NUMERICAL STUDY ON TURBULENT FLOW AND HEAT TRANSFER IN CIRCULAR COUETTE FLOWS

Abstract

A numerical study is performed to investigate heat transfer and fluid flow in the entrance and fully developed regions of an annulus, consisting of a rotating, insulated inner cylinder and a stationary, heated outer cylinder. Several different k-ε turbulence models are employed to determine the turbulent kinetic energy, its dissipation rate, and the heat transfer performance. The governing boundary layer equations are discretized by means of a control volume finite difference technique and numerically solved using the marching procedure. In the entrance region the axial rotation of the inner cylinder induces a thermal development and causes an increase in both the Nusselt number and the turbulent kinetic energy in the inner cylinder wall region. In the fully developed region, an increase in the Taylor number causes an amplification of the turbulent kinetic energy over the whole cross section, resulting in a substantial enhancement in the Nusselt number. These transport phenomena are also affected by the radius ratio and Reynolds number.     

Unsteady inflow effects on the wake shed from a high-lift LPT blade subjected to boundary layer laminar separation

An experimental investigation on the near and far wake of a cascade of high-lift low-pressure turbine blades subjected to boundary layer separation over the suction side surface has been carried out, under steady and unsteady inflows. Two Reynolds number conditions, representative of take-off/landing and cruise operating conditions of the real engine, have been tested. The effect of upstream wake-boundary layer interaction on the wake shed from the profile has been investigated in a three-blade large-scale linear turbine cascade. The comparison between the wakes shed under steady and unsteady inflows has been performed through the analysis of mean velocity and Reynolds stress components measured at midspan of the central blade by means of a two-component crossed miniature hot-wire probe. The wake development has been analyzed in the region between 2% and 100% of the blade chord from the central blade trailing edge, aligned with the blade exit direction. Wake integral parameters, half-width and maximum velocity defects have been evaluated from the mean velocity distributions to quantify the modifications induced on the vane wake by the upstream wake. Moreover the thicknesses of the two wake shear layers have been considered separately in order to identify the effects of Reynolds number and incoming flow on the wake shape. The self-preserving state of the wake has been looked at, taking into account the different thicknesses of the two shear layers. The evaluation of the power density spectra of the velocity fluctuations allowed the study of the wake unsteady behavior, and the detection of the effects induced by the different operating conditions on the trailing edge vortex shedding.     

Entrance region flow of a power-law fluid in concentric annuli with rotating inner wall

The laminar flow of a power-law non-Newtonian fluid in the entrance region of a concentric annulus is investigated numerically. The inner cylinder rotates with a constant angular velocity while the outer cylinder is stationary. Using the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. A Crank Nicolson method is used to obtain the velocity components and the pressure at each step of the axial direction. The development of the axial velocity profile, transverse (radial and tangential) velocity profiles, pressure drop have been studied. Computations are obtained for various axial positions and various flow indices.     

Direct numerical simulation of turbulent flow in a vertical channel with buoyancy orthogonal to mean flow

The effect of buoyancy on turbulent air flowing horizontally between two differentially heated vertical plates has been investigated using direct numerical simulation. Grashof number ranges between zero and 4.0 × 10⁶ and the Boussinesq approximation is used in the buoyant term. In this particular configuration, the buoyancy forces result in skewed mean velocity profiles with non-zero anti-symmetric spanwise component W. The resulting flow has the features of three-dimensional turbulent boundary layer flows. In particular, suppression of the primary Reynolds stress in near-wall region is observed. Titled streaks with significant destruction of the associated vortical structures are highlighted. The induced mean spanwise strain enhances the turbulence intensities in the channel core. The effect of buoyancy on mean quantities and second-order statistics including Reynolds stress components and turbulent heat fluxes are presented and analyzed with detailed budgets of their transport equations which are believed to be helpful to testify and improve turbulence models incorporating buoyancy effect.     

Conventional and conditional Prandtl number in a turbulent plane wake

Conventional and conditional measurements of several turbulence quantities and particularly of the turbulent Prandtl number are presented for the nearly self-preserving region of a slightly heated wake of a circular cylinder. To verify that the measurements were made in the self-preserving region, and to also serve as a check on measurement accuracy, three stations in the wake were used. The identification of the turbulent regions in the outer part of the wake was based on the behaviour of the probability density function of the temperature fluctuation. Conventional distributions of the turbulent diffusivities of momentum and heat vary considerably in the outer part of the wake. This variation is not reduced when only turbulent zone averages are considered. The turbulent Prandtl number varies significantly in the turbulent part of the flow.     

Flow characterization in the near‐wake region of a horizontal axis wind turbine

An experimental study is conducted to investigate the flow dynamics within the near‐wake region of a horizontal axis wind turbine using particle image velocimetry (PIV). Measurements were performed in the horizontal plane in a row of four radially distributed measurement windows (tiles), which are then patched together to obtain larger measurement field. The mean and turbulent components of the flow field were measured at various blade phase angles. The mean velocity and turbulence characteristics show high dependency on the blade phase angle in the near‐wake region closer to the blade tip and become phase independent further downstream at a distance of about one rotor diameter. In the near‐wake region, both the mean and turbulent characteristics show a systemic variation with the phase angle in the blade tip region, where the highest levels of turbulence are observed. The streamlines of the instantaneous velocity field at a given phase allowed to track a tip vortex which showed wandering trend. The tip vortices are mostly formed at r/R > 1, which indicates the wake expansion. Results also show the gradual movement of the vortex region in the axial direction, which can be attributed to the dynamics of the helical tip vortices which after being generated from the tip, rotate with respect to the blade and move in the axial direction because of the axial momentum of the flow. The axial velocity deficit was compared with other laboratory and field measurements. The comparison shows qualitative similarity. Copyright © 2015 John Wiley & Sons, Ltd.     

Laminar forced convection from a rotating horizontal cylinder in cross flow

The influence of non-dimensional rotational velocity, flow Reynolds number and Prandtl number of the fluid on laminar forced convection from a rotating horizontal cylinder subject to constant heat flux boundary condition is numerically investigated. The numerical simulations have been conducted using commercial Computational Fluid Dynamics package CFX available in ANSYS Workbench 14. Results are presented for the non-dimensional rotational velocity α ranging from 0 to 4, flow Reynolds number from 25 to 40 and Prandtl number of the fluid from 0.7 to 5.4. The rotational effects results in reduction in heat transfer compared to heat transfer from stationary heated cylinder due to thickening of boundary layer as consequence of the rotation of the cylinder. Heat transfer rate increases with increase in Prandtl number of the fluid.     

Characterizing the response of a wind turbine model under complex inflow conditions

A horizontal axis wind turbine model was tested in a closed‐circuit wind tunnel under various inflow conditions. Separate experiments placed the test turbine (i) in the wake of a three‐dimensional, sinusoidal hill, (ii) in the wake of another turbine and (iii) in the turbulent boundary layer, as a reference case. Simultaneous high‐frequency measurements of the turbine output voltage, rotor angular velocity along with streamwise and wall normal velocity components were collected at various locations through the turbine's miniature direct‐current (DC) generator, a high‐resolution laser tachometer and cross‐wire anemometer, respectively. Validation trials were conducted first in order to characterize the test turbine's output and response to the baseline turbulent boundary layer. Analysis was performed by comparing the cross‐wire anemometry measurements of the incoming flow with the turbine voltage output to investigate the unsteady rotor kinematics under different flow perturbations. Using spectral, auto‐correlation and cross‐correlation methods, it was found that the flow structures developing downwind of the hill leave a stronger signature on the fluctuations and spectrum of the rotor angular velocity, as compared with those flow structures filtered or deflected by placing a turbine upwind. In summary, we show that the effects on downwind turbines of complex terrain and multi‐turbine arrangements are consistent with the induced modifications by the hill or turbine on the large scale structures in the incoming flow. Copyright © 2014 John Wiley & Sons, Ltd.     

Forced convection heat transfer from a circular cylinder in crossflow to air and liquids

Local and average heat transfer by forced convection from a circular cylinder is studied for Reynolds number from 2 × 10³ to 9 × 10⁴ and Prandtl number from 0.7 to 176. For subcritical flow, the local heat transfer measurement indicates three regions of flow around the cylinder: laminar boundary layer region, reattachment of shear layer region and periodic vortex flow region. The average heat transfer in each region is calculated and correlated with the Reynolds number and the Prandtl number. The Nusselt number in each region strongly depends on the Reynolds number and the Prandtl number with different power indices. An empirical correlation for predicting the overall heat transfer from the cylinder is developed from the contributions of heat transfer in these three regions.     

Modeling of the microconvective contribution to wall heat transfer in subcooled boiling flow

In the present work, the two-phase turbulent boundary layer in subcooled boiling flow is investigated. The bubbles in the near-wall region have a significant effect on the dynamics of the underlying liquid flow, as well as on the heat transfer. The present work develops a single-fluid model capable of accounting for the interactions between the bubbles and the liquid phase, such that the two-phase convective contribution to the total wall heat transfer can be described appropriately even in the framework of single-fluid modeling. To this end, subcooled boiling channel flow was experimentally investigated using a laser-Doppler anemometer to gain insight into the bubble-laden near-wall velocity field. It was generally observed that the streamwise velocity component was considerably reduced compared to the single-phase case, while the near-wall turbulence was increased due to the presence of the bubbles. Since the experimentally observed characteristics of the liquid velocity field turned out to be very similar to turbulent flows along rough surfaces, it is proposed to model the near-wall effect of the bubbles on the liquid flow analogously to the effect of a surface roughness. Incorporating the proposed approach as a dynamic boundary condition into a well-established mechanistic flow boiling model makes it possible to reflect adequately the contribution of the microconvection to the total wall heat transfer. A comparison against the experimental data shows good agreement for the predicted wall shear stress as well as for the wall heat flux for a wide range of wall temperatures and Reynolds numbers.     

Using oscillations to enhance heat transfer for a circular cylinder

An experimental investigation into the effects of transverse oscillations on the heat transfer from a circular cylinder in cross-flow was carried out. The cylinder’s heat transfer coefficient was measured for a wide range of oscillation frequencies and amplitudes. Heat transfer enhancement was found to be strongly dependent on synchronization with harmonics of the natural shedding frequency, the cylinder wake mode, and the cylinder transverse velocity. For representative oscillation conditions, the velocity and temperature fields in the near wake were measured using digital particle image thermometry and velocimetry (DPIT/V). This revealed several mechanisms that explain the observed heat transfer enhancement.     

Turbulence characteristics and vortical structures in combined-convection boundary layers along a heated vertical flat plate

Time-developing direct numerical simulations are performed for the combined-convection boundary layers created by imposing aiding and opposing freestreams to the pure natural-convection boundary layer in air along a heated vertical flat plate to clarify their structural characteristics. The numerical results reveal that with a slight increase in freestream velocity, the transition region moves downstream for aiding flow and upstream for opposing flow. This fact correlates well with the existing experimental results showing that the transition delays for aiding flow and quickens for opposing flow in the practical space-developing boundary layer. Thereby, for aiding flow, turbulence characteristics indicate the behavior proceeding to the laminarization of the boundary layer. On the other hand, for opposing flow, the large scale fluid motions are apparent and become larger than those for the pure natural-convection boundary layer with increasing freestream velocity. For the occurrence of such fluid motions, the budgets of turbulent energy and two-point spatial correlations in the turbulent combined-convection boundary layers are also examined. Consequently, it is found in the spatial correlations that the turbulence structures are mainly controlled by fluid motions in the outer region of the boundary layer.     

Forced Convection Laminar Film Condensation of Downward Flowing Vapor on a Single Horizontal Elliptic Cylinder or a Bank of Elliptical Tubes

A numerical study is performed on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on a single horizontal elliptic cylinder or a bank of elliptical tubes. Temperature, velocity distribution, and heat transfer coefficient of the fully developed flow are carried out with a fully implicit finite difference scheme. The equality of shear stress at the liquid-vapor interface is used as the coupling condition between the two phases. The inertia and convection term are retained in the analysis. Outside of the vapor boundary layer, the vapor phase velocity is obtained from potential flow. The method of source density distribution on the body surface is used for determination of the external vapor velocity in elliptical tube banks. The effect of inundation produced by condensate on upper ellipses is taken into account by assuming that the vapor velocity field is not affected by the condensate flow from one elliptic cylinder to another. Based on the obtained solutions of flow field, the effect of surface tension, the interaction because of the ellipse spacing, and the inundation on the heat transfer coefficient and the boundary layer separation point have been evaluated. The results of this analysis are discussed especially in function of eccentricity e (effect of the surface tension). The heat transfer in interellipse space is analyzed and compared with the theoretical and experimental results of other authors. Good agreement is shown.     

Effects of a kind of non-smooth blade on the unsteady flow field at the exit of an axial fan

An experimental investigation of effects of a kind of streamwise-grooved blade on the unsteady flow field at an exit of an axial-flow fan was performed. The flow field at 25% chord downstream from the trailing edge at hub was measured using a fast-response five-hole pressure probe at different mass-flow conditions. The unsteady flow of the grooved blades was compared with that of the smooth blades. The measurement results indicate that： （1） the grooved blades restrain the velocity fluctuation and the pressure fluctuation by modulating the blade boundary layers, which contributes to the flow loss reduction in the hub region and in the rotor wake region at the design condition; （2） the stream-wise grooves play an important role in restraining the radial migration in the blade boundary layer and abating the tip flow mixing, which contributes to the flow loss reduction in the tip region at the design condition; （3） at the near stall condition, the grooved surface can not reduce the flow loss, even increase the loss nearby when the separation happens in the blade boundary layer.     

Turbulent Free Convection from a Vertical,Isothermal Plate

Abstract

The temperature and velocity fields adjacent to an isothermal, vertical plate have been calculated by finite-difference methods using the time-averaged equations of conservation. Effective diffusivities for turbulent transfer were computed from differential balances for the turbulent kinetic energy and the rate of dissipation of turbulent energy, using the empirical coefficients previously evaluated for forced convection together with an additional Prandtl-number-dependent coefficient associated with the buoyant production of turbulent kinetic energy. Although the turbulent boundary layer almost approaches an asymptotic condition, the slight development requires a two-dimensional solution proceeding from the leading edge through the laminar and turbulent regimes. It was necessary to trigger the transition from laminar to turbulent motion, but the ultimate turbulent behavior was found to be independent of the point of triggering. The computed velocity fields, temperature fields, and rates of heat transfer are in agreement with prior experimental data for air within their uncertainty. Excellent agreement was also obtained with the data for water, and fair agreement with the data for spindle oil.     

Heat and mass transfer with condensation in laminar and turbulent boundary layers along a flat plate

An experimental and numerical study of heat and mass transfer in an incompressible boundary layer with condensation over a flat plate is presented. The air-steam flow at atmospheric pressure is saturated; its velocity is smaller than 6 m s⁻¹; the Reynolds number calculated with the abscissa along the plate ranges from 10⁴ to 10⁵ for the laminar boundary layer and from 3 × 10⁵ to 10⁶ for the turbulent one. The temperature différence between the main flow and the cold wall does not exceed 20°C. A finite-difference method is used to calculate the velocity, temperature and concentration fields; the numerical results are in good agreement with experiments for laminar and turbulent boundary layer.     

Quadratic mixed convective nanofluid flow past a moving yawed cylinder in the presence of thermal radiation and diffusive liquids

The fluid flow around a yawed cylinder helps to understand the practical implications for undersea applications, such as managing transference, separating the boundary layer above submerged blocks, and suppressing recirculating bubbles. As many authors such as Roy, Chiu and Lienhard, Roy and Saikrishnan, and Revathi et al. have analyzed a boundary layer flow over a yawed cylinder, and their work sticks to only forced convection, we are interested to work on mixed convection flow. Therefore, the work of these researchers has stimulated us to work on the present article. As a result, we have examined the work on triple diffusion quadratic mixed convective nanofluid flow over a moving yawed cylinder. The impact of yaw angle, which exists due to the inclination of a vertically moving cylinder away from the origin, is mathematically investigated in the present paper by converting the governing equations into a compatible form using appropriate nonsimilar transformations and the quasilinearization technique. Nanofluids have crucial usages in science and technology, marine engineering, and applications in industries such as plastic, polymer industries, cancer home therapy, and building sciences. Many processes in new engineering areas occur at high temperatures, and knowledge of radiation heat transfer becomes very important for designing the pertinent equipment. Nuclear power plants, gas turbines, and the various propulsion devices for aircraft, missiles, satellites, and space vehicles are examples of such engineering areas. The finite difference approximation is employed to solve the resulting equations. Enhancing the magnitude of thermal radiation enhances the temperature of the liquid and the energy transport strength. However, liquid hydrogen and liquid oxygen species concentration patterns are reduced in nanofluid compared to traditional liquids. At the same time, the outcomes behave conversely in the case of their wall gradients. Furthermore, the temperature of the liquid enhances the enhancing values of Brownian motion and thermophoresis characteristics. Moreover, nanoparticle mass transport augments with enhancing yaw angle and Lewis number values. Both species' concentration profiles decrease for increasing values of yaw angle. The velocity profiles increase for increasing values of velocity ratio parameter in the spanwise and chordwise directions.     

Heat transfer by shock-wave/boundary layer interaction on a flat surface with a mounted cylinder

The detailed convective heat transfer is observed on a flat surface where the cylinder is mounted in a supersonic flow field. During the test, the thermal image of a wall temperature distribution is taken by an infra-red camera under the constant heat flux condition on the flat surface. From the measured wall temperature information, heat transfer coefficients are calculated. The shadow graph and the oil flow tests are conducted to examine the shock-wave structure and the surface shear flow around the protruding body, respectively. The entire flow also is simulated numerically. The upstream flow Mach number, total pressure and Reynolds number are about 3, 600 kPa and 2.3 × 10⁶, respectively. The swept-back effect of a cylinder to the approaching flow is considered in the range from 0° to 30°. From the results, the large increase of heat transfer is observed in a shock-wave/turbulent boundary layer interaction region and the peak heating appeared especially on a flow reattachment region. When the cylinder is swept backward to the main flow, the heat flux promotion decreases as much as its effective area. These results will provide the valuable information for the thermal analysis in a complicated shock-induced separation region.     

Free Convection Heat Transfer from Vertical Slender Cylinders: A Review

The effect of transversal curvature of a vertical cylinder becomes important where the thermal boundary layer thickness is comparable or thicker then the radius of cylinder. The cylinder slenderness criterion for laminar free convection for fluids of Prandtl numbers from 0.01 to 100 is presented. The classical analysis of the laminar free convection heat transfer from vertical cylinders is shown. Some results of numerical calculations of the turbulent boundary layer on a vertical cylinder using modified integral method are given. Experimental data concerning the laminar-turbulent transition suggest that the critical Grashof number for a vertical flat plate is Gr _cr ≈ 10⁹ and for a vertical cylinder is Gr _cr ≈ 4 × 10⁹. Theoretical, numerical, and experimental data for free convection heat transfer from vertical slender circular cylinders are surveyed. A separate section of the paper is devoted to the presentation of the list of selected correlation equations. Some of them are compared graphically. In the laminar region, the correlation equation based on the numerical calculations is validated with the recent experimental results for Prandtl number of 0.71 and for the cylinder height to diameter ratio from 1 to 60. In the turbulent region, few experimental data are available, and some results indicate that the effect of transversal curvature on the average convective heat transfer is very weak.     

Impact of wall roughness and turbulence level on the performance of a horizontal axis wind turbine with the U‐RANS solver THETA

The presented work investigates the impact of different sheared velocity profiles in the atmospheric boundary layer on the characteristics of a wind turbine by modifying the wall roughness coefficients in the logarithmic velocity profile. Moreover, the rotor and wake characteristics in dependence of the turbulence boundary conditions are investigated. In variant I, the turbulence boundary conditions are defined in accordance to the logarithmic velocity profile with different wall roughness lengths. In variant II, the turbulent kinetic energy and turbulent viscosity remain independent of the velocity profile and represent the free‐stream turbulence level. With an increase of the shear in the velocity profile, the amplitudes in the 3/rev characteristics of rotor thrust and rotor torque, induction factors, and effective angles of attack are increased. In variant I, the overall levels of thrust coefficient are hardly affected by the velocity profiles resulting from different wall roughness length values. The power coefficient is reduced about 1%. Conversely, compared with variant II, a difference of 2% in the power coefficient has been detected. Moreover, the wake recovery process strongly depends on the turbulence boundary condition. Simulations are carried out on an industrial 900‐kW wind turbine with the incompressible U‐RANS solver THETA.