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Members of the aerospace fan community have systematically developed computational methods over the last five decades. The complexity of the developed methods and the difficulty associated with their practical application ensured that, although commercial computational codes date back to the 1980s, they were not fully exploited by industrial fan designers until the beginning of the 2000s. The application of commercial codes proved to be problematic as, unlike aerospace fans, industrial fans include electrical motors and other components from which the flow will invariably separate. Consequently, industrial fan designers found the application of commercial codes challenging. The decade from 2000 to 2010 was focused on developing techniques that would facilitate converged solutions that predicted the fans’ performance characteristics over the stable part of their operating range with reasonable accuracy, using a practical computational effort. In this paper, we focus on elucidating aspects of the flow physics that one cannot easily study in a laboratory environment, discussing the challenges involved and the relative merits of the available modelling techniques. The paper ends with a discussion of the practical problems associated with the use of commercial codes in a development environment and finally the legislation that is driving the need for aerospace style computation methods.

Industrial fan designers have historically relied on empirical design methodologies based upon an Euler analysis of velocity triangles [

The historic view that the empirical approaches to industrial fan design constitute a form of competitive advantage has resulted in a lack of cooperation and collaboration between industrial fan manufacturers. In contrast, aerospace fan designers have cooperated and collaborated, with the result that the available computational methods have progressed steadily over the last five decades. A result has been steadily improving aerospace fan efficiencies, with the drive for improved fan efficiency originating from efficiency as a source of competitive advantage. In the industrial fan community low cost has historically been the primary source of competitive advantage. However, this focus on lowest cost has recently changed because of new regulations in the European Community and planned regulation in the USA.

Within the European Union (EU), Commission Regulation number 327/2011 became legally binding on 1 January 2013, setting minimum fan and motor efficiency grades (FMEGs) for commercial and industrial fans [

In the USA, the US Department of Energy has been monitoring activity within the European Union. On 1 February 2013 the US federal government published a framework document in the Federal Register, outlining the approach to fan efficiency regulation within the USA [

With both Europe and the USA now regulating or declaring intent to do so, it is likely that Asian countries will introduce regulations setting minimum industrial fan or fan and motor efficiencies. Currently, Malaysia, Korea, and Taiwan have considered adopting fan efficiency requirements based on the Air Movement and Control Association (AMCA) Standard 205

Given today’s regulatory environment it is reasonable to assume that in all global regions, minimum fan or fan and motors efficiencies will become mandatory and then increase over time. As a direct result, the pressure on industrial fan designers will increase to both develop fans with high peak efficiency and specify them such that they operate closer to their peak efficiency point when installed. In response to this pressure, industrial fan designers have started to adapt aerospace fan design methodologies for application in the industrial fan design process [

Commercial CFD codes first became available in the early 1980s. However, modelling the physical flow equations involved significantly simplifying assumptions. The mesh generation techniques were rudimentary, and the available hardware to run the codes lacked computational power with the result that meshes were inevitably coarse. Over the last three decades, engineers have systematically addressed these issues, and today commercially available CFD codes model the flow equations accurately. Engineers can construct well-conditioned meshes and the available hardware is adequate to achieve mesh-independent results. Consequently, it is now possible to predict an industrial fan’s performance characteristics using commercially available CFD codes with reasonable accuracy.

In this paper, we first provide an overview of the computational methods utilised in the industrial fan design process. We start with a description of Reynolds-Averaged Navier-Stokes (RANS) turbulence modelling. We then move on to consider how one may apply the RANS technique in practice, followed by a consideration of the application of unsteady RANS, hybrid large eddy simulation (LES)/RANS, and Large Eddy Simulation as part of the industrial fan design process. We conclude with a consideration of the potential of open-source CFD codes.

An issue when considering using CFD in any turbomachinery application is that, even in the most favourable cases, Reynolds numbers are high resulting in complex flow-fields. A direct numerical simulation (DNS) of the Navier-Stokes equations would require fine computational grids and therefore a computational effort beyond that available within the industrial fan community. Consequently, the only viable approach available to industrial fan designers when attempting to solve the Navier-Stokes equations is RANS. A key aspect of a RANS simulation is using turbulence models that constitute a range of simplifying computational approaches for modelling aspects of the blade-to-blade flow-field fluid dynamics [

Reynolds-Averaged Navier-Stokes equations refers to a process of Reynolds-averaging the quantities within the equations. We express the generic

Successive averaging of the equations themselves results in the creation of a series of additional unknowns called Reynolds stresses and in the case of heat transfer, Reynolds fluxes. Solving the RANS equations requires a closed system of equations modelling these additional unknowns.

Moving from a direct numerical simulation to a RANS simulation reduces the required computational effort for a converged solution to a level practical within the industrial fan community. However, the tradeoff is a need to develop methods of modelling the turbulent flow’s underlying physics. This requirement is responsible for the significance of turbulence models in RANS codes. The appropriate choice of turbulence model for the application has a primary influence on the accuracy of the fan blade-to-blade flow-field’s resulting prediction.

For incompressible flows (without heat transfer), the RANS equations read

In (

The limitations that occur with using Prandtl’s mixing length approximation are a reason why the majority of eddy viscosity models rely on one or more transport equations to derive a value for eddy viscosity. Spalart-Allmaras’ one-equation model [

computation of lift and drag coefficients of isolated aerofoils,

forming a baseline RANS closure for Detached Eddy Simulations (DES).

When studying the modelling of lift and drag coefficients, Rábai and Vad [

Two-dimensional Spalart-Allmaras computations of pressure coefficient for an isolated compressor blade (line) and three-dimensional measurements of pressure coefficient made in a compressor cascade at midspan (dots), from Rábai and Vad [

When dealing with internal flows, one can overcome the limitations of a one-equation model with a two-equation model. The currently favoured two-equation models are either the

On the left-hand side of (

Channel flow computed using a direct numerical simulation (DNS). Normalised turbulent frequency (

There is a general consensus within the computational fluid dynamics community that the

The use of two-equation models has become established within the industrial fan community. Pinelli et al. [

Characteristics computed using a RANS simulation with a

When studying and modelling the fluid mechanics of industrial fans, researchers have concluded that the key phenomena of interest are induced by large velocity gradients that occur with the presence of solid walls. When using a RANS approach to wall treatment, one can formulate every model into what we may characterise as either a high- or low-Reynolds formulation. The difference between the two is integrating transport equations at the walls into the computational method.

When one studies the normalised velocity profile for channel flow at increasing Reynolds numbers, it is apparent that the profile is independent of Reynolds number. Researchers have studied the impact of Reynolds number on near-wall flow; [

Channel flow computed using a Direct Numerical Simulation (DNS). Normalised velocity (

The high-Reynolds formulation integrates transport equations into the computational method using wall functions that model fluid behaviour through the viscous sub-layer to the wall. The first node of the computational grid is placed in the flow’s fully turbulent region (

the boundary layer is attached,

the local turbulent energy is in equilibrium.

The above assumptions are not valid when the flow is separated, there is an adverse pressure gradient, or there is a wall curvature or impinging flow onto the wall. Those in the field inevitably associate industrial fans with separated flow. Their geometry induces adverse pressure gradients in the flow-field as a consequence of the fan blades’ curvature. Impinging flow onto walls is inevitable because of blade tip-to-casing flow and blade wake impingement on static components. Consequently, the use of wall functions in a high-Reynolds formulation facilitates a reduction in the computational effort required for the simulation, but the wall functions themselves have their deficiencies.

A RANS model may address these deficiencies by integrating up to the wall. However, in order to integrate up to the wall, we must reformulate the RANS equations to account for viscous effects in the near-wall region. We may reformulate the equations by incorporating a logarithmic function of either Reynolds number based on friction velocity (

We may reformulate the RANS equations to at least partly account for viscous effects in the near-wall region by using a low-Reynolds formulation. When using a low-Reynolds formulation the mesh needs to be refined in the wall-normal direction. The objective is to ensure that the first grid node lies in the viscous sub-layer (

grid spacing near the solid boundaries (blades, hub and casing) in order to fulfil the requirements of either low- or high-Reynolds formulations,

estimating the number of cells required in order to achieve a grid independent solution.

When considering the required number of cells to achieve a grid independent solution, it is noteworthy that not all the computational domain parts are equally important. For example, we associate the blade tip-to-casing region with a tip-leakage vortex, and in order to model this flow feature, it requires a relatively high grid density. However, we must associate this cell clustering in regions of known flow-field features with a smooth transition from regions of low to high cell density. We must avoid cells with a large aspect ratio or those that are heavily distorted. Despite this caveat, we can minimise the required number of cells to achieve a grid independent solution through a grid refinement process, and therefore industrial fan designers routinely employ grid refinement.

One may also use grid refinement to cluster cells near to every wall. This maximises the probability that there will be a node in the viscous sub-layer and hence that a low-Reynolds formulation will accurately model the flow-field physics. A way to check that grid refinement has successfully resulted in a node in the viscous sub-layer is to adapt the RANS formulation, with the formulation now checking the

A low-Reynolds formulation typically requires a grid with twice the number of required cells for a grid-independent high-Reynolds formulation. Despite the increase in computational effort that occurs with low-Reynolds formulations, industrial fan designers have judged the improvement in accuracy that occurs with low-Reynolds formulations to be more important than the increase in computational effort. Therefore, the majority of industrial fan designers use a RANS formulation with low-Reynolds formulation to predict overall fan performance over the stable part of the fan’s characteristic.

A limiting factor in a RANS formulation occurs with the definition of eddy viscosity, (

The eddy viscosity’s third order tensorial formulation in (

Numerical prediction and experimentally measured performance characteristics for a tunnel ventilation fan, from Corsini et al. [

An alternative to a non-linear eddy viscosity model when accounting for the anisotropy of Reynolds stresses is the elliptic relaxation models

Incorporating either a non-linear eddy viscosity model or an elliptic relaxation model constitutes an increase in complexity over that of a basic RANS formulation. The next level of complexity is the addition of second moment closure (SMC), also known as Reynolds stress models (RSM). The addition of SMC requires the RANS formulation to solve additional transport equations for the Reynolds stresses [

As we discussed at the beginning of this paper, a drawback of a RANS approach is the assumptions on which the model relies. When studying physical transport phenomenon, Hanjalić et al. [

The above provides an insight into the difficulty that occurs with using a RANS simulation to predict an industrial fan’s blade-to-blade flow-field. The active research that occurs with tailoring RANS simulations to specific applications indicates that we cannot assume “standard” RANS models to give an accurate prediction of either an industrial fan’s blade-to-blade flow-field or its overall performance. In essence, one must select or develop a RANS model to reproduce the flow-field physics relevant to each application. Pope [

A way to improve results with the Reynolds-averaged approach without adding application specific models is to solve the unsteady RANS equations. An unsteady RANS approach still does not account for the turbulence energy cascade from large-scale structures. However, an unsteady RANS is able to reproduce unsteady flow phenomena such as the blade tip-to-casing leakage vortex and the development of secondary flow features in the blade hub region. Piotrowski et al. [

The primary drawback that engineers associate with an unsteady RANS approach when compared with a RANS approach is the increase in the required computational effort to compute a solution. The increase in computational effort is a consequence of the need to simulate the flow-field over a period of time to correctly model the time varying fluctuation of velocity, pressure, and flow-field features. Yang et al. [

If the CFL number remains below its maximum allowable value, the flow-field’s time based resolution remains adequate for the mesh’s spatial resolution that one uses for the computations. In essence, the finer the mesh, the smaller the maximum allowable time step in an unsteady RANS computation. Within the industrial fan community it is common practice to increase the time step such that

The challenges that occur with computing both the blade-to-blade flow-field and overall fan characteristic are application specific. We may split the applications into two basic groups, axial and centrifugal fans. First, we will consider axial fans.

When modelling an axial industrial fan’s blade-to-blade flow-field the least complex configuration that one can model is the rotor alone. If one neglects static components then one can carry out the computations in the rotating frame of reference, and, consequently, there is no requirement to account for the computational mesh’s movement. Those researchers who have used a rotor-only approach augment the RANS momentum equation with terms that represent Coriolis and centrifugal forces [

A disadvantage that occurs with applying periodic boundary conditions is that they can fail to model accurately turbulent structures if one associates those structures with long wavelengths or length scales. The limitations that occur with applying periodic boundary conditions are not an issue with a RANS approach as the approach itself does not model the turbulent structures that periodic boundary conditions fail to model. Consequently, the use of periodic boundary conditions does not degrade the RANS simulation’s accuracy.

An unsteady RANS simulation is able to model major unsteady blade-to-blade flow-field features [

It is only necessary to extend an unsteady RANS computational domain to the entire fan when attempting to gain insight into phenomena that affect the entire rotor. Vanella et al. [

A further consideration when using a rotor-only simulation for either a RANS or unsteady RANS simulation is the computational domain’s axial extent up- and downstream of the blade leading and trailing edge. For a fan with well-conditioned inflow characteristics, Corsini and Rispoli [

A final consideration when using a rotor-only simulation for either a RANS or unsteady RANS simulation is the definition of inflow conditions. Engineers typically associate industrial fans with relatively low inlet flow velocities, and therefore it is reasonable to assume that the inflow is incompressible. It is therefore possible to define an inlet velocity profile and either a fixed turbulence level or a turbulence profile that accounts for the inlet velocity profile. A typical velocity profile would be the profile that engineers associate with fully developed pipe flow. A typical midstream turbulence level would be three percent, rising to ten percent in the near-wall region as velocity reduces [

When considering compressible flows an alternative approach is the fix static pressure at the outlet and total pressure and mass flow rate at the inlet. Hirsch [

A practice that has become established in the industrial fan community is to prerotate the flow into an axial fan inlet [

When the required pressure developing capability exceeds that of a single fan by a factor of between two and two and a half, a common practice within the industrial fan community is to configure two fans, counterrotating in series [

mixing plane,

frozen rotor, or

an unsteady coupling with moving mesh.

The mixing plane approach is the approach that researchers first developed when they attempted to model the interaction of counter-rotating blade rows or the interaction between a rotating and static blade row. The approach is based on the assumption that one could undertake separate steady-state simulations for each rotor or the rotor and the stator. One would then calculate circumferentially averaged velocity, pressure, and turbulence variables at the rotor’s outflow and use these calculated values as the inflow conditions for the second rotor or stator [

A disadvantage of the mixing plane approach is that wakes that form the first rotor mix out at the mixing plane, rather than mix out gradually as they wash down-stream into the second rotor or the stator. Mixing out wakes instantaneously at the mixing place results in the inability of the mixing plane approach to simulate the wake’s impact from the first rotor on the second rotor or stator. The effect of wakes from a rotor on a downstream stator is real, and one should model them. If one neglects them, the resultant simulation is still capable of predicting with reasonable accuracy the blade-to-blade flow-field and the rotor and stator’s overall performance. However, this is not the case with a counter-rotating fan. The effect of wakes from the first rotor on the second is significant enough for a mixing plane approach to reduce the second rotor blade-to-blade flow-field prediction’s accuracy so far that it is no longer possible to accurately compute the overall fan performance.

A better approximation of rotor-rotor or rotor-stator interaction than the mixing plane approach is the frozen rotor approach. The primary advantage of the frozen rotor approach is that the rotor to rotor or rotor to stator coupling does not require a moving mesh. The relative position of the two rows is fixed in time, with relative motion managed using different frames of reference and adding Coriolis and centrifugal forces to the momentum equation in the rotating frame of [

Industrial fan designers have favoured the frozen rotor approach, as the resultant RANS or unsteady RANS simulations are able to predict the overall fan performance characteristic with good accuracy. This does not mean that the approach is without drawbacks. Adding Coriolis and centrifugal forces to the momentum equation in the rotating frame of reference constitutes an approximation of the flow-field physics that limits the resulting simulations’ accuracy. To accurately simulate the flow-field physics it is necessary to undertake a fully unsteady coupling of the two blade rows. This requires a moving-mesh that can increase the required computational effort by up to an order of magnitude compared to a frozen rotor simulation. The increase in computational effort is a consequence of the required time to account for the interaction between the blade rows. The minimum number of interactions depends on clocking the two rows, with Yang et al. [

The modelling considerations that apply to an axial fan are unchanged for a centrifugal fan, with one exception. When modelling centrifugal fans, one cannot reduce the computational effort by modelling a single blade passage with imposed periodic boundary conditions. Centrifugal fan simulations must be full rotor simulations, and, consequently, they inherently require more computational effort than an axial fan single blade passage flow-field simulation.

Issues with inflow and outflow boundary conditions are similar for both axial and centrifugal fans. However, centrifugal fans require additional consideration of the computational domain’s extent up- and downstream of the rotor. At the fan inlet it is customary to add a hemisphere with a diameter two to three times the fan inlet’s diameter or location at which total pressure is specified [

With a centrifugal fan simulation it is not possible to use the mixing plane approach when modelling the fan rotor and stator. The mixing plane approach relies on circumferentially averaging velocity and pressure. A high circumferential pressure imbalance characterises centrifugal fans, and, therefore, any simulation must be capable of modelling this unbalance [

In practice, an unsteady RANS simulation is best able to simulate the flow features that occur with fan stall. Yang et al. [

Numerically predicted and experimentally measured characteristic of a centrifugal fan originally developed for application in the cement industry. Computation conducted using a high-Reynolds number standard

The computational methods that we have discussed so far have been concerned with predicting the blade-to-blade flow-field through the blade passage of either axial or centrifugal fans. In a development environment the objective is to facilitate a prediction of the fan’s characteristic for either an existing geometry or a proposed new geometry. Although the computational methods can account for inflow and out-flow boundary conditions, the simulations are essentially standalone fan simulations. One does not account for the system within which the fan is to be embedded.

The majority of industrial fans are embedded into a system. These systems may be complex, with multiple fans and dampers interacting and, consequently, inducing significant variations in fan inflow and out-flow conditions. As industrial fans must operate in a system, there is a need to be able to predict the system’s performance and the impact of that system on the fans embedded within it. However, the computational approaches that work well when modelling an axial or centrifugal fan’s blade-to-blade flow-field are not suitable for modelling a system. A fan’s characteristic time scale is invariably related to the fan’s rotation speed, with high speed centrifugal blowers operating at up to 10,000 rpm. In contrast, the complex systems within which industrial fans are embedded have characteristic time scales related to the speed of sound, and, consequently, in large systems the system’s characteristic time scale is typically between one and ten seconds.

To model the flow-field accurately through a system the computation must extend over a time period longer than the system’s characteristic time scale. In practice, this would require one to calculate the fan’s blade-to-blade flow-field over hundreds or thousands of revolutions. The required computational effort to calculate a blade-to-blade flow-field over so many revolutions is orders of magnitudes greater than that available to industrial fan designers. Consequently, the computational methods that they apply to an axial or centrifugal blade-to-blade flow-field’s predictions are not suitable for predicting system performance. Therefore, one must predict system performance by synthesising the fan’s effect on the system within which it is embedded.

When considering how to model the fan’s impact on the system within which it is embedded the least complex approach is to treat the fan as a discontinuity of static pressure. This requires knowing the fan’s pressure and volume characteristic, such that one may relate correctly the flow rate through the fan to the pressure discontinuity across it. The system model then treats the fan as a surface or single layer of cells across which it applies the discontinuity. In this way, the effect of a fan on a system may be synthesised using a “volume condition.” Angeli [

The least complex approach to modelling a fan installed in a system is the volume condition approach. More complex approaches are the actuator disc and actuator line approaches. Betz [

More sophisticated codes are able to compute the exchange of momentum between the blades and fluid at runtime using the boundary element method (BEM) to dynamically recompute the blade’s lift and drag as a function of the current velocity profile. With the actuator disc approach the exchange of momentum is treated as constant at different radial positions and not dependant on the azimuthal coordinates [

Numerical predictions of the volumetric effectiveness of an array of fans (symbols) and experimental measured performance of the array (line). Computations based on the synthesised actuator disk model approach, from van der Spuy et al. [

The actuator line approach is similar to the actuator disc approach. However, unlike the actuator disc approach, the actuator line approach considers every fan blade and the fan blades’ rotation within the computational domain. Sørensen and Shen [

Erosion of both axial and centrifugal fan blades is a major issue for industrial fan designers. Engineers classically associate axial fans in induced draft power and centrifugal fans in cement application with gas passing through the fan containing erosive particles. These particles both change the aerodynamic profile and reduce the fan blades’ chord length. The combined effect is a reduced fan pressure developing capability and efficiency. Predicting erosion patterns is critical during blade design optimisation to minimise susceptibility to erosion and, subsequently, to predict the rate of material loss and, consequently, the fan maintenance schedule. Therefore, developing computational methods that can predict erosion is critical when developing new industrial fans intended for application in erosive environments.

We may achieve numerical prediction of erosion in one of two ways: Lagrangian computation of particle dispersion via single particle tracking [

Once one has computed the particle trajectory, either via single particle tracking or via cloud particle tracking, erosion may be predicted by considering the velocity and angle at which particles impact solid walls. Erosion is a function of velocity, angle of impact, and impact energy.

Tabakoff et al. [

Global impact frequency after 10,000 hours of operation: pressure side (a) and suction side (b), from Corsini et al. [

The success of those researchers who have used computational methods to predict erosion illustrates that computational methods have progressed beyond an isolated prediction of the blade-to-blade flow-field through a fan rotor. This progress manifests itself in two primary areas of research, the computation of aeroelastic induced vibration and computation of overall noise level and noise spectrum. Using the three-dimensional computational fluid dynamic code of He and Denton [

When modelling the physics of all turbomachinery flow, RANS approach limitations hinder the accuracy with which one can model the blade-to-blade flow-field. Consequently, a RANS approach limits the accuracy with which one may calculate industrial fan performance characteristics. The RANS approach is not able to model the turbulence’s spectral content and is not sensitive to the flow-field’s multiscale features. Scholars who have studied the flow-field physics within all turbomachinery classes are increasingly turning to large Eddy simulations (LES) to overcome RANS approach limitations.

The principle issue with all large Eddy simulations is the formidable computations effort. The computational effort is simply beyond the reach of even the largest industrial fan manufacturers at the time of writing. The required computational hardware to successfully run a large Eddy simulation is between two and three orders of magnitude greater than that currently available to industrial fan designers. Despite this reservation, high performance computing (HPC) facilities are developing rapidly, exploiting massively parallel clusters of individual processors. Despite the promise of the high performance computing facilities, at the time of writing the costs to use them is beyond the reach of industrial fan manufacturers.

Further, the use of high performance computing facilities requires that an expert rewrites and optimises the computational methods to run across thousands of individual processors. To further compound matters, the commercial CFD code industry sells commercial CFD codes on a “per processor” basis that effectively makes the cost of running the codes across more than a handful of processors prohibitive. We may therefore conclude that it is likely to be another five years before industrial fan manufacturers can realistically consider a large Eddy simulation approach to predict a fan’s performance characteristic.

Despite the challenges that large Eddy simulation poses, turbomachinery designers are moving towards large Eddy simulation based computational methods. This movement has been difficult, in part, as a consequence of Large Eddy Simulation based computational methods requiring a higher level of user capability than RANS based computational methods. However, Large Eddy Simulation based methodologies offer the possibility to compute unsteady phenomena, such as those that occur with stall inception, unsteady blade and bearing loads, vibration, and noise. The industrial fan community widely anticipates predicting the unsteady flow-field parameters responsible for generating overall fan noise and spectrum. A computational method that could give a reliable prediction of not only a fan’s aerodynamic characteristics, but also acoustic characteristics would be useful during new fan design, development, and optimisation.

Although full Large Eddy Simulation methodologies are still some years away from routine application within the industrial fan community, there is progress with “hybrid” approaches. These hybrid approaches are based on sensitising an unsteady RANS approach to instabilities. Notable examples are detached Eddy simulations (DES) and scalar-adaptive simulations (SAS). Other hybrid methods utilise a combined Large Eddy Simulation and RANS approach, with the actuator disc and actuator line approaches also offering the possibility of combining with a Large Eddy Simulation approach.

The detached Eddy simulation approach is a sensitised Large Eddy Simulation method based on the unsteady RANS Spalart-Allmaras model. The Detached Eddy Simulation approach is the most widely used of the available hybrid methodologies as it is able to account for the turbulence spectral content in turbomachinery simulations. At the time of writing, industrial fan designers have not reported in the literature the use of the Detached Eddy Simulation approach. Therefore, we may conclude that the computational effort that engineers associate with a Detached Eddy Simulation approach remains beyond that available within the industrial fan community at the present time.

The scalar-adaptive simulation approach is similar to the Detached Eddy Simulation approach as it utilises a methodology based on an unsteady RANS methodology [

Finally, hybrid Large Eddy Simulation/RANS methodologies solve the unsteady RANS equations in the near-wall region and the Large Eddy Simulation equations in the flow’s main core. This hybrid approach reduces the required computational effort for a full Large Eddy Simulation whilst still accounting for large-scale structures in the majority of the flow. This models a part of the turbulence spectrum. Piotrowski et al. [

A challenge of using a hybrid Large Eddy Simulation/RANS methodology is the interface between the two. Borello et al. [

In theory, one can couple the actuator disk and actuator line approaches with a RANS or Large Eddy Simulation computation. This would allow the resulting hybrid simulation to reproduce large-scale structures’ unsteady interaction. Sørensen and Shen [

Finally, Davidson [

Numerically predicted vortical structures through the blade passage of a tunnel ventilation fan, computed using a Large Eddy Simulation (LES). These structures are visualised with isosurfaces of vortical structure deduction parameter (

As Borello et al.’s methodology [

The numerically predicted vortical structures through a tunnel ventilation fan’s blade passage, computed using a Large Eddy Simulation (LES). These structures are visualised with isosurfaces of vortical structure deduction parameter (

Time histories of the axial and peripheral moment components

Authors of commercial CFD codes do not champion hybrid methodology development. They are slow to respond to market demands for more advanced hybrid methodologies, preferring instead to exploit a monopolistic position in the market with well-proven RANS based methodologies that converge reliably. As a direct result the last decade has seen the widespread adoption of open-source codes. Foremost, amongst the open-source CFD codes that industrial fan designers have adopted are OpenFOAM [

The current generation of open-source codes meets the scalability standards of large High Performance Computing facilities, and, consequently, they can take advantage of rapidly developing massively parallel computation capabilities. An additional advantage of open-source computational fluid dynamic codes is that one can couple them with other codes. For example, the open-source optimising code DAKOTA [

Computational methods have become established within the industrial fan community. Despite the inevitability of separated flow through industrial fans, engineers have developed computational methods that simulate both the blade-to-blade flow-field and overall fan performance and to an accuracy that is of practical use to industrial fan designers.

For the first time, the legislative environment within Europe and the planned legislative environment in the USA are setting minimum fan and motor efficiency levels. This change in legislative environment is driving industrial fan designers to adopt computational methods as they are now legally required to improve fan performance to at least the legal minimum. This legislative imperative is resulting in industrial fan designers adopting open-source code in an ongoing effort to spread the use of computational codes from analysis based research applications into development and order related engineering application. Within the next five years it is likely that the industrial fan community will have abandoned commercial codes in favour of open-source alternatives.

Today the industrial fan community routinely uses computational fluid dynamic codes as design tools. Commercial codes incorporating a basic RANS methodology with either a

As either an axial or centrifugal fan approaches peak pressure, and therefore its stability limit, classical RANS based methodologies with wall functions reach their capability limit. The hypotheses that engineers used to derive all RANS methodologies are no longer valid. As a fan approaches stall, flow-field structures become more complex, and, consequently, it is no longer possible to accurately predict the fan’s performance characteristics.

Despite the inability of RANS based methodologies to predict a fan’s characteristic when stalled, the numerical prediction is still able to identify that the fan is stalling. Industrial fan designers are primarily focused on ensuring that their designs do not operate in stall. Consequently, it is enough for a computational method to predict that the fan will stall, and that is why RANS based methodologies remain the favoured methodologies within the industrial fan community.

If the computational method is required to predict a fan’s characteristic performance when stalled, a methodology that better models the flow-field physics is required. Moving from a high- to low-Reynolds formulation in the RANS methodology improves the flow-field physics’ modelling. However, a low-Reynolds formulation requires a substantial increase in grid resolution close to walls. Consequently, a low-Reynolds formulation typically requires twice the computational effort required for a high-Reynolds formulation. Despite the increase in computational effort, today industrial fan designers favour RANS methodologies with a low-Reynolds formulation.

Computational fluid dynamics codes offer industrial fan designers the possibility of simulating in detail the blade-to-blade flow-field. Codes incorporating a basic RANS methodology predict a fan’s overall performance characteristics well, but the limitations inherent in their formulation make them less suitable for studying the blade-to-blade flow-field. Real insight requires a code based on an unsteady RANS methodology incorporating advanced low-Reynolds models, a Detached Eddy Simulation (DES) or a Scalar-Adaptive Simulation (SAS). These unsteady RANS based methodologies have the potential to simulate the blade-to-blade flow-field as a fan approaches stall. They can predict critical flow-field structures within the blade passage, providing industrial fan designers with the necessary insight to develop a design.

An industrial fan designer would classically develop a design to delay the onset of stall or improve fan efficiency at a desired operating point. However, insight into, for example, the nature of blade tip leakage flow features can facilitate the development of blade tip features that minimise the tip leakage vortex’s intensity while maintaining its vorticity above a critical threshold value such that it does not burst. Thus, an industrial fan designer is able to effectively develop blade tip treatments that minimise fan acoustic emissions. As such, insight into an axial or centrifugal fan’s blade-to-blade flow-field facilitates the achievement of a broad range of development goals.

Industrial fan designers have successfully integrated commercial computational fluid dynamic codes into the design process. The cost of the necessary computer hardware to run these codes has become progressively more affordable. Despite the reduced computer hardware costs, commercial computational fluid dynamic codes remain out of reach of many industrial fan designers working for smaller fan companies. This is because the cost of a licence for a commercial code remains high. The code author’s policy of charging a licence fee for each processor results in a commercial code licence for a multiprocessor computer being typically an order of magnitude larger than the hardware’s cost.

Industrial fan designers are increasingly working with the codes OpenFOAM and CODE_SATURNE. These codes are licence-free and can run on clusters of computers. This offers industrial fan designers the possibility of networking office computers. Computers that the engineering department uses during the day with design software may be used at night as part of a cluster to run open-source computational fluid dynamics codes. At the time of writing OpenFOAM and CODE_SATURNE have user interfaces that are less user friendly than commercial codes. Despite this caveat, the open-source movement generally has made dramatic progress over the last five years. Therefore, it is likely that open-source computational fluid dynamic codes will become dominant within the industrial fan community, as that community struggles to develop more efficient products in response to current and planned future legislation mandating minimum fan and motor efficiency.

Velocity [m/s]

Cartesian coordinates [m]

Indices [-]

Turbulent kinetic energy [m^{2}/s^{2}]

Distance from the wall [m] [-]

Courant-Friedrichs-Lewy number, usually referred to as CFL or Courant number [-]

Reynolds stresses [m^{2}/s^{2}]

Numerical coefficients [-]

Normal-to-the-wall component of the Reynolds stresses [m^{2}/s^{2}]

Elliptic relaxation function [1/s]

Rate of strain tensor (symmetric component of the velocity gradient) [1/s]

^{2}]

Normalised wall distance [-]

Reynolds number based on reference velocity and length

Reynolds number based on friction velocity

Production of

Friction velocity [m/s]

Time [s].

Dissipation rate of turbulent kinetic energy [m^{2}/s^{3}]

Turbulence frequency [1/s]

Kronecker delta

Kinematic viscosity [m^{2}/s]

Turbulent kinematic viscosity or eddy viscosity [m^{2}/s]

von Karman constant [-]

Generic quantity

Zeta [-]

Rate of rotation tensor (antisymmetric component of the velocity gradient) [1/s]

Dissipation of

Distance from the wall of the first cell centre [m]

Wall shear stress [m^{2}/s^{2}].

Boundary element method

Computational fluid dynamics

Detached eddy simulations

Direct numerical simulation

High performance computing

Large eddy simulations[-]

Reynolds stress models (same as SMC)

Scale adaptive simulations

Second moment closure (same as RSM)

Unsteady Reynolds-averaged Navier-Stokes

Shear stress transport.

The authors declare that there is no conflict of interests regarding the publication of this paper.