Computation of Radiation Heat Transfer in Aeroengine Combustors

In this report the highlights of the research completed for the NASA are summarized. This research has been completed in the form of two Ph.D. theses by Chai (1994) and Parthasarathy (1996). Readers are referred to these theses for a complete details of the work and lists of references. In the following sections, first objectives of this research are introduced, then the finite-volume method for radiation heat transfer is described, and finally computations of radiative heat transfer in non-gray participating media is presented

Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [ P. Asinari and I. V. Karlin Phys. Rev. E 79 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially

Aerothermal modeling program, phase 2

The main objectives of the Aerothermal Modeling Program, Phase 2 are: to develop an improved numerical scheme for incorporation in a 3-D combustor flow model; to conduct a benchmark quality experiment to study the interaction of a primary jet with a confined swirling crossflow and to assess current and advanced turbulence and scalar transport models; and to conduct experimental evaluation of the air swirler interaction with fuel injectors, assessments of current two-phase models, and verification the improved spray evaporation/dispersion models

Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device

The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves, the Kelvin-Helmholtz and rotational interchange instabilities. A general linear dispersion relation for partially ionized collisional plasmas including these modes is derived and analyzed. For LAPD relevant profiles including strongly driven flows it is found that all three modes can have comparable growth rates and frequencies. Detailed comparison with solutions of the analytic dispersion relation demonstrates that BOUT accurately reproduces all characteristics of linear modes in this system.Comment: Published in Physics of Plasmas, 17, 102107 (2010

On the transient thermal response of thin vapor chamber heat spreaders: governing mechanisms and performance relative to metal spreaders

Vapor chambers can offer a passive heat spreading solution for thermal management in electronics applications ranging from mobile devices to high-power servers. The steady-state operation and performance of vapor chambers has been extensively explored. However, most electronic devices have inherently transient operational modes. For such applications, it is critical to understand the transient thermal response of vapor chamber heat spreaders and to benchmark their transient performance relative to the known behavior of metal heat spreaders. This study uses a low-cost, 3D, transient semi-analytical transport model to explore the transient thermal behavior of thin vapor chambers. We identify the three key mechanisms that govern the transient thermal response: (1) the total thermal capacity of the vapor chamber governs the rate of increase of the volume-averaged mean temperature; (2) the effective inplane diffusivity governs the time required for the spatial temperature profile to initially develop; and (3) the effective in-plane conductance of the vapor core governs the range of the spatial temperature variation, and by extension, the steady-state performance. An experiment is conducted using a commercial vapor chamber sample to confirm the governing mechanisms revealed by the transport model; the model accurately predicts the experimental measurements. Lastly, the transient performance of a vapor chamber relative to a copper heat spreader of the same external dimensions is explored as a function of the heat spreader thickness and input power. The mechanisms governing the transient behavior of vapor chambers are used to explain the appearance of key performance thresholds beyond which performance is superior to the copper heat spreader. This work provides a foundation for understanding the benefits and limitations of vapor chambers relative to metal heat spreaders in transient operation and may inform the design of vapor chambers for improved transient performance

On the Transient Thermal Response of Thin Vapor Chamber Heat Spreaders: Optimized Design and Fluid Selection

Vapor chambers provide highly effective heat spreading to assist in the thermal management of elec- tronic devices. Although there is a significant body of literature on vapor chambers, most prior research has focused on their steady-state response. In many applications, electronic devices generate inherently transient heat loads and, hence, it is critical to understand the transient thermal response of vapor cham- bers. We recently developed a semi-analytical transport model that was used to identify the key mech- anisms that govern the thermal response of vapor chambers to transient heat inputs (Int. J. Heat Mass Trans. 136 (2019) 995–1005). The current study utilizes this understanding of the governing mechanisms to develop design guidelines for improving the performance of vapor chambers under transient operating conditions. Two key aspects of vapor chamber design are addressed in this study: first, a parametric op- timization of the wall, wick, and vapor-core thicknesses; and second, the selection of the working fluid. A protocol is demonstrated for selecting these parameters given the external vapor chamber envelope di- mensions and boundary conditions. The study helps provide a framework for designing vapor chambers subject to transient heat loads, and to differentiate such design from the practices followed traditionally for steady-state operation

A Validated Time-Stepping Analytical Model for 3D Transient Vapor Chamber Transport

Advances in the computational performance of electronic devices have created a clear need for improved methods of passive thermal management. This has led to renewed interest in the use of vapor chambers as heat spreaders in applications ranging from mobile devices to high-performance-computing and power electronics systems. While there has been significant effort to develop vapor chambers for these applications, their designs have largely relied on steady-state analyses and performance prediction. In many applications, however, the heat load is inherently transient in nature. Heat spreader design must consider transient performance in response to these use-case scenarios. While detailed numerical models of transient vapor chamber operation have been developed, a transient modeling approach with low computational cost is needed for parametric study and quick assessment of vapor chamber performance in system-level models. In the current work, a low-cost, transient vapor chamber model is developed targeting the geometries and operating conditions typical of thermal management applications. The model considers mass, momentum, and energy transport in the vapor chamber wall, wick, and vapor core as well as phase change at the wick-vapor interface. The governing equations are simplified to a system of first-order differential equations based on a scaling analysis and assuming a functional form for the temperature profile along the thickness dimension. The errors in the temperature and pressure fields due to these simplifying assumptions are estimated for a wide range of operating conditions. These estimates indicate low errors in the model predictions over the range considered. For two example cases, the model predictions are compared to a finite-volume-based numerical model. Any deviation from the numerical model prediction is on the same order as the errors estimated based on the simplifying assumptions. The time-stepping analytical model is demonstrated to have a computational cost reduction of three to four orders of magnitude compared to the finite-volume based model

Working-Fluid Selection for Minimized Thermal Resistance in Ultra-Thin Vapor Chambers

The behavior of a vapor chamber is strongly coupled to the thermophysical properties of the working fluid within. It is well known that these properties limit the maximum power (heat load) at which a vapor chamber can operate, due to incidence of the capillary limit. At this limit, the available capillary pressure generated within the wick structure balances the total pressure drop incurred along the path of fluid flow within the wick. A common figure of merit prioritizes working fluids that maximize this capillary-limited operating power. The current work explores working fluid selection for ultra-thin vapor chambers based on a thermal performance objective, rather than for maximized power dissipation capability. A working fluid is sought in this case that provides the minimal thermal resistance while ensuring a capillary limit is not reached at the target operating power. A resistance-network-based model is used to develop a simple analytical relationship for the vapor chamber thermal resistance as a function of the working fluid properties, operating power, and geometry. At small thicknesses, the thermal resistance of vapor chambers becomes governed by the saturation temperature gradient in the vapor core, which is dependent on the thermophysical properties of the working fluid. To satisfy the performance objective, it is shown that the choice of working fluid cannot be based on a single figure of merit containing only fluid properties. Instead, the functional relationship for thermal resistance must be analyzed taking into account all operating and geometric parameters, in addition to the thermophysical fluid properties. Such an approach for choosing the working fluid is developed and demonstrated

Screening effects in flow through rough channels

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome from numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, when inertial effects become relevant, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. In addition, we find that, while the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case, i.e., ``the rougher the better''. We show that this complex behavior is closely related with the presence and relative intensity of recirculation zones in the reentrant regions of the rough channel.Comment: 4 pages, 5 figure