CFD and experimental investigation of AM surfaces with different build orientations

From the surface roughness characterization, we also learned that the ideal shape for spatter deposits could be a sphere, an elliptical, an oblate, a prelate, or a rugby ball. Therefore, in the early stage we also modeled the small numbers of spherical particles on top of weld-tracked surfaces and carried out the CFD simulations. However, when we tried to increase the number of particles according to the particle densities determined in table 1, we struggled with meshing. Therefore, we started working on different shapes for the particles (rectangular, hexagonal, octagonal and cuboids) and found that the cuboid with similar surface area is the best among them because it gives the similar results (in terms of Nu and ΔP) as we got from the spherical ones and these also allowed us to accommodate the numbers of particles according to the particle densities without having any issue with the meshing. Comparison of Nu for cuboid and hemispherical particles has also been discussed in figure 3 of [8]. Since, the difference between the results for both particles is negligible (less than 1%) and therefore we do not need to account for any numerical coefficients to compensate for the differences in the numerical results.

Therefore the spatter deposits were modeled according to the approach discussed in [8]. In this approach, spatter deposits have been represented as cuboid particles and for the distribution of particles, particle densities were calculated on the basis of particle histogram discussed in [9].

On the basis of build-orientation shown in figure 3 and distribution of spatter deposits, hydraulic diameter and interface surface area was calculated for each case ans shown in table 2.

Table 2. Hydraulic diameters for various surfaces.

Surfaces	$\bar{{D}_{H}}$ (μm)	As (mm2)
Smth	2000.00±0.0	240.0
SWP	1996.89±2.70	244.8
Paral	1907.62±0.02	264.0
PWP	1906.93±0.05	268.8
Trans	1970.27±25.74	268.8
TWP	1970.79±24.91	273.6
45° Inclin	1900.08±3.59	288.0
45° IWP	1891.23±16.41	295.2

Equation used to calculate hydraulic diameter is as follows:

$$\begin{eqnarray}&&{D}_{H}=\displaystyle \frac{4{A}_{c}}{{P}_{Ch}}\end{eqnarray} \tag{ 1 }$$

In CFD, the surface area was calculated using the surface integral of each cell at the fluid-inconel interface.

For most thermo-fluid problems, it is not necessary to resolve minute fluctuations of turbulent flow. Therefore, the majority of numerical simulations for turbulent flow problems can be done with Reynolds-averaged Navier–Stokes (RANS) equations [11]. For a particular turbulent flow problem, it is required to use a suitable RANS model based on applications.

For our study, we are using the k-ω RANS model because this model allows an accurate near wall treatment which is recommended for rough surfaces. Also this model is well suited for wall bounded and low Reynolds number flows. In the k-ω RANS model, two transport equations are solved for kinetic energy k and turbulent frequency ω and it also has straightforward Dirichlet boundary conditions, which leads to significant advantages in numerical stability [11].

In this study, we are using shear stress transport (SST), a variant of the k-ω model which is a combination of the original Wilcox k-ω model [11] for near walls and the standard k–ε model away from walls [12].

The proposed problem to study the heat-transfer characteristics of various AM surfaces is a coupled thermal-fluid problem. The coupling is taken into account by using the conjugate heat transfer (CHT) technique. In this technique, RANS equations for the fluid flow and the heat conduction equation for heat transfer within the solid are interactively solved to steady-state and for that the time-marching algorithm is used [13]. The surface temperature is obtained by solving the RANS equations and then can be used as a boundary condition to determine the heat flux through the solid surface. Thereafter, this heat flux is used as a boundary condition for solving the RANS equations furthermore in the next time-step. This procedure has been repeated until a solution is reached out to the steady-state [13].

For the meshing, prismatic boundary layer cells were used to resolve the boundary layers at fluid-solid interfaces. In order to capture the circulation near walls, the growth size of prismatic layers were kept 15 percent of the base size with an increment of layer size of 1.2.

The smallest size of the particle considered in this study is 12.5 μm and the smallest cell size of the mesh is 4.2 μm and the numbers of cells to define the boundary of the deposits adjacent to the wall are 12. Figure 1(a) shows the meshing of particles and number of cells adjacent to the wall.

To get results with acceptable accuracy and independent of grid sizes, grid independence analysis was performed. In this analysis, the surface average temperature of outlet has been used as a criterion for mesh sufficiency. Various trades had been carried out to optimize the mesh size ranging from 85000 to 5 million cells (figure 1(b))and the optimized cells were 3 million (approximately).

The effects of AM surface roughness on heat transfer were studied using the average Nusselt number, Nu, given by [4].

$$\begin{eqnarray}&&Nu=\frac{q\mbox{''}{\bar{D}}_{H}}{{K}_{f}\left({T}_{s}-{T}_{m}\right)}.\end{eqnarray} \tag{ 2 }$$

This definition has been used previously by Snyder et al to evaluate the extent of convective heat transfer for different AM channels [4].

Figures 5 and 6 show the CFD simulation results of Nu for various channels for both turbulent and laminar flow conditions, respectively. The simulations show that the Nu changes with build orientation, with transverse weld track orientation (Trans) performing the best for turbulent flow (figure 5). Figure 5 also shows that the effects of spatter deposits are minimal for transverse (Trans versus TWP) and inclined (Inclin versus IWP) track surfaces while it has a greater impact on parallel (Paral versus PWP) track and smooth (Smth versus SWP) surfaces.

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As the Reynolds number decreases and flow becomes laminar, the addition of tracks without particles reduces Nu (Smth versus Paral versus Trans versus Inclin in figure 6), presumably due to stagnation of fluid in the valleys of the weld tracks. We also find that the addition of particles for laminar flow improves heat transfer for all the cases compared to the same geometry without particles. The particles create wakes that improve diffusion and mixing among adjacent fluid layers, increasing convective heat transfer.

To highlight the role of surface texture more clearly, we look at the percent change in the Nusselt number by using the smooth surface without particles (Smth) as a reference. This is shown for the turbulent flow condition in figure 7 (notice the zero percent value change for Smth).

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The figure has been divided into two regions (light blue and light yellow) to highlight the surface feature dominating the heat transfer characteristics observed for turbulent flow (track orientation versus particles).

We see that the presence of particles alone for turbulent flow causes an 18% increase in the Nusselt number for the smooth (SWP) surface (yellow region). The parallel tracks alone increase Nu by 4% but it jumps to 17% with the addition of particles (PWP). Thus, the addition of tracks parallel to the flow increases heat transfer, but the addition of particles increases heat transfer more significantly. The blue region highlights the channel behavior with the addition of tracks at an angle to the flow (transverse and inclined). In contrast, here we see a significant improvement caused by the track orientation alone (28% for Trans and 25% for Inclin). The addition of particles only slightly changes these numbers and interestingly slightly reduces heat transfer compared to what is seen with adding particles to smooth and parallel conditions.

As seen in figure 6, when the mass flow rate is low and the flow becomes laminar, an AM surface texture has a quite different effect. With laminar flow, the addition of tracks, regardless of their orientation, consistently reduces the percentage change in Nu (figure 8) because, as discussed above, the stagnation of the fluid in the track valleys effectively reduces the hydraulic diameter of the channel.

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The addition of particles counters this with generation of wakes that improve diffusion and mixing among adjacent fluid layers, increasing Nu.

4.1.1. Effect of surface area on heat transfer

To characterize the fluid flow due to the effects of roughness, results have been evaluated in terms of pressure drop and the friction factor. Here the pressure drop is defined as the difference between inlet and outlet surface average pressure,

$$\begin{eqnarray}&&{\rm{\Delta }}P\,=\,{P}_{i}-{P}_{o}.\end{eqnarray} \tag{ 3 }$$

The friction factor is defined as [6]

$$\begin{eqnarray}&&f=\frac{2\cdot {\rm{\Delta }}P\cdot {\bar{D}}_{H}}{\rho \cdot L\cdot {v}^{2}}.\end{eqnarray} \tag{ 4 }$$

For both turbulent and laminar flow, the pressure drop increases with added surface texture (figures 9 and 10), and the amount depends on the track orientation and particle details. While the trends are similar for turbulent and laminar flow, the highest pressure drop is at a different condition for turbulent (highest at TWP) versus laminar (highest at Inclin) flow, indicating the difference in diffusion among fluid layers in the two flow conditions is important.

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4.2.1. Effect of surface area over pressure drop

From the literature [14], it has been suggested that roughness increases the interface (fluid-solid) surface area and this causes higher resistance in the direction of fluid flow, thus leading to increased pressure drop. This would suggest pressure drop should track with increasing surface area which is a measure of increasing roughness. Again, this is not directly the case. For turbulent flow (figure 11) pressure drop tracks with increasing roughness (added surface area), but departs from this trend for the inclined tracks with and without particles. For laminar flow (figure 12) pressure drop tracks with roughness but clearly departs from the trend for the inclined with particle geometry. This suggests that the details of the fluid mixing given the texture geometry and the flow condition are important for predicting the pressure drop.

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In order to evaluate the overall performance of the AM channels, we define a performance factor that assesses the combined effects of both the thermal and the fluid flow characteristics. We calculate a performance factor (PF) as

$$\begin{eqnarray}&&PF=0.01\cdot \displaystyle \frac{Nu}{f}.\end{eqnarray} \tag{ 5 }$$

The performance factor is a dimensionless number where a high PF value indicates high convective heat transfer with low pressure drop (low friction factor). A large Nusselt number is obviously desirable and a low pressure drop is important if pumping power requirements are a consideration. Also, table 4 depicts the friction factor values for various surfaces and at different flow conditions. The IWP surface has the highest values of performance factor for both laminar and turbulent flow conditions (figures 13 and 14), meaning it is the best performing surface.

An experimental setup has been designed as discussed in section 3. It has been fabricated such that the side and upper walls of the channel should be of high temperature resin using stereolithography (SLA).

The experimental set-up (figure 16) has been designed such that the maximum temperature at the metal-plastic interface should not exceed the deflection temperature of high-temperature resin. Figures 15 and 17 show the flow loop and actual setup respectively.

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This test-section is equipped with converging and diverging sections at inlet and outlet (figure 18) respectively for the smooth entry and exit of the fluid from the test section.

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To measure temperature along the length of the channel and also at the inlet and outlet, calibrated 5 KΩ thermistors have been used. To provide constant heat supply, four 12 V and 40W ceramic cartridge heaters are used.

For the experimental investigation, an Inconel part with smooth surface ($\underline{{R}_{q}}=5\,\mu {\rm{m}}$) has been fabricated at UNC Charlotte machine shop. For this, a forged Inconel-625 rod was machined and carbide tools were used for drilling of holes (shown in figure 16).

The experimental setup incorporates two different materials, Inconel-625 and high temperature Formlab resin, as shown in figure 4. The side and upper walls are made of resin while the bottom part of the channel was made of inconel. The purpose of using two different materials is to isolate the effects of AM surfaces by reducing the heat loss to the side and upper walls. The use of plastic walls keeps the majority of the thermal loss to the AM surface and thus enables the study of the effect of different AM surfaces. However, the LPBF is an expensive technique (in terms of time, cost and post processing) and more suitable for high temperature alloys such as inconel and not for the carbon resin materials. On the other hand, SLA is less expensive, requires minimal post-processing and highly recommended for the polymers like carbon resins. Therefore, that part was prepared by SLA [15, 16].

The SLA part has been fabricated in 3-D printing facilities of UNC Charlotte. In this facility, Formlab SLA 3-D printer has been used.

Fabrication of the SLA part has been done in the following three stages and figure 19 depicts all these stages.

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In the first stage, part is fabricated using 3-D CAD model which takes 6–7 h, in the second stage fabricated part is cleaned using Formlab after wash for 30 min and in third stage the cleaned SLA part is dried using Formlab cure for 10 min and after that our part is ready to use.

Validation of CFD results has been done by performing various experiments with different inlet temperatures and heat inputs at different flow conditions with the smooth Inconel-625 channel. Both experimental and CFD results are discussed in the following subsections.

5.4.1. Results with different inlet temperatures

For the preliminary investigation, experiments were performed without the heat supply but with different inlet temperatures (20 °C, 25 °C and 30 °C) at laminar flow conditions. These results were then compared with CFD results (shown in figures 20 and 21).

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In figure 20, temperatures are plotted along the length of the channel and in figure 21, outlet temperature and pressure drop have been plotted for different inlet temperatures without heat input. We see from the experiment that the temperature repeatability is on the order of ±0.2°. From this limited sampling, we estimate the experimental pressure drop is 0.22 ± 0.02 kPa on average over these temperature conditions compared to the constant CFD pressure drop of 0.22 kPa for all temperatures.

5.4.2. Results with constant heat supply

Experiments were performed with constant heat inputs and at different Reynolds numbers using smooth Inconel parts. In figures 22–23, experiments were performed at two different flow conditions (laminar and turbulent) and two heat inputs (q' = 50.258 W and 85.57 W).

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For repeatability tests, the same experiments were performed at two different times. From figures 22–23 It can be observed that CFD results are in good agreement with experimental results however the gap between CFD and experimental results increased compared to the results shown in figures 20–21.

The differences we observe between CFD and experimental results is considered small in the CFD community [4, 5], given the challenges of estimating many realistic experimental parameters for the CFD simulations and the many sources of uncertainty in the experiments.

A detailed uncertainty analysis is underway to establish a quantitative comparison. Preliminary estimates suggest the experimental uncertainty in the heat supply and the location of the temperature readings are significant and reasonably account for the observed differences with simulation.