A New Analytical Approach To Calculate a Slippage inside a Progressing Cavity Pump with a Metallic Stator Using a Middle Streamline and a Structural Periodicity

Summary Simplified and 3D models have been studied to predict the performance of progressing cavity pumps (PCPs). Simplified models were mainly made for metallic stator PCP performance. Their purpose was to represent the relationship between pump flow rate and differential pressure. Previous studies proposed to solve the system of mass conservation equations. In these studies, the geometry of the gap area was not clearly represented by neglecting the curvatures of stator and rotor. In addition, only frictional loss was considered, but local loss by gradual contraction or expansion of the gap area was not considered. In this study, we present a new analytical approach considering curvature and local loss. The depth of the gap area and local loss could be calculated analytically by a middle streamline and a curvature. On the basis of periodicity of distribution of cavities, simplified calculation for a slippage was possible without a system of mass conservation equations. Therefore, this model represents clearer geometry and a more simplified approach. The results show that this model shortens the calculating time and facilitates programing; in addition, the model validation is good in matching with experimental data.

Large D black holes in an environment

We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $$ \mathcal{O} $$ O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.

Using Virtual Reality for Teaching the Derivation of Conservation Laws in Fluid Mechanics

In many fields of study, physical sub-areas are treated mathematically in order to teach students the tools for optimization in their professional lives. In the derivation of the fundamental conservation equations theoretical con-structs or infinitesimal elements are used, additionally engaging a Taylor expansion of the variables. For undergraduates, this often means that the understanding of the physical interrelationships is left out in the cold. Practical experiments are not possible for clarification, since important quantities in the mathematical for-mulation can only made visible in experiments with extreme effort or are even in-accessible like theoretical constructs or infinitesimal values. Numerical calcula-tions may be used to show some quantities, but students cannot carry them out for themselves. Therefore, a virtual-reality laboratory for fluid mechanics is creat-ed with the software UNREAL ENGINE 4. This enables the students to learn the derivation of conservation laws and to influence the flow in order to experience and examine the basics of theoretical constructs. The results are evaluated in self-assessments, exercises, tutorials associated to the fluid mechanics course, and the results of an exam. Benefits for the use of virtual reality (VR) in teaching conser-vation laws were ascertained.

Analytical Formulation-Based Soot Modelling in Ethylene Laminar Jet Diffusion Flames

Soot volume fraction predictions through simulations carried out on OpenFOAM® are reported in diffusion flames with ethylene fuel. A single-step global reaction mechanism for gas-phase species with an infinitely fast chemistry assumption is employed. Traditionally soot formation includes inception, nucleation, agglomeration, growth, and oxidation processes, and the individual rates are solved to determine soot levels. However, in the present work, the detailed model is replaced with the soot formation and oxidation rates, defined as analytical functions of mixture fraction and temperature, where the net soot formation rate can be defined as the sum of individual soot formation and oxidation rates. The soot formation/oxidation rates are modelled as surface area-independent processes. The flame is modelled by solving conservation equations for continuity, momentum, total energy, and species mass fractions. Additionally, separate conservation equations are solved to compute the mixture fraction and soot mass fraction consisting of source terms that are identical and account for the mixture fraction consumption/production due to soot. As a consequence, computational time can be reduced drastically. This is a quantitative approach that gives the principal soot formation regions depending on the combination of local mixture fraction and temperature. The implemented model is based on the smoke point height, an empirical method to predict the sooting propensity based on fuel stoichiometry. The model predicts better soot volume fraction in buoyant diffusion flames. It was also observed that the optimal fuel constants to evaluate soot formation rates for different fuels change with fuel stoichiometry. However, soot oxidation strictly occurs in a particular region in the flame; hence, they are independent of fuel. The numerical results are compared with the experimental measurements, showing an excellent agreement for the velocity and temperature. Qualitative agreements are observed for the soot volume fraction predictions. A close agreement was obtained in smoke point prediction for the overventilated flame. An established theory through simulations was also observed, which states that the amount of soot production is proportional to the fuel flow rate. Further validations underscore the predictive capabilities. Model improvements are also reported with better predictions of soot volume fractions through modifications to the model constants based on mixture fraction range.

Utilizing Matrix Completion for Simulation and Optimization of Water Distribution Networks

Simulation of Water Distribution Networks (WDNs) constitutes a key element for the planning and management of water supply systems. This simulation involves estimating the flows and pressures by solving a linear set of mass conservation equations and a nonlinear set of energy conservation equations. The literature presents different formulations of heads-flows equations to derive the flows and heads in WDN. These formulations differ in terms of dimensionality, computational cost, and solution accuracy. Whereas this problem has been the subject of active research in the past, in the last decades a state of stagnation was reached and no new formulations were introduced. In this study, we propose a novel formulation that utilizes a matrix completion technique to construct a reduced-size nonlinear system of equations that guarantees both mass and energy conservation. Unlike former formulations that rely on the topology of the network, in the proposed method we employ a matrix completion technique in which arbitrary entries are added to the equation system to facilitate its solution. The advantages of the proposed method are demonstrated in simulation and optimization settings. In the former, the method demonstrates improved scalability and accuracy as compared with other widely known formulations. In the latter, the new formulation leads to smaller optimization problems, which are otherwise intractable when the classical formulation is used. Our results reopen an old debate on the best formulation for WDN simulation and optimization tasks and show that the matrix completion technique is a viable solution option for the problem.