Charles A. Petty

Crossflow of elastic liquids through arrays of cylinders

Abstract The flow of a dilute solution of polyisobutylene in polybutene transverse to unidirectional arrays of cylinders has been investigated at Reynolds numbers less than 0.1. Two different arrays were used—a triangular pitch array and a rectangular pitch array. Both arrays have a porosity of 0.704, the same bed length and comprise identical cylinders. Steady state permeation experiments were run over a range of superficial velocities in both arrays, to study the onset of departure from Darcys law. The rheology of the fluid was evaluated in shear before and after each set of runs. While departures from Darcys law occurred in both arrays at similar values of Deborah number, mechanical degradation of the polymer solution was much more severe with the triangular pitch array than with the rectangular pitch array. Specifically, after several runs through the triangular array the relaxation time was halved while the change in viscosity was relatively minor; this reveals loss of the high molecular weight tail in the original polymer. This degradation was irrecoverable; no recovery was noted after two weeks. Measurements of molecular weight distribution on the same samples in Odells laboratory confirm that the highest molecular weight components are degraded. Finite element simulations of Stokes flow were carried out for the two different geometries to determine extensional strain rates along the flow direction in several regions. This was followed by calculations of polymer chain deformation in these regions, with the nonlinear elastic dumbbell model. These calculations reveal that the maximum stretch rate in the triangular pitch array occurs along the streamline joining the stagnation points on adjacent cylinders; this leads to nearly complete extension of the polymer chain at a nominal Deborah number of 1 in the triangular array. However, in the rectangular pitch array, the maximum stretch rate occurs along streamlines considerably removed from the stagnation points, and the polymer chains are not extended along those streamlines up to a Deborah number of 1.

Flow predictions within hydrocyclones

The aim of this article is to illustrate the type of internal flows that can develop within hydrocyclone separators at low and high Reynolds numbers based on the Navier-Stokes equation and the RANS-equation, respectively. The following three examples are used: a 5 mm hydrocyclone; a 76 mm Rietema hydrocyclone; and a 250 mm hydrocyclone with different cone angles. The simulations provide an estimate of the mean pressure and mean velocity fields of the continuous phase in the absence of an air core and a dispersed phase.

MEASUREMENTS OF MEAN VELOCITY PROFILES IN A HYDROCYCLONE USING LASER DOPPLER ANEMOMETRY

A quantitative study of the axial and tangential components of the mean velocity in a 3″-hydrocyclone using laser doppler anemometry has revealed multiple reverse flows in the vortex core. Flow visualization by dye injection shows that these flows are coherent over a significant portion of the hydrocyclone and that little radial mixing occurs between these secondary flows and the outer helical flow. A 2:1 contraction in the vortex finder plays an important role in causing four distinct simultaneous countercurrent flows in the conical section of the hydrocyclone.

An algebraic preclosure theory for the Reynolds stress

An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space–time relaxation of a convective-diffusive Green’s function with the space–time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τR associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and, (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τRS∼1, where...

ISOTROPIC PRESTRESS THEORY FOR FULLY DEVELOPED CHANNEL FLOWS

The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, (I+τR∇〈u_〉)T⋅〈u_′u_′〉⋅(I+τR∇〈u_〉)=τR2〈f_′f_′〉. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation τR2〈f_′f_′〉. Closure requires a phenomenological model for the anisotropic prestress 2kH, defined by 2kH≡τR2〈f_′f_′〉−2αI/3. The prestress coefficient α(=τR2〈f_′⋅f_′〉/2) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time τR, and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (δ+=395) are used to evaluate the behavior of the Reynolds stress for an isotropic prestress (IPS) correlation (i.e., H=O). The IPS theory predicts the existence of a nonzero primary normal st...

THE EFFECT OF TURBULENT MIXING ON MASS TRANSFER NEAR FLUID-FLUID INTERFACES FOR LARGE SCHMIDT NUMBERS*

Turbulent fluctuations cause interfacial fluid to mix rapidly with fluid from the bulk. This effect is analyzed for fluid-fluid interfaces by assuming that concentration fluctuations are primarily produced by velocity fluctuations normal to the interface. The theory yields an a priori relationship between the mass transfer coefficient and the space-time structure of the turbulence which compares favorably with experimental data and other theoretical approaches.

Motion of a deformed sphere with slip in creeping flows

The motion of a rigid particle whose surface is a slightly deformed sphere is studied for creeping flows with the assumption of slip on the particle. Expressions are obtained for the hydrodynamic force and torque exerted by the fluid on a deformed sphere using an asymptotic method introduced by H. Brenner, wherein the normalized amplitude of the deviation from sphericity is assumed to be a small parameter. The Stokes’ resistance calculated by this method is validated by comparing with existing solutions the limiting cases of no slip and perfect slip. The equations describing the motion of a deformed sphere with a slip surface in a simple shear flow are also derived and solved. The motion of the deformed sphere is shown to differ significantly from the no-slip case for low values of a dimensionless parameter that incorporates the slip coefficient. The period of rotation of the deformed sphere is longer, and for cases where the slip coefficient is low, the spheroid rotates to a fixed angle and reaches a quasi-steady orientation.Copyright

Stability of polymerizing liquid flow in porous media

ABSTRACT This paper examines the flow stability of a polymerizing liquid in an anisotropic porous medium. The polymerization reaction leads to an increasing viscosity along the flow direction, particularly behind the advancing resin/air front, and may cause the miscible displacement process to become unstable and uneven. A linearized stability analysis of the flow within the filled region behind the liquid / air interface has been conducted. This reveals that under a moderate adverse viscosity gradient, the polymerization reaction has the potential for stabilizing the flow process by damping out disturbances of wavelengths above a critical size. Guidelines are provided for adjusting the composition of the reacting liquid and the anisotropic medium permeability to stabilize the flow process.

Defects in Resin Transfer Molded Plaques Due to Resin Age Distribution During Mold Filling

Abstract This paper examines the development and consequence of flow structures and possible defects arising in multiple shot injection or multiple-gated injection of two-component resins mixed in-line into a mold with and without fiber preforms. This work may also be relevant to the packing stage. Experiments were run where a premixed batch of vinyl ester resin with peroxide and tracer dye, displaces another older batch of premixed resin in a mold. Polymerization of resin as it flows through the preform during the filling stage sets up an increasing viscosity profile along the fluid filled region and viscous fingering is observed as expected. The types of flow patterns associated with this phenomenon have been explored with random and woven fibrous media packed in a clear mold. The molded plaques were cut up and tested in 3-point bend so that the flexural moduli of specimens with various flow structures could be compared. The flow structures observed include fingers with rounded ends and fingers with multiple tips. Such flow structures lead to regions in the plaques where ‘packets’ of fluid with different extents of polymerization due to differences in age are juxtaposed prior to gelation of the resin. It was found that finger structures with several sharply defined interfaces tended to decrease the value of the flex modulus by up to 32 %, depending on the preform characteristics. Multiple finger tips with diffuse boundaries do not seem to be detrimental to the flex modulus, but multiple tips with sharp boundaries have lowered the flex modulus by 32%.

TURBULENT TRANSPORT OF A PASSIVE SCALAR FIELD

Several statistical theories of the transport of a passive scalar quantity make use of a Greens function and statistical properties of the fluid velocity field. The theories are applied to the problems of mean gradient transport in a turbulent fluid and of turbulent transport to a wall or a fluid interface. For the case of mass transfer by a uniform mean concentration gradient in homogeneous turbulence, a weak mixing hypothesis leads to results similar to those of Kraichnans direct interaction approximation (D1A). Further use of a smoothing hypothesis leads to an algebraic expression for the eddy diffusivity which compares well with the DIA and with laboratory experiments.