Onset Of Secondary Flow Research Articles

Global nonlinear stability of convection in a heat generating fluid filled channel with a moving boundary

The energy method is employed to investigate the stability of a steady convective flow in a heat generating fluid arising due to the combined effect of buoyancy, shear and pressure gradient. By introducing a suitable generalized energy functional and using energy inequalities sufficient conditions for the existence of such a flow are found. An analysis through the variational principles is then made to find sharper limits for nonlinear stability. Comparisons are made with linear results in the literature and it is shown that the linear theory fails to capture the physics of the onset of secondary flow.

Taylor-Couette Instabilities in Flows of Newtonian and Power-Law Liquids in the Presence of Partial Annulus Obstruction

The flow inside a horizontal annulus due to the inner cylinder rotation is studied. The bottom of the annular space is partially blocked by a plate parallel to the axis of rotation, thereby destroying the circumferential symmetry of the annular space geometry. This flow configuration is encountered in the drilling process of horizontal petroleum wells, where a bed of cuttings is deposited at the bottom part of the annulus. The velocity field for this flow was obtained both numerically and experimentally. In the numerical work, the equations which govern the three-dimensional, laminar flow of both Newtonian and power-law liquids were solved via a finite-volume technique. In the experimental research, the instantaneous and time-averaged flow fields over two-dimensional meridional sections of the annular space were measured employing the particle image velocimetry (PIV) technique, also both for Newtonian and power-law liquids. Attention was focused on the determination of the onset of secondary flow in the form of distorted Taylor vortices. The results showed that the critical rotational Reynolds number is directly influenced by the degree of obstruction of the flow. The influence of the obstruction is more perceptible for Newtonian than for non-Newtonian liquids. The more severe is the obstruction, the larger is the critical Taylor number. The height of the obstruction also controls the width of the vortices. The calculated steady-state axial velocity profiles agreed well with the corresponding measurements. Transition values of the rotational Reynolds number are also well predicted by the computations. However, the measured and predicted values for the vortex size do not agree as well. Transverse flow maps revealed a complex interaction between the Taylor vortices and the zones of recirculating flow, for moderate to high degrees of flow obstruction.

Onset of secondary flow and enhancement of heat transfer in horizontal convergent and divergent channels heated from below

Experiments for the onset and development of the buoyancy driven secondary air flow and enhancement of heat transfer in a horizontal convergent and a divergent channel have been carried out. The bottom wall of the channel is horizontal and heated uniformly, while the top wall is insulated and inclined with respect to the horizontal plane so as to create a convergence angle of 3° for the convergent channel, or a divergence angle of 3° for the divergent channel. The aspect ratio (width to height) and the ratio of channel length to height at the entrance of the channel is 6.67 and 15, respectively. The Reynolds number ranges from 200 to 2000, the buoyancy parameter, Gr/ Re 2, from 2.5 to 907 and Pr of the air flow is 0.7. Flow structure inside the channel is visualized by injecting smoke at the inlet flowing along the bottom wall. The onset of secondary flow appearing as transverse instability wave and onset of initial protrusion of the bottom heated layer are identified. Secondary flow structures observed are somewhat different from the case in the parallel-plate channel. This is attributed to the destabilization effect of the deceleration in the divergent channel which results in a much earlier initiation of secondary flow and more pronounced enhancement in the heat transfer, and the stabilization effect of the acceleration in the convergent channel which results in a much later initiation of the secondary flow and less pronounced enhancement in the heat transfer. However, the deceleration flow in the divergent channel and the acceleration in the convergent make the average Nusselt numbers approach the results of the parallel-plate channel. Correlation results for the onset of the secondary flow and enhancement of the heat transfer will be presented and discussed.

FLOW PATTERNS OF MIXED CONVECTION IN A HORIZONTAL SQUARE CHANNEL FLOW

An experimental study of mixed-convection heat transfer flow of a CuSO4 + H2SO4 + H2O solution in a horizontal channel was performed. Unstable temperature gradients imposed by a heated bottom initiated an ascending (secondary) flow of light boundary layer fluid into the free stream. The shadowgraph technique was used to visualize the flow and to determine the nature and effect of thermally driven secondary flows in a horizontal channel with heated top and bottom surfaces and insulated side walls. The ranges of the parameters studied in the present work for the square channel are Pr = 5–7, Re = 100–1,000, and Grqb = 2·8 × 106−2·5 × 107. Flow visualization revealed Ike existence of four regimes corresponding to laminar forced convection, laminar mixed convection, transitional mixed convection, and turbulent free convection. Also, the onset of secondary flow was found to be delayed by decreasing the Grash of number and / or by increasing the Reynolds number. A direction for future study of mixed thermosoluta...

Free-surface Taylor vortices

The hydrodynamic instability of a viscous incompressible flow with a free surface is studied both numerically and experimentally. While the free-surface flow is basically two-dimensional at low Reynolds numbers, a three-dimensional secondary flow pattern similar to the Taylor vorticies between two concentric cylinders appears at higher rotational speeds. The secondary flow has periodic velocity components in the axial direction and is characterized by a distinct spatially periodic variation in surface height similar to a standing wave. A numerical method, using boundary-fitted coordinates and multigrid methods to solve the Navier–Stokes equations in primitive variables, is developed to treat two-dimensional free-surface flows. A similar numerical technique is applied to the linearized three-dimensional perturbation equations to treat the onset of secondary flows. Experimental measurements have been obtained using light sheet techniques to visualize the secondary flow near the free surface. Photographs of streak lines were taken and compared to the numerical calculations. It has been shown that the solution of the linearized equations contains most of the important features of the nonlinear secondary flows at Reynolds number higher than the critical value. The experimental results also show that the numerical method predicts well the onset of instability in terms of the critical wavenumber and Reynolds number.

?Paradoxical? circulating rarefied gas flow in a short rotating cylinder with a fixed end face

The intensity of this flow decreases with increase in the rarefaction of the gas up to a value of the Knudsen number Kn = 1 and then remains constant. The direction of circulation characteristic of a continuum is preserved. We have now investigated the onset of secondary flows with decrease in the height of a rotating cylinder with a fixed end face. It has been established that for a dimensionless height h = H/a = 0.25, where a is the radius of the cylinder, a two-vortex circulating flow structure develops. At first glance, the direction of one of the vortices might appear paradoxical. 1. FORMULATION OF THE PROBLEM AND METHOD OF CALCULATION We will consider the problem of the rarefied gas flow in a rotating cylinder established after the upper end face is brought to a stop. We assume that the rate of rotation of the cylinder corresponds to a Mach number M --- o~a/(3,RTo) 1/2 = 1.94, where o~ is the angular velocity, T O is the initial temperature of the gas and the cylinder surfaces, R is the gas constant, and "y is the specific heat ratio of the gas. Initially the gas density has a Boltzmann exponential radial distribution, its value on the lateral surface remaining constant as h varies. The Knudsen number, defined as Kn = X/H, where )~ is the molecular mean free path, was varied in the steady state from 0.1 at the side walls to 0.6 near the axis when h = 1 and from 2 to 5 when h = 0.06. It was assumed that the molecules interact with each other as "rigid spheres," while the interaction with the surfaces of the cylinder is assumed to be perfectly diffuse. In the calculations we used the direct statistical modeling method with a "majorant" molecular collision frequency [2] which makes it possible to reduce the time taken for the problem to reach the steady state and save computer memory by using fewer model particles than in the scheme usually employed [3]. The domain investigated was divided into 20 cells radially and 6--10 ceils vertically depending on the distance between the ends of the cylinder. In determining the flow characteristics the total volume of the statistical sample amounted to 5" 107 particles. As criteria of the completion of the transient process we used the conditions of constancy of the total moment of the friction forces and zero total radial mass flux. The typical time required to arrive at a steady-state solution was 2--3 h for calculations made on a EC 1061 computer.

Onset of secondary flow in the modulated Taylor-Couette system.

The critical Reynolds number for the linear instability of primary flow is calculated for a Taylor-Couette system in which the rotation rate of either cylinder is modulated sinusoidally in time. The method used is based on that of Hall (J. Fluid Mech. 67, 29 (1975)) and is restricted to small amplitudes of modulation but allows for a finite gap. For the case of outer-cylinder modulation, we find that the critical Reynolds number is larger than that for the unmodulated system, while, if the inner cylinder is modulated, it is smaller.

Dispersion of solutes during blood flow through curved tubes.

The dispersion of I 131 and I 131 -HSA in plasma and whole pig's blood has been studied by observing the clearance of a well mixed bolus, containing the radioactive labelled solute, at a point downstream, during flow through flexible straight and curved tubes. The dispersion of I 131 -HSA in plasma flow through a straight tube is consistent with a mechanism of diffusion superimposed on a parabolic velocity profile. In curved tubes, secondary flows produce additional dispersion of I 131 -HSA in plasma. With whole blood additional dispersion of I 131 -HSA occurs in straight tubes owing to the tumbling and rolling of red blood cells near the vessel wall. The onset of secondary flows and increased dispersion in curved tubes requires a relatively high flow rate with whole blood owing to its increased viscosity at low shear rates. At high flow rates, above a velocity of 10 cm s−1, a phase separation of cells and plasma occurs, with the formation of a relatively stagnant cell-free plasma layer on the inner wall of the bend.

Current-induced instabilities in rotating hydromagnetic flows between concentric cylinders

The stability of hydromagnetic flow produced in a thin annular region between concentric cylinders by the interaction of a superimposed radial current and an axial magnetic field is examined both when the bounding cylinders are stationary and when rotating. After deriving the small gap approximation equations for the steady-state one-dimensional azimuthal flow and for the corresponding induced electric potential, the equations governing the growth of infinitesimal axisymmetric disturbances are obtained and solved at neutral stability by use of the Galerkin method. Stability results for the nonrotating cylinder case are shown to be expressible in terms of existing results for the stability of hydromagnetic flow produced by an azimuthal pressure gradient. It is found, in our thin film approximation, that the radial current must generally exceed a certain critical value before the one-dimensional flow breaks down into a three-dimensional pattern. Rotation of the outer cylinder enhances stability while rotation of the inner cylinder produces a greater tendency toward instability as reflected by lower Dean numbers at the onset of secondary flow.

Maximum density effects on convective instability of horizontal plane poiseuille flows in the thermal entrance region

A linear stability analysis is used to study the conditions marking the onset of secondary flow in the form of longitudinal vortices for plane Poiseuille flow of water in the thermal entrance region of a horizontal parallel-plate channel by a numerical method. The water temperature range under consideration is 0∼30°C and the maximum density effect at 4°C is of primary interest. The basic flow solution for temperature includes axial heat conduction effect and the entrance temperature is taken to be uniform at far upstream location jackie=−∞ to allow for the upstream heat penetration through thermal entrance jackie=0. Numerical results for critical Rayleigh number are obtained for Peclet numbers 1, 10, 50 and thermal condition parameters (λ 1, λ 2) in the range of −2.0≤λ 1≤−0.5 and −1.0≤λ 2≤1.4. The analysis is motivated by a desire to determine the free convection effect on freezing or thawing in channel flow of water.

An Experimental Study of Internal Hygrocysts

The onset of the stable laminar secondary flow (hygrocysts) that arises when a partially filled container is rotated about a horizontal axis has been experimentally studied. Nearly 500 sets of data on thirteen fluid systems were obtained and analyzed using a multiple linear regression computer program. Numerous dimensionless correlation models were investigated, the best being a power law relationship between the Reynolds number, volume fraction, and Weber number. Anomalous behavior was observed in that as the volume fraction approached unity, the critical speed of the onset of the secondary flow approached zero, indicating non-rigid body motion (driven by the lateral body force) in completely filled horizontal rotating containers.

Onset of Secondary Flow in the Viscous Flow of Helium II between Rotating Cylinders

The difference in the values of the crit. velocities and Reynolds nos. for secondary flow in the viscous flow of He II between rotating cylinders were reconciled by introducing a new crit. Reynolds no. which takes into account the length and radius of the cylinder.

Stability of rotational couette flow of polymer solutions

AbstractThe onset of secondary flow between rotating cylinders (Taylor vortices) was observed for a dilute polymer solution whose viscometric flow properties were characterized rheogoniometrically. The critical Taylor number (flow onset) was predicted accurately by linear stability theory with a stress constitutive equation describing viscometric behavior. The cell spacing differed significantly from that predicted by linear theory. A nonlinear analysis shows that Linear theory will predict the ultimate cell size only for an inelastic liquid. For an elastic liquid a larger wave number (closer spacing) is a lower energy configuration than the linear theory spacing. This is consistent with experiment.

Finite amplitude convection with longitudinal vortices in plane poiseuille flow—the effect of uniform axial temperature gradient

Finite amplitude convection with longitudinal vortex rolls for a steady hydrodynamically and thermally fully developed laminar forced flow between two infinite horizontal flat plates subjected to axially uniform wall heat flux is approached by a finite-difference solution using a combination of a boundary vorticity method and a line iterative relaxation technique. The governing equations with Boussinesq approximations are solved up to four times the critical value for the parameter ( PrReRa). The onset of secondary flow in the form of longitudinal vortex rolls is indicated by a critical value ( PrReRa)∗ which can be obtained by linear stability analysis with infinitesimal disturbance. The wave number in the post-critical flow regime is assumed to be that predicted by the linear stability analysis. The heat transfer mechanism is clarified by a detailed study of the field characteristics for flow and temperature using air ( Pr = 0.7) as an example. A series of photographs depicting the gradual development of the longitudinal vortex rolls for air is also presented. Flow and heat transfer results are presented for Pr = 0.1, 0.7, 2, 10 and 100. A study of the Prandtl number effect reveals that the effect of secondary flow on pressure-drop parameter fRe can be neglected for Pr ⩾ 10 and an asymptotic behavior for heat transfer results exists for Pr ⩾ 2 in the post-critical regime.

Experiments on the Onset of Longitudinal Vortices in Laminar Forced Convection Between Horizontal Plates

An experimental investigation is carried out to determine the onset of longitudinal columnar vortices due to buoyant forces for fully developed laminar forced convection between two infinite horizontal plates, each wall subjected to identical uniform axial temperature gradient but maintained at temperatures T1 and T2 (T1 > T2, T1 < T2, and T1 = T2) at lower and upper surfaces, respectively. The limiting case with vanishing axial temperature gradient and heating from below (T1 > T2) is known to have a critical Rayleigh number of 1708 and is used to check the accuracy of the testing apparatus. The onset of secondary flow is determined by a direct flow-visualization technique using cigarette smoke, and confirmed by a transverse temperature-profile measurement using a single thermocouple traverse. Experimental results for the critical Rayleigh number are compared with theory and the agreement is found to be good.

Natural convection in a rectangular cavity transient behavior and two phase systems in laminar flow

An analysis is presented for transient laminar natural convection in a rectangular cavity containing either one fluid or two immiscible liquids. The resultant differential equations were integrated numerically and computed results are presented for the transient streamline patterns and for the isotherms, for a variety of conditions including high, low and intermediate values of the Prandtl number. The computed results agree with experimental data, both obtained in this study, and reported by other investigators. Such comparison is presented regarding temperature profiles, velocity profile, transient behavior and the onset of secondary flows.