tidal cycle.

In an example of an application of a unit according to the disclosure, and as shown in FIgure 1, an ADCP unit 20 may thus be deployed gathering high-resolution time resolved data for one or more lunar cycles. A microstructure proriler 200 may also be deployed, measuring small scale (e.g. sub 1 m) scales.

In SlO the unit 1, e.g. the modules 110 and/or 120. implements conventional post-processing to the data (windowed averaging or other filtering), producing mean profiles at different points in the tidal cycle. Analysis and treatment of the high resolution ADCP data from the unit 20 produces turbulent spectra, but they are usually highly noisy, band limited and suffer from haystacking. Analysis of the data from the Microstructure Profiler 200 produces a partial turbulent spectrum at the small scales (outside the band of measurement of the ADCP) with good confidence but at a single point in the water column.

Tnerefrwe, preferably, the unit 1 uses data from the module 110 where a CSM according to the dtsdosure is preferably applied to the mean flow profiles from the ADCPs 20 to ascertain PDFs 41 of structural content, and their evolution throughout the tidal cycle. Smooth turbulent spectra across the entire relevant bandwidth are produced for each profile.

These turbulent spectra produced by the module 110 are conwared by the module 5 to the ADCP data from the unit 20 and may be found to be within the measurement error. However if at the small scales they do not match with data from the location of the Microstructure Profiler 200, the module 5 implements a reconciliation algorithm, and thus reapplies the CSM according to the disclosure using the module 110 and good quality data from the Microstructure Profiler 200, in order that the physical model applied better represents motion at the dissipative scales for which reliable data is available.

Using the updated CSM data, PDF5 41 of turbulent structural content (size and strength distributions as a function of time) are used to create a field of eddies and calculate fluctuations in velocity components in the flow as a function of time.

These components are superimposed onto velocity components from other effects (e.g. self influence or influence of other turbines, influence from waves on the free surface and bulk motion) to calculate the velocity field at the control points of a Free Vortex Model. The simulation Is time-stepped.

allowing computation of loads and energy yield as a function of time, including the dynamics associated with turbulence.

Using this example analysis, dynamic loadings and turbine behaviour as a result of turbulence and as a function of time can be calculated In a low order (computatlonally efficient) manner. Wave loadIngs and pressure gradients (e.g. due to bathymetric effects) may also be Included through superpositIon

of appropriate potential flow fields.

The approach described above reveals dynamics of the fluid flow for a period of time; however due to Its computational efficiency, the approach may be applied to multiple or many scenarios in order to ascertain statistics related to hydrodynamic loads, load distributions, generated power and other performance vanables.

This many-run' use can therefore be used to ascertain peak loadings in normal usage and under extreme environmental loading scenarios, useful in certification processes and specification of component strength and design.

The many-run use can also be used to ascertain lifetimes of componentry (knowledge of load spectra allows liFetime and Fatigue studies to be canled out), useful in financial modeling as well as costtvalue engineering of devices.

The many-run use can also be used to provide predictions of the energy yield of potentIal and existing turbine arrays which take site turbulence into account.

Use of CSM to aid selection of an inlet condition for a higher order CFD process can be used in a smaller number of high oider simulations -computatlonally expensIve but allowing independent validation of some of the scenario cases run to improve confidence in the lower order simulation technique.

The above embodiments are to be understood as lustratlve examples of the invention.

Further embodiments of the invention are envisaged. It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the -19-embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not desthbed above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.

Claims

-20 -CLAIMS1. A method for approximating at least one quantity representative of turbulence in a marine flow, comprising a unit (1): determining at least one mean profile of the marine flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and using at least one said determined signature to perform a deconvolution of the mean profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter.
2. The method according to claim 1, further comprising the unit (1): performing a convolution of the at least one probability density function (41) with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the marine flow.
3. The method (1) according to any one of claims 1 or 2, further comprising the unit (1): outputting the at least one probability density function (41) and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a control unit (300) configured to control an operation of an array of at least one device (3) adapted to convert kinetic energy of the turbulent marine into electrical energy.
4. The method (1) according to any one of claims 1 or 2, further comprising the unit (1): outputting the at least one probability density function (41) and/or the turbulent spectra and/or the Reynolds stress distributions of the marine flow to a design unit (101) configured to perform a design of at least one device (3) adapted to be placed in the marine flow.
5. The method according to any one of claims I to 4, wherein the selected eddy type comprises at least one of the following: type A, and/or type B, and/or type C, and/or a single line element, and/or a ring.
6. The method according to any one of claims ito 5, further comprising the unit (1): receiving simulation data and/or measurement data in order to determine the mean profile, and: -21 -determining the mean profile using at least one of the following: an analytical solution, an analytical fit to unconverped measurement data, and/or a converged average of raw measurement data.
7. The method according to any one of claims I to 6, where a mean flow of the marine flow over a first time window associated with turbulent motions in the liquid is below a predetermined threshold, further comprising the unit (1): applying a filtered value or using data over a second time window narrower than the first time window, so as to generate a mean flow of the marine flow.
8. The method (I) according to any one of claims Ito 7, further comprising the unit (1): performing the approximating one or more times.
9. A method for approximating at least one quantity representative of turbulence in a fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy, comprising a unit (1): determining at least one mean profile of the fluid flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; using at least one said determined signature to perform a deconvolution of the mean profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter; and outputting the determined at least one probability density function (41) to a simulation unit (101, 300) configured to simulate, in a simulation domain, a behaviour of the turbulent fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy for design or operation purposes.
10. The method according to claim 9, further comprising the unit (1): performing a convolution of the at least one probability density function (41) with the at least one determined signature for each eddy type, in order to determine turbulent spectra and/or Reynolds stress distributions of the fluid flow; and outputting the determined turbulent spectra and/or Reynolds stress distributions of the fluid flow to the simulation unit (101, 300).
11. The method according to claim 9, further comprising the unit (1): -22 -generating a distribution field of the selected at least one eddy type, oriented in the streamwise direction (31) of the fluid flow; determining a velocity u(x,y,z,t) induced by the generated distribution field, at at least one control point (x,y,z) at an instant t, by implementing a Biot-Savart law; and advecting the generated distribution field through the simulation domain in the flow direction over time.
12. The method according to any one of claims 9 to 11, further comprising the unit (1): outputting the determined probability density function (41) and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit (101, 300) configured to use at least one of the following models: a Free Vortex Model, a Lifting Line and/or Surface Analysis, a Panel model, and/or a Blade Element Momentum Model.
13. The method according to claim 10, further comprising the unit (1): outputting the turbulent spectra and/or the Reynolds stress distributions of the fluid flow to the simulation unit (101, 300) configured to use Synthetic Eddy Methods, for finite volume and particle based Computational Fluid Dynamics analyses, such as Large Eddy Simulation and Smoothed Particle Hydrodynamics.
14. The method according to any one of claims 12 or 13, further comprising the unit (1) outputting the determined probability density function (41) and/or turbulent spectra and/or the Reynolds stress distributions of the fluid flow and/or the induced velocity to the simulation unit (300) forming a control unit (300) configured to control an operation of an array of at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy and/or the simulation unit (101) forming a design unit (101) configured to perform a design ofat least one device (3) adapted to be placed in the fluid flow.
15. The method according to any one of claims 11 to 14, further comprising the unit (1) distributing the at least one eddy type: randomly in the streamwise direction and in the cross-stream direction; and/or according to a predetermined distribution function.
16. The method according to any one of claims 9 to 15, further comprising the unit (1): maintaining the eddy type constant overtime, or modifying the eddy type as a result of a self-influence and/or an influence of at least one device (3) placed in the turbulent fluid flow and/or at least a wake. fin

-Li -
17. The method according to any one of claims ito 16, further comprising: at least one module (110) of the unit (1) performing the deconvolution; at least one module (120) of the unit (1) determining at least one quantity representative of the turbulence in the flow; and a reconciliation module (5) reconciling outputs of the modules (110, 120).
18. The method according to claim 17, further comprising an optimisation module (51) implementing Machine Learning and/or Artificial Intelligence to the reconciliation module (5).
19. The method according to any one of claims 17 or 18, wherein the reconciliation module (5) implements a Projection Onto Convex Sets, POCS, algorithm.
20. The method (1) according to any one of claims 9 to 19, further comprising the unit (1): performing the approximating one or more times.
21. A unit (1) for approximating at least one quantity representative of turbulence in a marine flow, configured to: determine at least one profile of the marine flow; select at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determine a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and use at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter.
22. A unit for approximating at least one quantity representative of turbulence in a fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy, configured to: determine at least one mean profile of the fluid flow; select at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determine a velocity signature and/or a turbulent intensity signature, for each selected eddy type; -24 -use at least one said determined signature to perform a deconvolution of the mean profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter; and output the determined at least one probability density function (41) to a simulation unit (101, 300) configured to simulate, in a simulation domain, a behaviour of the turbulent fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy for design or operation purposes.
23. The unit according to any one of claims 21 or 22, implemented at least partially as software or firmware.
24. The unit according to any one of claims 21 to 23, implemented at least partially in a physical casing.
25. A method for approximating at least one quantity representative of turbulence in a marine flow, comprising a unit (1): determining at least one profile of the marine flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; and using at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter.
26. A method for approximating at least one quantity representative of turbulence in a fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy, comprising a unit (1): determining at least one profile of the fluid flow; selecting at least one eddy type representative of the turbulence, wherein each eddy type comprises at least one eddy size parameter and an eddy strength parameter; determining a velocity signature and/or a turbulent intensity signature, for each selected eddy type; using at least one said determined signature to perform a deconvolution of the profile, in order to determine, for each selected eddy type, at least one probability density function (41) as a function of the at least one size parameter and/or the strength parameter; and -25 -outputting the determined at least one probability density function (41) to a simulation unit (101, 300) configured to simulate, in a simulation domain, a behaviour of the turbulent fluid flow interacting with at least one device (3) adapted to convert kinetic energy of the turbulent fluid flow into electrical energy for design or operation purposes.
27. Computer readable storage media having instructions stored thereon which are operable to program a programmable processor to carry out a method according to any one of claims 1 to 20 or or 26 and/or to program a suitably adapted computer to provide a unit according to any one of claims 21 to 24.