A one-dimensional model is derived for natural convection in a closed loop. The model accounts for a non-symmetric arrangement of heat sources and sinks. A nonlinear analysis of these equations is performed as well as experiments to validate the model predictions. Distinct subcritical regions are observed in addition to a variety of stable steady flow regimes. An absolutely unstable range also exists which is characterized by a chaotic time behaviour of the flow quantities

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090000817

Dynamical behaviour of natural convection in a single-phase loop

A 1-D/2-D model and experimental results for a closed-loop thermosyphon with vertical heat transfer sections

Numerical investigation of natural circulation in a 2D-annular closed-loop thermosyphon

Flow stability in a natural circulation loop: influences of wall thermal conductivity

In a natural circular loop, the thermal convection demonstrates various spatial patterns and temporal instabilities. Problem consists in determining them with respects to thermal boundary conditions. To this end a multiple scales analysis is applied which resembles the inherent characteristic of the pattern formation in the Rayleigh-Benard convection. A three-dimensional nonlinear model is proposed by incorporating the flow modes derived along the analysis. The differences of thermal boundary condition are reflected by a coefficient & For small δ, numerical solution to the model shows that only temporal instability exists and Lorenz chaos is possible, otherwise, for large values both spatial and temporal instabilities occur leading to cellular flow and intermittency chaos. The model predicted some additional phenomena opening for experimental observation. It seems significant that this study proposes an algorithm for the control of flow stability and distribution by varying the thermal boundary condition.

Spatial and Temporal Stabilities of Flow in a Natural Circulation Loop: Influences of Thermal Boundary Condition

Velocity and temperature profiles were measured at the entrance and exit to the heating section of a toroidal thermosyphon loop operating under steady flow conditions for a range of heat inputs. Velocity measurements were made with a laser-Doppler velocimeter and temperature measurements with a small thermocouple probe. Detailed results are presented for the longitudinal and circumferential components of the velocity for four heat inputs. The data for cross-stream secondary flows and streamwise flow reversals emphasize the importance of including three-dimensional effects in analyses of these systems.

An Experimental Study of Natural Convection in a Toroidal Loop

Fluid temperature measurements are reported for a natural convection loop operating in the steady state regime Averaged and fluctuating measurements were made for a toroidal thermosyphon oriented in the vertical plane that was heated over the lower half and cooled over the upper half The measurements were made along the tube diameter at the entrance and exit of the heating sections for heat inputs from 1400 to 8410 w/m2 The amplitude of the temperature fluctuations exceeded 10 °C near the inner walls indicating the effects from recirculating flow regions at the entrances to the heating and cooling sections

https://link.springer.com/content/pdf/10.1007/BF01009288.pdf

C. H. Stern

Papers

An Experimental Study of Natural Convection in a Toroidal Loop

Measurements in a natural convection loop