One-dimensional model for the Rijke tube

1989 ◽  
Vol 202 ◽  
pp. 83-96 ◽  
Author(s):  
C. Nicoli ◽  
P. Pelcé
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Dimensional Model ◽  
Unsteady Heat Transfer ◽  
Order Unity ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
One Dimensional ◽  
The Stability ◽  
Stability Limits

We develop a simple model in which longitudinal, compressible, unsteady heat transfer between heater and gas is computed in the small-Mach-number limit. This calculation is used to determine the transfer function of the heater, which plays an important role in the stability limits of the thermoacoustic instability of the Rijke tube. The transfer function is determined analytically in the limit of small expansion parameter γ, and numerically for γ of order unity. In the case ρμ/cp = constant, an analytical solution can be found.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

scholarly journals A one-dimensional tearing mode equation for pedestal stability studies in tokamaks

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
J. W. Connor ◽  
R. J. Hastie ◽  
C. Marchetto ◽  
C. M. Roach
Keyword(s):  
Cross Section ◽  
Approximate Equation ◽  
Stability Studies ◽  
Dimensional Model ◽  
Tearing Mode ◽  
One Dimensional ◽  
Tearing Modes ◽  
The Stability ◽  
Poloidal Flux

Starting from expressions in Connor et al. (Phys. Fluids, vol. 31, 1988, p. 577), we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna & Callen (Phys. Plasmas, vol. 1, 1994, p. 2308) and Nishimura et al. (Phys. Plasmas, vol. 5, 1998, p. 4292), but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. the Joint European Torus (JET). We discuss how this one-dimensional model for tearing modes, which assumes a single poloidal harmonic for the perturbed poloidal flux, compares with a model that includes poloidal coupling Fitzpatrick et al. (Nucl. Fusion, vol. 33, 1993, p. 1533).

One-Dimensional Zonal Model for the Unsteady Heat Transfer Analysis in an Open Volumetric Air Receiver

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Gurveer Singh ◽  
Vishwa Deepak Kumar ◽  
Laltu Chandra ◽  
R. Shekhar ◽  
P. S. Ghoshdastidar
Keyword(s):  
Heat Transfer ◽  
High Heat ◽  
Operating Conditions ◽  
Heat Transfer Analysis ◽  
Transfer Model ◽  
High Heat Flux ◽  
Unsteady Heat Transfer ◽  
Volumetric Heating ◽  
One Dimensional ◽  
Zonal Model

Abstract The open volumetric air receiver (OVAR)-based central solar thermal systems provide air at a temperature > 1000 K. Such a receiver is comprised of porous absorbers, which are exposed to a high heat-flux > 800 Suns (1 Sun = 1 kW/m2). A reliable assessment of heat transfer in an OVAR is necessary to operate such a receiver under transient conditions. Based on a literature review, the need for developing a comprehensive, unsteady, heat transfer model is realized. In this paper, a seven-equations based, one-dimensional, zonal model is deduced. This includes heat transfer in porous absorber, primary-air, return-air, receiver casing, and their detailed interaction. The zonal model is validated with an inhouse experiment showing its predictive capability, for unsteady and steady conditions, within the reported uncertainty of ±7%. The validated model is used for investigating the effect of operating conditions and absorber geometry on the thermal performance of an absorber. Some of the salient observations are (a) the maximum absorber porosity of 70–90% may be preferred for non-volumetric and volumetric-heating conditions, (b) the minimum air-return ratio should be 0.7, and (c) the smallest gap to absorber-length ratio of 0.2 should suffice. Finally, suggestions are provided for extending the model.

One Dimensional Model for Rotating Channels in the Turbine System: Part 2 — Formulation and Validation for Film Condensation

2013 ◽  
Author(s):  
Murali Krishnan R. ◽  
Zain Dweik ◽  
Deoras Prabhudharwadkar
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Steam Turbine ◽  
Compressible Flow ◽  
Saturation Temperature ◽  
Film Condensation ◽  
Bulk Temperature ◽  
Dimensional Model ◽  
One Dimensional

This paper provides an extension of the previously described [1] formulation of a one-dimensional model for steady, compressible flow inside a channel, to the steam turbine application. The major challenge faced in the network simulation of the steam turbine secondary system is the prediction of the condensation that occurs during the engine start-up on the cold parts that are below the saturation temperature. Neglecting condensation effects may result in large errors in the engine temperatures since they are calculated based on the boundary conditions (heat transfer coefficient and bulk temperature) which depend on the solution of the network analysis. This paper provides a detailed formulation of a one-dimensional model for steady, compressible flow inside a channel which is based on the solution of two equations for a coupled system of mass, momentum and energy equations with wall condensation. The model also accounts for channel area variation, inclination with respect to the engine axis, rotation, wall friction and external heating. The formulation was first validated against existing 1D correlation for an idealized case. The wall condensation is modeled using the best-suited film condensation models for pressure and heat transfer coefficient available in the literature and has been validated against the experimental data with satisfactory predictions.

Experimental studies of the propagation of combustion in solids

1992 ◽  
Vol 339 (1654) ◽  
pp. 387-394 ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Analysis ◽  
Steady State ◽  
Chemical Kinetics ◽  
Profile Analysis ◽  
Numerical Models ◽  
Experimental Studies ◽  
Dimensional Model ◽  
Thermal Methods ◽  
One Dimensional

The application of thermal methods to the study of steady-state combustion is described. Such methods provide a route to information on heat transfer and chemical kinetics which forms a basis for the implementation of numerical models. The experimental results from thermal analysis and temperature profile analysis have been examined within the context of a simple pseudo one-dimensional model of propagation offering some confirmation of the validity of the approach.

A One-Dimensional Model for Heat Transfer in Engine Exhaust Systems

2005 ◽  
Author(s):  
Huiyu Fu ◽  
Xiangdong Chen ◽  
Ian Shilling ◽  
Steve Richardson
Keyword(s):  
Heat Transfer ◽  
Dimensional Model ◽  
Engine Exhaust ◽  
One Dimensional ◽  
Exhaust Systems

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

scholarly journals UNSTEADY HEAT TRANSFER IN A HORIZONTAL GROUND HEAT EXCHANGER

2018 ◽  
Vol 40 (4) ◽  
pp. 34-40
Author(s):  
B.I. Basok ◽  
B.V. Davidenko ◽  
I.K. Bozhko ◽  
M.V. Moroz
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Three Dimensional ◽  
Heat Transfer Agent ◽  
Ground Heat Exchanger ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Unsteady Heat Transfer ◽  
Pump System ◽  
Heat Pump System

By the three-dimensional model of heat transfer in the system "ground - horizontal ground heat exchanger - heat transfer agent", an analysis of the efficiency of the horizontal multi-loop heat exchanger, which is an element of the heat pump system, was carried out. Based on the results of numerical simulation, the time dependence of the heat transfer agent temperature at the outlet from the ground heat exchanger and the amount of heat extracted from the ground is determined. The results of calculations by the presented model are satisfactorily agree with the experimental data.

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