# Characterization and prediction of swirl-induced enhanced heat transfer in sinusoidal-corrugated plates.

INTRODUCTIONHeat exchangers are employed in a number of industrial thermal systems. Their vast range of applications makes it imperative to devise means to increase the heat transfer performance. This study is concerned with plate heat exchangers (PHEs) and their design, which find usage in such diverse areas as food processing, pharmaceutical, chemical industries, and heating, ventilating and air conditioning (HVAC). One mechanism for enhancing their heat transfer performance is to produce swirl or vortical flow by perturbing the axial flow laterally so as to disturb the boundary layer and replace the near-wall fluid by that in the core of the flow. This generates greater mixing and higher temperature gradients at the wall leading to an enhancement in heat transport. One way to alter the flow and generate vortices is to use corrugated plates, as is the case in plate heat exchangers (PHEs) (Wang et al. 2007). PHEs can not only provide a compact enhanced heat exchanger, but also have the flexibility of operation where additional surface area can be simply increased by adding more plates. In fact, conventional heat exchangers are being substituted by corrugated-plate heat exchangers not only for their high thermal effectiveness but also due to the small approach temperature operation that they provide (Muley et al. 1999; Shah and Focke 1988; Wang et al. 2007).

The most commonly used plate pattern in a PHE is the chevron plate (Wang et al. 2007; Shah and Focke 1988; Ektesabi et al. 1987). A typical chevron-plate with sinusoidal corrugations is shown in Figure 1. The surface geometry is characterized by the corrugation inclination angle [beta], the wavelength [lambda], and the plate spacing 2a. The surface patterns not only govern the increase in effective heat transfer surface area, but also lead to the interruption of the boundary layer development in the inter-plate channels, and induce swirl in the flow as it passes through the cross-corrugated path. A number of arrangements of cross-corrugated channels can be obtained by altering the corrugated inclination angle within the range of 0[degrees]< [beta] < 90[degrees]. An inclination angle of 0[degrees] corresponds to a duct bounded by two out-of phase-sinusoidal-plates, and an angle of 90[degrees] yields a duct bounded by two in-phase sinusoidal corrugated parallel wavy-plates. The latter flow configuration is the one under consideration in the current study. The peaks and troughs of this duct are in the same vertical plane as can be seen in Figure 1. The spacing between the two plates is 2a and the corrugation wavelength is 2X (see third sketch in Figure 1b). The geometry considered is modeled as a two-dimensional wavy-parallel-plate channel as the plate spacing is much smaller than the width of the plate. The corrugation aspect ratio [gamma] (= 4a/2[lambda]) describes the waviness of the profile, and a flat parallel-plate channel is obtained when the corrugation aspect ratio is zero.

[FIGURE 1 OMITTED]

A number of studies have focused on the flow behavior and heat and mass transport in corrugated plate channels with different geometries (Focke et al. 1985; Metwally and Manglik 2004; Muley and Manglik 1997; Muley and Manglik 2000; Wang et al. 2007; Zhang et al. 2004; Zimmer et al. 2002). Some studies (Asako et al. 1988; Gschwind et al. 1995; Nishimura et al. 1986; Rush et al. 1999) while considering in-phase corrugated plates, as shown in Figure 1b, have however used a large plate separation (>2a). Their prediction of early transition to turbulence at Re < 1000 can be attributed to this feature (Nishimura et al. 1990; Rush et al. 1999) where otherwise laminar flow can prevail for higher Re (Wang et al. 2007). The waviness is found to induce swirling at larger Reynolds numbers in the flow, which consequently boosts heat and mass transfer significantly. Here it should be noted that formation of swirl structures in the flow does not necessarily indicate an unsteadiness and a turbulent regime (Metwally and Manglik 2004; Muley and Manglik 2000). Several experimental investigations (Bereiziat et al. 1995; Focke et al. 1985; Gschwind et al. 1995; Muley et al. 1999; Zimmer et al. 2002) have shown that the flow in PHE channels with plate separation of 2a, as well as in other cross corrugated geometries, remains laminar at Re ~ 1000. Introduction of swirl makes the flow three dimensional in character, which promotes better mixing and hence enhanced convection.

Metwally and Manglik (2004) have studied the effect of Prandtl number as well as different geometric parameters in periodically fully developed flow and heat transfer in corrugated channels with constant wall temperature. They find that the swirling of the flow elevates heat transfer in the channels, and two distinct regions can be identified in the friction factor and Nusselt number plots, namely, a no-swirl and a swirl region. The current work concentrates on understanding the scaling that influences the creation of these two distinct regions, and the development of predictive correlations for both friction factors and Nusselt numbers.

SCALING ANALYSIS AND RESULTS

Sinusoidal plate-surface corrugations alter the flow pattern and enhance heat-transfer in the channels of a PHE in two ways. For a given length of heat exchanger, the corrugations provide a longer effective flow path for heat-transfer. The available heat-transfer area increases with the corrugation aspect ratio and, as shown by Muley et al. (1999), is accompanied by an increase in both the isothermal friction factor and the Nusselt number. This is the dominant enhancement feature for momentum and heat transfer at lower flow velocities. However, for flow conditions often experienced in most applications, it is the generation of swirl which accounts for a major portion of the enhancement observed in such corrugated channels. The sinusoidal corrugations help in imparting an accelerating effect to the flow at the peaks, aiding in momentum and energy transport. Also, with an increasing severity in the surface waviness, secondary fluid circulation, or swirl is generated at the trough sections. The intensity of the swirl increases with an increase in y and Re, thus contributing to larger velocity and temperature gradients. The convective heat transfer is further influenced by a third parameter, the Prandtl number; fluids having a larger Prandtl number exhibit greater heat transfer. While a general critical Reynolds number cannot characterize the transition between the two regimes, it is possible, as will be shown, for a single suitably scaled Reynolds number to provide a reasonable approximation of the transition region. The results obtained by Metwally and Manglik (2004), which illustrate the enhanced performance and demarcation of the two flow regimes are graphed in Figures 2 and 3. These results are used as a basis for the current investigation, where the enhanced behavior is scaled to devise correlations.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The momentum and heat transfer in the swirl flow region is influenced by the secondary recirculation or swirl flows that are generated in the troughs of the wavy channel. The swirl regime is governed by the interplay of the viscous ([mu][V.sub.s]/[d.sup.2]), inertia ([rho][V.sup.2.sub.s]/d), and the waviness-induced centrifugal forces ([rho][V.sup.2.sub.s]/2[lambda]). While the inertia and centrifugal forces promote secondary circulation, the viscous force retards it. In this force balance, [V.sub.s] is the common reference or velocity scaling. For the fluid motion along the prescribed flow geometry, as depicted in Figure 4, the component along the sinusoidal corrugations (u/cos[theta]) provides this reference velocity, [V.sub.s]. Accordingly, a swirl Reynolds number, [Re.sub.s], based on this velocity component can be defined as

[Re.sub.s] = [rho](4a)(u/cos [theta])/[mu] - Re/cos [theta] = Re [square root of 1 + [[gamma].sup.2]] (1)

where Re is the Reynolds number based on the mean axial or bulk flow velocity (Metwally and Manglik, 2004).

[FIGURE 4 OMITTED]

In the absence of swirl, the increase in friction-factor and Nusselt number, compared to those in equivalent flat-parallel-plate channels, as observed by Metwally and Manglik (2004), can be attributed to the increased effective flow length provided by the corrugations. Therefore, in the no-swirl region, the effect of the increased flow length on f and Nu can be scaled by the dimensionless parameter [phi], which is given by

[phi] = Effective length/Projected length = [square root of 1 + [[gamma].sup.2]] (2)

A statistical analysis of the no-swirl regime of the available results, based on the parameter [phi], yields the following equations for the isothermal friction factors and the Nusselt numbers, respectively.

f[Re.sub.s]/[(f[Re.sub.s]).sub.flat-plate] = f[Re.sub.s]/24 = [[phi].sup.4] (3)

Nu/[Nu.sub.flat-plate] = Nu/7.54 = [[phi].sup.2] (4)

In the swirl flow regime, the effect of viscous, inertia, and centrifugal forces can be captured by the scaling factor that is a function of both [Re.sub.s] and the severity of the corrugation waviness, [gamma]. This scaling parameter was statistically found to be quantified as,

Corrugation Effects ~ ([Re.sub.s], [gamma]) ~ [[gamma].sup.2.5][Re.sup.0.7.sub.s] (5)

Applying the corrugation effects to the results of Metwally and Manglik (2004), the following equations for friction factor and Nusselt number in the swirl regime are obtained:

f[Re.sub.s]/24 = 0.15 [[gamma].sup.2.5] [Re.sup.0.7.sub.s] (6)

Nu/7.54 = 0.0058/[[phi].sup.2] [([[gamma].sup.2.5][Re.sup.0.7.sub.s]).sup.0.3][Pr.sup.0.45] (7)

Extended asymptotic analysis and appropriate matching of Eqs. (3) and (6), along with Eqs. (4) and (7) yield the following predictive correlations for the isothermal friction factors and the Nusselt numbers, respectively, over the entire spectrum of Reynolds numbers:

f[Re.sub.s] = 24 [[phi].sup.4][[1 + [{0.15/[[phi].sup.4] [[gamma].sup.2.5][Re.sup.0.7.sub.s]}.sup.4]].sup.1/4] (8)

Nu = 7.54 [[phi].sup.2] {1 + 0.0058/[[phi].sup.2] [([[gamma].sup.2.5][Re.sup.0.7.sub.s]).sup.0.3][Pr.sup.0.45]} (9)

The plots for the comparisons between the available results for friction factors and the Nusselt numbers (Metwally and Manglik 2004) and those from the predictive correlations are shown in Figures 5 and 6, respectively.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

CONCLUSIONS

The thermal-hydrodynamic performance of in-phase sinusoidal wavy-plate channels, which describe the inter-plate flow ducts in washboard-type ([beta] = 90[degrees]) chevron plates in a PHE has been characterized in both the no-swirl and swirl flow regimes. The scaling of the enhanced convection arising from the corrugation effects and increased effective length has been established, and predictive correlations are developed. These equations are found to be in good agreement with the available computational data of Metwally and Manglik (2004). Also, they provide a reliable predictive tool for designing and optimizing wavy-plate channels and their enhanced heat-transfer performance for a variety of applications.

NOMENCLATURE

a = amplitude of wall waviness

f = Isothermal Fanning friction factor

Nu = Nusselt Number

Pr = Prandtl Number

Re = Reynolds Number

u = velocity component in x direction.

[beta] = included angle in chevron-plate corrugations

[theta] = angle wall surface makes with horizontal

[gamma] = wall corrugation aspect ratio (4a/2X)

[lambda] = corrugation half wavelength

[mu], = dynamic viscosity

[??] = density

Subscripts

s = swirl flow condition

w = at wall

m = bulk or mean value

REFERENCES

Asako, Y., Nakamura, H., and Faghri, M. 1988. Heat transfer and pressure drop characteristics in a corrugated duct with rounded corners, International Journal of Heat and Mass Transfer, 31: 1237-1244.

Bereiziat, D., Devienne, R., and Lebouche, M. 1995. Local flow structure for non-Newtonian fluids in a periodically corrugated wall channel, Journal of Enhanced Heat Transfer, 2(1-2): 71-77.

Ektesabi, M.R.M., Sako, M., and Chiba, T. 1987. Fluid flow and heat transfer in wavy sinusoidal channels (1st Report, numerical analysis of two dimensional laminar flow field), Nippon Kikai Gakkai Ronbunshu Bhen, Transactions of JSME, 53(487): 722-730.

Focke, W.W., Zachariades, J., and Olivier, I. 1985. The effect of the corrugation inclination angle on the thermohydraulic performance of plate heat exchangers, International Journal Heat and Mass Transfer, 28(8): 1469-1479.

Gschwind, P., Regele, A., and Kottke, V. 1995. Sinusoidal wavy channels with Taylor-Goertler vortices, Experimental Thermal and Fluid Sciences, 11: 270-275.

Metwally, H.M. and Manglik, R.M. 2004. Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels, International Journal of Heat and Mass Transfer, 47(10-11): 2283-2292.

Muley, A. and Manglik, R.M. 1997. Enhanced heat transfer characteristics of single-phase flows in a plate heat exchanger with mixed chevron plates, Journal of Enhanced Heat Transfer, 4(3): 187-201.

Muley, A. and Manglik, R.M. 2000. Enhanced thermal-hydraulic performance optimization of chevron plate heat exchangers, International Journal of Heat Exchangers, 1(1): 3-18.

Muley, A., Manglik, R.R., and Metwally, H.M. 1999. Enhanced heat transfer characteristics of viscous liquid flows in a chevron-plate heat exchanger, Journal of Heat Transfer, 121(4): 1011-1017.

Nishimura, T., Kajimoto, Y., and Kawamura, Y. 1986. Mass transfer enhancement in channels with wavy walls, Journal of Chemical Engineering, Japan, 19(2): 142-144.

Nishimura, T., Ohori, Y., and Kajmoto, Y., Kawamura, Y. 1990. Occurrence and structure of Taylor-Goertler vortices induced in two-dimensional wavy channels for steady flow, Journal of Chemical Engineering, Japan, 23(6): 697-703.

Rush, T.A., Newell, T.A., and Jacobi, A.M. 1999. An experimental study of flow and heat transfer in sinusoidal wavy passages, Journal of Heat and Mass Transfer, 42: 1541-1553.

Shah, R.K., and Focke, W.W. 1988. Plate heat exchangers and their design theory, in: R.K. Shah, E.C. Subbarao, R.A. Mashelkar (Eds.), Heat Transfer Equipment Design Hemisphere, New York, 227-254.

Wang, L., Sunden, B. and Manglik, R.M. 2007. Plate Heat Exchangers: Design, Applications and Performance, WIT Press, Southampton, UK.

Zhang, J., Kundu, J. and Manglik, R.M. 2004. Effect of fin waviness and spacing on the lateral vortex structure and laminar heat transfer in wavy-plate-fin cores, International Journal of Heat and Mass Transfer, 47(8-9): 1719-1730.

Zimmer, C., Gschwind, P., Gaiser, G., and Kottke, V. 2002. Comparison of heat and mass transfer in different heat exchanger geometries with corrugated walls, Experimental Thermal and Fluid Sciences, 26: 269-273.

S. Rajendran

Student Member ASHRAE

D.S. Kalaikadal

Student Member ASHRAE

R.M. Manglik, PhD

Member ASHRAE

S. Rajendran and D.S. Kalaikadal are graduate research assistants at Thermal-Fluids & Thermal Processing Laboratory, and R. M. Manglik is a Professor in the Department of Mechanical Engineering, University of Cincinnati, Cincinnati, Ohio.

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Author: | Rajendran, S.; Kalaikadal, D.S.; Manglik, R.M. |
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Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2013 |

Words: | 2412 |

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