Loss Mechanism and Assessment in Mixing Between Main Flow and Coolant Jets with DDES Simulation

Transcription

1 Proceedings of Shanghai 2017 Global Power and Propulsion Forum 30 th October 1 st November, Loss Mechanism and Assessment in Mixing Between Main Flow and Coolant Jets with DDES Simulation Zhen Zhang, Tsinghua University z-z13@mails.tsinghua.edu.cn Beijing, P. R. China Xin Yuan Tsinghua University yuanxin@mail.tsinghua.edu.cn Beijing, P. R. China Xinrong Su* Tsinghua University suxr@mail.tsinghua.edu.cnl Beijing, P. R. China ABSTRACT Film cooling has become one of the most important cooling methods in gas turbines. The mass flow of the coolant increases with the turbine inlet temperature and reaches around 20% of main flow for advanced power plant gas turbines. To understand the mixing loss mechanism and assess the amount of loss are important for a cooling design. This work simulated a fundamental mixing case and an Inlet Guide Vane (IGV) with leading edge film cooling with Delayed Detached Eddy Simulation (DDES), showing the flow structures and turbulence properties of the mixing process and analysing the loss mechanism from the aspect of entropy production. Results show that the mixing processes are unsteady. In the IGV case, leading edge jet flows are bended towards the wall by the main flow and thus induce flow separation, especially at the blade pressure side. Besides, loss appears at the strong shear region near the wall and the vortex interaction region downstream, which are caused by viscous stress and Reynolds stress, respectively. INTRODUCTION Researches on film cooling in literature (Bogard and Thole, 2006) mainly focused on the influence on film effectiveness of the film cooling hole configurations (hole shape, ratio of length and diameter, jet angle et al.), the coolant jets parameters (blowing ratio, density ratio, velocity ratio and mass flow ratio) and the main flow conditions (stream wise pressure gradient, blade surface curvature and turbulence intensity). These influences were discussed at different regions of the flow passage. However, the loss due to the mixing process in the interaction between jets and main flow was less frequently discussed. In the limited researches in literature, the mixing loss and its impact on the turbine efficiency were investigated in three aspects: experiments in cascades, analytical loss models and simulations. Existing experiments mainly focused on the influence of the position and intensity of coolant jets on the overall efficiency. Ito (Ito, 1976) and Ito et al. (Ito et al., 1980) measured the impact of coolant jets with different intensity from one row of cooling holes at pressure or suction side of a blade on the total pressure loss penalty downstream. Results showed that jets from suction side induced transition at suction side boundary layer and thus significantly increased loss. For conditions with turbulent boundary layers, weak jets slightly increased loss while strong jets decreased loss. Yamamoto et al. (Yamamoto et al., 1991) studied the influence of coolant jets from a slot at various position in axis direction on the aerodynamic performance. Results showed that jets changed the structure of secondary flow in the passage and thus influenced loss. Jets from suction slot have less influence. Similarly, Hong et al. (Hong et al., 1997) replaced the slot with a row of cooling holes and got similar results. Day et al. (Day et al., 1998; Day et al., 1999) used a different definition of loss, which considered the total pressure of jet flows, to evaluate the influence of coolant jets. They measure both profile and endwall loss and showed that coolant jets thickened the wake region and thus increase loss. Osnaghi et al. (Osnaghi et al., 1997) studied the influence of jets from various positions (leading edge, pressure side, suction side and trailing edge) on the thermal dynamic loss. Results showed that thermal dynamic loss increased with the momentum flux of coolant jets and was independent of the density ratio of coolant and main flow. Denton (Denton, 1993) proposed to quantize the loss from the aspect of entropy production. He analysed the loss sources in a passage and gave empirical formulations to assess loss. Some analytical loss models were put forward to estimate the mixing loss in film cooing. Hertsel (Hartsel, 1972) presented a control volume based loss model, which assumed the mixing process was at a constant pressure and the mixing loss could be added to the overall loss by a linear superposition. Specifically, this loss model assumed mixing occurred in a mixing layer, which was thicker than boundary layer. After the mixing between jets and main flow in the mixing layer, fluids inside and outside the mixing layer independently expended to the exit pressure with an isentropic process, and then mixed

2 with each other. Urban (Urban et al., 1998) developed this constant-pressure mixing model and used it in a cascade. Based on Hertsel s model, Lim et al. (Lim et al., 2012) estimated the mixing loss in a turbine stage and showed that mixing loss reduced the aerodynamic efficiency by 0.7%. Numerical studies in literature focused less on the mixing loss due to film cooling. Walters and Leylek (Walters and Leylek, 2000) simulated the configuration of Ito s ((Ito, 1976) experiment. Different turbulence models were compared and the Realizable k-ε (RKE) turbulent model was chosen. Results showed that coolant jets influenced aerodynamic efficiency in two ways: the first is the mixing between jets and main flow, the second is that coolant jets changed the boundary layer condition at blade surface. Lin et al. (Lin et al., 2016) used RANS (SST turbulent model), DES and SAS to simulate film cooling of a plate. The simulated total pressure penalty was lower than experimental result at the downstream part of the jet and higher at upstream part. From the above discussion, film cooling has a significant influence on the aerodynamic performance. However, existing control volume based loss models totally ignore the flow details in the mixing process, which are important for loss production. Besides, RANS methods cannot precisely predict the flow structures at small scale. The present work uses DDES method to simulate a fundamental mixing case and reveals both large scale flow structures and small scale turbulence properties. Based on the understanding of the flow field, the mixing loss mechanism is analysed. Results show that the mixing loss appears at the strong shear region and the downstream vortex interaction region and is related to viscous and Reynolds stress, respectively. These analyses are adopted in an IGV case with leading edge film cooling. Results show that coolant jets at leading edge are bended towards the blade surface by the interaction with main flow, which induces flow separation downstream and increases loss. The mixing loss due to the leading edge film cooling occurs at the strong shear region near the hole exit and the vortex interaction region downstream the hole exit. Besides, the mixing loss is related to the velocity gradient of the instantaneous flow field. NUMERICAL METHODS Film cooling flow is characterized by strong mixing between the main stream and the coolant, also a series of vortices with different length scales. Various existing literature show that it is difficulty to accurately predict the small-scale flow structures and the turbulent fluctuation properties in the film cooling process with current RANS simulation tool. Benefiting from the rapid increase of the computational resource, scale-resolving simulation, such as Large Eddy Simulation (LES) or the hybrid RANS/LES emerge as affordable and valuable tools in predicting complex flow phenomena in turbomachinery. In this work, the DDES type hybrid RANS/LES is employed to simulate the film cooling in both a very simple case and an IGV case. Current DDES simulation is conducted with a wellproved in-house code which is based on the multi-block structured finite volume method. The Navier-Stokes equation can be expressed in the following integral form as t UdV + F nda = G n da (1) where F n denotes the convective flux and G n the viscous flux. In the current code the prefect gas is assumed and the Sutherland law is used to get the molecular viscosity. Current DDES simulation is based on the Spalart- Allmaras one-equation turbulence model. The original Detached Eddy Simulation was proposed by Spalart and Allmaras which uses RANS model inside the boundary layer and LES model elsewhere. To overcome the modelled-stress depletion (MSD) issue in the original DES model, a shield function is introduced to protect the boundary layer and the new model is termed as DDES (Spalart et al., 2006). For the DDES type simulation, the numerical dissipation should be carefully kept at low value in order not to dissipate the small scale turbulent structures. In this work, a high order method is used to discretize the convective term defined in Equation (1). It is based on a novel fifth-order method (Su et al., 2013) which is verified to be accurate and stable. Also, in order to further reduce the numerical dissipation, a vorticity based parameter is used to automatically adjust the local numerical dissipation and in this manner the highly vortical region is resolved with minimal dissipation. In the unsteady simulations, the dual time step method is employed and the physical time step is chosen according to the unsteady behaviour of the studied flow problem. The discretized governing equation is solved with an efficient implicit time marching method which permits the usage of large Courant Friedrichs Lewy (CFL) number up to For further convergence acceleration, multigrid method is also employed. COMPUTATIONAL SETUP FOR THE FUNDAMENTAL CASE Before the investigation of the interaction between main flow and coolant jets in IGV, a simplified case with experiments carried by Kacker and Whitelaw (Kacker and Whitelaw, 1968a; Kacker and Whitelaw, 1968b; Kacker and Whitelaw, 1969; Kacker and Whitelaw, 1971) was studied first to delineate the fundamental mixing mechanism between the main flow and jets. The configuration of the test rig is shown in Fig.1 and the region enclosed by dashed lines was chosen as the computational domain. The computational domain starts 4D upstream of the slot outlet and ends 86D downstream with height of 24D. The width and span of the lip are 1.14D and 3D respectively. A structured mesh of 5M points was generated with averaged y+ less than 1. To better capture the coherent structures in the mixing region, the region behind the lip was filled with nearly cubic elements. Figure 1 Test rig configuration and computational domain 2

3 The inlet and outlet flow conditions are given in Table.1. The slot width based Reynolds number, 12000, and the blowing ratio, 1.25, are kept identical to and the Mach number higher than the experiment. The walls of the lip and the bottom wall of the domain are set to be no-slip wall condition and the upper wall of the domain is set to be symmetric boundary condition. Periodic conditions are forced at the lateral walls. The SA-based DDES is applied with implicit time marching scheme. The physical time step is 1e-5s for unsteady simulation. The result was averaged for 5 flow through times or 118 vortex shedding periods. Table.1 Computational flow conditions Tt_m Pt_m Tt_c Pt_ct Pout [K] [kpa] [K] [kpa] [kpa] RESULTS AND DISCUSSION FOR THE FUNDAMENTAL CASE Figure 2 shows the comparison between numerical and experimental results (Ivanova and Laskowski, 2014). As for the turbulence property, DDES method gives good prediction. Figure 4 Streamwise velocity distribution Figure 2 Turbulent kinetics energy (x=10d) To understand the large scale flow structure, the present work gives the flow topology for mixing process, as shown in Fig. 3, which is the abstraction of the time-averaged flow field. In the mixing process, the flow field can be regarded as three regions, from top to bottom: main flow region, mixing region and jet flow region. The distribution of different velocity components is shown in Fig. 4 and 5. In the mixing region, the flow direction component is negative upstream and speeds up to reach main flow velocity. As for the height direction component, both scale and gradient are significant only in the upstream part of the mixing region. Figure 5 Transverse velocity distribution Figure 6 shows the distribution of turbulence kinetic energy. The turbulence concentrates at the upstream part of the mixing region, which implies that the turbulence is produced by the free shear flows caused by the interaction between jets and the main flow. To further discuss the turbulence property, the present work choose three sets of points from jet flow region, mixing region and main flow region respectively and draw the corresponding Lumley triangles (Lumley and Newman, 1977). The Lumley triangle can reveal the anisotropy properties of the turbulence. Comparison of Fig. 7 shows the the mixing process contains various anisotropy properties. In main flow region, the turbulence have two dominant directions. In jet flow region and mixing region, the turbulence has one dominant direction, which are in different directions for the two regions. In existing RANS model, the linear Boussinesq relation is adopted in which the Reynolds stress is assumed to be isotropic. Fig. 7 explains why with existing RANS model it always fails to accurately predict the film cooling performance, mainly due to the missing of turbulent anisotropic property. Figure 3 Flow topology for mixing process 3

4 Figure 6 Turbulence kinetics energy distribution Figure 7 Lumley triangle for various positions: Jet flow region (up) mixing region (middle) main flow region (bottom) Figure 8 shows the total dissipation rate of the time averaged flow field. From the integral results, 79.4% of the mixing loss (out of the boundary layer) is located at the coremixing region (shown with a black rectangular). Figure 9 and 10 show the dissipation rates due to Reynolds and viscous stress, respectively. The loss due to Reynolds stress is located downstream the lip, where there are strong vortex interactions. This part of loss accounts 90.7% of the mixing loss in the core mixing region. The loss due to viscous stress is located at the strong shear region close to the lip and accounts 9.3%. Figure 8 Total dissipation rate Figure 9 Dissipation rate due to Reynolds stress Figure 10 Dissipation rate due to viscous stress Figure 11 and 12 show the distribution of the Q criterion and dissipation rate of an instantaneous flow filed. The loss occurs at the strong shear region close to the lip and the vortex interaction region downstream. The latter is due to the small scale vortex because there is a noteworthy correspondence between the Q criterion and the dissipation rate distributions. Comparing with Fig. 10, we can conclude that mixing loss is mainly due to the small vortex structures and the turbulent fluctuations. After being averaged by time, the resource of this part of loss shows in the form of Reynolds stress. 4

5 Figure 11 Instantaneous Q criterion Figure 14 Instantaneous velocity gradient ( U/ Y) Figure 12 Instantaneous dissipation rate Figure 13 and 14 compare the distribution of a component of instantaneous dissipation rate (accounting 35.1%) and the corresponding velocity gradient. Their relationship is shown as Φ 12 = τ xy U Y where τ xy, for instantaneous flow field, is determined by the velocity gradient as τ xy = 1 2 μ( U Y + V X ) (3) The instantaneous velocity gradient U/ Y dominates in the mixing process. So we only consider the relationship between Φ 12 and U/ Y. The comparison in Fig. 13 and 14 reveals that the dissipation is determined by the velocity gradient and for this case, the mixing loss is significantly affected by the velocity gradient U/ Y close to and downstream the lip. (2) COMPUTATIONAL SETUP FOR THE IGV CASE Film cooling is characterized by a mixing process between jets and main flow near the wall. The fundamental mixing case models and simplifies this kind of flow by changing the mixing angle to be zero, thus only one dominate mixing direction left. Based on this simplification, the fundamental mixing case reveals the basic mixing loss mechanism. Then the present work simulates another case, which represents real turbine surroundings, to further discuss the mixing loss in a turbine with film cooling. The simulated object is an IGV with leading edge film cooling. Figure 15 shows the mesh at the symmetry plane of the calculation domain. Detailed geometry data can be found in the experiment report (Ardey and Wolff, 2001). The hole and blade surfaces are set as non-slip wall. Periodic boundary condition is set in azimuthal direction and symmetry boundary condition in spanwise direction. The total pressure is 196.2hPa at main flow inlet and 200.6hPa at the hole inlet. Total temperature is 303K at main flow inlet and 300K at the hole inlet. Static pressure at outlet is 145.9hPa. The physical time step is 2e-6s for unsteady simulation. The result was averaged for 270 vortex shedding periods or 174 characteristic times for pressure side hole. Figure 15 Mesh for the IGV case Figure 13 Instantaneous Dissipation rate component (Φ12) RESULTS AND DISCUSSION OF THE IGV CASE Figure 16 shows the comparison between experimental and numerical results of the blade surface pressure distribution. The comparison shows the present work precisely predicts the general parameters of the IGV case. 5

6 exits and the vortex interaction region downstream. The results reveal that in this IGV case the loss appears mainly due to the small-scale vortex structures. According to the analysis of the fundamental case, the loss depends on the velocity gradient caused by the interaction of jets and main flow. Figure 16 Blade surface pressure distribution Figure 17 shows the flow structure at the blade leading edge. There are two film cooling holes on both sides of the stagnation point. The jets interact with main flow and are bended to the blade surface. The bended jets induce flow separation and the separation is more severe at the pressure side. Figure 18 shows the limited stream lines at the blade surface. The pressure side is on the left. From the limited stream lines, the flow separation at the pressure side can be observed. There exist several separation regions and their boundaries are shown. Besides, the re-attaching point occurs downstream. Figure 19 Instantaneous Q criterion Figure 20 Instantaneous dissipation rate Figure 17 Flow structure at leading edge Figure 18 Limiting stream line near the leading edge Figure 19 and 20 show the comparison between instantaneous Q criterion and dissipation rate distribution. The comparison shows that the flow structure in the IGV with film cooling is more complicated. The loss mainly exists at hole CONCLUSIONS The present work uses DDES method to simulate a fundamental mixing case and successfully captures both large scale flow structures and small scale turbulence properties. Based on the understanding of the flow field, the mixing loss mechanism is analysed. Results show that the mixing loss is related to both viscous and Reynolds stress at the strong shear region and the downstream vortex region, respectively. These analyses are adopted in an IGV case with leading edge film cooling. Results show that coolant jets at leading edge are bended towards the blade surface by the interaction with main flow, which induces flow separation downstream and increase loss. The mixing loss due to the leading edge film cooling occurs at the strong shear region near the hole exit and the vortex interaction region downstream the hole exit. Besides, the mixing loss is related to the velocity gradient of the instantaneous flow field. The present work reveals the detailed flow structures and the loss mechanism of the mixing process, 6

7 covering the shortage of the widely used control volume based loss models. NOMENCLATURE P t_m: total pressure of the main flow P t_c: total pressure of the coolant flow D: coolant jet outlet width T t_m: total temperature of the main flow T t_c: total temperature of the coolant flow ACKNOWLEDGMENTS The authors would like to express appreciation for the support of the National Natural Science Foundation of China (Project No , Project No and Project No ). REFERENCES [1] Bogard D. G., and Thole K. A. (2006). Gas turbine film cooling. Journal of Propulsion and Power, 22(2), [2] Ito S. (1976). Film Cooling and Aerodynamic Loss in a Gas Turbine Cascade. PhD Thesis, University of Minnesota. [3] Ito S., Eckert E. R. G., and Goldstein R. J. (1980). Aerodynamic loss in a gas turbine stage with film cooling. Journal of Engineering for Power Transactions of the Asme, 102(4), 964. [4] Yamamoto A., Murao R., and Kondo Y. (1991). Cooling-air injection into secondary flow and loss fields within a linear turbine cascade. Journal of Turbomachinery, 113(3), [5] Hong Y., Fu C., Gong C., and Wang Z. (1997). Investigation of Cooling-Air Injection on the Flow Field within a Linear Turbine Cascade. ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition (pp.v001t03a103). [6] Day C. R. B., Oldfield M. L. G., Lock G. D., and Dancer S. N. (1998). Efficiency Measurements of an Annular Nozzle Guide Vane Cascade with Different Film Cooling Geometries. ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition (pp.v004t09a088). [7] Day C. R. B., Oldfield M. L. G., and Lock G. D. (1999). The influence of film cooling on the efficiency of an annular nozzle guide vane cascade. Journal of Turbomachinery, 121(121), [8] Osnaghi C., Perdichizzi A., Savini M., Harasgama P., and Lutum E. (1997). The Influence of Film-Cooling on the Aerodynamic Performance of a Turbine Nozzle Guide Vane. ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition (pp.v001t03a105). [9] Denton J. D. (1993). Loss mechanisms in turbomachines. Journal of Turbomachinery, 115:4(4), V002T14A001. [10] Hartsel J. (1972). Prediction of effects of mass-transfer cooling on the blade-row efficiency of turbine airfoils. AIAA 10th Aerospace Sciences Meeting. [11] Urban M. F., Hermeler J., and Hosenfeld H. G. (1998). Experimental and Numerical Investigations of Film-Cooling Effects on the Aerodynamic Performance of Transonic Turbine Blades. ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition (pp.v004t09a096). [12] Lim C. H., Pullan G., and Northall J. (2012). Estimating the Loss Associated With Film Cooling for a Turbine Stage. ASME Turbo Expo 2010: Power for Land, Sea, and Air (Vol.134, pp ). [13] Walters D. K., and Leylek J. H. (2000). Impact of filmcooling jets on turbine aerodynamic losses. Journal of Turbomachinery, 122(3), V003T01A093. [14] Lin X. C., Liu J. J., and An B. T. (2016). Calculation of Film-Cooling Effectiveness and Aerodynamic Losses Using DES/SAS and RANS Methods and Compared With Experimental Results. ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition (pp.v02ct39a039). [15] Spalart P. R., Deck S., Shur M. L., Squires K. D., Strelets M. K., and Travin A. (2006). A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theoretical and Computational Fluid Dynamics, 20(3), 181. [16] Su X., Sasaki D., and Nakahashi K. (2013). On the efficient application of weighted essentially nonoscillatory scheme. International Journal for Numerical Methods in Fluids, 71(2), [17] Kacker S. C. and Whitelaw J. H. (1969). An experimental investigation of the influence of the slot-lipthickness on the impervious-wall effectiveness of the uniformdensity, two-dimensional wall jet. Int. J. Heat Mass Transfer, vol. 12, pp [18] Kacker S. C. and Whitelaw J. H. (1968). The effect of slot height and slot-turbulence intensity on the effectiveness of the uniform density, two-dimensional wall jet. Journal of Heat Transfer, no. 11, pp [19] Kacker S. C. and Whitelaw J. H. (1968). Some properties of the two-dimensional, turbulent wall jet in a moving stream. Journal of Applied Mechanics, no. 12, pp [20] Kacker S. C. and Whitelaw J. H. (1971). The turbulence characteristics of two-dimensional wall-jet and wall-wake flows. Journal of Applied Mechanics, vol. 3, pp [21] Ivanova E., and Laskowski G. M. (2014). LES and hybrid RANS/les of a fundamental trailing edge slot. ASME Turbo Expo 2014: Turbine Technical Conference and Exposition (pp.v05bt13a030-v05bt13a030). American Society of Mechanical Engineers. [22] Lumley J. L., and Newman G. R. (1977). The return to isotropy of homogeneous turbulence. Journal of Fluid Mechanics, 436(1), [23] Ardey S. and S. Wolff. (2001). TEST CASE: Leading Edge Film Cooling on the High Pressure Turbine Cascade AGTB. Universität der Bundeswehr München, Fakultät für Luft- und Raumfahrttechnik Institut für Strahlantriebe, Institutsbericht LRT - Inst /01 7