University of Maiduguri Faculty of Engineering Seminar Series Volume 6, december 2015 IMPINGEMENT JET COOLING OF GAS TURBINE COMBUSTOR WALL OF HEAT FLUX IMPOSED HOT - SIDE: CONJUGATE HEAT TRANSFER INVESTIGATIONS USING COMPUTATIONAL FLUID DYNAMIC * El-jummah A. M. 1, Abubakar A. B. 2, Andrews G. E. 3 and Staggs J. E. J. 3 1 Department of Mechanical Engineering, University of Maiduguri - Nigeria 2 Department of Mechanical Engineering, Ramat Polytechnic Maiduguri - Nigeria 3 Energy Research Institute, University of Leeds, LS2 9JT, UK * al-jummah@hotmail.com; +2348037803678 Abstract Conjugate Heat Transfer (CHT) computational fluid dynamic (CFD) investigations were carried out for 10 10 array of gas turbine (GT) impingement cooling jet holes. The grid model geometries are for variable diameter D at constant impingement pitch X and gap Z, which shows that X/D and Z/D ratios are also varied, but Z/D variation is not a significant factor as Z is held constant. Computations were conducted for the same mass flux G of 1.076 kg/sm 2 using a cooling air temperature of 288 K and a fixed heat flux of 47.5 kw/m 2 imposed at the hot face of the target wall or combustor liner. The main objective is to computationally investigate the influence of the heat flux, which is typical of that used in a GT combustion chamber transition duct and is equivalent to a heat transfer coefficient (HTC) of 100 W/m 2 K. Experimentally, 775 K hot gas stream was used to heat the hot side target wall and was conducted using a Nimonic-75 wall material similar to that used in the CFD. The predicted surface average HTC h and percentage pressure loss ΔP were shown to agree well with the experimental work. The CFD prediction also shows that surface average Nusselt number reduced from 52.9 to 37.8 at the impingement point as D increases and as X/D decreases. The result also shows that thermal variations occurred along the length of the wall material and its thickness, which indicates that the wall hot gas stream hence the heat flux also varies. Also predicted is the dependence of pressure loss on flow-maldistribution. Keywords: Conjugate heat transfer, predictions, impingement jet, heat flux, Nimonic-75 material, heat transfer coefficient, pressure loss, thermal variation, flow-maldistribution. 1.0 Introduction Advances in gas turbine (GT) thermal efficiency for future enhancement in power generation rely on improved wall cooling of the GT combustor and turbine blades, as GT combustion temperatures deteriorates the metal materials of the component parts (Arthur and Dilip, 2010). To achieve high temperature operation of the GT components, the combined use of effective cooling techniques with sufficient thermal resistance material walls is important and impingement jet cooling of Figure 1 is shown to be one of the most effective cooling technologies (Andrews and Hussain, 1984, Huitenga and Norster, 2014). The important design flat wall geometrical variables are shown in Figure 2a and are the dimensionless pitch to diameter X/D, gap to diameter Z/D and length to diameter L/D ratios, as well as the dimensional hole density n (m -2 ) or number of holes N in the direction of the cross-flow in the impingement gap (El-jummah et al., 2014a, b). Seminar Series Volume 6, 2015 Page 58
Figure 1: Low NOx impingement cooling combustor (Huitenga & Norster, 2014) (a) (b) Figure 2: Impingement cooling CFD domain and experimental rig (El-jummah, 2015) This present CFD impingement cooling geometries, are similar to that investigated experimentally and is shown in Figure 2b (Abdul et al., 1988), which is typical of a low NOx primary zone GT combustor wall where the impingement efflux is discharged as the main combustion air. Impingement cooling is also used for cooling combustor transition ducts or for the primary low NOx region (primary zone only cooling) and then the impingement air is passed into the combustor as film cooling or as part of the dilution air, a method used in several industrial gas turbines. The geometries modelled are for varied D of 3.27, 2.33, 2.18 and 1.38, where X is kept constant at 15.24 mm and Z at 10.00 mm hence X/D and Z/D ratios varies from 4.66-11.04 and 3.06-7.25, respectively, even though Z/D (El-jummah et al., 2013b) variations are not significant as Z is kept constant (El-jummah et al., 2014b). The L/D and n (m -2 ) or N (El-jummah et al., 2014a) Seminar Series, Volume 6, 2015 Page 59
variations are significant but are not look into here, as this are investigations by their own right, L/D deals with hole length entry effects that critically affects the vena contracta hole issues. Model computations were carried out at the same mass flux G of 1.076kg/sm 2 for a coolant air temperature of 288 K and hot - side heat flux of 47.5 kw/m 2 equivalent to the experimental gas temperature of 775 K using Nimonic-75 wall material. 2.0 CFD Methodology 2.1 Grid Model Geometry Figure 2a shows the symmetrical representation (doted red lines) of the computational domain, which is one row of impingement half holes and was used to modelled the grid geometry of Figure 3, created based on the experimental rig shown in Figure 2b. This was in order to minimized the number of cells in the geometry as the flow is assumed to be in variant from one row of hole to another in the transverse direction, hence only one row of holes is required to be modelled which therefore resolved the flow aerodynamics. Figure 3 is a 3D structured grid model that was discretized in an ANSYS ICEM meshing tool. The cell concentration was higher at the impingement and target surfaces and the walls are represented by cells of the same cross sectional area that are rectangular but quadrilateral around the air hole surfaces. The cells size in the impingement gap has been calculated using Equations 1 and 2, the hole jet velocity Vj and Reynolds number Re for the total number of air holes across the 152.4 mm square array and the coolant mass flux G. An assumed value of 60 for y + (but the predicted y + ~ 35) was initially used in calculating the cell y - dimension, thus the smallest size of the cell was found in the air hole which was shown to adequately resolve the flow aerodynamics in the holes (Eljummah, 2015, El-jummah et al., 2014b, El-jummah et al., 2015). V j G 4G A X D 2 C d P 2RT P 0.5 (1) G 4 Re An Seminar Series, Volume 6, 2015 Page 60 0.5 2.2 Boundary Conditions All the CHT computational variables were calculated based on the plenum inlet coolant air temperature of T = 288 K, density ρ of 1.225 kg/m 3 and imposed hot - side wall heat flux q" = 47.5 W/m 2 using Nimonic - 75 material. The boundary conditions (El-jummah et al., 2014a, b, El-jummah et al., 2015) used at the plenum inlet/outlet, sides surfaces (plenum, gap and test walls) and inside test/hole wall surfaces are: the velocity (= G/ρ) inlet/outflow, symmetry/adiabatic, wall, coupled thermal conditions, respectively. 2.3 Grid Model Simulation The present investigations were computed using the standard k - ε turbulence model in ANSYS CFD Fluent, the computational procedures that has been previously validated for short hole as used in impingement and effusion cooling flows (El-jummah et al., 2015). The convergence criteria were set at 10-5 for continuity, 10-11 for energy and 10-6 for TKE k, DTKE ε and momentum (x, y and z velocities), respectively. The minimum orthogonal (2)
Figure 3: Computational 3D model grid for single exit flow impingement cooling system quality and aspect ratio, for all the geometries modelled were fixed at 0.61 and 3.53, respectively. The number of cells in all computational zones have been shown to be adequate and was based on the grid sensitivity tests that was previously predicted (Eljummah et al., 2013b). 3.0 Results and Discussion 3.1 Validation Case The only available measured data that have been used here to validate the CHT CFD predictions, are the percentage pressure loss and the surface average heat transfer coefficient (HTC) h (Abdul and Andrews, 1990, El-jummah et al., 2014b), these were found from work by El-jummah et al. (2014b). The predicted static pressure loss across the impingement jet wall as a function of X/D is shown in Figure 4a. This was determined as the pressure difference between the air supply plenum chamber and the static pressure on the impingement gap side of the jet wall at the centre of two impingement jet holes, which is similar to that shown in Equation 3. The experimental works only considered the exit hole pressure loss and are used here for this comparison. Figure 4a show that the predicted pressure loss agrees well with the measured data, except for the highest X/D of 11.04, which is considered to be the influence of Mach number M as the jet velocity is high hence M > 0.3 could be high in the computation. Interestingly, the predicted HTC (using Equation 4) of this X/D (11.04) in Figure 4b agrees with the measurement, this could mean that the aerodynamics could not be predicted with that range of M but the heat transfer would. The effects of the high turbulence generated with high X/D of 11.04 or high ΔP may also require that the measurement should be carried out using a more sophisticated device. Also agreed with the measured data and within the 10 % error bars in Figure 4b is the predicted HTC for the lower X/D, this is expected as the pressure loss also agrees with the measured data, once the aerodynamics are correct the HTC must also be correct (El-jummah et al., 2015). Seminar Series, Volume 6, 2015 Page 61
P P Seminar Series, Volume 6, 2015 Page 62 h T 4RT C s d q T P 2 G 2 2 nd 3.2 Aerodynamics and CHT Predictions The predicted impingement hole velocity enables the mean velocity of each hole to be determined, which was calculated in the middle of the hole to avoid any inlet and outlet flow recirculation zones. This predicted mean velocity for each hole is shown in Figure 5a which have been normalised to the mean velocity for all the holes as X/D varies and is called the flow-maldistribution. The flow-maldistribution was set by the total mass flux G for which these computations were conducted. El-jummah et al. (2015) showed that the flow-maldistribution with the leading holes receiving 7 % less air, while the trailing holes receiving 9 % more air was in excellent agreement with a simple 1D computation. It also shows that 16 % total flow-maldistribution was predicted, which reduces as cross-flow is minimized or X/D is increased as Figure 5a shows. This strongly supports the view that flow-maldistribution was driven by the static pressure difference along the duct. Figure 5b show the predicted static pressure loss across the impingement wall as a function of hole number and for all X/D, which show that ΔP increases along the gap with hole number. El-jummah et al. (2013b) predicted that the lower flow through the leading holes gave a lower pressure loss P. They showed that the difference in static pressure between the first hole pressure loss and the last is the pressure loss of the cross-flow down the gap, which was added to a 0.45 % pressure loss to that across the first hole and was the influenced of the flow-maldistribution, as Figure 5a show. The use of a heated wall in the experimental work and in all practical applications of impingement jets for cooling, results in heating of the impingement jets due to reversed jets flow (El-jummah et al., 2014a, b). Using the dimensionless temperature relations from work by El-jummah et al (2013a - c, 2014a, b) found based on Equations 5 shows that the reversed jets can be determined. This was shown to give the metal normalized temperature T * variations predicted by the conjugate heat transfer CFD as Figure 6a & b shows. Equation 5 was used when the imposed hot side condition is the temperature (K) called Tw, but if the hot side is an imposed heat flux (W/m 2 ) as in the present work Tw = Tm (the mean temperature) and T = TN = TL (temperature along the hole number and in the localized metal wall thickness). Equation 5 could also be reversed as Figure 6 (a & b) shows and is the reason why the normalized T * decreases along the gap instead of increasing (Figure 6a), as cross-flow reduces the cooling and as the jet flow penetrate into the wall (Figure 6b) and cools it (Abdul and Andrews, 1990, El-jummah et al., 2014b), which is also shown in Figure 7i for the target wall. Figure 6b shows that for all X/D, cooling in-line with the jets is much better than between the jet flows. T * T T T T w (3) (4) (5)
(a) (b) Figure 4: Comparison of predicted pressure loss and heat transfer with measured results (a) (b) Figure 5: Comparison of predicted hole flow-maldistribution and % pressure loss (a) (b) Figure 6: Comparison of predicted wall X 2 average and thickness local temperatures Seminar Series, Volume 6, 2015 Page 63
(i) Test walls Nusselt number (ii) Hole wall HTC (W/m 2 K) Figure 7: Surface distribution of impingement test and hole walls heat transfer hd Nu k f 3.3 Surface Distribution of Heat Transfer Equation 6 is the dimensionless Nusselt number Nu that originates from Equation 4 and was used in predicting the wall surface distribution of the impingement test walls Nu shown in Figure 7i, while Equation 4 was used for Figure 7ii. Nusselt number contour plots in Figure 7ia on the impingement jet wall indicates heating as the jets reverses, while that on the target surface in Figure 7ib is cooling as the jets impinges on it. Both the two surface Nu shows that as X/D is increased, heating or cooling also increases, which are also similar to the 3D holes shown in Figure 7ii as a result of the jet heated flows in the impingement holes. Figure 7ii shows that the regions of the hole length entry effects are well resolved (El-jummah et al., 2015, El-jummah, et al., 2013a). 4.0 Conclusions The CFD predicted pressure loss and surface average heat transfer coefficient h as a function of impingement X/D with Z/D ratios in the cross-flow direction showed good agreement with the measured data. It also indicates that the aerodynamics were adequately predicted, as both the flow-maldistribution and thermal length entry effects have also been predicted correctly and were based on the correctness of the pressure loss. The prediction also showed that surface average Nusselt number reduced from 52.9 to 37.8 at the impingement point as D increases and is also the influence of turbulent flows. Conjugate heat transfer CFD, is shown to be an adequate tool in the prediction of metal temperatures in gas turbine impingement cooling systems and should be used in optimization for optimum cooling configurations. It has also been shown to give good predictions of this cooling system, hence is a viable tool for gas turbine combustor and turbine blade cooling design. Seminar Series, Volume 6, 2015 Page 64 (6)
References Abdul Husain R. A. A. and Andrews G. E. 1990. Full Coverage Impingement Heat Transfer at High Temperature. Proc. ASME Int. Gas Turbine & Aeroengine Congress & Eposition, 90-GT-285, 1-12. Abdul Husain R. A. A., Andrews G. E., Asere A. A. and Ndiema C. K. W. 1988. Full Coverage Impingement Heat Transfer: Cooling Effectiveness. Proc. ASME Int. Gas Turbine & Aeroengine Congress, 88-GT-270, 1-9. Andrews G. E. and Hussain C. I. 1984. Impingement Cooling of Gas Turbine Components. High Temperature Technology, 2 (2), 99-106. Arthur H. L. and Dilip R. B. 2010. Gas Turbine Combustion (Third Edition): Alternative Fuels and Emissions, New York, CRC Press, Taylor and Francis Group. El-jummah A. M. 2015. Impingement and Impingement/Effusion Cooling of Gas Turbine Components: Conjugate Heat Transfer Predictions. Ph. D Thesis, University of Leeds. El-jummah A. M., Abdul Hussain R. A. A., Andrews G. E. and Staggs J. E. J. 2014a. Conjugate Heat Transfer CFD Predictions of Impingement Heat Transfer: Influence of the Number of Holes for a Constant Pitch to Diameter Ratio X/D. Proc. ASME Gas Turbine Conference, GT-25268, 1-14. El-jummah A. M., Abdul Hussain R. A. A., Andrews G. E. and Staggs J. E. J. 2014b. Conjugate Heat Transfer Computational Fluid Dynamic Predictions of Impingement Heat Transfer: The Influence of Hole Pitch to Diameter Ratio X/D at Constant Impingement Gap Z. Trans. ASME J. Turbomachinery, 136 (12), 1-16. El-jummah A. M., Andrews G. E. and Staggs J. E. J. 2015. Conjugate Heat Transfer CFD Predictions of Metal Walls with Arrays of Short Holes as Used in Impingement and Effusion Cooling. Proc. GTSJ Int. Gas Turbine Congress, IGTC TS - 266, 1-9. El-jummah, A. M., Abdul Hussain R. A. A., Andrews G. E. and Staggs J. E. J. 2013a. Conjugate Heat Transfer CFD Predictions of the Surface Averaged Impingement Heat Transfer Coefficients for Impingement Cooling with Backside Cross-flow. Proc. ASME IMECE Conference, IMECE-63580, 1-14. El-jummah, A. M., Andrews, G. E. and Staggs, J. E. J. 2013b. Conjugate Heat Transfer CFD Predictions of the Influence of the Impingement Gap on the Effect of Cross-Flow. Proc. ASME Heat Transfer Conference, HT-17180, 1-12. Huitenga H. and Norster E. R. 2014. Development Approach to the Dry Low Emission Combustion System of MAN Diesel & Turbo Gas Turbines. Proc. ASME Turbo Expo, GT- 25164, 1-10. Seminar Series, Volume 6, 2015 Page 65