C.J. Hoogendoorn

Natural-convection flow in a square cavity calculated with low-Reynolds-number turbulence models

The laminar and turbulent natural-convection flow in a two-dimensional square cavity heated from the vertical side is numerically calculated up to a Rayleigh number of 1014 for air and up to 1015 for water. Three different turbulence models are compared: the standard k-e model with logarithmic wall functions and the low-Reynolds-number models of Chien, and Jones and Launder. The position of the laminar-turbulent transition in the vertical boundary layer strongly depends on the turbulence model used. Moreover, multiple solutions for the transition position can occur for a fixed Rayleigh number at the same numerical grid. The thermal stratification in the core of the cavity breaks up when the flow becomes turbulent. Comparison of the averaged wall-heat transfer with experiments for the hot vertical plate and for tall vertical cavities shows that the standard k-e model gives a too high prediction, whereas the low-Reynolds-number models are reasonably close to the experiment.

The effect of turbulence on heat transfer at a stagnation point

An experimental study on heat transfer of impinging circular jets shows the effect of turbulence for the stagnation zone. The work relates to cases of small nozzle-to-plate distances. A new measuring technique using liquid crystals has been employed. The effect of jet turbulence is described by the same type of relationship as given in the literature for stagnation point heat transfer for cylinders. It is shown that the relative increase at the stagnation point for impinging jets is the same as for cylinders in a free stream. For small zD values Nu at the stagnation point is smaller than for points in the region directly around it, but only in those cases where the turbulence level in the issuing jet is low ( 5 and for a turbulent primary jet stream.

Laminar convective heat transfer in helical coiled tubes

Abstract An experimental and numerical study has been made on convective heat transfer in coiled tubes. The experiments have been carried out for tube diameter/coil diameter ratios from 1 100 to 1 10 , Prandtl numbers from 10 to 500 and Reynolds numbers from 20 to 4000. The heat transfer has been studied for two boundary conditions: for a uniform peripherally averaged heat flux and for a constant wall temperature. Attention has been paid to the heat transfer in the thermal entry region as well as in the fully developed thermal region. The results obtained and the relations proposed could be explained from and are based on the flow behaviour.

Numerical study of laminar and turbulent natural convection in an inclined square cavity

Two-dimensional numerical simulations of the natural convection flow of air in a differentially heated, inclined square cavity were performed for both laminar and turbulent flows. The angle of inclination of the cavity was varied from 0° (heated from below) to 180° (heated from above). For Rayleigh numbers between 104 and 1011 the natural convection flow has been calculated. A detailed analysis was made for Rayleigh numbers of 106 and 1010. The standard k−e model for turbulence was used in the prediction of turbulent flows. Numerical predictions of the heat flux at the hot wall and the influence of the angle of inclination on the Nusselt number are presented. The Nusselt number shows strong dependence on the orientation of the cavity and the power law dependence on the Rayleigh number of the flow. Flow patterns and isotherms are shown to give greater understanding of the local heat transfer. For the high Rayleigh number calculations hysteresis of the solution was found at a transition of flow patterns.

Transition to time-periodicity of a natural-convection flow in a 3D differentially heated cavity

Abstract The steady and time-periodic flow of air in a differentially heated cubical cavity has been studied numerically, using the finite-volume method. In the steady flow regime, the scaling in the boundary layer along the wall has been investigated. In the periodic flow regime, the calculated frequency was almost the same as for the two-dimensional square cavity, suggesting that the same instability mechanism is in both cases responsible for the bifurcation. There was, however, a strong three-dimensionality in the distribution of the amplitude of the oscillations.

Comparison of turbulence models for the natural convection boundary layer along a heated vertical plate

Abstract With a numerical code for solving the boundary-layer equations, the performance of different turbulence models for the natural convection boundary layer for air along a heated vertical plate is tested. The algebraic Cebeci-Smith model, the standard k-e model with wall functions for k and e and different low-Reynolds number k-e models are tested. The Cebeci-Smith model calculates a too low wall-heat transfer and turbulent viscosity. The standard k-e model with wall functions gives a too high wall-heat transfer, but the velocity and temperature profiles agree reasonably with experiments. Accurate wall-heat transfer results require the use of low-Reynolds number k-e models; the models of Lam and Bremhorst, Chien, and Jones and Launder perform best up to a Grashof number of 1011. For larger Grashof numbers the Jones and Launder model is best. A sensitivity study shows that the wall-heat transfer with the standard k-e model largely depends on the choice of the wall functions for k and e. Replacing these wall functions by zero wall conditions for k and e and adding the functions D and ƒ μ of the Chien model to the standard k-e model gives a simple, but accurate low-Reynolds number k-e model for the natural convection boundary layer.

Convective heat transfer on a plate in an impinging round hot gas jet of low Reynolds number

Abstract An experimental study has been made of the local heat transfer on the plane isothermal surface in the normal impinging round hot jet of combustion products produced by a rapid heating tunnel burner. A conductivity heat plug, impact tubes and fine wire thermocouples were used to measure heat flux, mean velocity and temperature distributions. Some centerline relative turbulence intensity measurements were done with a Laser Doppler Anemometer. All measurements were obtained at two efflux Reynolds numbers 1860 and 1050; the density ratio between hot combustion products and ambient air was 7.6. Heat transfer was measured at distances between 2 and 20 D. The stagnation point heat transfer within the distances x D ⩽ 5 is in good agreement with Sibulkins laminar boundary layer theory. In the developed region x D ⩾ 8 strong free jet turbulence effects augmenting the convective heat transfer were observed. The radial heat transfer distributions are qualitatively consistent with those known in the impinging cold jet investigations at low Reynolds numbers.

Scaling of the laminar natural-convection flow in a heated square cavity

Abstract The steady laminar natural-convection flow of air and water in a square heated cavity is calculated for increasingly large Rayleigh number. The flow is calculated by solving both the Navier-Stokes equations and the boundary-layer equations. The results are used to determine the proper scalings of the flow in the different asymptotic flow regions: vertical boundary layers, core region, corner region and horizontal boundary layers. In particular the scalings according to the Navier-Stokes equations agree with the asymptotic model for the core and vertical boundary layers as proposed by Gill [ J. Fluid Mech. 26 , 515–536 (1966)].

Comparative experimental and numerical investigation of a piloted turbulent natural-gas diffusion flame

A turbulent natural-gas diffusion flame is investigated both experimentally and numerically. Measuredquantities involve mean velocity, turbulence characteristics, mean temperatures, visualisation of the OH reaction zone and passive scalar concentration, and statistical analysis of OH concentrations. The configuration is a laboratory-scale piloted diffusion flame with annular coflowing air, placed in a ventilated confinement, of well-defined initial and boundary conditions. The fuel jet velocity is 23.2 m/s, and the annular air velocity is 5.1 m/s. The techniques used are laser-Doppler anemometry (LDA), thermocouple measurements, and 1D- and 2D-laser induced fluorescence (LIF). The mathematical model is based on a constrained-equilibrium conserved-scalar model, resembling a laminar flamelet model, with a standard k-e turbulence model and a four-flux radiation model. Comparisons up to 42 jet diameters downstream of the burner nozzle show good agreement for meanaxial velocity and temperatures. The turbulence quantities are qualitatively reproduced by the k-e turbulence model. The OH radical concentrations are underpredicted because of the lack of superequilibrium effects in the chemistry model. In addition, the profile shapes do not correspond very well. The data support the applicability of a conserved-scalar model with an assumed β-function probability density function (PDF) shape for mean temperature predictions. For OH predictions, however, the conserved-scalar approach does not hold.

Numerical determination of wall functions for the turbulent natural convection boundary layer

In an analytical way George and Capp (Int. J. Heat Mass Transfer22 813–826 (1979)) and Cheesewright (“The scaling of turbulent natural convection boundary layers in the asymptotic limit of infinite Grashof number”, paper presented at Euromech Colloquium 207 (1986)) have derived wall functions for the natural convection boundary layer along a heated vertical plate. These wall functions are compared here with numerical calculations for air, using a k-e turbulence model with low-Reynolds number modifications. George and Capps wall function for the temperature in the inner layer agrees with the calculations, but their wall function for the velocity does not. George and Capps defect laws for the velocity and the temperature in the outer layer are also numerically found, but Cheesewrights wall function for the velocity in the (lower part of the) outer layer does not agree.