9 research outputs found
Topology Optimization of Two Fluid Heat Exchangers
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
A topology optimization method in rarefied gas flow problems using the Boltzmann equation
This paper presents a topology optimization method in rarefied gas flow problems to obtain the optimal structure of a flow channel as a configuration of gas and solid domains. In this paper, the kinetic equation, the governing equation of rarefied gas flows, is extended over the entire design domain including solid domains assuming the solid as an imaginary gas for implicitly handling the gas-solid interfaces in the optimization process. Based on the extended equation, a 2D flow channel design problem is formulated, and the design sensitivity is obtained based on the Lagrange multiplier method and adjoint variable method. Both the rarefied gas flow and the adjoint flow are computed by a deterministic method based on a finite discretization of the molecular velocity space, rather than the DSMC method. The validity and effectiveness of our proposed method are confirmed through several numerical examples
On recovering the second-order convergence of the lattice Boltzmann method with reaction-type source terms
This study derives a method to consistently recover the second-order
convergence of the lattice Boltzmann method (LBM), which is frequently degraded
by the improper discretisation of required source terms. The work focuses on
advection-diffusion models in which the source terms are dependent on the
intensity of transported fields. The main findings are applicable to a wide
range of formulations within the LBM framework. All considered source terms are
interpreted as contributions to the zeroth-moment of the distribution function.
These account for sources in a scalar field, such as density, concentration or
temperature. In addition to this, certain immersed boundary methods can be
interpreted as a source term in their formulation, highlighting a further
application for this work.
This paper makes three primary contributions to the current state-of-the-art.
Firstly, it identifies the differences observed between the ways source terms
are included in the LBM schemes present in the literature. The algebraic
manipulations are explicitly presented in this paper to clarify the differences
observed, and identify their origin. Secondly, it derives in full detail, the
implicit relation between the value of the transported macroscopic field, and
the sum of the LBM densities. Moreover, this relation is valid for any source
term discretization scheme, and three equivalent forms of the second-order
accurate collision operator are presented. Finally, closed-form solutions of
this implicit relation are shown for a variety of common models.
The second-order convergence of the proposed LBM schemes is verified on both
linear and non-linear source terms. Commonly used diffusive and acoustic
scalings are discussed, and their pitfalls are identified. Moreover, for a
simplified case, the competing errors are shown visually with isolines of error
in the space of spatial and temporal resolutions
Comparison of free-surface and conservative Allen-Cahn phase-field lattice Boltzmann method
This study compares the free-surface lattice Boltzmann method (FSLBM) with
the conservative Allen-Cahn phase-field lattice Boltzmann method (PFLBM) in
their ability to model two-phase flows in which the behavior of the system is
dominated by the heavy phase. Both models are introduced and their individual
properties, strengths and weaknesses are thoroughly discussed. Six numerical
benchmark cases were simulated with both models, including (i) a standing
gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in
liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vertical and
(vi) oblique impact of a drop into a pool of liquid. Comparing the simulation
results with either analytical models or experimental data from the literature,
four major observations were made. Firstly, the PFLBM selected was able to
simulate flows purely governed by surface tension with reasonable accuracy.
Secondly, the FSLBM, a sharp interface model, generally requires a lower
resolution than the PFLBM, a diffuse interface model. However, in the limit
case of a standing wave, this was not observed. Thirdly, in simulations of a
bubble moving in a liquid, the FSLBM accurately predicted the bubble's shape
and rise velocity with low computational resolution. Finally, the PFLBM's
accuracy is found to be sensitive to the choice of the model's mobility
parameter and interface width
Adjoint Lattice Boltzmann for topology optimization on multi-GPU architecture
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint formulation is used to calculate sensitivity of the LBM solution to several type of parameters, both global and local. The numerical scheme for solving the adjoint problem has many properties of the original system, including locality and explicit time-stepping. Thus it is possible to integrate it with the standard LBM solver, allowing for straightforward and efficient parallelization (overcoming limitations typical for the discrete adjoint solvers). This approach is successfully used for the channel flow to design a free-topology mixer and a heat exchanger. Both resulting geometries being very complex maximize their objective functions, while keeping viscous losses at acceptable level
Combining computational fluid dynamics and magnetic resonance imaging data using lattice Boltzmann based topology optimisation
This thesis presents the combination of magnetic resonance imaging (MRI) measurements and computational fluid dynamics (CFD) to reduce statistical measurement noise and identify objects and finer structures in the MRI data. Using a lattice Boltzmann based topology optimisation approach, the method allows those solutions that best match the measured flow field but satisfy the macroscopic conservation laws of fluid flow, here mass and momentum conservation. This combination is formulated as a distributed control problem that minimises the distance between measured and simulated flow field, the latter being the solution of a parametrised Boltzmann equation with Bhatnagar-Gross-Krook collision operator, where the controls represent the porosity distributed in the domain. The problem is solved with an adjoint lattice Boltzmann method using the open source software OpenLB