NATURAL CONVECTION IN A VERTICAL ANNULUS BOARDED BY AN INNER WALL OF FINITE THICKNESS

Numerical investigation is performed to analyze natural convection heat transfer characteristics within a corrugated surface enclosure filled with fluid under the Rayleigh-Bénard (RB) instability. The impact of the geometric contribution associated with the convective RB effect, is analyzed to provide qualitative heat transfer and flow structure. Such thermal process is applying for improving the engineering Polymerase chain reaction (PCR) process to amplify a target DNA sample. The grid generation is used to transform the physical complex domain to a computational regular coordinate. The governing differential equations are discretized by Finite volume approach using a quadratic scheme approximation. The main objective of this work is to analyze the combined physical and geometric effects characterizing the corrugated enclosure, on the behavior of convective flow and to enlarge the active isothermal area favorable for the elementary process actions. Under the effect of the different control parameters defined by the dimensionless mathematical model, we demonstrate the existence of critical corrugations amplitude as a function of Ra-λ, describing the bifurcation from monocellular towards a bicellular flow. The active isothermal zone are identified, quantified and physical explanation and predictive expression were established.

The wellbore dynamics of CO₂ injectors is of great importance to all CO₂ geological storage and utilization technologies. Natural convection heat transfer of the annular fluid was found to have a non-negligible influence on CO₂ temperature distribution in the injection well, which determines CO₂ properties when entering the reservoir and thus influences CO₂ injectivity, storage and utilization efficiencies. An experimental system was set up in the study combining supercritical pressure CO₂ flowing inside the inner tube and natural convection of the annular water. The uniform heat flux was given to the outer cylinder to represent the geothermal heat flux from the surrounding rock. The natural convective heat transfer coefficient and the CO₂ temperature increase were acquired with different heat fluxes, CO₂ inlet temperatures, inlet pressures and mass flow rates. Measurements were made after establishing steady-state conditions. The fitted correlations of natural convective heat transfer coefficient and equivalent thermal conductivity of the annular water were obtained and compared with the direct simulation of the natural convection in Ordos and an offshore CCS projects, showing good consistency. The results indicated that obtained equivalent thermal conductivity of the annular water could be a useful parameter for simplification and validation of modeling CO₂ injectors.

Based on distributed temperature sensing (DTS) and pressure data well bore thermodynamics and heat transfer are determined for the CO₂ injection well in Ketzin, Germany. The DTS signal is decomposed in two components, a mean value and a spatial derivation. The mean value and the pressure data are the basis for a thermodynamically phase state calculation. The derived heat transfer is of high accuracy for shallow depth but the sensitivity to measurement errors increases for deeper parts of the well when the phase change becomes isentropic. These limitations are compensated by a new evaluation of DTS signals. The derivation of the DTS signal is proportional to the radial heat flux. The proportionality factor is calibrated under conditions when the thermodynamic method provides accurate results. The combination allows to determine heat transfer for all operational conditions and the entire well. The analyses is used to determine thermodynamics, maintain stable injection conditions and may be applied for minimising the heating energy.

A two-dimensional (2D) axisymmetric (radial) model, considering the effects of the fluid in annulus and heat transfer with surrounding rocks is developed to investigate the flow and thermal behavior of CO₂ in injection well during its geological sequestration. The mass equation, the momentum equations with turbulent model and energy equation are solved both in the wellbore flow direction and the radial direction using computational fluid dynamics (CFD) method. Real-gas properties are employed to ensure the calculation accuracy. The wellhead pressure and bottomhole temperature behavior with injection time are predicted. The impact of natural convection of water in the annulus on flow and thermal behavior of injected CO₂ are also studied. Besides, factors impacting the bottomhole temperature of CO₂ are analyzed. It is found that the work done by pressure (compressibility), potential energy loss and the heat exchange with surrounding rocks are three major factors leading to an increase in the bottomhole temperature of CO₂ comparing to the injection temperature. With an increase in injection mass flow rate, the wellhead pressure decreases firstly and then increases, and the bottomhole temperature of CO₂ decreases nonlinearly. However, both of them increase linearly with an increase in the injection temperature. This study may help deepen our understanding of the mechanisms of CO₂ injection and generate quantitative information in support of design, monitoring and risk assessment of the CO₂ geological sequestration.

The heat transfer due to natural convection of air in a square cavity with two differentially heated opposite walls and the other two adiabatic is numerically studied in the laminar regime as both the Rayleigh number and the inclination angle of the cavity change. The range of the inclination angle covers a whole revolution. The lattice Boltzmann method with two distribution functions, one for particles and the other for temperature is used. The method is validated with a benchmark result for a vertical cavity. A general power law dependence of the Nusselt number with respect to the Rayleigh number with the coefficient and exponent as functions of the inclination angle is presented. For a fixed Rayleigh number, hysteresis as the inclination angle increases or decreases is found. The range of inclination angles for hysteresis depends on the Rayleigh number.

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.