Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

NUMERICAL PREDICTION OF SEMI-CONFINED JET IMPINGEMENT AND COMPARISON WITH EXPERIMENTAL DATA

The standard k–ε eddy viscosity model of turbulence in conjunction with the logarithmic law of the wall has been applied to the prediction of a fully developed turbulent axisymmetric jet impinging within a semi-confined space. A single geometry with a Reynolds number of 20,000 and a nozzle-to-plate spacing of two diameters has been considered with inlet boundary conditions based on measured profiles of velocity and turbulence. Velocity, turbulence and heat transfer data have been obtained using laser–Doppler anemometry and liquid crystal thermography respectively. In the developing wall jet, numerical results of heat transfer compare to within 20% of experiment where isotropy prevails and the trends in turbulent kinetic energy are predicted. However, stagnation point heat transfer is overpredicted by about 300%, which is attributed directly to the turbulence model and inapplicability of the wall function.     

Effect of cavity aspect ratio on flow and heat transfer characteristics in pipes: a numerical study

Using the standard k–ε turbulence model, a two-dimensional turbulent pipe flow was simulated with and without square cavities. Effect of cavity aspect ratio on flow and heat transfer characteristics was investigated. Uncertainty was approximated through experimental validation and grid independence. The simulation revealed circulation inside the cavities. Cavity boundaries were shown to contribute significantly toward turbulence production. Cavity presence was shown to enhance overall heat transfer through the wall, while increasing pressure drop significantly across the pipe. It was predicted that cavities with higher aspect ratio enhance heat transfer more while increasing pressure drop.     

The effect of the low Reynolds number k-e turbulence models on simulation of the enhanced and deteriorated convective heat transfer to the supercritical fluid flows

One of the most important challenges in mathematical modeling of convective heat transfer to the turbulent flow of a supercritical fluid is the turbulence modeling. The turbulence modeling, like other aspects of the supercritical fluid flows, seems to be high affected by the large variations of the fluid properties which needs to be further investigated. A two dimensional CFD code has been developed and used in this study to examine a number of the low Reynolds number k-e turbulence models. Both flow conditions corresponding to the heat transfer enhancement and deterioration have been studied. The results appear to be quite sensitive to the choice of the turbulence model, especially in the deteriorated regime of heat transfer. The turbulence model assisting the two-dimensional numerical model of the present study to best fit the experiments has been determined for both cases of the enhanced and deteriorated heat transfer. That is while the jump in the wall temperature occurring in the deteriorated regime of heat transfer is over- predicted by the present numerical code regardless of the turbulence model used.     

Study into thermal stresses due to turbulent flow in pipes

Flow through pipes with heat transfer finds wide applications in industry. The thermal stresses, which develop in the pipe limit the heat transfer rate in pipe flow. In the present study, a turbulent flow in thick pipe with external heating is considered. The flow and temperature fields in a pipe and in the fluid are predicted using a numerical scheme; which employs a control volume approach. A k- model is introduced to account for the turbulence. The thermal stresses developed in the pipe due to heat transfer are predicted. The simulations are repeated for different pipe materials and fluids. It is found that the temperature gradient in the pipe changes rapidly in the vicinity of the solid-fluid interface. This change is not affected considerably by the Reynolds number. The effective stress developed at mid-plane of the pipe is independent of the Reynolds number; however, the pipe material affects the effective stress considerably.     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Comparative Study of DNS,LES and Hybrid LES/RANS of Turbulent Boundary Layer with Heat Transfer Over 2d Hill

This paper first presents the turbulent heat transfer phenomenon of the boundary layer over a 2-dimensional hill using the direct numerical simulation (DNS). DNS results reveal turbulent heat transfer phenomena in the boundary layer over a 2-dimensional hill affected by the flow acceleration and the concave wall at the foreface of a hill, the convex wall at the top of the hill, and the flow deceleration, separation, and reattachment and the concave wall at the back of the hill. The prediction of turbulent heat transfer, the turbulence models of LES and HLR should be assessed in such heat transfer because these models have seldom been evaluated in the complex turbulent heat transfer. Therefore, this paper also presents evaluations of predictions of LES and HLR in the complicated turbulent heat transfer which is the boundary layer with heat transfer over a 2-dimensional hill. Consequently, this paper obviously shows the detailed turbulent heat transfer phenomena of a boundary layer over a 2-dimensional hill via DNS, and the evaluation results of prediction accuracy of LES and HLR for the heat transfer. LES and HLR give good prediction in comparison with DNS results, but the predicted reattachment and separation points are slightly different from DNS.     

Transients in flow and local heat transfer due to a pressure wave in pipe flow

The effect of a pressure wave on the turbulent flow and heat transfer in a rectangular air flow channel has been experimentally studied for fast transients, occurring due to a sudden increase of the main flow by an injection of air through the wall. A fast response measuring technique using a hot film sensor for the heat flux, a hot wire for the velocities and a pressure transducer have been developed. It was found that in the initial part of the transient the heat transfer change is independent of the Reynolds number. For the second part the change in heat transfer depends on thermal boundary layer thickness and thus on the Reynolds number. Results have been compared with a simple numerical turbulent flow and heat transfer model. The main effect on the flow could be well predicted. For the heat transfer a deviation in the initial part of the transient heat transfer has been found. From the turbulence measurements it has been found that a pressure wave does not influence the absolute value of the local turbulent velocity fluctuations. They could be considered to be frozen.Nomenclature A surface area (m²) - D diameter (m) - h heat transfer coefficient (Wm^–2 K^–1) - p pressure drop (Pa) - P pressure (Pa) - Q heat flow (W) - R tube radius (m) - T bulk temperature (K) - T _s surface temperature (K) - t time (s) - u velocity (m/s) - V voltage (V) - y distance from wall (m) - viscosity (N s m^–2) - kinematic viscosity (m^–2 s^–1) - density (kg m^–3) - _w wall shear stress (N m^–2) - Nu Nusselt number - Re Reynolds number     

A New Low-Reynolds-Number One-Equation Model of Turbulence

In this study, we propose a new Low-Reynolds-Number (LRN)one-equation model, which is derived from an LRN two-equation(k-ε) model. The derivation of the transport equation, in principle, is based on the assumption that the turbulent structure parameter remains constant. However, the relation for the turbulent structure parameter a ₁(=|− |/k) is modified to account for near-wall turbulence. As a result, the present one-equation model contains a term which takes the near-wall limiting behavior explicitly into account. Thus, the present model provides the correct wall-limiting behavior of turbulence in the vicinity of the wall and can be applied to the analysis of heat transfer. The validity of the present model is tested in channel flows, boundary layer flows with and without pressure gradient, plane wall jet, and flow with separation and reattachment. The calculated results showed good agreement with the direct numerical simulation (DNS) and experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Reynolds averaged simulation of flow and heat transfer in ribbed ducts

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and three-dimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v²–f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Comparison of near-wall treatment methods for high Reynolds number backward-facing step flow

A comparison of near-wall treatment methods using different turbulence models for flow over a backward-facing step is presented. A Reynolds number (Re) of about 38,000 (U _∞ = 44.2 m/s), based on the step height and the mean stream velocity, was considered. An appropriate near-wall treatment method is critical to the choice of turbulence model used to predict wall-bounded flow. Predictions were obtained by applying standard wall functions, non-equilibrium wall functions and a two-layer model with six different turbulence models. These results were compared with data by Driver and Seegmiller (“Backward-facing step with inclined opposite wall—experiments by driver and seegmiller”, 1985a, http://cfd.me.umist.ac.uk/ercoftac [2003, Jan 31]). Non-equilibrium wall functions with modified k ? ? models predicted the closest reattachment length. However, the two-layer model gave results more representative of the entire flow pattern. The predictions show that a proper combination of turbulence models and near-wall treatment methods give reliable results.     

Spectral transport model for turbulence

The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a one-point model for the system that is substantially like the familiar K- model. This yields preliminary estimates of the present model's parameters and points to the way to improved modeling of flows beyond the applicability of the K- method.     

Shock waves and turbulence in a hypersonic inlet

A numerical investigation for an axisymmetric hypersonic turbulent inlet flow field of a perfect gas is presented for a three-shock configuration consisting of a biconic and a cowl. An upwind parabolized Navier-Stokes solver based on Roe's scheme is used to compute an oncoming flow Mach numberM =8, temperatureT =216 K, and pressureP =5.5293×10³ N/m². In order to assess the flow quantities, the interaction between shock and turbulence, and the inlet efficiency, three different flow calculations — laminar, turbulent with incompressible and compressible two-equationk- turbulence models — have been performed in this work.Computational results show that turbulence is markedly enhanced across an oblique shock with step-like increases in turbulence kinetic energy and dissipation rate. This enhancement is at the expense of the mean kinetic energy of the flow. Therefore, the velocity behind the shock is smaller in turbulent flow and hence the shock becomes stronger. The entropy increase through a shock is caused not only by the amplification of random molecular motion, but also by the enhancement of the chaotic turbulent flow motion. However, only the compressiblek- turbulence model can properly predict a decrease in turbulence length scale across a shock. Our numerical simulation reveals that the incompressiblek- turbulence model exaggerates the interaction between shock and turbulence with turbulence kinetic energy and dissipation rate remaining high and almost undissipated far beyond the shock region. It is shown that proper modeling of turbulence is essential for a realistic prediction of hypersonic inlet flowfield. The performed study shows that the viscous effect is not restricted in the boundary layer but extends into the main flow behind a shock wave. The loss of the available energy in the inlet performance therefore needs to be determined from the shock-turbulence interaction. The present study predicts that the inlet efficiency becomes relatively lower when turbulence is taken into account.     

Turbulent heat transfer in a flat plate boundary layer disturbed by a cylinder

Augmentation of heat transfer from a flat plate using a turbulence promoter has been studied. A circular cylinder 8 mm in diameter was placed in the turbulent boundary layer detached from the flat plate. It was located parallel to the plate and perpendicular to the flow direction. Clearance, c, between the cylinder and the flat plate was varied in nine steps: c=0, 1, 2, 3, 4, 6, 11, 20 and 29.5 mm. Measurements were made of the local heat transfer coefficients, mean velocity profiles, turbulence intensity profiles, static pressure and skin friction. Experimental results showed that the heat transfer deterioration which occurs just downstream of the cylinder at c=0 mm can be removed by displacing the cylinder a small distance from the wall. The improvement in heat transfer is mainly due to the unsteadiness of the recirculating flow on the plate and the effect of intense turbulence arriving at the near wall region from the lower shear layer of the cylinder wake. Heat transfer augmentation is most effective when c=4 mm and becomes less effective when c is increased more than 6 mm. The enhancement disappears far downstream from the cylinder.     

Turbulence structure and heat and mass transfer mechanism at a gas-liquid interface in a wind-wave tunnel

Turbulence structure and heat and mass transfer mechanism across a wavy sheared gas-liquid interface are fluid-mechanically investigated in a wind-wave tunnel. Heat and mass transfer velocities are reported and the relationship between the scalar transfer velocities and the turbulence structure is discussed. In addition, three-dimensional direct numerical simulation is carried out to investigate the flow structure over a rigid-wavy wall similar to that over the wave. The results show that the organized motion in the air flow intermittently appears on the front side of the wave crest, and its structure is rather similar to the flow structure over the rigid-wavy wall. The organized motion in the air flow induces the organized motion in the water flow and the organized motion renews the air-water interface. The scalar transfer across a wavy sheared gas-liquid interface is controlled by the organized surface-renewal motion in the water flow     

Performance of RNG Turbulence Modelling for Forced Convective Heat Transfer in Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in straight ducts using the RNG (Re-Normalized Group) turbulence method.

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts with different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with the RNG κ?ε model and the RNG non-linear κ-ε model of Speziale. The turbulent heat fluxes are modeled by the simple eddy diffusivity (SED) concept, GGDH and WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models arc implemented for an arbitrary three dimensional duct.

Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non-staggered grid arrangement. The pressure-velocity coupling is handled by using the SIMPLEC-algorithm. The convective terms are treated by the QUICK, scheme while the diffusive terms are handled by the central-difference scheme. The hybrid scheme is used for solving the κ and ε equations.

The overall comparison between the models is presented in terms of friction factor and Nusselt number. The secondary flow generation is also of major concern.