Thermofluiddynamic experiments with a heated and rotating circular cylinder in crossflow

Heat transfer experiments with a heated and rotating circular cylinder in an air crossflow were performed for subcritical freestream-Reynolds-number 8.3 · 10³ < Re _f < 7.1 · 10⁴ and for Nusselt-numbers up to 300. The experiments took into consideration important practical parameters such as freestream-turbulence intensity, aspect ratio, blockage ratio and temperature loading. The measured values were standardized to the ‘idealized case’ to allow adequate comparison with pertinent literature. The results encompass the range of velocity ratios α (circular/freestream-velocity) between zero and 2.5. For values α > 0.5, the typical Nusselt-number behaviour noted by some authors has been confirmed. For small velocity ratios α < 0.5, however, there are significant deviations from the heat transfer coefficients previously believed to be constant.     

FLOW-INDUCED VIBRATION OF A CIRCULAR CYLINDER AT LIMITING STRUCTURAL PARAMETERS

Transverse oscillation of a dynamically supported circular cylinder in a flow at Re=100 has been numerically simulated using a high-resolution viscous-vortex method, for a range of dynamical parameters. At the limiting case with zero values of mass, damping and elastic force, the cylinder oscillates sinusoidally at amplitudeA /D=0·47 and frequency fD/U_∞=0·156. For zero damping, the effects of mass and elasticity are combined into a new, “effective” dynamic parameter, which is different from the classic “reduced velocity”. Over a range of this parameter, the response exhibits oscillations at amplitudes up to 0·6 and frequencies between 0·15 and 0·2. From this response function, the classic response in terms of reduced velocity can be obtained for fixed values of the cylinder/fluid ratio m^*. It displays “lock-in” at very high values of m^*.     

Numerical Simulation of the Negative Magnus Effect of a Two-Dimensional Spinning Circular Cylinder

Based on the finite volume method, the flow past a spinning circular cylinder at a low subcritical Reynolds number (Re =1 × 10 ⁵), high subcritical Reynolds number (Re =1.3 ×10 ⁵), and critical Reynolds number (Re =1.4 ×10 ⁵) were each simulated using the Navier-Stokes equations and the γ-Re _?? transition model coupled with the SST k?ω turbulence model. The system was solved using an implicit algorithm. The freestream turbulence intensity decay was effectively controlled by the source term method proposed by Spalart and Rumsey. The variations in the Magnus force as a function of the spin ratio, α were obtained for the three Reynolds numbers, and the flow mechanism was analyzed. The results indicate that the asymmetric transitions induced by spin affect the asymmetric separations at the top and bottom surfaces of the circular cylinder, which further affects the pressure distributions at the top and bottom surfaces of the circular cylinder and ultimately result in a negative Magnus force, whose direction is opposite to that of the classical Magnus force. This study is the first to use a numerical simulation method to predict a negative Magnus force acting on a spinning circular cylinder. At the low subcritical Reynolds number, the Magnus force remained positive for all spin ratios. At the high subcritical Reynolds number, the sign of the Magnus force changed twice over the range of the spin ratio. At the critical Reynolds number, the sign of the Magnus force changed only once over the range of the spin ratio. For relatively low spin ratios, the Magnus force significantly differed by Reynolds number; however, this variation diminished as the spin ratio increased.     

Numerical studies of slow viscous rotating flow past a sphere. III

The flow of steady incompressible viscous fluid rotating about the z-axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Re_ω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non-linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’. The results obtained by solving the non-linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Re_ω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non-linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Re_ω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Study of the aerodynamic characteristics of cone-sphere models in a hypersonic flow

The aerodynamic characteristics of cone-sphere models are studied at Mach numbers M = 6, 8.4, and 12 to 13 over a wide Reynolds number range. Models of a braking device (sphere) were connected with a load (frustum of a cone) by means of shrouds. The dependences of the aerodynamic coefficients C _x and C _y on the angle of attack α were obtained for different relative dimensions of the load and the braking device, shroud lengths, and Mach and Reynolds numbers. The effect of the above-mentioned parameters on the aerodynamic characteristics of the models is analyzed. The C _x (Re_D) dependences of load-parachutemodels in a symmetric flow are determined over the wide Mach and Reynolds number ranges 6 ≤ M ≤ 13 and 3 · 10³ ≤ Re_D ≤ 3 · 10⁶.     

Combined convection and wall conduction effects in laminar pipe flow: numerical predictions and experimental validation under uniform wall heating

Laminar combined convection in horizontal circular ducts is investigated both numerically and experimentally, under uniform wall heating. A series of experiments for the heating of water in a long horizontal copper tube are simulated numerically in order to assess the reliability of the theoretical results. Peripheral and axial wall conduction effects, inherently present in the experiments, are accounted for in the numerical model. The cross validation of experimental and numerical data allows significant conclusions to be reached on conjugate conduction and convection with buoyancy effects in horizontal duct flows. Buoyancy is considered for values of the modified Rayleigh number,Ra _qo , up to 5·10⁶; the forced convection contribution is considered for two values of the entry Reynolds number,Re _o=500 and 1000.     

Transition modes in adiabatic spiral vortex flow in narrow and wide annular gaps

The stability of flow in a concentric annulus formed by rotating cylinders is well understood, but there is little information concerning the transitions which occur after the onset of spiral vortex flow. For both the arrow and wide gap cases (N = 0·8 and N = 0·955), it has been shown that the initial spiral flow breaks down from a quasiperiodic to a chaotic mode. Three axial Teynolds numbers were studied, viz., Re_a = 500, 1500, 2500. The introduction of digital techniques provided qualitative and quantitative information regarding the flow behaviour. The effects reported for Re_a > 0 and recent results of other workers for Re_a = 0 have been compared. The phenomenon of re-emergent flows has been observed at very high Taylor numbers and high axial Reynolds numbers.     

A boundary element formulation using the simple method

A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.³² However, the new method demands a much larger computer strorage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re = 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re =46·6.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Aerodynamics and heat transfer in a separated flow in an axisymmetric diffuser with sudden expansion

Results of a numerical study of the influence of a positive pressure gradient in an axisymmetric diffuser with sudden expansion of a circular tube on aerodynamics and turbulent heat transfer in regions of flow separation, reattachment, and relaxation are reported. The air flow prior to separation is assumed to be fully turbulent and to have a constant Reynolds number Re _D1 = 2.75 · 10⁴. The tube expansion degree is 1.78, and the apex half-angle of the diffuser is varied from 0 to 5°. It is found that an increase in the pressure gradient leads to a decrease in the heat transfer intensity in the separation region, and the maximum heat release point moves away from the flow separation point. The calculated results are compared with experimental data. It is shown that the behavior of the separated flow behind the step becomes significantly different as the streamwise pressure gradient changes.     

Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer 2. Effect of the porous coating location

The effect of the location of a passive porous coating on natural disturbances in a hypersonic boundary layer is studied experimentally. The experiments are performed in the flow around a sharp cone aligned at a zero angle of attack with the free-stream Mach number M_∞ = 5.8, stagnation temperature T ₀ = 370 ± 5 K, and unit Reynolds numbers Re_1∞ = 2.6 · 10⁶, 4.6 · 10⁶, 6.6 · 10⁶, and 10⁷ m^?1. The wave characteristics of the boundary layer are calculated with the use of the linear stability theory for flow parameters corresponding to experimental values. A comparison of experimental and predicted results shows that the presence of a porous coating in the region where the second mode is unstable leads to reduction of its amplitude at the measurement point, whereas the presence of a porous coating in the region of second mode stability leads to enhancement of the amplitude.     

A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.     

Stationärer Stoff- und Wärmeübergang an stationär quer angeströmten Zylindern

The steady forced convection mass and heat transfer from circular cylinders has been investigated. The full mass transport differential equation has been integrated numerically. The employed velocity distributions are known [1]. The most important result is reproduced in a correlation for the mass transfer, which regards the turbulence intensity in the flow of the cylinders. This mass transfer law is proofed theoretically and experimentally in the range of Schmidt numbers from Sc=0.73 up to S=3.3×10⁴; however it is valid for 0≤Sc∞. It can be used for all values of Re Sc greater than Re Sc=7.3×10^?5 and for all values of the Reynolds number less than the critical value, Re_kr. The critical Reynolds number, Re_kr, is a known function of the turbulence intensity [1]. For values of Re Sc less than Re Sc=7.3 x10^?5 the mass transfer can be predicted by an analytical equation that based on Oseen type linearization of the differential equation. The conditions are illustrated, which allow to calculate the quantities for heat transfer by means of the correlations for the mass transfer.     

Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier–Stokes equations using the Petrov–Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number Re_N and that based on the total velocity is defined as the total Reynolds number Re_T. Simulations are conducted for two Reynolds numbers of Re_N=500 and Re_T=500, two flow attack angles of α=0° and 45° and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0° and 45°. For a constant normal Reynolds number of Re_N=500, the mean drag and lift coefficients at α=0° are very close to those at α=45°. The difference between the root mean square (RMS) lift coefficient at α=0° and that at α=45° is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0° and 45° are similar to each other. The present simulations show that the agreement in the force coefficients between the 0° and 45° flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for Re_N=100–600, α=0° and 45° and G/D=1. Flow for G/D=1 is found to be two-dimensional at Re_N=100 and weak three-dimensional at Re_N=200. While well defined biased flow can be identified for Re_N=300–600, the gap flow for Re_N=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Flow past a square cylinder at low Reynolds numbers

Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re ? 150. A stabilized finite‐element formulation is employed to discretize the equations of incompressible fluid flow in two‐dimensions. For the first time, values of the laminar separation Reynolds number, Re_s, and separation angle, θ_s, at Re_s are predicted. Also, the variation of θ_s with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. θ_s=180^° at Re = Re_s. For Re > 5, θ_s approaches the limit of 135 ^°. The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re^?0.66. Flow characteristics at Re ? 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free‐stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

Die Messung von konvektiven Stoffübergangszahlen bei Sorption mit chemischer Bindung

The method, which was developed byThoma, is expanded by using sulphuric-, oxalic- and amido sulfuric-acid instead of phosphoric-acid. The 10 N sulphuric-and the 1,9 N amidosulfuric-acid are qualified for velocities up to 20 m/s and rate of chemical reaction from 20 to 50%. By greater velocities than 20 m/s only the 15 N sulphuric-acid is qualified by rates of chemical reactions up to 25%. Phosphoric- and oxalic-acid are not qualified by turbulent flow. — Measurements were done at the plate and the annular in the range 7 · 10³<Re< 3sd10⁵ by velocities from 1 to 60 m/s. — The results confirm the well known laws. The points of measurement have a scattering range of ±15%. The Sherwood-Number can be calculated by the present conditions on the premises, that the velocity of reaction is greater than the mass transfer coefficient.