Control Volume Approach Research Articles

Flow characteristics of external gear pumps considering trapped volume

This article investigates the volume change law of trapped fluid in the meshing process and the flow characteristics of external gear pumps under the following two cases: the pump design with and without relief groove. In this study, a mathematical modeling of gear pairs is deduced based on the meshing theory and a complete set of mathematical equations of tooth profile, and the flow rate equation is derived based on law of conservation of mass across the changing boundaries of a control volume. During the process, the function of the pump displacement is established, which is formed by two parts: tooth space volume and trapped volume. In addition, using a control volume approach, the trapped volume and flow rate characteristics of the pump under different design parameters of gears are discussed. The results show that the curve of trapped volume is similar to a parabola and the pump designed with a large number of teeth, module, and pressure angle easily obtained good flow rate characteristics under the same condition, which have a great benefit for designing the relief grooves and external gear pumps.

A fully coupled depth-integrated model for surface water and groundwater flows

This paper presents the development of a fully coupled surface water and groundwater flow model. The governing equations of the model are derived based on a control volume approach, with the velocity profiles of the two types of flows being both taken into consideration. The surface water and groundwater flows are both modelled based on the unified equations and the water exchange and interaction between the two types of flows can be taken into account. The model can be used to simulate the surface water and groundwater flows simultaneously with the same numerical scheme without other effort being needed to link them. The model is not only suitable for the porous medium consisting of fine sediments, but also for coarse sediments and crushed rocks by adding a quadratic friction term. Benchmark tests are conducted to validate the model. The model predictions agree well with the data.

Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity

In this study, a transient heat transfer process of freezing water inside a two-dimensional square cavity has been investigated numerically. Water was used as a phase-change medium, and the numerical model has been created with control volume approach by using C++ programming language. To be able to accelerate the numerical calculations, CUT (Consistent-Update-Technique) algorithm has been implemented in the numerical code. Span-wise variations of the vertical component of the velocity have been represented in comparison with the experimental measurements from the literature at various vertical positions to examine the accuracy of the numerical scheme. The influence of natural convection has been considered by comparing the conduction and convection dominated solidification under same boundary conditions. Comparative results have been obtained regarding time-wise variations of the cold wall temperature and the dimensionless effectiveness. Moreover, the streamlines and isotherms have been represented to understand the differences between the conduction and convection driven phase change processes.Results indicate that natural convection becomes remarkable and has different forms at the initial periods of the phase change process. Increasing the effect of natural convection in the cavity increases the cooling rate of water. Near the density inversion temperature of water (4°C), temperature variations fluctuate and counter currents observed in the domain.

Numerical investigation of inward solidification inside spherical capsule by using temperature transforming method

Abstract In this study, a numerical analysis of the inward solidification of phase change material inside spherical capsule is carried out. The spherical capsule that is subjected to convection from the outside surface initially is not at its melting temperature. The control volume approach and temperature transforming method are applied to solve the dimensionless energy equation. The model solution results are validated through a comparison with published experimental data for similar case and it shows a considerably good agreement. The analysis results show that the larger diameter spherical capsules have significantly greater solidification time compared to those with smaller diameters of spherical capsules. In addition, the entropy generation inside spherical capsule is analyzed. It is found that the entropy generation increases with increasing sphere capsule diameter, attains a maximum and then decreases.

On the wake flow of asymmetrically beveled trailing edges

Trailing edge and wake flows are of interest for a wide range of applications. Small changes in the design of asymmetrically beveled or semi-rounded trailing edges can result in significant difference in flow features which are relevant for the aerodynamic performance, flow-induced structural vibration and aerodynamically generated sound. The present study describes in detail the flow field characteristics around a family of asymmetrically beveled trailing edges with an enclosed trailing-edge angle of $$25^\circ$$ and variable radius of curvature R. The flow fields over the beveled trailing edges are described using data obtained by particle image velocimetry (PIV) experiments. The flow topology for different trailing edges was found to be strongly dependent on the radius of curvature R, with flow separation occurring further downstream as R increases. This variation in the location of flow separation influences the aerodynamic force coefficients, which were evaluated from the PIV data using a control volume approach. Two-point correlations of the in-plane velocity components are considered to assess the structure in the flow field. The analysis shows large-scale coherent motions in the far wake, which are associated with vortex shedding. The wake thickness parameter $$y_{f}$$ is confirmed as an appropriate length scale to characterize this large-scale roll-up motion in the wake. The development in the very near wake was found to be critically dependent on R. In addition, high-speed PIV measurements provide insight into the spectral characteristics of the turbulent fluctuations. Based on the time-resolved flow field data, the frequency range associated with the shedding of coherent vortex pairs in the wake is identified. By means of time-correlation of the velocity components, turbulent structures are found to convect from the attached or separated shear layers without distinct separation point into the wake.

Thermal Analysis of Mobile Thermal Battery with Aluminum Mesh Subjected to Solar-Concentrated Heating

AbstractSolar thermal heating analysis of a tube in the presence of metallic meshes, resembling the mobile thermal battery, is carried out. The influence of metallic meshes on the heat-transfer rates inside the tube is examined in detail. Structured aluminum meshes are incorporated into the tube while stagnant water is assumed as the working fluid inside the tube. Numerical analysis using the control-volume approach is incorporated to solve the governing equations of heat transfer and fluid flow inside the tube. The dimensionless temperature parameter is introduced to quantify the excessive local heating inside the tube with and without meshes under the solar-concentrated irradiation. It is found that aluminum meshes act like a conduction tree and enhance the heat-transfer rates in water inside the tube. The local excessive heating and large temperature difference are avoided inside the tube when the aluminum meshes are used inside the tube. The influence of natural convection current on the heat-transfer...

Simple method for monitoring transient thermal stresses in pipelines

ABSTRACTThis paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler components.

Numerical study of double-diffusive convection developed within horizontal partially porous enclosure

The present work deals the heat and mass transfer generated in horizontal partially porous enclosure. The vertical walls are subjected to of uniform conditions of temperature and concentration whereas the horizontal walls are assumed to be adiabatic and impermeable. The set of equations describing the double diffusive convection are solved numerically using the numerical control volume approach. The numerical results are presented and analyzed in terms of streamlines, isotherms, isoconcentrations lines and for the average Nusselt and Sherwood numbers.

Numerical solution of Navier stokes equation using control volume and finite element method

<p>The aim of this paper is twofold first we will provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.</p>

Numerical and experimental investigation of a counter-current two-phase thermosyphon with cascading pools

An innovative design of a counter-current two-phase thermosyphon is investigated for the in-plane cooling of flat product structures. The thermosyphon features multiple pools staggered along the entire evaporator section, in which liquid flowing toward the bottom of the thermosyphon can be stored. The pools are used to cascade the working fluid to the evaporator end cap. Liquid accumulates in the pools until they overflow, thereby spreading the working fluid across the entire evaporator length rather than creating one liquid pool at the bottom end cap. Multiple of such thermosyphons operating in parallel can be used for low-gradient planar cooling of vertically oriented surfaces. A numerical model using a control volume approach is developed to predict and to validate the experimental results of this innovative design. The main advantages of the control volume approach are the adaptability of the entire model and the fast computational speed in comparison to elaborate fluid dynamics models. Empirical correlations are used for the modeling of the heat transfer coefficients and friction factors of the counter-current flow. A proof of principle is given by observing a prototype that was milled into a copper bar. Next to logging temperature measurements, the prototype had a glass top plate to visually record the working fluid behavior. The model presented is well suitable for the early stages of thermosyphon design studies and for the impact evaluation of design changes.

Mathematical Modeling of Cooling High-Temperature Cylindrical Workpieces

The paper presents the results of modeling the process of cooling a cylindrical metal workpiece made of structural steel by a flowing cooling medium. The authors give a mathematical description of their solution for the problem of convective heat exchange that occurs when a longitudinal water flow is used for cooling. The control volume approach has been used for solving the systems of equations. The parameters of the flow field are calculated by the SIMPLE algorithm. The mathematical model factors in the presence of vapor being generated at the boundary between the high-temperature workpiece and the cooling water flow. It uses the effective vapor volume fraction calculated according to the heat-balance equation. The calculation results obtained by using the proposed model are compared to calculations by a mathematical model that uses criterial equations for determining the boundary conditions on the surface of a high-temperature cylindrical work piece in contact with the water flow. The authors discuss cases of cooling metal workpieces with different initial heating temperatures. The results of the numerical calculations of the heat exchange parameters are analyzed with regard to the time of the cooling process as well as in regard to whether the vapor presence on the cylinder surface is or is not taken into account.

The application of automatic differentiation techniques for the prediction of rotor-dynamic coefficients of labyrinth seals

The article describes the development of bulk-flow code for the prediction of rotor-dynamic coefficients of labyrinth seals. The code is based on the so-called single control volume approach by Childs and Scharrer [1] and the the forces are evaluated using the automatic differentiation technique. The resulting code is very simple and provides reasonable predictions of stiffness and damping coefficients at short computational time.

Evaluating Diffusion and Aging Mechanisms in Blending of New and Age-Hardened Binders During Mixing and Paving

As virgin pavement material sources become scarcer and costlier, the use of higher quantities of reclaimed asphalt pavement (RAP) in the production of new asphalt mixes becomes desirable. A major concern associated with the use of high percentages of RAP in new mixes is the interaction between age-hardened and new binders because the performance of the mix can be highly influenced by the properties of the composite binder. The objective of this study was to use asphalt binder testing and diffusion and aging theory to investigate the evolution of blending of virgin and RAP binders during asphalt mix production, storage, and placement. The rheological properties of a two-layer asphalt binder sample composed of virgin and simulated RAP binder and conditioned over time at different temperatures were measured with a dynamic shear rheometer. The conditioning process simulated the hot-mix asphalt (HMA) and warm-mix asphalt (WMA) time–temperature paths during mixing, storage, and placement. The diffusion and aging coefficients for the composite binder were estimated by comparing measured shear stiffness values with those predicted with a diffusion model and considering asphalt binder aging over time. The diffusion model was solved numerically with the finite control volume approach. On the basis of the preliminary laboratory test results, full blending of the age-hardened binder and the new binder was observed during HMA mixing and construction, while only partial blending was achieved during WMA production and construction. The blending of age-hardened and new binders could potentially be improved with the aid of warm-mix admixtures, rejuvenating agents, or both.

Partition Effect on Thermo Magnetic Natural Convection and Entropy Generation in Inclined Porous Cavity

In this study natural convection heat transfer fluid flow and entropy generation in a porous inclined cavity in the presence of uniform magnetic field is studied numerically. For control of heat transfer and entropy generation, one or two partitions are attached to horizontal walls. The left wall of enclosure is heated with a sinusoidal function and right wall is cooled isothermally. Horizontal walls of the enclosure are adiabatic. The governing equations are numerically solved in the domain by the control volume approach based on the SIMPLE technique. The influence of Hartmann number, inclination angle, partition height, irreversibility distribution ratio, and partition location is investigated on the flow and heat transfer characteristics and the entropy generation. The obtained results indicated that the partition, magnetic field and rotation of enclosure can be used as control elements for heat transfer, fluid flow and entropy generation in porous medium.

Dynamic Simulation and Validation of a Vent and Safety Valve for Cryogenic Flight Tanks

High Thrust Cryogenic Rocket Stages entail the use of a Vent and Relief Valve which can cater to a higher discharge rate. The Vent function is called for during ground servicing operations like tank chilling and pressurant replenishment and during flight to take care of the decrease in ambient pressure and boil-off losses. The Relief function acts as a redundant feature to protect the tanks from catastrophic failure due to structural damage caused by over-pressurization. Nevertheless, this valve needs to be characterized for both these functions during ground tests. This paper describes the modelling of and experimentation on an Inverted Type Pilot Operated Vent and Safety Valve. A mathematical model for simulating the dynamic behavior of this tank-mounted valve is developed. For this, a set of non-linear, first order, coupled ordinary differential equations, based on laws of conservation of mass and energy, are derived using fixed control volume approach. The numerical solution of these equations is obtained using fourth order Runge-Kutta method. The pressure, temperature, flow rate, seat stress and lift thus obtained are plotted to find the characteristic parameters such as cracking pressure, full flow pressure, reseal pressure, opening and closing response, tank pressure decay rate and full flow rate. The valve performance is studied for the effect of main valve outlet orifice and the pilot valve outlet orifice using these simulations. These results are validated by comparing it to the test results.

Advanced Materials for Applications at High Temperature: Fatigue Assessment by Means of Local Strain Energy Density

The interest on fatigue assessment of steel and other alloys at high temperature has increased continuously in the last years. However, high cycle fatigue of notched components at high temperature has not been deeply investigated experimentally and theoretically. The present paper investigates the accuracy of Strain Energy Density (SED) averaged over a control volume approach when applied to high‐temperature fatigue data from notched components. In the present work, a large bulk of high‐temperature fatigue data, taken from the literature and regarding notched components made of different advanced materials, is reanalyzed. In detail: C45 carbon steel at 250 °C, Inconel 718 at 500 °C, and directionally solidified superalloy DZ125 at 850 °C are considered. The main advantage of SED averaged over a control volume is that different geometries can be summarized in a single narrow scatter band. From an industrial viewpoint, the use of a geometry‐independent parameter (and fatigue curve) leads to a considerable advantage in terms of time and cost.

Two-dimensional thermosolutal natural convective heat and mass transfer in a bi-layered and inclined porous enclosure

In this study we focus on the double diffusive convection generated in a horizontal bi-layered porous cavity. All porous layers-cavity may occupy different positions relative to the horizontal axis for inclination angle values0°≤ α ≤60°. Each porous layer is considered homogeneous, isotropic and saturated with the same fluid. The vertical walls are subjected to of uniform conditions of temperature and concentration whereas the horizontal walls are assumed to be adiabatic and impermeable. The set of equations describing the double diffusive convection within the enclosure are solved numerically using the numerical control volume approach. A scale analysis for predicting mass transfer rate is represented for the case, where the two porous layers in the cavity are arranged vertically and for solute-driven flows (N >> 1). The numerical results are presented and analyzed in terms of streamlines, isotherms, isoconcentrations lines and for the average Nusselt and Sherwood numbers.

Influence of the Geometric Parameter on the Regimes of Natural Convection and Thermal Surface Radiation in a Closed Parallelepiped

We have performed a numerical analysis of the stationary regimes of thermogravitational convection and thermal surface radiation in a closed differentially heated parallelepiped. The mathematical model formulated in dimensionless natural velocity–pressure–temperature variables was realized numerically in the control volume approach. Analysis of the radiative heat exchange was carried out on the basis of the surface radiation approach with the use of the balance method in the Polyak variant. We have obtained three-dimensional temperature and velocity fields, as well as dependences for the mean Nusselt number reflecting the influence of the geometric parameter, the Rayleigh number, and the reduced emissive factor of the walls on the flow structure and the heat transfer.

Three-dimensional analysis of flow blockage accident in Tehran MTR research reactor core using CFD

In the present study, a 3D simulation of flow blockage accident which may occur in the coolant channels of a fuel assembly of Tehran research reactor (TRR) is investigated using CFD code. Consideration is given to the scenario in which partial blockage of hot channel occurs due to buckling of its fuel plates towards the inside. Governing conservation laws are solved using Control volume approach and pressure field is coupled to the velocity field through the SIMPLE algorithm. Flow convergence is considered when the residual for all flow variables are less than 10−5. The simulation is performed under four different obstruction levels of the nominal flow area, i.e., 0%, 20%, 50% and 70%. By solving momentum and energy equation in three channels with their fuel plates, it is found that heat transfer is substantially affected by channels flow field. In the blockage accident, decrease in flow rate of the obstructed channel decreases cooling capacity of the obstructed channel as a result of hydraulic resistance augmentation. The obtained results show that above the 50% blockage, critical phenomena will appear which may compromise the clad integrity. Moreover, in the 70% blockage scenario, the clad temperature in the obstructed channel reaches the value associated with nucleate boiling temperature at the operative pressure.

Impact of Microstructure on Dielectric Nanocomposites With High-<italic>k</italic> Interfacial Layers

Current dielectric nanopowder research in wide bandgap insulators has revealed an order of magnitude increase in dielectric permittivities over bulk values [1] – [3] . Researchers in this area postulate that interfacial layers at material boundaries have enhanced polarizability because of local relaxation mechanisms, such as rotational dipoles or localized space charge polarization [1] , [3] . Equivalent macroscopic electromagnetic models that have low- k grain/particle cores with average diameters ranging from 5 to 40 nm and high- k thin encapsulating layers with thicknesses from 0.8 to 1.0 nm are simulated in this paper using finite-element method and control-volume approach. The purpose of this investigation is to explore the impact of the microstructure on the overall electrical properties of these types of materials. To help validate this simulation approach, laminate geometries of silicon dioxide and silicon nitride are fabricated and tested by the authors. From these test samples, an effective permittivity model of interfacial layers for simple laminate geometries is extracted and is used to predict the macroscopic behavior of more complicated nanocomposites. Furthermore, the impact of the conductivity of low- k cores is also explored with the assumption that the high- k interfacial boundaries remain perfectly insulating. For low-conductivity cores, it is shown that the real part of the permittivity decreases with increasing particulate/grain size that is generally consistent with nanopowder research in [3] . However, at higher core conductivities, this dependence completely changes such that the real permittivity increases with increasing particulate/grain size. This change in dependence is due to charges accumulating at core boundaries producing a Maxwell–Wagner effect.