CFD evaluation of pressure drop across a 3-D filter housing for industrial gas turbine plants

Abstract

This paper investigated the flow distribution and total pressure drop across a designed 3-D filter housing integrated with a 3-stage filtration system using computational fluid dynamics (CFD). The filter housing model was proposed for a heavy-duty industrial gas turbine plant operating at an average ambient temperature of 20°C.The pressure drops across the classes of filters were 652.8 Pa, 2692.2 Pa, 887.8 Pa, 776.2 Pa and 2304.2 Pa for I-GB, GB-GA, GA-FA, FA-HA, and HA-O, respectively. The results obtained indicated an acceptable total pressure drop of 7.2% for the entire filter housing before filter clean-up. Although the CFD simulation result shows that small outlet flow velocity and transonic flows exist at the outlet of the filter housing, the designed filter housing was proved compatible with the studied GT, for inlet flow conditions between 600≤W _air≤610 kg/s and 60≤v _air≤70 m/s for the air flow rate and velocity, respectively. Furthermore, the designed filter housing could be adopted for the studied GT and locations of Usan and Maiduguri in Nigeria, and other locations with similar environmental conditions.

Graphical abstract

Keywords

computational fluid dynamics (CFD) / pressure drop / flow distribution / filter housing / gas turbine

1 Introduction

Gas turbine (GT) filters play a significant role in sustaining the operational performance of a GT plant. The shape and design configuration of the filter housing can lead the air flow in an unrestricted manner into the compressor [1,2]. For this reason, filter housings for GTs are designed for optimum performance to be compatible with the inlet flow conditions of the GTs [3]. The better design and shape of filter housings can evade compressor surge and improve performance since the pressure drop attendant with the filters, and the flow channels of the filter housing affect the overall performance of the GT. It is important to keep the flow conditions at a minimum pressure drop by adopting a filtration system that suits its operational environment [1]. Optimal use of filters can considerably minimize the cost, frequent replacement of filters and uphold GT power output for a reasonable period [3]. Numerical modeling today plays a significant role in the understanding of filter performance and filter housing design for adequate air flow distribution [4–6]. CFD is well-thought-out as the most cost-effective solution for flow investigation of inlet systems lengthways with filter media [1,7,8]. Though, in recent times, the use of CFD to study flow distribution and optimization in thermal systems has gained recognition. Scholars used CFD calculations to simulate the temperature and flow distribution in a solar collector (flat plate) comprising 16 risers linked to a U-configuration [9]. Moreover, the effect of buoyancy on fluid and temperature distribution was studied using CFD [10]. In addition, the air induction system and pressure drop across pleated filters were studied using CFD [6,11], and the results obtained in Hosseinzadah et al. [6] using CFD were in agreement with the experimental data. Further applications of CFD include the design of turbomachinery, automotive system, and gas turbine filter housing [1,12,13].

This paper focuses on the flow distribution and pressure drop across a designed 3-D filter housing incorporated into a 3-stage filtration system using CFD. It also investigates the compatibility of the studied filters and the designed filter housing with a GT plant applicable for power generation in Usan and Maiduguri locations of Nigeria.

2 Methodology

2.1 CFD simulation of filtration system in filter housing

ANSYS CFX 14.0 was adopted for the CFD simulation and analysis of the flow distribution across the filter housing [14,15]. It was equally used to determine the compatibility of the studied filters with the GT plant assumed to operate in Usan and Maiduguri, Nigeria with an averaged ambient temperature of 20°C. The studied GT at the ISO design condition, has a capacity of 202.7 MW, compressor pressure ratio of 18.2, and exhaust gas exit temperature and exhaust gas flow rate of 774°C and 624 kg/s, respectively [2,16].

Moreover, the geometry of the filter housing with incorporated filters was created using CATIA V5. The created geometry was simplified by sectioning half part of the filter housing (Fig. 1). The housing mainly comprises of the inlet louvers (as air passes through the direction of the arrows), filters (G4, F9, and H12) and the housing duct. The G4 and F9 filters are found at the first and second stage of the filtration system. The G4 filter is capable of filtering coarse particles greater than 10 microns while the F9 filter traps fine particles greater than one micron. Furthermore, the H12 is the high-efficiency particulate arresters found at the last stage of the filtration system. It has a capturing efficiency of 99.99% and is capable of filtering particles greater than 0.01 micron.

The generated mesh for the filter housing occur in two categories (structured and unstructured) which consist of the filters and the inlet louvers (Fig. 2(a) and 2(b)), whereas Fig. 3(a) and 3(b) show the structured and unstructured boundary layer and the longitudinal section of mesh and hexa-core respectively. The structured and unstructured meshes were meshed to form a hybrid mesh that had a better quality with fewer elements of approximately two million cells and an acceptable boundary layer (Fig. 4).

2.2 Grid convergence and refinement study of independent filters

In the CFD simulation of different filters, a pre-mesh was created and converted to a block unstructured mesh. (Fig. 5 (a)). This mesh was selected for the different 3-D geometries to produce the same number of cells so that the set boundaries was not affected by the flow for convergence of the solutions. The filter instrument was divided into two different regions (filter region and outer flow region) to ease the meshing process (Fig. 5 (b)). In addition, the generated filter mesh comprises the coarse, practical, and fine meshes. The grid convergence plots for created meshes are depicted in Fig. 5 (c) with the fine mesh having the best result. Moreover, the quality of fine mesh produced was uniform with the aspect ratio and the determinant equal to 1 with a minimum angle of 90°. The flow characteristics, boundary conditions and material properties are thus defined as

Static pressure at filter outlet and inlet= 0 Pa and 101325 Pa.

The flow was considered subsonic at the flow regime.

There was an isotropic porosity loss since the pressure gradient ΔP/x was kept constant.

The initial air flow velocity was between 1≤v≤6 m/s.

The turbulence medium intensity at the inlet of the filters= 5%.

The filter pressure loss came only from the porosity.

The density of air, ρ _air293Kwas defined to be 1.205 kg/m³ and the dynamic viscosity

\mu =1.\mathrm{91}\times {\mathrm{10}}^{-\mathrm{5}}\hspace{0.17em}\mathrm{Pa}\cdot s.

2.3 Quadratic loss coefficient (QLC) of filters

The QLC was used to model porous media to define a momentum source term (pressure drop) in the momentum equation. The model is based on Darcy’s law relating pressure drop to velocity as presented in Eq. (1):

(1) {\displaystyle \frac{-\partial p}{\partial x_i}}={\displaystyle \frac{\mu }{k_p}}{u}_i+k_c{\displaystyle \frac{\rho }{\mathrm{2}}}\left|u\right|u_i,

where k _p, uand k _c are permeability resistance coefficient, flow velocity and loss coefficient, respectively. The term (k _c ρ/2) is the quadratic loss coefficient while μ and ρ are the kinematic viscosity and air density. The values of μ and ρ are determined at a temperature of 20°C (293 K) as μ ₂₉₃ =1.205 kg/m² and ρ ₂₉₃=1.91×10⁻⁵ Pa·s. Additionally, the thickness of the filter wall x was defined at 0.13 m for the G4 filter and 0.1 m for both the F9 and H12 filters. The experimental volumetric flow rate, the change in pressure and the derived Darcy equations from the experimental plots were used to determine the intrinsic and inertial permeability (k _p and k _c) of the filters. A quadratic loss coefficient of 15.656,54.264, and 44.603 was obtained for G4, F9 and, H12 filters respectively.

2.4 Real mesh and grid convergence for filter housing

The data obtained from the hybrid mesh were used to ascertain the mesh quality and also adopted for the final CFD simulation. In the structured mesh, the determinant was greater or equal to 1, the aspect ratio was less than 83, and the minimum angle was equal to 90°. In the unstructured mesh the determinant was equal to 10000 elements. Elements less than 0.2 were considered bad elements while those greater than 0.2 were considered good ones. The aspect ratio was approximately 100, and the minimum angle was equal to 2500 elements. Elements less than 18° were considered bad elements while those greater than 18° were considered good ones. However, the overall quality of the mesh proved acceptable and stable since only 0.38 % of bad elements were observed. The total number of elements in the hybrid mesh was (2611671) consisting of tetrahedral elements (303158), pyramid elements (9982), wedges-boundary layer elements (506420) and hexahedral elements (1792111). The size of the smallest elements near the wall was 0.5 mm. Figures 6 and 7 demonstrate the basic indicators of the convergence history plot for the hybrid mesh and RMS residuum for the filter housing respectively.

2.5 Boundary conditions for filter housing

2.5.1 Materials properties

The hybrid mesh was exported to CFX5PRE with the material properties and boundary conditions as follows: R = 287.058 J/(kg·K), P ₀ = 101325 Pa, T ₀ = 293.15 K (20°C), W _air = 305 kg/s, µ ₂₉₃ = 1.91×10⁻⁵ Pa, r ₂₉₃ = 1.205 kg/m³, g = 1.4, N _chmb = 6, N _chan = 18, x _G = 0.13 m, x _F = 0.01 m, x _H = 0.01 m, and A ₀ = 1.2 ×0.1768 m². Equations (2) to (6) were simplified to obtained results for ρ ₁ , P ₁ ,T ₁ and v ₁. The ISO design parameters of the gas turbine and the environmental conditions for the studied locations are available in Refs. [16,17].

(2) \mathrm{solve}[\{W_{\mathrm{air}}=A_{\mathrm{1}}{\rho }_{\mathrm{1}}{v}_{\mathrm{1}}\};[v_{\mathrm{1}}]],

(3) \mathrm{solve}\left[\left\{T_{\mathrm{1}}=T_{\mathrm{0}}-{\displaystyle \frac{v_{\mathrm{1}}^{\mathrm{2}}}{\mathrm{2}{C}_{\mathrm{p}}}}\right\}；[T_{\mathrm{1}}]\right],

(4) \mathrm{solve}\left[\left\{{\displaystyle \frac{P_{\mathrm{0}}}{P_{\mathrm{0}}^{\gamma }}}={\displaystyle \frac{P_{\mathrm{1}}}{P_{\mathrm{1}}^{\gamma }}}\right\};[P_{\mathrm{1}}]\right],

(5) \mathrm{solve}\left[\left\{{\displaystyle \frac{P_{\mathrm{1}}}{{\rho }_{\mathrm{1}}}}=R{T}_{\mathrm{1}}\right\}；[{\rho }_{\mathrm{1}}]\right],

where

(6) A_1=A_{\mathrm{0}}{N}_{\mathrm{chan}}=1.2\times \mathrm{0.}\mathrm{1768}\times \mathrm{18}=3.{\mathrm{818}\mathrm{m}}^2.

2.5.2 Flow characteristics

The fluid (air) was assumed steady with ideal gas characteristics. The fluid properties such as the specific heat, thermal conductivity and viscosity were assumed constant along the flow field. In addition, at the turbulent regime, the fluid was prescribed to be composed of compressible viscous flows. The compressible behavior of the fluid was also taken into consideration for a precise simulation (since M>0.3). The simulations were conducted using the porosity specifications, quadratic loss terms of the filters and the physical values of the boundary conditions. Likewise, the wall effect was considered in the simulation, and it was assumed that there were inlet louvers, filters and flow volume in the sub-domain. Besides, the flow regime was subsonic and flow direction normal to the boundary conditions at inlet and outlet. The medium intensity at inlet and outlet was prescribed to be 5%. An opening boundary condition was prescribed at the outlet in case of vortex, with arelative outlet pressure of 40000 Pa (after abortive iterations) which is used by the CFX solver to calculate the inlet total pressure automatically. The total temperature loss (which depends on v ²) was part of the boundary condition at the opening, which had to be kept by the solver.

2.6 General governing equations

The governing equation for describing the fluid flow consisted of the Navier-Stokes, the conservation of mass, energy and momentum equations [7,8].

(7) {\displaystyle \frac{\partial }{\partial x_i}}+(\rho u_i)=\mathrm{0},

(8) {\displaystyle \frac{\partial }{\partial x_j}}(\rho u_i{u}_j)=-{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[u\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}+{\displaystyle \frac{\mathrm{2}}{\mathrm{3}}}{\partial }_{ij}{\displaystyle \frac{\partial u_k}{\partial x_k}}\right)-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}\right].

The fluid region is the three-dimensional geometry of the internal volume. This paper applies the k- e model for the turbulent fluid characteristics. Equation (8) contains two additional transport equations different from the applied conservation equation. However, the variables solved include the turbulent kinetic energy (TKE) and dissipation rate (DPR) derived from the transport equation for the mean-square (MSQ) vorticity fluctuation. Expressions for the realizable transport k- \epsilon model is presented in Eqs. (9) and (10) [14,15,18]. The convergence history plots for RMS residuum is equally depicted in Fig.7,

(9) {\displaystyle \frac{\partial }{\partial t}}(\rho k)+{\displaystyle \frac{\partial }{\partial x_i}}(\rho k{u}_i)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\delta }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_{\mathrm{b}}-\rho \epsilon -Y_M+S_k,

(10) {\displaystyle \frac{\partial }{\partial t}}(\rho \epsilon )+{\displaystyle \frac{\partial }{\partial x_i}}(\rho \epsilon u_i)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+\rho C_{\mathrm{1}\epsilon }{S}_{\epsilon }-\rho C_{\mathrm{2}}{\displaystyle \frac{{\epsilon }^{\mathrm{2}}}{k+\sqrt{v\epsilon }}}-C_{\mathrm{1}\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{\mathrm{3}\epsilon }{G}_{\mathrm{b}}+S_{\epsilon },

where

(11) {\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^{\mathrm{2}}}{\epsilon }},

(12) G_k={\mu }_t{S}^{\mathrm{2}},

(13) G_{\mathrm{b}}=-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}{\displaystyle \frac{\partial u_j}{\partial x_i}},

(14) Y_M={\displaystyle \frac{C_{M}k\epsilon }{C^{\mathrm{2}}}}.

The Reynolds stress tensor, R _ij and the modulus of the mean rate-of-strain tensor S are defined as

(15) R_{ij}=-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j},

(16) S=\sqrt{\mathrm{2}{S}_{ij}{S}_{ij}},

where C _{1 ε}, C _{2 ε}, C _{3 ε}, C _M, C and C _μ are turbulence constants given as C _{1 ε}=1.44, C _{2 ε}=1.92, C _{3 ε}=﹣0.33, C _M=1.998, C=1.88, C _μ=0.09,σ _k=1.0,σ _ε=1.3.

3 Results and discussion

The CFD simulation for the configuration was launched on a result file, and the solutions were obtained and analyzed with CFX5POST of the post-processor.

3.1 Wall function (Y ⁺)

The hybrid wall function approach was used since it aimed to emulate a high (Y⁺) wall treatment for the coarse meshes and the low (Y⁺) wall treatment for the fine mesh. The acceptable Y⁺, which was the scalable wall function, was obtained by running different simulations, while the Y⁺ function was checked, and the mesh was modified (with assumptions between 2 mm to 5 mm) until an acceptable value was obtained (Fig. 8).

The wall function was scalable; therefore the settings can treat Y ⁺ in a wide range. The Y ⁺ value should be less than 300 and the Y ⁺ obtained in this paper falls within the acceptable limit, which range between 37≤Y ⁺≤250 [14].

3.2 Pressure drop and velocity streams

Figure 9(a) presents the static pressure (SP) and total pressure (TP) on the walls of the filter housing. The SPs at inlet and outlet of the housing stand at 102 kPa and 70 kPa, respectively. The SP and TP plots are clearly illustrated in red and green planes, respectively (Fig. 9(b)). The reason for high SP at the inlet is attributed to low inlet velocity while the high velocity of the exiting fluid causes the low SP experienced at housing outlet. Besides, from the centre of the curvature of the streamlines in the red plane, there is a high-pressure drop in the middle of the vortex showing pressure increase on the curved streamlines when going further to the centre of the vortex curvature (Fig. 9(c)). The vectors are also represented in projected streamlines as demonstrated in Fig.9(d). Furthermore, the outlet of the filter housing to the silencer and bypass duct witnesses a velocity of 175 m/s (Fig.10(a)) and Mach number of approximately 0.5 (Fig. 10(b)) while Fig. 10(c) and (d) presents the vectors in 2 dimensions (2D). The Mach number obtained is acceptable since the flow is within the sonic region. Nonetheless, arranging filters close to each other helps reduce vortices, and thus minimizes filter pressure drop.

Figure 11 shows the performance of each inlet filtration stage with respect to the pressure drop. I-GB indicates the inlet of the filter housing to stage before the G class filter. GB-GA indicates the stage before the G class filter to the stage after the G class filter. GA-FA indicates the stage after the G class filter to the stage after the class F filter. FA-HA indicates the stage after the F class filter to the stage after H class filter. HA-O indicates the stage after the H class filter to the outlet of the filter house, and I-O indicates the inlet to the outlet of the filter housing.

The pressure drop experienced before and after the G4 filter (I-GB) and (GB-GA) was 652.8 Pa and 2692.2 Pa, respectively. Similarly, the pressure drop before and after the F9 and H12 filters, (GB-FA) and (FA-HA) are 88.78 Pa and 776.2 Pa respectively while the pressure drop for the entire filter housing from the inlet to outlet (I-O) was 7.313 kPa. This value represents the overall pressure drop across the filters and holds for operational GT since the turbine performance, and longevity can be sustained within this limits as well as component degradation, FOD, and compressor fouling. Hence, it can be inferred that the designed filter housing with the environmental conditions of Usan and Maiduguri is compatible with the studied GT plant. Nonetheless, this calculation was conducted only for specified operating mass flow rate and velocity flow between 600≤W _air≤610 kg/s and 60≤v _air≤70 m/s, respectively.

Figure 12 presents the TP distribution across the filters in the filter housing. It also shows the meshed interface of the structured and unstructured meshes that produce 0.38% bad meshes. The effect of the bad meshes was negligible since it did not interrupt the TP distribution across the entire filtration system.

Additionally, the TP across the filters from G4 to H12 ranged from 129 kPa to 118 kPa.

4 Conclusions

This paper investigated the flow distribution and pressure drop across a 3-D filter housing incorporated into a 3-stage filtration system based on CFD analysis. The overall number of elements obtained in the hybrid mesh of the designed filter housing was approximately 2611671. About 0.38% of bad quality elements existed which was within the acceptable mesh quality. The quadratic loss coefficient of 15.656, 54.264 and 44.603 were obtained for G4, F9, and H12 filters, respectively, while the Y ⁺ got was scalable with values of 37≤ Y ⁺≤250. Besides, the filter housing exited to the silencer and bypass duct witnessed a velocity of 175 m/s and a Mach number of 0.5 which was acceptable as it fell within the sonic regime. Thus, the pressure drops across the classes of filters was 652.8 Pa, 2692.2 Pa, 887.8 Pa, 776.2 Pa and 2304.2 Pa for I-GB, GB-GA, GA-FA, FA-HA, and HA-O respectively, while the total pressure drop across the filter housing stood at 7313.2 Pa. The filter housing was found compatible and operational with the studied GT plant in the two locations, under specified inlet conditions between 600≤W _air≤610 kg/s, mass flow rate of the air and 60≤v _air≤70 m/s for flow velocity.

Additionally, the designed filter housing can also be compatible with any heavy duty industrial GT with such inlet flow conditions. The 7.2% pressure drop obtained was saved for the GT since the system did not experience high outlet flow velocity and transonic flows at the outlet. Arranging filters closer to each other during installation in the flow channels would reduce vortices and thus result in decreased pressure drop and inlet mass flow rate. From the operational point of view, another way to reduce the pressure drop is to reduce the number of filters in the filter housing. This is obtainable by applying a two-stage filtration system instead of three stage systems as considered in this paper.

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