Arun Prakash Raghupathy

Boundary-Condition-Independent Reduced-Order Modeling of Heat Transfer in Complex Objects by POD-Galerkin Methodology: 1D Case Study

This technical note presents an introduction to boundary-condition-independent reduced-order modeling of complex electronic components using the proper orthogonal decomposition (POD)-Galerkin approach. The current work focuses on how the POD methodology can be used along with the finite volume method to generate reduced-order models that are independent of their boundary conditions. The proposed methodology is demonstrated for the transient 1D heat equation, and preliminary results are presented.

Boundary-Condition-Independent Reduced-Order Modeling of Complex Electronic Packages by POD-Galerkin Methodology

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by employing the proper orthogonal decomposition (POD)-Galerkin methodology. Detailed models of complex electronic packages that consume large computational resources are used within system-level models in computational fluid dynamics (CFD)-based heat transfer analysis. If a package-level model that reduces computational resources (reduced-order model) and provides accurate results in many different flow situations (boundary-condition-independent model) can be deployed, it will accelerate the design and analysis of the end products that make use of these packages. This paper focuses on how the proper orthogonal decomposition-Galerkin methodology can be used with the finite volume method (FVM) to generate reduced-order models that are boundary-condition-independent. This method is successfully used in the present study to generate boundary-condition-independent reduced-order models for 1-D and 2-D objects for isothermal and isoflux boundary conditions. Successful implementation of the method is also shown on 2-D objects made of multiple materials and multiple heat generating sources for isoflux boundary conditions.

A Comparative Study of Chemical Mechanisms in the Simulation of One -Dimensional Detonation

In this study we validate reaction mechanisms in the prediction of detonation quantities. This is done to understand modeling of detonatio n and to validate the software Fluent 6.1 for use in Pulse Detonation Engine simulations. One -dimensional detonation is simulated with a hydrogen -air mixture for two mixture compositions using flow -adaptive grids. The mechanisms’ capability to predict the detonation velocity and von Neumann spike in pressure is studied. The resulting detonation structure is also compared with the ZND structure. A lean (equivalence ratio of 0.44), and stoichiometric hydrogen -air mixture is used in this study. Four differe nt mechanisms, based on the nature of detail of the chemical model, are studied. It is seen that a very fine grid with a detailed chemistry model was able to capture the ZND structure, but resulted in the failure of self -sustaining the detonation. It is found that the numerical resolution required to resolve the reaction zone was dependent on the richness of the mixture. It is also observed that a mechanism, which did not allow modeling of the intermediates, also resulted in failure of predicting a self -sustaining detonation wave. All the other mechanisms predicted the detonation velocity within less than 2 % error when compared to the theoretical CJ value.

Boundary-condition-independent reduced-order modeling of complex 2D objects by POD-Galerkin methodology

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by the POD-Galerkin methodology. Detailed models of complex electronic packages are used within system-level models in Computational Fluid Dynamics (CFD)-based heat transfer analysis. At times, these package-level models are complicated, and their simulation tends to consume large amounts of computational resources. This problem is compounded further if multiple instances of these models are used within the system. If a package-level model that reduces computational resources (reduced-order model), and provides results in many different flow situations (boundary-condition-independent model) can be deployed, it will accelerate the design and analysis of the end products that make use of these components. This work focuses on how the Proper Orthogonal Decomposition (POD)-Galerkin methodology can be used with the Finite Volume (FV) method to generate reduced-order models that are boundary-condition-independent. This method is successfully used in the present study to generate boundary-condition-independent reduced-order models for 1D and 2D objects. Successful implementation of the method is also shown on 2D objects made of multiple materials and multiple heat generating sources. Also, the final BCI ROM in each case is found to work extremely well (errors less than 1%) even for boundary conditions outside the range in which it was generated, making it a truly boundary-condition-independent model.

Thermal management challenges in forced convection tablets

Handheld devices with computing capabilities that match laptops and desktops have recently emerged as market drivers in the consumer electronics industry. To accommodate such high performance in small form-factors like that of a tablet is a thermal management challenge. In touch-interactive electronics devices like tablets, skin temperature is as important as the processor temperature. Cooling by natural convection alone is insufficient to address the higher power density found in this class of high-performance tablet. Therefore, these devices require forced convection solutions. This study presents the thermal management challenges of a forced convection tablet using experimental and computational techniques. One such thermal challenge stems from the blower speed versus ergonomic requirements of acoustics. To understand more about this relation, the tablet is experimentally characterized for acoustics for several controlled blower speeds. The tablet is also characterized using airflow bench tests, infrared thermography and thermocouple measurements. The system-level thermal model of the tablet is constructed using FloTHERM XT®. The validated model serves as a test vehicle to study alternate thermal management strategies and understand their impact on the overall product design.

A simplified CFD modeling technique for Small Form factor Pluggable transceiver

Small Form-factor Pluggable (SFP) transceivers are commonly used in fiber optics based networks. Detailed CFD model demands a lot of mesh counts and is computationally prohibitive in system and board level simulations. In the present study, detailed SFP models have been simulated at 24 different boundary conditions consisted of four system airflow velocities, three power dissipations and two PCB board thermal conductivities. A two-resistor compact model has been derived based on the simulated heat fluxes and case temperatures of detailed SFP models. The case temperatures simulated from two-resistor model are benchmarked to the results from detailed SFP model. The two-resistor model has been compared with detailed SFP and DELPHI models strictly under the same condition. It has been shown with consistent accuracy. The advantages of using this model lie on modeling simplicity requiring the least grid resolution, easy scalability to different power dissipations, and great compatibility of various SFP packages. The limitations of two-resistor model are discussed at the end.

Boundary-condition-independent reduced-order modeling of 3D objects by the POD-Galerkin methodology

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by the POD-Galerkin methodology. This work focuses on how the Proper Orthogonal Decomposition (POD)-Galerkin methodology can be used with the Finite Volume (FV) method to generate reduced-order models that are boundary-conditionindependent. The method has been successfully implemented to generate boundary-condition-independent reduced-order thermal models for 1D and 2D objects. In this paper, the POD-Galerkin methodology is extended to generate a boundary-condition-independent model for a simple 3D object and a 3D object with a single heat source. Specific objectives of extending the methodology to 3D objects is to identify the correct number and type of snapshots used for constructing the reduced-order model and to identify the minimum number of POD basis vectors to generate the boundary-conditionindependent reduced order model. Boundary-conditionindependent reduced-order models generated for the 3D objects for isoflux boundary conditions show less than 4% relative error for a range of heat transfer coefficient of h = 1 W/m2K and h = 1000 W/m2K. The biggest advantage of this methodology is the potential of being integrated into commercial computational fluid dynamics software with minimal modifications.

Influence of temperature gradient on electromigration failures in 3D packaging

In this paper, influence of temperature gradient in interconnects due to Joule heating in 3D packaging on electromigration failure is presented. Blacks Mean Time to Failure (MTF) model relates exponentially to the temperature of interconnects which is assumed to be constant hence does not take into account temperature gradient. The developed electromigration model incorporates the driving force due to temperature gradient in addition to the effects of current density, vacancy concentration gradients and stress gradients in the interconnects and due to coefficient of thermal expansion mismatch with surrounding materials. Effectiveness of the developed finite element model is illustrated complex C4 solder bumps of flip-chip packages using COMSOL Mutliphysics software. It is shown that for same current density in the complex C4 solder bumps of flip-chip packages it is possible that failure times could be lower for lower solder average temperature with higher temperature gradient than for higher solder temperature with low temperature gradient.

Experimental and computational evaluation of phase change materials for handheld computing

In the current work, numerical evaluation of phase change material along with experimental validation of the same in a handheld device is presented. The value addition and driving force towards the use of phase change material (PCM) is not only due to limited heat dissipation capability and computational sprinting power load patterns in processors but also to have better user experiences of these hand held devices such as low touch temperatures, no fan noise and possibility of extended battery life by reducing the discharge cycles without fan loads. Direct placement of PCMs on the die or encapsulating the heat pipe, that has the quickest response to temperatures as a passive thermal management strategy is explored in this study. This paper proposes an accurate phase change model for transient thermal management using COMSOL Multiphysics® software. Impact of geometry of PCM material and its properties on the transient behavior of the CPUs temperature is provided. The model validations are carried out by comparing the results with controlled experimental results. The PCM material and their material properties are being provided by Outlast Technologies.

Application of phase change materials in handheld computing devices

With peak loads in the order of minutes and ergonomic considerations limiting surface temperatures and acoustical noise, handheld devices, such as smart phones or tablets, are excellent candidates for use of phase change materials (PCMs). The experimental and numerical evaluation of such materials used to enhance the performance of a forced convection cooled tablet is presented in this study. The PCM design parameters, including specific heat capacity, operating points (i.e., melt temperatures), thermal conductivity, and volume of phase change required for a specific time delay, are examined in the context of a tablet application.