Flow Topology Optimization of a Cooling Passage for a High …download.xuebalib.com/7vhs104V6EJ.pdf · internal cooling passages within high pressure turbine blades in . order to

FLOW TOPOLOGY OPTIMIZATION OF A COOLING PASSAGE FOR A HIGH PRESSURE TURBINE BLADE

J. Iseler

Dassault Systèmes SIMULIA Karlsruhe, Germany

T. J. Martin United Technologies Research Center

East Hartford, United States

ABSTRACT

This paper deals with a topology optimization of internal cooling passages within high pressure turbine blades in order to deliver fully three dimensional designs that optimize the local flow physics. By applying the implemented optimality criteria, a new individual passage design with minimized amount of recirculation is achieved, leading to a reduced total pressure loss. In contrary to traditional parametric approaches, where a CFD run is needed after each design modification, the applied topology optimization acts as a co-simulation and is finished after a single run where the initial geometry represents the available design space. The CFD runs for optimization and the subsequent verification of the flow passages assume steady state take-off conditions. The verification includes a flow simulation to check the pressure loss of the optimized passage design. In a second step, a loosely coupled conjugate heat transfer procedure including external turbine flow, coolant flow and heat conduction of the solid (blade, platform and attachment) is applied to predict the impact on the heat transfer. By running a FEM simulation afterwards, the stresses are computed and compared with those from the reference design.

NOMENCLATURE CFD Computational Fluid Dynamics FEA Finite Element Analysis CHT Conjugate Heat Transfer AM Additive Manufacturing Re Reynolds number Q Heat Flux Tgas External (hot gas) temperature TW Wall temperature pW Wall pressure

p0 Static pressure at inlet Z Quasi-sensitivity Porosity Step size for line search algorithm Design variable

INTRODUCTION

In modern turbofan and turbojet engines for aircraft, increases in rotor speed and turbine inlet temperature offer the greatest improvements to performance in terms of increased thrust-to-weight ratio and fuel efficiency [1]. However, increased performance is limited by the integrity and durability of the turbine module, mainly the turbine airfoils, against very high and cyclic structural and thermal loads. In fact, turbine airfoils are designed such that they are subject to the highest possible centrifugal and temperature loads while they extract work as efficiently as possible from the high pressure and high temperature core flow. To meet these demands, turbine airfoils must be designed to the absolute limit of their thermal and structural capability while maintaining or increasing their durability against multiple failure modes such as creep, oxidation, corrosion, and fatigue, which become rapidly worse as temperatures reach their material limits. Damage to the high pressure turbine usually sets the limit of the entire engine, and ultimately the aircraft’s availability, because the limiting life determines the time the engine can spend in continuous service between inspections, maintenance and overhauls.

The goal of a turbine airfoil design team is to provide an aerodynamic shape and internally cooled thin-walled structure that will maintain extremely high structural and thermal loads, and that will meet a specified service life against

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all modes of damage. Turbine airfoils are supplied with cooling air extracted from the high pressure compressor which flows past the burner and into the stationary vanes and rotating blades. This cooling air passes through very small and ever-increasingly complex three-dimensional internal cooling flow passages that act as miniature heat exchangers, with turbulators [2, 3], rows of pin fins [4] and pedestals, impingement jets, flow bifurcations and sharp bends that can separate and recirculate. The cooling air is forced to exit the airfoil through rows of film cooling holes and ejection slots at the airfoil tips and edges and out into the engine core flow, which can degrade the aerodynamic performances as it cools the part and protects it from exposure to the hot combustion product gas.

The design of these internal passages requires great care so that the performance improvement derived from operating at high temperatures is not more than offset by the aerodynamic penalties associated with using the coolant air. The objective of the turbine airfoil cooling design is to achieve a target life limited by temperature and thermo-mechanical stress with the least amount of cooling air. This is achieved by adding internal heat transfer enhancements, however cooling air pressure losses increase proportionally with them, and the total pressure available is limited. Typically, primitive geometries are used for turns and flow bifurcations, and the losses within these coolant passages are not optimized to account for local flow physics. As a result, huge flow separations and pressure losses can occur which do not contribute to heat transfer enhancement. Flow topology optimization is a method that can produce efficient internal cooling geometries without extensive trial and error.

Fig. 1: Advancement of turbine airfoil cooling and materials

technology

Figure 1 illustrates the progression of turbine airfoil

materials and cooling technology over the past 70 years, showing various turbine airfoil cooling configurations and technologies in terms of their cooling effectiveness,

(TgasTwall)/(TgasTcool), versus turbine inlet gas temperature, Tgas, and year of entry into service. Modern high pressure turbine airfoils are constructed from single crystal (SX) castings of nickel-base superalloys, and coated with intermetallic environmental barrier coatings (EBC) and ceramic thermal barrier coatings (TBC). Superalloys materials are designed to have high mechanical strength, resistance to deformation at high stress and temperature, increased fracture toughness, stability, and resistance to corrosion and oxidation at high temperature [5]. Coatings are added to further protect the strong substrate material against these high temperatures, and to resist corrosion and oxidation, but these coatings sinter at high temperature and spall under thermal cyclic loading. The airfoil cooling images and design points are shown with respect to a superalloy, and increasing temperature capability corresponds to a vertical shift on the chart. As one can see from the figure, modern turbine airfoils operate in a hot gas environment with temperatures well beyond material limits of the superalloys and ceramic-based coatings, which makes internal cooling a required technology for the foreseeable future, and the technological progression is expected to continue to ever-increasing complexity, and even into the regime where the boundaries between the structural solid, heat conduction and convection are indistinguishable.

This discussion frames two questions, manufacturability and engineering capability. First, recent advances in additive manufacturing [6] and alternate methods for producing ceramic and refractory metal cores for investment castings have raised the possibility to significantly advance the state of the art with the detail and precision necessary to cast smaller and more complex features for improved internal cooling performance, rapid prototyping, and reductions in manufacturing lead times and development costs.

In regards to engineering capability, conventional wisdom is that our ability to design and analyze these parts has exceeded our ability to produce them. This perhaps remains to be true for conventional manufacturing processes; however, this paradigm can flip when we change materials and manufacturing processes. Perhaps today or in the near future, we can manufacture components whose physics we cannot reliably predict and therefore, we fail to produce designs that operate efficiently up to their material limits. The purpose of this paper is to investigate the use of a developing technology, called non-parametric design, also known as topology optimization, where physics-based modeling acts as the guiding objective, constraints and design variables for optimization.

OPTIMIZATION TECHNOLOGIES Existing approaches to optimization can be divided

into two groups: parameter-based optimization and non-parametric approaches. While parameter-based methods have been established for the design process of cooled turbine airfoils, non-parametric approaches are increasingly considered as an efficient method that can work in tandem with parametric methods to further improve performance and expand the captured design space.



A parametric approach suffers from one requirement – namely the parameterization of the CAD model. For a turbine blade geometry, this process may take months. In contrast to that, non-parametric approaches are mesh-based methods and come along without any parameterized geometry. As a result, the optimization task can be achieved at a fraction of the time needed for a parametric optimization. Additionally, more individual shapes tailor-made for the specific flow conditions are received. That is possible, since those methods can handle a huge amount of design variables. There exist mainly two non-parametric approaches for flow problems - namely the shape optimization and the topology optimization. While shape optimization [7, 8] is rather meant for small design changes, topology optimization delivers entire new design ideas. A broad introduction to this method is given by Bendsoe and Sigmund [9]. The initial geometry does typically represent the maximum available design space. During the optimization, a new material distribution inside of the design space is obtained via assigning a porosity quantity for each cell. Dependent on a predefined optimality criteria [10, 11] or sensitivities [12, 13], the value of this quantity will be high or low. For fluid mechanics, typical objectives are pressure drop, flow uniformity, tumble and swirl. Recently, topology optimization was applied for fluid-thermal problems [14]. Pietropaoli et al. [15] considered a coolant flow that passes through a two-dimensional heated box and defined total pressure loss and outlet temperature as objective functions. In order to address thermal quantities, a thermal diffusivity coefficient was introduced as a function of the porosity. In general, the result of a topology optimization represents a design proposal, which will typically be simplified via a CAD tool afterwards. USED TOPOLOGY OPTIMIZATION METHOD

The applied tool Tosca Fluid represents a topology optimization method which delivers a geometry proposal for an optimum channel design with respect to low pressure drop within a specified domain. The method is focused on internal steady-state single phase incompressible duct flows as described by the Reynolds-averaged Navier-Stokes equations (RANS) [16]:

vvDpvv )(2)( (1)

0 v (2)

where v and p represent velocity vector and pressure, respectively. The effective kinematic viscosity is the sum of the molecular and turbulent viscosity. D is the rate of the strain tensor. Moreover, equation 1 contains the porous resistance term v . This term is a function of the velocity and the porosity . By adding this term, a flow resistance is introduced via a volume force. With an infinite high value of , a solid-like behavior is achieved. The idea of topology optimization is now

to apply porosity (and consequently also the force term) on a cell-based manner in order to reach the extremum of the considered objective. This process can be expressed as solidification or sedimentation process. In the simplest case, the optimized geometry contains only those cells, where =0.

There are mainly two strategies are available for obtaining the ideal porosity distribution in matters of the considered objective function. The more prominent strategy is based on the results of an adjoint solver run: By solving the adjoint (Navier-Stokes) equations after the primal solver run, sensitivities for the considered objective function J can be computed for all cells. Those sensitivities reflect the dependency of J on changes of the porosity. By transferring the sensitivities to a gradient method afterwards (for example the steepest descent approach), an updated porosity distribution can be computed. The optimization loop consists therefore of a primal solver run (1), an adjoint solver run (2) and the application of the gradient method (3). The process can be stopped, after the sensitivities have become very small (∂J/∂≈ 0) As a result, a local minimum of the objective function is obtained.

The second strategy, which is pursued here, follows the idea of optimality criteria. The criterion used here postulates that a minimization of the amount of recirculation typically leads to a significant reduction in total pressure loss. Therefore, recirculation represents the considered objective function. The recirculation zones are identified by a strong deviation of the local flow direction compared to a reference flow direction. That is: If the angle difference localreffor a cell n is beyond a predefined threshold value krit, then n will be considered as a recirculation cell. The angle differenceand the porosity are now linked in a way that cells with krit are treated with an increased porosity. As a result, the angle difference represents the essential element of the minimization process. Since is treated in this minimization process similar to sensitivities, the angle differences are named quasi-sensitivities. The basis of those quasi-sensitivities is calculated through the dot product of the local velocity field and the reference velocity field:

reflocal

reflocal

vv

vvz

(3)

The reference velocity field is obtained prior to the

optimization through a flow simulation based on a huge dynamic viscosity value. The values of the quasi-sensitivities range from -1 to 1 (fig. 2). When both directions are in line (left picture), the quasi-sensitivities equal -1. Opposite flow directions (right picture) lead to a value of 1.

Fig. 2: Quasi-sensitivities dependent on flow direction



In order to achieve the elimination of all backflow zones, a line search algorithm is used. In general, the algorithm determines a descent direction along which the considered objective function will be reduced. It then computes a step size deciding the distance that should be moved towards that direction. Direction and distance are calculated again from the new point in each iteration-step until a local minimum is reached. In case of the applied topology optimizer, the direction is given by the quasi-sensitivities. Note, that the algorithm is not processed for the porosity but for the design variable :

0),1(0,

11

11

zzzzrk

rk

rk

rk

rk

rk

(4)

with є in iteration k. z and represent the quasi-sensitivity and the step size. Based on the available design variables, the porosity values () can be computed afterwards.

Fig. 3: Optimization process. Top: Available design space geometry

(initial design). Center: Flow field inside of initial geometry.

Bottom: Flow field after optimization run

Figure 3 documents the prevention of backflow by means

of the solidification process. As a result, a significant reduction of total pressure drop is likely. As CFD solver and topology optimizer are coupled, only one single CFD run is needed for a complete topology optimization. With this approach, topology optimization for even large scale channel flow applications can be conducted in an acceptable timeframe. The optimization ends with a CFD model in which the flow is prevented in some cells. In order to obtain a duct design without those cells, a subsequent extraction is done. This is followed by a smoothing step, leading to the final design proposal (fig. 4) that can be exported afterwards. The received design typically reveals a

rough shape with some artefacts. As a result the obtained design proposal typically needs to be modified with the help of a CAD tool afterwards. This redesign step incorporates an interpretation of the optimized result and follows additional constraints like manufacturing restrictions. To finally check the performance of the new design, a CFD verification run based on the reconstructed geometry is needed.

Fig. 4: Top: Optimization result, including prevented

backflow areas colored in red. Bottom: Design proposal after

extraction and smoothing

APPLICATION EXAMPLE – COOLING DUCT OF A HIGH PRESSURE TURBINE

This paper deals with a topology optimization of the turn geometries belonging to a 3-pass serpentine of a high pressure turbine blade. The usage of the described topology optimization method allows an automated creation of individual flow passages with minimized amount of recirculation. As a result, cooling air is transferred at low pressure loss through the passages. Moreover, the prevention of dead water zones may lead to a homogenization of the temperature field and an avoidance of hot spot areas. This leads to a reduction of temperature gradients and possibly smaller stresses. By reducing the stresses itself, an improvement of blade life is possible, as well. In order to evaluate those quantities (pressure drop, stresses), a three step procedure have been defined for take-off conditions with a topology optimization of tip and root turn (1), a verification run for the turbine blade via loosely coupled conjugate heat transfer procedure (2) and a finite element analysis (3).

APPLIED TURBINE BLADE GEOMETRY

Fig.5 shows the used turbine blade geometry representing a generic example from the open literature. The airfoil belongs to a first stage blade row with a blade count of 44. The blade height and tip radius are 50.8 mm and 254.2 mm, respectively, which results in a hub tip ratio of 0.8. With a rotational speed of 16800 RPM a tip velocity of 447.2 m/s is obtained. The considered airfoil includes overall six cavities for cooling purposes. In order to reduce the complexity of the geometry and the amount of runtime, only convection cooling was considered – impingement and film cooling were neglected. The available 3-pass serpentine includes the tip and root turn connecting the straight passages. The coolant enters the



serpentine on the bottom left side (cavity #3) and leaves it through a tip hole on the right (cavity #5).

Fig. 5: Used high pressure turbine blade geometry

TOPOLOGY OPTIMIZATION AND CAD-REDESIGN For topology optimization purposes, a separate CFD

model was created, which solely includes the 3-pass serpentine with tip and root turn. The computational domain was split into regions representing the straight passages (grey) and zones for the design spaces of the turns colored in blue. Although not optimized, the straight passages were included in order to provide realistic inflow conditions at the design space inlets and realistic flow directions at the design space outlets.

Fig. 6: 3-pass serpentine including design space

geometries colored in blue

The computational mesh of the 3-pass serpentine

consists of overall 400 K elements. For the optimization run, an incompressible turbulent, steady-state coolant flow was assumed and computed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations. The impact of the turbulence on the time averaged flow was predicted by the realizable k-epsilon turbulence model [17, 18]. A mass flow inlet and a pressure outlet boundary condition were defined for inlet and outlet, respectively. All walls were treated as adiabatic ones. The definition of the CFD model was followed by the setup of the optimization itself: This encompasses the import of the CFD model, the assignment of the region to be optimized and the iteration number for the optimization run. In the discussed example, it took overall 13 hours to run the optimization for both turn geometries on four cores.

Fig. 7: Topology optimization workflow

Fig. 7 documents the obtained subset of cells after the

extraction step and the subsequent smoothing. For both turns, individual shaped designs are obtained. Since recirculation zones occurred close to the design space outlets, a rough transition (between turn and passage downstream) was observed. Therefore, the obtained designs were manually adjusted here in order to permit a smooth transition. Table 1: Used parameters for verification run

Inlet mass flow rate 0.0225 kg/s Total inlet temperature Tt,in 850 K Static outlet pressure P s,out 2.5+06 Pa Rotational speed 16800 RPM

After that, a CFD verification run was undertaken for

the 3-pass serpentine for initial and optimized turn geometries - based on the parameters shown in table 1. Those parameters were gained from a research in turbomachinery literature (e.g. [20]). On the contrary to the topology optimization, the ideal gas law was applied here. Apart from that, same settings were used for the physical model. The CFD results confirmed that the recirculation areas have been minimized inside of the turns (fig. 8). However, backflow areas can be seen in the passages



downstream. Those areas would have been prevented by allowing an optimization of the passages as well. However, that was not targeted in this study. Compared to the reference design including the design spaces, a significant pressure loss reduction was achieved with 16% for tip turn and even 26% for the root turn.

Fig.8: Streamlines for reference design (left) and optimized

design (right)

The next step was to redesign the obtained passages

via CAD tool (fig. 9). Redesign means, that on the one hand, the overall shape is maintained, while on the other hand, local inappropriate features are eliminated. The first step of this process was to import the design proposal as .stl files. This was followed by a deletion of the inappropriate features and a local and global smoothing afterwards. After that, the surface was transferred into a subdivision surface and connected smoothly to the passages downstream and upstream via blend feature. Then, a fine-tuning step was conducted by locally dragging patches, edges and nodes of the subdivision surface. Finally, after the surface has been closed, a 3D part was created.

Fig. 9: CAD redesign of optimized turn geometries

A subsequent CFD verification run should reveal the

impact of the redesign work on the flow behavior. In fact, the provision of smoother walls and improved transition to the passages led to a further reduction of the total pressure loss - especially for the root turn. Here, an additional decrease by 24 % is obtained, which results from an attached flow at the beginning of cavity #5 (see fig. 10).

Fig.10: Flow behavior at root turn for raw (left) and redesigned

geometry

LOOSELY COUPLED CHT ANALYSIS The results of the CFD verification run for the 3-pass

serpentine proved that there is a high potential for total pressure loss reduction, if topology optimized turn channels are used. In order to quantify this reduction more accurately and at the same time investigate the impact on the heat transfer, a coupled conjugate heat transfer analysis was defined. In this paper, a loosely coupled process was applied. Many simulations have shown that the loosely-coupled process converges efficiently and provides temperature and heat flux results that are just as accurate as the full conjugate procedure [19].

By running this analysis, heat transfer between external flow and solid as well as between solid and coolant plus heat conduction in the solid are predicted. The following strategy was chosen: Run the loosely coupled CHT analysis for the reference design (1), export the distribution of the heat transfer coefficient along blade surfaces and the blade hub (2) and reuse them as convective boundary condition for a subsequent analysis of the turbine blade including the optimized turn designs (3) and finally map the thermal quantities on a FE model in order to evaluate the stresses (4).

Fig. 11 describes the process of the loosely coupled CHT analysis conducted for the reference design. The discussed process is similar to what have proposed by Storoselski et al. [5]. However, instead of using a FE solver for computing heat conduction and a 1-D cooling flow network tool for predicting the heat transfer to the coolant, a CFD analysis was applied to solve flow behavior, heat conduction and heat convection.



Fig. 11: Loosely coupled conjugate heat transfer analysis

The initial step of the process is to predict the exhaust

gas flow passing through turbine blade row. First, all walls are treated as adiabatic walls (Qgas = 0). After this initial simulation is done, the obtained gas temperatures Tgas on the wall boundaries are exported and scaled with 0.85. This scaled gas temperature values are then reused as initial guess for the wall temperatures (TW = 0.85*Tgas) and applied as temperature boundary condition for the blade surfaces and the hub wall. As the heat transfer between blade and casing is neglected, the casing wall is treated as adiabatic wall again. With that, the external flow (& heat transfer) simulation is rerun. After convergence has been achieved, the distribution of heat transfer coefficient, hgas = Qgas/(Tgas-Tw), is exported and the initial step is finished.

With that, a closed loop including internal and external flow (& heat transfer) simulation is applied. The loop starts with the internal flow simulation using the heat transfer coefficients obtained from the initial step as thermal boundary condition. This simulation predicts the coolant flow behavior, the heat conduction in the solid and the heat transfer between solid and coolant. After the run is finished, the obtained wall temperatures are transferred to the external flow simulation and reused as temperature boundary condition. The exhaust gas simulation will solve the flow behavior in the blade passage and the heat transfer between blade/hub and the solid. As a result, a new distribution of the heat transfer coefficients is obtained. With providing the new heat transfer coefficients to the subsequent internal flow simulation, the loop is closed. This loop was run, till similar values were obtained for the averaged blade wall temperature.

The exhaust gas flow passing the turbine blade row was predicted with the CFD solver ANSYS Fluent. The exhaust gas was treated as a steady-state single-component compressible flow and predicted by computing the Reynolds-Averaged Navier-Stokes equations with a coupled solver. A second order scheme was applied to solve convective and viscous fluxes. The impact of the turbulence on the turbine flow was predicted with the realizable k-epsilon turbulence model. A stagnation inlet and a static pressure outlet were applied as inflow and outflow boundary conditions. By using periodic boundary conditions, only one blade passage was applied for the flow simulation. The impact of the vanes located upstream on the turbine blade flow was neglected here.

Table 2: Used parameters for external flow simulation

Total inlet pressure Pt,in,abs 4.0e+06 Pa Inflow angle alfa1 12.5° Static outlet pressure Ps,out 2.5+06 Pa Rotational speed 16800 RMP

The parameters used for this simulation task are

extracted from turbomachinery literature and displayed in table 2. The temperature at the inlet plane was prescribed with a radial profile shown in fig. 12. This profile reveals a peak temperature of 1715 K at 70% span. Hub wall and tip wall are set to 1350 K and 1450 K, respectively.

Fig. 12: Prescribed profile of total inlet temperature T t,in

The computational domain is discretized by a

hexahedral mesh (see fig. 13) with y+ values close to 1. The tip gap was resolved with 25 elements. According to high Reynolds numbers (Re = 1.5e+06) and a requested element aspect ratio below 100, overall 2.6+06 elements were needed.

Fig. 13: Computational mesh for external flow simulation



The internal flow (& heat transfer) simulation was

applied with the CFD solver STAR-CCM+. The coolant was considered as a steady-state compressible air flow and predicted by computing the Reynolds-Averaged Navier-Stokes equations with a coupled solver. A two-layer approach [21] of the realizable k-epsilon turbulence model with all-y+ wall treatment was used and a second order scheme was chosen to compute the fluxes. Convective boundary conditions are used for the blade surfaces and the hub wall, while a linear radial temperature profile was prescribed for the attachment walls with 850K at the bottom and 1300K at top. It was ensured, that a consistent formulation for the computation of the heat transfer coefficients was applied for both CFD solvers. Table 3 summarizes the aerothermal parameters. Table 3: Applied parameters for internal flow simulation

Inlet mass flow rate for cavity #3

0.0225 kg/s

Total inlet pressure P t,in,abs

for cavity #1/#2 and #6 3.0+06 Pa

Total inlet temperature T t,in 850 K Static outlet pressure Ps,out

for cavity #1 and #2 2.6+06 Pa

Static outlet pressure Ps,out

for cavity #5 and #6 2.5+06 Pa

Rotational speed 16800 RMP

Note, that a mass flow inlet boundary condition was used for the 3-pass serpentine instead of a total pressure inlet. This was done in order to compare the pressure drop for reference and optimization case at the design mass flow rate. The design mass flow rate was obtained from a prior analysis for the reference case, where the total pressure inlet boundary condition (P t,in,abs =3.0+06 Pa) was used for cavity #3, as well.

The solid parts, namely the blade and attachment walls, were treated as a single crystal nickel superalloy material. The temperature-dependent specifications for density, thermal conductivity and specific heat were taken from Dye et al. [22] and implemented into the CFD model. A thermal barrier coating (TBC) was not considered. For the fluid regions as well as for the solid regions, a computational mesh with polyhedral cells and prim layers with overall 2.9e+06 elements was established. Conformal interfaces were used between fluid domain and solid in order to prevent impreciseness due to interpolation errors. However, according to the high Reynolds numbers in the cavities, a trade-off between accuracy of the solution and computational costs was needed anyway which meant to not resolve the viscous sublayer of the coolant flow. RESULTS OF LOOSELY COUPLED CHT ANALYSIS

As described in the last chapter, the loosely coupled CHT analysis is solely conducted for the reference design. For the optimized case, only an internal flow (& heat transfer)

analysis was needed, as no modifications of the heat transfer coefficients at blade surfaces and hub walls were assumed.

In the discussed study, the loosely coupled CHT analysis was stopped after four loops of external and internal flow simulation plus exchange of thermal quantities. Fig. 14 and 15 show the pressure load for suction and pressure side and the relative Mach number distribution for the blade passage at mid-span, respectively. It can be seen, that the turbine flow is attached and fully subsonic at mid-span. The overall maximum Mach number is 0.77 and located next to the blade tip (not shown).

Fig. 14: Pressure distribution at mid-span

Fig. 15: Mach number distribution at mid-span

Fig. 16 shows the resulting streamlines inside of the

cavities for the reference case. For the 3-pass serpentine, only minor differences can be identified compared to the analysis, where solely the serpentine flow itself was computed. Location and extent of the flow separations are very similar. According to the lack of guide vanes in cavity #6, the flow is not able to realize the 90° turn towards the trailing edge. As a result, a huge separation zone has established here.



Fig. 16: Streamlines for reference case

Besides the flow behavior in the cavities, the

temperature field in the solid was of interest in order to identify higher (spatial) variations. This was motivated by the fact, that there exists a correlation between thermal stresses and temperature gradients along the solid [23]. Higher gradient are assumed between outer and inner walls, since the blade is faced to huge exhaust temperatures at the blade surfaces and to low coolant temperatures at the cooling channel walls. Moreover, temperature gradients are caused by a radial variation of the temperature (see fig. 12). Local and steady flow separations of the coolant flow may also induce higher temperature gradients as no fresh coolant air is able to enter the separation zone. Thus, a zone with different heat transfer exists here.

Fig. 17 shows the temperature gradient distribution for several heights (34%, 53%, 72%, and 90% of blade height). Higher values are visible near the leading edge next to the stagnation point and at the trailing edge for those areas, where the coolant flow of cavity #6 mainly traverses towards the trailing edge slot. The peak gradients are located at the transition between cooled ribs and the hot suction side wall.

Fig. 17: Temperature gradients at blade walls and ribs

The following two pictures refer to the results of the

verification case for the optimized turn geometries. The

streamline plot (fig. 18) confirms the minimization of backflow in the two turn geometries of the 3-pass serpentine. By comparing the total pressure losses of reference case and optimization case, a reduction of 24% for the optimized tip turn and 50% for the new root turn is obtained. This reduced pressure loss could now be used to insert an increased number of turbulators in the 3-pass serpentine or to apply a higher number of film cooling holes there.

Fig. 18: Streamlines for reference case and optimization case

The distribution of the temperature gradients is

displayed in fig. 19. For the lower three slices, only minor changes can be identified with regard to the reference case. However, a considerable reduction of the peak values can be seen for the top section – namely at the position of the optimized tip duct. Obviously, the elimination of the recirculation areas provoked besides the pressure drop reduction a local homogenization of the temperature distribution as well.

Fig. 19: Temperature gradient distribution for optimization case



STRESS ANALYSIS As a change of the flow channels leads to a

modification of the blade solid, a subsequent finite element analysis was required in order to evaluate the stress distribution. The study was set up as a linear elastic analysis. It was assumed, that blade and root solid consists of the same material. No contact definitions were used in this study. As material, the single crystal nickel superalloy CMSX-4 was applied. The temperature-dependent specifications for density, Young’s modulus, Poisson’s ratio and thermal expansion were taken from Dye et al. [22]. A thermal barrier coating (TBC) was not considered.

Fig. 20: Mises stress distribution for reference case

Fig. 21: Mises stress distribution for optimization case

According to the simplified attachment geometry, the

geometry was only fixed on the bottom side. As initial step, a uniform temperature of 288 K was defined. By applying the mapped temperature values and prescribing a centrifugal body force for the considered rotational speed, thermal and mechanical stresses can be computed in the subsequent step. The obtained stresses represent therefore a superposition of thermal and mechanical stresses. The used computational mesh consists of overall 1.6E+06 quadric tetrahedral elements. Fig. 20 and fig. 21 depict the Mises stress distribution for the reference and the optimization case at several radial positions. It can be seen, that the highest stresses appear at the center of the

ribs. Altogether, only smaller differences can be identified for reference and optimization case. From that, it can be concluded, that the usage of the optimized channels does not lead to an adverse structural behavior.

SUMMARY High pressure turbines of future jet engines will be

faced to significant higher temperatures and pressures. As a result, a more efficient cooling is needed for those components compared to what is available today. One possibility to reach this target is to improve the internal cooling by delivering channels with large surface area and lower pressure loss. Both causes the increase of heat transfer for the same coolant mass flow rate: While surface area and heat transfer are correlated directly, the improvement of heat transfer through pressure drop reduction is realized by adding additional heat transfer enhancements (e.g. turbulators), resulting in increased convective cooling efficiency. Alternatively, film cooling could be increased, leading to a reduced blade surface temperature.

In the discussed paper, a topology optimization method based on an optimality criteria (OC) was applied to automatically create those channels. By using this approach, the amount of recirculation is minimized. The initial geometry represents the available design space provided by the user. By extracting the recirculation zones from this initial geometry, a new design with low pressure loss and large surface area is obtained.

A generic model of a high pressure turbine originating from the open literature was used here. The airfoil belongs to a first stage blade row. The blade height and tip radius are 50.8 mm and 254.2 mm, respectively, which results in a hub tip ratio of 0.8. The considered airfoil includes two cavities with a common inlet near leading edge, a 3-pass serpentine and a trailing edge supply cavity. The tip turn and the root turn of the 3-pass serpentine were considered for a topology optimization. It took overall 13 hours to run the optimization for both turn geometries on four cores.

A conjugate heat transfer analysis was undertaken in order to accurately predict the flow losses, heat transfer and heat conduction for the reference and optimization case at take-off conditions. The results of this analysis showed a significant reduction of the total pressure loss for optimized tip turn (-24%) and root turn (-50%). Moreover, a homogenization of the solid temperature field nearby the optimized tip turn was achieved. By mapping the solid temperatures from the CFD model on a FE model, a final stress analysis was undertaken for reference and optimization case. Only smaller differences could be identified for the Mises stress distribution. From that, it can be concluded, that the usage of the optimized channels does not lead to an adverse structural behavior. Future studies may include a fatigue analysis in order to investigate, whether the usage of the optimized turn ducts also affects blade life for a predefined duty cycle.



ACKNOWLEDGMENTS The described work was created as part of an internal

study, which highlights the benefits of using simulation and optimization technologies in the design process from the very beginning. The author gratefully acknowledge the provision of the FEA results by Deepak Goyal from Dassault Systèmes.

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[12] Othmer, C., De Villiers, E., Weller, H.G., 2007, Implementation of a continuous adjoint for topology optimization of ducted flows, Proceedings of the 18th AIAA [13] Othmer, C., 2008, A Continuous Adjoint Formulation for the Computation of Topological and Surface Sensitivities of Ducted Flows, International Journal For Numerical Methods In Fluids, 2008, 58. [14] Dede, E. M., 2011, Experimental Investigation of the Thermal Performance of a Manifold Hierarchical Microchannel Cold Plate, Proceeding of the ASME 2011 [15] Pietropaoli, M., Ahlfeld, R., Montomoli, F., Ciani, A., D’Ercole, M., 2016, Design for additive manufacturing: Internal channel optimization, GT2016-57318, Proceedings of ASME Turbo Expo 2016 [16] Schlichting, H., 1979, Boundary-Layer Theory, McGraw-Hill, New York [17] Launder, B. E., Spalding, D., 1974, The numerical computation of turbulent flows, Comput. Meth. Appl. Mech. Eng. 3, 269-289. [18] Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J., 1994, A New k-ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation, NASA TM 106721. [19] Martin, T. J., Dulikravich, G. S., 2002, Analysis and Multi-Disciplinary Optimization of Internal Coolant Networks in Turbine Blades, AIAA J Prop Pwr, 18(4), pp. 896-906. [20] Bräunling, Willy J.G., 2009, Flugzeugtriebwerke, Springer-Verlag Berlin Heidelberg [21] Rodi, W., 1991, Experience with Two-Layer Models Combining the k-e Model with a One-Equation Model Near the Wall, 29th Aerospace Sciences Meeting, January 7-10, Reno, NV, AIAA 91-0216. [22] Dye, D., Conlon K.T., Lee, P.D., Rogge, R.B., Reed, R.C., 2004, Welding of Single Crystal Superalloy CMSX-4: Experiments and Modeling, The Minerals, Metals & Materials Society, 2004, p. 485-491 [23] Eifel, M., 2011, Experimentelle und numerische Untersuchung verschiedener Innengeometrien konvektions-gekühlter Turbinenschaufeln, Dissertation, RWTH Aachen



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