Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at α < 15°, forming a small separation bubble, and full separation occurs at α ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at α ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Irradiation-Induced Solute Clustering in a Low Nickel FeMnNi Ferritic Alloy

Understanding the radiation embrittlement of reactor pressure vessel (RPV) steels is required to be able to operate safely a nuclear power plant or to extend its lifetime. The mechanical properties degradation is partly due to the clustering of solute under irradiation. To gain knowledge about the clustering process, a Fe−1.1 Mn−0.7 Ni (at.%) alloy was irradiated in a test reactor at two fluxes of 0.15 and 9 ×10¹⁷ n _E > 1MeV .m^− 2.s^− 1 and at increasing doses from 0.18 to 1.3 ×10²⁴ n _E > 1MeV .m^− 2 at 300°C. Atom probe tomography (APT) experiments revealed that the irradiation promotes the formation in the α iron matrix of Mn/Mn and/or Ni/Ni pair correlations at low dose and Mn–Ni enriched clusters at high dose. These clusters dissolve partially after a thermal treatment at 400°C. Based on a comparison with thermodynamic calculations, we show that the solute clustering under irradiation can just result from an induced mechanism.     

Experimental investigation on turbulent flow in a square-sectioned 90-degree bend

The development of steady, turbulent flow in a 90° section of a curved square duct was studied at a Reynolds number of 4 × 10⁴ by hot-wire anemometer. The curved duct has a cross-section measuring 80 × 80 mm and a curvature radius ratio of 4 and is connected with a long, straight duct at its both ends. The longitudinal and lateral components of mean and fluctuating velocities, and the Reynolds stresses were measured by the method of rotating a probe with an inclined hot-wire. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross-section were illustrated in the form of contour map. The development of the primary flow was found to be connected with a strong pressure gradient near the outer and inner wall and a secondary flow induced in the cross-section of the bend by a pressure difference between the outer and inner wall and a centrifugal force acting on the fluid; the fluid is accelerated near the inner wall and decelerated near the outer wall between the bend angle ϕ ≅ 0° and ϕ ≅ 30°, but an increase and decrease of the fluid velocity are reversed between ϕ ≅ 30° and ϕ ≅ 90°. The fluctuating velocity correlations, i.e. the Reynolds stresses follow a complicated progress according to the complex development of the primary flow. The results obtained can be available to verify various types of turbulence models and to develop new models. Received: 10 May 1999/Accepted: 15 March 2000     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

An experimental investigation of the ELAC 1 configuration at supersonic speeds

Supersonic flight of aerospace planes is of marked interest since several flow regimes characterized by different local flow structures have to be flown through. This problem was investigated experimentally for the hypersonic research configuration ELAC 1. The aim of the study was to detect the influence of the rounded leading edge, of the thickness distribution prescribed, and of the Reynolds number, especially on the flow on the leeward side of the configuration. The experiments were carried out in the transonic wind tunnel of Aerodynamisches Institut of RWTH Aachen, at a freestream Mach number Ma _∞=2, a unit Reynolds number of Re _∞=13×10⁶, angles of attack between ?3°?α?10°, and in a wind tunnel of the Institute for Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The freestream Mach numbers covered in these experiments were varied between 2?Ma _∞?4, freestream Reynolds numbers per unit length between 25×10⁶?Re _∞?56×10⁶ and angles of attack between ?3°?α?10°. Flow visualization studies, measurements of surface pressure distributions and of aerodynamic forces were used to analyze the flow. The results, which will also be compared with numerical data, clearly indicate marked differences in the location of the separation and reattachment lines, and the formation of the primary, secondary and tertiary vortices, for the flow regimes investigated.     

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0∼4.7)×10⁷/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30° for a sweepback angle of 67.6°. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10° and secondary separation were detected at deflection of ϑ≥20°. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements atM≥6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers. The project supported by China Academy of Launch Vehicle Technology     

Hypersonic interference heating in the vicinity of surface protuberances

The understanding of the behaviour of the flow around surface protuberances in hypersonic vehicles is developed and an engineering approach to predict the location and magnitude of the highest heat transfer rates in their vicinity is presented. To this end, an experimental investigation was performed in a hypersonic facility at freestream Mach numbers of 8.2 and 12.3 and Reynolds numbers ranging from Re _∞/m = 3.35 × 10⁶ to Re _∞/m = 9.35 × 10⁶. The effects of protuberance geometry, boundary layer state, freestream Reynolds number and freestream Mach numbers were assessed based on thin-film heat transfer measurements. Further understanding of the flowfield was obtained through oil-dot visualizations and high-speed schlieren videos. The local interference interaction was shown to be strongly 3-D and to be dominated by the incipient separation angle induced by the protuberance. In interactions in which the incoming boundary layer remains unseparated upstream of the protuberance, the highest heating occurs adjacent to the device. In interactions in which the incoming boundary layer is fully separated ahead of the protuberance, the highest heating generally occurs on the surface just upstream of it except for low-deflection protuberances under low Reynolds freestream flow conditions in which case the heat flux to the side is greater.     

Drag reduction change of polyethyleneoxide solutions in pipe flow

Change of drag reduction (DR) along a tube (D=2 mm, L=4 m) was experimentally investigated. To attain turbulent flow with Re=8 × 10⁴, a tank operated under high pressure up to 16 MPa. Solutions of different brands of polyethyleneoxide (PEO) with concentrations from 1 ppm to 100 ppm were tested. The results indicate that DR is not a constant value but depends on the time and intensity of interaction between the polymer and the turbulent flow. There are three regions with different behaviors of DR: growth, maximum, and slope down. Maximum DR coincides with the Virk ultimate DR and can be described by the suggested simple formula . A decrease in the DR maximum has not been found even for high shear stresses τ _p < 800 Pa. DR dynamics for four brands of PEO with different molecular weight was studied. Direct experimentally determined DR may be greater than the Virk ultimate value if the change in velocity profile is not taken into account. The corrected DR never exceeds the ultimate DR. Received: 10 April 2000/Accepted: 24 May 2001     

Aerodynamic Characteristics of Transonic and Supersonic Flow over Rectangular Cavities

An experimental and computational investigation has been performed to investigate flow characteristics and flow-field structures for three types of rectangular cavities. The data presented herein was obtained with cavity length to depth ratio of 6, 10 and 15 at 0° of attack, yawing and rolling angles of 0° over free-stream Mach numbers of 0.6, 0.8, 1.2 and 1.5 at Reynolds numbers of 1.23 ×10⁷, 1.55 ×10⁷, 2.01 ×10⁷ and 2.26 ×10⁷ per meter. The results indicate that the shear-layer expands over the cavity leading edge and impinges on the cavity floor for closed cavity flow, whereas it bridges the open cavity. The static pressure distributions are relatively uniform with the exception of a small adverse gradient occurring ahead of the rear face inside open cavity. Cavity length to depth ratio is a key geometrical parameter to define cavity flow types and influent pressure distributions inside cavities, and its decrease induces a decrease in pressure gradient. Increase in free-stream Mach numbers results in the trend that cavity flow types transform from closed to transitional cavity flow and from transitional to open cavity flow.     

Shear banding during nonlinear creep with a solution of monodisperse polystyrene

Creep experiments with a solution of polystyrene (M _w = 2.6 MDa, 16 vol.%, 25 °C) in diethyl phthalate are reported for stresses between 100 and 2,500 Pa (≈ 3G _N ⁰/4). The aim was to look for a flow transition as reported for strongly entangled poly(isobutylene) solutions. The experiments with the polystyrene solution were repeated for cone angles of 2, 4, and 6° (radius 15 mm) and showed no dependence on cone angle. The Cox–Merz rule was not fulfilled for stresses beyond about 800 Pa. The tangential observation with a CCD camera showed that the edge took a concave shape because of the second normal stress difference. Beyond 1,000 Pa, the concave edge develops into a crevice, thus substantially reducing the effective cross-section. This leads to runaway in a constant torque experiment. At p ₂₁ = 800 Pa, head-on particle tracking confirms that the originally linear velocity profile takes a gooseneck shape, thus revealing shear banding. When the creep stress is stepped down to 100 Pa, this velocity profile evolves back to a linear one. The conclusion from this work is that even if nonlinear creep experiments are reproducible and a steady state is reached, this does not mean that the flow field is homogeneous. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5

The paper reports on experiments carried out over a wide range of Reynolds numbers in a high pressure wind tunnel. The model was a sharp-edged rectangular cylinder with aspect ratio height/width 1:5 (width/span ratio 1:10.8), which was investigated in both basic orientations, lengthwise (4×10³<Re<4×10⁵) and perpendicular to the flow (2.7×10⁴<Re<6.4×10⁵). The Reynolds number is based on the height of the model normal to the flow. Steady and unsteady forces were measured with a piezoelectric balance. Thus along with steady (i.e. time averaged values) including the base pressure coefficient, also power spectra and probability density functions were measured yielding for example Strouhal numbers, higher statistical moments, etc. A response diagram for the vortex resonance phenomenon was taken for the natural bending motion of the slender model. If lift coefficient for constant angle of attack is plotted against Reynolds number, a significant Reynolds number effect is seen. For α=4°, the curve shows an inflection point and the lift varies between 0.3 and 0.6. For α=6° and 2° there are similar variations shifted to lower and higher values of Re, respectively. Probably the shapes of separation bubbles that depend on the Reynolds number are responsible for these effects. No Reynolds number effects were observed when the long side was normal to the flow, an orientation where reattachment at the side walls is not possible. Comparing both basic cases (α=0° and 90°), the interpretation of the probability distributions of lift force leads to the conclusion that the possibility of reattachment (α=0°) seems to enhance the degree of order in the vortex shedding process.     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.     

Second-order nonlinear differential equations with infinite set of periodic solutions

For the differential equation u″ = f(t, u, u′), where the function f: R × R ² → R is periodic in the first variable and f (t, x, 0) ≡ 0, sufficient conditions for the existence of a continuum of nonconstant periodic solutions are found. Published in Neliniini Kolyvannya, Vol. 11, No. 4, pp. 495–500, October–December, 2008.     

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

Airfoil flow instabilities induced by background flow oscillations

 The effect of background flow oscillations on transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to oscillating chocking of the flow caused by the plate, the airfoil flow periodically accelerated and decelerated. This led to strong variations in the surface pressure and the airfoil loading. The results are presented for two angles of attack, α=4° and α=8.5°, which correspond to the attached and separated steady airfoil flows, respectively. Received: 6 June 2000 / Accepted: 18 October 2001     

Three-dimensional Turbulent Boundary Layer in a Shrouded Rotating System

A thre-dimensional direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed annular rotor-stator cavity characterized by a large aspect ratio G = (b − a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Ω considered is equivalent to the rotational Reynolds number Re = Ωb ²/ν= 9 .5 × 10⁴ (ν the kinematic viscosity of water). This corresponds to a value at which experiment has revealed that the stator boundary layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the computed solution with velocity measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence by comparing the turbulence properties with available data in the literature (Lygren and Andersson, J Fluid Mech 426:297–326, 2001). An approximately self-similar boundary layer behavior is observed along the stator. The wall-normal variations of the structural parameter and of characteristic angles confirm that this boundary layer is three-dimensional. A quadrant analysis (Kang et al., Phys Fluids 10:2315–2322, 1998) of conditionally averaged velocities shows that the asymmetries obtained are dominated by Reynolds stress-producing events in the stator boundary layer. Moreover, Case 1 vortices (with a positive wall induced velocity) are found to be the major source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson (J Fluid Mech 426:297–326, 2001).     

The ultra-low Reynolds number airfoil wake

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re _c ), 5.3 × 10³–5.1 × 10⁴, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re _c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re _c  ≥ 1.05 × 10⁴ but is absent at Re _c  = 5.3 × 10³. The observation is connected to the presence of the separation bubble at high Re _c but absence of the bubble at ultra-low Re _c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re _c .