Uwe Rosendahl

Choked flows in open capillary channels: theory, experiment and computations

This paper is concerned with flow-rate limitations in open capillary channels under low-gravity conditions. 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. In this study the steady one-dimensional momentum equation is solved numerically for perfectly wetting incompressible liquids to determine important characteristics of the flow, such as the free-surface shape and limiting volumetric flow rate. Using the ratio of the mean liquid velocity and the longitudinal small-amplitude wave speed a local capillary speed index

Stability limits of unsteady open capillary channel flow

S_{ca}

Investigation of forced liquid flows in open capillary channels

is introduced. A reformulation of the momentum equation in terms of this speed index illustrates that the volumetric flow rate is limited. The maximum flow rate is reached if

Convective dominated flows in open capillary channels

S_{ca}\,{=}\,1

Flow Rate Limitation in Open Capillary Channel Flows

locally, a phenomenon called choking in compressible flows. Experiments with perfectly wetting liquids in the low-gravity environment of a drop tower and aboard a sounding rocket are presented where the flow rate is increased in a quasi-steady manner up to the maximum value. The experimental results are in very good agreement with the numerical predictions. Furthermore, the influence of the

CRITICAL VELOCITY IN OPEN CAPILLARY CHANNEL FLOWS

S_{ca}

Experimental investigation on flow rate limitations in open capillary vanes

on the flow-rate limit is confirmed.

Design and performance of an experiment for the investigation of open capillary channel flows

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.

Cryo-Laboratories for Test and Development of Propellant Storage and Management Technologies

We investigate a forced flow through an open capillary channel consisting of two parallel plates under microgravity condition. The aim of the experiments is to determine the maximal volume flux that can be withdrawn from the channel. The theoretical approach with a one-dimensional Bernoulli equation leads to a non-linear ordinary differential equation for the radius of curvature along the free surface of the channel. Both laminar and entrance pressure losses are taken into account as well as the flow conditions before the inlet of the channel. Several experiments with different channels and fluid properties were performed in the Bremen drop tower. The theory shows good agreement with the experimental data for a wide range of the non-dimensional parameters Ohnesorge number, gap ratio and channel length. The knowledge of the maximum volume flux is necessary to prevent gas ingestion at the channel outlet which is un-desired for applications in surface tension tanks.

Investigation of Flow Rate Limitation in Open Capillary Channel

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...