Turbulent flow in a circular separationless diffuser at Reynolds numbers smaller than 2000

The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re₂ in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re < 2000, in the exit section of a diffuser with the generator slope of 0.3° and a length equal to 70 entry diameters a developed turbulent flow is formed for Re₂ > 1000. For Re₂ > 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re₂ in the exit section. For Re₂ ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model.     

Application of the Dorodnitsyn finite element method to swirling boundary layer flow

The Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two-layer eddy viscosity model of Cebeci and Smith¹ with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included-angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (w_e/u_e = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.     

Numerical investigation of flow and heat transfer in a gas-droplet separated turbulent stream using the Reynolds stress transfer model

The results of the numerical modeling of flow structure, turbulence, and heat transfer in a gas-droplet stream after sudden tube expansion on the basis of the Eulerian approach are presented. The gas phase turbulence was modeled using the Reynolds stress transfer model modified to allow for the presence of particles. The results are compared with those obtained using the two-equation k-ε model. The latter results overestimate the heat transfer in the separation flow as compared with the Reynolds stress transfer model. The heat transfer is shown to considerably increase, when evaporating droplets are incorporated in the separation flow (by a factor of more than 1.5 compared with the case of a single-phase flow at a small mass concentration of the droplets M _L1 ≤ 0.05). The addition of the disperse phase in the turbulent gas flow leads a slight increase in the recirculation zone length. Good agreement with the experimental data indicates the adequacy of the numerical model developed.     

Numerical prediction of turbulent flow in a conical diffuser usingk-ε model

Fully developed incompressible turbulent flow in a conical diffuser having a total divergence angle of 8° and an area ratio of 4∶1 has been simulated by ak-ε turbulence model with high Reynolds number and adverse pressure gradient. The research has been done for pipe entry Reynolds numbers of 1.16×10⁵ and 2.93×10⁵. The mean flow velocity and turbulence energy are predicted successfully and the advantage of Boundary Fit Coordinates approach is discussed. Furthermore, thek-ε turbulence model is applied to a flow in a conical diffuser having a total divergence angle of 30° with a perforated screen. A simplified mathematical model, where only the pressure drop is considered, has been used for describing the effect of the perforated screen. The optimum combination of the resistance coefficient and the location of the perforated screen is predicted for high diffuser efficiency or the uniform velocity distribution.     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

Heat transfer and flow around a circular cylinder with tripping-wires

An experimental study was conducted on the heat transfer under the condition of constant heat flux and the flow around a circular cylinder with tripping-wires, which were affixed at ± 65° from the forward stagnation point on the cylinder surface. The testing fluid was air and the Reynolds number Red, based on the cylinder diameter, ranged from 1.2 × 10⁴ to 5.2×10⁴. Especially investigated are the interactions between the heat transfer and the flow in the critical flow state, in relation to the static pressure distribution along the cylinder surface and the mean and turbulent fluctuating velocities in the wake. It is found that the heat transfer from the cylinder to the cross flow is in very close connection with the width of near wake.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins

Experiments were performed to determine the heat transfer and pressure drop characteristics in the entrance and fully developed regions of tubes with internal wave-like longitudinal fins. The test tube has a double-pipe structure, with the inner tube as an insertion. The wave-like fins are in the annulus and span its full width. Experiments were conducted for two cases: one with the inner tube blocked (no air flowing through it) and the other with the inner tube unblocked. The outer tube was electrically heated. Local and average heat transfer coefficients and friction factors were measured. The friction factor and Nusselt number correlations in the fully developed region were obtained in the Reynolds number range of 9×10² to 3.5×10³. It has been found that the wave-like fins enhance heat transfer significantly with the blocked case being superior. In addition, the in-tube heat transfer process is characterized by an earlier transition from laminar to turbulent flow and Reynolds number-dependent thermal entrance length. Received on 12 May 1998     

Heat Transfer Influenced by Turbulent Airflow Inside an Axially Rotating Diffuser

The paper presents a study of heat transfer between the turbulent airflow and the inner wall surface of an axial diffuser rotating around its longitudinal axis. Heat transfer was assessed through the measurement of a time-dependent temperature field of the diffuser inner wall surface. Measurements of the instantaneous flow velocity components were performed by a laser–Doppler anemometry system, which delivered information on mean velocity components as well as on the turbulence intensity. A significant increase of all three mean velocity components was observed near the rotating diffuser wall in comparison with a non-rotating diffuser. Temperature field measurements were carried out by means of infrared thermography. The experiment showed a significant dependence of the temperature field on the turbulent flowfield induced by diffuser rotation. A strong influence of the flow separation and reattachment on the temperature distribution was observed, while rotation was found to suppress the occurrence of flow separation from the diffuser wall. Properties of the velocity field such as turbulent kinetic energy were directly coupled with the temperature distribution in order to gain the information on how to enhance or reduce heat transfer by changing the integral parameters of the diffuser (e.g. rotation frequency or amount of flow).     

Flow boiling heat transfer in a vertical spirally internally ribbed tube

 Experiments of flow boiling heat transfer and two-phase flow frictional pressure drop in a spirally internally ribbed tube (φ22×5.5 mm) and a smooth tube (φ19×2 mm) were conducted, respectively, under the condition of 6×10⁵ Pa (absolute atmosphere pressure). The available heated length of the test sections was 2500 mm. The mass fluxes were selected, respectively, at 410, 610 and 810 kg/m² s. The maximum heat flux was controlled according to exit quality, which was no more than 0.3 in each test run. The experimental results in the spirally internally ribbed tube were compared with that in the smooth tube. It shows that flow boiling heat transfer coefficients in the spirally internally ribbed tube are 1.4–2 times that in the smooth tube, and the flow boiling heat transfer under the condition of smaller temperature differences can be achieved in the spirally internally ribbed tube. Also, the two-phase flow frictional pressure drop in the spirally internally ribbed tube increases a factor of 1.6–2 as compared with that in the smooth tube. The effects of mass flux and pressure on the flow boiling heat transfer were presented. The effect of diameters on flow boiling heat transfer in smooth tubes was analyzed. Based on the fits of the experimental data, correlations of flow boiling heat transfer coefficient and two-phase flow frictional factor were proposed, respectively. The mechanisms of enhanced flow boiling heat transfer in the spirally internally ribbed tube were analyzed. Received on 1 December 1999     

Oscillating flow in a 2-D diffuser

Separating oscillating flows in an internal, adverse pressure gradient geometry are studied experimentally. Simultaneous velocity and pressure measurements demonstrate that the minor losses associated with oscillating flow in an adverse pressure gradient geometry can be smaller or larger than those for steady flow. Separation is found to begin high in the diffuser and propagate downward. The flow is able to remain attached further into the diffuser with larger Reynolds numbers, small displacement amplitudes, and smaller diffuser angles. The extent of separation grows with L ₀/h. The minor losses grow with increasing displacement amplitude in the measured range 10 < L ₀/h < 40. Losses decrease with increasing Re _δ in the measured range of 380 < Re _δ < 740. It is found that the losses increase with increasing diffuser angle over the measured range of 12° < θ < 30°. The nondimensional acoustic power dissipation increases with Reynolds number in the measured range and decreases with displacement amplitude.     

Heat transfer and skin-friction in a turbulent boundary layer under a non-equilibrium longitudinal adverse pressure gradient

The experimental data on the effect of weak and moderate non-equilibrium adverse pressure gradients (APG) on the parameters of dynamic and thermal boundary layers are presented. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re^** = 5500. The APG region was a slot channel with upper wall expansion angles from 0 to 14°. The profiles of the mean and fluctuation velocity components were measured using a single-component hot-wire anemometer. The friction coefficients were determined using two methods, namely, the indirect Clauser method and the direct method of weighting the lower wall region on a single-component strain-gage balance. The heat transfer coefficients were determined by a transient method using an IR camera. It is noticed that in the pressure gradient range realized the universal logarithmic region in the boundary layer profile is conserved. The values of the relative (divided by the parameters in zero gradient flow at the same value of Re^**) friction and heat transfer coefficients, together with the Reynolds analogy factor, are determined as functions of the longitudinal pressure gradient. The values of the relative friction coefficient reduced to c_f/c_f0 = 0.7 and those of the heat transfer to St/St₀ = 0.9. A maximum value of the Reynolds analogy factor (St/St₀)/(c_f/c_f0) = 1.16 was reached for the pressure gradient parameter β = 2.9.     

Experimental investigation of flow and heat transfer in rectangular cross-sectioned duct with baffles mounted on the bottom surface with different inclination angles

In this study, steady-state forced convection heat transfer and pressure drop characteristics in a horizontal rectangular cross-sectioned duct, baffles mounted on the bottom surface with different inclination angles were investigated experimentally in the Reynolds number range from 1 × 10³ to 1 × 10⁴. The study was performed under turbulent flow conditions. Effects of different baffle inclination angles on flow and heat transfer were studied. Results are also presented in terms of thermal enhancement factor. It is observed that increasing in baffle inclination angle enhances the heat transfer and causes an increase in pressure drop in the duct.     

Experimental investigation of heat transfer in vertical upward and downward supercritical CO2 flow in a circular tube

An experimental investigation of turbulent heat transfer in vertical upward and downward supercritical CO₂ flow was conducted in a circular tube with an inner diameter of 4.5 mm. The experiments were performed for bulk fluid temperatures from 29 to 115 °C, pressures from 74.6 to 102.6 bar, local wall heat fluxes from 38 to 234 kW/m², and mass fluxes from 208 to 874 kg/m² s. At a moderate wall heat flux and low mass flux, the wall temperature had a noticeable peak value for vertical upward flow, but increased monotonically along the flow direction without a peak value for downward flow. The ratios of the experimental Nusselt number to the value obtained from a reference correlation were compared with Bo^* and q⁺ distributions to observe the buoyancy and flow-acceleration effects on heat transfer. In the experimental range of this study, the flow acceleration predominantly affected the heat-transfer phenomena. Based on an analysis of the shear-stress distribution in the turbulent boundary layer and the significant variation of the specific heat across the turbulent boundary layer, a new heat-transfer correlation for vertical upward and downward flow of supercritical pressurized fluid was developed; this correlation agreed with various experimental datasets within ±30%.     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

NUMERICAL STUDIES OF TRANSITIONAL TURBULENT PULSATILE FLOW IN PIPES WITH RING–TYPE CONSTRICTIONS

Pulsatile flows in the vicinity of mechanical ring-type constrictions in pipes were studied for transitional turbulent flow with a Reynolds number (Re) of the order of 10⁴. The Womersley number (Nw) is in the range 30–50, with a corresponding Strouhal number (St) range of 0·0143–0·0398. The pulsatile flows considered are a pure sinusoidal flow, a physiological flow and an experimental pulsatile flow profile for mechanical aortic valve flow simulations. Transitional laminar and turbulent flow characteristics in an alternating manner within the pulsatile flow fields were studied numerically. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity and turbulent shear stress are smaller during the acceleration phase than during the deceleration period. Various parametric equations have been formulated through numerical experimentation to better describe the relationships between the instantaneous flow rate (Q), the pressure loss (ΔP), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max) for turbulent pulsatile flow in the vicinity of constrictions in the vascular tube. An elliptic relationship has been found to exist between the instantaneous flow rate and the instantaneous pressure gradient. Other linear and quadratic relations between various flow parameters were also obtained.     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Control of an axisymmetric subsonic air jet by plasma actuator

It is known that surface non-thermal plasma actuators have proved their efficiency for aerodynamics flow control. In this study, a dielectric barrier discharge (DBD) is mounted on the diffuser of an axisymmetric turbulent air jet in order to control the flow separation along a 12-degree diffuser bevel. The momentum created by the actuator is applied to separate an air flow naturally attached to the diffuser for air flow velocity up to 40 m s⁻¹. Laser sheet visualizations and LDV measurements are achieved to characterize the unforced and forced air jet. The flow separation, the induced velocity fluctuations, the jet mixing improvement and vectoring are investigated. The main results of this study demonstrate that DBD actuators are suitable to fully detach the air flow along the bevel for a velocity of 20 m s⁻¹ and that a jet vectoring between 13.5° and 5.5° could be achieved for velocity ranging between 20 and 40 m s⁻¹. Considerations about a potential improvement of the jet mixing are also introduced and the laser sheet visualization attests that induced flow perturbations are highly 3D.     

Heat transfer characteristics in a sudden expansion pipe equipped with swirl generators

This investigation is aimed at studying the heat transfer characteristics and pressure drop for turbulent airflow in a sudden expansion pipe equipped with propeller type swirl generator or spiral spring with several pitch ratios. The investigation is performed for the Reynolds number ranging from 7500 to 18,500 under a uniform heat flux condition. The experiments are also undertaken for three locations for the propeller fan (N = 15 blades and blade angle of 65°) and three pitch ratios for the spiral spring (P/D = 10, 15 and 20). The influences of using the propeller rotating freely and inserted spiral spring on heat transfer enhancement and pressure drop are reported. In the experiments, the swirl generator and spiral spring are used to create a swirl in the tube flow. Mean and relative mean Nusselt numbers are determined and compared with those obtained from other similar cases. The experimental results indicate that the tube with the propeller inserts provides considerable improvement of the heat transfer rate over the plain tube around 1.69 times for X/H = 5. While for the tube with the spiral spring inserts, an improvement of the heat transfer rate over the plain tube around 1.37 times for P/d = 20. Thus, because of strong swirl or rotating flow, the propeller location and the spiral spring pitch become influential on the heat transfer enhancement. The increase in pressure drop using the propeller is found to be three times and for spiral spring 1.5 times over the plain tube. Correlations for mean Nusselt number, fan location and spiral spring pitch are provided.     

Comparison of the Eulerian and Lagrangian approaches in studying the flow pattern and heat transfer in a separated axisymmetric turbulent gas-droplet flow

The Eulerian and Lagrangian approaches are used to perform a numerical study of the disperse phase dynamics, turbulence, and heat transfer in a turbulent gas-droplet flow in a tube with sudden expansion with the following ranges of two-phase flow parameters: initial droplet size d ₁ = 0–200 µm and mass fraction of droplets M _L1 = 0–0.1. The main difference between the Eulerian and Lagrangian approaches is the difference in the predictions of the droplet mass fraction: the Eulerian approach predicts a smaller value of M _L both in the recirculation region and in the flow core (the difference reaches 15–20%). It is demonstrated that the disperse phase mass fraction calculated by the Lagrangian approach agrees better with measured data than the corresponding value predicted by the Eulerian approach.