GT NUMERICAL COMPUTATION OF THE JET IMPINGEMENT COOLING OF HIGH PRESSURE RATIO COMPRESSORS

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1 Proceedings of ASME Turbo Expo 2013 GT2013 June 3-7, 2013, San Antonio, Texas, USA GT NUMERICAL COMPUTATION OF THE JET IMPINGEMENT COOLING OF HIGH PRESSURE RATIO COMPRESSORS Elmar Gröschel ABB Turbo Systems AG Schweiz Bruggerstrasse 71a, 5401 Baden, Switzerland Carsten Lipfert ABB Turbo Systems AG Schweiz Bruggerstrasse 71a, 5401 Baden, Switzerland Wolfgang Erb ABB Turbo Systems AG Schweiz Bruggerstrasse 71a, 5401 Baden, Switzerland Daniel Rusch ABB Turbo Systems AG Schweiz Bruggerstrasse 71a, 5401 Baden, Switzerland ABSTRACT The material temperature field of a centrifugal compressor wheel is one important factor for the life time analysis of a compressor stage. Due to increasing thermal loads of advanced compressor stages, the thermal stresses and/or material temperature levels can exceed the allowed limits for a prescribed exchange interval and cooling techniques are needed to reduce the wheel temperature. One efficient cooling technique is the air impingement cooling. Unlike in gas turbines the impingement cooling is located in the back face region of the compressor wheel. From a computational point of view this means that the impingment jet is located in the stationary frame of reference and the cooled wall is located in the rotating frame of reference. In such a case the heat transfer problem becomes unsteady. The paper introduces a novel CHT-mixing plane interface for the frame change between stationary fluid domain and rotating solid domain to overcome the intrinsic unsteadiness caused by the jet impingement. Fluid mixing plane interfaces between rotor and stator are very common in industries to exploit periodic symmetries and to avoid time consuming unsteady compuations. However, the commercial solvers do not provide a mixing plane interface between Address all correspondence to this author. fluid and solid domains. First, the new mixing plane approach is validated for a representative test case against a time resolved computation. In the second step, the new method is applied to a compressor stage. Two operating conditions, each with three different cooling mass flows have been computed. The comparison of the wheel temperature field corresponds very well to the computational results for all operating conditions. The temperature field analysis reveals valuable information on the heat transfer in highly loaded compressor stages which can be exploited in the design process of the compressor cooling. NOMENCLATURE ṁ Mass flow rate [kg s 1 ] q Heat flux [W m 2 ] p Pressure [Pa] n inner Number of inner iterations per heat transfer exchange interval n outer Number of exchange intervals until convergence n b Number of bands in CHT-MPI model r b Radius of band b in CHT-MPI model TVE Inlet total temperature [K] 1 Copyright c 2013 by ASME

2 TVA Outlet total temperature [K] T max Maximum temperature variation allowed for subsequent life cycle analysis [K] TVR i Compressor wheel temperature at discrete monitor points i [K] TVR i Non-dimensionalized compressor wheel temperature defined by TVR i = TVR i TVEd TVA [ ] d TVE d Greeks ε Lower error limit for convergence [ ] η is Total isentropic efficiency [ ] π Total pressure ratio [ ] Subscripts BB Blowby flow c Cooling air d Design point SPL Sealing air flow s Solid f Fluid i Temperature monitor position in compressor wheel v Compressor Total conditions Acronyms VDRS Compressor wheel solid VDR Compressor flow passage channel RR Compressor back face region ZWB Partition wall CFD Computational Fluid Dynamics CHT Conjugate Heat Transfer CHT MPI Conjugate Heat Transfer-mixing plane interface HCF High cycle fatigue LCF Low cycle fatigue SST k ω Shear Stress Transport Low-Re turbulence model Symbols <. > Area averaged quantity INTRODUCTION The compressor wheel temperature is one sensitive quantity in the replacement interval determination of turbocharger components. The temperature has an impact on various possible material failure mechanisms such as HCF, LCF and creep. Material properties are closely related to the temperature field. These effects have to be taken into account in the stress simulation and the following life cycle computations. The accurate prediction of the temperature field is therefore a key factor in the design process. Today s advanced turbochargers are designed for high pressure ratios π v which coincides with increasing wheel temperatures. To achieve high pressure ratios it is required to cool the compressor wheel. The cooling air is taken from the compressor mass flow downstream of the intercooler and must be limited to a minimum as it decreases the overall turbocharger performance. The increase of cooling efficiency is an exhaustive subject in the gas turbine industry for decades. However, there is a lack of publications in public literature that deal with the cooling of turbocharger compressor wheels. One efficient cooling system which is widely used in the gas turbine community is the impingement cooling located inside the vanes. The blade wall is cooled by high speed jet flows generating high heat transfer coefficients at the blade walls. Unlike in gas turbines, the impingement cooling of compressor wheels is located in the back face region and the wall to be cooled is rotating. In the last decade fully coupled CFD conjugate heat transfer simulations have been evolved to compute the convective and conductive heat transfer between fluid and solid domains, e.g. in [1], [2], and [3]. However, the simulation of impingement cooling of a rotating wall is an unsteady heat transfer problem. Depending on the rotational speed the compressor back wall experiences a pulsating cooling air jet, which implies an unsteady heat transfer coefficient. To circumvent time consuming unsteady CFD-CHT simulations, the present paper proposes a CHT-mixing plane interface (CHT-MPI) between fluid (stationary) and solid (rotating) domains. The new method exploits different time scales of common turbocharger compressors between pulsating cooling air frequency and time scales of the material temperature variation due to thermal inertia (low Stanton number). The mixing plane concept corresponds to the commonly used fluid mixing plane interface between impeller and diffusor, which originates from work of Denton in [4] and [5]. The present paper is organized as follows. The CHT-mixing plane approach is first presented followed by a thorough validation against fully unsteady computations as well as the analysis of important model parameters. Finally, the CHT-mixing plane approach is applied to a cooled compressor stage. Two operating conditions, each with three different cooling mass flows are computed. The compressor wheel temperature is compared to temperature measurements at the same flow conditions. CHT-mixing plane method The CHT-mixing plane interface is closely related to the fluid mixing plane interface. Fig. 1 shows the physical realization of the CHT-MPI for a compressor stage cooling. Starting counterclockwise from top right to bottom right, the top right illustrates the enlargement of the upper back side of the compressor wheel and the cooling bore, the top left image is a snapshot of the instantaneous heat flux distribution at the fluid side of the fluid to solid interface generated by the impingement cooling. At the bottom left the image depicts unsteady heat flux distribution of two monitor points, q f luid 1 and q f luid 2, fixed with the compressor wheel at the same radial but different circumferential positions. The last figure illustrates the circumferential area averaged heat 2 Copyright c 2013 by ASME

3 flux at the solid side of the interface for discrete bands transfered from the fluid to the solid side. The time average t of the periodically unsteady signal can be replaced by a circumferential area average procedure θ. This is shown here by the dashed line which is computed from the depicted monitor points. The circumferential area average is split into discrete radial bands r b represented by the black lines. For each discrete band the area averaged value is computed at the fluid side and stored in a 1-D vector field of length n b. These values are linearly interpolated on the solid boundary side of the interface in the next iteration step. The same procedure is applied vice versa for the temperature distribution. The method conserves the integrated heat flux on both sides, fluid and solid side. This conjugate heat transfer coupling method is also called flux forward temperature back (FFTB) method according to the transfer direction of quantities relative to the fluid domain, e.g. [2]. The method reaches convergence if the difference of the integrated heat flux on both sides of the interface falls below a limit ε and if the heat flux of each band shows a steady behaviour. Fig. 2 shows the flow chart of this method. Two main parameters of the CHT-mixing plane interface can be identified and are subsequently analysed. n inner is the maximum number of iterations for each exchange interval. n outer is the number of exchange intervals until convergence is reached. Also, a mesh independence study has been performed. Figure 2. Flow chart CHT-mixing plane interface. CHT-mixing plane validation case The validation case is a detail simulation of the compressor wheel back face region near the trailing edge as indicated in Fig. 3(a). The computational domain consists of the upper part of the back face region (RR), the compressor wheel (VDRS), the partition wall (ZWB), and the cooling bore (KL). The partition wall is the wall located on the opposite side of the compressor wheel, cf. Fig. 7. VDRS and ZWB are solid domains and RR is fluid domain. The steady simulation with CHT-MPI is a pitch model according to the cooling bore symmetry, whereas the unsteady simulation is a full 360 degree model. The reason for this is that periodic transient fluid-solid interfaces for equal pitch models are not yet implemented in the commercial solver used in this study. Figure 1. CHT-mixing plane interface. Boundary conditions The flow and thermal boundary conditions were chosen to represent typical flow and thermal conditions in the transonic compressor stage and are given in Tab. 1. The flow field is assumed to be turbulent. The flow boundary condition profiles for inlet and outlet were extracted from a preceding compressor stage simulation including the back face region. The cooling 3 Copyright c 2013 by ASME

4 Boundary conditions Inlet Outlet Cooling air Total Pressure Mass flow Total Temperature cooling air Total Temperature Mass flow cooling air Velocity Direction Table 1. Flow boundary conditions (a) Computational setup of impingement validation case. lowed for subsequent life cycle computations, which means, that within the limits of the RANS model the new CHT-MPI method reproduces the heat transfer between impingement jet and rotating compressor wheel for typical and relevant turbocharger compressor flow conditions very well. The computational time of this method is approximately 17 times faster than the unsteady approach (cf. Tab. 2). (b) Mesh. Figure 3. Computational domain and mesh. mass flow rate and total temperature were obtained from experiments. Thermal boundary conditions for temperature profiles were interpolated from experimental results. Figure 4. Unsteady CFD-CHT simulation vs. new CHT-MPI method. Heat flux (left) and temperature (right) profiles over radius at interface between RR and VDRS. T max indicates the maximum temperature variation allowed for subsequent life cycle computations. Unsteady vs CHT-MPI Fig. 4 shows the heat flux and temperature profiles at the interface between back face region RR and compressor wheel VDRS for both steady (blue) and unsteady (green) simulation. The unsteady profiles have been extracted at same position (same bands) and have been area averaged in the same way as for the new CHT-MPI method. The results for heat flux and temperature between steady and unsteady simulation are consistent with each other, in particular in the region close to the impingement jet. The figure also shows the maximum temperature variation al- steady unsteady Computation time 500 minutes 8400 minutes Table 2. Computation time steady vs unsteady simulation on a single processor. 4 Copyright c 2013 by ASME

5 Sensitivity parameter analysis In the following, the mesh resolution and the CHT-MPI model parameters to optimize convergence time are analyzed in more detail. Four grids of different mesh resolution have been generated in such a way that the first cell in grid1 is located in the log law region, in grid2 in the buffer layer and in grid3 and grid4 in the viscous sublayer, see Tab. 3. For each grid, The y + profiles over radius are displayed in Fig. 5 confirming the different mesh resolutions. The heat flux and temperature profiles in Fig. 5 show that even with a resolved boundary layer, the temperature and heat flux profiles (computed by a lower number of bands compared to Fig. 4) do not collapse to the same profile, indicating that a grid independent solution has not been achieved. The final solution varies within a certain band width. That is mostly due to the fact that current turbulence models are not optimized to compute temperature boundary layers and heat transfer. The turbulence model in the present study is the SST k ω model which has been reported in literature, e.g. [6] and [7], to be one of the most reliable turbulence models for heat transfer predictions and in particular for impingement cooling. However, the temperature profiles are within the temperature accuracy T max required by the subsequent life cycle analysis. Note that the grid resolution of grid4 is too fine and not feasible for a full compressor stage simulation (including seal labyrinths etc.). A grid resolution as in grid1 or grid2 is more realistic in terms of feasibility in the design process. However, a certain uncertainty must be taken into account. Another issue is the setting of parameters n inner and n outer in the CHT-MPI model. After n inner iterations the simulation stops and writes out the result file. The CHT-MPI model computes the new heat flux and temperature profiles and restarts the simulation. This generates a certain amount of input and output traffic, which has to be taken into account. Also, the numerical stability is affected by the number of inner iterations. Fig. 6 shows the convergence plots of heat flux and temperature for a certain band at the CHT-MPI for different n inner iteration numbers. Tab. 4 summarizes the computation time for different n inner iteration numbers. It should be noted, that these numbers give a hint on how to choose the model parameters and they are adjusted in the subsequent full compressor simulation. Furthermore a high number of bands n band has been chosen (close to grid resolution) since it increases solution accuracy without being a time cinsuming procedure. It was found that a relaxation of the heat flux and temperature profiles after each iteration was not necessary to stabilize the solver. Compressor stage CFD-CHT simulation In the following, the new CHT-MPI is applied to a full compressor stage. All variables are non-dimensionalized by the design operating point OP1 from experiment (full load) and are indicated by subscript d. Two operating points at full load (100%) Mesh Resolution grid1 grid2 grid3 grid4 Number of mesh points Figure 5. < y + > Table 3. Mesh resolution. Mesh influence on heat flux and temperature distribution at mixing plane interface. The radius is non-dimensionalized by its maximum value. and part load (90%) have been defined. For each operating point, three different cooling mass flows were specified. All cooling operating points and names are given in Tab. 5. Simulation setup The computational setup is shown in Fig. 7. The topology consists of four major domains representing the compressor flow channel (VDR), the back face region (RR), the solid compres- 5 Copyright c 2013 by ASME

6 Inner and outer iteration n inner 15 s/iteration n outer 195 s/iteration time until convergence in s shaft. All other outer boundary walls are set to adiabatic. From the thermal analysis of the validation case it was found that the mesh resolution should include the viscous sublayer y + < 5. The major part of the mesh fulfills this requirement as seen in Tab. 6. Table 4. time. Influence number of inner and outer iterations on convergence Figure 7. Compressor stage topology and boundary conditions. Figure 6. Covergence of heat flux and temperature at mixing plane interface. Table 5. (a) Load mass flow ṁ c. Operating points and names ṁ c1 ṁ cd / Name ṁ c2 ṁ cd / Name ṁ c3 ṁ cd / Name 100% 1 / OP / OP2 0 / OP3 90% 0.78 / OP / OP5 0 / OP6 Operating points and names according to load and cooling sor wheel (VDRS) and the solid partition wall (ZWB). For the compressor flow total flow conditions at the inlet and static flow conditions at the outlet are prescribed. Mass flow boundary conditions for sealing air, ṁ SPL, and blow by ṁ BB are extracted from experiments for each operating point. In addition, it is necessary for CFD-CHT computations to specify thermal boundary conditions at the outer system boundaries. Temperature profiles are interpolated from experimental results at the back side of the partition wall and at the cut surface of the Number of mesh points Mesh Resolution VDR RR VDRS ZWB 2.1e06 2.0e06 2.4e06 0.8e06 < y + > Table 6. Mesh resolution. Computational results The computational results are presented in two steps. First, the thermodynamic integral quantities for all operating points OP1 to OP6 are discussed, see Tab 7. Operating points OP3 and OP6 have been computed without the new CHT-MPI since no cooling mass flow is involved. Mass flow and total outlet temperature are in accordance to the experimental results and differ by less than 1%. The numerical results for total pressure ratio π v and isentropic efficiency η is are throughout a few percent higher compared to the experimental results. The difference is mainly due to the missing volute in the simulation. From experience the expected losses generated in the volute agree with those missing in the numerical simulation. Accounting the differences between 6 Copyright c 2013 by ASME

7 numerical and experimental results to volute losses is substantiated by the fact that these losses increase with rotational speed which is also reflected in the present results. There is an overall agreement between numerical and experimental thermodynamics. In a second step, the compressor wheel temperature field is discussed in detail. Fig. 8 and Fig. 9 display the meridional temperature field for two operating points at full and part load, respectively. From top to bottom each figure shows temperature results for full, reduced and zero cooling mass flow. All temperature values TV R i are non-dimensionalized by TVR i = TVR i TVEd TVA with d TVE d TVEd and TVA d the inlet and outlet mass flow averaged total temperature at design point OP1. This value can vary between zero (temperature at monitor point is equal to inlet total temperature) and one (temperature at monitor is equal to outlet total temperature). On the left side, the 2D meridional temperature field of the compressor wheel and the location of the discrete temperature monitor points TVR i is shown. On the right side, the comparison between numerical and experimental results is shown for each monitor point. The error bars for the experiemtnal and numerical results indicate the maximum temperature variation at a discrete point allowed for the subsequent life cycle computation and the temperature variation within a sphere of 3mm diameter respectively. That information helps to identify monitor points with steep temperature gradients, which in itself are sensitive to temperature sensor application accuracy. Since experimental temperature measurements in the rotating frame of reference are very challenging, some of our sensors have fallen out during measurement. That is sensor TVR 8 for OP1 and sensor TVR 6 for OP5 and OP6. However, neighbour measurement points (e.g. TVR 7 ) agreed very well between experimental and numerical results for these oprating points indicating that the simulation computes the temperature field accurately. The numerical results agree well with experimental results over a wide range of temperature values at various locations and operating points. That is in particular true for the cooled cases OP1, OP2, OP4, and OP5 where measured and computed results agree very well. The temperature distribution gives an insight into the driving heat transfer mechanisms inside the compressor wheel. The blades and the main channel passage flow cool down the compressor wheel, whereas the back face region heats it up. The impingement cooling is a very efficient method to reduce the compressor wheel temperatures locally close to the compressor trailing edge. The cooling effect can also be observed throughout the compressor wheel indicating the coupling effect with the main passage flow. The results also show heat transfer from the turbine side to the compressor wheel. To emphasize the quality and importance of the new CHT-mixing plane interface the temperature field has been computed by an alternative model. In that model, the cooling jet flow is represented by a slit flow with same flow conditions. In this way the problem can be computed by the conventional CFD-CHT method since it becomes axissymmetric and periodic symmetries can be exploited. The results are shown in Fig. 10. On the top and from left to right, the temperatures are displayed for the various monitor points. They confirm that the alternative model by the slit flow fails to compute the temperature field correctly. The reason for the success of the new CHT-mixing plane becomes obvious when comparing the back face flow field on the bottom of Fig. 10. With the slit model, not only important flow structures such as the impingement of the jet flow but also the vortice structures are not captured correctly. These structures are very important for the heat transfer between fluid and solid and are successfully computed by the new CHT-mixing plane approach. Finally, Fig. 11 shows the wall heat fluxes for the compressor wheel for OP1 and OP3 revealing the relevant heat transfer mechanisms. The wall heat fluxes are non-dimensionalized by the same reference value. Positive values indicate heat transfer into the compressor wheel. For both cases more than 60% of the integrated heat flux enters the compressor wheel via the labyrinth seal. For the uncooled case, the heat flux enters from the back face region and leaves the compressor wheel via the main passage flow, particularly near the blade suction side on the hub side. With cooling, the pattern changes and close to the hub side trailing edge a part of the heat flux points into the compressor wheel. As a consequence, fully coupled CFD-CHT computation must be performed to be able to predict the compressor wheel temperature field accuratly. Thanks to the new CHT-MPI method, also impingement cooled compressor designs can be computed successfully. Thermodynamics of all operating points Π is /Π is d η is /η is d ṁ v /ṁ vd TVA /TVA d Sim. Exp. Sim. Exp. Sim. Exp. Sim. Exp. OP OP OP OP OP OP Table 7. Numerical vs. experimental results of compressor thermodynamics for all operating points specified in Tab Copyright c 2013 by ASME

8 (a) Temperature distribution OP1. (a) Temperature distribution OP4. (b) Temperature distribution OP2. (b) Temperature distribution OP5. (c) Temperature distribution OP3. (c) Temperature distribution OP6. Figure 8. Compressor wheel temperature distribution, temperature measurement locations and comparison to experimental results. Error bars in experimental results (in blue) indicate the temperature variation allowed for subsequent life duration computations. Error bars in numerical results (in red) indicate the temperature variation of a 3mm diameter sphere around each measurement point. Figure 9. Compressor wheel temperature distribution, temperature measurement locations and comparison to experimental results. Error bars in experimental results (in blue) indicate the temperature variation allowed for subsequent life duration computations. Error bars in numerical results (in red) indicate the temperature variation of a 3mm diameter sphere around each measurement point. Conclusion The present paper presents a new method, called CHTmixing plane interface, to compute impingement cooling of compressor wheels. Impingement cooling of a rotating wall is an unsteady heat transfer problem. The CHT-mixing plane interface is based on the well known fluid mixing plane interface between rotor and stator which is state-of-the-art in industrial applications. It is also a bandwise average procedure to make the problem steady. The method fullfills the requirement to conserve the integrated heat flux between fluid and solid domain. First, the method has been validated against an unsteady approach. The new CHT-mixing plane approach shows the same results as the unsteady procedure at a substantially lower computational cost. Various parameters of the model were analyzed. The method shows a very robust and numerically stable behaviour. Secondly, a full compressor stage at two operating points and three different cooling mass flows ranging from zero to full cooling mass flow has been computed via CFD-CHT including the new CHT-mixing plane interface. Flow and thermal boundary conditions have been extracted from experiments. The temperature field computed from the CHT-mixing plane inter- 8 Copyright c 2013 by ASME

9 (a) Impingement cooling modeled by new CHT-MPI (left) vs impingement cooling represented by a slit model (middle) vs uncooled (right) case. face matches the experimental results at various discrete monitor points inside the compressor wheel very well confirming the high qualitity of the new approach. A comparison of results with those from an alternative, steady model, called slit model, confirms the necessity to resolve the impingement jet flow structures to a certain level. Important flow structures are captured by the new approach. The analysis of the 3D temperature field reveals important heat transfer mechanisms contributing to the compressor wheel temperature field. The new method makes new options available such as optimizing the impingement cooling in a fully coupled way. Also, the parallel optimization of the labyrinth seal and the cooling becomes feasible in the future. (b) 3D flow field: impingement cooling modeled by new CHT-MPI (left) vs impingement cooling represented by a slit model (right). Figure 10. Improvement of new CHT-MPI vs. alternative cooling model. (a) Wall heat flux OP1. (b) Wall heat flux OP3. Figure 11. Wall heat flux distribution compressor wheel back and front side. Fluxes are non-dimensionalized by maximum values of OP3 for back and front side respectively. Left: positive values indicate heat flux into the compressor wheel. Right: negative values indicate heat flux from compressor wheel into the main flow. 9 Copyright c 2013 by ASME

10 REFERENCES [1] Verstraete, T., Alsalihi, Z., and der Brambussche, R. V., Numerical Study of the Heat Transfer in Micro Gas Turbines.. ASME Journal of Turbomachinery, 129, pp [2] Verstraete, T., Alsalihi, Z., and der Brambussche, R. V., A comparison of conjugate heat transfer methods applied to an axial helium turbine.. I MECH E Part A Journal of Power and Energy, 221, pp [3] Heuer, T., and Engels, B., Numerical analysis of the heat transfer in radial turbine wheels of turbo chargers.. ASME Paper(GT ). [4] Denton, J. D., and U.K.Singh, Time marching methods for turbomachinery flow calculation.. VKI Lecture Series. [5] Denton, J. D., and D.C.Prince, An improved timemarching method for turbomachinery flow calculation.. Journal of engineering for power, 105, pp [6] Zu, Y., Yan, Y., and Maltson, J., CFD prediction for multi-jet impingement heat transfer.. ASME Paper(GT ). [7] Mangani, L., and Maritano, M., Conjugate heat transfer analysis of NASA C3X film cooled vane with an objectoriented CFD code. ASME Paper(GT ). 10 Copyright c 2013 by ASME