Velocity profile measurement by ultrasonic doppler method

The ultrasonic velocity profile measuring method has been developed at PSI for application in fluid mechanics and fluid flow measurement. It uses pulsed ultrasonic echography together with the detection of the instantaneous Doppler shift frequency. This method has the following advantages over the conventional techniques: (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field. After a brief introduction of its principle, the characteristics and specifications of the present system are given. Then examples in fluid engineering for oscillating pipe flow, T-branching flow of mercury, and recirculating flow in a square cavity are described that confirm the method's advantages. Several other works under way by other investigators are introduced. A potential for in-depth study of fluid dynamics is demonstrated by several examples from an investigation of modulated wavy flows in a rotating Couette system. The position-averaged power spectrum and the time-averaged energy spectral density were used to study the dynamic characteristics of the flow, and subsequently the velocity field was decomposed into its intrinsic wave structure based on two-dimensional Fourier analysis.     

A variant of the low-Reynolds-number two-equation turbulence model applied to variable property mixed convection flows

Previous work has demonstrated that the low-Reynolds-number model of Launder and Sharma (1974) offers significant advantages over other two-equation turbulence models in the computation of highly non-universal buoyancy-influenced (or “mixed convection”) pipe flows. It is known, however, that the Launder and Sharma model does not possess high quantitative accuracy in regard to simpler forced convection flows. A variant of the low-Reynolds-number scheme is developed here by reference to data for constant property forced convection flows. The re-optimized model and the Launder and Sharma formulation are then examined against experimental measurements for mixed convection flows, including cases in which variable property effects are significant.     

Regularity and asymptotic behavior of solutions of nonautonomous differential equations

The existence of a nonautonomous approximate inertial manifold is shown for problems of the formu + Au + N(t,u)=0, in whichA is a self-adjoint operator with compact resolvent in a Hilbert spaceH. The operatorN(t, u) = G(u) + F(t, u) is nonlinear withG a monotone gradient that is locally Lipschitz fromD(A ^1/2) intoH, andF:⁺×HH a Lipschitz perturbation that is Hölder continuous int. Weak solutions are shown to be uniformly locally Hölder continuous intoD(A) with equicontinuity in families of solutions with ¦u(0)¦ r.A priori estimates of ¦Au(t)¦ are also verified and used in a skew-product flow to show there is a global attractor whose component elements form a equicontinuous family of solutions.     

Inelastic constitutive equations for complex flows

A new class of inelastic constitutive equations is presented and discussed. In addition to the rate-of-strain tensor, the stress is assumed to depend also on the relative-rate-of-rotation tensor, a frame-indifferent quantity that brings information about the nature of the flow. The material functions predicted by these constitutive equations are given for simple shear and uniaxial extension. A special case of these equations takes the Newtonian form, except that the viscosity is a function of the invariants of both kinematic tensors on which the stress depends. This simple constitutive equation has potential applications in liquid flow process simulations, since it combines simplicity with the capability of responding independently to shear and extension, as real liquids seem to do. Finally, possible forms for the new viscosity function are discussed.     

Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH

Temporal sequences of planar laser-induced fluorescence (PLIF) images of several high-speed, transient flowfields created in a reflection-type shock tunnel facility were acquired. In each case, the test gas contained either nitric oxide or the hydroxyl radical, the fluorescent species. The processes of shock reflection from an endwall with a converging nozzle and of underexpanded free jet formation were examined. A comparison was also made between PLIF imaging and shadow photography. The investigation demonstrated some of the capabilities of PLIF imaging diagnostics in complex, transient, hypersonic flowfields, including those with combustion.Nomenclature A spontaneous emission rate - A _las cross sectional area of laser sheet - B laser absorption rate - C _opt constant dependent on optical arrangement, collection efficiency, etc. - D nozzle throat diameter - E _p laser pulse energy - f _J Boltzmann fraction of absorbing state - g spectral convolution of laser and absorption lineshapes - k Boltzmann constant - M _s incident shock Mach number - N noise, root-mean-square signal fluctuation - P static pressure - P ₁ initial pressure of test gas in shock tube - P _a free jet ambient pressure - P _s stagnation pressure - Q electronic quenching rate of excited state - S PLIF signal - t time between shock reflection and image acquisition - T static temperature - T _s stagnation temperature - _a mole fraction of absorbing species     

Grain inertia and fluid viscosity dominated granular flow rheology: a thermodynamic analysis

We analyze a combined theory of granular flow where both the particle density and the interstitial fluid viscosity play a role in the constitutive equations which describe the rheology of the particulate phase. Such a theory combines the more classical inertial-type theories of dry and aerated granular flow with the viscosity-dominated theory recently discussed by Jenkins and McTigue. We also develop a pseudo-thermodynamic theory valid for the general case, of which our recent pseudo-thermodynamic theory for the inertial case is seen to be an asymptotic limit. Finally, we discuss propagation of particulate phase pressure waves.     

Secondary flows and particle centrifugation in slightly tilted rotating pipes

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the cross-sectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the pipe. The solutions are used to derive analytical expressions for trajectories of solid or liquid particles entrained in the gas and being subject to centrifugation and the said secondary flows. It is shown that despite centrifugation, particles can be locked into circulatory trajectories thus remaining suspended in the gas flowing through the pipe.     

Macroscopic theory of orientation transitions in the extensional flow of side-chain nematic polymers

A macroscopic continuum mechanical model for incompressible side-chain nematic polymers, under isothermal conditions is given. The model is a synthesis of a transient network model and the standard nematorheological model. Simplifications in the model yield constitutive equations that are identical to well known Theological models for polymer melts and for low molar mass nematics. A detailed analysis of four possible composite orientation modes of polymer backbone and mesogenic side groups in uniaxial extensional flow is given. It is shown that the thermal sensitivity of the viscoelastic parameters leads to thermally-induced orientation transitions. The extension rate sensitivity of the competition between elastic and flow orienting effects leads to flow-induced orientation transition. The role of smectic A fluctuations in thermally-induced transitions during uniaxial extensional nematic flow is elucidated. The model is able to predict and explain the experimentally observed orientation modes and thermally-induced orientation transitions of a side-chain nematic polymer subjected to uniaxial extensional flow.     

A stream tube model for miscible flow

A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.Nomenclature A total cross-section area of the sample - C (resident) concentration of tracer - D,D ^* dispersion coefficient - F flux of tracer - G probability distribution function for permeability in the stream-tube segments - I tracer intensity (mass crossing a surface per unit time) - K permeability - L length of the medium - M number of stream tubes in the medium - N number of segments along a stream tube - P pressure - Q total flow rate in the sample - a length of an elementary stream-tube segment - g probability distribution function for permeability in the space - i, j indices, tube numbers - q flow rate in each stream tube - s variable cross-section area of a stream tube - t, t time - u front velocity - x space variable in the flow direction - small local variation in time - , _t longitudinal, transverse dispersivity - porosity of the porous medium - correlation length in the permeability field - viscosity of the fluid - time for filling an elementary stream tube segment - standard deviation of a stochastic variable - probability distribution of arrival times (Gaussian)