Abstract

In the present paper, two lattice geometries suitable for near surface and double wall cooling were developed and tested. The first type of unit cell consisted of six ligaments of 0.5 mm diameter joined at a common vertex near the middle. The second type of unit cell was derived from the first type by adding four mutually perpendicular ligaments in the middle plane. Two lattice configurations, referred to as L1 and L2, respectively, were obtained by repeating the corresponding unit cell in streamwise and spanwise directions in an inline fashion. Test coupons consisting of these lattice geometries embedded inside rectangular cooling channel with dimensions of 2.54 mm height, 38.07 mm width, and 38.1 mm in length were fabricated using Inconel 718 powder and selective laser sintering (SLS) process. The heat transfer and pressure drop performance was then evaluated using steady-state tests with constant wall temperature boundary condition and for channel Reynolds number ranging from 2800 to 15,000. The lattices depicted a higher heat transfer compared with a smooth channel and both the heat transfer and pressure drop increased with a decrease in the porosity from L1 to L2. Steady-state conjugate numerical results revealed formation of prominent vortical structures in the inter-unit cell spaces, which diverted the flow toward the top end wall and created an asymmetric heat transfer between the two end walls. In conclusion, these lattice structures provided an augmented heat transfer while favorably redistributing the coolant within channel.

Introduction

In pursuit for advancing the gas turbine efficiency, the turbine inlet temperature is slated to rise beyond 1700 °C. The heat transfer enhancement in an internal flow channel may be brought about by promoting mixing and turbulence within the bulk flow of the coolant. Traditionally, pin fin banks have provided a way to achieve these goals. The cylindrical body of the pins protrudes within the bulk flow and promotes mixing in coolant. On the other hand, the near end wall flow interacts with the foot of the pins and forms what is known as a horseshoe vortex [1,2]. These horseshoe vortices near the end wall help in eroding away the boundary layer and promote the convective heat transfer. The heat transfer is further helped by the extended surface area of the pin bodies. In addition to these heat transfer enhancement benefits, pin fins also play a role as the structural load bearing member and can be implemented in thinner sections of the blades, such as the trailing edge, to maintain desired levels of structural strength [3]. Chyu et al. [4] have shown that the heat transfer in pin fins typically increase up to the third or fourth row and then achieve a steady value. Siw et al. [5,6] analyzed the impact of various pin fin geometries, including detached pin fins, and concluded that these geometries are capable of providing the desired cooling in narrow passages.

Another category of geometries which resemble the pin fins in their multifaceted behavior of heat transfer and strength augmentation are lattice geometries. These extended surface geometries are typically obtained by repeating a unit cell in an array-like arrangement. The lattice structures have been widely used to enhance the structural strength of a component while keeping the mass low. In addition to structural applications, these lattice structures could also enhance the heat transfer by way of promoting mixing and providing extended surfaces to further help convection, for example, as shown by Wadley and Queheillalt [7]. One of the common types of lattice unit cell design comprises a tetrahedral geometry. Such a unit cell has been subjected to numerous structural design analysis. Gao and Sun [8] numerically analyzed fluid flow and heat transfer in channels with regular tetrahedral unit cells made from carbon-fiber reinforced resin matrix. Internal heat generation was specified and forced water was used as a coolant. They found out that multiform vortical structures were formed, which enhanced the heat transfer. Kim et al. [9] performed both experimental and numerical heat transfer study on ultralight weight lattice material. They concluded that the local dominant features were the flow separation on the struts and the vortex structures. The horseshoe vortex caused a 180% higher increase heat transfer compared with the other region in the flow. In addition, the strut was found to produce 40% of the total heat transfer. Shen et al. [10] performed numerical heat transfer and fluid flow analysis on single-layer Kagome and wire woven bulk Kagome type lattice. They concluded that the topology greatly affected the heat transfer with single-layer Kagome producing about 26–31% higher heat transfer among the two.

In the above studies, the unit cells were at a much larger length scale than that suitable for blade cooling applications. These unit cells were also arranged in a staggered configuration. In the presented work, an inline configuration of Kagome type lattice unit cells at a more realistic length scale, from the standpoint of gas turbine blade cooling, has been studied. Two configurations for the unit cells were generated and both experimental and numerical analysis was carried out. The test coupons were manufactured using SLS technique.

Typically, the geometry of these unit cells is relatively complex and difficult to fabricate using conventional manufacturing processes. The advancements in additive manufacturing have provided a new way to realize these geometries, especially at the scale suitable for application within a gas turbine blade.

Description of Test Geometries

The lattices used for this study were generated from two types of unit cells. The unit cells are shown in Fig. 1. The first type of unit cell was formed by three intersecting ligaments and the diameter of each of the ligament was 0.5 mm. These ligaments were generated by first defining three circles around an origin point such that they had a shared center. However, the planes containing the three circles were mutually perpendicular. These circles were then extruded in both directions along the normal to their plane. In this way, three ligaments were generated on the top and three on the bottom half of the unit. The ends of the ligaments on each side formed an isosceles triangle, with the top and bottom triangles being 60 deg rotated with respect to each other. Finally, they were trimmed down to a height of h = 2.54 mm. The second type of unit cell was derived from the first type but with four mutually perpendicular ligaments added in the middle plane. As shown in Fig. 2, when arranged in an array, the type 1 unit cells did not have contact with each other, while type 2 unit cells were connected at the spanwise and streamwise ligaments. These unit cells were arranged in an inline array containing 8 rows and 9 columns as shown in Fig. 3. Such a lattice obtained from type 1 unit cells was called L1, while that obtained from type 2 unit cells was called L2. The two lattices varied in terms of the porosity, defined as
ρ=1volsolidvoltotal
(1)
as well as the total wetted surface area, but they had the same footprint area on the end walls, as summarized in Table 1.
Fig. 1
Unit cell geometries
Fig. 1
Unit cell geometries
Close modal
Fig. 2
Connectivity: (a) isolated units for L1 and (b) interconnected units for L2
Fig. 2
Connectivity: (a) isolated units for L1 and (b) interconnected units for L2
Close modal
Fig. 3
Arrangement of unit cells in the lattice structure (top view)
Fig. 3
Arrangement of unit cells in the lattice structure (top view)
Close modal
Table 1

Geometry details

ParameterL1L2
Channel height, h (m)0.002540.00254
Channel width, w (m)0.038070.03807
Hydraulic diameter, Dh (m)0.004760.00476
Ligament diameter, d (mm)0.50.5
Channel wetted area, Ach (m2)0.0042870.004951
Lattice footprint area (m2)0.0001470.000147
Lattice surface area (m2)0.0013400.001849
Porosity, ρ0.950.93
ParameterL1L2
Channel height, h (m)0.002540.00254
Channel width, w (m)0.038070.03807
Hydraulic diameter, Dh (m)0.004760.00476
Ligament diameter, d (mm)0.50.5
Channel wetted area, Ach (m2)0.0042870.004951
Lattice footprint area (m2)0.0001470.000147
Lattice surface area (m2)0.0013400.001849
Porosity, ρ0.950.93

The test coupons consisted of these lattice structures embedded inside a channel of 2.54 mm height (h), 38.07 mm width (w), and 38.1 mm in length (l), as shown in Fig. 4(a). The coupons were fabricated using Inconel 718 powder through SLS process which is a layer by layer laser-based powder bed fusion process. During the fabrication, standard process parameters, as specified by the system vendor for Inconel 718, were used. While preparing to fabricate such complex geometries, it is imperative to consider the build direction beforehand. An improper orientation can lead to formation of large overhangs and increased roughness. The coupons were built in a vertical orientation, such that the channel length was perpendicular to the print bed. This fabrication orientation was selected because it greatly decreased the number of overhangs and increased the chances of obtaining similar roughness on the channel walls, in contrast to an inclined or flat orientation in which the bottom facing surfaces form an overhang and tend to have much larger roughness. The vertical print orientation also ensured that most of the ligaments in the lattice unit cells were at an angle to the build direction. As such, these ligaments were self-supported and removed the need for any support structures which were not possible to include inside the channel. A sample of printed coupon with L1 lattice is shown in Fig. 4(b).

Fig. 4
(a) Overview of coupon dimensions, (b) printed sample lattice, and (c) sample of the measured surface profile
Fig. 4
(a) Overview of coupon dimensions, (b) printed sample lattice, and (c) sample of the measured surface profile
Close modal
A sample coupon was printed within the same batch with similar parameters as the main test coupons. The roughness profile for this sample coupon was obtained using the KLA-Tencor Alpha Step IQ Profilometer. A section of the 2D line scan obtained from the profilometer is shown in Fig. 4(c). Repeated measurements were taken at multiple locations and from these measurements, the Ra parameter was calculated for each scanned profile as
Ra=1ni=1i=n|ziμ|
(2)

The average Ra value obtained for the walls was 28.45 µm.

The coupon walls also incorporated holes to insert thin gauge K-type thermocouples having 0.76 mm (0.003 in.) in diameter. Additional thermocouples were also embedded within the copper blocks close to the coupon walls. These thermocouples provided a real-time measurement of the wall temperature at multiple locations near the inlet and the outlet and served as a means to validate the constant wall temperature boundary condition.

Experimental Setup

The fabricated test coupons were subjected to steady-state heat transfer tests with constant wall temperature boundary condition. The description of the test setup has been provided in Ref. [11] and shown in Fig. 5. The coupon to be tested was sandwiched between two copper blocks which were semicircular in geometry. A thin layer of thermally conducting paste was applied between the coupon and the copper block interfaces to maintain proper thermal contact. A thin heater strip was attached on the outside of the copper block and served as the heat source. A thick layer of insulating foam was then wrapped on top of the heater to provide thermal insulation and minimize heat loss through the other side. This setup was then placed between two polyvinyl chloride (PVC) flanges and fastened with the help of four bolts which constrained this subassembly from top and bottom direction with respect to the coupon longitudinal axis. Next, this subassembly was placed between two PVC blocks which housed the inlet and the outlet flow transition units. A layer of thermally insulating gasket was attached to both the inlet and outlet side of the blocks to ensure no leakage of coolant as well as minimizing heat losses. These PVC blocks were then joined using four threaded bolts to constraint the assembly along the length of the coupon.

Fig. 5
Cross section of the steady-state test rig [11]
Fig. 5
Cross section of the steady-state test rig [11]
Close modal

The test procedure was similar to that described in Ref. [11] for coupons containing internal cooling channels with inline wall jets, and the schematic of the test bench is shown in Fig. 6. The air from a compressed air supply line served as the coolant and was introduced into the test section from the inlet side. The flowrate of the coolant was set with the help of a rotameter with a rotating knob control. Once the coolant achieved a steady flowrate, the heater was turned on to heat the coupon walls up to a desired level. The test setup was then allowed to reach a steady state, wherein all the temperatures in the test domain changed slower than 0.1 °C for every 2 min. The readings from the thermocouples, along with the pressure readings at the inlet, outlet, and the flow meter outlet, were recorded.

Fig. 6
Test setup schematic [11]
Fig. 6
Test setup schematic [11]
Close modal

Numerical Analysis Setup

Along with the experimental analysis, steady-state numerical analysis was carried out in order to get the flow field details for both the L1 and L2 lattice structures. Both fluid and solid domains were modeled together to perform a conjugate heat transfer analysis. In order to reduce the computational load, only a part of the actual coupon was considered and consisted of all of the eight rows but only three columns of the unit cells in L1 and L2. ansys icem package was used to generate an unstructured mesh for both the domains. The first cell height near the walls was an important consideration due to the use of the SST- turbulence model, which prefers y + < 1. Thus, inflation layers were introduced at all the fluid solid domain interfaces by specifying the first cell height. These layers also helped in capturing the boundary layer flow near the walls. Figure 7 shows the boundary conditions and meshed domains.

Fig. 7
(a) Numerical analysis domain, (b) inflation layer at the solid fluid interface, and (c) meshed lattice unit cells in L1
Fig. 7
(a) Numerical analysis domain, (b) inflation layer at the solid fluid interface, and (c) meshed lattice unit cells in L1
Close modal

The prepared mesh was imported into ansys cfx module to perform a steady-state conjugate numerical simulation. The solid domain was considered to have Inconel 718 properties at full density. The boundary conditions were deduced directly from the experimental data for channel Re of ∼7600. The inlet was specified as air at constant velocity and temperature of 296 K, and a static pressure was specified at the outlet. A constant wall temperature of 309 K was prescribed on the top and bottom coupon walls, while the front and back walls of the coupon were treated as adiabatic. Since only three columns of the lattice unit cells were modeled, the side surfaces in the fluid and solid domains were treated as translational periodic boundaries. This approximated the coupon to be of infinite width and neglected any side wall effects on the fluid flow on the modeled domain.

An interface was defined between the fluid and solid domains such that heat energy could be exchanged between the two. High-order numerical scheme was selected for all the equations and convergence was assumed when the root-mean-square value for the residuals became less than 10−6 and the domain imbalances were smaller than 0.01. Additionally, monitoring points were defined to track fluctuations in values of important variables within the domain.

To compare the numerical results with the experimental results, Nu value was obtained using log mean temperature difference method (LMTD) as in case of experiments. A grid independence study was completed with four different mesh densities using the L1 lattice structure. These meshes consisted of 3.78 million, 4.45 million, 6.48 million, and 10.13 million elements, respectively. The result from the grid independence study is shown in Table 2 and Fig. 8. The difference between the mesh with 10 million elements and that with 6.5 million elements was about 1%. Thus, 10 million mesh densities were selected for conducting further simulations. Figure 9 shows the Nu number obtained from numerical simulations together with the experimental results for three-channel Re.

Fig. 8
Effect of mesh density on calculated Nu
Fig. 8
Effect of mesh density on calculated Nu
Close modal
Fig. 9
Comparison between numerically obtained Nu with experimental data for three channel Re
Fig. 9
Comparison between numerically obtained Nu with experimental data for three channel Re
Close modal
Table 2

Variation in Nu with number of mesh elements

Mesh density (in millions)Nu
10.1384.21
6.4883.29
4.4580.85
3.7879.93
Mesh density (in millions)Nu
10.1384.21
6.4883.29
4.4580.85
3.7879.93

As can be seen, the numerical results showed reasonable agreement with the trend in experimentally obtained Nu; however, the Nu values were underpredicted. The numerical simulations did not take into account the roughness induced in the coupons due to the SLS fabrication process. As shown in Refs. [11,12], a smooth channel fabricated using SLS process shows both higher heat transfer as well as higher pressure drop. The heat transfer in an additively manufactured smooth channel was observed to be up to 1.7 times of that predicted by a smooth channel correlation [11]. In the current study, the channel hydraulic diameter was larger than that used in Ref. [11]. In addition, the coupons in Ref. [11] were fabricated at an angle of 45 deg to the build plate, in contrast to the vertical fabrication orientation used for the current study. As such, the roughness induced on the walls would be different in the two cases. However, the effect of roughness on the heat transfer was still expected to be present, causing the observed deviation between the numerical and experimental Nu values.

Data Reduction

The heat transfer and pressure drop performance of the two lattice geometries were compared in terms of Nu and f values. Due to the constant wall temperature boundary condition, the LMTD method was used to calculate heat transfer coefficient and obtain the Nu. The LMTD is defined in Eq. (3)
LMTD=(TwallTin)(TwallTout)ln(TwallTin)(TwallTout)
(3)
The heat flux into the domain was obtained from the voltage and current readings recorded during the steady-state experiments. The heat flux was calculated as
q=V.IAch
(4)

This heat flux represented the total heat flux from the heater into the test domain. However, there was a finite amount of heat loss through conduction to the outside of the test setup surfaces. These losses were estimated by using a 1D analysis on the thermocouple data obtained on the interfaces. The heat losses for the tests are shown in Fig. 10. It was observed that the heat losses were within 3% for the entire tested Re range. This process was similar to that followed in Ref. [11].

Fig. 10
Conduction losses at various channel Re
Fig. 10
Conduction losses at various channel Re
Close modal
The net heat flux was obtained by subtracting the conduction heat losses from the heater. The heat transfer coefficient was then computed based on this net heat flux and the LMTD obtained from Eq. (3), as
htc=qqlossLMTD
(5)
The overall Nu number was then calculated using the htc value, the channel hydraulic diameter, and the fluid thermal conductivity as
Nu=htcDchk
(6)
The augmentation in Nu at different Re was compared with that of a smooth channel. The Re was calculated based on the channel hydraulic diameter, as
Re=UDchν
(7)
This definition of Re made it possible to compare the heat transfer results with a standard smooth channel correlation for Nusselt number. This smooth channel Nusselt number, Nu0, was calculated using the well-known Gnielinski correlation
Nu0=f08(Re1000)Pr1+12.7(f08)1/2(Pr2/31)
(8)
The f0 in Eq. (8) was obtained using the Petukhov correlation, as given by Eq. (9)
f0=(0.790lnRe1.64)2,3000Re5×106
(9)
Further, the friction factor was obtained from the measured pressure drop data, using Eq. (10)
f=(ΔpΔx)DchρU22
(10)

Using Eqs. (9) and (10), the f/f0 ratio was evaluated to obtain augmentation in pressure drop.

Uncertainty Analysis

The experimental uncertainties involved in this work were evaluated using the methods suggested by Kline and McClintock [13]. Since the test setup and methods used were adopted from Ref. [11], the calculated uncertainties were similar. The uncertainty in the evaluated LMTD was calculated to range from 3% to 11% and was caused by the uncertainty in temperature measurement instrument. As a result, the uncertainty in the Nu estimation lied between 5% and 10%. In case of Re estimation, the uncertainty was estimated to be from 5% to 10% and was due to the uncertainties in mass flowrate measurement. Similarly, the estimated uncertainty in the pressure measurement was calculated to be 2–8%.

Results and Discussion

Flow Field.

The interaction between the coolant flow and the lattice structures gave rise to a complex flow field. The orientation of the ligaments, with respect to the oncoming flow, varied between the top and the bottom half of both unit cell types. For the top half of a unit cell, two ligaments were present in the upstream, while only one ligament was present in the downstream. On the other hand, for the bottom half it was just the opposite. As a result, the flow fields in the two halves of the channel varied significantly. Figure 11 shows the velocity contour and velocity vectors at four different planes along the streamwise direction for a unit cell in L1 and L2. Near the top end wall of both L1 and L2, the oncoming flow was diverted by the inclined ligaments and gave rise to counterrotating vortex pair in the wake. Since the lattice contained an inline arrangement of the unit cells, the counterrotating vortex pairs from upstream unit cells interacted with the pairs from the immediately downstream unit cell and increased in size toward the outlet. In addition, these flow structures induced another weak counterrotating vortex pair near the bottom end wall that was not very dominant in L1.

Fig. 11
Velocity contour plot showing (a) the counterrotating vortex pair in wake of ligaments and (b) comparison of wake downstream from third and sixth rows in L1 and L2, looking upstream from the outlet
Fig. 11
Velocity contour plot showing (a) the counterrotating vortex pair in wake of ligaments and (b) comparison of wake downstream from third and sixth rows in L1 and L2, looking upstream from the outlet
Close modal

In case of L2 lattice, the flow became more complex due to the presence of additional ligaments. As shown in Fig. 11, the counterrotating vortex pair near the top wall was still present. However, the velocity vectors indicated that the strength of these vortex was greater compared with that in the L1 lattice structure. This increase was caused by the interaction of the flow with the spanwise ligaments, which were absent in L1. In addition, the counterrotating vortex pair located near the bottom end wall also became more prominent due to the presence of the streamwise ligament.

In both cases, the vortex in the top half of the channel was stronger and caused a net upwash of the coolant toward the top end wall. The counterrotating vortices near the bottom end wall also created a local downwash of the coolant; however, this effect was more evident in L2.

Figure 12 shows the velocity contour and vector plot on planes moving from 0.1 h above bottom end wall to 0.1 h below the top end wall. Within the lower half, the coolant near the bottom end wall first impinged on the upstream leg and formed a horseshoe type vortex. The flow then separated from the ligament in the downstream direction forming a wake region. The separated flow moved toward the center of the unit cell due to the low pressure wake and flowed through the opening formed between the two downstream ligaments, where it was accelerated due to the decreased flow area available. This acceleration of the flow led to larger wake region in the downstream of these ligaments.

Fig. 12
Flow field at three locations within the channel (flow left to right)
Fig. 12
Flow field at three locations within the channel (flow left to right)
Close modal

It was observed in Fig. 12 that the bulk velocity increased significantly on moving from the middle channel plane toward the top end wall. The strong vortex structures present in the inter-unit cell passages created an upwash movement of coolant from the bottom end wall toward the top end wall. These vortical flow structures also decreased the net available flow area for the coolant. A combination of these two effects led to the observed higher coolant velocity in the top half of the channel. In addition, for both L1 and L2, strong impingement was present on the leading edges of the upstream ligaments in the top half of the channel.

Lattice Wall Temperature.

Figure 13 shows the temperature distribution on the surface of the solid lattice unit cells for both L1and L2 lattices from top view. The unit cells in L1 reached a higher temperature compared with those in the L2 lattice. In both cases, the unit cell temperature increased in the downstream direction. The coldest region for the L1 lattice was located near the middle node, while the additional spanwise and streamwise ligaments in L2 had the lowest temperature. The area averaged temperature for L1 lattice surface was ∼6% higher compared with L2.

Fig. 13
Surface temperature of lattice unit cells for channel Re = 7600: (a) L1 lattice and (b) L2 lattice (flow from left to right)
Fig. 13
Surface temperature of lattice unit cells for channel Re = 7600: (a) L1 lattice and (b) L2 lattice (flow from left to right)
Close modal

Experimental Heat Transfer.

Figure 14 shows the overall heat transfer in terms of the Nu number versus the channel Re. It was observed that the Nu increased for both L1 and L2 type lattices with an increase in Re. This increase in heat transfer can be attributed to enhanced mixing and stronger near wall vortices at higher flowrates, which cause more coolant to flow toward the end walls.

Fig. 14
Nusselt number variation with channel Re for L1 and L2 lattices
Fig. 14
Nusselt number variation with channel Re for L1 and L2 lattices
Close modal

The L1 lattice depicted a lower Nu compared with the L2 type lattice over the full range of Re tested. At the lowest Re, the L1 lattice achieved Nu of 50.9, while the L2 lattice achieved a Nu of 61, which is ∼20% higher. The L2 lattice was able to create stronger vortical flow even at the lower flowrates. In addition, the presence of greater number of ligaments in L2 created additional mixing in the channel. However, with the increase in the Re, the difference between the heat transfer in the two configurations decreased, changing from ∼20% to ∼13%.

Figure 15 compares the augmentation in Nu provided by the two lattice configurations, as compared with that of a smooth channel obtained from the Gnielinski correlation. Both the configurations depicted a higher heat transfer compared with the smooth channel. The augmentation in Nu was observed to range from ∼5 to 6 times at the lowest Re, to ∼4.2–4.8 times at the higher Re. As before, the highest enhancement was obtained for the L2 type lattice, followed by the L1 type lattice. The L1 type lattice depicted ∼22% lower augmentation for the lowest Re compared with the L2 lattice. For the higher Re values, the L2 depicted ∼12% higher augmentation in Nu in comparison with L1 type lattice. However, the augmentation with respect to the smooth channel seemed to level off at ∼4.5 when the Re approached values >15,000.

Fig. 15
Enhancement in Nu for L1 and L2 lattices compared with Gnielinski correlation
Fig. 15
Enhancement in Nu for L1 and L2 lattices compared with Gnielinski correlation
Close modal

Numerical Heat Transfer.

The local heat transfer distribution on the top and bottom plates, for both L1 and L2, are shown in Figs. 16 and 17. The highest heat transfer was observed near the upstream of vertices where the ligament was connected with the end wall, owing to the horseshoe vortex formation. This phenomenon was similar to those observed in pin fins [1]. Both, the top and the bottom plates, depicted regions of high and low heat transfer. In general, the heat transfer increased in the downstream direction, which was due to the greater mixing caused by stronger vortical flow (Fig. 11(b)). For the top plate of both L1 and L2, the regions of high heat transfer were located in the wake of the upstream ligaments toward the outer side of the unit cells. These regions corresponded with the location of the counterrotating vortex pairs and the shape of these regions differed between the two cases. In case of L1, these regions were observed to be narrower compared with L2, wherein the regions were more like “heart” shaped. This was caused by the existence of additional spanwise and streamwise ligament in L2 which diverted more coolant toward the end walls. In addition, the region confined between the vertices of the unit cells also depicted higher heat transfer for L2 compared with L1.

Fig. 16
Local heat transfer distribution on top plates for (a) L1 lattice and (b) L2 lattice at channel Re = 7600
Fig. 16
Local heat transfer distribution on top plates for (a) L1 lattice and (b) L2 lattice at channel Re = 7600
Close modal
Fig. 17
Comparison of local heat transfer coefficient distribution on bottom end wall for (a) L1 lattice and (b) L2 lattice at channel Re = 7600
Fig. 17
Comparison of local heat transfer coefficient distribution on bottom end wall for (a) L1 lattice and (b) L2 lattice at channel Re = 7600
Close modal

As shown in Fig. 17, the high heat transfer regions on the bottom end walls were located in the wake of the downstream ligaments for each unit cell. Once again, the heat transfer increased in the downstream direction toward the exit, caused by the greater amount of mixing and turbulence. L2 showed a higher heat transfer overall compared with L1 and this enhancement was about 47% based on the area averaged heat transfer coefficient. The stronger vortex pairs fomed near the bottom end wall in L2 created a strong fountain like effect which impinged the coolant on the end wall, thereby causing this increase in the local heat transfer. Thus, the heat transfer pattern between the top and the end wall varied for both L1 and L2, with much greater asymmetry in case of L1.

Figure 18 shows the local heat transfer coefficient distribution on the surface of the lattice unit cells for L1 and L2. The upstream faces of the ligaments were subjected to impingement from the coolant flow. As a result, higher heat transfer coefficients were located on these faces. On the other hand, flow separation led to lower heat transfer coefficients on the downstream surfaces of the ligaments. The top half of the unit cells in both lattices had higher heat transfer coefficient values, mainly due to the presence of stronger vortices.

Fig. 18
Distribution of heat transfer coefficient on the surface of unit cells at channel Re = 7600: (a) L1 lattice and (b) L2 lattice
Fig. 18
Distribution of heat transfer coefficient on the surface of unit cells at channel Re = 7600: (a) L1 lattice and (b) L2 lattice
Close modal

Pressure Drop.

Figure 19 shows the friction factor comparison between the two lattice structures tested. The L1 lattice depicted a lower friction factor compared with the L2 type lattice. The friction factor for the L1 lattice was seen to first increase with Re, from ∼1.4 at Re of ∼2900, to about 1.7 at Re of ∼6000. On further increase in the Re, the value for f remained more or less stagnant at about 1.7, decreasing slightly near the largest Re value of ∼15,000. In comparison, the friction factor for L2 type lattice remained at a value of ∼3.5 from Re = 2800–7800. With an increase in the Re, the friction factor value decreased gradually to a value of ∼3.1.

Fig. 19
Friction factor versus channel Re for the two lattices
Fig. 19
Friction factor versus channel Re for the two lattices
Close modal

Figure 20 displays the increase in the friction factor of the tested lattice structures compared with that of a smooth channel obtained from Eq. (9). For both the designs, the enhancement in friction factor increased with an increase in Re. The friction factor enhancement for L1 type lattice increased from ∼30 to ∼50 when the Re increased from ∼2900 to ∼7600. With a further increase in the Re value, the f/f0 value approached a value of ∼57.7. On the other hand, the L2 lattice showed an increase in the friction factor enhancement from ∼77 at Re = ∼ 2800, to ∼104 at Re = ∼ 7800. When Re increased further, the f/f0 value approached ∼110.

Fig. 20
Enhancement in friction factor for the lattices compared with a smooth channel
Fig. 20
Enhancement in friction factor for the lattices compared with a smooth channel
Close modal

When the two lattice designs were compared with each other, the f/f0 value for L1 lattice structure ranged from 70% to 150% lower than that for the L2 lattice structure. The increase in the pressure drop in case of the lattice geometries was mainly due to three factors: first and foremost, the presence of lattice structure in the channel led to creation of blockage for the coolant flow. Second, both L1 and L2 had larger total wetted surface area compared with the smooth channel. Third, the lattice structure interacted with the coolant flow and gave rise to strong secondary flows. These factors combined together to produce an augmented pressure drop compared with a smooth channel for similar Re.

Among the two lattices, the L2 type structure offered a larger blockage due to the presence of additional ligaments. In addition, the secondary flows in L2 lattice were observed to be stronger than those in L1. Thus, in general, L1 offered lower pressure drop compared with L2 type lattices.

The thermal performance between different traditional geometries and additively manufactured lattice geometries has been compared in Fig. 21 adapted from Ref. [14]. As expected, L1 performed much better than L2 due to lower pressure drop. The overall performance of L1 was comparable with that of rib turbulators and pin fins. However, the presented lattice geometries provide a lot of scope for optimization in terms of geometrical parameters as well as unit cell arrangement. As such, the performance of such geometries could be further enhanced.

Fig. 21
Comparison of performance between traditional geometries [14] and L1, L2 lattice geometries
Fig. 21
Comparison of performance between traditional geometries [14] and L1, L2 lattice geometries
Close modal

Conclusion

In the presented work, two unit cell designs were used to generate two lattice structures. These geometries were fabricated using SLS fabrication process and subjected to experimental and numerical analysis. Steady-state heat transfer experiments with constant wall temperature boundary conditions were conducted by varying the coolant flowrates. The experimental results showed that the SLS fabricated coupons with lattice structures were able to achieve ∼4–6 times higher Nu compared with a smooth channel. This heat transfer enhancement was followed with a higher pressure drop and the friction factor ranged from 30 to 104 times that of a smooth channel.

Among the two geometries, L2 type lattice consisting of six ligaments attached to the end walls with additional four ligaments in spanwise and streamwise direction, provided from 13% to 20% higher Nu compared with L1. On the other hand, the augmentation from L2 over smooth channel ranged from 12% to 22% higher than L1. This higher heat transfer in L2 was attributed to the creation of stronger secondary flows in the channel as compared with the L1 lattice. The four additional ligaments also helped in further promoting mixing in the channel and contributed to the overall heat transfer enhancement over L1. On the other hand, the L1 depicted 70–150% lower friction factor compared with the L2 lattices for the tested channel Re range. The performance of these geometries was observed to be similar to that of rib turbulators and pin fins. However, the performance of the lattice geometries could be further enhanced by optimizing geometric parameter and unit cell arrangement.

Numerical results revealed that a very complex flow field existed within the channel. The interaction between the inclined lattice ligaments near the top end wall led to creation of strong vortex structure in the wake region. These vortex structures led to an asymmetric heat transfer coefficient distribution between the top and bottom end walls for L1. On the other hand, relatively uniform and higher heat transfer was observed for both the end walls in L2. This was due to further strengthening of the vortical flow structures which enhanced mixing and turbulence in L2. In addition to heat transfer augmentation, such flow features indicate that lattice geometries can be used to manipulate the flow field and obtain a more favorable redistribution of the coolant.

Acknowledgment

This material is based upon work supported by the Department of Energy (DOE) under Award Number DE-FE-0025793.

Nomenclature

     
  • f=

    friction factor

  •  
  • h=

    channel height

  •  
  • k=

    thermal conductivity of air (W/(m·K))

  •  
  • l=

    length

  •  
  • m=

    mass flowrate (kg/s)

  •  
  • n=

    number of samples in roughness measurement

  •  
  • q=

    heat rate (W)

  •  
  • w=

    width

  •  
  • x=

    streamwise distance

  •  
  • z=

    height

  •  
  • A=

    wetted area (m2)

  •  
  • C=

    heat capacity (J/(kg·K))

  •  
  • D=

    hydraulic diameter (m)

  •  
  • I=

    current

  •  
  • Q=

    heat rate (W)

  •  
  • T=

    temperature

  •  
  • U=

    bulk mean velocity of channel (m/s)

  •  
  • V=

    voltage

  •  
  • y+=

    dimensionless first cell height

  •  
  • htc=

    heat transfer coefficient (W/(m2·K))

  •  
  • vol=

    volume

  •  
  • Nu=

    Nusselt number

  •  
  • Pr=

    Prandtl number

  •  
  • Ra=

    arithmetic mean

  •  
  • Re=

    Reynolds number

Greek Symbols

     
  • μ=

    mean

  •  
  • ρ=

    porosity

  •  
  • ν=

    kinematic viscosity (m2/s)

Superscripts

     
  • °=

    degree

  •  
  • ″=

    flux

Subscripts

     
  • ch=

    channel

  •  
  • i=

    ith sample

  •  
  • in=

    inlet

  •  
  • loss=

    heat lost

  •  
  • 0=

    smooth channel

  •  
  • out=

    outlet

  •  
  • solid=

    solid part

  •  
  • total=

    sum total

  •  
  • wall=

    wall

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