The use of CFD and multi-objective optimisation techniques to customise an industrial pre-mixer

Many small/medium-sized enterprises (SMEs) lack the sufficient expertise or funds to undertake the design of all components from first principles or “scratch”, and instead must resort to utilising “commercial-off-the-shelf” (COTS) devices. Considering this problem, a specific, industrially focussed case study has been undertaken, which attempts to assess the suitability of a COTS pre-mixer for use with a specific burner and fuel source. The burner formed the radiative source in a heat exchanger, used in a “pressure let-down station line heater”, to maintain the temperature of piped natural gas above 0 ^∘C at gas pressure reducing stations. The pre-mixer must achieve certain mixing requirements to ensure a satisfactorily clean burn. Multi-objective optimisation has been used to assess, what, if any gains in performance can be made. With regards the optimisation procedure, on identification of the most appropriate sampling and interpolation/meta-modelling approaches, two different optimisation algorithms have been implemented for verification purposes: an evolutionary-based Genetic Algorithm (GA); and, the deterministic Nelder Mead. Prior to any optimisation, a robust Computational Fluid Dynamics (CFD) model of the pre-mixer had to be implemented and validated.

Industrial burners which utilise a gaseous fuel supply are classified according to how the fuel and oxidiser are mixed; in Pre-mix Burners, as implied by the name, all of the oxidiser required for combustion is inspirated and completely mixed prior to initiation of combustion (Baukal and Charles 2012). For this category of burner, increasing the excess air (oxidiser) results in a leaner mix that subsequently lowers the resulting flame temperature and reduces levels of Nitrogen Oxides (N O _x ) emissions (Bussman and Baukal 2009). The minimisation of such pollutants is a highly desirable outcome, due to the health risks they pose and their environmental impact; with legislation in place for industry to reduce the production of such harmful emissions (Porter and Van der Linde 1995). Consequently, especially low emissions are a highly marketable aspect of commercial combustion systems.

The oxidiser and gaseous fuel are supplied to the burner via a pre-mix device; where the mixing is achieved by supplying at least one of the mixing agents in the form of a high speed jet (Baukal and Charles 2012). In these cases, the specific mechanism of mixing is termed “entrainment” (Zhang 2007). Typically, the gaseous fuel is supplied at a high velocity, with a high-low velocity interface generating shear and resulting in entrainment of the oxidiser (Baukal and Charles 2012).

A simplified cross-section of the pre-mixer considered for this work, is shown in Fig. 1, where the dimensions of the mixer have been provided in terms of the gas jet nozzle’s exit diameter, D. As illustrated by Fig. 1 the pre-mixer consists of a convergent nozzle which creates a gaseous jet of fuel, that passes into a chamber section which contains a further constriction (or throat), that provides an additional draw due to the drop in pressure caused by the “venturi” effect (Danardone et al. 2011). Subsequently, the velocity of the jet is more effectively increased, producing a greater pressure draw for the ambient air into the mixer’s venturi chamber. An “adjuster plate” is incorporated into the design which can be moved to obstruct the quantity of air drawn through into the chamber. Generally, literature reports that an entrainment pre-mixer’s operation is affected by several specifications, including: the venturi throat area; throat position; and, gas inlet location (Danardone et al. 2011).

Previous work which has considered the simulation of pre-mix devices, focussed on the assessment of the extent or quality of mixture between a gaseous fuel source and air supply. An approach of utilising the species transport model without reaction, in the commercial software package Fluent, has been implemented successfully to assess mixing between constituents. Yeap et al. (2001) clearly showed through CFD predictions that the incorrect location of the fuel injection point contributed to inhomogeneous mixing, with combustion efficiency dependant on the degree of homogeneous mixing of the air and fuel. They assessed the extent of mixing by plotting the averaged air-to-fuel ratio (AFR) value in radial planes at several axial locations downstream. Similarly, Yusaf and Yusoff (2000) adopted this approach and plotted the resulting natural gas concentrations in the radial and axial directions, to show the changes in concentration due to mixing. Additionally, measures such as standard deviation (σ) can be used as a post processing step to assess the extent of mixing between species in a CFD simulation. In work by Singh (2008), this type of approach was implemented, with “an intensity of segregation as a measure of mixing defined as the second-moment variance of concentration distribution”.

Simulation of turbulence is a critical part of modelling a device which pre-mixes gases for combustion; when the turbulence energy dissipation rate (𝜖) increases, turbulence and shear between the fuel and air streams increases resulting in a faster mix (Zhang 2007). In the majority of work reviewed on simulation of pre-mixer type devices, the Standard k- 𝜖 turbulence model is utilised. Gorjibandpy and Sangsereki (2010) found that the Standard k- 𝜖 model provided the best balance between computational time and accuracy for a subsonic internal flow in a air-gas venturi mixer used for a bi-fuel diesel engine. Yusaf and Yusoff (2000) employed the Standard k- 𝜖 model for a steady-state simulation of a 3D, eight hole, air-gas mixer, which provided realistic results for a well-bounded high Reynolds number flow.

Typically, the pre-mixers are available as COTS. This research work has considered such a device, with the intention of using a validated CFD simulation of the pre-mixer coupled with a Goal Driven Optimisation (GDO) process, to establish if the COTS device is optimised for its specific use. Subsequently in Section 3, a brief description of the experimental procedure implemented to attain measurements from an operational pre-mixer has been provided. These experimental results were then used in validating the CFD model, the implementation of which has been described in Sections 4 and 5. Section 6 provides an overview of the optimisation techniques which were coupled with the CFD model to investigate the proficiency of the pre-mixer’s operation. A summary of results from this work is provided in Section 7; with, conclusions regarding the outcome of the investigation provided in Section 8. The following Section 2, provides further background to that provided in Section 1 regarding the pre-mixer’s operation, focusing upon the aspects of its performance that must be optimised and the parameters which affect these.

A full convergence and mesh sensitivity study was undertaken, with the steady-state solution considered converged when the discharge from the pre-mixer’s outlet was found to differ by no more that 1 %. Mesh independence was achieved with a mesh size consisting of 46,000 elements, i.e. an element dimension of δ; with meshes considered of the order: 0.25 δ; 0.5 δ; δ; 2.0 δ; and, 3.5 δ. The mesh sensitivity results are summarised in Table 3. It should be noted, that δ equates to approximately 2.5D.

Figure 4 provides a comparison between the experimentally measured and simulated discharge at the pre-mixer’s outlet; with varying adjuster plate location, when considering air as the only medium. It is evident that a similar trend is captured; where, pulling back the adjuster plate beyond a certain distance from the venturi chamber inlet, no longer has any effect on the quantity of air inspirated. The discharge velocity values levelled out to a maximum value of approximately 18 m/s (experimentally), and 16.5 m/s (simulated). It can be concluded that the simulation has accurately captured the fluid dynamics of the pre-mixer. The difference between the experimental and simulated results could potentially be attributed to a slight disruption of the flow due to the intrusive experimental measurement techniques employed.

Figure 5 shows the velocity and pressure contours from the simulation with the adjuster plate at a position of 7.06D mm from the venturi chamber’s inlet. The negative pressure draw created at the venturi chamber throat and the subsequent effect this has on velocity is evident.

Based on the validated axi-symmetric model, which had only considered air as the working medium, further simulations were undertaken utilising the multi-species model, to simulate the mixing and interaction of air with natural gas in the pre-mixer. Figure 6 shows an example of the species contours generated for methane and air, when natural gas is supplied at the gas inlet and the adjuster plate is located at a position of 7.06D mm from the venturi chamber’s inlet.

Utilising the output parameters from the CFD simulation, values were calculated at the pre-mixer’s outlet for σ _M , σ _A and A F R _m , these are summarised in Table 4.

Following validation of the CFD model, it was necessary to establish the most appropriate sampling and interpolation approach to be used for the pre-mixer’s optimisation. Using a sample set generated from the DoE - Central Composite (Face Centred Enhanced) approach, it was possible to compare the ”Goodness of Fit” (GoF) charts (Ansys 2013) for each interpolation approach.

The GoF chart presents a view of output parameter values predicted from the interpolation/response surface, versus values calculated from the CFD simulation (i.e. the sampling points). The closer the points fit a straight line, the better the prediction. In addition to using the sampling values, “verification points” were also included i.e. randomly generated design points; with these clearly identified in the GoF plots shown in Fig. 7.

These verification points provided a further opportunity with which to assess the accuracy of the interpolation techniques; but, were particularly important in the assessment of the Kriging technique. The Kriging approach interpolates through all sampling points, which results in a GoF illustrating data which is exactly fitted to the straight line (Rios and Sahinidis 2013). The inclusion of the verification points overcomes this issue, as their proximity to the straight line can be used to assess the actual predictive accuracy of the interpolation. It is evident from the plots, shown in Fig. 7, that each of the interpolation approaches gives reasonably accurate predictions, with the exception of one of the verification points, for which each of the interpolation methods has struggled. It is potentially because this point lies in a region with little information from the sampling set, which has led to inaccuracies for the interpolation. However, as all three approaches have the same problem, this point has been discounted in assessing which interpolation approach is most appropriate.

An in-depth analysis of the optimised results (Thompson 2015), established that OSF, implemented with a maximum number of 50 iterations to establish the sample set (Ansys 2013), when used with a Kriging interpolation provided the most robust optimisation approach for the pre-mixer considered. A summary of these results is provided in Table 5. The analysis was based on an approach using the DoE sampling method and comparing the NSGA-II optimised results after considering the three interpolation methods. From Table 5 it can be seen that the second-order response surface failed to minimise the σ values measuring the extent of mixing, whilst achieving an A F R _m value of 21 (Thompson 2015). The Neural Network (NN) approach effectively minimised the σ values, improving mixing by approximately 15 % but at the expense of attaining an A F R _m value of 21 (Thompson 2015). The Kriging approach performed better, achieving an improvement in mixing of approximately 37 %, but with an AFR that was still 5 % below 21 (Thompson 2015). Consequently, both the DoE and OSF sampling approaches were compared using the Kriging interpolation method. From Table 5 it can be seen that the latter provided more balanced results with regards to the requirements of the optimisation; achieving an improvement in mixing of approximately 16 % and an AFR value only 2 % from the required 21 . Typically, OSF is a more efficient sampling scheme when implementing complex meta-modelling techniques like Kriging. Subsequently, these sampling and interpolation methods were implemented for a full optimisation based study of the pre-mixer.

Generally, on reviewing the results from the NSGA-II optimisation process, it became evident that there was conflict between achieving an A F R _m value of 21 and reducing the σ values to as close to zero as possible. That was, the further the A F R _m value deviates from 21, the greater the reduction in σ values as compared to the initial design’s. The results for two (DP1 and DP2), three (DP1 to DP3), and four (DP1 to DP4) parameters, are summarised in Table 6, where the best result from the Pareto set of three optimised results has been presented as multiples of the gas jet nozzle’s diameter D, for each case. A bracketed percentage value is provided alongside the parameter dimension which indicates the change required in the pre-mixer’s optimised design parameters as compared to the initial design. Considering the σ values, the percentage difference bracketed alongside represents a decrease in the σ value from the initial design (i.e. an improvement in mixing). For the A F R _m values, a percentage difference from the required value of 21 is provided along with ↑, indicating the A F R _m value is above 21, or ↓ if below.

Results from implementing the Nelder Mead Method for the four design parameters is presented in Table 7, which provides a comparison with the initial design and NSGA-II optimisation.

Considering the four parameter optimisation; Fig. 8 provides the global sensitivities of the output objectives with respect to the input parameters. It is clearly evident from this chart that the radius of the venturi chamber’s throat (DP2) is the parameter the objective function measures (i.e. σ and A F R _m ) are most effected by; the length that the fuel jet extends into the venturi chamber (DP4) has limited, if any effect; whilst, both the position of the adjuster plate (DP1) and the length of the venturi chamber (DP3) have a comparatively moderate effect.

The outcome of the extensive optimisation based investigation is that the current design of the COTS pre-mixer can, with slight modification to of its design of provide improvement in mixing quality. Both the NSGA-II and Nelder Mead algorithms verified this to be around 30 %, whilst maintaining the AFR within 2-3 % of the required value. Overall conclusions regarding the optimisation work are provided in the final Section 8.