Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Computational fluids domain reduction to a simplified fluid network

The primary goal of this project is to demonstrate the practical use of data mining algorithms to cluster a solved steady-state computational fluids simulation (CFD) flow domain into a simplified lumped-parameter network. A commercial-quality code, “cfdMine” was created using a volume-weighted k-means clustering that that can accomplish the clustering of a 20 million cell CFD domain on a single CPU in several hours or less. Additionally agglomeration and k-means Mahalanobis were added as optional post-processing steps to further enhance the separation of the clusters. The resultant nodal network is considered a reduced-order model and can be solved transiently at a very minimal computational cost. The reduced order network is then instantiated in the commercial thermal solver MuSES to perform transient conjugate heat transfer using convection predicted using a lumped network (based on steady-state CFD). When inserting the lumped nodal network into a MuSES model, the potential for developing a “localized heat transfer coefficient” is shown to be an improvement over existing techniques. Also, it was found that the use of the clustering created a new flow visualization technique. Finally, fixing clusters near equipment newly demonstrates a capability to track temperatures near specific objects (such as equipment in vehicles).

Implementation of monotonic higher order upwind scheme in KIVA 4

KIVA is a FORTRAN code developed by Los Alamos national lab to simulate complete engine cycle. KIVA is a flow solver code which is used to perform calculation of properties in a fluid flow field. It involves using various numerical schemes and methods to solve the Navier-Stokes equation. This project involves improving the accuracy of one such scheme by upgrading it to a higher order scheme. The numerical scheme to be modified is used in the critical final stage calculation called as rezoning phase. The primitive objective of this project is to implement a higher order numerical scheme, to validate and verify that the new scheme is better than the existing scheme. The latest version of the KIVA family (KIVA 4) is used for implementing the higher order scheme to support handling the unstructured mesh. The code is validated using the traditional shock tube problem and the results are verified to be more accurate than the existing schemes in reference with the analytical result. The convection test is performed to compare the computational accuracy on convective transfer; it is found that the new scheme has less numerical diffusion compared to the existing schemes. A four valve pentroof engine, an example case of KIVA package is used as application to ensure the stability of the scheme in practical application. The results are compared for the temperature profile. In spite of all the positive results, the numerical scheme implemented has a downside of consuming more CPU time for the computational analysis. The detailed comparison is provided. However, in an overview, the implementation of the higher order scheme in the latest code KIVA 4 is verified to be successful and it gives better results than the existing scheme which satisfies the objective of this project.

The effect of demand, tank parameters, and pumping stations on energy use in municipal drinking water distribution systems

Two of the indicators of the UN Millennium Development Goals ensuring environmental sustainability are energy use and per capita carbon dioxide emissions. The increasing urbanization and increasing world population may require increased energy use in order to transport enough safe drinking water to communities. In addition, the increase in water use would result in increased energy consumption, thereby resulting in increased green-house gas emissions that promote global climate change. The study of multiple Municipal Drinking Water Distribution Systems (MDWDSs) that relates various MDWDS aspects--system components and properties--to energy use is strongly desirable. The understanding of the relationship between system aspects and energy use aids in energy-efficient design. In this study, components of a MDWDS, and/or the characteristics associated with the component are termed as MDWDS aspects (hereafter--system aspects). There are many aspects of MDWDSs that affect the energy usage. Three system aspects (1) system-wide water demand, (2) storage tank parameters, and (3) pumping stations were analyzed in this study. The study involved seven MDWDSs to understand the relationship between the above-mentioned system aspects in relation with energy use. A MDWDSs model, EPANET 2.0, was utilized to analyze the seven systems. Six of the systems were real and one was a hypothetical system. The study presented here is unique in its statistical approach using seven municipal water distribution systems. The first system aspect studied was system-wide water demand. The analysis involved analyzing seven systems for the variation of water demand and its impact on energy use. To quantify the effects of water use reduction on energy use in a municipal water distribution system, the seven systems were modeled and the energy usage quantified for various amounts of water conservation. It was found that the effect of water conservation on energy use was linear for all seven systems and that all the average values of all the systems' energy use plotted on the same line with a high R 2 value. From this relationship, it can be ascertained that a 20% reduction in water demand results in approximately a 13% savings in energy use for all seven systems analyzed. This figure might hold true for many similar systems that are dominated by pumping and not gravity driven. The second system aspect analyzed was storage tank(s) parameters. Various tank parameters: (1) tank maximum water levels, (2) tank elevation, and (3) tank diameter were considered in this part of the study. MDWDSs use a significant amount of electrical energy for the pumping of water from low elevations (usually a source) to higher ones (usually storage tanks). The use of electrical energy has an effect on pollution emissions and, therefore, potential global climate change as well. Various values of these tank parameters were modeled on seven MDWDSs of various sizes using a network solver and the energy usage recorded. It was found that when averaged over all seven analyzed systems (1) the reduction of maximum tank water level by 50% results in a 2% energy reduction, (2) energy use for a change in tank elevation is system specific, and (2) a reduction of tank diameter of 50% results in approximately a 7% energy savings. The third system aspect analyzed in this study was pumping station parameters. A pumping station consists of one or more pumps. The seven systems were analyzed to understand the effect of the variation of pump horsepower and the number of booster stations on energy use. It was found that adding booster stations could save energy depending upon the system characteristics. For systems with flat topography, a single main pumping station was found to use less energy. In systems with a higher-elevation neighborhood, however, one or more booster pumps with a reduced main pumping station capacity used less energy. The energy savings for the seven systems was dependent on the number of boosters and ranged from 5% to 66% for the analyzed five systems with higher elevation neighborhoods (S3, S4, S5, S6, and S7). No energy savings was realized for the remaining two flat topography systems, S1, and S2. The present study analyzed and established the relationship between various system aspects and energy use in seven MDWDSs. This aids in estimating the amount of energy savings in MDWDSs. This energy savings would ultimately help reduce Greenhouse gases (GHGs) emissions including per capita CO 2 emissions thereby potentially lowering the global climate change effect. This will in turn contribute to meeting the MDG of ensuring environmental sustainability.