Megan F. Watkins 1,2 Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27606 e-mail: mfwatki2@ncsu.edu Yesaswi N. Chilamkurti Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27606 e-mail: ynchilam@ncsu.edu Richard D. Gould Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27606 e-mail: gould@ncsu.edu Analytic Modeling of Heat Transfer to Vertical Dense Granular Flows The high packing fractions of dense granular flows make them an attractive option as a heat transfer fluid or thermal energy storage medium for high temperature applications. Previous works studying the heat transfer to dense flows have identified an increased thermal resistance adjacent to the heated surface as a limiting factor in the heat transfer to a discrete particle flow. While models exist to estimate the heat transfer to dense flows, no physics-based model describing the heat transfer in the near-wall layer is found; this is the focus of the present study. Discrete element method (DEM) simulations were used to examine the near-wall flow characteristics, identifying how parameters such as the near-wall packing fraction and number of particle-wall contacts may affect the heat transfer from the wall. A correlation to describe the effective thermal conductivity (ETC) of the wall-adjacent layer (with thickness of a particle radius) was derived based on par- allel thermal resistances representing the heat transfer to particles in contact with the wall, particles not in contact with the wall, and void spaces. Empirical correlations based on DEM results were developed to estimate the near-wall packing fraction and number of particle-wall contacts. The contribution from radiation was also incorporated using a simple enclosure analysis. The ETC correlation was validated by incorporating it into dense flow models for chute flows and cylindrical flows and comparing with the experi- mental data for each. [DOI: 10.1115/1.4045311] Introduction The heat transfer to particulate flows has been studied for deca- des due to its various industrial applications, including drying and heating of particulates such as food grains and coal. More recently, the heat transfer characteristics of particle-based heat transfer fluids are of interest for concentrated solar power tower applications, as particles offer many intriguing characteristics over the current fluids. The present work studies the heat transfer behavior of internal gravity-driven dense granular flows. Internal granular flows are characterized by shearing at the wall boundaries and are driven by particle collisions. Dense flows dem- onstrate high packing fractions of approximately 60%. Studies of the heat transfer in a static particle bed indicate that the packing fraction plays a primary role in the heat transfer capabilities of the bed, as the primary pathway for heat transfer is through the inter- stitial gas [1]. Since the interstitial gas typically exhibits low ther- mal conductivity compared with the particle material, the effective thermal conductivity of a bed decreases with decreasing packing fraction. Therefore, the high packing fraction of dense flows makes them a viable option as a heat transfer fluid. While the heat transfer characteristics of static particle beds have been studied quite extensively both experimentally (for example, Refs. [2–4]) and theoretically (as summarized in Ref. [1]), the heat transfer to dense flows has been less widely studied. Sullivan and Sabersky [5] provided one of the pioneering works in the field with their experimental and theoretical analysis of the heat transfer to a vertical chute flow. Using a small rectan- gular cross section with a single heated wall, they examined the variation in the heat transfer measured for different particles types, particles sizes, and flowrates. In an attempt to understand the significance of the discrete nature of the flow, they compared their experimental results with an analytic solution for a contin- uum plug flow in their setup. Their experimental results did not agree with the results predicted by the continuum solution; instead, the granular flows demonstrated inferior heat transfer per- formance, which was attributed to the discrete nature of the flow and the discrete interaction of the particles with the heated wall. The analytic solution was modified to incorporate an increased thermal contact resistance at the heated wall, which accounted for reduced heat transfer due to a more structured arrangement of par- ticles adjacent to a surface. The contact resistance was represented as a thin air gap a fraction of a particle diameter thick (0.085 in their case) and was assumed constant for all test cases. The result- ing semi-empirical correlation relating the Nusselt number with the P eclet number showed better agreement with their experimen- tal results. Natarajan and Hunt [6] expanded upon the work of Sul- livan and Sabersky, studying longer heated lengths and higher flowrates. Their experimental results demonstrated similar trends to those observed by Sullivan and Sabersky for low velocity, high density flows; namely, an increasing Nusselt number with increas- ing P eclet number. At higher flowrates, however, Natarajan and Hunt observed a critical point after which the Nusselt number decreased and plateaued. The semi-empirical model developed by Sullivan and Sabersky captured the results observed for low velocity flows but was unable to capture the decrease observed at higher flowrates. The deviation from the model at higher flowrates was explained by recognizing that the density of the flow adjacent to the wall varies with flowrate, rendering the constant contact resistance assumption of Sullivan and Sabersky invalid when con- sidering a wide range of flowrates. Spelt et al. [7], Patton et al. [8], and Ahn [9] studied the heat transfer to inclined chute flows over a wide range of flowrates. Similar to Natarajan and Hunt, their results displayed a critical point after which the Nusselt number began to decrease with increasing P eclet number. Once again, the model developed by Sullivan and Sabersky captured the trends observed at lower flow- rates but was unable to capture the decrease observed at higher flowrates. It is important to note that the best agreement with the 1 Corresponding author. 2 Present address: Brayton Energy, LLC, Hampton, NH 03842. Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 28, 2019; final manuscript received October 13, 2019; published online December 9, 2019. Assoc. Editor: Evelyn Wang. Journal of Heat Transfer FEBRUARY 2020, Vol. 142 / 022103-1 Copyright V C 2020 by ASME Downloaded from http://asmedigitalcollection.asme.org/heattransfer/article-pdf/142/2/022103/6459931/ht_142_02_022103.pdf by guest on 24 October 2023