Weld Shape Optimization for Pillow Plate Heat Exchangers

Miniaturization of Plate Heat Exchangers (PHXs) is becoming a central research topic in order to utilize less material and less refrigerant charge to attain similar heat transfer performance, and hence contribute significantly into energy conservation and lower environmental impact. Thus, it is greatly desirable to obtain new designs to achieve this goal. Pillow Plate Heat Exchanger (PPHX) is a type of PHXs with a 3D complex wavy structure, but yet an economical manufacturing process positioning itself as a potential strong competitor among other types of PHXs. PPHXs have the advantage of simple manufacturing process which gives it great design flexibility, and allows new designs to be created simpler and less costly. However, PPHXs are more commonly found in chemical and process industry. Research on PPHXs in HVAC&R is very limited. It is desired to make use of PPHXs advantages in HVAC&R applications. This can be done by creating more efficient designs. The thermal-hydraulic performance of PPHXs is primarily altered by the weld shape, size, and pattern, as well as the pillow height. The shape, and size of the weld is one of the most sensitive parameters affecting the thermal-hydraulic performance of PPHXs. As the weld size is smaller and more streamlined, the pressure drop is reduced significantly. However, the heat transfer area is also reduced using a more streamlined weld shape. In this study, new designs for PPHXs are investigated using different weld shapes that are represented using Non-Uniform Rational B-Splines (NURBS. Each control point in the NURBS curve is a design parameter in the optimization problem. The optimization problem has 11 design parameters. The whole CFD simulation is automated using Parallel Parameterized CFD (PPCFD). Since the CFD simulation of 3D PPHXs is computationally very expensive, the automated CFD simulations and Approximation Assisted Optimization (AAO) reduce the computational time and resources required significantly. A meta-model, using Kriging method, is calculated and verified using random samples from the design space. Multi-Objective Genetic Algorithm (MOGA) utilizes the verified meta-model to calculate optimum designs which have the optimum weld shape and size. The potential enhancement can be up to 50% improvement in heat transfer coefficient and 20% reduction in pressure drop as compared to a selected PPHX baseline design. The optimum designs are also compared to optimum designs of PPHXs with circular spot welds. The potential improvement can be up to 20% in both heat transfer coefficient, and pressure drop

The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant

A finite membrane element formulation for surfactants

Surfactants play an important role in various physiological and biomechanical applications. An example is the respiratory system, where pulmonary surfactants facilitate the breathing and reduce the possibility of airway blocking by lowering the surface tension when the lung volume decreases during exhalation. This function is due to the dynamic surface tension of pulmonary surfactants, which depends on the concentration of surfactants spread on the liquid layer lining the interior surface of the airways and alveoli. Here, a finite membrane element formulation for liquids is introduced that allows for the dynamics of concentration-dependent surface tension, as is the particular case for pulmonary surfactants. A straightforward approach is suggested to model the contact line between liquid drops/menisci and planar solid substrates, which allows the presented framework to be easily used for drop shape analysis. It is further shown how line tension can be taken into account. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the membrane surface. The capabilities of the presented computational model is demonstrated by different numerical examples - such as the simulation of liquid films, constrained and unconstrained sessile drops, pendant drops and liquid bridges - and the results are compared with experimental data.Comment: Some typos are removed. Eqs. 13 and 105 are modified. Eqs. 64 and 73 are added; thus, the rest of equations is renumbered. All the numerical experiments are repeated. The example of Sec. 6.3 is slightly modifie

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier-Stokes equations

This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective--diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective--diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259--280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection--diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin (SUPG) and the Galerkin/least-squares method (GLS). The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.Comment: Update to postprint versio

Experimental study on the flow field of particles deposited on a gasoline particulate filter

The abatement of particulate matter in gasoline vehicle exhaust has prompted the development of gasoline particulate filters (GPFs). The spatial distribution of the deposited particles inside a GPF has profound implications for its regeneration behavior, ash-induced aging, and multiscale modeling efforts. The connection cones will affect the flow into the monolith and the package structure needed to meet the system space requirements. In this paper, nonuniform rational B-splines (NURBSs) were applied to the cone design to optimize the flow uniformity and particle distribution inside a gasoline particulate filter. NURBS and conventional cones were manufactured using 3D printing, and the velocity profiles and pressure drops were measured under the loading of synthetic particles. The results shows that the cone shape will influence the pressure drop and the velocity profile, which is evaluated as the uniformity index. The test results indicate that better performance is achieved when using the NURBS cone, especially at low particle loads. The results also show that the cone shape (which determines the velocity profile) influences the particle deposition distribution, although the apparent pressure drops are similar. These results are important for exhaust aftertreatment system (EATS) design and optimization, where the NURBS cone can improve flow uniformity, which causes better particle deposition distribution and lower pressure drop

Kinematic modelling of a 3-axis NC machine tool in linear and circular interpolation

Machining time is a major performance criterion when it comes to high-speed machining. CAM software can help in estimating that time for a given strategy. But in practice, CAM-programmed feed rates are rarely achieved, especially where complex surface finishing is concerned. This means that machining time forecasts are often more than one step removed from reality. The reason behind this is that CAM routines do not take either the dynamic performances of the machines or their specific machining tolerances into account. The present article seeks to improve simulation of high-speed NC machine dynamic behaviour and machining time prediction, offering two models. The first contributes through enhanced simulation of three-axis paths in linear and circular interpolation, taking high-speed machine accelerations and jerks into account. The second model allows transition passages between blocks to be integrated in the simulation by adding in a polynomial transition path that caters for the true machining environment tolerances. Models are based on respect for path monitoring. Experimental validation shows the contribution of polynomial modelling of the transition passage due to the absence of a leap in acceleration. Simulation error on the machining time prediction remains below 1%

Sum-factorization techniques in Isogeometric Analysis

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order $p$. Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approach is applied to Gauss quadrature, the computational complexity grows as $p^{d+2}$ instead of $p^{2d+1}$ as previously achieved.Comment: 34 pages, 8 figure