Wall Proximity Effects Research Articles

Fluid flow and heat transfer characteristics for a square prism (blockage ratio = 0.1) placed inside a wind tunnel

Experimental investigations in fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around a square prism at Reynolds number 2.6 × 104, blockage ratio 0.1, different height-ratios and various angles of attack. The static pressure distribution has been measured on all faces of the square prism. The results have been presented in the form of pressure coefficient, drag coefficient for various height-ratios. The pressure distribution shows positive values on the front face whereas on the rear face negative values of the pressure coefficient have been observed. The positive pressure coefficient for different height-ratios does not vary too much but the negative values of pressure coefficient are higher for all points on the surface as the bluff body approaches towards the upper wall of the wind tunnel. The drag coefficient decreases with the increase in angle of attack as the height-ratio decreases. The maximum value of drag coefficient has been observed at an angle of attack nearly 50° for the square prism at all height-ratios. The heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficient are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. Both local and average Nusselt numbers have been presented for various height-ratios. The variation of local Nusselt number has been shown with non-dimensional distance for different angles of attack. The variation of average Nusselt number has also been shown with different angles of attack. The local as well as average Nusselt number decreases as the height-ratio decreases for all non-dimensional distance and angle of attack, respectively, for the square prism. The average Nusselt number for the square prism varies with the angle of attack. But there is no definite angle of attack at which the value of average Nusselt number is either maximum or minimum.

Effect of wall proximity in fluid flow and heat transfer from a square prism placed inside a wind tunnel

Experimental investigations in fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around square prisms. Experiments have been carried out for the Reynolds number 4.9?104, blockage ratios are 0.1, 0.2, 0.3 and 0.4, different height-ratios, and various angles of attack. The static pressure distribution has been measured on all faces of the square prisms. The results have been presented in the form of pressure coefficient, drag coefficient for various height-ratios and blockage ratios. The pressure distribution shows positive values on the front face whereas on the rear face negative values of the pressure coefficient have been observed. The positive pressure coefficient for different height-ratios does not vary too much but the negative values of pressure coefficient are higher for all points on the surface as the bluff body approaches towards the upper wall of the wind tunnel. The drag coefficient decreases with the increase in angle of attack as the height-ratio decreases. The maximum value of drag coefficient has been observed at an angle of attack nearly 50? for square prism at all height-ratios. The heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficients are determined from the measured wall temperature and ambient temperature, and presented in the form of Nusselt number. Both local and average Nusselt numbers have been presented for various height-ratios. The variation of local Nusselt number has been shown with non-dimensional distance for different angles of attack and blockage ratios. The variation of average Nusselt number has also been shown with different angles of attack for blockage ratios. The local as well as average Nusselt number decreases as the height-ratio decreases for all non-dimensional distance and angle of attack for square prisms. The average Nusselt number for square prisms of different blockage ratio varies with the angle of attack. But there is no definite angle of attack at different block- age ratio at which the value of average Nusselt number is either maximum or minimum.

On the resistance of a spherical particle settling in a tube of viscous fluid

An idealized flow configuration is examined with an eye to the effects of wall proximity on the Stokes resistance of particles sedimenting in cylindrical ducts. A computer extended series (in blockage factor) for the drag force in on a spherical particle is presented, which complements the singular perturbation analysis of Bungay and Brenner [Int. J. Multiphase Flow 1 (1973) 25]. The convergence properties of shorter truncations of this series in the literature are poor. The extension and analysis here illustrate how capturing the singular character and recasting the series leads to improved convergence. More importantly, the study shows that the limiting factor in improving the convergence of the series is the ill-conditioned nature of the linear operator for the coefficients of the harmonic expansion. It is argued that whenever the bounding surfaces are incompatible with the natural geometry of the harmonics, ill-conditioning of the linear operator occurs. This arises in the near field description of microhydrodynamics simulations.

A Generalized Approximation for the Thermophoretic Force on a Free-Molecular Particle

A general, approximate expression is described that can be used to predict the thermophoretic force on a free-molecular, motionless, spherical particle suspended in a quiescent gas with a temperature gradient. The thermophoretic force is equal to the product of an order-unity coefficient, the gas-phase translational heat flux, the particle cross-sectional area, and the inverse of the mean molecular speed. Numerical simulations are used to test the accuracy of this expression for monatomic gases, polyatomic gases, and mixtures thereof. Both continuum and noncontinuum conditions are examined; in particular, the effects of low pressure, wall proximity, and high heat flux are investigated. The direct simulation Monte Carlo (DSMC) method is used to calculate the local molecular velocity distribution, and the force-Green's-function method is used to calculate the thermophoretic force. The approximate expression is found to predict the calculated thermophoretic force to within 10% for all cases examined. The sou...

A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder

A finite volume method based on a velocity-only formulation is used to solve the flow field around a confined circular cylinder in a channel in order to investigate lateral wall proximity effects on stability, Strouhal number, hydrodynamic forces and wake structure behind the cylinder for a wide range of blockage ratios (0.1<β⩽0.9) and Reynolds numbers (0<Re⩽280). For blockage ratios less than approximately 0.85 a first critical Reynolds number is identified at which a supercritical Hopf bifurcation of the symmetric solution occurs. For blockage ratios greater than about 0.687 and at Reynolds numbers exceeding the first critical Reynolds number a second curve of neutral stability is seen, representing a pitchfork bifurcation of the steady symmetric solution to one of two possible steady asymmetric solutions. Either side of the neutral stability curve for the pitchfork bifurcation our linear stability analysis and direct numerical simulations demonstrate that although the flow is linearly stable it is unstable to finite two-dimensional perturbations. At blockage ratios larger than about 0.82 the steady asymmetric solutions also become unstable through a Hopf bifurcation. In contrast with the first Hopf bifurcation of the symmetric solution at lower Reynolds numbers numerical calculations of the lift coefficient reveal that the oscillations are no longer symmetric in the rising and falling parts of each cycle. Very strong vortices shed from the cylinder and the wall cause drastic increases in the amplitudes of the lift and drag coefficients. A co-dimension 2 point where pitchfork and Hopf bifurcations occur simultaneously has been located in parameter space. Altogether, four distinct regions in the parameter space (β,Re)∈(0,0.9]×(0,280] have been identified, each corresponding to a different class of flow: (i) Steady symmetric flow, (ii) symmetric vortex shedding, (iii) steady asymmetric flow, and (iv) asymmetric vortex shedding, where a periodic-in-time flow is classed as symmetric or asymmetric depending on whether the time-average over one cycle of the lift coefficient is zero or not. Numerical solutions are computed on meshes having up to 1.8 million degrees of freedom. Extensive comparisons are made with the results available in the literature.

Experimental study of a laminar air boundary layer over a water surface

The formation of a laminar boundary layer over a water surface has been experimentally studied for the case of a low wind speed of 3.77 m/s without pressure gradient. Velocity profiles were measured using a small total head tube with an external diameter D=0.7 mm in order to detect the velocity as close to the air/water interface as possible. Precision data were obtained by close attention being paid to near boundary correction procedures arising from the effects of viscous, velocity gradient and wall proximity on the pressure tube. Measurements for the first time support Lock's theory.

The effects of wall proximity on vortex shedding from a square cylinder: Three-dimensional effects

The three-dimensional nature of turbulent vortex shedding from a square cylinder in the vicinity of a solid wall is investigated for a Reynolds number of 18 900 as a function of the gap height, S/D. Spanwise surface pressure measurements on the cylinder faces and on the solid wall are complemented by velocimetry data. It is observed that parallel and oblique shedding modes arise naturally. The number of vortex dislocations is clearly related to the variations in the oblique shedding angle. Dislocations occur with increasing probability as the gap height is decreased to S/D≈0.7. The dislocations are strongly associated with Type A instabilities and vortex splitting, which contribute significantly to phase-jitter. For gap heights close to that for vortex shedding suppression (0.5<S/D<0.7), dislocations occur less frequently. The vortex formation process is increasingly two-dimensional in this range, resulting in strong spanwise correlations and lower phase-jitter. These changes are observed as more sharply peaked frequency spectra, which have been interpreted as shedding frequency “tuning” in earlier studies.

Large Eddy Simulation of Turbulent Wake Behind a Square Cylinder With a Nearby Wall

Computations of the time-averaged and phase-averaged fluid flow and heat transfer based on large eddy simulation (LES) are presented for turbulent flows past a square cylinder with and without a nearby wall at a fixed Reynolds number of 2.2×104. The finite-volume technique was used to solve the time-dependent filtered compressible Navier-Stokes equations with a dynamic subgrid-scale turbulence model, and the numerical fluxes were computed using alternating in time the second-order, explicit MacCormack’s and the modified Godunov’s scheme. Results show some improvements in predicting the streamwise evolutions of the long-time-averaged streamwise mean velocity and total fluctuation intensity along the centerline over those predicted by using Reynolds stress models. A better overall centerline streamwise mean velocity distribution is also predicted by the present LES than by other LES. The wall proximity effect is studied through the comparison of turbulent wake flow past one free standing cylinder and one with a nearby wall, and is illustrated by the phase-averaged spanwise vorticity components and the vortex celerity of spanwise vortices. Moreover, documentation is given on the mechanisms responsible for the augmentation of heat transfer through the spanwise and longitudinal vortices as well as periodic and random fluctuations.

Crossed Waveguide Directional Couplers for High Power Applications

The small aperture coupling theory of the broad wall to broad wall (Moreno) coupler is reviewed and extended. It is shown that a lower limit on the directivity is given by the ratio of magnetic polarizability to electric polarizability for the coupling apertures. Hence directivity may be improved by using very narrow crossed slots for coupling The results of coupling measurements on a Moreno coupler are presented to demonstrate the accuracy of the small aperture theory. A small aperture design procedure has also been developed for the narrow wall to broad wall coupler, which takes into account the effect of wall proximity on slot coupling The measured results for the manufactured coupler are in excellent agreement with this theory.

Application of a non isotropic turbulence model to stable atmospheric flows and dispersion over 3D topography

A non isotropic turbulence model is extended and applied to three dimensional stably stratified flows and dispersion calculations. The model is derived from the algebraic stress model (including wall proximity effects), but it retains the simplicity of the "eddy viscosity" concept of first order models. The "modified k-epsilon" is implemented in a three dimensional numerical code. Once the flow is resolved, the predicted velocity and turbulence fields are interpolated into a second grid and used to solve the concentration equation. To evaluate the model, various steady state numerical solutions are compared with small scale dispersion experiments which were conducted at the wind tunnel of Mitsubishi Heavy Industries, in Japan. Stably stratified flows and plume dispersion over three distinct idealized complex topographies (flat and hilly terrain) are studied. Vertical profiles of velocity and pollutant concentration are shown and discussed. Also, comparisons are made against the results obtained with the standard k-epsilon model.

Modeling rotational effects in eddy-viscosity closures

A new approach to sensitize turbulence closures based on the linear eddy-viscosity hypothesis to rotational effects is proposed. The principal idea is to `mimic' the behavior of a second moment closure (SMC) in rotating homogeneous shear flow; depending on the ratio of the mean flow to the imposed rotational time scales, the model should be able to bifurcate between two stable equilibrium solutions. These solutions correspond to exponential or algebraic time dependent growth or decay of turbulent kinetic energy. This fundamental behavior of SMCs is believed to be of importance also in the prediction of non-equilibrium turbulence. A near-wall turbulence model which is based on the linear eddy-viscosity hypothesis is modified in the present study. Wall proximity effects are modeled by the elliptic relaxation approach. This closure has been successfully applied in the computation of complex, non-equilibrium flows in inertial frames of reference. The objective of the present study is to extend the predictive capability of the model to include flows dominated by rotational effects. The new model is calibrated in rotating homogeneous turbulent shear flow and subsequently tested in three different cases characterized by profound effects of system rotation or streamline curvature. It is able to capture many of the effects due to imposed body forces that the original closure is incapable of. Good agreement is obtained between the present predictions and available experimental and DNS data.

An investigation of wall-proximity effect using a typical large-scale five-hole probe

Effects of wall proximity on the calibration of a typical cone-type five-hole probe with a cobra-shaped stem have been investigated for various probe-wall orientations with the variation of yaw angle. In order to obtain a negligibly small boundary-layer thickness to the probe-head diameter, a large-scale five-hole probe is employed in a well-established laminar boundary layer, and the probe Reynolds number is kept to be 3.53×104, which is a representative Reynolds number in turbomachinery flows. The wall-proximity effect, which is closely related to the complicated three-dimensional flow change due to the presence of the wall is found to be pronounced only when the wall proximity is less than two times the probe-head diameter. In general, larger orientation angle between the wall and the probe head results in smaller wall-proximity effect in flow angle measurements. In this study, changes in the pitch and yaw angles due to the wall proximity are evaluated through a typical non-nulling reduction procedure. The results may provide a useful guideline in the near-wall measurement.

Investigation of Wedge Probe Wall Proximity Effects: Part 1—Experimental Study

Conventional three-hole wedge probes fail to measure the correct static pressure when operating in close proximity to a wall or boundary through which the probe is inserted. The free-stream pressure near the outer wall of a turbomachine may be overindicated by up to 20 percent dynamic head. This paper reports a series of experiments aimed at quantifying this so-called “wall proximity effect.” It is shown from a factorial experiment that probe wedge angle, stem design, and free-stream Mach number all have a significant influence. The yaw angle sensitivity of wedge probes is also found to depend on the proximity of the probe to the wall of introduction. Flow visualization studies on large-scale probe models are described, and a qualitative model of the probe local flow structures is developed. This model is used to explain the near-wall characteristics of the actual size wedge probes. In Part 2 of this paper, the experimental data are used to validate CFD calculations of the flow field around a wedge probe. A simple analytical model of the probe/flow interaction is developed from the CFD solutions.

Investigation of Wedge Probe Wall Proximity Effects: Part 2—Numerical and Analytical Modeling

An experimental study of wedge probe wall proximity effects is described in Part 1 of this paper. Actual size and large-scale model probes were tested to understand the mechanisms responsible for this effect, by which free-stream pressure near the outer wall of a turbomachine may be overindicated by up to 20 percent dynamic head. CFD calculations of the flow over two-dimensional wedge shapes and a three-dimensional wedge probe were made in support of the experiments, and are reported in this paper. Key flow structures in the probe wake were identified that control the pressures indicated by the probe in a given environment. It is shown that probe aerodynamic characteristics will change if the wake flow structures are modified, for example by traversing close to the wall, or by calibrating the probe in an open jet rather than in a closed section wind tunnel. A simple analytical model of the probe local flows was derived from the CFD results. It is shown by comparison with experiment that this model captures the dominant flow features.

Expanding the limits of “equilibrium” second-moment turbulence closures

The paper discusses possibilities for refinements of conventional “equilibrium” second-moment turbulence closure models, aimed at improving model performances in predicting turbulent flows of greater complexity. In focus are the invariant modelling of the low-Re-number and wall proximity effects, as well as extra strain-rates and control of the turbulence length-scale. In addition to satisfying most of the basic physical constraints, the main criterion for model validation was the quality of reproduction of flow and turbulence details, particularly, in the vicinity of a solid wall, in a broad variety of non-equilibrium flows featured by different phenomena. It is demonstrated that the new model, which includes several new modifications, but also some proposed in the past, can satisfactorily reproduce a range of attached and separating flows with strong time- or space-variations or abrupt changes of boundary conditions. Cases considered cover a wide range of Re-numbers involving in some cases also the laminar-to-turbulent or reverse transition.

Anomaly in dendritic growth data — effect of density change upon solidification

We examine recent dendritic growth data obtained by Glicksman and co-workers [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISIJ Int. 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston, MA, 1995, in press; M.E. Glicksman, M.B. Koss, L.T. Bushnell and J.C. LaCombe, in: Modelling of Casting, Welding and Advanced Solidification Processes VII, Eds. M. Cross and J. Campbell, (The Minerals, Metals and Materials Society, 1995); private communication] in microgravity. These authors have pointed out an anomaly in the data, when compared with theoretical predictions. In particular, a systematic deviation of the growth Pe´clet number from an Ivantsov's theory was noted at the intermediate supercooling range. This work considers effects due to density change upon solidification. This requires a careful reexamination of the definition of material parameters, and an evaluation of effects due to the solidification-induced fluid flow (“Stefan wind”). A consistent application of carefully obtained material parameters clearly eliminates the discrepancy between the theory and experimental data. However, the effect of fluid flow due to the solid-melt density change is shown to be of minor importance to the particular experiment and material under consideration. We conclude by presenting an Ivantsov's theory modified for the wall proximity effect and corrected for density change upon solidification that matches the entire range of supercooling levels used in Glicksman's experiments.

Thermal diffusion dominated dendritic growth — an analysis of the wall proximity effect

It is demonstrated that using a simple correction to the original Ivantsov solution to account for wall proximity effects is sufficient to describe the Peclet number microgravity data of Glicksman et al. [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISLJ International 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston MA, 1995, in press] at low supercooling. The analytical correction provides for the enhanced diffusive heat transfer when the thermal diffusion length becomes comparable to the physical chamber dimension. The wall proximity effect is also responsible for the existence of a lower supercooling limit below which the dendrite cannot grow in a steady-state manner. It is concluded that Glicksman's USMP-2 microgravity data is thermal diffusion dominated and thus entirely appropriate for comparison with dendritic growth theories.

Oscillating Flow About Two and Three-Dimensional Bilge Keels

Abstract The paper describes an experimental investigation of the damping provided by bilge keels in an oscillating flow (in a large U-shaped water tunnel). Rectangular and square flat plates were placed adjacent to a solid boundary (with no gap) in order to simulate flow about bilge keels. The single free edge of the rectangular plate and the three free edges of the square plates were beveled to 60-deg angles so as to form sharp edges with included angles of about 60 deg. For comparison, another sharpedged rectangular plate was tested without the wall proximity effects. All plates were held normal to the direction of the ambient flow. The Fourier-averaged drag and inertia coefficients were then calculated as a function of a suitable Keulegan-Carpenter number through the use of the instantaneous force acting on each plate.

Calculation of complex near‐wall turbulent flows with a low‐Reynolds‐number k‐ϵ model

AbstractAn improved low‐Reynolds‐number k‐ϵ model has been formulated and tested against a range of DNS (direct numerical simulation) and experimental data for channel and complex shear layer flows. The model utilizes a new form of damping function adopted to account for both wall proximity effects and viscosity influences and a more flexible damping argument based on the gradient of the turbulent kinetic energy on the wall. Additionally, the extra production of the inhomogeneous part of the viscous dissipation near a wall has been added to the dissipation equation with significantly improved results. The proposed model was successfully applied to the calculation of a range of wall shear layers in zero, adverse and favourable pressure gradients as well as backward‐facing‐step separated flows.

Flow and transport modeling in the sea-breeze. Part I: A modifiedE ? ? model with a non-equilibrium level 2.5 closure

In order to overcome shortcomings of the conventionalE — ∈ model and to develop a more general model applicable to the variety of atmospheric conditions observed, for example, during a land-sea breeze cycle, a modifiedE — ∈ model is proposed. The model is a simplified form of an algebraic stress model including wall proximity effects of Gibson and Launder (1978). The proposed model is similar to the popular Mellor and Yamada (1982) level 2.5 model but does not employ a local equilibrium assumption in the algebraic equations for Reynolds stresses. The resulting model shows a wider realization region under unstable conditions than the Mellor and Yamada model.