Corrugation Angle Research Articles

A fast modelling tool for plate heat exchangers based on depth-averaged equations

In this study, the depth-averaged flow and energy equations for plate heat exchangers are presented. The equations are derived by integrating the original 3D flow and energy equations over the height of the gap between the bottom and top plates. This approach reduces the equations from 3D to 2D but still takes into account the frictions on the surfaces and heat transfer through the plates. The depth-averaging reduces the elapsed time of CFD simulations from hours to minutes. Thus, it is very practicable modelling method in real time design work. 2D CFD simulations with depth-averaged equations are compared with full 3D models for five different corrugation angles and corrugation lengths. The simulation results show that the 2D model predicts with relatively good accuracy the profile of the pressure drop and the temperature change as a function of the corrugation angle and the function of the corrugation length. In order to get more extensive information about the significance of the different geometry parameters on the efficiency of the heat exchanger, we simulated 30 different geometries with the fast 2D model. The results suggest that the temperature change is not as sensitive for the geometrical modifications as the pressure drop.

Flow and heat/mass transfer in a wavy duct with various corrugation angles in two dimensional flow regimes

In this study, two dimensional heat/mass transfer characteristics and flow features were investigated in a rectangular wavy duct with various corrugation angles. The test duct had a width of 7.3 mm and a large aspect ratio of 7.3 to simulate two dimensional characteristics. The corrugation angles used were 100°, 115°, 130°, and 145°. Numerical analysis using the commercial code FLUENT, was used to analyze the flow features. In addition, the oil-lamp black method was used for flow visualization. Local heat/mass transfer coefficients on the corrugated walls were measured using a naphthalene sublimation technique. The Reynolds number, based on the duct hydraulic diameter, was varied from 700 to 5,000. The experimental results and numerical analysis showed interesting and detailed features in the wavy duct. Main flow impinged on upstream of a pressure wall, and the flow greatly enhanced heat/mass transfer. On a suction wall, however, flow separation and reattachment dominantly affected the heat/mass transfer characteristics on the wall. As the corrugation angle decreased (it means the duct has more sharp turn), the region of flow stagnation at the front part of the pressure wall became wider. Also, the position of flow reattachment on the suction wall moved upstream as the corrugation angle decreased. A high heat transfer rate appeared at the front part of the pressure wall due to main-flow impingement, and at the front part of the suction wall due to flow reattachment. The high heat/mass transfer region by the main-flow impingement and the circulation flow induced at a valley between the pressure and suction walls changed with the corrugation angle and the Reynolds number. As the corrugation angle decreased, the flow in the wavy duct changed to transition to turbulent flow earlier.

Friction factors of power-law fluids in chevron-type plate heat exchangers

In the present work laminar flows of Newtonian and power-law fluids through cross-corrugated chevron-type plate heat exchangers (PHEs) are numerically studied in terms of the geometry of the channels. The plates area enlargement factor was a typical one (1.17), the corrugation angle, β, varied between 30° and 60° and the flow index behaviour, n, between 0.25 and 1. Single friction curves fRe g = K for both Newtonian and non-Newtonian fluids are proposed for each β by developing an adequate definition of the generalised Reynolds number, Re g. The coefficient K compares well with experimental data, for all (seven) values of β, and depends on the tortuosity coefficient, τ. It was found that, for each β, τ decreases with the decrease of n. Food fluids are frequently processed in PHEs and usually behave as non-Newtonian fluids. This study can be useful in engineering applications as well as in the characterization of transport phenomena in PHEs.

Cold model test and industrial applications of high geometrical area packings for separation intensification

With a particular focus on the separation intensification of distillation and adsorption columns, this paper reports the hydrodynamic and mass transfer performance of four novel packings, characterized by wave-like corrugation angles, and specific geometric areas ranging up to 2000 m 2/m 3. The relation between specific geometrical area, pressure drop, capacity and separation efficiency are discussed as a function of gas and liquid loads. As expected with increasing specific geometrical area the efficiency increases significantly, however, this occurs at the cost of a corresponding decrease in capacity. The expected efficiency advantage could be exploited for separations intensification in pressure drop insensitive applications, as evidenced by the presented industrial examples of applications of the packings for distillation and stripping.

Experimental investigation on the airside performance of fin-and-tube heat exchangers having herringbone wave fins and proposal of a new heat transfer and pressure drop correlation

The heat transfer and friction characteristics of fin-and-tube heat exchangers having herringbone wave fins were experimentally investigated. Eighteen samples having different fin pitches (1.34 mm to 2.54 mm) and tube rows (one to four) were tested. For all the samples, the waffle depth and the corrugation angle of the fin was 1.14 mm and 11.7o respectively. Results showed that the j factors were insensitive to fin pitch, while f factors increased as the fin pitch increased. As the number of tube rows increased, both the j and f factors decreased. However, the effect of tube row diminished as the Reynolds number increased, at least for j factors. Existing correlations failed to adequately predict the present data. A new correlation was developed based on existing data, which significantly improved the predictions of the present data.

Effect of rounding of protruding edge on convection heat transfer in a converging–diverging channel

Experiments were performed to determine convection heat transfer characteristics for the rounding of the protruding peaks of a corrugated channel. Results were carried out for a Prandtl number of 0.7 in the Reynolds number range from 2000 to 5000 for the corrugation angle of 30 o and channel height of 5 mm. In order to determine the channel having the best performance, the channels were also compared by considering the flow area goodness factor. The heat transfer performance for the channel with rounded corrugation peak is greater than that for the sharp peak about 100%.

Steam Condensation in Parallel Channels of Plate Heat Exchangers — An Experimental Investigation

An experimental investigation has been carried out to find the pressure difference of the process of steam condensation across the port to channel in plate heat exchangers. In the present study, low corrugation angle (30°) plates have been used for different number of channels, namely, 10 and 80. The process steam entered at 1 bar with a small degree of superheat. Water has been used as the cold fluid. The pressure probes are inserted through the plate gasket into both the inlet and exit ports of the channel. The pressure drop of the process steam has been measured and recorded at the first, middle, and last channels at different flow and exit conditions for each plate package of the heat exchanger. Also, the overall pressure drop has been measured at different conditions at the outlet of the process steam, i.e., full and partial condensation. The pressure drop measurements have indicated that there is a considerable variation in pressure drop from the first channel to the last channel due to flow maldistribution. The experimental data has been analyzed to show how the flow maldistribution affects the pressure drop of a plate condenser. (Less)

Experimental study on forced convection heat transfer characteristics in a converging diverging heat exchanger channel

The convective heat transfer characteristics in a periodic converging–diverging heat exchanger channel are investigated experimentally. Experiments were performed for Prandtl number 0.7, for corrugation angle of 30°. In order to determine the channel having the best performance, the channels also compared by considering the flow area goodness factor.

Better Thermal Calculations Using Modified Generalized Leveque Equations for Chevron Plate Heat Exchangers

Plate heat exchangers are becoming vital process energy exchange equipment in chemical industries. The present work looks into the applicability of the Generalized Leveque Equation (GLE), which is used to generate thermal performance calculations for chevron-type plates utilized in plate and frame heat exchangers. New Modified Generalized Leveque Equations are proposed to improve calculation accuracy, which will enhance energy utilization and cost reduction in the design stage. A case study was selected to examine the GLE applicability when implemented to pure and mixed chevron plates. The GLE and other modified equations are compared with known classical correlations for different corrugation angles of 30°, 45°, 50°, 60° and 65° as pure chevron plates, and 45°/90°, 23°/90°, 45°/45°, 23°/45°, and 23°/23° as mixed chevron plates. Both the GLE and single Modified Generalized Leveque Equation (MGLE) gave good results only for 30° and 50° pure chevron angles and failed to give acceptable results in 45°, 60° and 65° chevron angles; both, however, gave acceptable results with all tested mixed angles. Also, the GLE has the tendency to be more applicable in the laminar region where Re < 2100, but the inaccuracy increases when applied in the turbulent region, while MGLE gave slightly lower relative error at high Re. Based on the classification of soft and hard chevron plates, two new Modified Generalized Leveque Equations, MGLE(1) and MGLE(2), were developed from the set of Kumar's data for pure chevron plates. The proposed system of equations are capable of providing excellent results for both pure and mixed chevron angles when compared with a large set of classical correlations available in the literature.

CFD modeling of columns equipped with structured packings: I. Approach based on detailed packing geometry

AbstractA three‐dimensional computational fluid dynamics (CFD) modeling approach based on detailed packing geometry for packed columns equipped with structured packings is presented. Simulations have been carried out by commercial CFD package FLUENT. Complex packing geometries were implemented by generating fine meshes for flow domains inside packed columns. Turbulence was modeled by the standard k‐ϵ model with FLUENT's enhanced wall treatment. Experiments on single‐phase pressure drop through Flexipac 3Y structured packing have been carried out in a 0.3‐m ID packed column with air flow to validate the modeling approach. A circular column and a rectangular column have been simulated with three different structured packings—BX packing with corrugation angles of 45° and 30° and Flexipac 3Y. One‐component single‐phase flow and two‐component single‐phase flow with species dispersion (mass transfer) have been simulated. Predicted pressure drop are in good agreement with the experimental data and data from literatures. The simulation results also demonstrated the ability of the CFD approach to capture the anisotropic characteristic of flow in structured packings. Copyright © 2007 Curtin University of Technology and John Wiley &amp; Sons, Ltd.

Laminar flow in chevron-type plate heat exchangers: CFD analysis of tortuosity, shape factor and friction factor

Laminar or low Reynolds number flows are usually obtained when liquid foods with high viscosity are processed in plate heat exchangers (PHEs). The tortuosity coefficient is a key parameter used by PHEs manufacturers to estimate Fanning friction factors and convective heat transfer coefficients. Using the finite-element computational fluid dynamics program POLYFLOW ®, fully developed laminar flows in double-sine chevron-type PHEs passages are analysed in this work. The corrugation angle and channel aspect ratio of the passages vary in a broad range, PHEs with common area enlargement factors and with high area density being studied. The tortuosity coefficient and the coefficient K (Kozeny's coefficient in granular beds) from the friction factor correlations increase with the increase of the channels aspect ratio and the decrease of the chevron angle. The shape factor from the PHEs passages also increases with the decrease of the chevron angle and is weakly influenced by the channel aspect ratio. In this paper, relations to predict the tortuosity coefficient and shape factor are proposed, the coefficient K being predicted resorting to the tortuosity coefficient and shape factor. The coefficient K compares well with literature data in the region of common chevron angles, channels aspect ratio and area enlargement factor.

Effects of corrugation angle on developing laminar forced convection and entropy generation in a wavy channel

This paper investigates the effects of corrugation angle (β) on the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The studied cases cover β = 10-, 15-, 20-, 25-, 30- and 35°, whilst Reynolds number (Re) is varied as 100, 200 and 400. The analyzed flow characteristics include recirculating flows, secondary vortices, temperature distributions, and friction factor as well as Nusselt number. In particular, the effects of corrugation angle on the distributions and magnitudes of local entropy generation resulted from frictional irreversibility (S ′′′ ) and heat transfer irreversibility (S ′′′ ) are separately discussed in detail in the present paper. Based on the minimal entropy generation principle, the optimal corrugation angle and favorable Re are reported.

How to Surpass Conventional and High Capacity Structured Packings with Raschig Super-Pak

Raschig Super-Pak is a novel development in structured packing product technology that is fundamentally different to the well known corrugated perforated or non-perforated, textured sheet metal structured packings. It comprises of a systematic sequence of smooth sinusoidal waves above and below the plain of the metal sheet. Tests at the Ruhr University of Bochum showed that the new open structure resulted in very high capacities low pressure drops and excellent mass transfer efficiencies. Encouraged by these early successes, total reflux distillation tests with Raschig Super-Pak 300 were conducted at the Separations Research Program, University of Texas at Austin. Results in terms of useful capacity, mass transfer efficiency, pressure drop and pressure drop per theoretical stage are presented. Comparisons with the Montz standard B1-250 and high capacity B1-250M structured packings tested under identical conditions will be shown. In addition results are compared against F.R.I. tested Mellapak M250Y and MellapakPlus M252Y structured packings for the same test fluid at 0.34 and 1.65 bar system pressures. Overall Raschig Super-Pak 300 exhibits higher useful capacities and lower pressure drops compared not only with standard 45° corrugation angle 250 m 2 m −3 surface area structured packings but also with the high capacity counterpart types as well. Remarkably these gains were achieved without any adverse effects on mass transfer efficiency. This observation is reflected in the lower pressure drop per theoretical stage of Raschig Super-Pak 300 compared to the 250 m 2 m −3 surface area structured packings. These highly encouraging results provide industry with an alternative choice for smaller column diameter and/or higher capacity: the Raschig Super-Pak.

Dynamical modeling and experimental validation of a micro-speaker with corrugated diaphragm for mobile phones

As the design trend of modern cellular phones evolves to be miniaturization and versatile sound in quality, the electro-mechanical components including the micro-speaker are essential toward size reduction and broad frequency range of sound. To reduce size, a diaphragm type micro-speaker is commonly employed in industry, while to broaden the sound frequency range corrugations on the diaphragm are adopted. The corrugations are generally capable of leading to fairly flat response over a broad range since diaphragm stiffness is decreased in axial direction. To confirm the aforementioned capability, the modeling on a corrugated diaphragm is performed first using finite element method (FEM) to obtain the associated dynamic equations in terms of modal coordinates; then the equations are next combined with the magneto-electrical model of the voice coil motor (VCM) that is attached to the bottom side of the diaphragm. Finally, the acoustic effects of the air inertia on the diaphragm and vents of the outer case are modeled using basic acoustic theories. Assembling all derived system equations and solving them, the frequency response of the micro-speaker in sound pressure level (SPL) can be simulated. It shows that the diaphragm corrugation in fact helps flatten the SPL response of the micro-speaker (especially in high frequency range) to lessen sound distortion. Furthermore, the corrugation angle approximately below 45° is favored over other angles or flatter SPL response. Experiments are also conducted to verify the theoretical findings.

Comprehensive Mass Transfer Model for Distillation Columns Equipped with Structured Packings

A new mechanistic model for the evaluation of mass transfer performance in columns equipped with structured packings is proposed. The model is developed by taking into account the interactions of falling film with the gas phase, and thus, it includes the effects of both the physical properties of the working fluids and the geometrical characteristics of the packings. The model does not introduce any adjustable parameter but relies on the semiempirical equations developed earlier for the prediction of the pressure drop and the mass transfer coefficients in absorption processes. The model has been validated using experimental data obtained under total reflux conditions with different systems at different operating conditions, including the conventional and high capacity packings of different specific surface areas and different corrugation angles. The results indicated that simple mechanistic models can be used with confidence to describe the fluid dynamics within the packings. The adoption of the present model is suggested for systems for which experimental data are not available, while for experimentally tested systems, higher prediction accuracy could be obtained using different models, based on a larger number of adjustable parameters that have to be tuned on the experimental data. The knowledge of the liquid film hydrodynamic behavior can also allow understanding of the reasons for some observed deviations in performance such as the efficiency “hump” occurring at specific operating conditions in distillation columns.

EFFECT OF SPACING OF FASTENERS USED TO ATTACH THE CORRUGATED SHEAR PLATE TO THE ENVELOPE FRAME ON ITS ELASTIC BUCKLING BEHAVIOR

The search for light weight and efficient structural elements is a continuing process. Reducing the structural weight and improving the load carrying capabilities of steel frames will allow designers to add additional capabilities while reducing cost. Corrugated steel plate shear walls offer several advantages when used to resist both vertical and lateral forces in a building. This paper is devoted to the buckling behavior of steel frames with corrugated steel shear walls. The system consists of two parts, the first one is the envelope steel frame and the second is the infill corrugated steel shear wall. The corrugated steel plates are connected to the surrounding frame beam and columns. The buckling load factor of this system depends on the interaction of many factors including the corrugation configuration of steel plate, the angle of corrugation, the depth of corrugation, the thickness of corrugated plate and the spacing of the fasteners used to attach the corrugated sheets to the steel frame, in addition to the restraint conditions and the external load action. Steel frames with trapezoidal or triangular corrugated steel shear panel were modeled using the finite element software Cosmos/m 2.8 and a linear analysis was performed. In the current study, elastic buckling behavior of steel frames with corrugated shear wall is investigated using finite element approach. The elastic buckling behavior is expressed as normalized load factor which is defined as the ratio between the buckling load of the frame with corrugated plate to the buckling load of the frame without corrugated plate. Parametric analyses were carried out to investigate the effect of spacing between fasteners used to attach the corrugated plate to the envelope frames without or with one, two, and three stiffeners for frames subject to vertical loads only or vertical loads with horizontal loads. The results showed that the spacing between fasteners has significant influence on the elastic buckling behavior of the steel frames with corrugated shear wall.

Quasi-P-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces

In this paper we have derived reflection and transmission coefficients of qP-waves at a corrugated interface between two different elastic half-spaces of monoclinic type. Using Rayleigh’s method, the expressions for reflection and transmission coefficients are derived in closed form for a specific interface and for the first order approximation of the corrugation. Numerical computations are performed for a specific model and the results obtained have been shown graphically. The variation of the modulus of reflection and transmission coefficients with the angle of incidence, frequency and corrugation of the interface are shown separately. These coefficients are found to be strongly influenced by the angle of incidence, frequency, elastic parameters and amplitude of the corrugation of the interface. It is found that (i) the modulus of reflection and transmission coefficients at the plane interface are independent of corrugation of the interface and that of frequency of the incident wave, (ii) the reflection and transmission coefficients of regularly reflected and transmitted waves are found to be greater than that of irregularly reflected and transmitted waves, (iii) the coefficients of irregularly reflected and transmitted waves are found to increase and decrease with increase of corrugation and frequency parameters respectively. The results of Singh and Khurana [Singh, S.J., Khurana, S., 2001. Reflection and transmission of P- and SV-waves at the interface two between monoclinic elastic half-spaces. Proc. Natl. Acad. Sci. India 71(A) (IV), 305–319] have been reduced from the present problem.

An experimental investigation of the port flow maldistribution in small and large plate package heat exchangers

An experimental investigation has been carried out to find the flow and the pressure difference across the port to channel in plate heat exchangers for a wide range of Reynolds number, 1000–17 000. In the present study, low corrugation angle plates have been used for different number of channels, namely, 20 and 80. Water has been used as working fluid for both hot and cold fluids. The pressure probes are inserted through the plate gasket into both the inlet and exit ports of the channel. The pressure drop is recorded at the first, middle and last channels for each plate package of the heat exchanger. Also, the overall pressure drop has been measured for various flow rates. This overall pressure drop is a function of the flow rate, the cross-sectional area ratio of channel to port and number of channels per fluid. A simplified non-dimensional channel velocity has been suggested based on the channel pressure drop and the mean channel pressure drop of plate package, to measure the deviation of the particular channel flow rate from the mean channel flow rate. The results indicated that the flow maldistribution increases with increasing overall pressure drop in the plate heat exchangers. The experimental results are verified with M.K. Bassiouny and H. Martin’s [Chemical Engineering Science 39(4) (1984) 693 and 701] analytical results.

Experimental study on flow and local heat/mass transfer characteristics inside corrugated duct

The present study investigates the flow and heat/mass transfer characteristics of wavy duct for the primary surface heat exchanger application. Local heat/mass transfer coefficients on the corrugated duct side walls are measured using a naphthalene sublimation technique. The flow visualization technique and a numerical analysis using a commercial code, FLUENT, are used to understand the overall flow structures inside the duct. The corrugation angle of the wavy duct is 145° and the duct aspect ratio is 7.3. The Reynolds numbers, based on the duct hydraulic diameter, vary from 100 to 5000. The results show that complex secondary flows and transfer processes exist inside the wavy duct resulting in non-uniform distributions of the heat/mass transfer coefficients on the duct side walls. At low Reynolds numbers ( Re ⩽ 1000), relatively high heat/mass transfer regions like cell shapes appear on both pressure- and suction-side walls due to the secondary vortex flows called Taylor–Görtler vortices perpendicular to the main flow direction. However, at high Reynolds numbers ( Re > 1000), these secondary flow cells disappear and boundary layer type flow develop on pressure-side wall. On the suction-side wall, high heat/mass transfer region appears by the flow reattachment. The average heat/mass transfer coefficients are higher than those of the smooth circular duct and pressure drop increases due to the secondary flows inside wavy duct.

Buckling strength assessment of corrugated panels in offshore structures

There is an increasing trend of living quarters in offshore structures being constructed using corrugated panels in order to save construction time and cost. Different from corrugated bulkheads in ship structures, the corrugated panels used in the living quarters are designed in triangular or trapezoidal profile with unequal flanges and with a corrugation angle between 45° and 90°. Industry needs have prompted the American Bureau of Shipping to develop design recommendations for the buckling strength assessment of these corrugated panels. This paper describes the main features and the principles of the recommendations based on ABS experience, along with the technical background. The modeling uncertainty associated with the recommended criteria has been established by comparing the predictions with laboratory tests and finite element analysis results. Two design examples are provided to demonstrate the application of the recommendations.