Neil Zuckerman

Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling

Publisher Summary This chapter presents a discussion on jet impingement heat transfer. The chapter describes the applications and physics of the flow and heat transfer phenomena, available empirical correlations and values they predict, and numerical simulation techniques and results of impinging jet devices for heat transfer. The relative strengths and drawbacks of the Reynolds stress model, algebraic stress models, shear stress transport, and v 2 f turbulence models for impinging jet flow and heat transfer are compared in the chapter. The chapter provides select model equations as well as quantitative assessments of model errors and judgments of model suitability. The review of recent impinging jet research publications identified a series of engineering research tasks that are important for improving the design and resulting performance of impinging jets: (1) clearly resolve the physical mechanisms by which multiple peaks occur in the transfer coefficient profiles, and clarify which mechanism(s) dominate in various geometries and Reynolds number regimes, (2) develop a turbulence model, and associated wall treatment if necessary, that reliably and efficiently provides time-averaged transfer coefficients, (3) develop alternate nozzle and installation geometries that provide higher efficiency, meaning improved Nu profiles at either a set flow or set blower power, and (4) further explore the effects of jet interference in jet array geometries, both experimentally and numerically. This includes improved design of exit pathways for spent flow in array installations.

Impingement Heat Transfer: Correlations and Numerical Modeling

Uses of impinging jet devices for heat transfer are described, with a focus on cooling applications within turbine systems. Numerical simulation techniques and results are described, and the relative strengths and drawbacks of the κ-e, κ-ω, Reynolds stress model, algebraic stress models, shear stress transport, and ν2f turbulence models for impinging jet flow and heat transfer are compared.

Radial slot jet impingement flow and heat transfer on a cylindrical target

To better understand and facilitate design of an impinging jet device, the heat transfer on a cylindrical target exposed to radial impinging slot jets was investigated using numerical methods. Numerical models were created to test the performance of the shear stress transport, standard and realizable k-e, v 2 f, and Reynolds stress model turbulence models vs published test data. Based on the validation study, the v 2 f model was ultimately selected for further work. Models were then constructed to simulate a cylinder exposed to a radial array of slot jets. Parametric variations were conducted to produce information about the influence of jet speed, number of nozzles, and other independent design variables, upon heat transfer. The number of nozzles was varied from 2 to 8, jet Reynolds number Re from 5,000 to 80,000, and target diameter from 5 to 10 times the nozzle hydraulic diameter. The physics of the flows are discussed, finding, for example, that interaction of adjacent opposed wall jets caused a static pressure rise and resulted in flow separation on the surface of the cylindrical target. This separation and the fountain flow between the two wall jets greatly influenced the local heat transfer, causing a rise in Nusselt number Nu of an order of magnitude. The resulting average Nu values varied from 19 to 217 and were condensed into a correlation equation incorporating the ratio of nozzle width to target diameter, number of nozzles, Reynolds number, and Prandtl number.

The Relationship Between the Distributions of Slot-Jet-Impingement Convective Heat Transfer and the Temperature in the Cooled Solid Cylinder

A conjugate heat transfer investigation was conducted to better understand the effects of an impinging radial slot jet cooling device on both the heat transfer rates and temperature fields in the fluid, and especially in the cylindrical solid cooled by this device. The study used numerical methods to model a configuration in which a set of four radially positioned slot jets cooled a cylindrical steel target using air with a jet Reynolds number of 20,000. A steady-state v 2 f Reynolds averaged Navier-Stokes model was used with a representative two-dimensional section of the axisymmetric target and flow domain. Boundary conditions, heat intensity, target wall thickness, and thermal conductivity were varied to study the effects of the impingement cooling on the temperature distribution in the solid. For Biot (Bi) numbers between 0.0025 and 0.073, temperatures in the solid were clearly affected by lateral conduction, and temperature variation in the solid was an order of magnitude smaller than the variation in the surface heat transfer coefficient. For the case of constant heat flux, the area-weighted standard deviation in the solid temperature was found to correlate well with the dimensionless parameter Z ≡ Bi(d/t eq)2, where d is the cylinder diameter and t eq is the equivalent wall thickness, and a correlation equation was developed.

Atomistic Visualization of Anisotropic Wave Propagation in Crystals

Presented here is a new molecular dynamics simulation approach for visualizing multidimensional acoustic wave-packet propagation in anisotropic materials. This approach allows examination of longitudinal wave propagation in a selected frequency range and may also be extended to track transverse motions. The obtained results agree with analytical predictions and experimental measurements of quasilongitudinal wave front propagation in the literature. Additionally, spectral analysis reveals minor levels of frequency redistribution as the wave packet propagates, which is indicative of phonon-phonon scattering. The present approach provides new capabilities for phonon-focusing studies and offers an alternative to existing experimental and Monte Carlo techniques used for these studies.

Combined Kinetic Monte Carlo—Molecular Dynamics Approach for Modeling Phonon Transport in Quantum Dot Superlattices

A new kinetic Monte Carlo method for modeling phonon transport in quantum dot superlattices is presented. The method uses phonon scattering phase functions and cross sections to describe collisions between phonons and quantum dots. The phase functions and cross sections are generated using molecular dynamics simulation, which is capable of including atomistic effects otherwise unavailable in Monte Carlo approaches. The method is demonstrated for a test case featuring a Si-Ge quantum dot superlattice, and the model is compared against published experiments. It is found that molecular dynamics-derived cross sections must be weighted by diffuse mismatch model-type weighting factors in order to satisfy detailed balance considerations. Additionally, it is found that thin alloy “base layer” films strongly reduce thermal conductivity in these systems and must be included in the modeling to obtain agreement with published experimental data.

Monte Carlo Modeling of Phonon Transport Using Scattering Phase Functions

The calculation of heat transport in nonmetallic materials at small length scales is important in the design of thermoelectric and electronic materials. New designs with quantum dot superlattices (QDS) and other nanometer-scale structures can change the thermal conductivity in ways that are difficult to model and predict. The Boltzmann Transport Equation can describe the propagation of energy via mechanical vibrations in an analytical fashion but remains difficult to solve for the problems of interest. Numerical methods for simulation of propagation and scattering of high frequency vibrational quanta (phonons) in nanometer-scale structures have been developed but are either impractical at micron length scales, or cannot truly capture the details of interactions with nanometer-scale inclusions. Monte Carlo (MC) models of phonon transport have been developed and demonstrated based on similar numerical methods used for description of electron transport [1-4]. This simulation method allows computation of thermal conductivity in materials with length scales LX in the range of 10 nm to 10 μm. At low temperatures the model approaches a ballistic transport simulation and may function for even larger length scales.© 2008 ASME

Atomistic Visualization of Ballistic Phonon Transport

Heat transfer in solid materials at short time scales, short length scales, and low temperatures is governed by the transport of ballistic phonons. In anisotropic crystals, the energy carried by these phonons is strongly channeled into well-defined directions in a phenomenon known as phonon focusing. Presented here is a new molecular dynamics simulation approach for visualizing acoustic phonon focusing in anisotropic crystals. An advantage of this approach over experimental phonon imaging techniques is that it allows examination of phonon propagation at selected modes and frequencies. The spatial, mode, and frequency dependence of ballistic energy transport gained with this approach will be useful for understanding heat transfer issues in high frequency electronics and short time scale laser-material interactions.Copyright

Dependent Scattering of Acoustic Phonons From Particles Embedded in an Anisotropic Medium

Dependent scattering of acoustic phonons by multiple nanometer-scale inclusions in anisotropic media is investigated using a new molecular dynamics simulation technique. The spectral-directional characteristics of the scattering are found by calculation of three-dimensional scattering phase functions and cross sections for inclusions of varying sizes in various spatial arrangements. The technique enables computation of the effects of reflected wave interference and sequential scattering, mode conversion, lattice strain, elastic anisotropy, and atomic-scale granularity on acoustic phonon scattering from structured inclusions. The results will improve understanding and prediction of heat transfer in quantum-dot superlattices and other engineered thermal materials with nanometer-scale structures.Copyright