Natural Convection in a Concentric Annulus

In this application, AcuSolve is used to simulate natural convection in the annular space between a heated inner pipe and an outer concentric pipe. AcuSolve results are compared with experimental results adapted from Kuehn and Goldstein (1978). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with flow induced by natural convection.

Problem Description

The problem consists of two concentric cylinders with air filling the void between them, as shown in the following image, which is not drawn to scale. The radius of the inner cylinder is 0.0178 m and the radius of the outer cylinder is 0.0463 m. The inner cylinder is held at a fixed temperature of 373 K while the outer cylinder is held at 327 K. The temperature gradient drives the flow due to buoyancy effects.
Figure 1. Critical Dimensions and Parameters for Simulating Natural Convection in a Concentric Annulus

The simulation was performed as a two dimensional problem by restricting flow in the out-of-plane direction through the use of a mesh that is one element thick. In addition, the half symmetry of the geometry is exploited to allow for modeling only half of the geometry. These characteristics allow for accurate simulation of the flow while minimizing computational time.
Figure 2. Mesh (Half of a Concentric Annulus) used for Simulating Natural Convection in a Concentric Annulus

AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. Air density decreases due to heating by the inner cylinder, leading to convective currents within the annulus. As air approaches the outer cylinder, it is cooled by the outer wall, causing the density to increase. This results in heavier air sinking toward the bottom of the assembly.
Figure 3. Temperature Contours and Velocity Vectors

Figure 4. Temperature as a Function of Distance From the Center of the Inner Cylinder


The AcuSolve solution compares well with analytical results for natural convection in a concentric annulus. In this application, flow is driven by a decrease in density as air is heated. The local variations in density result in the higher density fluid sinking to the bottom of the annulus while the lower density fluid rises to the top. This transfer of momentum is a continuous process which results in the convective currents that are visible in the solution. The AcuSolve temperature results compare very closely with the experimental results.

Simulation Settings for Natural Convection in a Concentric Annulus

HyperMesh CFD database file: <your working directory>\annulus_heat\


  • Problem Description
    • Analysis type - Steady State
    • Abs. pressure offset - 101325.0 N/m2
    • Temperature equation - Advective Diffusive
    • Turbulence equation - Laminar
    • Gravitational acceleration - { 0, -9.80665, 0 }
  • Auto Solution Strategy
    • Relaxation factor - 0.2
    • Flow - On
    • Temperature - On
  • Material Model
    • Air
      • Type - Boussinesq
      • Density - 1.225 kg/m3
      • Expansivity - 0.0034722 1/K
      • Reference temperature - 288 K
      • Isothermal compressibility - 0.0 m2/N
      • Viscosity - 2.081e-5 kg/m-sec


  • Volumes
    • Fluid
      • Element Set
        • Material model - Air
    • Surfaces
      • ID
        • Simple Boundary Condition
          • Type - Wall
          • Temperature BC type - Value
          • Temperature - 373.0 K
      • Max_Z
        • Simple Boundary Condition
        • Type - Symmetry
      • Min_Z
        • Simple Boundary Condition
        • Type - Symmetry
      • OD
        • Simple Boundary Condition
          • Type - Wall
          • Temperature BC type - Value
          • Temperature - 327.0 K
      • Symmetry
        • Simple Boundary Condition
        • Type - Symmetry
    • Nodes
      • Node 1
        • Pressure
          • Type - Zero


T.H. Kuehn and R. J. Goldstein. "An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli". Journal of Heat Transfer 100:635-640. 1978.