Energy Equations For Incompressible Flow Research Articles

Large eddy simulation of separated flow to investigate heat transfer characteristics in an asymmetric diffuser subjected to constant wall heat flux

In the present study, heat transfer characteristics of an asymmetric diffuser with separated flow has been studied. The flow separation is triggered due to wall expansion in two directions. Large Eddy Simulation (LES) approach is adopted to solve the turbulent separated flow and heat transfer in such diffuser at Reynolds number of 10000. For this purpose, a finite volume solver is extended in the OpenFOAM framework to solve the energy equation for incompressible flow. The extended solver has been adjusted to deal with backscatter phenomena and to prevent non-physical heat transfer results and numerical instability. An appropriate grid resolution is employed to perform LES calculations and predict the characteristics of the heat transfer within the separated flow. The numerical results are validated against measurements and Direct Numerical Simulation (DNS) results. The present study showed that the low mean velocity and turbulent kinetic energy (TKE) in a separated flow region are responsible for generating high temperature hot spots resulted from significant reduction of heat transfer from the walls. It has been observed that the heat transfer from the wall is increased slightly before the flow re-attachment region. The applicability of the Reynolds analogy in the separated flow zone for this problem has been examined. Moreover, the analysis of the computational performance showed that increasing the number of computational cells can improve, to certain extent, the convergence rate of the solver and therefor, reduced the computation cost.

Thermohydrodynamic analysis and tribological optimization of a curved pocket thrust bearing

Texture patterns implemented on thrust bearing surfaces have been proven very beneficial in terms of load carrying capacity and friction coefficient. In the present study, the potential of thrust bearings with a curved pocket stator geometry is investigated for realistic operating conditions. Bearing performance is quantified by means of Computational Fluid Dynamics (CFD) simulations based on the numerical solution of the Navier-Stokes and energy equations for incompressible flow, taking into account conjugate heat transfer at the bearing stator and rotor. After defining a reference slider design, optimization problems are formulated and solved, to arrive at optimal curved pocket designs. Here, the slider convergence ratio, as well as the pocket size, shape and depth, are defined in terms of proper design variables, whereas the load carrying capacity and friction coefficient constitute the problem's objective functions. The present results illustrate a superior performance of the curved open pocket slider designs in comparison to corresponding open square pocket sliders. Optimal solutions are characterized by parallel slider geometries. The improved performance of optimal designs can be attributed to reduced side leakage, in comparison to open square pocket geometries. The good performance of a thrust bearing with a corresponding curved pocket geometry is verified. Overall, the present optimal geometries are rather easy to manufacture, which makes them an attractive choice for the design of thrust bearings operated in a wide range of rotor speeds.

Performance comparison between textured, pocket, and tapered-land sector-pad thrust bearings using computational fluid dynamics thermohydrodynamic analysis

Different geometry patterns of the surface of thrust bearings have been proven very beneficial in terms of bearing load-carrying capacity and friction coefficient. In this study, four different types of sector-pad thrust bearings have been cross-evaluated for operation under realistic operating conditions: (a) an open pocket bearing, (b) a closed pocket bearing, (c) a tapered-land bearing, and (d) a bearing partially textured with rectangular dimples. Bearing performance has been computed by means of computational fluid dynamics simulations based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Conjugate heat transfer at the bearing pad and rotor has been taken into account. Initially, for a reference design of each bearing, the effects of varying rotational speed and minimum film thickness have been investigated. Further, characterization of each bearing for a constant level of thrust load has been performed. Finally, the effects of varying the depth of each geometry pattern have been studied. The present results illustrate a superior performance of the open pocket bearing in comparison to the other bearing types.

Thermohydrodynamic analysis of a textured sector-pad thrust bearing: effects on mechanical deformations

In this paper, a computational investigation of thermohydrodynamic performance and mechanical deformations of a fixed-geometry thrust bearing with artificial surface texturing is presented. A parallel eight-pad bearing is considered; the surface of each pad is partially textured with square dimples. Here, a CFD-based thermohydrodynamic modeling approach, recently introduced by the authors, is used to calculate the performance of the bearing; the THD results are then used to quantify the deformations of the bearing mechanical parts. The bearing is modelled as a sector-shaped channel, consisting of a smooth rotating wall (thrust collar) and a partially textured stationary wall (bearing pad). The bearing performance characteristics are computed by means of numerical simulations, based on the numerical solution of the Navier-Stokes and energy equations for incompressible flow, as well as on the solution of the elasticity equations for the bearing solid parts. Here, a reference texture geometry is considered, while proper thermal and structural boundary conditions are implemented. For representative film thickness values, the effect of rotational speed and collar thickness on bearing performance is quantified, and the resulting pad and rotor deformation fields are computed. It is found that, due to oil heating, the load carrying capacity decreases with rotational speed for values higher that approximately 2000 rpm. The computed rotor deformation field is representative of a fixed support beam, characterized by substantially higher levels than those of the bearing pad. Rotor deformations increase substantially at low values of collar thickness.

Computational Fluid Dynamics Thermohydrodynamic Analysis of Three-Dimensional Sector-Pad Thrust Bearings With Rectangular Dimples

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of computational fluid dynamics (CFD) simulations, based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth, and texture density on the bearing performance indices (load carrying capacity, friction torque, and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass, momentum, and kinetic energy. This deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems. Finite difference schemes in a collocated grid system are also analyzed, and a violation of kinetic energy conservation is revealed. The predicted conservation properties are demonstrated numerically in simulations of inviscid white noise, performed in a two-dimensional periodic domain. The proposed fourth order schemes in a staggered grid system are generalized for the case of a non-uniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow.

Conservative Properties of Finite Difference Schemes for Incompressible Flow. 1st Report. Analytical Requirements, Discrete Operators and Schemes in a Regular Grid System.

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as large eddy simulation (LES) or direct numerical simulation (DNS). In the first report, conservative properties of the continuity, momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Convective schemes in a proper set are commutable if the corresponding discretized continuity is satisfied. The proper combination of discretized continuity and pressure terms is required for kinetic energy conservation. The skew-symmetric form is the only proper second-order accurate convective scheme in intuitive convective schemes in a regular grid system. Proper second-order accurate divergence and advective forms are indicated. We need not consider proper rotational form if proper advective form is indicated, since the requirement for the rotational form is that it equals the advective form. Proper fourth-order accurate convective schemes in a regular grid system are obtained from a relatively simple extension of the proper second-order schemes.

LAMINAR NATURAL CONVECTION IN VERTICAL TUBES WITH ONE END OPEN TO A LARGE RESERVOIR: A NUMERICAL SOLUTION

Abstract A two-dimensional finite difference computer program in cylindrical coordinates has been developed to solve the case of laminar natural convection in a vertical tube open to a large reservoir. Such a device, the open thermosyphon, is used in a number of applications, including the cooling of gas turbines, geothermal energy extraction, and thermosyphon solar water heaters. The objectives of this work were to study the nature of fluid flow and the heat transfer rate along the tube wall. A semi-implicit, time marching, finite difference solution procedure was used, satisfying continuity, momentum, and energy equations for incompressible flow. Results show three well-defined flow regimes appearing as functions of the tube length-to-radius (aspect) ratio. Fluid motion in the tube and heat transfer rates became oscillatory at long time intervals. Plots of streamlines and isotherms at selected times for different aspect ratio tubes are also presented to show the transient behavior of fluid motion.