Conjugate heat transfer analysis of bubble growth during flow boiling in a rectangular microchannel

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance CFD code NEK5000 [1]. The goal of the project is to develop a new two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) [2-3] previously developed at Argonne, but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2019. This report focuses on the FY2019 development and validation of the Conjugate Heat Transfer (CHT) model for the NEK-2P Two-Phase, Computational Fluid Dynamics (CFD) code. The NEK-2P CHT model calculates the coupled behavior of the fluid and solid domains. In the fluid domain NEK-2P calculates the vapor and liquid phase temperatures, velocities and mass fractions. In the solid domain only the temperatures are calculated. The fluid and solid domains are coupled with a heat flux boundary condition at the fluid-solid interface. The heat flux and the wall temperatures at the fluid-solid interface are updated using the NEK-2P wall heat-flux partitioning model. A wall heat flux boundary condition is also applied to the exterior surface of the solid domain. The CHT model validation was illustrated through the analysis of three of the Becker Critical Heat Flux (CHF) tests. Reasonably good agreement with measured data was obtained in predicting the CHF location and post CHF wall temperature behavior illustrating the ability of the NEK-2P CHT model to simulate the CHF phenomena for a wide range of thermal-hydraulic conditions. Apart from the CHT model development and validation, initial simulations were performed for the Virginia Tech. (VT) 3x3 bare rod bundle experiments including both cold and boiling flow simulations.

This study presents a novel, simplified model for the time-efficient simulation of transient conjugate heat transfer in round tubes. The flow domain and the tube wall are modeled in 1D and 2D, respectively and empirical correlations are used to model the flow domain in 1D. The model is particularly useful when dealing with complex physics, such as flow boiling, which is the main focus of this study. The tube wall is assumed to have external fins. The flow is vertical upwards. Note that straightforward computational fluid dynamics (CFD) analysis of conjugate heat transfer in a system of tubes, leads to 3D modeling of fluid and solid domains. Because correlation is used and dimensionality reduced, the model is numerically more stable and computationally more time-efficient compared to the CFD approach. The benefit of the proposed approach is that it can be applied to large systems of tubes as encountered in many practical applications. The modeled equations are discretized in space using the finite volume method, with central differencing for the heat conduction equation in the solid domain, and upwind differencing of the convective term of the enthalpy transport equation in the flow domain. An explicit time discretization with forward differencing was applied to the enthalpy transport equation in the fluid domain. The conduction equation in the solid domain was time discretized using the Crank–Nicholson scheme. The model is applied in different boundary conditions and the predicted boiling patterns and temperature fields are discussed.

<div class="section abstract"><div class="htmlview paragraph">Engine life and effectiveness can be improved with effective cooling. In designing and optimization process, simulation plays a vital role. The cooling mechanism of the air cooled engine is mostly dependent on the fin design of the cylinder head and block. The heat is conducted through the engine parts and convected to air through the surfaces of the fins. Insufficient removal of heat from engine will lead to high thermal stresses and lower engine efficiency.</div><div class="htmlview paragraph">To simulate the cooling mechanism of the naturally aspirated engines, Three Dimensional CFD analyses with the SC/Tetra code is done. This gives a good scope in analyzing the existing fin design and proposes the optimized design. The boundary conditions required for carrying the CFD analysis such as the heat transfer co-efficient, cylinder temperature, has been generated by carrying One Dimensional engine cycle simulation. Engine assembly is imported into SC/Tetra code and conjugate heat transfer analysis is conducted to understand the effectiveness of heat transfer through the fins. Conjugate heat transfer analysis provides a clear view on heat transfer through solid and fluid domain. Detailed study on the heat transfer of the cylinder head and block has been done. Fin increases the convective heat transfer rate. A detailed parametric study of heat transfer on fins is done and Theoretical analysis has been carried out to achieve an optimal fin design for effective heat transfer. Theoretical analysis aids in speeding up the design optimization problem. Conjugate heat transfer analysis of engine assembly with modified fins is performed.</div><div class="htmlview paragraph">The results of heat transfer through the existing fins and modified fins are compared. There is a considerable increase in the heat transfer with the modified fins. A methodology for optimizing the fin heat transfer and fin performance is proposed.</div></div>

In this study, the effects of the thermal boundary conditions at the engine walls on the predictions of Large-Eddy Simulations (LES) of a motored Internal Combustion Engine (ICE) were examined. Two thermal boundary condition cases were simulated. One case used a fixed, uniform wall temperature, which is typically used in conventional LES modeling of ICEs. The second case utilized a Conjugate Heat Transfer (CHT) modeling approach to obtain temporally and spatially varying wall temperature. The CHT approach solves the coupled heat transfer problem between fluid and solid domains. The CHT case included the solid valves, piston, cylinder head, cylinder liner, valve seats, and spark plug geometries. The simulations were validated with measured bulk flow, near-wall flow, surface temperature, and surface heat flux. The LES quality of both simulations was also discussed. The CHT results show substantial spatial, temporal, and cyclic variability of the wall heat transfer. The surface temperature dynamics obtained from the CHT model compared well with measurements during the compression stroke, but the absolute magnitude was 5 K (or 1.4%) off and the prediction of the drop in temperature after top dead center suffered from temporal resolution limitations. Differences in the predicted flow and temperature fields between the uniform surface temperature and CHT simulations show the impact of the surface temperature on bulk behavior.

Investigations of the conjugate heat transfer and windage effect in stepped labyrinth seals

A conjugate heat transfer simulation of air in a rectangular cooling channel with 45-deg ribs is presented in this paper. The test channel length is 400mm and the ratio of width to height is 1. The hydraulic diameter of the channel is 40mm and the thickness of channel wall is 3mm. The rib height is 1.9mm and the distance between nearby ribs is 19mm. The flow field and the temperature field in the solid channel are obtained by using ANSYS CFX. An energy source is added in the solid domain to simulate the Low-Voltage High-Current heating method in the experiment. The GGI method is adopted for the mesh connection between the fluid domain and solid domain. The SST turbulence model and automatic wall function in ANSYS CFX are used to simulate the flow and heat transfer in near-wall region. The numerical results show great agreement with the experimental data. The temperature distribution on the channel outer wall is shown and analyzed. The Nusselt number field on the channel wall is shown and illustrated by the flow field shown by the Vortex Core Technology. There are four secondary flow vortex cores between ribs in near wall region and a strong secondary flow can be seen in main flow region. The angled ribs leads to the unbalanced temperature and Nusselt number field on the outer wall and the inner wall of the channel respectively. The distribution law of the Nusselt number on inner wall is not similar with the one of temperature on the outer wall. But the overall distribution of outer wall temperature field is more homogeneous compared with that of the inner wall Nusselt number. Some recommendations for optimization are given based on the flow field and Nusselt number distribution.

A numerical procedure is presented to simulate conjugate heat transfer in generalized coordinates and used in some typical turbomachinery applications. The discretized equations at the solid-fluid interface are obtained using energy conservation principles and computational nodes are placed exactly on that interface, thus yielding the corresponding temperatures directly, without the need for inter- or extrapolation from neighboring nodes. The temperature field over both the fluid and the solid domains is computed implicitly, i.e., without iterating between the two. The computer code used for the computations is based on the finite-volume method and the SIMPLE algorithm along with various turbulence models. Both a version of the low-Reynolds-number k-ϵ model suitable for recirculating flows with heat transfer and the standard k-ϵ have been used, with suitable modifications. The successful treatment of the boundary condition at the solid-fluid interface has been verified by comparing against analytical solutions for laminar, conjugate heat transfer over a flat plate of finite thickness. The agreement was found to be quite good, when temperature profiles were compared at various streamwise distances from the leading edge. Further applications have been sought in the field of turbomachinery and as the main test case, the turbulent flow and heat transfer in labyrinth seals has been selected. Two such configurations have been considered, a straight-through and a stepped labyrinth seal. Results were compared with measured data obtained for the same configurations and the agreement was found to be satisfactory. In addition, the applicability of the current method to a film-cooling problem and the merits of it are being demonstrated.

Use of the method of manufactured solutions for the verification of conjugate heat transfer solvers

Microchannel boiling heat transfer offers a promising solution to address extreme high heat flux in miniaturized and high-density integrated electronic devices. In this work, we performed numerical studies to elucidate the complex flow boiling process in a square microchannel using the open-source platform OpenFOAM. The governing equations of the two-phase flow was solved based on the finite volume framework, and the surface tension together with phase change models were incorporated to study the wettability and conjugate heat transfer in the microchannel. First, the stability of the liquid film shows that smaller contact angles lead to thicker and stable liquid films near the solid wall, while larger contact angles result in thinner and fragile films. Second, the heat transfer, represented by the dimensionless parameter Nu, shows that smaller contact angles result in higher and more uniform distribution of Nu. The velocity gradient causes the Nu to be higher for the sidewalls than for the bottom wall. The contact angle also affects the peak value of Nu. Small contact angles result in large solid wall temperature gradients and more efficient heat transfer. Finally, the simulation results show that smaller thermal conductivity of the solid results in larger temperature gradient in the flow direction, implying that the conjugate heat transfer is less efficient. Overall, the present numerical findings provide useful guidance for efficient thermal management in electronic devices.

Conjugate heat transfer investigation of cooled turbine using the preconditioned density-based algorithm

In this work, we numerically study the three-dimensional conjugate mixed convection heat transfer in a horizontal annulus equipped by longitudinal and transversal fins attached on its internal surface of outer cylinder. The external pipe and fins are heated by an electrical current passing through their small thickness while the inner pipe is kept adiabatic. We investigate the effects of adding longitudinal and transversal fins on the fluid dynamic and the heat transfer performances. The number of longitudinal fins varies from two to eight fins while the number of transvers ones is equal to four. The convection in the fluid domain is conjugated to thermal conduction in the pipes and fins solid thickness. The physical properties of the fluid are thermal dependent and the heat losses from the external pipe surface to the surrounding environment are taken account. The model equations of continuity, momenta and energy are numerically solved by the finite volume method with a second order spatiotemporal discretization. The Prandtl, the Reynolds and the Grashof numbers are fixed at 8.082, 399.02 and 12801 respectively. The obtained results showed that the axial Nusselt number increases with the increasing of number of fins. Moreover, the longitudinal fins configuration showed a more significant improvement in heat transfer than that of the transverse fins.

A combined combustion and conjugate heat transfer analysis of a hybrid draft biomass cookstove

<div class="section abstract"><div class="htmlview paragraph">In the last decades numerical simulations have become reliable tools for the design and the optimization of silencers for internal combustion engines. Different approaches, ranging from simple 1D models to detailed 3D models, are nowadays commonly applied in the engine development process, with the aim to predict the acoustic behavior of intake and exhaust systems. However, the acoustic analysis is usually performed under the hypothesis of infinite stiffness of the silencer walls. This assumption, which can be regarded as reasonable for most of the applications, can lose validity if low wall thickness are considered. This consideration is even more significant if the recent trends in the automotive industry are taken into account: in fact, the increasing attention to the weight of the vehicle has lead to a general reduction of the thickness of the metal sheets, due also to the adoption of high-strength steels, making the vibration of the components a non negligible issue. In this work, a CFD compressible solver capable to describe the fluid-structure interaction problem has been implemented and validated. The approach is based on the adoption of two different domains for the solution of the governing equation for the fluid and for the structure. At each time-step, the pressure field computed on the fluid domain is used as an input for the solution of the displacement of the structure. A mesh motion strategy is adopted, for both the fluid and solid domain, in order to describe the deformation of the walls. The solver has been applied for the simulation of the acoustic behavior of a simple expansion chamber, considering different wall thickness, in order to investigate the effect of the structure vibration on the transmission loss. Results have been validated resorting to experimental measurements available in the literature.</div></div>

Conjugate heat transfer (CHT) considers the simultaneous solution of heat transfer in adjacent solid and fluid domains. If solved with a partitioned approach, temperature and heat flux are exchanged to achieve a thermal equilibrium at the interface. Gauss-Seidel iterations, however, are only stable for a limited range of Biot numbers because temperature and heat flux are exchanged unmodified. In order to extend the stability range of Gauss-Seidel iterations, static relaxation, Aitken relaxation or quasi-Newton methods can be used. These methods are tested on a heated flat plate problem, both in steady state and transient simulations, and their convergence behaviour is analysed. Using temperature as input for the fluid solver and heat flux as input for the solid solver converges best for steady state simulations, while the opposite is most stable for transient cases. Furthermore, the quasi-Newton method converges slightly better than the relaxation methods in transient simulations with rapid changes at the interface.

Giant unilamellar vesicles (GUVs) composed of different phospholipid binary mixtures were studied at different temperatures, by a method combining the sectioning capability of the two-photon excitation fluorescence microscope and the partition and spectral properties of 6-dodecanoyl-2-dimethylamino-naphthalene (Laurdan) and Lissamine rhodamine B 1,2-dihexadecanoyl- sn-glycero-3-phosphoethanolamine ( N-Rh-DPPE). We analyzed and compared fluorescence images of GUVs composed of 1,2-dilauroyl- sn-glycero-3-phosphocholine/1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DLPC/DPPC), 1,2-dilauroyl- sn-glycero-3-phosphocholine/1,2-distearoyl- sn-glycero-3-phosphocholine (DLPC/DSPC), 1,2-dilauroyl- sn-glycero-3-phosphocholine/1,2-diarachidoyl- sn-glycero-3-phosphocholine (DLPC/DAPC), 1,2-dimyristoyl- sn-glycero-3-phosphocholine/1,2-distearoyl- sn-glycero-3-phosphocholine (DMPC/DSPC) (1:1 mol/mol in all cases), and 1,2-dimyristoyl- sn-glycero-3-phosphoethanolamine/1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPE/DMPC) (7:3 mol/mol) at temperatures corresponding to the fluid phase and the fluid-solid phase coexistence. In addition, we studied the solid-solid temperature regime for the DMPC/DSPC and DMPE/DMPC mixtures. From the Laurdan intensity images the generalized polarization function (GP) was calculated at different temperatures to characterize the phase state of the lipid domains. We found a homogeneous fluorescence distribution in the GUV images at temperatures corresponding to the fluid region for all of the lipid mixtures. At temperatures corresponding to phase coexistence we observed concurrent fluid and solid domains in the GUVs independent of the lipid mixture. In all cases the lipid solid domains expanded and migrated around the vesicle surface as we decreased the temperature. The migration of the solid domains decreased dramatically at temperatures close to the solid-fluid→solid phase transition. For the DLPC-containing mixtures, the solid domains showed line, quasicircular, and dendritic shapes as the difference in the hydrophobic chain length between the components of the binary mixture increases. In addition, for the saturated PC-containing mixtures, we found a linear relationship between the GP values for the fluid and solid domains and the difference between the hydrophobic chain length of the binary mixture components. Specifically, at the phase coexistence temperature region the difference in the GP values, associated with the fluid and solid domains, increases as the difference in the chain length of the binary mixture component increases. This last finding suggests that in the solid-phase domains, the local concentration of the low melting temperature phospholipid component increases as the hydrophobic mismatch decreases. At the phase coexistence temperature regime and based on the Laurdan GP data, we observe that when the hydrophobic mismatch is 8 (DLPC/DAPC), the concentration of the low melting temperature phospholipid component in the solid domains is negligible. This last observation extends to the saturated PE/PC mixtures at the phase coexistence temperature range. For the DMPC/DSPC we found that the nonfluorescent solid regions gradually disappear in the solid temperature regime of the phase diagram, suggesting lipid miscibility. This last result is in contrast with that found for DMPE/DMPC mixtures, where the solid domains remain on the GUV surface at temperatures corresponding to that of the solid region. In all cases the solid domains span the inner and outer leaflets of the membrane, suggesting a strong coupling between the inner and outer monolayers of the lipid membrane. This last finding extends previous observations of GUVs composed of DPPE/DPPC and DLPC/DPPC mixtures (Bagatolli and Gratton, 2000, Biophys. J. 78:290–305).