R.Žitný, J.ThýnR.Žitný, J.ThýnDepartment of Process EngineeringDepartment of Process Engineering

CTU in Prague, Faculty of Mechanical CTU in Prague, Faculty of Mechanical EngineeringEngineering

E-mail: E-mail: zitny@fsid.cvut.czzitny@fsid.cvut.cz

Acknowledgement: Research is subsidized by Acknowledgement: Research is subsidized by

J04/98: 212200008J04/98: 212200008

CONCLUSIONS:•Asymmetry and instability of parallel flows can be explained by natural convection.

•Stability of flow can be improved by increasing friction losses, e.g. by narrowing lateral channels.

•Model and experiments predict that the cross-flow is suppressed (or even reversed) at non-isothermal flow.

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1. INTRODUCTION:Parallel flows are typical for many apparatuses e.g. shell&tube or plate heat exchangers, heaters, reactors. Sometimes instabilities or non-uniform distribution of flow in parallel channels occur if the apparatus operates at non-isothermal conditions. Parallel flow instabilities have been observed also in lateral channels of direct ohmic heater.

2. DIRECT OHMIC HEATER:Volumetric heat source enables in principle more uniform heating, important e.g. for food processing (sterilization). Problems are with overheating at walls, e.g. at the surface of electrodes which must be cooled. The current design makes use processed liquid flowing in lateral channels for the electrodes cooling. Electrodes of heater are perforated - cross flow from lateral channels should improve uniformity of temperatures in central channel and uniformity of residence times. This design is suitable for very viscous liquids (sauces, juices,....), i.e. for creeping flow (Re<<1) when natural convection can be neglected.

3. PROBLEMS - BUOYANCYThere are problems with heating of low viscous liquids (e.g. water, milk), associated with influence of buoyancy and natural convection.

• ASYMMETRY of parallel flows in lateral channels. If one of parallel flows slows down its temperature increases, and liquid in this channel becomes lighter. This creates driving force (pressure difference) promoting circulation from “fast“ channels to the “slow“ channel thus increasing initial small disturbance. One parallel stream is delayed or even stopped if the temperature increase is too high. • CROSS-FLOW suppression. Warmer liquid in the central channel is lighter than liquid in lateral channels and corresponding pressure profile forces liquid to flow through perforation in opposite direction (out of the heating zone).

4. MATHEMATICAL DESCRIPTIONTheoretical analysis which does not take into account cross-flow through perforation predicts two solutions of temperature and flow-fields:

Symmetric solution (flow-rates and temperatures in lateral channels are equal) Asymmetric solution exists within a certain range of flow-rates and heating power.

Asymmetric solution can be interpreted as a magnitude of disturbance causing instability of flow. Mathematical model identifies parameters having significant influence upon the stability limits, e.g. width of lateral channels.

More details can be found inhttp://www.fsid.cvut.cz/en/u218/peoples/zitny/imagohm/instabil/instabil.doc

5. CONTROL VOLUME MODELCross-flow through perforation has been respected in a simple integral model, based upon

•Mass balances•Heat transfer•Momentum•Tracer balances

of control volumes characterised by:•parabolic velocity profile (experimentally evaluated umax/umean=1.73 at 30 ml/s, theory 1.744)

•linear increase of temperature•residence times - serie of mixers

Responses to tracer injection will be compared with experiments.

6. EXPERIMENTSStimulus - response technique (injection of a tracer and measurement responses) has proved to be useful for detection of cross-flow. As tracers KCl (conductivity method), KMnO4 (visualisation), Tc99 (radioisotope) were used. Asymmetries of flow are better observed by thermometers arranged along the lateral channels..

H

L

Warm liquid (Te) stands in the right channel ifp1-p0=0gL[1-(Te-T0)]

T0,p0,Q

Narrow channel (H=8mm) without heating. Very large cross flow.

Wide channel (H=18mm) without heating

Wide channel (H=18mm) 5kW-cross flow suppressed

Narrow channel (H=8mm) 5kW. Cross-flow suppressed.

h

Flow-rate 32 ml/s, H=8 mm, full electrode

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Q [kW]

T [

C]

R1(left up)

R2 (right up)

R3 (left middle)

R4 (right middle)

T3 (left electrode)

T4 (right electrode)