An Implicit Scheme for Cascade Flow and Heat Transfer Analysis

1999 ◽  
Vol 122 (2) ◽  
pp. 294-300 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Implicit Scheme ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Computational Time ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Intermediate Time ◽  
The Difference

A new efficient implicit scheme, based on the second-order time and spatial difference algorithm for solving steady flow by using time-marching Navier–Stokes equations, was developed for predicting turbine cascade flows and heat transfer. The difference scheme comprises an explicit part in the intermediate time-step and an implicit part in the local time-step. The viscous flux vectors are decomposed to simplify the flow calculation in the explicit step. The time difference terms are expressed in terms of the viscous dependent terms that appear in the diffusion terms in the form by adding eigenvalues of viscous flux matrices into the time derivation term. In the presently proposed scheme, the two-sweep procedure is used in the implicit step instead of employing a traditional matrix operation to save the computational time. This method has been used to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with other published computations. The comparisons for both surface pressure and heat transfer coefficient showed good agreement with the experiments. [S0889-504X(00)01702-5]

scholarly journals An Implicit Scheme for Cascade Flow and Heat Transfer Analysis

1999 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Implicit Scheme ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Computational Time ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Intermediate Time ◽  
The Difference

A new efficient implicit scheme, based on the second-order time and spatial difference algorithm for solving steady flow by using time-marching Navier-Stokes equations, was developed for predicating turbine cascade flows and heat transfer. The difference scheme comprises an explicit part in the intermediate time-step and an implicit part in the local time-step. The viscous flux-vectors are decomposed to simplify the flow calculation in the explicit step. The time difference terms are expressed in terms of the viscous dependent terms which appear in the diffusion terms in the form by adding eigenvalues of viscous flux matrices into the time derivation term. In the presently proposed scheme, the two-sweep procedure is used in the implicit step instead of employing a traditional matrix operation to save the computational time. This method has been used to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with other published computations. The comparisons for both surface pressure and heat transfer coefficient showed good agreement with the experiments.

scholarly journals Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections

2020 ◽  
Vol 10 (22) ◽  
pp. 7952
Author(s):  
Qiang Wang ◽  
Boran Zhang ◽  
Pengyao Yu ◽  
Guangzhao Li ◽  
Zhijiang Yuan
Keyword(s):  
Stokes Equations ◽  
Water Entry ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Surface Evolution ◽  
Mesh Method ◽  
The Difference ◽  
Dynamics Method

The bow-flared section may be simplified in the prediction of slamming loads and whipping responses of ships. However, the difference of hydrodynamic characteristics between the water entry of the simplified sections and that of the original section has not been well documented. In this study, the water entry of several different bow-flared sections was numerically investigated using the computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations. The motion of the grid around the section was realized using the overset mesh method. Reasonable grid size and time step were determined through convergence studies. The application of the numerical method in the water entry of bow-flared sections was validated by comparing the present predictions with previous numerical and experimental results. Through a comparative study on the water entry of one original section and three simplified sections, the influences of simplification of the bow-flared section on hydrodynamic characteristics, free surface evolution, pressure field, and impact force were investigated and are discussed here.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

A parallel partition of unity method for the nonstationary Navier-Stokes equations

2017 ◽  
Vol 27 (8) ◽  
pp. 1675-1686 ◽  
Author(s):  
Guangzhi Du ◽  
Liyun Zuo
Keyword(s):  
Stokes Equations ◽  
Partition Of Unity ◽  
Navier Stokes ◽  
Computational Time ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Standard Galerkin Method

Purpose The purpose of this paper is to propose a parallel partition of unity method (PPUM) to solve the nonstationary Navier-Stokes equations. Design/methodology/approach This paper opted for the nonstationary Navier-Stokes equations by using the finite element method and the partition of unity method. Findings This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method but saves a lot of computational time. Originality/value In this paper, a PPUM is proposed for nonstationary Navier-Stokes. At each time step, the authors only need to solve a series of independent local sub-problems in parallel instead of one global problem.

Numerical Simulation of a Synthetic Jet Actuator Using a Simplified Periodic Boundary Condition

2010 ◽  
Author(s):  
Antonio Pascau ◽  
Nelson Garci´a
Keyword(s):  
Stokes Equations ◽  
Synthetic Jet ◽  
Navier Stokes ◽  
Computational Time ◽  
Test Case ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Synthetic Jet Actuator ◽  
Collocated Grid ◽  
Face Velocity

When using a collocated grid for the discretization of the unsteady Navier-Stokes equations special care has to be taken in the evaluation of the cell face velocity as if it is not properly calculated the resulting flow field may be dependent on the time step. This dependency increases as the time step is reduced so this problem can be of paramount importance in rapidly varying flows. As an illustration of the problem in a flow of industrial interest a synthetic jet has been chosen. Although the primary goal of the paper is not to compare computational and experimental results, the assessment with experimental data will highlight the discrepancies in the computational results with different time steps. For comparison purposes a well documented case was chosen: the first test case of the synthetic jet workshop organized by NASA in 2004, but with the new 2006 data. This flow is produced by a moving diaphragm at one of the sides of a cavity connected to an otherwise stagnant air through a slot. Near the slot exit the flow is almost bidimensional so in order to reduce computational time it has been modelled in a 2D domain with a transpiration velocity at the bottom boundary of a simplified cavity. This velocity tries to reproduce the waveform of the measurements at the slot exit with an appropriate combination of Fourier modes.

Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Giulio Croce ◽  
Olga Rovenskaya ◽  
Paola D'Agaro
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mach Number ◽  
Heat Sink ◽  
Conjugate Heat Transfer ◽  
Stokes Equations ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Navier Stokes Equations

A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

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