Challenges in permeability characterisation for modelling the manufacture of wind turbine blades

As wind turbine blades continue to increase in size, and market competition grows, lean manufacturing has become even more important for OEMs. The rapid development of new blade designs, with greater performance, and reduced production waste are driving the need for predictive modelling of the blade infusion process. Such simulations are reliant upon Darcy’s Law for the description of fluid flow through porous materials and therefore depend greatly on the permeability properties of the blade preform materials. The characterisation of fabric permeability, although unstandardised, has been well studied in recent years as the focus of numerous international benchmarking efforts. However, the effective permeability properties of infusion consumables, core materials, and pre-cast elements are not so well defined or validated, despite their significance on infusion behaviour. Hence, the great variety of preform materials, stacking configurations, geometric features, and transition regions in wind turbine blades present considerable challenges in terms of permeability characterisation and subsequent modelling. This article reviews some of the challenges, opportunities, and alternatives for characterising permeability in common blade preform materials, along with examples of how these properties have been applied in numerical models to better simulate the resin infusion manufacturing process for wind turbine blades.


Introduction
Wind turbine blades are the largest and most complex composite structures being built today.As they continue to grow in size, they become more challenging to manufacture, and more costly to repair when manufacturing goes wrong.Subsequently, the ability to simulate their manufacture and predict potential issues with the manufacturing strategy is becoming more and more valuable.Figure 1 shows the composite layup of a thin sandwich structure representative of the materials involved in the vacuum infusion of a wind turbine blade.Here the composite preform consists of two configurations of glass Non-Crimp Fabric (NCF), unidirecitonal and biaxial, that act as the composite skins either side of a light-weight foam core with a complex arrangement of perpendicular, intersecting, machined grooves that are designed to improve both formability and rein flow.Additionally, consumable layers of resin distribution media, a perforated release film, and peel ply may be placed on top of the composite preform, inside the vacuum bag, to enhance the resin flow and ultimate part quality.The prediction of flow through, and filling of, these materials then becomes highly dependent on the properties of each material and their complex interactions.This article reviews the simulation of both the vacuum infusion process, used to manufacture wind turbine blades, and the important considerations related to material permeability for many of the common blade materials (as shown in Figure 1).

Vacuum infusion process modelling 2.1. Background
In the absence of consistent naming conventions for Liquid Composite Moulding (LCM) manufacturing processes [1], this article will refer simply to the process used for manufacturing wind turbine blades as 'vacuum infusion'.Other common names for similar processes include Vacuum Assisted Resin Transfer Moulding (VARTM), Resin Infusion under Flexible Tooling (RIFT), Vacuum Assisted Resin Injection (VARI), and Seemann Composites Resin Infusion Molding Process (SCRIMP), just to name a few.The vacuum infusion process fundamentally consists of the layup of reinforcing preform materials against a rigid mould before being sealed under a flexible tooling, typically a thin polymeric film.Then vacuum pressure is applied at an outlet port, such that resin from a higher (often ambient) pressure is driven into the preform, flowing towards the outlet, while the flexible tooling and reinforcing material is held in place by external ambient pressure.
When it comes to modelling this process, LCM simulations generally prioritise the prediction of resin flow behaviour during mould filling in order to avoid catastrophic dry spots.However, such models can also provide a useful estimate of the filling times with different infusion strategies [2,3,4], and more sophisticated models can also aim to predict saturation and void content [5,6], or local fibre volume fractions across a part [7].These filling simulations can then also be coupled with curing kinetics models [8] in order to better predict residual stresses and part distortion [9].Independent of the model complexity, the potential for optimising cycle times, reducing costs, and eliminating considerable trial-and-error in manufacturing is therefore particularly valuable to OEMs.
Many commercial and academic software packages exist for LCM simulation.Notably, the use of PAM-Composites/PAM-RTM (ESI Group) [10,11], RTM-Worx (Polyworx) [2,12,13], and LIMS (University of Delaware) [14] have been well demonstrated as tools specifically developed for composites manufacturing applications.While the more general Computational Fluid Dynamics (CFD) packages like ANSYS Fluent (ANSYS, Inc.) [15], COMSOL Multiphysics (COMSOL Inc.) [16], and OpenFOAM (The OpenFOAM Foundation) [11] have also been well demonstrated in this field.Depending on the desired scale of the infusion simulation, the assumptions and approximations necessary for modelling can vary significantly.Fundamentally, at the microscopic level, resin flow through a porous preform materials can be described by creeping (Stokes) flow since the fluid viscosity is relatively large and its velocity is relatively slow (meaning Re ≪ 1).However, despite the apparent simplicity of such a fluid dynamics model, the geometric complexity and stochastic nature of these materials makes accurate flow prediction particularly difficult.Micro-scale models, considering the flow between individual fibres in a preform, may simply rely on conventional Computational Fluid Dynamics (CFD) packages to predict 2D or 3D flow, based on simple geometric approximations or real scans from X-ray micro-tomography [17].As the simulation scale increases though, reasonable limits on the size and number of constitutive elements in the model necessitate significant degrees of homogenisation or geometric simplification.For example, at the meso-scale, where researchers often attempt to simulate fluid flow through stacked reinforcement materials or repeated unit cells, tow bundles are commonly homogenised and treated as a continuous porous or solid material [18,19,16].Then at the macroscale, details of the fabric weave and architecture are often eliminated in the homogenisation of fabrics to be treated as continuous layers, in order to simulate the full preform behaviour in larger parts [3,4].Finally, in the case of blade-scale (or boat hull) simulations, it may be necessary to homogenise the complete preform stack into a single equivalent material [20,21,2].
Figure 2 demonstrates the increasing limitations on element sizes as the dimensions of a model increases.Assuming the use of a full 3D model, consisting of a maximum of 10 7 or 10 8 total elements with reasonable aspect ratios, it becomes impossible to model individual plies of reinforcement fabric at the blade scale (let alone the consumable layers that are an order of magnitude thinner).Even at the meso-scale, it is often unreasonable to try to simulate individual fibres.Hence, at these larger simulation scales, where fibre bundles, fabric plies, or the whole layup needs to be approximated by a homogeneous porous material, the volume-averaged flow through these materials is then most commonly described by Darcy's Law, as shown in Eqn. 1 (assuming the fluid is incompressible and Newtonian).Here v is the averaged flow velocity, K is the permeability tensor for the porous material, µ is the viscosity of the fluid, and ∇p is the pressure gradient: For the purpose of vacuum infusion modelling, the viscosity of the fluid can easily be characterised as a function of temperature using standard viscometers or rheometers.Similarly, in most processes the pressure gradient is able to be monitored or controlled with relative ease.However, the characterisation of permeability properties poses a much greater challenge, as is discussed in detail in Section 3.
A further complication to this process is the well-documented dual-scale nature of the flow through fibrous reinforcement materials [22], where the flow within fibre tows is often driven by capillary forces but flow in the larger gaps between tows is dominated by viscous forces.Depending on the flow velocity, v, viscosity, µ, and ambient surface tension, γ, of the resin (commonly combined as in Eqn. 2 to form the Capillary number, Ca), the significance of viscous or capillary forces in the flow can be assessed.At high Ca, viscous flow drives the infusion as assumed by Darcy's Law, but can result in micro-void formation within the lagging tows.Alternatively at low Ca, capillary forces will lead the infusion through the tows with the potential for macro-void formation between the tows.Hence, an ideal infusion case may attempt to control the resin flow rate such that the capillary and viscous forces are well balanced to minimise void formation throughout the composite [23].This becomes especially important when high vacuum is not used to drive the infusion (i.e. for conventional Resin Transfer Moulding, RTM [5]) as there is a significant volume of air remaining within the composite mould.In most LCM processes however, the resin viscosity and infiltration velocity tend to result in a capillary number ranging from 10 −3 to 10 −1 [22], such that capillary forces can be neglected and flow is assumed to be Darcian and dominated by viscous forces [23].

Applications
Across existing literature, there are many examples of LCM process modelling.Early investigations of the Seemann Composites Resin Infusion Molding Process (SCRIMP) accounted for many of the same material systems and features seen in wind turbine blades, including distribution media, peel ply, and a low density core material with machined grooves to improve infusion [24,25].These studies also applied Control Volume/Finite Element Models (CV/FEM) for meso-scale filling analysis, observing good experimental agreement.Similarly, Dai et al [26] applied an academic software package (RTMSIM) to model the vacuum infusion of foam core composite sandwich panels, comparing the use of either distribution media or core grooves as flow enhancing options.Despite neglecting compaction and deformable bag behaviour, by assuming rigid tool moulds like conventional Resin Transfer Moulding (RTM), these early small-scale models still saw good experimental agreement.
Other work by Poodts et al [27] demonstrated the manufacturing and modelling of a 20 mm thick Carbon Fibre Reinforced Polymer (CFRP) component by RTM.This work showed significant asymmetry in the flow behaviour of the real parts due to fibre rearrangement and racetracking, which could not be predicted in the simulation software without manual manipulation.Such problematic fibre rearrangement was likely the result of the very high injection pressures (3-10 bar).For a vacuum infusion process, where injection pressures are typically 1 bar or less, such fibre rearrangement is therefore not expected to be an issue.
Another study comparing numerical and experimental RTM filling showed good agreement for the prediction of 2D flow around in-mould obstructions, using both PAM-RTM and OpenFOAM [11].However, for a second case with a narrow gap (around 1 mm) between dissimilar preform materials, the definition and prediction of race-tracking in the open channel was much less reliable, particularly as its geometry is difficult to accurately replicate.Furthermore, it was noted that any such gaps, spaces, infusion channels, or deep grooves cannot be simulated as open channels with dedicated Darcy-based solvers, but instead must be approximated as porous domains, with 100% porosity, and an equivalent permeability [11].
Correia et al [14] extended the application of their LIMS RTM software to the simulation of VARTM processes by defining a proportionality constant that accounts for the effects of fibre compaction, fibre volume fraction (porosity), and permeability as a result of using a deformable bag.This approach was then used to highlight filling time differences between RTM and VARTM processes.Further modelling complexity has been introduced by Trochu et al [6], who not only considered compaction effects but also investigated saturation and void formation.In this work, 2D and 3D LCM simulations for automotive composite parts were used to demonstrate how controlled flow rates (targeting an optimal capillary number) can improve mechanical performance in the final part by reducing overall void content.
At a larger scale, since part thickness is often much smaller than the width and length dimensions, it is quite common to neglect through-thickness flow and simulate the domain as a 2D shell with 3D curvature, often termed a 2.5D model [28].Early examples of this modelling approach within RTM-Worx, for the vacuum infusion of wind turbine blade (20 m) and boat hull (16 m) structures, have been introduced by Brouwer et al [2], although details of the material definitions were absent from the work.
Other research considering the experimental and simulated vacuum infusion of sandwich assemblies has shown a good prediction of filling times and flow behaviour for core materials, with a complex two-sided and interconnected groove arrangement, for boat hull applications [13].In order to reduce the geometric complexity of the model for RTM-Worx, two approaches were evaluated.First, a number of horizontal and vertical circular pipe elements were used to approximate rectangular core grooves with a similar cross-sectional area in 2.5D models.Secondly, a further simplification was applied (both for the core material and for the complete sandwich assembly), accounting for the thickness and porosity of each material layer in order to define equivalent properties for a single 2.5D layer [13].The permeability of this equivalent layer could then be derived empirically from simple 1D flow sandwich infusion experiments.Ultimately, this approach was well validated when applied to a complete boat hull infusion with similar materials, despite the reduction to a 2.5D model.Related work by the same authors showed that the simulated 1D flow behaviour across different sandwich assemblies (in terms of squared flow distance relative to time) is calculated to be somewhat linear, based on the reliance of Darcy's Law [12].In spite of general agreement between filling time predictions, the experiments exhibit greater non-linearity as a result of through-thickness flow behaviour.Subsequently, considerable error was observed between the simulated and experimental flow front positions during filling, particularly while the flow in the lower laminate lagged behind that of the upper laminate.Hence, the simulation results ultimately resemble a simple linear approximation of the non-linear experimental results.
In order to better account for transverse flow behaviour, a two-layer simulation approach (consisting of separate resin distribution media and reinforcement preform layers) has been proposed [29].This relies on an approximation of the through-thickness interactions and flow between two layers with very different permeability properties.This method has been applied to the infusion of a 3.5 m wind turbine blade, however the analysis was lacking realistic permeability properties and experimental validation.Alternatively, a multi-layered shell element method for 3D resin flow simulation has been developed in order to better account for through-thickness flow than conventional shell elements or other 2.5D approximations that rely on permeability averaging techniques [21].This approach was applied to macro-scale components, providing better estimates of the saturation and filling behaviour of different layers in the mould, but did not include experimental validation.Recent work by Yan et al [3] has observed good qualitative agreement between PAM-RTM infusion models and the experimental production of foam-core sandwich spoiler structures.Part thickness variations and final filling times were quite well predicted (10-15% deviation), while the models also helped to identify possible causes for manufacturing defects, but the determination of the foam core channel permeability remained unexplained.
Most relevantly, Koefoed [30] performed a comprehensive investigation of vacuum infusion process modelling for the manufacture of wind turbine blades.This work leveraged the fact that vacuum infusion strategies for full blades commonly rely on a linear infusion technique, where span-wise line inlets are used to fill the blade preforms in a chord-wise direction.Subsequently, the models and experiments in this study could be scaled down to prioritise realistic flow through 2D cross-sections from different areas of the blade, rather than attempting to model the full blade infusion.This presents an efficient method of predicting the filling behaviour around complex transition regions in the presence of reinforcement, core, and high permeability distribution media.Furthermore, this approach avoids the need for full 3D models, that would be beyond computational capabilities, or 2.5D shell models that require significant simplifications of the through-thickness flow behaviour.
Ultimately, across all applications and modelling methods, the characterisation and definition of permeability properties remains a key factor to the success and accuracy of any infusion simulation.Hence, the following section will focus on the various aspects of permeability that are most relevant to common wind turbine blade materials.

Permeability considerations
3.1.Reinforcement fabrics 3.1.1.Architecture and stacking Inherently, the internal structure and architecture of the reinforcing preform will have a significant effect on its permeability.For example, comparisons of engineering textiles with different weaving patterns, for the same fibre type, tow size, fibre volume fractions, and fibre sizings, have revealed significant differences in permeability [31].The key observation from this work was the association of permeability properties with the size and frequency of pore spaces: where a higher number of large pore spaces correlated with higher permeability.Evidently, any modification to a reinforcement fabric that may alter its pore sizes or distribution will significantly affect its permeability.Subsequently, meso-scale simulation of flow through fabric repeating unit cells has become a popular method for predicting permeability properties based on fabric architecture [32].
The stitching of fabrics and preforms has also been shown to significantly affect both inplane and through-thickness permeability, effectively creating channels for fluids to more easily pass through.For example, Talvensaari et al [33] observed that a greater number of stitches could increase the in-plane permeability of preforms, but also that stacking multiple stitched preforms together can result in higher in-plane permeability than the same number of plies in a single stitched preform stack.However, other work by Drapier et al [34] focusing on transverse (through-thickness) permeability, showed that such changes to the stacking arrangement had no measurable influence on transverse permeability.In this case, the stitching pattern was also determined to have no effect, with only the stitching density being seen to significantly affect the transverse permeability.For woven fabrics, the stochastic nature of nesting between different fabric layers has also been identified as the potential main source of scatter in the permeability behaviour of fabrics [35].
3.1.2.Deformation Another challenge to the characterisation and modelling of fabric permeability behaviour is the relatively compliant and deformable nature of the material.Inherently, as a result of the high performance reinforcing fibres, these materials are resistant to tensile deformation in the fibre directions, but depending on their architecture they are often prone to bending, shearing, and compression.In particular, in-plane shearing and out-of-plane compaction have both been seen to significantly affect permeability behaviour.For example, experimental characterisation of the in-plane permeability for a plain-woven carbon fibre fabric at 40°shearing has shown more than a 2-fold increase in its principal permeability, a 3-fold increase in anisotropy, and a 20°shift in the principal permeability direction from an undeformed state [36].Numerical investigations have also documented changes of a similar magnitude for glass fabrics [16].
Perhaps more importantly for vacuum infusion processes, that are reliant on ambient pressure across the vacuum bag, the transverse (out-of-plane) compaction of fibrous reinforcement materials can have a significant effect on its filling performance.Evidently, with increasing compaction pressure the fibre volume fraction increases, meaning the size and frequency of pores between tows and fibres will decrease, along with the permeability.Commonly, for the purpose of permeability characterisation, the fibre volume fraction, V f , is defined by Eqn.3: where n is the number of fabric layers, t is the total thickness of the preform stack, w A is the fabric areal weight (kg/m 2 ) and ρ f is the density of the constituent fibres.However, during infusion, as resin travels through a fibrous reinforcement two important phenomena occur [1].Firstly, at the advancing flow front the fibres are lubricated, enabling a further reduction in thickness (and increase of local fibre volume fraction, V f ) under the same bag compaction force [37].Secondly, while the flow front continues ahead, the local pressure will continually increase and the overall compaction force that results from the pressure differential across the vacuum bag will therefore reduce.This results in considerable relaxation of the preform, along with an increase in thickness, decrease in V f , and therefore also an increase in local permeability.Subsequently, many researchers have noted the importance of modelling dry compaction and wet relaxation properties in order to capture such effects and improve the fidelity of infusion models [10].This interaction between permeability and fibre volume fraction has been traditionally defined using the Kozeny-Carman equation: where the product kd 2 is an empirical constant determined from experimental fitting.However, recent literature suggests that the use of a power-law model (Eqn.5) instead of the Kozeny-Carman equation can be more accurate [10], as similar models are used for describing compaction behaviour (Eqn.6) [38].
where A, B, C, and D are empirical constants and σ f is the transverse compaction stress applied to the preform.International benchmarking of fabric compaction behaviour has been recently reported, however significant scatter (as much as 50% relative standard deviation) has been observed across the results of different labs using the same materials [39].Earlier work has also investigated the relationships between textile compaction, injection pressure, porosity, and permeability more broadly for LCM processes [40].Notably, in the case that injection pressure is lower than the compaction pressure, as is typical for vacuum infusion processes, then the permeability of the fabric should remain independent of the injection pressure.

Other fabric modifications
Other, less-studied, influencing factors for fabric permeability are micro-scale modifications, such as fibre sizings or the addition of a tackifier/binder material.
Generally the fibre sizing is selected for matrix compatibility and its effect on the ultimate mechanical performance of the composite, however its chemistry will also affect permeability.
A thorough study of four different engineering fabrics, both with and without various sizings, using three different test fluids, showed that the removal of sizings from fibres usually improved permeability (by up to 213%) [41].The exception was a carbon fibre fabric with 68K tows, for which the authors observed no tow gaps.Hence, the explanation for improved permeability in the other fabrics was the clustering of sizing-removed tows that created larger inter-tow gaps.A similar observation of improved permeability (30%), after the sizing was removed from carbon fibres during a recycling process, has also been observed in recent literature [42].
The addition of binder materials, to facilitate preforming and a more efficient layup in large structures, can also modify infusion behaviour.Rohatgi and Lee [43], for example, identified that a thermoplastic binder was more likely to increase flow resistance if it was concentrated between tows rather than inside them, since permeability tends to be largely dependent on the flow behaviour through inter-tow gaps.Similarly, Shih et al [44] also noted the significance of the location of an epoxy tackifier, which appeared to shrink the tows from within and increase the size of inter-tow gaps.In the maximum case, at relatively high binder concentration (17%), the permeability was seen to increase by a factor of 4.5 relative to the control preform.However, other research has seen little change in permeability when using a thin thermoplastic film tackifier [45].
Preliminary research at DTU Wind has also demonstrated the significance of a binder material on the permeability properties of a unidirectional NCF, as shown in Figure 3.Here 1D channel flow experiments showed a 75% increase in permeability along the fibre direction for the material with binder, compared to the same fabric without, at a similar fibre volume fraction.This difference is attributed to small scale changes in the pore distribution as a result of the binder pre-consolidation phase (conducted under pressure at elevated temperature).

Characterisation methods
Despite extensive study over the last few decades, the characterisation of fabric permeability remains unstandardised.In generally, there are several popular methods for the experimental characterisation of in-plane and through-thickness permeability that have also been the focus of extensive international benchmarking efforts [46,47,48,38].Fundamentally, experimental methods are commonly classified by their flow dimensions (1D 'channel' or 'through-thickness', 2D 'radial', or 3D), with either saturated (steady-state) or unsaturated (wetting) flow, and are controlled by either a constant flow rate or constant injection pressure.At this stage, 1D channel flow experiments for the characterisation of in-plane permeability have shown the greatest repeatability and reliability in benchmarking [47], demonstrating considerable improvements over a less-prescriptive first round of benchmarking [46].Alternatively, predictive permeability characterisation models are also an attractive area of research in order to overcome many of the tedious and temperamental aspects of the experimental approaches.In addition to the previously mentioned micro-and meso-scale modelling approaches for virtual permeability characterisation [16,17,18,32], there have also been efforts to develop iterative, macro-scale, simulation-enhanced methods for 3D permeability characterisation [49].These are designed to support experimental procedures for greater accuracy and reliability overall, compared with conventional 3D methods that are based on the theoretical calculations for, and transformations from, an equivalent isotropic flow [50,51].Recently, the development of a novel, non-destructive, 3D permeability measurement method has also shown considerable potential by relying on air flow and pressure sensors along with an artificial neural network for the interpretation of results [52].However the neural network interpreter still needs further development.
Other novel modifications to experimental methods have also been suggested.In one case, permeability values at three different fibre volume fractions have been characterised from a single 1D channel flow experiment by relying on several sequential flow regions with an increasing number of layers for the same cavity height [53].More recently, characterisation techniques have been proposed to capture preform compaction, expansion, and permeability over a range of fibre volume contents, from a single vacuum-bagged 1D flow experiment representative of the real manufacturing conditions [10].Despite the obvious efficiency advantages, this approach has only been validated using an acrylic mat material and not the typical engineering textiles that are used as composite reinforcements.

Core materials and pre-cast elements
Given that wind turbine blades contain significant quantities of materials other than fabric reinforcements, the effect of these materials on infusion behaviour also becomes an important consideration.Pre-cast elements, such as root inserts or pultruded carbon fibre profiles, are solid, impermeable components that are not expected to directly affect resin flow conditions aside from acting as a non-slip boundaries.However, in the layup of these structures there are commonly small gaps between repeated elements, which will act as open channels for fluid flow and facilitate significant race-tracking behaviour.Similarly, foam or balsa core materials for blade structures are commonly machined with various inter-connected grooves that also act as open flow channels during infusion.As was noted in Section 2.1, when modelling at large scales, it is no longer feasible to explicitly simulate these channels and it becomes necessary to 1293 (2023) 012009 IOP Publishing doi:10.1088/1757-899X/1293/1/01200910 develop an approximation or homogenisation of their effect on flow.This is commonly done by developing an equivalent permeability for the channels, or for the whole core material.
Since most dedicated infusion modelling approaches rely on Darcian flow, many early researchers treated channels as a porous medium with an equivalent flow capacity.This requires the definition of an effective permeability (where V f = 0) and the assumption of fully-developed duct flow.Several approaches have been suggested to this end, but the two most common approximations for the effective permeability of a rectangular channel are either to assume a non-slip (zero velocity) condition at the interface with the fabric reinforcement [54], or to consider this interface as permeable and therefore reliant on an empirical slip condition (nonzero boundary velocity) [24].The latter is more realistic but very difficult to characterise and apply [55].Other examples of equivalent permeability definitions based on similar principles, and the simulation of LCM for boat hull structures or balsa-core sandwich structures can be seen in literature as well [26,28].Hammami et al [56] proposed a further simplification of channel flow based on geometric models, independent of channel width, and neglecting transverse flow.However these equivalent permeability approximations were limited in their application and showed relatively poor agreement with experimental testing.
Alternatively, a number of other studies have instead attempted to characterise channel flow behaviour experimentally.Markicevic et al [57] performed channel flow experiments to assess the influence of dimensional parameters for both the channel and an adjacent preform material.This work reflected the significance of channel size but also the importance of the preform thickness on the leading velocity of the channel flow, illustrating a strong dependency between the channel and preform properties as they relate to infusion.In support of infusion models for wind turbine blade structures, Koefoed [30] performed vacuum-bagged 1D infusion of a balsa wood core panel alone.The observation of a good linear fit of the squared flow front over time, in this case, supported the use of Darcy's law for the definition of an effective core permeability.Conversely, similar 1D permeability characterisation experiments for foam core materials (with typical perforations and infusion channels, also for wind turbine blades), demonstrated poor fitting with Darcy's description of flow through a porous media [58], suggesting alternative methods for characterising and simulating core materials are necessary.
Additionally, the surface condition of core and pre-cast materials may also affect resin flow, this is particularly true for structural foams that can have vastly different pore structures.Generally these will be closed-cell foams, with minimal resin uptake by design, but the outer few millimetres of these foams will still absorb a considerable volume of resin and influence the flow.Such boundary layer effects are expected to only have a small influence on the creeping flow of an infusion problem, however this may still affect simulation fidelity, and a thorough investigation of these effects is yet to be conducted.

Consumable materials
In addition to the fabric reinforcement and core materials that make up the structural composite, consumable materials such as resin distribution media (also known as high permeability media or flow mesh/media), peel ply, and release film can significantly affect resin flow.This is particularly the case for the distribution media, as by design it has a much higher permeability than the reinforcing fabrics, in order to enhance overall infusion speeds.Research investigating the infusion of common consumable materials has shown how the permeability of stacked knitted distribution media layers can be 10% lower than that of a single layer, due to nesting effects [25].The same study also isolated the combination of flow media and peel ply layers (on top of a realistic impermeable preform), which resulted in a 50% reduction in permeability.In spite of this, infusion experiments considering the filling times of similar glass fibre stacks counterintuitively showed slower filling when the peel-ply was removed.This was again attributed to nesting effects when the distribution media was compacted directly against the glass fibre reinforcement layers.Overall then, the peel ply was considered to have a beneficial effect in separating the distribution media from direct nesting with the reinforcement fabrics, overcoming any potential flow resistance that it might add in the thickness direction [25].Ultimately mould filling times were found to be highly dependent on the permeability of the distribution media, and relatively insensitive to the preform permeability.
Many researchers have also investigated permeability averaging techniques in order to homogenise the properties of multiple layers, typically including a layer of resin distribution media, for simplified modelling of infusion processes.The simplest approach is to consider a weighted arithmetic average (i.e. the rule of mixtures), however this does not account for transverse flow across different fabric layers.This oversight becomes particularly important in cases where a high permeability distribution media is leading the flow adjacent to a low permeability material like the reinforcing fabrics.Hence, Calado and Advani [59] developed a 'transverse flow' averaging technique that shows significant improvement in the accuracy of flow modelling and allows for dimensional reduction of large flow problems.However, the implementation of this averaging technique requires a numerical solver, and is applicable only in cases where the flow direction aligns with the principal permeability direction and the pressure gradient is therefore assumed to be linear.Bancora et al [60] later proposed an extension to this approach by developing a 'generalised effective permeability' scheme that can account for non-uniform ply thickness and flow through off-axis plies.Experimental work has also demonstrated the issues with rule of mixture averaging for materials with very different permeabilities.Specifically, the measured permeability of a distribution media layer was seen to be 1-2 orders of magnitude higher than that of a glass fibre preform, and the apparent/equivalent permeability predicted by the rule of mixtures subsequently deviated from the measured values by an order of magnitude [61].This work also identified a linear relationship for the apparent lag distance between flow in the distribution media layer and the preform fabric, as the fabric thickness increases.Alternatively, in support of meso-scale flow simulations through a 3D woven fabric unit cell, equivalent permeability calculations have been developed based on an analogy to the conductance of electrical conductors [62].In this case, an area-weighted arithmetic mean and length-weighted harmonic mean were used for the averaging calculations of materials with different permeabilites in parallel or series respectively.Despite good agreement for some cases, these methods do not account for transverse flows from leading parallel layers, and their results showed unrealistic predictions when the permeabilities of adjacent materials differed by more than a few orders of magnitude.

Conclusions
Although some notable cases of infusion simulations for wind turbine blade manufacturing have been demonstrated for many years, infusion process modelling is still not mainstream practice in the wind industry.This is attributed to two main challenges that greatly affect the accuracy and potential of such models: simulation scale and permeability characterisation.In order to model three-dimensional flow through the thick and complex combination of materials in a wind turbine blade, even at the reduced macro-scale for a single panel section, significant homogenisation and simplification of the materials is necessary.However, the characterisation and averaging of permeability behaviour remains unreliable due to many interacting factors like nesting, compaction, and race-tracking.In particular, the characterisation of effective permeability values for core materials, that accurately account for the influence of deep cuts, infusion channels, and perforations is a key challenge to resolve.Similarly, the effects of consumable materials and precast elements, and how to accurately incorporate these into numerical flow models, also remain fundamental challenges.Hence, several on-going projects at DTU Wind aim to investigate and resolve some of these issues, in order to develop more reliable process models for the infusion of wind turbine blade structures.

2 Figure 1 .
Figure 1.Representative layup of a thin sandwich structure for a wind turbine blade.

9 Figure 3 .
Figure 3. Permeability properties of a unidirectional NCF, with and without binder. )