Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Diogo B. Pitz ◽  
John W. Chew ◽  
Olaf Marxen ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fourier Method ◽  
Spectral Element ◽  
Two Dimensions ◽  
High Order ◽  
Experimental Results ◽  
Element Approximation ◽  
Stable Algorithm ◽  
Element Discretization

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretization in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretize the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretization. Numerical results obtained for the rotor/stator cavity compare favorably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.

Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method

2016 ◽  
Author(s):  
Diogo B. Pitz ◽  
John W. Chew ◽  
Olaf Marxen ◽  
Nicholas J. Hills
Keyword(s):  
Numerical Method ◽  
Boussinesq Approximation ◽  
Spectral Element ◽  
High Order ◽  
Element Approximation ◽  
Cavity Flows ◽  
Governing Equations ◽  
Stable Algorithm ◽  
Numerical Predictions ◽  
Rotating Cavity

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, similarly to a finite element method, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation, and no subgrid modelling is included in the governing equations. Numerical results obtained for the rotor/stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. For the buoyancy-driven flow, the energy equation is coupled to the momentum equations via the Boussinesq approximation, which has been implemented in the code considering two different formulations. Numerical predictions of the Nusselt number obtained using the traditional Boussinesq approximation are considerably higher than available experimental data. Much better agreement is obtained when the extended Boussinesq approximation is employed. It is concluded that the numerical method employed has considerable potential for further investigations of rotating cavity flows.

scholarly journals Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology

2021 ◽  
Author(s):  
◽  
Celine Cattoen
Keyword(s):  
Variational Formulation ◽  
Numerical Relativity ◽  
Cosmological Parameters ◽  
Spectral Element ◽  
Space Time ◽  
High Order ◽  
Einstein Equations ◽  
Element Discretization ◽  
Friedmann Equations ◽  
Hubble Flow

<p>Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions. That is, one does not assume the Friedmann equations (Einstein equations) unless and until absolutely necessary. On the other hand, cosmodynamics is the part of cosmology that relates the geometry to the density and pressure using the Friedmann equations. In both frameworks, we consider the amount of information and the nature of the constraints we can obtain from the Hubble flow in a FLRW universe. Indeed, the cosmological parameters contained in the Hubble relation between distance and redshift provide information on the behaviour of the universe (expansion, acceleration etc...). In the first framework, it is possible to concentrate more directly on the observational situation in a model-independent manner. We perform a number of inter-related cosmographic fits to supernova datasets, and pay particular attention to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. In the second framework, we use the class of w-parameter models which has become increasingly popular in the last decade. We explore the extent to which a constraint on the w-parameter leads to useful and non-trivial constraints on the Hubble flow in terms of cosmological parameters H(z), density p(z), density parameter O(z), distance scales d(z), and lookback time T(z). On another front, Numerical Relativity has experienced many breakthroughs since 2005, with full inspiral-merger-ringdown simulations now possible. One of the main goals is to provide very accurate templates of gravitational waves for ground-based and space-based interferometers. We explore the potential of a very recent and accurate numerical method, the Spectral Element Method (SEM), for Numerical Relativity, by treating a singular Schwarszchild black hole evolution as a test case. Spectral elements combine the theory of spectral and pseudo-spectral methods for high order polynomials and the variational formulation of finite elements and the associated geometric flexibility. We use the BSSN formulation of the Einstein equations with the method of the moving punctures. After applying the variational formulation to the BSSN system, we present several possible weak forms of this system and its spectral element discretization in space. We use a Runge-Kutta fourth order time discretization. The accuracy of high order methods can deteriorate in the presence of discontinuities or sharp gradients. We show that we can treat the element that contains the puncture with a filtering method to avoid artificial and spurious oscillations. These might form and propagate into the domain coming from discontinuous initial data from the BSSN system.</p>

Numerical Simulation of Thermal Performance of a High Aspect Ratio Thermal Energy Storage Device

2012 ◽  
Author(s):  
Jingde Zhao ◽  
Jorge L. Alvarado ◽  
Ehsan M. Languri ◽  
Chao Wang
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Energy Storage ◽  
Aspect Ratio ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
High Aspect Ratio ◽  
Numerical Study ◽  
Experimental Results ◽  
Heat Transfer Analysis

Heat transfer analysis of a high aspect ratio thermal energy storage (TES) device was carried out numerically. The three dimensional numerical study was performed to understand the heat transfer enhancement which results from internal natural convection in a high aspect ratio vertical unit. Octadecane was used as phase change material (PCM) inside TES system, which consisted of six corrugated panels filled with PCM. Each panel had a total of 6 tall cavities filled with PCM, which were exposed to external flow in a concentric TES system. Unlike traditional concentric-type TES devices where heat transfer by conduction is the dominant heat transport mechanism, the high aspect ratio TES configuration used in the study helped promote density-gradient based internal convection mechanism. The numerical model was solved based on the finite volume method, which captured the whole transient heat transfer process effectively. The time-dependent temperature profiles of the PCM inside a single TES panel are compared with the experimental results for two cases. Numerical and experimental results of the two cases showed a reasonable agreement. Furthermore, convection cells were formed and sustained when the PCM melted within the space between the solid core and the walls. The promising results of this numerical study illustrate the importance of internal natural convection on the speed of the PCM melting (charging) process.

Numerical and Experimental Studies of Fluid Flow and Heat Transfer in a Model Experiment for Hydrothermal Growth

2016 ◽  
Vol 254 ◽  
pp. 237-242
Author(s):  
Daniel Ursu ◽  
Radu Negrila ◽  
Alexandra Popescu ◽  
Ioan Grozescu ◽  
Daniel Vizman
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Natural Convection ◽  
Temperature Difference ◽  
Experimental Studies ◽  
Experimental Results ◽  
Convection Flow ◽  
Bottom Part ◽  
Flow And Heat Transfer ◽  
Liquid Flows

Understanding of the natural convection flow in hydrothermal autoclaves is essential for the control of the growth rate and the quality of the grown crystals. This paper presents an analysis of the natural convection fluid flow and heat transfer and show the comparison between simulation and experimental results for the experimental model in a small size autoclaves, fill with water. A numerical model based on finite volume method has been developed to simulate the heat transfer and fluid convection in the vessel. Results show that the flow will strongly affect the temperature distribution. It can be observed that in the upper region the liquid flows up in the middle of the vessel and flows down in lateral parts near the walls. The temperature difference between experimental and simulation results is less than 1 °C in the upper part and between 2 and 3 °C in the bottom part. Velocity measurements show a good qualitative agreement between simulation and experimental results. The value of the z-component of velocity along the symmetry axis slightly increase with the increases of temperature difference ΔT .

Heat Transfer From an Oscillating Horizontal Wire

1971 ◽  
Vol 93 (2) ◽  
pp. 239-240 ◽  
Author(s):  
B. F. Armaly ◽  
D. H. Madsen
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Path Length ◽  
Experimental Results ◽  
Thin Wire ◽  
Reciprocating Motion ◽  
Total Path Length ◽  
The Wire ◽  
Horizontal Wire

The effect of vibration on heat transfer by natural convection has been investigated experimentally using a thin wire, 0.010 in. in diameter, and air as a convection medium. Horizontal reciprocating motion of varying amplitudes, peak-to-peak values of 0–2.655 in., and frequencies, 0–20 cps, was applied to an electrically heated horizontal wire. The average wire velocity (frequency times total path length traveled per cycle by the wire) was used to correlate and predict the experimental results.

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