PHE’s are usually much more thermally efficient than their shell-and-tube counterparts, particularly for liquid/liquid duties. Film coefficients can be two to four times those for tubular units of the same duty, at the same or even lower pressure drops (Bond, 1981). At normal working ranges the overall heat transfer coefficient U can be expected to be 2300-5800 W/( m2 · K), depending on plate corrugation and flow conditions (Raju and Chand, 1980). The highest U value that could be achieved by a PHE was reported up to 8500 W/(m2 · K), making it capable of working with film coefficients three to five times higher than tubular or spiral-plate designs (Carlson, 1992). The augmented heat transfer performance of a PHE is due to several enhancement mechanisms, which directly result from the complex plate surface characteristics. These surface effects include disruption and reattachment of boundary layers, swirling motion of the fluids, continuous change in flow directions and velocity, combining to promote early transition to turbulence and produce exceptionally high film coefficients of heat transfer.
The analogy between heat and momentum transfer would indicate that as the heat transfer is improved there is a higher pressure drop penalty as well. In fact, it is widely noticed that increase of the friction factor is far quicker than that of the Nusselt number with increasing chevron angles. Thonon et al. (1995) reported that at the same Reynolds numbers, when compared with smooth channels the
enhancement of heat transfer is up to 6 times but at the same time the friction factor can be increased by a factor of one hundred. However, in practice for the same heat transfer area or at the same cooling/heating duties, pressure drops in a PHE are usually lower (Troupe et al., 1960), due to the fact that the flow velocities in a PHE unit are usually very low, and the flow channel length is always much shorter than that in tube-type exchangers.
Of all the dimensional parameters that describe a PHE channel, the chevron angle
βis probably the most important. Generally both heat transfer and pressure drop increase with higher chevron angles. Mixed plate channels are commonly evaluated with the averaged chevron angle (Bond, 1981, Heavner et al., 1993), though a rigorous examination of this treatment is not found in published works. The surface enlargement factor φ might have similar effects, as deeper corrugations increase the effective surface area as well as promote greater swirl and mixing, resulting in higher heat transfer rate and pressure drop. A comparison of experimental data from several sources by Mulley and Monglik (1999) has confirmed this. When the hydraulic diameter dh =2b/φ is used, the
effect of φ can be regarded as included in that of the hydraulic diameter; in other cases, this effect is usually ignored since an accurate quantitative evaluation of φ is difficult to obtain. Another parameter not usually attended to is the channel aspect ratio. While its effect on the exchanger thermal-hydraulic performance is apparent, this parameter has hardly become a consideration in any available correlations. High aspect ratio (a “narrow” channel) at the same heat transfer area will increase the flow velocity for given heat transfer area and thus increase pressure drops; low aspect ratio will bring problems of flow distribution inside individual channels and so will reduce the exchanger efficiency. It is also noticed that in the open literature geometrical parameters are rarely all given in detail. It is widely recognized in the research community that turbulence is attained in PHE’s at much lower Reynolds numbers than in circular tubes, however, the values of the critical Reynolds number, Recrit, are reported differently from
various sources from 10 to 500 (Raju and Chand, 1980, Carlson, 1992, Reppich, 1999, etc.). This may partially be due to the particular plate configurations tested. Cooper and Usher (1983) pointed out that it is difficult to predict the flow pattern in a particular PHE unit without testing it. However, it seems quite safe to conclude, from those reported values, that all types of PHE will be in the turbulent flow region at Re > 500, and in the laminar region at Re < 10. In most cases the transient region is in the Re range of 10-150. The early transition of flow patterns in PHE’s might be explained by two main reasons:
1. Corrugation features. Corrugations break down the stagnant insulating film at the plate surface and trigger turbulence (Raju and Chand, 1980). It is
obvious that a higher chevron angle and deeper corrugation will promote higher levels of disturbance and earlier transition.
2. Actual flow velocity. In the corrugated channel, the actual flow would most likely follow the corrugations rather than flow in the vertical direction (Focke et al, 1985). As a result, the actual flow velocity is much higher than the mean value in the vertical direction, which is used to calculate the Reynolds number.
PHE's could be treated as pure co-current or counter-current heat exchangers in principle if end effects are neglected. For a shell-and-tube exchanger this can hardly be the case, due to cross flows resulting from baffles. For a two-channel PHE, pure counter-current flow may be assumed; for multiple channel units, a correction factor of the LMTD (Log Mean Temperature Difference) is sometimes recommended. Buonopane et al. (1963) initially addressed the issue and reported that for lateral-corrugated plates, with packs in a 1 pass/ 1 pass counter-current arrangement, an average correction factor of 0.95 should be applied to the LMTD. Marriott (1971) later presented a chart for approximate values of the correction factor as functions of the Ntu (Number of transfer units) for various pass arrangements, which confirmed Buonopane et al’s correction factor value. Kandlikar and Shah (1989) also tabulated correction factor values based on a more refined numerical analysis. Usher (1970) pointed out that corrections are needed when the flow departs from the two-channel equal flow condition, to account for flow ratio, number of passes and end effects of passes, and these can only be determined empirically.
Pressure Drop Components
Pressure drop in a PHE consists of three contributions: (1) frictional pressure drop within the core (plate passages), (2) pressure drop due to elevation change, (3) pressure drop in inlet and outlet manifolds (ports). Of these, the frictional pressure drop is of main interest and has been addressed in various empirical correlations in the open literature. Elevation pressure drop is calculated in a straightforward way by P=ρgh. For the manifold pressure drop, an accurate evaluation method is not available. A very widely cited equation by Shah and Focke (1988) gives an estimation of the manifold pressure drop, without a reference, as: 2 manifolds pass inlet 1.5 2 G P N
ρ
∆ = ⋅ ⋅ (2.86)The manifold pressure drop is usually considered much smaller than the other components. Generally the manifold pressure drop is lower than 10% of the
overall pressure drop, but can be as high as 30% or higher in certain designs (Shah and Sekulic, 2003). Bond (1981) pointed out that different port designs, producing variation in manifold roughness, could result in the overall pressure drop to be two to three times higher than the passage pressure drop.