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Fluid System Stability Analysis Techniques

Fluid systems, or networks, consist of multiple components that work together to achieve some desired thermofluid state. For any generic application, this fluid state can be a combination of the fluid pressure, flow rate, enthalpy, or species concentration. Fluid system components, such as pumps and valves, are often governed by nonlinear differential equations, resulting in complex component-to-component interactions. System-level fluid network stability occurs when the flow through the system can maintain a steady-state solution in the presence of small perturbations, which depends on these component interactions. System instability, however, can go undetected until issues arise during integrated system testing. This presentation explores a method for system designers to think of the fluid network as an assembly of components, each with their own thermofluid surfaces of partial stability, called nullclines. The intersections of all nullclines yields system-level solutions, called equilibrium points. When designers define operating points, they are tuning system parameters so that these equilibrium points move to the desired location in the thermofluid state plane. However, linearization theory shows us that the dynamic behavior around these points can be unstable. The local stability of these equilibrium points can be assessed analytically with eigen-analysis, or numerically by propagating state-plane samples to construct a phase portrait. Investigating a phase portrait can help designers gain a qualitative understanding of a system’s dynamic performance. This understanding can then help inform requirement definitions, component selection, and operational procedures. This presentation includes an example of the phase portrait technique on a system featuring a centrifugal pump and a back-pressure regulator (BPR). Numerical modeling of this system suggests that equilibrium points on the left-hand side of the pump curve are dynamically unstable.

Fluid System↗

NASA NTRS2004

Injection Induced Mixing in Flows Separating From Smooth Surfaces

An analytic model for predicting the effect of unsteady local surface injection on the flow separating from a streamlined body at angle of attack is proposed. The model uses the premise that separation control results from enhanced mixing along the shear layer that develops between the main stream and the fluid in the underlying recirculation zone. High-Reynolds-number asymptotic methods are used to connect the unsteady surface injection to an instability wave propagating on the separating shear layer and then to the large-scale coherent structures that produce the increased mixing. The results is a tool that can guide the choice of fluid-actuator parameters to maximize flow-control effectiveness and may also facilitate computer-based numerical experiments.

Adamczyk, John J.↗

NASA NTRS1986

Experiments on annular liquid jet instability and on the formation of liquid shells

An annular jet flow of liquid surrounding a flow of gas at its core is extremely unstable. Experiments are described in which such a flow is generated by an annular nozzle operated at fairly specific conditions. It is shown that periodic, axisymmetric oscillations arise spontaneously within the cylindrical sheet emerging from the nozzle and grow with such rapidity along the axial dimension that a sealing-off and encapsulation of the core gas occurs within a few jet diameters. This is closely followed by a pinchoff of the liquid between adjacent bubbles. The liquid shells set free thereby assume spherically symmetric form under capillary forces, and each contains a precisely uniform measure of gas and of liquid on account of the extremely high frequency-stability of the process. Description is given of the fluid dynamic processes by which the shells are formed, and mention is made of exploiting the instability for the production of rigid shells for technological applications.

Kendall, J. M.↗

NASA NTRS1973

Ion streaming instabilities with application to collisionless shock wave structure

The electromagnetic dispersion relation for two counterstreaming ion beams of arbitrary relative strength flowing parallel to a dc magnetic field is derived. The beams flow through a stationary electron background and the dispersion relation in the fluid approximation is unaffected by the electron thermal pressure. The dispersion relation is solved with a zero net current condition applied and the regions of instability in the k-U space (U is the relative velocity between the two ion beams) are presented. The parameters are then chosen to be applicable for parallel shocks. It was found that unstable waves with zero group velocity in the shock frame can exist near the leading edge of the shock for upstream Alfven Mach numbers greater than 5.5. It is suggested that this mechanism could generate sufficient turbulence within the shock layer to scatter the incoming ions and create the required dissipation for intermediate strength shocks.

Golden, K. I.↗

NASA NTRS2009

Modeling Unsteady Cavitation and Dynamic Loads in Turbopumps

A computational fluid dynamics (CFD) model that includes representations of effects of unsteady cavitation and associated dynamic loads has been developed to increase the accuracy of simulations of the performances of turbopumps. Although the model was originally intended to serve as a means of analyzing preliminary designs of turbopumps that supply cryogenic propellant liquids to rocket engines, the model could also be applied to turbopumping of other liquids: this can be considered to have been already demonstrated, in that the validation of the model was performed by comparing results of simulations performed by use of the model with results of sub-scale experiments in water. The need for this or a similar model arises as follows: Cavitation instabilities in a turbopump are generated as inlet pressure drops and vapor cavities grow on inducer blades, eventually becoming unsteady. The unsteady vapor cavities lead to rotation cavitation, in which the cavities detach from the blades and become part of a fluid mass that rotates relative to the inducer, thereby generating a fluctuating load. Other instabilities (e.g., surge instabilities) can couple with cavitation instabilities, thereby compounding the deleterious effects of unsteadiness on other components of the fluid-handling system of which the turbopump is a part and thereby, further, adversely affecting the mechanical integrity and safety of the system. Therefore, an ability to predict cavitation- instability-induced dynamic pressure loads on the blades, the shaft, and other pump parts would be valuable in helping to quantify safe margins of inducer operation and in contributing to understanding of design compromises. Prior CFD models do not afford this ability. Heretofore, the primary parameter used in quantifying cavitation performance of a turbopump inducer has been the critical suction specific speed at which head breakdown occurs. This parameter is a mean quantity calculated on the basis of assumed steady-state operation of the inducer; it does not account for dynamic pressure loads associated with unsteady flow caused by instabilities. Because cavitation instabilities occur well before mean breakdown in inducers, engineers have, until now, found it necessary to use conservative factors of safety when analyzing the results of numerical simulations of flows in turbopumps.

Hosangadi, Ashvin↗

NASA NTRS1992

On the role of secondary instabilities in laminar-turbulent transition of 2D and 3D boundary layers

The accurate prediction of laminar/turbulent transition is one of the fundamental problems in engineering fluid mechanics. There is almost unanimous consent that such a transition criterion should come from stability theory. Linear primary stability theory describes the initial stage of transition, but falls short of predicting transition. Only in conjunction with empirical correlations, the widely used e(sup n) method is obtained, which, however, lacks a solid physical base. Three-dimensional secondary instabilities are known to play an important role in the transition process. However, no use has been made so far of secondary instabilities, instability interactions or wave resonances to define a 'transition location'. The paper summarizes new attempts to identify certain interaction and resonance phenomena within the laminar-turbulent transition regime in two and three-dimensional boundary layers which are associated with rapid structural and temporal changes of fluctuations beyond their exponential growths.

Dallman, Uwe↗

NASA NTRS2007

Reverse-Tangent Injection in a Centrifugal Compressor

Injection of working fluid into a centrifugal compressor in the reverse tangent direction has been invented as a way of preventing flow instabilities (stall and surge) or restoring stability when stall or surge has already commenced. The invention applies, in particular, to a centrifugal compressor, the diffuser of which contains vanes that divide the flow into channels oriented partly radially and partly tangentially. In reverse-tangent injection, a stream or jet of the working fluid (the fluid that is compressed) is injected into the vaneless annular region between the blades of the impeller and the vanes of the diffuser. As used here, "reverse" signifies that the injected flow opposes (and thereby reduces) the tangential component of the velocity of the impeller discharge. At the same time, the injected jet acts to increase the radial component of the velocity of the impeller discharge.

Skoch, Gary J.↗

NASA NTRS1984

Alternative experiments using the geophysical fluid flow cell

This study addresses the possibility of doing large scale dynamics experiments using the Geophysical Fluid Flow Cell. In particular, cases where the forcing generates a statically stable stratification almost everywhere in the spherical shell are evaluated. This situation is typical of the Earth's atmosphere and oceans. By calculating the strongest meridional circulation expected in the spacelab experiments, and testing its stability using quasi-geostrophic stability theory, it is shown that strongly nonlinear baroclinic waves on a zonally symmetric modified thermal wind will not occur. The Geophysical Fluid Flow Cell does not have a deep enough fluid layer to permit useful studies of large scale planetary wave processes arising from instability. It is argued, however, that by introducing suitable meridional barriers, a significant contribution to the understanding of the oceanic thermocline problem could be made.

Hart, J. E.↗

NASA NTRS1987

Centrifugal inertia effects in two-phase face seal films

A simplified, semianalytical model has been developed to analyze the effect of centrifugal inertia in two-phase face seals. The model is based on the assumption of isothermal flow through the seal, but at an elevated temperature, and takes into account heat transfer and boiling. Using this model, seal performance curves are obtained with water as the working fluid. It is shown that the centrifugal inertia of the fluid reduces the load-carrying capacity dramatically at high speeds and that operational instability exists under certain conditions. While an all-liquid seal may be starved at speeds higher than a 'critical' value, leakage always occurs under boiling conditions.

Basu, P.↗

NASA NTRS1989

Excitation of linearly stable waves in a multispecies plasma

Excitation of electrostatic modes as a result of the injection of an argon beam into a multispecies plasma is investigated. It is shown that the injection of a warm artificial beam into a thermal plasma may excite waves of significant amplitude with a range of phase velocities which are linearly stable. These waves appear as a result of the correlation between motions of an individual particle in a Vlasov fluid. When the free energy is derived from a warm beam and the linear instability diminishes due to the large temperature of the beam, the competing mechanism of thermal fluctuations is responsible for the main excitation of waves. This mechanism is valid for the various modes in a multispecies plasma, with a higher enhancement at the lower-hybrid than at the ion-ion-hybrid modes.

Roth, Ilan↗

NASA NTRS1989

Laboratory and theoretical models of planetary-scale instabilities and waves

The continuous low-g environment of the orbiting space shuttle provided a setting for conducting geophysical fluid model experiments with a completely consistent representation of sphericity and the resultant radial gravity found on astrogeophysical objects. This is possible because in zero gravity an experiment can be constructed that has its own radial buoyancy forces. The dielectric forces in a liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is applied. The Geophysical Fluid Flow Cell (GFFC) experiment is an implementation of this idea in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large ac voltage. The GFFC flew on Spacelab 3 in May 1985. Data in the form of global Schlieren images of convective patterns were obtained for a large variety of configurations. These included situations of rapid rotation (large Taylor numbers), low rotation, large and small thermal forcing, and situations with applied meridional temperature gradients. The analysis and interpretation of the GFFC-85 data are being conducted. Improvements were developed to the GFFC instrument that will allow for real-time (TV) display of convection data and for near-real-time interactive experiments. These experiments, on the transition to global turbulence, the breakdown of rapidly rotating convective planforms and other phenomena, are scheduled to be carried out on the International Microgravity Laboratory (IML-1) aboard the shuttle in June 1990.

Hart, John E.↗

NASA NTRS1992

Study Of Disturbances In Rotating Plane Poisseuille Flow

Report describes computer-simulation of instability and transition to turbulence in plane Poisseuille flow in rotating channel. Motions of fluid governed by Navier-Stokes equations of incompressible flow, using periodic boundary conditions in streamwise and spanwise directions. Principal parameters affecting flow are Reynolds and rotation numbers.

Kim, John↗

NASA NTRS1923

The decay of a simple eddy

The principal result obtained in this report is a generalization of Taylor's formula for a simple eddy. The discussion of the properties of the eddy indicates that there is a slight analogy between the theory of eddies in a viscous fluid and the quantum theory of radiation. Another exact solution of the equations of motion of viscous fluid yields a result which reminds one of the well-known condition for instability in the case of a horizontally stratified atmosphere.

Bateman, H↗

NASA NTRS1997

Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Quenching

For about a half century, the stabilization of a steady planar deflagration on a heat-sink-type flat-flame burner has been of extraordinary service for the theoretical modeling and diagnostic probing of combusting gaseous mixtures. However, most engineering devices and most unwanted fire involve the burning of initially unmixed reactants. The most vigorous burning of initially separated gaseous fuel and oxidizer is the diffusion flame. In this useful idealization (limiting case), the reactants are converted to product at a mathematically thin interface, so no interpenetration of fuel and oxidizer occurs. This limit is of practical importance because it often characterizes the condition of optimal performance (and sometimes environmentally objectionable operation) of a combustor. A steady planar diffusion flame is most closely approached in the laboratory in the counterflow apparatus. The utility of this simple-strain-rate flow for the modeling and probing of diffusion flames was noted by Pandya and Weinberg 35 years ago, though only in the last decade or so has its use become internationally common place. However, typically, as the strain rate a is reduced below about 20 cm(exp -1), and the diffusion-flame limit (reaction rate much faster than the flow rate) is approached, the burning is observed to become unstable in earth gravity. The advantageous steady planar flow is not available in the diffusion-flame limit in earth gravity. This is unfortunate because the typical spatial scale in a counterflow is (k/a)(sup 1/2), where k denotes a characteristic diffusion coefficient; thus, the length scale becomes large, and the reacting flow is particularly amenable to diagnostic probing, as the diffusion-flame limit is approached. The disruption of planar symmetry is owing the fact that, as the strain rate a decreases, the residence time (l/a) of the throughput in the counterflow burner increases. Observationally, when the residence time exceeds about 50 msec, the inevitably present convective (Rayleigh-Benard) instabilities, associated with hot-under-cold (flame-under-fresh-reactant) stratification of fluid in a gravitational field, have time to grow to finite amplitude during transit of the burner.

Fendell, Francis↗

NASA NTRS1993

A review of design concepts for the Advanced Fluids Module (AFM) project

This paper reviews preliminary fluid module design concepts for the Advanced Fluids Module (AFM) project. The objective of this effort is to provide a facility that can handle a wide variety of fluids experiments. Sample science requirements were written and conceptual designs were subsequently generated during the last year. Experiments from the following fluid physics subject areas were used as conceptual design drivers: static and dynamic interfacial phenomena; bubble/droplet thermocapillary migration; surface tension convection and instabilities; thermal/solutal convection; pool boiling; and multiphase flow. After the conceptual designs were completed, the next phase attempted to combine experiments capabilities into a multipurpose, multiuser apparatus configured for the Space Station Freedom. It was found that all the fluid subject areas considered could be accommodated by three basic types of fluids modules. These modules are the Static Fluid Cell Module, the Dynamic Fluid Cell Module, and the Multiphase Flow Module. Descriptions of these preliminary modules designs and their particular sub-systems (e.g., fluid and thermal systems) are discussed. These designs will be refined as the nature of the flight program becomes clearer over the next six to twelve months.

Hill, Myron E.↗

NASA NTRS1975

Liquid neon heat transfer as applied to a 30 tesla cryomagnet

A 30-tesla magnet design is studied which calls for forced convection liquid neon heat transfer in small coolant channels. The design also requires suppressing boiling by subjecting the fluid to high pressures through use of magnet coils enclosed in a pressure vessel which is maintained at the critical pressure of liquid neon. This high pressure reduces the possibility of the system flow instabilities which may occur at low pressures. The forced convection heat transfer data presented were obtained by using a blowdown technique to force the fluid to flow vertically through a resistance heated, instrumented tube.

Papell, S. S.↗

NASA NTRS1992

Granular instability in fluidized beds: A small-over-large instability

For different particle diameters arranged in a gas fluidized bed, a new gravitational instability is predicted. The first order stability analysis yields conditions for growth of the most unstable wavenumber both as a function of particle diameter and dimensionless Bond number. Gravity acts to distribute the greater fluid mass associated with smaller particles, while surface tension stabilizes the entire bed against accelerations. The phenomenon, called the 'Small-over-Large' (SL) instability, evolves somewhat akin to a Rayleigh-Taylor mechanism and in addition to fundamental interest, carries implications for predicting solute redistribution and gravitational alignments in particle beds and chemical separation columns.

Noever, David A.↗

NASA NTRS2000

The Effect of a Rotating Magnetic Field on Flow Stability During Crystal Growth

The effect of a rotating magnetic field on the stability of flow in crystal growth configurations has been experimentally modeled using liquid gallium contained in a finite cylinder and heated from below. Several distinct flow regions were determined as a function of the Rayleigh and Hartmann numbers. At low values of the Rayleigh and Hartmann numbers, a region of stationary flow exists. As the rotating magnetic field is increased, the critical Rayleigh number bounding the stationary flow region can increase by a factor of 10. However, the rotating magnetic field itself induces an instability at a critical value of the Hartmann number independent of the Rayleigh number. In the stationary flow region, the rotating magnetic field can induce fluid motion with velocities several orders of magnitude larger than typical semiconductor crystal growth velocities. Thus, a rotating magnetic field can be used to achieve the benefits of forced convection without triggering deleterious instabilities.

Volz, Martin P.↗