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Register a new userTopology Optimization of Two Fluid Heat Exchangers
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Lukas Christan H{o}gh{o}j
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A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluid flows. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated fluids, as well as a minimum wall thickness between them. Under the assumption of laminar steady flow, the two fluids are modelled separately, but in the entire computational domain using the Brinkman penalization technique for ensuring negligible velocities outside of the respective fluid subdomains. The heat transfer is modelled using the convection-diffusion equation, where the convection is driven by both fluid flows. A stabilized finite element discretization is used to solve the governing equations. Results are presented for two different problems: a two-dimensional example illustrating and verifying the methodology; and a three-dimensional example inspired by shell-and-tube heat exchangers. The optimized designs for both cases show an improved heat transfer compared to the baseline designs. For the shell-and-tube case, the full freedom topology optimization approach is shown to yield performance improvements of up to 113% under the same pressure drop.
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A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence assumption. A test case of application in terms of the turbulent rough wall channel flow shows that a considerable reduction of the objective function can be obtained by this method. The transformation from porous media to solid walls may have important effect on the optimization results.
We develop a two-fluid model (TFM) for simulation of thermal transport coupled to particle migration in flows of non-Brownian suspensions. Specifically, we propose a closure relation for the inter-phase heat transfer coefficient of the TFM as a function of the particle volume fraction, particle diameter, magnitude of the particle phases shear-rate tensor, and the thermal diffusivity of the particles. The effect of shear-induced migration in the particulate phase is captured through the use of state-of-the-art rheological closures. We validate the proposed interphase heat transfer coupling by calibrating it against previous experiments in a Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, the shear and thermal gradients aid each other to increase the particle migration when temperature difference between the inner and outer walls, $Delta T = T_mathrm{in} - T_mathrm{out} < 0$. Meanwhile, for $Delta T > 0$, the shear and thermal gradients oppose each other, resulting in diminished particle migration, and a more uniform distribution of the particulate phase across the gap. Within the TFM framework, we identify the origin and functional form of a thermo-rheological migration force that rationalizes our observations. We also investigate the interplay of shear and thermal gradients in the presence of recirculating regions in an eccentric Couette cell (with offset axis and rotating inner cylinder). Simulations reveal that the system Nusselt number increases with the eccentricity $E$ for $Delta T > 0$, but a maximum occurs for $Delta T < 0$ at $E = 0.4$. This observation is explained by showing that, for $E>0.4$ and $Delta T < 0$, significant flow recirculation enhances particle inhomogeneity, which in turn reduces heat transfer in the system (compared to $Delta T > 0$).
We numerically investigate turbulent Rayleigh-Benard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $Ra=10^8$, Prandtl number $Pr=4.38$, and Weber number $We=5$. We vary the relative thickness of the upper layer between $0.01 le alpha le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 le lambda_k le 10$. Two flow regimes are observed: In the first regime at $0.04lealphale0.96$, convective flows appear in both layers and $Nu$ is not sensitive to $alpha$. In the second regime at $alphale0.02$ or $alphage0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $Nu$ is sensitive to $alpha$. To predict $Nu$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann-Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $Nu$ and for the temperature at the interface well agree with our numerical results and previous experimental data.
This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can be described by the surface Navier-Stokes equations defined on 2-manifolds or two-dimensional manifolds, where the elementary tangential calculus is implemented in terms of exterior differential operators expressed in a Cartesian system. Based on the topology optimization model for fluidic flows with porous medium filling the design domain, an artificial Darcy friction is added to the area force term of the surface Navier-Stokes equations and the physical area forces are penalized to eliminate their existence in the fluidic regions and to avoid the invalidity of the porous medium model. Topology optimization for steady and unsteady surface flows can be implemented by iteratively evolving the impermeability of the porous medium on the 2-manifolds, where the impermeability is interpolated by the material density derived from a design variable. The related partial differential equations are solved by using the surface finite element method. Numerical examples have been provided to demonstrate this topology optimization approach for surface flows, including the boundary velocity driven flows, area force driven flows and convection-diffusion flows.
We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $Lambda$ to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier--Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent $theta=2.9pm0.2$.
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