Aleksander Grah

Stability limits of unsteady open capillary channel flow

This paper is concerned with steady and unsteady flow rate limitations in open capillary channels under low-gravity conditions. Capillary channels are widely used in Space technology for liquid transportation and positioning, e.g. in fuel tanks and life support systems. The channel observed in this work consists of two parallel plates bounded by free liquid surfaces along the open sides. The capillary forces of the free surfaces prevent leaking of the liquid and gas ingestion into the flow. In the case of steady stable flow the capillary pressure balances the differential pressure between the liquid and the surrounding constant-pressure gas phase. Increasing the flow rate in small steps causes a decrease of the liquid pressure. A maximum steady flow rate is achieved when the flow rate exceeds a certain limit leading to a collapse of the free surfaces due to the choking effect. In the case of unsteady flow additional dynamic effects take place due to flow rate transition and liquid acceleration. The maximum flow rate is smaller than in the case of steady flow. On the other hand, the choking effect does not necessarily cause surface collapse and stable temporarily choked flow is possible under certain circumstances. To determine the limiting volumetric flow rate and stable flow dynamic properties, a new stability theory for both steady and unsteady flow is introduced. Subcritical and supercritical (choked) flow regimes are defined. Stability criteria are formulated for each flow type. The steady (subcritical) criterion corresponds to the speed index defined by the limiting longitudinal small-amplitude wave speed, similar to the Mach number. The unsteady (supercritical) criterion for choked flow is defined by a new characteristic number, the dynamic index. It is based on pressure balances and reaches unity at the stability limit. The unsteady model based on the Bernoulli equation and the mass balance equation is solved numerically for perfectly wetting incompressible liquids. The unsteady model and the stability theory are verified by comparison to results of a sounding rocket experiment (TEXUS 41) on capillary channel flows launched in December 2005 from ESRANGE in north Sweden. For a clear overview of subcritical, supercritical, and unstable flow, parametric studies and stability diagrams are shown and compared to experimental observations.

Convective dominated flows in open capillary channels

This paper is concerned with convective dominated liquid flows in open capillary channels. The channels consist of two parallel plates bounded by free liquid surfaces along the open sides. In the case of steady flow the capillary pressure of the free surface balances the differential pressure between the liquid and the surrounding constant pressure gas phase. A maximum flow rate is achieved when the adjusted volumetric flow rate exceeds a certain limit leading to a collapse of the free surfaces. The convective dominated flow regime is a special case of open capillary flow, since the viscous forces are negligibly small compared with the convective forces. Flows of this type are of peculiar interest since the free surfaces possess a quasisymmetry in the flow direction. This quasisymmetry enables the application of a new effective method for evaluation of the flow limit. The flow limit is caused by a choking effect. This effect is indicated by the speed index, S, which is defined by the ratio of the flow vel...

Dynamic stability analysis for capillary channel flow: One-dimensional and three-dimensional computations and the equivalent steady state technique

Spacecraft technology provides a series of applications for capillary channel flow. It can serve as a reliable means for positioning and transport of liquids under low gravity conditions. Basically, capillary channels provide liquid paths with one or more free surfaces. A problem may be flow instabilities leading to a collapse of the liquid surfaces. A result is undesired gas ingestion and a two phase flow which can in consequence cause several technical problems. The presented capillary channel consists of parallel plates with two free liquid surfaces. The flow rate is established by a pump at the channel outlet, creating a lower pressure within the channel. Owing to the pressure difference between the liquid phase and the ambient gas phase the free surfaces bend inwards and remain stable as long as they are able to resist the steady and unsteady pressure effects. For the numerical prediction of the flow stability two very different models are used. The one-dimensional unsteady model is mainly based on the Bernoulli equation, the continuity equation, and the Gauss–Laplace equation. For three-dimensional evaluations an open source computational fluid dynamics (CFD) tool is applied. For verifications the numerical results are compared with quasisteady and unsteady data of a sounding rocket experiment. Contrary to previous experiments this one results in a significantly longer observation sequence. Furthermore, the critical point of the steady flow instability could be approached by a quasisteady technique. As in previous experiments the comparison to the numerical model evaluation shows a very good agreement for the movement of the liquid surfaces and for the predicted flow instability. The theoretical prediction of the flow instability is related to the speed index, based on characteristic velocities of the capillary channel flow. Stable flow regimes are defined by stability criteria for steady and unsteady flow. The one-dimensional computation of the speed index is based on the technique of the equivalent steady system, which is published for the first time in the present paper. This approach assumes that for every unsteady state an equivalent steady state with a special boundary condition can be formulated. The equivalent steady state technique enables a reformulation of the equation system and an efficient and reliable speed index computation. Furthermore, the existence of the numerical singularity at the critical point of the steady flow instability, postulated in previous publication, is demonstrated in detail. The numerical singularity is related to the stability criterion for steady flow and represents the numerical consequence of the liquid surface collapse. The evaluation and generation of the pressure diagram is demonstrated in detail with a series of numerical dynamic flow studies. The stability diagram, based on one-dimensional computation, gives a detailed overview of the stable and instable flow regimes. This prediction is in good agreement with the experimentally observed critical flow conditions and results of three-dimensional CFD computations.Spacecraft technology provides a series of applications for capillary channel flow. It can serve as a reliable means for positioning and transport of liquids under low gravity conditions. Basically, capillary channels provide liquid paths with one or more free surfaces. A problem may be flow instabilities leading to a collapse of the liquid surfaces. A result is undesired gas ingestion and a two phase flow which can in consequence cause several technical problems. The presented capillary channel consists of parallel plates with two free liquid surfaces. The flow rate is established by a pump at the channel outlet, creating a lower pressure within the channel. Owing to the pressure difference between the liquid phase and the ambient gas phase the free surfaces bend inwards and remain stable as long as they are able to resist the steady and unsteady pressure effects. For the numerical prediction of the flow stability two very different models are used. The one-dimensional unsteady model is mainly based on t...

Free surfaces in open capillary channels—Parallel plates

This paper is concerned with forced flow through partially open capillary channels under microgravity conditions. The investigated channel consists of two parallel plates and is bounded by free liquid surfaces along the open sides. The curvature of the channel’s gas-liquid interface, which is exposed to the ambient pressure, adjusts to the pressure difference across the interface in accordance with the Young-Laplace equation. Flow within the channel becomes unstable when the free surface collapses and gas ingestion into the flow path occurs—a process that is also referred to as the “choking” phenomenon. During stable flow, the behavior of the free surface is influenced by flow conditions, geometric properties of the channel, and the pre-defined system pressure. In this work, a previously published stability theory is verified for a wide range of model parameters. A detailed study is provided for stable flow in capillary channels, including static and dynamic solutions. The results of the Capillary Channel Flow (CCF) experiment are evaluated and are found to agree well with numerical predictions. A clear limit is determined between stable and unstable flows. It is shown that the model can predict the shape of the free surface under various flow conditions. A numerical tool is employed to exploit the mathematical model, and the general behavior of free surfaces in said capillary channels is studied. Studies are conducted in both viscous and convective flow regimes and in the transition area between the two. The validity of the model is confirmed for a wide range of geometrical configurations and parameters.