The effects of turbulence characteristics on sphere drag

Further results are reported in determining the drag coefficient of spheres in terms of the turbulence characteristics of the flow in which they are immersed. C_D contours are given on plots of turbulence scale versus intensity and show distinct regions where artificially low and high drag can be experienced. The results are shown to be in accordance with theory based on published results for flow conditions upstream and downstream of the spheres.

A Strouhal number (St) based on turbulence macroscale and the r.m.s. value of the fluctuating component of axial velocity is shown to be very appropriate in this application.     

Inertial instability of the Stewartson -layer

Inertial stability of a vertical shear layer (Stewartson E^1/4-layer) on the sidewall of a cylindrical tank with respect to stationary axisymmetric perturbations is inverstigated by means of a linear theory. The stability is determined by two non-dimensional parameters, the Rossby number Ro = U/2ΩL and Ekman number E = v/ΩH², where U and L = (E/4)1/4H are the characteristic velocity and width of the shear layer, respectively, Ω the angular velocity of the basic rotation, v the kinematic viscosity and H the depth of the tank.

For a given Ekman number, the flow is more unstable for larger values of the Rossby number. For E = 10⁻⁴, which is a typical value of the Ekman number realized in rotating tank experiments, the critical Rossby number Ro_c for instability and the critical axial wavenumber m_c non-dimensionalized by L⁻¹ are found to be 1.3670 and 8.97, respectively. The value of Ro_c increases and that of m_c decreases with increasing E.     

On the dispersion of a solute in Poiseuille flow of a third-grade fluid in a channel

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls are extended to the flow of non-Newtonian viscoelastic fluid (known as third-grade fluid) using a generalized dispersion model which is valid for all times after the solute injection. The exact expression is obtained for longitudinal convective coefficient K₁(Γ), which shows the effect of the added viscosity coefficient Γ on the convective coefficient. It is seen that the value of the K₁(Γ) for Γ≠0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K₂(t,Γ) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C_m of the solute over the channel cross-section is determined at a fixed instant after the solute injection for several values of the added viscosity coefficient.     

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E, the skin-friction at the plate decreases with increase in the permeability parameter K₁. However for the same value or Pr and E, the heat transfer rate at the plate increases with increasing K₁. The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K₁ with Pr = 0.73. It is also shown that for fixed values of K₁, and KPr, the skin-friction increases with increase in the dissipation parameter E.     

Droplet combustion experiments in varying forced convection using microgravity environment

A new microscopic model of the interaction between droplet flames and fine vortex tubes which compose a coherent structure of turbulence was developed. Three non-dimensional numbers were introduced to extend the length scale and time scale so as to be suitable for microgravity experiments using droplets of combustion of about 1 mm in diameter. An experimental apparatus for combustion of a single droplet and that of an array of two droplets in varying airflow was developed, and experiments were performed in microgravity and normal gravity at pressures up to 2.0 MPa for n-nonane and ethanol as fuels. Variations of the instantaneous burning rate constant, K_i, in response to the varying flow velocity was successfully observed. At high pressure, the effects of droplet Reynolds number Re on K_i was clearly seen, while the effects of natural convection, which increases K_i with Re, was seen in normal gravity even in the forced airflows. As for the experiments on combustion of an array of two droplets, K_i reduction of the downstream droplet became weak when the flow direction was varied. However, the K_i reduction of the downstream droplet for flow direction variations was clearly seen for n-nonane droplets but almost not for ethanol droplets. The interaction mechanism between upstream and downstream droplets is considered to result from the elimination of oxidizer supply to the downstream droplet, indicating strong interaction effects of n-nonane droplets for a stoichiometric oxygen-fuel ratio of n-nonane (i.e., 14.0) greater than that of ethanol (i.e., 3.0).     

On drag, Strouhal number and vortex-street structure

A phenomenological model for the vortex-shedding process behind bluff cylindrical bodies is proposed. Relationships between Strouhal frequency St, drag coefficient c_D, Reynolds number Re and geometric wake parameters are obtained from mass conservation, momentum conservation in the transverse direction and energy considerations. For the first time, Roshko's (Technical Report TN 3169, NACA, US Government Printing Office, Washington DC, 1954) experimental discovery of vortex-street similarity behind different cylinders is analytically derived. In addition, the empirically obtained Strouhal-frequency laws of Roshko (Technical Report TN1191, NACA, US Government Printing Office, Washington DC, 1954) and Fey (Phys. fluids A 10 (1998) 1547) are also reproduced. Measurements of St and c_D including their Re dependency for flows around cylinders with circular, square, triangular, semi-circular and other cross sections agree favorably with the proposed model.     

The instability of rhombic cell flows

Instability of two-dimensional periodic flows with rhombic cell structure represented by the stream function Ψ=cos kx+cosy is investigated. Stability characteristics are obtained for the Reynolds number R=1, 2, 3 and 4 and the ratio of the diagonals of the cell . Variation of the critical Reynolds number R_c with k is obtained, and the square cell flow (k=1) is found to be most stable (R_c=√2). It is found that R_c → 1 as k → 0, which leads to a finite gap between this limiting R_c and R_c=√2 for K=0 (Ψ=cos y).     

The turbulent character and pressure loss produced by periodic symmetric ribs in a circular duct

The structural character and steady-state statistics of the turbulence inside a rib-wall circular duct is investigated by the large-eddy simulation (LES) methodology. The impetus of this study is to gain an understanding of the principle physics attributing to minimizing the pressure recovered (or maximizing the pressure loss) within the core flow. For a rib periodicity with height (h) to pitch (p) ratio p/h=5, the computational results show that the majority of turbulence produced due to the rib’s presence is concentrated near the rib crest leading edge. Pairs of counter-rotating streamwise vortices form soon after the leading edge that are quickly convected radially toward the core flow. The turbulent activity within the duct trough region is negligible compared to the turbulence levels of the core flow. At this rib periodicity, the separated shear layers from the trailing edge of each rib nearly reattach to the trough floor before reaching the next rib. The resultant irrecoverable pressure loss in the form a centerline frictional coefficient is verified by an ‘at-sea’ test on board a US Navy submarine. Based on the duct diameter, their Reynolds numbers are Re_D^LES=8×10³ and (Re_D^exp)_avg=4×10⁶, respectively.     

Laboratory observations of interactions of forced plumes with stratified shear layers

Plumes of fluid are often observed in nature to interact with stratified shear layers. Examples of this include chimney plumes hitting inversion-layer ceilings; sewage plumes impinging on unmixed fresh/saltwater interfaces; descending plumes of cold water formed at ice-leads interacting with the oceanic thermocline; and volcano plumes interacting with atmospheric interfaces. Controlled laboratory studies of these phenomena have not previously been described in the literature, and as a result there is a lack of understanding regarding their morphology and dynamics. Thus, a novel set of experiments is described here in which the behaviour of a turbulent plume is observed in the presence of a two-layer ambient. The lower layer, into which the plume initially emerges, is quiescent and at a relatively high density. The upper layer is forced to flow uniformly across the top of the lower layer, and has a lower density. The flow of the resulting plume is characterised by (a) its vertical and lateral spreading in the lower layer; (b) the nature of its extension upstream and downstream at the interface; and (c) the extent to which it penetrates into the upper layer. The behaviour is found to be governed by three non-dimensional parameters: the initial gradient Richardson number of the interface Ri_G, the ratio of the upper layer crossflow speed to the speed of the plume when it first impinges on the interface U_F/U_PI, and the ratio of the plume Monin–Obukhov lengthscale to the lower layer depth L_MO/H_L. Regime diagrams are presented showing the effects of changing these parameters on the plume flow, quantitative relationships are determined, and practical applications of the results are considered.     

Rime- and glaze-ice accretion due to freezing rain falling vertically on a horizontal thermally insulated overhead line conductor

A theory of atmospheric icing due to freezing rain on an overhead line conductor (OHLC) is developed. The rain falls vertically on a horizontal OHLC that is thermally insulated. It is assumed that the collection efficiency of the accretion surface is unity and that this surface is in thermodynamic equilibrium with the environment.

For air temperature T_A 0°C and raindrop temperature T_D 0°C, the freezing rain accretes as rime ice, provided that the temperature of the ice surface T_l < 0°C. The evolution equation governing the mass transfer at the accretion surface is solved analytically, yielding the shape of the rime-ice surface. Equations governing the thermal state of the rime-ice deposit are also given. These determine the onset of wet growth or glaze accretion at the upper stagnation line during suitable environmental conditions.

For environmental conditions producing an ice surface at temperature T_l = 0°gC, the freezing accretes as glaze. Equations governing the heat and mass transfer at the surface determine the shape of the glaze surface and the downward viscous motion of the unfrozen water. For T_D < 0°C, glaze evolution equations are developed for T_A 0°C and T_A 0°C. Analytical solutions of these equations are obtained. In particular, when T_D < −T_A < 0°C, the evolution equation predicts a novel limiting growth that is triangular in shape. Further study of the mass and heat transfer conditions, in the neighborhood of this final stage of glaze accretion, shows that it is maintained in thermodynamic equilibrium with its warm air environment.     

A survey of experimental heat transfer data for nucleate pool boiling of liquid metals and a new correlation

The experimental data for heat transfer during nucleate pool boiling of saturated liquid metals on plain surfaces are surveyed and a new correlation is presented. The correlation is h = Cq^0.7p_r^m, where C and m are, respectively, 13.7 and 0.22 p_r < 0.001 and 6.9 and 0.12 for p_r > 0.001 (h is in W/m² K and q in W/m²). This correlation has been verified with data for K, Na, Cs, Li, and Hg from 17 sources over the reduced pressure (p_r) range of 4.3 × 10⁻⁶ to 1.8 × 10⁻². The correlation of Subbotin et al. was found unsatisfactory, but a modified correlation was developed that also gives good agreement with most of the data.     

Effusing core at the center of A potential vortex

Experiments were carried out to measure the base pressure distribution of a flow field induced by a potential vortex with its axis normal to a stationary disk. The center base pressure coefficient of the vortex, C₀(0), was found to be proportional to Reynolds number from Re = 2.0 × 10³ to Re > 2.5 × 10⁴, where Re is based on the disk radius and azimuthal velocity at the disk edge. This behavior of C₀(0) is at variance with the experimental results of Phillips (Phys. Fluids, 27, 2215, 1984) and Khoo (M. Eng. Thesis, Natl. Univ. Singapore, 1984), which showed vastly different trends depending on Re. Plausible reasons are suggested for the apparent discrepancies observed. Finally, the extent of the effusing core at the center, r₁ (taken to be the radial position where departure from the outer potential flow took place), was found to be proportional to Re^−1/2 for all Re values considered.     

Sound emission by a vortex ring passing through a circular hole in a large flat plate

Acoustic emission has been studied experimentally when a vortex ring passes through a circular hole in a large flat plate, along its normal axis. The speed of the vortex ring is made high enough for the sound emission to be detectable, but can be regarded as sufficiently low in comparison to the sound speed. Substantial monopole and quadrupole components are observed in the detected wave profiles. Translational motion of the vortex ring in the presence of the flat plate with a hole has been observed optically, and its relation with the sound emission is determined. In this case, the power law of the acoustic pressure amplitude of monopolar vortex sound versus the translation speed U of the vortex ring is first measured in detail and is found to be U^2.1–U^2.4. This means that experimentally determined powers for the monopole components in the two half-spaces also agree approximately with the corresponding values predicted by the theory of vortex sound.     

A new model for fatigue crack propagation in 4340 steel

An investigation on fatigue crack propagation under mode I loading has been performed. Fatigue crack growth data in the case of plane strain mode I have been obtained by performing experiments on compact tension specimens of 4340 steel for increasing ΔK_I, decreasing ΔK_I, and constant ΔK_I loading conditions. Fatigue crack extension predictions have been obtained for Khan's proposed equation [1989], together with the widely used and [1963] and [1967] equations. Khan's equation overcomes the drawbacks associated with the Paris and Forman equations, such as the inclusion of all the three stages of fatigue crack propagation, the nondimensionality of the constant, “C”, and also the accuracy in life prediction. Within the context of Linear Elastic Fracture Mechanics and the types of loading performed at the crack tip, it has been shown that Khan's model can accurately predict the crack growth data from near threshold value to the unstable fracture; these predicted values are much more accurate than those from the Paris and Forman equations.     

Large-scale structure of a leading-edge separation bubble with local forcing

The Karhunen-Loeve (K-L) expansion is used to extract coherent structures from a leading-edge separation bubble with local forcing. A leading-edge separation bubble is simulated using the discrete vortex method, where a time-dependent source forcing is perturbed near the separation point. Based on the wealth of numerical data, the K-L procedure is applied in a range of the forcing amplitude (A₀ = 0, 0.5, 1.0 and 1.5) and forcing frequency (0 f_FH/U_∞ 0.3). Application of K-L procedure reveals that the eigenstructures are changed noticeably by local forcings. In an effort to investigate the mechanism of decreasing reattachment length (x_R), dynamic behaviors of the expansion coefficients and contributions of the eigenfunctions are scrutinized. As the forcing amplitude increases, large-scale vortex structures are formed near the separation point. Furthermore, the flow becomes more organized, which results in the reduction of x_R. Two distinctive regimes are classified: the regime of decreaing x_R and the regime of increasing x_R. The K-L global entropy indicates that x_R is closely linked to the organization of the flow structure.     

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

Formation of multiple shocklets in a transonic diffuser flow

Multiple shocklets are frequently generated in transonic diffuser flows. The present paper investigates the formation of these shocklets with a high-speed CCD camera combined with the schlieren method. It is observed that compression waves steepen while propagating upstream, and eventually become new shock waves. The ordinary shock wave is found to move upstream beyond the nozzle throat or to disappear while moving downstream depending on the pressure ratio across the nozzle. This phenomenon is also analyzed with the one-dimensional Euler equations by assuming a pressure disturbance given by the sine function at the channel exit. The calculated results are found to reproduce quite well the experimental behavior of the shocklets. The effect of the frequency of disturbance is also studied numerically, and it is shown that the multiple shocklet pattern appears when the amplitude of disturbance is not large and the diverging part of the channel downstream of the ordinary shock wave is long. Received 26 June 1998 / Accepted 15 March 1999     

Non-Local Interactions and Feedback Instability in a High Reynolds Number Flow

The question of non-locality is considered for a model supersonic flow at high Reynolds number in a channel formed between two parallel plates of different length, using the channel length as a control parameter. Examples are given of time-periodic stable and unstable flows forced by a disturbance positioned in the middle of the channel. It is shown that in certain parameter ranges the flow in a channel of ever increasing length is not approximated by the solutions obtained for infinitely long channels. This is interpreted in terms of a feedback interaction between the flow near the channel ends and the disturbance source. Feedback is shown to result from a slow upstream decay of disturbances coupled with a relatively fast downstream growth of instability waves. For a free (non-forced) flow, the feedback is found to lead to a form of global or resonant instability. Examples of growth rate calculations for the feedback modes are given.     

Changes in some mechanical properties of a loamy soil under the influence of mechanized forest exploitation in a beech forest of central Belgium

Modification of some soil mechanical properties (penetration resistance and consolidation pressure) induced by vehicle compaction during mechanized forest exploitation was studied in an acid and loamy leached forest soil of the loessic belt of central Belgium. In situ penetration tests and laboratory Bishop–Wesley cell tests were undertaken for the two main soil horizons of a beech high-forest, i.e. the eluvial E horizon (5–30 cm depth) and the underlying clay-enriched B_t horizon (30–60 cm depth). Both undisturbed and wheel-rutted soil areas were studied (E and B_t horizons vs. E_g and B_tg horizons).

Results show that: The experimental overconsolidation pressure of the eluvial reference horizon (E) is about 50 kPa higher than the value calculated from soil overburden pressure; this probably results from suction action during dry periods. The clay-enriched reference horizon (B_t) shows the same trends. In wheel-rutted areas, seven years after logging operations, the E_g horizon memorizes only 14.5% of the wheel induced stress due to forest machinery.

In the compacted B_tg horizon, the experimental overconsolidation pressure represents 96% of the exerted theoretical stresses due to harvesting actions. The good recording of the exerted stresses, after seven years, can be explained by: (1) The B_tg depth which keeps it from seasonal variations i.e. from desiccation–moistening or freeze–thaw cycling; (2) amorphous and free iron accumulation inducing a “glue” effect of the B_tg soil matrix, which could stabilize the soil structure and prevent recovery to initial conditions. These results provide clear evidence that on loessic materials, soil compaction due to logging operations leads to modifications in both physical (bulk density, total porosity) and mechanical (penetration resistance and consolidation pressure) soil properties.