Body-fitted Coordinates Research Articles

Research on modeling method of non-axisymmetric endwall based on body-fitted coordinates

Due to the large bending of turbine blades, there is strong three-dimensional flow in cascade channel, the three-dimensional flow at the endwall of blades generates extremely complex heat transfer characteristics. The design concept of high heat load turbine blades, particularly comprehensive optimization of flow and heat transfer at the endwall, has gained increasing attention. In this paper, we have developed a three-dimensional endwall parameterized modeling platform based on Body-Fitting Coordinates and introduced a novel approach for streamwise direction and normal direction concerning endwall profile construction. The endwall modeling was optimized using Genetic Algorithm to obtain a modified one with low heat transfer level on the premise that the aerodynamic loss is not increased. The analysis indicates that the reduction of aerodynamic loss with the modified endwall is relatively marginal, whereas the heat transfer intensity on the endwall surface experiences a significant decrease. Additionally, employing an endwall model can effectively mitigate the lateral pressure gradient in the cascade channel, which exerts a pronounced influence on suppressing secondary vortex development in the cascade.

Generalized lattice Boltzmann method for radiative transfer problem in slab and irregular graded-index media.

The lattice Boltzmann method (LBM) has been developed as a powerful solution method in computational fluid dynamics and heat transfer. However, the development of the LBM for solving radiative transfer problems has been far from perfect. This paper proposes a generalized form of the lattice Boltzmann model for the multidimensional radiative transfer equation (RTE) in irregular geometry with a graded index based on body-fitted coordinates. The macroscopic RTE is recovered from Chapman-Enskog analysis, which provides two possible procedures to formulate the Boltzmann equation in graded-index media and irregular geometries. These proposed models have been tested by considering one-and two-dimensional problems of the RTE, and the benchmark solutions reported in the literature were used for comparisons. Afterwards, the LBM is used to analyze the radiation transport in graded-index media for various forms of scattering law, refractive index, boundary reflection, laser and optical properties, and temperatures. The graded-index function and the geometry type have a significant effect on radiative transport in cases in which the refractive index matches or mismatches the boundary. It is also apparent that the developed LBM is an efficient, powerful, robust, and accurate solver for radiative transport in inhomogeneous media with a graded-index function and irregular geometries.

LES/DNS fluid-structure interaction simulation of non-linear slender structures in Nektar++ framework

Nektar++ is a spectral/hp element open-source framework written in C++ for the construction of classical low-order h-type as well as higher-order p-type finite element solvers. It seeks to overcome the implementation challenges of the complex data structures associated with high-order finite element methods; hence, providing an efficient, flexible and HPC scalable platform for the development of solvers for partial differential equations using the spectral/hp element method. In the present work, capabilities of Nektar++ is leveraged for development of two fluid-structure interaction (FSI) solvers for simulations of highly deformable nonlinear slender structures. The FSI solver uses the incompressible Navier-Stokes (NS) solvers of Nektar++ for fluid flow while the structural dynamics is modelled using Geometrically-Exact Composite Beams (GECB). The open-source SHARPy framework is linked to Nektar++ and used for structural simulation. Aiming at high-fidelity (LES/DNS) FSI simulations, the thick-strip approach is used to reduce computational costs. In this approach, the full 3D fluid domain is represented with series of smaller 3D domains normal to the local axis of the structure and having a finite thickness in the spanwise direction where periodicity is also assumed. Hence, while reducing the computational costs by avoiding the discretization of equations over the entire slender structure, the strip thickness allows capturing the local 3D turbulent wake and accurately predict the fluid forces on the structure. Two approaches are adopted to avoid the dynamic remeshing due to the large and non-linear deformation of the structure. In the first approach, the transformed the NS equations are solved in the non-inertial body-fitted coordinates while in the second approach the NS equations are formulated in the moving frame of reference and solved with the spectral/hp element method. A hybrid parallelisation approach of Nektar++ is extended for the thick-strip method which allows having non-constant cross-section along the structural span as well as efficient and flexible use of computational resources, and excellent HPC performance for the FSI simulations. The capability of the FSI solver is demonstrated via several examples.

A grid based ADI method for the problem of two phase solidification

This paper proposes a transformation based, unconditionally stable, Alternating Direction Implicit (ADI) scheme for solving two-phase Stefan problems of solidification in arbitrary bounded domains. The governing equations of each phase are transformed, from a complex physical domain to a fixed rectangular domain, using body-fitted coordinates. ADI method is used to solve the transformed equations of each phase separately. The unconditional stability of the proposed ADI scheme is discussed numerically using von-Neumann method. Several numerical experiments are carried out for the case of stable solidification to verify the applicability of the proposed method. An excellent agreement has been found between the numerically generated values and the exact/existing solutions. Further, the developed scheme has also been tested on the problems of unstable solidification with mild surface tension and kinetic mobility. Once again the interface location with time has been computed very accurately.

An ADI based body-fitted method for Stefan problem in irregular geometries

This paper deals with a two dimensional Stefan problem of solidification in arbitrary bounded domains. To realize this, the governing equations are transformed from a complex physical domain to a simpler computational domain using body-fitted coordinates and the corresponding transformed equations are solved using an alternating direction implicit (ADI) method. Stability analysis of the proposed ADI scheme, applied to the transformed equations, is discussed using von Neumann method. The developed scheme is then used to solve problems which are initially defined in some regular geometries like rectangular or circular but changes with time to some complex shapes. Comparisons with the existing schemes show that the developed scheme produced better solutions.

Application of decentralized fuzzy inference method for the inverse geometry design of radiative enclosures

The decentralized fuzzy inference method (DFIM) is applied to solve the inverse geometry design of a 2D radiative enclosure filled with gray participating medium. The heat transfer process in the irregular enclosure is solved using the discrete ordinate method in body-fitted coordinate. The simulated surface heat flux is employed as measurement signals. The design task is formulated as an inverse problem which is solved by the DFIM. Retrieval results illustrate that the design purpose of producing a uniform distribution of radiative heat flux on the design surface can be successfully satisfied using the present method. The DFIM is proved to be more efficient than other inverse techniques. Moreover, the effects of the number of measurement points and radiative properties of participating medium on the inverse design results are investigated. The DFIM is effective in designing the geometry of radiative enclosures for different kinds of participating media.

Numerical Study of Bubble Rising Motion in a Vertical Wedge-Shaped Channel Based on a Modified Level Set Method

A modified level set method coupled with local-reinitialized process and volume-corrected method is employed to simulate bubble motions in complex channels. The volume-corrected process helps to adjust the mass loss due to bubble simulation by standard level set method and local reinitialization of level set function eliminates the numerical dissipation due to nonorthogonality of the boundary mesh. For solving the problem of two-phase flow with a complex boundary, the mesh generation is employed in the physical plane in body-fitted coordinates. All parameters in the physical domain are transformed into a computational domain, where the governing equations are discretized on collocated grids using the finite volume method and the SIMPLE algorithm to decouple the velocities and the pressure. The continuum surface force model is employed to deal with the surface tension of bubbles. By simulating bubble rising in a wedge-shaped channel, the method is demonstrated to be effective to solve the bubble motion in a complex physical plane.

Global Stability Analysis of Spatially Developing Boundary Layer: Effect of Streamwise Pressure Gradients

The paper presents a global stability analysis of the two-dimensional incompressible boundary layer with the effect of streamwise pressure gradient. A symmetric wedge flow is considered at different values of the dimensionless pressure gradient parameter βH. The pressure gradient dp/dx in the flow direction is zero, when βH = 0, favorable (negative) for βH > 0, and adverse (positive) for βH < 0. The base flow is computed by numerical solution of Falkner—Skan equation. The Reynolds number is based on the displacement thickness δ* at the inflow boundary. The stability equations governing the flow are derived in body-fitted coordinates. The stability equations are discretized using the Chebyshev spectral collocation method. The discretized equations, together with boundary conditions, form a general eigenvalue problem and are solved using Arnoldi’s algorithm. The temporal global modes are computed for βH = 0.022, 0.044, and 0.066, for favorable and adverse pressure gradients. The temporal growth rate ωi is found to be negative for all the global modes. The ωi value is smaller for the favorable pressure gradient (FPG) than for the adverse pressure gradient (APG) at the same Reynolds number (Re = 340). Thus, the FPG has a stabilizing effect on the boundary layer. The comparison of the spatial eigenmodes and spatial amplification rates for FPG and APG show that FPG has a stabilizing effect, whereas APG has a destabilizing effect on the disturbances.

Numerical Study on Hydrothermal Performance Factor Using Jet impingement and Nanofluid

In this study, thermal-hydraulic performance of a confined slot jet impingement with Al2O3-water nanofluid has been numerically investigated over Reynolds number ranges of 100-1000. Two triangular ribs are mounted at a heated target wall; one rib located on the right side of the stagnation point and another one located on left side of the stagnation point. The governing momentum, continuity and energy equations in the body-fitted coordinates terms are solved using the finite volume method and determined iteratively based on SIMPLE algorithm. In this study, effects of Reynolds number, rib height and rib location on the thermal and flow characteristics have been displayed and discussed. Numerical results show an increase in the average Nusselt number and pressure drop when Reynolds number and rib height increases. In addition, the pressure drop and average Nusselt number increases with decrease the space between the stagnation point and rib. The maximum enhancement of the average Nusselt number is up to 39 % at Reynolds number of 1000, the rib height of 0.3, rib location of 2 and nanoparticles volume fraction of 4%. The best thermal-hydraulic performance of the impinging jet can be obtained when the rib height of 0.2 and rib location of 2 from the stagnation point with 4% nanoparticles volume fraction.

Performance of characteristic numerical boundary conditions for mixed convective flows past a heated square cylinder using a non-Boussinesq approach

This work represents an investigation of the performance of characteristic numerical boundary conditions on the unconfined 2D mixed convective flow of air past a heated square cylinder governed by a non-Boussinesq flow model. The working fluid (air) is taken to be thermally perfect with variable thermo-physical and transport properties. The fully compressible Navier-Stokes equations are transformed using body-fitted coordinates and solved using particle velocity upwind (PVU-M+) scheme on a structured O-type grid. To investigate the performance of characteristic numerical boundary conditions, the gravity aligned upward flow past a heated square cylinder at (α = 0°, M = 0.1 and 0.2, Re = 100, Fr = 0.5 and 1.0, Pr = 0.71, γ = 1.4, and ε = 0.07 and 1.0) is considered. The overheat ratio (ε) is defined as (Tw – T∞)/T∞, where Tw and T∞ are the uniform cylinder and free stream temperatures, respectively. In order to determine the proper choice of boundary conditions to be imposed on the far boundary, algebraic characteristic boundary conditions of Euler equations (AECBC) are considered in a local 1D sense normal to the far boundary. In this work, two sets of algebraic characteristic boundary conditions are considered. In one set (BC Set I), AECBC is used over the entire far boundary. While in the other set (BC Set II), AECBC is used over a portion of far boundary, that is characterized by normal flow velocity magnitude in excess of a threshold value, and entropy preserving extrapolating conditions for pressure and density over the remaining portion of the far boundary. It is shown that BC Set I generates spurious wave reflections and numerical noise from the far boundary, whereas BC Set II eliminates these numerical artifacts and captures the flow physics far more accurately.

Numerical and experimental study the effects of river width changes on flow characteristics in a flume

The gradual characteristics of variations in transverse width often occur in mountain river because of the effect of geological conditions and river evolutions. This will influence flow and sediment transport due to the variations of flow structures resulted from the river width changes. A flume experiment that was conducted to explore how flow characteristics perform with the varied channel width, showing the connection of the flow parameters, flow rate and channel width. For example, the longitudinal water depth and velocity change along with the transition width of flume. On the other hand, a depth-averaged two-dimension model was proposed according to series of methods such as body-fitted coordinate, finite volume method, SIMPLER algorithm. The numerical results agreed well with the experimental observation in a flume, which showed that the model could reasonably simulate gradual channel transition flow. In addition, the validated numerical model was applied to simulate flow with different flow rates with the same imposed boundary condition in order to further analyse the effects of channel width variation on flow characteristics.

A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.

An improved social force model for pedestrian dynamics in shipwrecks

Evacuation in shipwrecks is still an open challenging problem and has not been incorporated by existing crowd simulation models. Motivated by this, we propose a simple but general model to characterize different scenarios of shipwrecks, based on the original social force model. Using a body-fitted coordinates, the psychological tendency of pedestrians to slip downhill has been incorporated to modeling evacuation behaviors on inclined decks of shipwrecks. Simulation results show that evacuation efficiency depends on the intricate relationship among the incline angle, the outlet direction as well as the desired velocity. It can be observed that when individuals try to move fast, evacuations against the downhill direction achieve maximum efficiency. In addition, we also consider the presence of “wicked pedestrians”, who might hurt others to gain advantage in evacuation. Intriguingly, the existence of only a few such offenders can decrease evacuation time, while continuously increasing their number is destined to inhibit evacuation efficiency. In conclusion, we give a framework focused on more complex evacuation dynamics, and hope for a better understanding of how to efficiently escape from such adverse environment.

Numerical Study on the Convective Heat Transfer of Nanofluid Flow in Channel with Trapezoidal Baffles

This article presents a numerical study on forced convection of nanofluid flow in a two-dimensional channel with trapezoidal baffles. One baffle mounted on the top wall of channel and another mounted on the bottom wall of channel. The governing continuity, momentum and energy equations in body-fitted coordinates are iteratively solved using finite volume method and SIMPLE technique. In the current study, SiO2-water nanofluid with nanoparticles volume fraction range of 0- 0.04 and nanoparticles diameters of 30 nm is considered for Reynolds number ranging from 100 to 1000. The effect of baffles height and location, nanopar-ticles volume fraction and Reynolds number on the flow and thermal fields are investigated. It is found that the average Nusselt number as well as thermal hydraulic performance increases with increasing nanopartiles volume fraction and baffle height but accompanied by increases the pressure drop. The results also show that the best thermal- hydraulic performance is obtained at baffle height of 0.3 mm, locations of baffles at upper and lower walls of 10 and 15 mm, respectively, and nanoparticles volume fraction of 0.04 over the ranges of Reynolds number.

Dynamic Heat Transfer Study of a Triangular-Shaped Latent Heat Storage Unit for the Attic Space of a Domestic Dwelling

Abstract A two-dimensional (2D) numerical study is carried out to investigate the thermal performance of an impure phase-change material (PCM) in an equilateral triangular-shaped double pipe heat exchanger. To tackle the irregular boundaries, a nonorthogonal body-fitted coordinate (BFC) transformation technique is employed. The nondimensional transformed curvilinear conservation equations for mass, momentum, and energy are written in terms of physical variables and they are solved using a control-volume based finite difference method on a staggered grid arrangement. The developed model is then used to study the effects of the inner tube wall temperature, the initial temperature of the solid PCM, and the shape, as well as the position of the inner tube in the annulus on the melting characteristics, and cumulatively stored energy. Various quantities such as average Nusselt numbers over the inner tube surface, the total and complete melt fractions, and the latent and total stored energies all as a function of the melting time are reported. A correlation for the average Nusselt number on the inner tube wall is also provided. The numerical results show that the shape and the placement of the inner tube are crucial for the efficient design of a latent heat thermal energy storage (LHTES) system. The storage of energy is greatly influenced by the change of the inner tube wall temperature compared to the change of initial solid PCM temperature.

Numerical simulation of thermal flow of power-law fluids using lattice Boltzmann method on non-orthogonal grids

In this study, a lattice Boltzmann model is proposed to investigate thermal flow of power-law fluids in irregular geometries. Non-orthogonal grids on the physical plane are adopted to accurately depict curved boundaries. With respect to power-law fluid, the evolutions of particle distribution functions for velocity and temperature fields on the computational plane are derived on the basis of the generalized form of interpolation-supplemented lattice Boltzmann method and the rheological equation. For forced convection, the double-distribution-function method is used to predict the temperature field. The coupled lattice BGK model is employed to consider the conditions under which the velocity and temperature fields are strongly coupled, such as natural convection. The adiabatic boundary and symmetry boundary in body-fitted coordinates are specifically prescribed. Numerical procedure is further validated by modeling a series of cases including forced convection over a stationary heated circular cylinder and natural convection in cavities and an annulus between concentric circular cylinders, respectively. Good agreements with available data in the literature are achieved. The numerical results demonstrate that the effect of rheological and thermodynamic properties of power-law fluid on the heat transfer performance and flow field in complex geometries can be suitably captured by present thermal lattice Boltzmann method on non-orthogonal grids.

Numerical Model of Liquid Film Formation and Breakup in Last Stage of a Low-Pressure Steam Turbine

Formation of thin liquid films on steam turbine airfoils, particularly in last stages of low-pressure (LP) steam turbines, and their breakup into coarse droplets is of paramount importance to assess erosion of last stage rotor blades given by the impact of those droplets. An approach for this problem is presented in this paper: this includes deposition of liquid water mass and momentum, film mass and momentum conservation, trailing edge breakup and droplets Lagrangian tracking accounting for inertia and drag. The use of thickness-averaged two-dimensional (2D) equations in local body-fitted coordinates, derived from Navier–Stokes equations, makes the approach suitable for arbitrary curved blades and integration with three-dimensional (3D) computational fluid dynamics (CFD) simulations. The model is implemented in the in-house solver MULTI3, which uses Reynolds-averaged Navier–Stokes equations κ – ω model and steam tables for the steam phase and was previously modified to run on multi-GPU architecture. The method is applied to the last stage of a steam turbine in full and part load operating conditions to validate the model by comparison with time-averaged data from experiments conducted in the same conditions. Droplets impact pattern on rotor blades is also predicted and shown.

Numerical study of convective heat transfer from tube bank in cross flow using nanofluid

In this paper, laminar convective heat transfer of Al2O3 -water nanofluid flow over tube banks under constant wall temperature conditions has been numerically investigated. The circular-tube banks with staggered arrangement are considered in this study. The governing equations have been solved using finite volume approach based on SIMPLE technique in body-fitted coordinates. The numerical simulations have been conducted for Reynolds number ranging from 100 to 600 with nanoparticles volume fraction ranging from 0 to 0.05. The effect of longitudinal pitch, transverse pitch and nanoparticle concentration on the streamwise and temperature contours, average Nusselt number, friction factor and thermal-hydraulic performance factor have been investigated and discussed. Results showed that the best performance is obtained at longitudinal pitch ratio of 1.5, transverse pitch ratio of 2.5 and nanoparticles volume fraction of 5% over the ranges of Reynolds number.

Study on accuracy of casting flow simulation

In the field of casting flow simulation, the application of body-fitted coordinate (BFC) has not been widely used due to the difficulty and low efficiency of grid generation, despite the availability of good quality analysis results. Cartesian coordinates, on the other hand, have been used predominantly in casting process simulations because of their relatively easy and fast grid generation. However, Cartesian grid systems cannot obtain accurate results because they cannot express the geometries properly. In this study, Cut Cell method was applied to solve this problem. The three-dimensional incompressible viscous governing equation was analyzed using a function defined for the volume and area of the casting in the cutting cell. Using the Cut Cell method, accurate flow analysis results were also obtained in the Cartesian grid systems. The tests of simple shape and the applications of actual casting product have been tried with Cut Cell method.

Wearable thermoelectric generator for harvesting heat on the curved human wrist

Wearable electronics and sensors for health monitoring are becoming increasingly popular as their functionality continues to grow. Wearable thermoelectric generators (TEGs) are attracting interest due to their ability to self-power these electronic devices or sensors by harvesting human body heat. For wearable TEGs, a flexible thermal interface layer (TIL) is used underneath the TEG for wearing on the human body. The large thermal resistance induced at the interface between the skin and the TEG currently limits improvements in the performance of wearable TEGs and needs to be evaluated. This paper develops a numerical model to investigate the performance of wearable TEGs on the curved human wrist. The TEG and bottom TIL are meshed using rectangular grids and the body-fitted coordinate (BFC) transformation, respectively. Using the finite volume method (FVM), the proposed model is calculated, and the temperature and voltage distributions in the TEG and bottom TIL are analyzed. The effects of the radii of curvature of the curved surface, the material properties, and the thicknesses of the TIL are investigated both numerically and experimentally. The results obtained in this research can be utilized for optimal structural designs for wearable TEGs and for material selection of the TIL to enhance the power generation for self-powered electronics.