Catherine Gorle

A framework for epistemic uncertainty quantification of turbulent scalar flux models for Reynolds-averaged Navier-Stokes simulations

Reynolds-averaged Navier-Stokes (RANS) simulations are a practical approach for solving complex multi-physics turbulent flows, but the underlying assumptions of the turbulence models introduce errors and uncertainties in the simulation outcome. The flow in scramjet combustors is an example of such a complex flow and the accurate characterization of safety and operability limits of these engines using RANS simulations requires an assessment of the model uncertainty. The objective of this paper is to present a framework for the epistemic uncertainty quantification of turbulence and mixing models in RANS simulations. The capabilities of the methodology will be demonstrated by performing simulations of the mixing of an underexpanded jet in a supersonic cross flow, which involves many flow features observed in scramjet engines. The fundamental sources of uncertainty in the RANS simulations are the models used for the Reynolds stresses in the momentum equations and the turbulent scalar fluxes in the scalar tran...

Thermal Modeling of Extreme Heat Flux Microchannel Coolers for GaN-on-SiC Semiconductor Devices

Gallium nitride (GaN) high-electron-mobility transistors (HEMTs) dissipate high power densities which generate hotspots and cause thermomechanical problems. Here, we propose and simulate GaN-based HEMT technologies that can remove power densities exceeding 30 kW/cm2 at relatively low mass flow rate and pressure drop. Thermal performance of the microcooler module is investigated by modeling both single- and two-phase flow conditions. A reduced-order modeling approach, based on an extensive literature review, is used to predict the appropriate range of heat transfer coefficients associated with the flow regimes for the flow conditions. Finite element simulations are performed to investigate the temperature distribution from GaN to parallel microchannels of the microcooler. Single- and two-phase conjugate computational fluid dynamics (CFD) simulations provide a lower bound of the total flow resistance in the microcooler as well as overall thermal resistance from GaN HEMT to working fluid. A parametric study is performed to optimize the thermal performance of the microcooler. The modeling results provide detailed flow conditions for the microcooler in order to investigate the required range of heat transfer coefficients for removal of heat fluxes up to 30 kW/cm2 and a junction temperature maintained below 250 °C. The detailed modeling results include local temperature and velocity fields in the microcooler module, which can help in identifying the approximate locations of the maximum velocity and recirculation regions that are susceptible to dryout conditions.

The deviation from parallel shear flow as an indicator of linear eddy-viscosity model inaccuracy

A marker function designed to indicate in which regions of a generic flow field the results from linear eddy-viscosity turbulence models are plausibly inaccurate is introduced. The marker is defined to identify regions that deviate from parallel shear flow. For two different flow fields it is shown that these regions largely coincide with regions where the prediction of the Reynolds stress divergence is inaccurate. The marker therefore offers a guideline for interpreting results obtained from Reynolds-averaged Navier-Stokes simulations and provides a basis for the further development of turbulence model-form uncertainty quantification methods.

Numerical Simulation of Advanced Monolithic Microcooler Designs for High Heat Flux Microelectronics

This study considers CFD simulations with conjugate heat transfer performed in the framework of designing a complex micro-scale cooling geometry. The numerical investigation of the three-dimensional, laminar flow (Reynolds number smaller than 480) and the solid conduction is done on a reduced model of the heat sink micro-structure to enable exploring a variety of configurations at a limited computational cost. The reduced model represents a unit-cell, and uses periodic and symmetry boundary conditions to mimic the conditions in the entire cooling manifold. A simulation of the entire heat sink micro-structure was performed to verify the unit-cell set-up, and the comparison demonstrated that the unit-cell simulations allow reducing the computational cost by two orders of magnitude while retaining accurate results. The baseline design for the unit-cell represents a configuration used in traditional electronic heat sinks, i.e. a simple channel geometry with a rectangular cross section, with a diameter of 50 μm, where the fluid flows between two cooling fins. Subsequently three types of modified geometries with feature sizes of 50 μm were considered: baffled geometries that guide the flow towards the hotspot region, geometries where the fins are connected by crossbars, and a woodpile structure without cooling fins. Three different mass-flow rates were tested. Based on the medium mass-flow rate considered, the woodpile geometry showed the highest heat transfer coefficient with an increase of 70% compared to the baseline geometry, but at the cost of increasing the pressure drop by more than 300%. The crossbar geometries were shown to be promising configurations, with increases in the heat transfer coefficient of more than 20% for a 70% increase in pressure drop. The potential for further optimization of the crossbar configurations by adding or removing individual crossbars will be investigated in a follow up study. The results presented demonstrate the increase in performance that can be obtained by investigating a variety of designs for single phase cooling devices using unit-cell conjugate heat transfer simulations.Copyright

Thermal Design of a Hierarchical Radially Expanding Cavity for Two-Phase Cooling of Integrated Circuits

A major challenge in the implementation of evaporative two-phase liquid-cooled ICs with embedded fluid microchannels/cavities is the high pressure drops arising from evaporation-induced expansion and acceleration of the flowing two-phase fluid in small hydraulic diameters. Our ongoing research effort addresses this challenge by utilizing a novel hierarchical radially expanding channel networks with a central embedded inlet manifold and drainage at the periphery of the chip stack. This paper presents a qualitative description of the thermal design process that has been adopted for this radial cavity. The thermal design process first involves construction of a system-level pressure-thermal model for the radial cavity based on both fundamental experiments as well as numerical simulations performed on the building block structures of the final architecture. Finally, this system-level pressure-thermal model can be used to identify the design space and optimize the geometry to maximize thermal performance, while respecting design specifications. This design flow presents a good case study for electrical-thermal co-design of two-phase liquid cooled ICs.Copyright

VALIDATION STUDY FOR VOF SIMULATIONS OF BOILING IN A MICROCHANNEL

This paper presents a comparison of Volume-of-Fluid simulation results with experiments [1] for two-phase flow and heat transfer in a micro channel. Mass transfer between the phases is modeled using a reduced-order model, requiring the definition of a time relaxation constant, r. A two-step solution procedure is used, where first a fixed temperature boundary condition is imposed at the heater to avoid overheating of the device during the initial development of the two-phase flow. After obtaining a quasi-steady-state solution this is changed to a heat flux boundary condition to determine the final solution. Results using three different values for r indicate that the value of the constant should vary throughout the domain. A final simulation where r is defined as a function of the streamwise location results in a prediction of the base temperature within 1K of the experimental result, a pressure drop within 30%, and a prediction of the location of transition from subcooled to saturated flow within 2mm.Copyright

High heat flux two-phase cooling of electronics with integrated diamond/porous copper heat sinks and microfluidic coolant supply

We here present an approach to cooling of electronics requiring dissipation of extreme heat fluxes exceeding 1 kW/cm2 over ~1 cm2 areas. The approach applies a combination of heat spreading using laser micromachined diamond heat sinks; evaporation/boiling in fine featured (5 μm) conformal porous copper coatings; microfluidic liquid routing for uniform coolant supply over the surface of the heat sink; and phase separation to control distribution of liquid and vapor phases. We characterize the performance of these technologies independently and integrated into functional devices. We report two-phase heat transfer performance of diamond/porous copper heat sinks with microfluidic manifolding at full device scales (0.7 cm2) with heat fluxes exceeding 1300 W/cm2 using water working fluid. We further show application of hydrophobic phase separation membranes for phase management with heat dissipation exceeding 450 W/cm2 at the scale of a single extended surface (~300 μm).

Full Scale Simulation of an Integrated Monolithic Heat Sink for Thermal Management of a High Power Density GaN-SiC Chip

Advances in manufacturing techniques are inspiring the design of novel integrated microscale thermal cooling devices seeking to push the limits of current thermal management solutions in high heat flux applications. These advanced cooling technologies can be used to improve the performance of high power density electronics such as GaN-based RF power amplifiers. However, their optimal design requires careful analysis of the combined effects of conduction and convection.Many numerical simulations and optimization studies have been performed for single cell models of microchannel heat sinks, but these simulations do not provide insight into the flow and heat transfer through the entire device. This study therefore presents the results of conjugate heat transfer CFD simulations for a complex copper monolithic heat sink integrated with a 100 micron thick, 5 mm by 1 mm high power density GaN-SiC chip. The computational model (13 million cells) represents both the chip and the heat sink, which consists of multiple inlets and outlets for fluid entry and exit, delivery and collection manifold systems, and an array of fins that form rectangular microchannels. Total chip powers of up to 150 W at the GaN gates were considered, and a quarter of the device was modeled for total inlet mass flow rates of 1.44 g/s and 1.8 g/s (0.36 g/s and 0.45 g/s for the quarter device), corresponding to laminar flow at Reynolds numbers between 19.5 and 119.3. It was observed that the mass flow rates through individual microchannels in the device vary by up to 45%, depending on the inlet/outlet locations and pressure drop in the manifolds. The results demonstrate that full device simulations provide valuable insight into the multiple parameters that affect cooling performance.Copyright

Numerical Optimization of Advanced Monolithic Microcoolers for High Heat Flux Microelectronics

This study considers the optimization of a complex micro-scale cooling geometry that represents a unit-cell of a full heat sink microstructure. The configuration consists of a channel with a rectangular cross section and a hydraulic diameter of 100 μm, where the fluid flows between two cooling fins connected by rectangular crossbars (50 × 50 μm). A previous investigation showed that adding these crossbars at certain locations in the flow can increase the heat transfer in the microchannel, and in the present work we perform an optimization to determine the optimal location and number of crossbars. The optimization problem is defined using 12 discrete design parameters, which represent 12 crossbars at different locations in the channel that can either be turned off and become part of the fluid domain, or turned on and become part of the solid domain. The optimization was done using conjugate heat transfer computational fluid dynamics (CFD) simulations using Fluent 15.0. All possible 4096 configurations were simulated for one set of boundary conditions. The domain was discretized using about 1 million nodes combined for the fluid and solid domains and the computational time was around 1 CPU hour per case. The results show that further improvements in heat transfer are feasible at an optimized pressure drop. The results cover a range of pressure drops from 25 kPa to almost 90 kPa and the heat transfer coefficient varies from 60 to 120 kW/m2K. The configurations on the Pareto front show the trend that crossbars closer to the maximal fluid-solid interface result in a more optimal performance than crossbars positioned farther away. In addition to performing simulations for all possible configurations, the potential of using a genetic algorithm to identify the configurations that define the Pareto front was explored, demonstrating that a 80% reduction in computational time can be achieved. The results of this study demonstrate the significant increase in performance that can be obtained through the use of computational tools and optimization algorithms for the design of single phase cooling devices.Copyright

Computational Modeling of Extreme Heat Flux Microcooler for GaN-Based HEMT

This study explores an extreme heat flux limit of microcooler for GaN-based HEMTs (high electron mobile transistors) which have local power densities exceeding 30 kW/cm2 using both solid conduction simulation and single-phase/two-phase conjugate simulations. Solid conduction simulation models are developed for full geometry of the microcooler to account for the overall thermal resistances from GaN HEMT to working fluid. This allows investigating the temperature distribution of the suggested microcooler. Parametric studies are also performed to investigate the impact of geometries and heat transfer coefficients on the junction temperature. The solid conduction simulation results using COMSOL Multiphysics agree well with single-cell ANSYS Fluent simulation results.Separately, fluid-solid conjugate CFD (Computational Fluid Dynamics) simulation models provide the detailed flow information in the microchannel using a single-channel geometry with symmetry boundary conditions. Single-phase CFD simulations obtain the lower bound of total pressure drop and heat transfer coefficient at the microchannel walls for a mass velocity range of G = 6000–24000 kg/m2-s. The local temperatures and velocity distributions are reported that can help with identifying the locations of the maximum velocity and recirculation regions that are susceptible to dryouts. Two additional alternative tapered inlet designs are proposed to alleviate the significant pressure loss at the entrance of the SiC channel. The impact of the tapered inlet designs on pressure drops and heat transfer coefficients is also investigated.Two-phase simulations in microchannel are conducted using Volume-of-Fluid (VOF) method embedded in ANSYS Fluent to investigate two-phase flow patterns, flow boiling, and temperature distributions within the GaN HEMT device and SiC etched mircochannels. A user-defined function (UDF) accounts for the phase change process due to boiling at the microchannel walls. The results show that the time relaxation factor, ri has a strongly influence on both numerical convergence and flow solutions.© 2015 ASME