Benchawan Wiwatanapataphee

Advanced approaches of modeling and measurement for turbulence and heat transfer

Turbulent flow and heat transfer are key issues in nature and numerous engineering applications such as human body, fluid machinery, machining facilities, and refrigeration systems. Insight into relevant transient and steady-state thermo-fluidic physics in such scenarios acts as constructive guidance for both engineers and scientists to improve the performance and reliability of facilities, analyze engineering failures, and understand complicated natural phenomena. Unfortunately, such complex fluid flow and heat transfer problems can rarely be solved analytically due to the strong nonlinearity of the Navier–Stokes equations and the complex nature of turbulence with heat transfer. Instead, advanced modeling and measurement techniques become compensatory yet powerful tools and have been widely used. Especially in recent years, a large number of advanced analytical, computational, and experimental techniques have been developed, which greatly contribute to the exploration of turbulence and heat transfer mechanisms. The main objective of this Special Issue is to bring important information on advanced modeling and measurement techniques together. Their feasibility and performance in investigating various engineering problems are evaluated. In this Special Issue, five original research papers were accepted for publication based on critical peer review by qualified reviewers. We hope that such a frontier of turbulence and heat transfer could be continued to track the updated trend year by year. An introductory review of the accepted papers is presented here. In the paper entitled ‘‘The impact research of control modes in steam turbine control system (digital electric hydraulic) to the low frequency oscillation of grid,’’ theoretical models for frequency domain analysis were developed to investigate the effects of steam turbine control modes on low-frequency oscillation of grid. The effectiveness of such theoretical analysis was well validated by simulation using the control system’s toolbox in MATLAB. In the paper entitled ‘‘Research on the aerodynamic characteristics of a lift drag hybrid vertical axis wind turbine,’’ the effects of various parameters on unsteady aerodynamic and starting performances of a newly designed lift drag hybrid vertical axis wind turbine were numerically investigated. The performances of various turbulence models were evaluated based on experimental data. Fruitful guidance for engineering design was also obtained. In the paper entitled ‘‘Pressure fluctuation prediction in pump mode using large eddy simulation and unsteady Reynolds-averaged Navier–Stokes in a pump-turbine,’’ both large eddy simulation and unsteady Reynolds-averaged Navier– Stokes equations in conjunction with a two-equation turbulence model were adopted to predict pressure fluctuation in pump mode of a pump-turbine. By comparisons between experimental and numerical results, the performances of these two different modeling methods were evaluated. In the paper entitled ‘‘Temperature field measurement of spindle ball bearing under radial force based on fiber Bragg grating sensors,’’ fiber Bragg grating temperature sensors were proven to be an effective method in the measurement of temperature distribution in outer ring of a spindle ball bearing. Such a temperature field is physically beneficial for the reduction of spindle thermal error. Finally, in the paper entitled ‘‘Experimental investigation of flow boiling heat transfer and pressure drops characteristic of R1234ze(E), R600a, and a mixture of R1234ze(E)/R32 in a horizontal smooth tube,’’ the effects of mass flux, heat flux, and quality of several refrigerants on flow boiling and pressure drop characteristics in a horizontal smooth tube was experimentally investigated. The corresponding experimental methods and findings from this study are useful for the design of evaporators.

The eigenvalue for a class of singular p-laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition

In this paper, we are concerned with the eigenvalue problem of a class of singular p-Laplacian fractional differential equations involving the Riemann–Stieltjes integral boundary condition. The conditions for the existence of at least one positive solution is established together with the estimates of the lower and upper bounds of the solution at any instant of time. Our results are derived based on the method of upper and lower solutions and the Schauder fixed point theorem.

Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

The spectral analysis for a singular fractional differential equation with a signed measure

In this paper, by using the spectral analysis of the relevant linear operator and Gelfands formula, we obtain some properties of the first eigenvalue of a fractional differential equation. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence of positive solutions are established.

Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion

Abstract In this paper, we consider the existence of nontrivial solutions for a class of fractional advection–dispersion equations. A new existence result is established by introducing a suitable fractional derivative Sobolev space and using the critical point theorem.

Mixed Traffic Flow in Anisotropic Continuum Model

An extended speed gradient model is developed to study the mixed traffic flow of two types of vehicles with different velocities and different lengths. Two new terms, representing the reaction of one type of vehicle to the other, are proposed and built into the dynamic speed evolution equations for fast cars and slow vehicles. With the developed model, the relation between the steady-state behavior of the mixed traffic flow system and two system parameters is analyzed, including the number density ratio R of the fast cars to the total vehicles and the vehicle length ratio α of the slow vehicle to the fast car. The formation and propagation of traffic jams, the dissolution process of the jams, and the local cluster effect of the mixed traffic system are also studied. The simulation results are reasonable and consistent with daily experience.

Analysis of flux flow and the formation of oscillation marks in the continuous caster

In the industrial process of continuous steel casting, flux added at the top of the casting mould melts and forms a lubricating layer in the gap between the steel and the oscillating mould walls. The flow of flux in the gap plays an essential role in smoothing the casting operation. The aim of the present work is to better understand the mechanics of flux flow, with an emphasis on such problems as how the flux actually moves down the mould, the physical parameters governing the consumption rate of the flux and the geometry of the lubricating layer. The problem considered is a coupled problem of liquid flow and multi-phase heat transfer. In the first part of the paper, the formation of the lubricating layer is analysed and a set of equations to describe the flux flow is derived. Then, based on an analysis of the heat transfer from the molten steel through the lubricating layer to the mould wall, a system of equations correlating the temperature field in the steel and flux with the geometry of the lubricating layer is derived. Subsequently, the equations for the flux flow are coupled with those arising from heat-transfer analysis and then a numerical scheme for the calculation of the consumption rate of flux, the geometry of the lubricating layer and the solidification surface of the steel is presented.

A study of transient flows of Newtonian fluids through micro-annuals with a slip boundary

In this paper, we study the pressure gradient driven transient flow of an incompressible Newtonian liquid in micro-annuals under a Navier slip boundary condition. By using the Fourier series expansion in time and Bessel functions in space, an exact solution is derived and is shown to include some existing known results as special cases. By analysing the exact solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure gradient, the flow rate increases with the increase in the slip parameter l almost linearly when l is large; while, for pressure fields with a wave form pressure gradient within a certain frequency range, as the slip parameter l increases, the amplitude of the flow rate increases first and then approaches a constant value when l becomes sufficiently large. It is also found that to achieve a given flow rate, one could have different designs and the graphs for the design are presented and discussed in this paper.

An Enthalpy Control Volume Method for Transient Mass and Heat Transport with Solidification

A single domain enthalpy control volume method is developed for solving the coupled fluid flow and heat transfer with solidification problem arising from the continuous casting process. The governing equations consist of the continuity equation, the Navier–Stokes equations and the convection–diffusion equation. The formulation of the method is cast into the framework of the Petrov–Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The use of the step test function and the constant flux approximation leads to the derivation of the exponential interpolating functions for the velocity and temperature fields within each control volume. The exponential fitting makes it possible to capture the sharp boundary layers around the solidification front. The method is then applied to investigate the effect of various casting parameters on the solidification profile and flow pattern of fluids in the casting process.

Effect of branchings on blood flow in the system of human coronary arteries

In this work, we investigate the behavior of the pulsatile blood flow in the system of human coronary arteries. Blood is modeled as an incompressible non-Newtonian fluid. The transient phenomena of blood flow through the coronary system are simulated by solving the three dimensional unsteady state Navier-Stokes equations and continuity equation. Distributions of velocity, pressure and wall shear stresses are determined in the system under pulsatile conditions on the boundaries. Effect of branching vessel on the flow problem is investigated. The numerical results show that blood pressure in the system with branching vessels of coronary arteries is lower than the one in the system with no branch. The magnitude of wall shear stresses rises at the bifurcation.