V-Spline Design for Enhanced Performance in Turbine Blade Internal Cooling Open Access

Gas turbine cooling and thermal management have been subject to intensive and varied research over the past few decades. Cooling approaches broadly focus on turbine airfoil blades, which operate under high operating thermal and centrifugal loads. To prevent thermally induced structural failure, engineers have introduced material changes and flow augmentation cooling. While the former has allowed for a 4 °C increment in turbine inlet temperature, the latter has resulted in a larger 11 °C increment [1].

Cooling mechanisms vary depending on the location of turbine airfoils where they are applied, but most of them utilize air bled from the compressor as the coolant. Film cooling is used for external blade surfaces, while a mixture of pin-fin, impingement and rib-turbulation is used for internal convective cooling of airfoil geometries. More specifically, the serpentine passages in the middle of the blades are subjected to rib-roughening which uses turbulence to increase heat transfer. Han and Webb [2,3] carried out experimental analyses, widely used for data correlation, of rectangular channels to understand the effects of rib-roughening on the friction factor and heat transfer. A wide variety of configurations have been developed and analyzed over time, with angled and V-shaped designs exhibiting optimal tradeoffs between heat transfer augmentation and cooling power required [4]. Other designs such as X-shaped ribs [5] also show promise in enhancing heat transfer away from the channel wall. In particular, the 60 deg and 45 deg V-shaped rib configurations provide better heat transfer augmentation in the family of V-shaped designs, due to pairs of counter-rotating recirculation cells along the divergent sides of the V-shape [6].

Multiple geometrical factors such as rib height, width, curvature, pitch-to-height (P/e) ratio and blockage ratio have been found to affect the rib-turbulators' cooling effectiveness. Taslim and Spring [7] identified an optimum P/e ratio for the highest attainable Nusselt number (Nu) and showed that Nu decreases with aspect ratio (AR). Their analyses considered manufacturing tolerances and operation-induced rib curvature due to erosion over time. For various P/e and AR values, Han [8] established that wider ribs increase heat transfer augmentation while keeping other flow conditions constant, and that normalized Nu increases with rib height and decreases with increasing rib spacing for a given constant Reynolds number (Re). Internal cooling of the blade also influences external blade temperatures, which was investigated numerically and experimentally by Dees et al. [9].

Thermal barrier coatings (TBCs) are also used to increase operating temperatures of turbine blades. They consist of ceramic coatings on blade surfaces to provide insulation from the high-temperature gases flowing through a turbine. The increased performance by using rare-earth element alloys in designing low-conductivity and high-toughness TBC coatings was described by Zhu and Miller [10]. A comprehensive review of TBC technologies developed and under current investigation is presented by Sahith et al. [11] as well.

The study of cooling mechanisms has benefited from improvements in computational power, allowing for high-performance numerical solvers to be more accessible and advantageous in the design and analysis of thermal loading/performance of gas turbines. Conjugate heat transfer (CHT) approaches offer a strong platform for comprehensive flow and thermal characterization for designing turbine geometries. Kim et al. [12] utilized ANSYS CFX and Mechanical to analyze circular passages for internal cooling of turbine blades. They used thermal load simulations to determine points of stress-induced failure and concluded that heat transfer coefficients (HTC) are greater near the tip than the hub. CHT is also fairly useful for sensitivity studies of variables such as TBC thickness or turbine inlet temperatures, and small changes in these variables have proven to induce significant changes in the average blade temperatures [13].

Traditional k-ω turbulence models have been shown to perform well in the prediction of experimental data in the middle regions of turbine blades, i.e., in rib-turbulated channels [14]. Singh et al. [15] used a commercial computational fluid dynamics (CFD) solver, ANSYS Fluent, to complement experimental analysis of two-pass 45 deg and V-shaped ribbed channels with numerical simulations. Generic effects of secondary flows and turbulent kinetic energy were presented, with detailed Nu distributions analyzed computationally and experimentally. Chyu and Siw [16] studied the effects of broken ribs on heat transfer and found that they have greater heat transfer enhancement compared to full ribs as the discontinuity in rib structure enables preservation of vortices formed by the impact of the fluid with the ribs. This allows for more robust heat exchange between the cooling fluid and channel walls, results of which have been experimentally verified by Kumar and Amano [17].

However, heat transfer alone is insufficient in evaluating the performance of a turbine blade design. For gas turbine blades, the principal failure mode is creep, followed by fatigue [18]. This is attributed to high temperature and centrifugal loading conditions that turbine blades are subjected to over long periods of time. Turbine blade designs and property evaluation studies have focused largely on heat transfer augmentations and less on the interplay between heat transfer and structural performance. Creep strain and fatigue stress weaken the structural integrity of the material and cause crack propagation [19]. Wee et al. [20] formulated equations that showed that creep damage because of variable loading on turbine blades has a more significant impact on failure than the magnitude of the creep strain, while establishing that increasing temperature values results in increasing creep strain values. The study also proved that the quantity of repetitive cycles of fatigue results in greater damage to the blade as compared to the magnitude of shear and principal stresses. Reyhani et al. [21] presented a sensitivity analysis of rib parameters on the temperature distribution and subsequent fatigue life calculation, thus highlighting the relation between rib geometries and structural performance. The chief variables used were TBC thickness, inlet cooling power, and turbine loading. They concluded that the minimum life for a blade will occur at the maximum temperature point, hence establishing the dominance of temperature on the creep life. Moreover, the temperature is directly affected by the effectiveness of the rib turbulation, which itself is a function of geometry characteristics [22].

In the case of fatigue, modern gas turbine blades are affected by a combination of low-cycle fatigue (LCF) and high-cycle fatigue (HCF) [23]. LCF is usually a product of aero-thermal loads and centrifugal loading caused by blade rotation, while HCF is mainly produced by vibrational loads on the blade. Arakere and Swanson [24] used maximum shear stress amplitude as a criterion to investigate HCF in single-crystal constituted gas turbine blades with the [001]-orientation being the primary crystallographic plane. This approach is useful because shear controls dislocation propagation in single-crystal alloys, which further dictates the deformation mechanisms. Kalluri et al. [25] analyzed the performance of PWA1480 in this plane, in particular the elastic response to loading. Although most conventional stress analyses consider static loading on the turbine blades, it is useful to consider the effect of time-dependent (transient) loads in fatigue analysis.

The failure of the turbine blade is dependent on structural properties, but as the quantitative and qualitative effects of flow physics and structural mechanics are interlinked, fluid-structural interaction (FSI) modeling offers a useful tool to study the combined effects of these two physical phenomena. However, FSI for CHT analysis has not been investigated in great depth, with few studies available in open literature. Ubulom [26] used fully coupled and decoupled FSI models to obtain the fatigue response of gas turbine blades through strain energy density functions, concluding that the fully coupled approach allows for higher mean stress and shear stress amplitude across the blade surface than when decoupled, hence resulting in a lower fatigue life. It was also established that the primary failure mode in turbine blades under high pressure and thermal loading is HCF (catalyzed by creep accumulation) since the elastic energy density across the blade was higher than the plastic energy at limiting conditions. This work aims to conduct a comprehensive analysis using FSI, introducing an updated methodology in the analysis of the performance of additional new designs. While conventional analyses examine either the thermal or structural performance of novel rib-turbulated designs, this study explores the combined effects for a holistic analysis of the novel designs introduced.

An iterative approach was adopted to solve for the channel flow physics, and subsequently the creep strain and fatigue life of the channel. This was followed by CHT analysis via one-way FSI using CFD and finite element analysis (FEA) solvers, ANSYS Fluent and ANSYS Mechanical, respectively. The CFD solver was used to obtain flow fields and thermal profiles for the coolant channel flow, and the thermal profile of the solid body was interpolated into the FEA solver. The iterative approach is briefly outlined in Fig. 1 and will be elaborated upon in later sections.

In the computer aided design model, geometries were created as either quarter or half-channel models depending on the design symmetries found along the channel length. Han et al. [27] identified that Coriolis force, arising from rotational effects, impacted the performance of cooling fluids. To restrict the number of independent variables in the problem and mitigate the effects of computational limitations, these rotational effects were not incorporated in the fluid flow analysis but only in the structural analysis, to allow for the usage of a symmetrical plane in the fluid analysis. These symmetry models, illustrated in Figs. 2 and 3, resulted in reduced computational time and memory used while preserving solution accuracy.

The complete channel geometry consisted of a metal channel with rib turbulators, a fluid domain representing the coolant gas and a TBC layer below the metal channel. Table 1 describes major geometrical parameters for the designed channels. The channel wall thickness was set as 0.5 mm to simulate a turbine blade that is as light as possible while still being within manufacturing capability [28].

A total of eight geometries were designed and analyzed using one-way FSI: straight (as baseline), angled, V-shaped, inverted V-shaped, V-shaped with spline, broken, extended broken, shortened broken. Figure 4 displays the top views of these various geometries.

These geometries were also translated such that the first rib's midpoint is at 265 mm from the axis of rotation, simulating the actual location of the channel with respect to the turbine hub, as shown in Fig. 5.

Rib fillets were introduced at all corners to simulate actual manufacturing geometry constraints. The default fillet radius for most edges was kept at 0.15 mm; however, regions with sharper edges such as those in V-models were given greater curvature. These fillet radii are highlighted in Fig. 6.

Flow reversal was turned off at the outlet to avoid nonphysical solutions since the channel represented the first pass of a multipass ribbed turbine blade channel. If the setting was not turned off, there existed a risk of some cooler air entering from the outlet causing artificial cooling at the tip. The k − ω shear stress transport (k − ω shear stress transport) model was used for the flow simulations, in line with past studies by Schüler et al. [30] and Su et al. [5]. Due to the presence of a metering valve at the cooling fluid inlet, the fluid flow would be slightly turbulent, and hence a turbulence intensity of 10% was specified.

A polyhedral mesh, as shown in Fig. 7, was utilized in this analysis, with the boundary layer thickness varied to capture the thermal properties of the fluid near the wall. The prism expansion ratio ranged from 1.2 to 1.4, and 3–7 prism layers with smooth transition were used, with exact values varied to obtain a y+ value equal to or less than 1. The fluid solution was obtained using default FLUENT settings and criterion (energy residual of 1 × 10⁻⁶). The computational results showed similar trends as identified from Han et al. [6], who experimentally quantified the performance of the models. However, some differences were observed as past experimental studies were conducted at room temperature, while our analysis factored in typical engine temperatures and geometry-based manufacturing constraints. A mesh sensitivity study was carried out and as shown in Table 2, the maximum temperature of the channel wall was within 1% of the mesh variation.

Only the upper segment of the channel, from 266.25 mm onwards as shown in Fig. 5, incorporated a TBC layer. This TBC layer, representing the blade airfoil segment, is exposed to thermal loading from the external freestream flow. The spanwise profile of freestream flow saw a lower flow temperature and HTC at the root/tip of the airfoil. At the airfoil midspan, the flow saw the highest temperature and HTC. The thermal profiles were modeled as parabolic equations. For the temperature equation, a constant difference of 150 °C was maintained between the airfoil root/tip and airfoil midspan. For the HTC equation, a constant difference of 100 W/m²K was maintained, with a maximum value of 700 W/m²K at the airfoil midspan. This is illustrated in Fig. 8, using the parabolic equation for the baseline model. The material properties of PWA1480 and TBC were also obtained [31,32], and the respective materials used for their application zones in the CFD analysis.

While related current work includes the effect of rotation in their CFD simulations, this work did not include the rotational effect for CFD analysis. The Coriolis effect and other side forces are difficult to manage for structural analysis as it leads to uneven stress at the channel cross section near the root. The actual turbine blade is curved and tilted so that the base of the blade design does not experience high bending stress where the centrifugal load of the tilted blade would balance the side forces. If the Coriolis force were included in the CFD simulation, the resulting temperature distribution would no longer be uniform on the cross section, resulting in nonuniform stress on the cross section of the simulated channel that may be unrepresentative of the loads experienced by the blade. Hence, with the focus of this work on the integration of CFD analysis with FEA for creep and fatigue, and to facilitate the comparison of rib-turbulator designs for creep and fatigue, the rotational effect was not included for the CFD analysis.

In the structural analysis, only the channel body was retained for analysis. The structural loading resulting from the rotation of the turbine blade was also considered; hence, a rotational velocity of 18,000 rpm about the channel's spanwise axis was imposed on the structure. For creep analysis, the channel was subject to 500 h of operation. The flow velocity in the Fluid Analysis section, along with the maximum temperature on the TBC wall, was varied for the baseline model until a creep strain of 3±0.025% was obtained. The value of 3% was approximated from the creep material curve by Hebser and Miner [33], showing that creep undergoes relatively stable growth until approximately 3% strain at an estimated temperature of 900 °C. Using the straight-ribbed model as a baseline, the specific fluid power required to obtain 3±0.025% creep strain at a baseline TBC wall temperature of 1650 °C was obtained. The other designs were then compared against this model, with variations in the inlet velocity and TBC wall temperature until the fluid power was within ±0.5% of the baseline and the creep was equal to 3±0.025%.

This methodology focused on using creep as the main normalizing factor given that the main failure mode for the turbine blade is creep, hence there being only one flowrate for each design. While this methodology limited the extension of the results obtained to different geometry requiring different flow rates, the main advantage was in accounting for the integration of the localized stress concentration factor with the localized wall temperature on structural creep and fatigue versus average flow performance in other fluid experiments. This methodology also allowed for the understanding of the relative temperature advantage of different rib designs and provided some insight on the magnitude of inlet velocity applied for the optimal creep result.

The structural analysis was performed with a hex-dominant mesh using a quadratic element order. The mesh size was 0.2 mm for most elements, with a face size of 0.1 mm and 2 levels of refinement for faces with high stress/creep. Mesh sizing was determined by refining the mesh to have a creep strain and fatigue stress convergence of 5%. The corresponding flow and thermal conditions at the 3% creep strain limit were used to calculate the fatigue life. The material for the solid body was set to PWA1480 [25], and the maximum shear stress criteria based on Arakere and Swanson's model [34] was used. Their study explored various failure criteria and concluded that the maximum shear stress amplitude was an effective fatigue failure criterion, based on the curve fit between the criterion and cycles to failure for experimental and simulated data. However, since the fatigue test was only conducted at a single temperature point at 650 °C, a correction factor was used to normalize the stress to account for the temperature effect. The correction factor is based on yield strength data of PWA1480 at different temperatures, obtained from Subramaniam et al. [34]. The yield strength ratio based on temperature at the fatigue location was used to adjust the shear stress to account for the temperature effect, before being used to calculate the design's fatigue life. This allowed for more accurate representation of the fatigue capabilities of our design.

The area-weighted pressure difference across the channel and Nu of the channel surfaces were obtained to quantify the models' thermal performance, and the former was used to calculate the specific fluid power for each design. These results are tabulated in Tables 3 and 4, respectively.

From Table 3, the various designs result in different pressure drops across the channel. The highest-pressure drop was observed from the broken rib design and the lowest from the broken-shortened rib. V-rib variants had largely similar pressure differences, varying from each other by less than 0.05%.

The changes in maximum external freestream temperature were also tabulated in Table 5, and together with Table 4, used to quantify thermal performance of the designs and hence their ability to promote heat transfer from the channel wall. From Tables 4 and 5, the broken rib models displayed poor thermal performance, with the broken-extended model even displaying a decrease in thermal performance. The angled rib model displayed a 20.5% improvement in maximum freestream temperature, but this performance was eclipsed by the large improvement that came with the V-spline design, which exhibited a 32.8% increase in maximum freestream temperature as compared to that of the baseline straight model.

This can be explained by analyzing the heat transfer performance via the Nu contours, shown in Fig. 9. Comparing the various designs, the straight rib model has higher heat transfer only in regions of turbulation-induced flow disruption at the tip of the rib. This contrasts with the other three designs, where the Nu is higher at both the rib-turbulated region and the channel base wall. Analyzing the broken rib model, it can be seen how the highest Nu is mostly between the ribs at the side of the channel and at the middle. It can be seen how the broken section in the middle results in higher Nu toward its sides only, suggesting overall reduced heat transfer capability. Overall, the angled design and V rib variants displayed higher average Nu as compared to the broken and straight rib designs. Comparing the Nu contours in Fig. 10, for the angled design, the area of high Nu reduced lengthwise along the rib, with the lowest areas approximately at 50–75% of rib length. On the other hand, the best performing V design variant, the V-spline design, displayed relatively higher Nu throughout the rib length due to its symmetrical design. Hence, this could explain how the V-spline has better heat transfer performance than the angled design, as both sides of the channel will have areas of high Nu.

This variation in heat transfer performance also has implications on the temperature distribution of the channel body as shown in Fig. 11. The angled design had a significantly higher temperature difference on the two side walls due to the nonsymmetrical heat transfer rate along the rib direction. While the V-spline design had displayed better heat transfer performance over the angled rib in this single channel analysis, the comparative performance improvements would likely extend to the analysis of multiple channels. The lower heat transfer performance on either side of the angled rib would cause a decrease in thermal performance in a multiple channel analysis, as the nonsymmetrical nature of the rib design means that a change in flow direction in a multichannel model would result in a lower maximum freestream temperature before the creep criterion is achieved. In contrast, the symmetrical nature of the V-spline design would be less affected by a change in flow direction.

The flow fields of various designs close to the channel base were then analyzed to hypothesize possible reasons for such performance. Figure 12 shows velocity streamlines of the straight rib model. The rib turbulators disrupted the cooling fluid flow and created high turbulence and flow vortices on the channel base wall, as shown in the side view of the straight rib model. However, the height of the vortices was only near the height of the ribs, limiting mixing with the cooler air in the upper segment.

Figure 13 shows velocity streamlines of the angled rib model. The nonorthogonality of the rib with respect to flow direction resulted in vortices forming above the ribs, starting from the section of each rib distal to the inlet. These vortices accumulated as they flowed along the channel length, increasing toward the other side of the channel as illustrated in the highlighted region of Fig. 13. The formation of the taller vortices increased the mixing of the cooling air over the upper segment above the rib-turbulators with hot air from the bottom segment next to the channel base wall. However, as shown from Fig. 13, the vortices only fully developed after the flow traveled for more than half of the channel near the airfoil midspan, thus limiting the heat transfer performance.

These limitations are overcome with the V design, with the V-spline design illustrated in Fig. 14. The vortices formed on both sides of the channel centerline, mixing within and across each half, therefore allowing for vortex formation to be completed at an earlier point; vortex formation completed at around rib #7 in the V spline design versus around rib #14 in the angled rib. This would have likely resulted in the Nu contour observations for the V-spline design along the rib length in Fig. 10 and consequently the high average Nu observed in Table 4. As a result, the V designs displayed higher heat transfer performance nearer to the blade root. This is important since the structural stress near the blade root is higher due to the centrifugal load from rotation thus making the region more susceptible to failure.

As mentioned in the Creep and Fatigue Analysis section, creep strains of the various models were kept constant by varying the flow inlet velocity. The locations of creep are displayed in Fig. 15. For the straight rib design, the creep occurred over the large area between ribs along the channel base wall. As a result, turbine blades with straight rib designs would be more prone to blade elongation since a large segment of the blade wall is subjected to high creep strain. On the other hand, high creep strains for other designs were localized at high stress locations such as the rib-channel junction of the middle rib for the broken design. For both angled and V-spline models, the maximum creep occurred on the side-wall of the rib–channel junction. Comparing the stress and temperature plots of the straight and V-spline models in Fig. 16, it can be seen that for the straight rib design, the maximum wall temperature occurred nearer to the midspan in between rib #14 and #15. In contrast, for the V-spline design, the maximum body temperature occurred at the blade tip with a significantly lower temperature near the blade root where the shear stress is higher.

As a result, the straight rib design experienced a high creep strain on the base wall, near the midspan of the blade at rib #8 as shown in Fig. 17. This creep was primarily caused by the high temperature of the wall with a magnitude near 1000 °C. Since it was near the midspan, the shear stress was moderately low—near 200 MPa. It was observed that both the temperature and shear stress were relatively constant along the rib length for the straight rib result. In contrast, the maximum creep strain for the V spline was located nearer to the blade root at rib #5, where the temperature was lower but the shear stress was higher. Areas of high creep strain were observed to localize near the fillet radius on both the side walls and the middle spline. The temperature near the middle spline was significantly higher, with a large thermal gradient of approximately 100 °C from the middle spline to the side wall over the channel width – a relatively short distance of 4 mm. This resulted in a large shear stress on the side wall due to thermal loading. As a result, the fillet radius on the side wall saw a high creep strain due to the higher shear stress while the fillet radius on the middle spline saw a high creep strain due to the higher temperature.

The fatigue life of all the nodes in the FEA model were calculated, and data from the node with the lowest fatigue life was obtained and used for analysis. As shown in Table 6, the broken rib designs displayed improvements in fatigue life ranging from 6.3% to 17.7%. The angled rib design also displayed a significant improvement in fatigue life, with a 39.3% improvement. While the V and V-inverted designs displayed a 96% and 98% reduction in fatigue life, respectively, which could be due to the high maximum shear stresses from the designs, the V-spline design displayed the highest fatigue performance, with a 74% improvement in fatigue life as compared to the baseline.

The poor fatigue performance of the V and V-inverted models could be attributed to the presence of the sharp corner at the tip of the V. Along with increased thermal loading around the sharp corner, there was also an increased stress concentration region. These combined effects resulted in low fatigue performance. As shown in Figs. 18 and 19, the V shape's tip on the first rib was the location of maximum shear stress concentration. Coupled with thermal loading, the location of minimum fatigue shifted to the V-tip at the third rib. This stress concentration on the V tip was resolved by introducing a spline through its middle. Besides removing the sharp corner, the spline in the V-spline model also acted as a strut, increasing the stiffness of the rib turbulators. While the highest maximum shear stress occurred on the third rib, thermal loading effects instead shifted the location of minimum fatigue to the 12th rib. The result of the addition of the spline was similar; the temperature and shear stress distributions were similar but the location of minimum fatigue shifted. Hence, this indicated that the addition of the spline did not change the flow (which would have resulted in a significant change in temperature). With the resolution of the high stress concentration of the V rib design via the addition of the spline, the high heat transfer rate of the V could then be a viable choice for the practical implementation of the design in rib-turbulated cooling.

A combination of heat transfer and structural analysis was used to evaluate the performance of 8 designs for rib-turbulated internal cooling of a turbine blade. One-way FSI was conducted to capture the thermal performance of the designs. The effects of temperature were then considered in analyzing the structural performance of the designs. The following conclusions were drawn:

1. The methodology introduced in this paper, where the effect of the flow behavior on the heat transfer performance and the effect of the geometry stress concentration on the structural performance are evaluated together, is a viable option in evaluating the performance of various rib-turbulated cooling designs.

2. The thermal performance of the V models generally shows a marked improvement over the thermal performance of the straight, angled, or broken rib models, with the V-spline model showing the highest improvement from a baseline of 32.8% in maximum freestream temperature at 3% creep strain.

3. The fatigue performance of the V and V-inverted models are poor, but the V-spline model overcomes these limitations of the models and possesses the highest improvement in fatigue life from baseline, at a 74.2% improvement.

The analysis showed that the maximum temperature of the V-spline could be increased by another 203 °C over the angled design versus only 36 °C for the V design just by the simple addition of a spline. These results suggest that the V-spline model could be a viable design for future rib-turbulated internal cooling, showing large improvements in thermal performance while also improving fatigue performance.

We wish to acknowledge the funding support for this project from Nanyang Technological University under the URECA Undergraduate Research Program.

The authors attest that all data for this study are included in the paper.

AR =

aspect ratio, W/H

CCF =

combined-cycle fatigue

CFD =

computational fluid dynamics

CHT =

conjugate heat transfer

FEA =

finite element analysis

FSI =

fluid-structural interaction

HCF =

high-cycle fatigue

LCF =

low-cycle fatigue

TBC =

thermal barrier coating

D_h =

hydraulic diameter (m)

e =

height of rib (mm)

h =

heat transfer coefficient, q/ΔT (W/m²K)

H =

channel height (mm)

L =

channel length (mm)

Nu =

Nusselt number, hDh/k

P =

pitch of rib (mm)

P/e =

pitch-to-height ratio

q =

local heat flux (W/m²)

Re =

Reynolds number, uDh/ν

T_in =

channel inlet temperature (°C)

T_w =

maximum wall temperature (°C)

u =

flow speed (m/s)

ν =

kinematic viscosity (m²/s)

W =

channel width (mm)

ΔT =

difference between local temperature and tin (°C)