Andrej Horvat

Numerical technique for modeling conjugate heat transfer in an electronic device heat sink

Abstract A fast running computational algorithm based on the volume averaging technique (VAT) is developed to simulate conjugate heat transfer process in an electronic device heat sink. The goal is to improve computational capability in the area of heat exchangers and to help eliminate some of empiricism that leads to overly constrained designs with resulting economic penalties. VAT is tested and applied to the transport equations of airflow through an aluminum (Al) chip heat sink. The equations are discretized using the finite volume method (FVM). Such computational algorithm is fast running, but still able to present a detailed picture of temperature fields in the airflow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient, Nusselt number and thermal effectiveness are compared with experimental data to verify the computational model and validate numerical code. The comparison also shows a good agreement between FVM results and experimental data. The constructed computational algorithm enables prediction of cooling capabilities for the selected geometry. It also offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.

WALL PROPERTIES AND HEAT TRANSFER IN NEAR-WALL TURBULENT FLOW

Direct numerical simulation of a passive scalar in fully developed turbulent channel flow is used to show that Nusselt number is not only a function of Reynolds and Prandtl number, but also depends on properties of a heating wall. Variable thickness of the heating wall and variable heater properties, combined in a fluid–solid thermal activity ratio , can change the Nusselt number of the turbulent channel flow for up to 1% at the same Reynolds and Prandtl number and at the same wall heat flux.

APPLICATION OF GALERKIN METHOD TO CONJUGATE HEAT TRANSFER CALCULATION

A fast-running computational algorithm based on the volume averaging technique (VAT) is developed and solutions are obtained using the Galerkin method (GM). The goal is to extend applicability of the GM to the area of heat exchangers in order to provide a reliable benchmark for numerical calculations of conjugate heat transfer problems. Using the VAT, the computational algorithm is fast-running, but still able to present a detailed picture of temperature fields in air flow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient C d and Nusselt number Nu were compared with finite-volume method (FVM) results and with experimental data to verify the computational model. The comparison shows good agreement. The present results demonstrate that the selected Galerkin approach is capable to perform heat exchanger calculations where the thermal conductivity of the solid structure has to be taken into account.

Heat transfer conditions in flow across a bundle of cylindrical and ellipsoidal tubes

ABSTRACT Transient numerical simulations of fluid and heat flow are performed for a number of heat exchanger segments with cylindrical and ellipsoidal form of tubes in a staggered arrangement. Based on the recorded time distributions of velocity and temperature, time-average values of Reynolds number, drag coefficient, and Stanton number are calculated. The drag coefficient and the Stanton number are smaller for the ellipsoidal tubes than for the cylindrical tubes. With an increasing hydraulic diameter, the difference between the two forms of tubes diminishes. To validate the selected numerical approach, the calculated time-average values are compared with experimental data. The time-average values are further used to construct the drag coefficient and the Stanton number as polynomial functions of Reynolds number and hydraulic diameter. The polynomial functions obtained are to be used as input correlations for a heat exchanger integral model.

Accuracy of the Operator Splitting Technique for Two-Phase Flow With Stiff Source Terms

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.Copyright

NUMERICAL AND EXPERIMENTAL INVESTIGATION OF BACKDRAFT

The article describes full-scale backdraft experiments in a shipping container using methane as a fuel. Numerical modelling has followed the experimental setup. The numerical simulations show the initial gravity current, the ignition, the spreading of flame in the enclosure, the external fireball, and the subsequent decay. The Detached Eddy Simulation (DES) approach has been used to model turbulence. In order to describe the combustion process of the mixture from the local ignition to progressive deflagration, three separate combustion models have been implemented for laminar, low- and high-intensity turbulence flow regimes. The calculated ignition time is slightly shorter than the average ignition time observed in the experiments. The fire front progresses through the combustible mixture, generating a cloud of hot gases that are accelerated from the container into the external environment. The velocity increases up to 20 m/s. When the fire front reaches the door, combustion continues outside the enclosure as the fuel has been pushed through the door. The comparison between the calculated time history of relative pressure and the pressure sensor record shows that the numerical simulations slightly overpredict the flame front speed, with a stronger pressure pulse and higher temperatures than the observations.

Drag Coefficient and Stanton Number Behavior in Fluid Flow Across a Bundle of Wing-Shaped Tubes

Transient numerical simulations of fluid and heat flow were performed for eight heat exchanger segments with cylindrical and wing-shaped tubes in staggered arrangement. Their hydraulic diameters dh were from 0.5824 to 3.899cm for the cylindrical tubes, and from 0.5413 to 3.594cm for the wing-shaped tubes. Based on the recorded time distributions of velocity uf(t) and temperature Tf(t), time average Reynolds number Re¯, drag coefficient C¯d, and Stanton number St¯ were calculated. In general, the drag coefficient and the Stanton number are smaller for the wing-shaped tubes than for the cylindrical tubes. However, with an increasing hydraulic diameter, these differences between both forms of tubes diminish. The time average values were further used to construct the drag coefficient and the Stanton number as polynomial functions C¯d(dh,Re¯) and St¯(dh,Re¯).

A Different Approach to Vent Flow Calculations in Fire Compartments using the Critical Flow Condition

In enclosure fires, density-driven vent flow through an opening to the fire compartment is directly dependent on the state of the fire and the evacuation of smoke and hot gases. If a fire is strongly under-ventilated, there may be heavy production of flammable gases. If a sudden opening occurs, e.g., a window breaks or a fireman opens a door to the fire compartment, fresh air enters the compartment and mixes with hot gases, thus creating a flammable mixture that might ignite and create a backdraft. In this article, we consider the critical flow approach to solve the classical hydraulic equations of density-driven flows in order to determine the gravity controlled inflow in a shipping container full of hot unburnt gases. One-third of the container’s height is covered by the horizontal opening. For the initial condition, i.e., just before opening the hatch, zero velocity is prescribed everywhere. When the hatch is opened, the incoming air flows down to the container floor and the hot gas flows out. The interface in between them (the neutral plane) can move up like a free surface in internal flows, making it possible to use the techniques of open channel hydraulics devised by Pedersen [1]. In this article the critical flow condition, known from classical hydraulics, is used providing a new equation for the vent flow problem. Two flow correction coefficients are considered at the opening, taking into account the uneven distribution of velocity (α) and the effect of mixing and entrainment (C). The value of these coefficients is evaluated using computational fluid dynamics simulations and physical model results performed for the same geometry. Together, these two coefficients form the flow correction coefficient used in practical formulas for vent flow in fire protection engineering. These are known to have a little different values for different geometries and flow situations. The resulting flow coefficient varies slowly with the density difference, shows a small variation with geometry and compares well with previously published data.

Modeling of Forced Convection in an Electronic Device Heat Sink as Porous Media Flow

An algorithm for simulation of conjugate heat transfer used to find the most suitable geometry for an electronic chip heat sink is described. Applying Volume Averaging Theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, was accomplished with drag and heat transfer coefficients, which were taken from the available literature and inserted into a computer code. The example calculations were performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section. The comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows a good agreement with the experimental data. The calculated temperature fields reveal the local heat flow distribution and enable further improvements of the heat sink geometry.© 2002 ASME