Male Heat exchanger topic Tubular heat exchanger A heat exchanger is a device used to transfer heat between two or more fluids. The change in power required from the first to the last stage is quite significant and it may not be reached in low-power loops. According to him, geysering is expected during subcooled boiling when the slug bubble detaches from the surface and enters the riser where the water is subcooledwhere bubble growth due to static-pressure decrease and condensation can take place. Thus, as the boiling boundary moves up the tube, the total pressure drop falls, potentially increasing the flow in an unstable innstability.

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DOI: These may be classified into static and dynamic instabilities [Lahey andPodowski ]. Examples of static instabilities include: flow excursion i. Similarly, dynamic instabilities include: density-wave oscillations, pressure drop oscillations, flow regime-induced instabilities and acoustic instabilities. Of these instability modes, the most important, and most widely studied, have been Ledinegg instabilities [Ledinegg ] and density-wave oscillations DWOs.

While the subsequent discussion will be focused on boiling systems, it should be noted that similar instabilities may also occur in condensing systems [Lahey and Podowski ]. A typical boiling loop includes a heated channel or channels , an unheated riser, a condenser, a downcomer in which a pump may be installed and a lower plenum.

Case 1 is for a positive displacement pump. Similarly, cases 3 and 4 represent the situation in which a centrifugal pump is used in the loop. We note that case 3 is unstable while case 4 is stable.

Excursive instability. While Ledinegg instability is known to be a problem in low pressure boiling systems, an increase of the system pressure, or an increase in the inlet orificing in the channel, can stabilize the system.

The quantification of density-wave oscillations requires an analysis of the mass, momentum and energy conservation equations of the boiling system. A detailed description of the analytical procedure has been given previously by Lahey and Podowski and will not be repeated here.

The essence of the analytical procedure is to determine first the neutral stability boundaries using a linear stability technique, then a nonlinear analysis is performed to identify bifurcation phenomena and to assess the dynamic response of the boiling system. In a linear stability analysis, the mass and energy conservation equations may be integrated in the axial direction either analytically [Lahey and Moody ] or using nodal techniques [Taleyarkhan et al.

The results of this analysis are then combined with the integrated and linearized momentum equation to satisfy the pressure drop boundary condition impressed on the boiling channel s or loop.

If we have any complex roots s having positive real parts the system is unstable. In a nuclear reactor there are also feedback loops associated with temperature- and void-reactivity feedback. This latter transfer function may be denoted, T s. As should be expected, the stability of a nuclear-coupled system is in general different from that given by Equation 6. As before, the stability of a BWR can be determined by solving for the roots, s, of Equation 8.

Finally, it should be noted that time domain evaluations may be performed with the nonlinear conservation equations leading to Hopf bifurcations e. There are many other things that could be said about two-phase instabilities. Indeed there is a voluminous literature on this subject [Lahey and Drew ]. Nonetheless, this introduction has given the essence of two-phase instability analysis and presented some of the key references so that the interested readers may develop a more indepth understanding.

Lahey, R. Ledinegg, M. Taleyarkhan, R. Heat Transfer, Weaver, L. References Garea, V.


Ledinegg instability



Two-Phase Instabilities


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