# Conjugate Heat Transfer and Fluid Flow Modeling for Liquid Microjet Impingement Cooling with Alternating Feeding and Draining Channels

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## Abstract

**:**

_{d}< 4000, compared with the reference LES model. For the experimental measurements in the range of 130 < Re

_{d}< 1400, the LES model, transition SST model and $k$-$\omega $ SST model all show less than 25% prediction error. Moreover, it is shown that the validity of the unit cell assumption for the temperature and flow distribution depends on the flow rate.

## 1. Introduction

^{2}-f (V2F) model. In [20], John Maddox compared the transition SST and the V2F turbulence models, and finally selected the transition SST model for the 3 × 3 jet array with common outlet flow based on the computational cost considerations. Subrahmanyam et al. [21] used Large Eddy Simulations (LES) to study the unsteady flow and heat transfer characteristics of a single impinging jet at Reynolds number of 20,000 at four normalized nozzle-to-impinging plate distances (0.5 ≤ z/d ≤ 2). Sung [22] used the standard two-equation k-ε turbulence model to study the effects of the jet pattern on single-phase cooling performance of hybrid micro-channel/micro-circular-jet-impingement.

## 2. Conjugate Heat Transfer and Fluid Flow Model

#### 2.1. Miroject Cooling Test Case

^{2}. The chip thickness is 0.2 mm. In order to study the flow impact on the chip temperature distribution, the conjugate heat transfer model within the CFD approach should include the fluidic part of the cooler, as well as the chip heat conduction part. In the next part, the details of the conjugate CFD model will be introduced and discussed.

#### 2.2. CFD Model Introduction

#### 2.3. Grid Sensitivity Study

^{+}in the viscous sublayer. For the solid domain mesh prism cells are used with a 20 µm mesh size. The grid convergence index (GCI) is used for the meshing sensitivity analysis.

_{23}and GCI

_{12}are the values of GCI computed by considering, respectively, ${f}_{2}$; ${f}_{3}$ and ${f}_{1}$; ${f}_{2}$.

#### 2.4. Modeling Methodology

^{2}is applied on the chip bottom to represent the power generation in the heating elements of the test chip. The fluid and solid interface is set as a flow-thermal coupled boundary condition. Since the cooler material is plastic with low thermal conductivity, the boundary walls of the fluid domain are set as adiabatic walls.

^{−5}for continuity, 10

^{−6}for energy and 10

^{−6}for k, ω and momentum (x, y and z components of velocity), respectively. For all the simulations, the net imbalance of overall mass, momentum and energy is kept below 0.02% [33,34]. In order to characterize the thermal and hydraulic performance of the cooler, the overall thermal performance and pressure drop are defined as dimensionless Nusselt and friction numbers, Nu and k, respectively. They are primarily a function of the Reynolds number Re:

## 3. Numerical Modeling Analysis

#### 3.1. Unit Cell Modeling Analysis

^{−7}s in this case, is calculated based on the cell size and inlet velocity. Two velocity points with the stagnation point and recirculation point are monitored during the URANS modeling. As shown in Figure 5, after 600 time steps, the flow is fully developed, and from then on, there is no velocity fluctuation observed, which reveals the steady phenomenon. Therefore, this flow problem is steady at Re = 2048. So, for all the following simulations, we choose the RANS solver instead of URANS solver.

^{−3}s. As shown in Figure 7, the flow is fully developed after around 10 iterations. In order to compare with the RANS model, the mean values of the variable are calculated by time-averaging of instantaneous results from 0.1 s to 0.5 s. The velocity and temperature simulation results with the LES model are shown in Figure 7. By using the LES model, the smaller scale flow behavior can also be captured. The simulated $N{u}_{\mathrm{avg}}$ and $N{u}_{0}$ for different RANS models are compared with the LES model at ${\mathrm{Re}}_{d}$ = 1024, as listed in Table 3. It can be seen that, on the one hand, the laminar model, $k$-$\omega $ SST and Transition SST model can produce better results than any of the high-Re models, matching $N{u}_{\mathrm{avg}}$ and $N{u}_{0}$ within 1% compared to the LES model, however by reducing the calculation time by a factor of 6. On the other hand, $k$-ε model and SA model show large $N{u}_{\mathrm{avg}}$ prediction errors up to 80%, and the $N{u}_{0}$ prediction errors are above 100%.

#### 3.2. Full Cooler Level Modeling Analysis

#### 3.3. Unit Cell versus Full Level Model

## 4. Experimental Validation

#### 4.1. Test Case Demonstration

#### 4.2. Experimental Set-Up

^{2}. All these cells contain a diode in the center of the cell as a temperature sensor, resulting in a detailed temperature map measurement with 32 × 32 ‘thermal pixels’ across the die surface. The voltage drop across the diode for a constant current is used as the temperature sensitive parameter of the sensor. The 95% confidence interval of the calibrated sensitivity is −1.55 ± 0.02 mV/°C for a current of 5 μA in the temperature range between 10 and 75 °C. The chip temperature sensors allow absolute temperature measurements with an accuracy of ± 2 °C.

#### 4.3. Results and Discussions

^{2}. Similar with the unit cell model analysis, different turbulence models are used for the full cooler level model, including laminar model, $k$-ε model, $k$-$\omega $ model, Transition SST model and SA model. It can be seen that the full CFD model with SA model overestimates the Nusselt number by a factor of 4 comparing with the experimental result. Moreover, the full model with $k$-ε model also shows very high prediction errors compared with the experiments. As expected, the LES model shows good agreement with the measurements. In general, the comparison shows that the laminar model, the $k$-$\omega $ model and the transition SST model show good agreement with the measured chip temperature, for the ${\mathrm{Re}}_{d}$ number from 130 to 1400.

## 5. Conclusions

_{d}< 4000, compared with the reference LES model. For the comparison with experimental measurements, the LES model, transition SST model and $k$-$\omega $ SST model all show less than 25% prediction error as the ${\mathrm{Re}}_{d}$ number ranging from 130 to 1400.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Jörg, J.; Taraborrelli, S.; Sarriegui, G.; De Doncker, R.W.; Kneer, R.; Rohlfs, W. Direct Single Impinging Jet Cooling of a mosfet Power Electronic Module. IEEE Trans. Power Electron.
**2018**, 33, 4224–4237. [Google Scholar] [CrossRef] - Wei, T.-W.; Oprins, H.; Cherman, V.; Van der Plas, G.; De Wolf, I.; Beyne, E.; Baelmans, M. High efficiency direct liquid jet impingement cooling of high power devices using a 3D-shaped polymer cooler. In Proceedings of the 2017 IEEE International Electron Devices Meeting (IEDM), San Francisco, CA, USA, 2–6 December 2017. [Google Scholar]
- Bhunia, A.; Chen, C.L. On the scalability of liquid microjet array impingement cooling for large area systems. J. Heat Transf.
**2011**, 133, 064501. [Google Scholar] [CrossRef] - Bhunia, A.; Chandrasekaran, S.; Chen, C.L. Performance improvement of a power conversion module by liquid micro-jet impingement cooling. IEEE Trans. Compon. Packag. Technol.
**2007**, 30, 309–316. [Google Scholar] [CrossRef] - Robinson, A.J.; Schnitzler, E. An experimental investigation of free and submerged miniature liquid jet array impingement heat transfer. Exp. Therm. Fluid Sci.
**2007**, 32, 1–13. [Google Scholar] [CrossRef] - Molana, M.H.; Banooni, S. Investigation of heat transfer processes involved liquid impingement jets: A review. Braz. J. Chem. Eng.
**2013**, 30, 413–435. [Google Scholar] [CrossRef] - Han, Y.; Lau, B.L.; Zhang, H.; Zhang, X. Package-level Si-based micro-jet impingement cooling solution with multiple drainage micro-trenches. In Proceedings of the 2014 IEEE 16th Electronics Packaging Technology Conference (EPTC), Singapore, 3–5 December 2014; pp. 330–334. [Google Scholar]
- Brunschwiler, T.; Rothuizen, H.; Fabbri, M.; Kloter, U.; Michel, B.; Bezama, R.J.; Natarajan, G. Direct Liquid Jet-Impringement Cooling with Micron-Sized Nozzle Array and Distributed Return Architecture. In Proceedings of the Thermal and Thermomechanical Proceedings 10th Intersociety Conference on Phenomena in Electronics Systems, San Diego, CA, USA, 30 May–2 June 2006; pp. 193–203. [Google Scholar]
- Natarajan, G.; Bezama, R.J. Microjet cooler with distributed returns. Heat Transf. Eng.
**2007**, 28, 779–787. [Google Scholar] [CrossRef] - Boldman, D.R.; Brinich, P.F. Mean Velocity, Turbulence Intensity, and Scale in a Subsonic Turbulent Jet Impinging Normal to a Large Flat Plate; NASA Lweis Center: Cleveland, OH, USA, 1977. [Google Scholar]
- Pope, S.B. Turbulent flows. Meas. Sci. Technol.
**2001**, 12, 11. [Google Scholar] [CrossRef] - Zuckerman, N. Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling. Adv. Heat Transf.
**2006**, 39, 565–631. [Google Scholar] - Viskanta, R. Heat transfer to impinging isothermal gas and flame jets. Exp. Therm. Fluid Sci.
**1993**, 6, 111–134. [Google Scholar] [CrossRef] - Bernhard, W. Multiple Jet Impingement—A Review. Heat Transf. Res.
**2011**, 42, 101–142. [Google Scholar] [CrossRef] - Narumanchi, S.V.J.; Hassani, V.; Bharathan, D. Modeling Single-Phase and Boiling Liquid Jet Impingement Cooling in Power Electronics; National Renewable Energy Laboratory (NREL): Golden, CO, USA, 2005. [Google Scholar]
- Womac, D.J.; Ramadhyani, S.S.; Incropera, F.P. Correlating Equations for Impingement Cooling of Small Heat Sources With Single Circular Liquid Jets. ASME J. Heat Transf.
**1993**, 115, 106–115. [Google Scholar] [CrossRef] - Garimella, S.V.; Rice, R.A. Confined and submerged liquid jet impingement heat transfer. ASME J. Heat Transf.
**1995**, 117, 871–877. [Google Scholar] [CrossRef] - Isman, M.K.; Pulat, E.; Etemoglu, A.B.; Can, M. Numerical Investigation of Turbulent Impinging Jet Cooling of a Constant Heat Flux Surface. Numer. Heat Transf. Part A Appl.
**2008**, 53, 1109–1132. [Google Scholar] [CrossRef] - Esch, T.; Menter, F. Heat transfer predictions based on two-equation turbulence models with advanced wall treatment. Turbul. Heat Mass Transf.
**2003**, 4, 633–640. [Google Scholar] - Maddox, J.F. Liquid Jet Impingement with Spent Flow Management for Power Electronics Cooling. Ph.D. Thesis, Auburn University, Auburn, AL, USA, 2015. [Google Scholar]
- Prabhakar, S.; Arun, K. Micro-Scale Nozzled Jet Heat Transfer Distributions and Flow Field Entrainment Effects Directly on Die. In Proceedings of the 18th IEEE ITHERM Conference, Las Vegas, NV, USA, 28–31 May 2019; pp. 1082–1097. [Google Scholar]
- Sung, M.K.; Mudadar, I. Effects of jet pattern on single-phase cooling performance of hybrid micro-channel/micro-circular-jet-impingement thermal management scheme. Int. J. Heat Mass Transf.
**2008**, 51, 4614–4627. [Google Scholar] [CrossRef] - Polat, S.; Huang, B.; Majumdar, A.S.; Douglas, W.J.M. Numerical Flow and Heat Transfer under Impinging Jets: A Review. Annu. Rev. Heat Transf.
**1989**, 2, 157–197. [Google Scholar] [CrossRef] - Behnia, M.; Parneix, S.; Dur, P. Accurate modeling of impinging jet heat transfer. In Center for Turbulence Research, Annual Research Briefs 1997; Stanford University: Stanford, CA, USA, 1997; pp. 149–164. [Google Scholar]
- Gao, S.; Voke, P.R. Large-eddy simulation of turbulent heat transport in enclosed impinging jets. Int. J. Heat Fluid Flow
**1995**, 16, 349–356. [Google Scholar] [CrossRef] - Beaubert, F.; Viazzo, S. Large Eddy Simulation of a plane impinging jet. Comptes Rendus Mécanique
**2002**, 330, 803–810. [Google Scholar] [CrossRef] - Hällqvist, T. Large Eddy Simulation of Impinging Jets with Heat Transfer Licentiate Thesis. Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 2006. [Google Scholar]
- Olsson, M.; Fuchs, L. Large eddy simulations of a forced semiconfined circular impinging jet. Phys. Fluids
**1998**, 10, 476–486. [Google Scholar] [CrossRef] - Anupam, D.; Rabijit, D.; Balaji, S. Recent Trends in Computation of Turbulent Jet Impingement Heat Transfer. Heat Transf. Eng.
**2012**, 33, 447–460. [Google Scholar] - Cziesla, T.; Biswas, G.; Chattopadhyay, H.; Mitra, N.K. Large-eddy simulation of flow and heat transfer in an impinging slot jet. Int. J. Heat Fluid Flow
**2001**, 22, 500–508. [Google Scholar] [CrossRef] - Draksler, M.; Končar, B.; Cizelj, L.; Ničeno, B. Large Eddy Simulation of Multiple Impinging Jets in Hexagonal Configuration—Flow Dynamics and Heat Transfer Characteristics. Int. J. Heat Mass Transf.
**2017**, 109, 16–27. [Google Scholar] [CrossRef] - Acikalin, T.; Schroeder, C. Direct liquid cooling of bare die packages using a microchannel cold plate. In Proceedings of the Fourteenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Orlando, FL, USA, 27–30 May 2014; pp. 673–679. [Google Scholar]
- Wei, T.-W.; Oprins, H.; Cherman, V.; Qian, J.; De Wolf, I.; Beyne, E.; Baelmans, M. High efficiency polymer based direct multi-jet impingement cooling solution for high power devices. IEEE Trans. Power Electron.
**2018**, 34, 6601–6612. [Google Scholar] [CrossRef] - Wei, T.-W.; Oprins, H.; Cherman, V.; Shoufeng, Y.; De Wolf, I.; Beyne, E.; Baelmans, M. Experimental Characterization of a Chip Level 3D Printed Microjet Liquid Impingement Cooler for High Performance Systems. IEEE Trans. Compon. Packag. Manuf. Technol.
**2019**. [Google Scholar] [CrossRef] - Penumadu, P.S. Numerical investigations of heat transfer and pressure drop characteristics in multiple jet impingement system. Appl. Therm. Eng.
**2017**, 110, 1511–1524. [Google Scholar] [CrossRef] - Menter, F.R.; Langtry, R.B.; Likki, S.R.; Suzen, Y.B.; Huang, P.G.; Völker, S. A correlation-based transition model using local variable—part I: Model formulation. J. Turbomach.
**2006**, 128, 413–422. [Google Scholar] [CrossRef] - Mishra, A.A.; Iaccarino, G. Uncertainty estimation for reynolds-averaged navier–stokes predictions of high-speed aircraft nozzle jets. AIAA J.
**2017**, 55, 3999–4004. [Google Scholar] [CrossRef] - Granados-Ortiz, F.J.; Arroyo, C.P.; Puigt, G.; Lai, C.H.; Airiau, C. On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust. Comput. Fluids
**2019**, 180, 139–158. [Google Scholar] [CrossRef] - Mishra, A.A.; Mukhopadhaya, J.; Iaccarino, G.; Alonso, J. Uncertainty Estimation Module for Turbulence Model Predictions in SU2. AIAA J.
**2018**, 57, 1066–1077. [Google Scholar] [CrossRef]

**Figure 1.**Test case of multiple jet impingement cooling with a 4 × 4 inlet nozzle array and a staggered 5 × 5 outlet nozzle array [15]: (

**a**) schematic view of the internal channels; (

**b**) computer-aided design (CAD) structure of the designed cooler.

**Figure 2.**Full computational fluid dynamics (CFD) model of the impingement jet cooler with 4 × 4 nozzle array and inside manifold fluid delivery system.

**Figure 4.**Meshing details of (

**a**) full model and (

**b**) unit cell model, (

**c**) shows the details of the boundary layer mesh between the fluid and solid interface.

**Figure 5.**Unsteady flow simulation—unsteady Reynolds-averaged Navier–Stokes (URANS) for V

_{in}= 5 m/s and ${\mathrm{Re}}_{d}$ = 2048. The velocity at two points as function of flow time (time step) is plotted.

**Figure 6.**Conjugate flow and thermal unit cell modeling for ${\mathrm{Re}}_{d}$ = 1024: top row—velocity streamlines in the unit cell model, and bottom row—temperature distribution in the active region of the Si chip for different turbulent models.

**Figure 7.**Large Eddy Simulations (LES) modeling results: (

**a**) velocity and temperature distribution at ${\mathrm{Re}}_{d}$ = 1024; (

**b**) flow velocity development as function of the time. (4 × 4 nozzle array, di = 0.6 mm).

**Figure 8.**$N{u}_{\mathrm{avg}}$–${\mathrm{Re}}_{d}$ correlations: Turbulence model comparison with different RANS models and benchmarked with LES model (30 $\le {\mathrm{Re}}_{d}\le $ 4000).

**Figure 9.**Nu

_{0}–${\mathrm{Re}}_{d}$ correlations: Turbulence model comparison with different RANS models and benchmarked with LES model (30 $\le {\mathrm{Re}}_{d}\le $ 4000).

**Figure 10.**$f$–${\mathrm{Re}}_{d}$ correlations: Turbulence model comparison with different RANS models and benchmarked with LES model (30 $\le {\mathrm{Re}}_{d}\le $ 4000).

**Figure 11.**Conjugate flow and thermal modeling with full CFD model: top row—velocity streamline, and bottom row—temperature distributions with different turbulent models (130 $\le {\mathrm{Re}}_{d}\le $ 1400).

**Figure 12.**Temperature comparison between the unit cell model (UC) and full cooler level model (FM) with transition SST turbulence model for different flow rate values (FL): (

**a**) FL = 100 mL/min; (

**b**) FL = 300 mL/min; (

**c**) FL = 650 mL/min; (

**d**) FL = 1000 mL/min; (

**e**) temperature comparison as a function of different flow rate.

**Figure 13.**Temperature profiles along the chip diagonal: comparison for unit cell and full model with transition Shear Stress Transport (SST) model under the flow rate of 300 mL/min and 650 mL/min.

**Figure 14.**Pressure drop of unit cell and full cooler level model as function of the total flow rate.

**Figure 15.**Test case demonstration of the microjet impingement cooler: (

**a**) photo of 3D printed cooler with 4 × 4 nozzle array; (

**b**) bottom view of the printed jet nozzles.

**Figure 16.**Experimental set-up of the impingement jet cooling: flow loop measurement system; temperature distribution measurement and microjet cooler.

**Figure 17.**Model comparison with full CFD model, unit cell model and experimental results data on $N{u}_{\mathrm{avg}}$-${\mathrm{Re}}_{d}$ number.

Temperature | GCI_{12} | Asymptotic Range of Convergence |
---|---|---|

Stagnation Temp | 0.002 | 0.99 |

Averaged chip Temp | 0.004 | 1.01 |

Model | Full Model | Unit Cell Model Reynolds-Averaged Navier–Stokes (RANS) | Unit Cell Model Large Eddy Simulations (LES) |
---|---|---|---|

Elements | 8.5 M | 0.4 M | 3 M |

Minimal Grid size | 80 µm | 20 µm | 1 µm |

Computation time | 24 h | 2 h | 12 h |

Turbulent Model | Re | Nu_{avg} | Nu_{avg} Difference | Nu_{0} | Nu_{0} Difference |
---|---|---|---|---|---|

LES model | 1024 | 35.14 | 0 | 39.42 | 0 |

Laminar model | 1024 | 34.92 | 0.6% | 39.42 | 0.1% |

$k$-$\omega $ SST | 1024 | 34.84 | 0.9% | 39.37 | 0.1% |

Transition SST | 1024 | 35.05 | 0.3% | 39.53 | 0.3% |

k-ε model | 1024 | 64.94 | 84.8% | 81.95 | 107.9% |

SA model | 1024 | 69.27 | 97.1% | 98.28 | 149.3% |

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**MDPI and ACS Style**

Wei, T.; Oprins, H.; Cherman, V.; Beyne, E.; Baelmans, M.
Conjugate Heat Transfer and Fluid Flow Modeling for Liquid Microjet Impingement Cooling with Alternating Feeding and Draining Channels. *Fluids* **2019**, *4*, 145.
https://doi.org/10.3390/fluids4030145

**AMA Style**

Wei T, Oprins H, Cherman V, Beyne E, Baelmans M.
Conjugate Heat Transfer and Fluid Flow Modeling for Liquid Microjet Impingement Cooling with Alternating Feeding and Draining Channels. *Fluids*. 2019; 4(3):145.
https://doi.org/10.3390/fluids4030145

**Chicago/Turabian Style**

Wei, Tiwei, Herman Oprins, Vladimir Cherman, Eric Beyne, and Martine Baelmans.
2019. "Conjugate Heat Transfer and Fluid Flow Modeling for Liquid Microjet Impingement Cooling with Alternating Feeding and Draining Channels" *Fluids* 4, no. 3: 145.
https://doi.org/10.3390/fluids4030145