Diameter-based Reynolds Number Research Articles

Effects of moderate Reynolds numbers on subsonic round jets with highly disturbed nozzle-exit boundary layers

The effects of moderate Reynolds numbers on the flow and acoustic fields of initially highly disturbed isothermal round jets at Mach number M = 0.9 and diameter-based Reynolds numbers ReD between 2.5 × 104 and 2 × 105 are investigated using large-eddy simulation under carefully controlled conditions. To the best of our knowledge, this is the first comprehensive study of its kind. The jets originate at z = 0 from a pipe nozzle of radius r0, in which a tripping procedure is applied to the boundary layers. At the nozzle exit, laminar-like mean velocity profiles of thickness δ ≃ 0.15r0 and momentum thickness δθ ≃ 0.018r0, yielding Reynolds numbers Reθ varying from 256 to 1856 depending on ReD, and peak turbulence intensities around 9% of the jet velocity, are thus obtained. As the Reynolds number increases, the mixing layers develop more slowly, with smaller integral length scales and lower levels of velocity fluctuations. The axial profiles of turbulence intensities become smoother, showing a clear overshoot around z = 2r0 at ReD = 2.5 × 104, but a monotonical growth at ReD = 2 × 105. Velocity spectra downstream of the nozzle exit also broaden with ReD, as expected. Large-scale components usually observed in turbulent boundary layers and shear layers, characterized by Strouhal numbers Stθ ≃ 0.013 around z = r0 and by azimuthal spacings λθ ≃ δ, remain dominant, although the contribution of fine-scale structures with λθ ⩽ δ/2 strengthens. Moreover, with rising ReD, the jet potential core lengthens slightly, but the flow properties do not change significantly farther downstream. Finally, lower sound pressure levels are generated, with a decrease of about 2 dB over the range of ReD considered.

Experiments on thermal response of low aspect ratio packed beds at high Reynolds numbers with varying inflow temperature

An experimental study for transient temperature response of low aspect ratio packed beds at high Reynolds numbers for a free stream with varying inlet temperature is presented. The packed bed is used as a compact heat exchanger along with a solid propellant gas-generator, to generate room temperature gases for use in applications such as control actuation and air bottle pressurization. Packed beds of lengths ∼200mm and 300mm were characterized for packing diameter based Reynolds numbers, Red ranging from 0.6×104 to 8.5×104. The solid packing used in the bed consisted of Ø9.5mm and Ø5mm steel spheres with suitable arrangements to eliminate flow entrance and exit effects. The ratios of packed bed diameter to packing diameter for 9.5mm and 5mm sphere packing were ∼9.5 and 18 respectively, with the average packed bed porosities around 0.4. Gas temperatures were measured at the entry, exit and at three axial locations along centre-line in the packed beds. The solid packing temperature was measured at three axial locations in the packed bed. An average Nusselt number correlation of the form Nud=3.91Red0.5 for Red range of 104 is proposed. For engineering applications of packed beds such as pebble bed heaters, thermal storage systems, and compact heat exchangers a simple procedure is suggested for calculating unsteady gas temperature at packed bed exit for packing Biot number Bid<0.1.

Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105

AbstractFive isothermal round jets at Mach number $M= 0. 9$ and Reynolds number ${\mathit{Re}}_{D} = 1{0}^{5} $ originating from a pipe nozzle are computed by large-eddy simulations to investigate the effects of initial turbulence on flow development and noise generation. In the pipe, the boundary layers are untripped in the first case and tripped numerically in the four others in order to obtain, at the exit, mean velocity profiles similar to a Blasius laminar profile of momentum thickness equal to 1.8 % of the jet radius, yielding Reynolds number ${\mathit{Re}}_{\theta } = 900$, and peak turbulence levels ${ u}_{e}^{\ensuremath{\prime} } $ around 0, 3 %, 6 %, 9 % or 12 % of the jet velocity ${u}_{j} $. As the initial turbulence intensity increases, the shear layers develop more slowly with much lower root-mean-square (r.m.s.) fluctuating velocities, and the jet potential cores are longer. Velocity disturbances downstream of the nozzle exit also exhibit different structural characteristics. For low ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, they are dominated by the first azimuthal modes ${n}_{\theta } = 0$, 1 and 2, and show significant skewness and intermittency. The growth of linear instability waves and a first stage of vortex pairings occur in the shear layers for ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} \leq 6\hspace{0.167em} \% $. For higher ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, three-dimensional features and high azimuthal modes prevail, in particular close to the nozzle exit where the wavenumbers naturally found in turbulent wall-bounded flows clearly appear. Concerning the sound fields, strong broadband components mainly associated with mode ${n}_{\theta } = 1$ are noticed around the pairing frequency for the untripped jet. With rising ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, however, they become weaker, and the noise levels decrease asymptotically down to those measured for jets at ${\mathit{Re}}_{D} \geq 5\ensuremath{\times} 1{0}^{5} $, which are likely to be initially turbulent and to emit negligible vortex-pairing noise. These results correspond well to experimental observations, made separately for either mixing layers, jet flow or sound fields.

Experimental investigation into vortex structure and pressure drop across microcavities in 3D integrated electronics

Hydrodynamics in microcavities with cylindrical micropin fin arrays simulating a single layer of a water-cooled electronic chip stack is investigated experimentally. Both inline and staggered pin arrangements are investigated using pressure drop and microparticle image velocimetry (μPIV) measurements. The pressure drop across the cavity shows a flow transition at pin diameter–based Reynolds numbers (Re d ) ~200. Instantaneous μPIV, performed using a pH-controlled high seeding density of tracer microspheres, helps visualize vortex structure unreported till date in microscale geometries. The post-transition flow field shows vortex shedding and flow impingement onto the pins explaining the pressure drop increase. The flow fluctuations start at the chip outlet and shift upstream with increasing Re d . No fluctuations are observed for a cavity with pin height-to-diameter ratio h/d = 1 up to Re d ~330; however, its pressure drop was higher than for a cavity with h/d = 2 due to pronounced influence of cavity walls.

Large-eddy simulation of the flow and acoustic fields of a Reynolds number 105 subsonic jet with tripped exit boundary layers

Large-eddy simulations (LESs) of isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number ReD of 105 originating from a pipe are performed using low-dissipation schemes in combination with relaxation filtering. The aim is to carefully examine the capability of LES to compute the flow and acoustic fields of initially nominally turbulent jets. As in experiments on laboratory-scale jets, the boundary layers inside the pipe are tripped in order to obtain laminar mean exit velocity profiles with high perturbation levels. At the pipe outlet, their momentum thickness is δθ(0)=0.018 times the jet radius, yielding a Reynolds number Reθ=900, and peak turbulence intensities are around 9% of the jet velocity. Two methods of boundary-layer tripping and five grids are considered. The results are found to vary negligibly with the tripping procedure but appreciably with the grid resolution. Based on analyses of the LES quality and on comparisons with measurements at high Reynolds numbers, fine discretizations appear necessary in the three coordinate directions over the entire jet flow. The final LES carried out using 252×106 points with minimum radial, azimuthal, and axial mesh spacings, respectively, of 0.20, 0.34, and 0.40×δθ(0) is also shown to provide shear-layer solutions that are practically grid converged and, more generally, results that can be regarded as numerically accurate as well as physically relevant. They suggest that the mixing-layer development in the present tripped jet, while exhibiting a wide range of turbulent scales, is characterized by persistent coherent vortex pairings.

Flow past confined delta-wing type vortex generators

This paper presents the results of an experimental study of flow structure in horizontal equilateral triangular ducts having double rows of half delta-wing type vortex generators mounted on the duct’s slant surfaces. The test ducts have the same axial length and hydraulic diameter of 4 m and 58.3 mm, respectively. Each duct consists of double rows of half delta wing pairs arranged either in common flow-up or common flow-down configurations. Flow field measurements were performed using a Particle Image Velocimetry Technique for hydraulic diameter based Reynolds numbers in the range of 1000–8000. The secondary flow field differences generated by two different vortex generator configurations were examined in detail. The secondary flow is found stronger behind the second vortex generator pair than behind the first pair but becomes weaker far from the second pair in the case of Duct1. However, the strength of the secondary flow is found nearly the same behind the first and the second vortex generator pair as well as far from the second vortex generator pair in the case of Duct2. Both ducts are able to create a counter-rotating and a second set of twin foci. Duct2 is able to create the second set of twin foci in an earlier streamwise location than Duct1, as these foci are well-known to their heat transfer augmentation. A larger vortex formation area and a greater induced vorticity field between vortex pairs are observed for Duct2 compared with Duct1. As the induced flow field between the vortex pairs increases the heat transfer, and as the flow field between the vortex cores is found larger in the case of Duct2, therefore, it is expected to obtain better heat transfer characteristics for Duct2 compared with Duct1.

Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder

An evaluation of four well-known Reynolds-Averaged Navier–Stokes (RANS)-based turbulence models was performed in comparison with the results of a dedicated experimental measurement on the near-wake of a circular cylinder in a large water (cavitation) tunnel using a state-of-the-art two-dimensional Digital Particle Image Velocimetry (DPIV) device. The turbulence models investigated were Spalart–Allmaras (S–A), Realizable k– ε (RKE), Wilcox k– ω (WKO) and Shear-Stress-Transport k– ω (SST), which were assessed based on their comparative performances in predicting some important flow field characteristics of the near-wake region of the experimental circular cylinder flow. Within the flow range investigated in this study, which implied a cylinder diameter-based Reynolds Number of 41,300, the qualitative and quantitative comparisons revealed that the application of the SST model to the wall-bounded unsteady flow – that experienced severe adverse pressure gradient, massive flow separation and vortex shedding – presents more successful predictions compared to other models investigated for such challenging flow conditions.

Turbulence and energy budget in a self-preserving round jet: direct evaluation using large eddy simulation

An axisymmetric jet at a diameter-based Reynolds number of 1.1 × 104 is computed by a large eddy simulation (LES) in order to investigate its self-similarity region. The LES combines low-dissipation numerical schemes and explicit filtering of the flow variables to relax energy through the smaller scales discretized. The computational domain extends up to 150 jet radii in the downstream direction, which is found to be large enough to discretize a part of this region. Turbulence in the self-preserving jet is characterized by evaluating explicitly from the LES fields the second- and third-order moments of velocity, the pressure–velocity correlations as well as the budgets for the turbulent kinetic energy and for its components. Reference solutions are thus obtained. They agree well with the experimental data given by Panchapakesan &amp; Lumley (J. Fluid Mech., vol. 246, 1963, p. 197) for a jet at the same Reynolds number. The distance required to achieve self-similarity in the LES, around 120 radii from the inflow, is particularly similar to that in the experiment. The discrepancies observed with respect to the data provided by Panchapakesan &amp; Lumley and by Hussein, Capp &amp; George (J. Fluid Mech., vol. 258, 1994, p. 31) for a jet at a higher Reynolds number, specially regarding the turbulence diffusion and the dissipation, are discussed. They appear largely resulting from the approximations made in the experiments to estimate the quantities that cannot be measured with accuracy. The role of the pressure terms in the energy redistribution is also clarified by the LES. Moreover, the turbulent energy budget is calculated in the jet from an equation derived from the filtered compressible Navier–Stokes equations, which includes the dissipation due to the explicit filtering. This has allowed us to assess the behaviour of the LES approach based on relaxation filtering (LES-RF) from the contributions of filtering and viscosity to energy dissipation. The filtering activity is particularly shown to adjust by itself to the grid and flow properties.

The relationship between the vortical structure and the wall shear stress in a blind trough cavity subject to a jet impingement

AbstractIn a blind trough cavity subject to a jet– impingement, the jet switching phenomenon has been known for decades. The large vortices, formed by the Kelvin– Helmholtz instability play a crucial role in this phenomenon– they are the main cause of the fluid entrainment phenomenon, which consequently evoke the Coanda effect and finally results in the jet switch. As the jet swings, the vortical structure inside the cavity changes together with the impinigement point. The aim of this article is to describe the relationship between the wall shear stress, i.e. the motion of the impingement point, and the vortical structure.The analysed data were obtained using the TR PIV system, the caity aspect ratios 16:24 and 18:24, jet hydraulic diameter based Reynolds numbers 3000, 11200 and 19600, and the impingement angles 0°, 5°, 10° and 15°. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.

Numerical investigation of the three-dimensional flow in a human lung model

The flow field at inspiration and expiration in the upper human airways consisting of the trachea down to the sixth generation of the bronchial tree is numerically simulated. The three-dimensional steady flow at a hydraulic diameter-based Reynolds number Re D=1250 is computed via a lattice-Boltzmann method (LBM). The simulation is validated by the experimental data based on particle-image velocimetry (PIV) measurements. The good agreement between numerical and experimental results is evidenced by comparing velocity contours and distributions in a defined reference plane. The results show the LBM to be an accurate tool to numerically predict flow structures in the human lung. Using an automatic Cartesian grid generator, the overall process time from meshing to a steady-state solution is <12 h. Moreover, the numerical simulation allows a closer analysis of the secondary flow structures than in the experimental investigation. The three-dimensional streamline patterns reveal some insight on the air exchange mechanism at inspiration and expiration. At inspiration, the slower near-wall tracheal flow enters through the right principal bronchus into the right upper lobar bronchus. The bulk mass flux in the trachea is nearly evenly distributed over the left upper, center and lower lobar bronchi and the right center and lower bronchi. At expiration, the air from the right upper lobar bronchus enters the right center of the trachea and displaces the airflow from the lower and center right bronchi such that the tracheal positions of the streamlines at inspiration and expiration are switched. The flow in the left bronchi does not show this kind of switching. The findings emphasize the impact of the asymmetry of the lung geometry on the respiratory air exchange mechanism.

Analysis of the turbulence in the suction chamber of an external gear pump using Time Resolved Particle Image Velocimetry

The use of air bubbles for the analysis of the turbulence in the suction chamber of a gear pump with Time Resolved Particle Image Velocimetry (TRPIV) is considered. It is the first time, as far as the authors know, that the flow inside a gear pump is observed with a non-intrusive technique. Although there are drawbacks of using air bubbles as flow tracers, it is the only option available in this case, since solid particles and water drops could drastically damage the steel-made gears. It is shown that if the bubbles are small enough (around 100 μm), the buoyancy is not a significant problem for the typical velocities involved in the experiments. On the other hand, if the number of particles per interrogation area is between 10 and 20, as is normally suggested in the literature, the modification of the speed of sound and, hence, the danger of having a compressible flow, is also negligible. Using air bubbles as tracers for the TRPIV, the turbulence for three experiments, at different diameter-based Reynolds numbers, is analysed. The time series of the velocity at different distances to the gearing zone of the gear pump are considered, as well as the wavenumber distribution of the density of energy, calculated from the vorticity field. The results show that for high enough Reynolds number the integral timescale of the turbulence, obtained from the autocorrelation function, is approximately the same as the gearing period. Also, the spectral distribution in frequency show an energy transport to large scale, as well as the spectral distribution in wavenumber. This latter shows also an stepper range related to the enstrophy cascade towards the small scales. That suggests the two-dimensionality of the turbulence created in the suction chamber.

Direct Computation of the Noise Generated by Subsonic Jets Originating from a Straight Pipe Nozzle

The noise generated by isothermal round jets at Mach number M = 0.9 and at the diameter-based Reynolds number ReD = 5 × 105, originating from a straight pipe nozzle, is computed directly using Large Eddy Simulation (LES), in order to highlight the potential influence of the inlet boundary conditions on the acoustic predictions. Two jets are simulated, displaying levels of fluctuating axial velocity at the nozzle exit respectively of 1.6% and 9% of the jet velocity, while the momentum thickness of the shear layers is nearly the same. The shear-layer development and the radiated sound fields obtained for the two jets are found to differ significantly. The shear layer of the jet with low initial turbulence levels develops for instance with higher turbulence intensities and a velocity flow field that is more correlated. In addition coherent annular vortices and pairings are clearly observed in this jet. Regarding the radiated noise, the jet with high initial turbulence levels provides sound levels and spectra in fairly good agreement with experimental data obtained for jets at Reynolds numbers ReD ≥ 5 × 105. The jet with low nozzle-exit turbulence levels is shown to generate more noise, which might result from vortex pairings in the shear layer as it was suggested by Zaman [1].

Handling of temperature dependence of viscosity in problems of incompressible medium flow around a cylinder

The viscous incompressible medium (water, air) flow past a circular cylinder is considered with regard for the temperature T dependent viscosity v. The influence of different boundary conditions for temperature on flow structure, the drag coefficient and its components due to the pressure and viscosity is investigated in the problem of the flow past a cylinder at rest for the (diameter-based) Reynolds number ReD = 40. A relation between the viscosity gradient along a normal to the body surface and the integral vorticity flux from the body surface into the boundary layer is discussed. Unlike the constant viscosity case the vorticity flux may be different from zero, which must lead because of the integral conservation law for the vorticity to an alteration of the far-field boundary conditions for the velocity. In the same connection, the problem is analysed on the heat spot entry into the computational region under consideration for the flow past a circular cylinder. The examples of the symmetrization of separated flow past a cylinder performing rotation oscillations in a uniform free stream (the Taneda problem) are considered. A comparison with flow computations for low Mach numbers M « 1 for the flow of a medium past a cylinder at rest is carried out. At the computation of the equation for heat transfer under the assumption of incompressibility of such media as air, it is proposed to retain the pressure derivative, which is typical of gases. In this case, a better agreement with the computations of compressible flows (for M « 1) is achieved, for example, at the determination of the sizes of a symmetric zone of flow separation past a circular cylinder. An unsteady flow in the neighborhood of the point of joining the zero streamline bounding a closed region of separated flow (the cavity) in a wake of the cylinder at rest is obtained by a numerical simulation at the Reynolds number equal to 40.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier–Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, Re W ⩽ 2.5 × 10 3. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov’s ν t-92; Secundov et al.’s two equation ν t– L; Wolfshtein’s k– l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k– ε models including those with wall distance based damping functions; Menter SST, k– ω and Spalding’s LVEL model. The use of differential equation distance functions (Poisson and Hamilton–Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with Re W ≈ 2.5 × 10 3 the mixing length and k– l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov ν t-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from Re W = 2500 to 250 surprisingly strengthens the cylinder’s disruptive influence. Importantly, results for Re W ≪ 250 are virtually identical to those for Re W = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder–Sharma k– ε, Menter SST and k– ω show, in accordance with physical reality, the cylinder’s influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model’s erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k– l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%.

Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.

HIGH-ORDER CURVILINEAR SIMULATIONS OF FLOWS AROUND NON-CARTESIAN BODIES

The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier–Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

Measurements of the flow over a low-aspect-ratio cylinder mounted on a ground plane

The flow over a finite-height cylinder of aspect ratio 1, with one end mounted on a ground plane and the other end free, has been studied by means of surface flow visualisation, particle image velocimetry (PIV) and surface pressure measurements. The diameter-based Reynolds number was 200,000. The mean flow topology has been identified in three areas: the horseshoe vortex system, the separated flow over the free-end and the wake region. Evidence is shown for the existence of a three-horseshoe vortex system, while the mean flow over the free-end consists of an arch vortex with its bases on the forward half of the free-end. There are two tip vortices coming off the free-end. The wake region is found to be highly unsteady, with considerable variation from the mean flow.

Turbulent Flow Hydrodynamic Experiments in Near-Compact Heat Exchanger Models With Aligned Tubes

Hydrodynamic experiments measuring longitudinal pressure-drop versus flow rate are conducted for turbulent flow of air (channel hydraulic diameter based Reynolds number range of 2300 to 6860) through near-compact heat exchanger models with rod bundles having aligned (inline) arrangement. Effects of the flow (Re), the geometry parameters, and number of rods of the test models on the nondimensional pressure-drop ξ are studied in detail. Treating the near compact heat exchanger model as a porous medium, a dimensional pressure-drop ΔP/L versus average velocity of flow (U) model similar in content to a non-Darcy porous medium model, is shown to fit the experimental data with fair accuracy. Variation in form drag related to, and induced by the flow and geometric parameters are shown to be the reason for the pressure-drop variations of different models. The relation between the porous medium type model (ΔP/L versus U) and the “ξ versus Re” model is discussed with careful attention to the differences in the two transitions viz. laminar to turbulent and viscous-drag to form-drag dominated flow inside the models. A proposed correlation for predicting ξ, ably capturing all of the form effects induced by the flow and geometric parameters, is found to give predictions with ±20% accuracy.

Flow and heat transfer in the wake of a surface-mounted rib with a slit

An experimental study of flow and heat transfer downstream of a surface-mounted rib with a slit is reported. The open area ratios of the slit rib considered are 10, 20, 30, 40 and 50% with respect to the total projected rib area. Experiments were conducted in a wind tunnel, mostly at a hydraulic diameter based Reynolds number of 32,100. The surface Nusselt number distribution was determined by liquid crystal thermography. Results show that the slit inside the rib enhances heat transfer and reduces pressure penalty, with an optimum performance seen at an open area ratio of 20%. To explain this result, a qualitative picture of the flow field behind the rib was obtained by smoke visualization. Time averages and turbulent statistics of the velocity and temperature fluctuations were measured in detail, using hotwire anemometry and cold wire anemometry respectively. For open area ratios less than 30%, measurements show that the flow through the slit modifies the reattaching shear layer from the top of the rib. The resulting reattachment length is smaller, the peak in Nusselt number is higher, and the average heat transfer from the heated surface is enhanced. For the rib with an open area ratio greater than 40%, the lower portion behaves as an independent small rib with its own reattachment region. Simultaneously, the flow downstream of the upper rectangular part shows characteristics of vortex shedding. Thus, the size of the slit is seen to be an additional parameter that can be used to control heat transfer from the solid surface, in comparison to the solid rib.