CHEMICAL ENGINEERINGTRANSACTIONS 
 

VOL. 52, 2016 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors:Petar Sabev Varbanov, Peng-Yen Liew, Jun-Yow Yong, Jiří Jaromír Klemeš, Hon Loong Lam 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN978-88-95608-42-6; ISSN 2283-9216 
 

Heat Transfer and Pressure Drop in Cross-Flow Welded Plate 

Heat Exchanger for Ammonia Synthesis Column 

Leonid L.Tovazhnyanskyya, Petro O.Kapustenkoa, Olexandr 

Y.Perevertaylenkoa,Genadiy L.Khavinb, Olga P.Arsenyeva*a, Pavlo Y.Arsenyevb, 

Alisher E.Khusanovc 

aNational Technical University “Kharkiv Polytechnical Institute”, Dep. ITPA, 21 Frunze st., Kharkiv, 61002, Ukraine 
bAO SPIVDRUZHNIST-T LLC, Krasnoznamenny per. 2, off. 19, 61002, Kharkiv, Ukraine 
cM.Auezov South Kazakhstan State University, Tauke hana Avenue, 160012 Shymkent, Kazakhstan 

o.p.arsenyeva@gmail.com 

Plate Heat Exchanger (PHE) is one of the modern types of compact heat transfer equipment, which can 

significantly enhance the heat recuperation and improve efficiency of energy usage in many industrial 

applications. The construction of welded PHE (WPHE) can significantly widen the range of its application on 

temperature and pressure. The results of experimental study of heat transfer and pressure drop in a model of 

WPHE specially designed for work in ammonia synthesis columns are presented. The model consists of the 

round plates with special form of corrugations. The plates are welded together forming a pack with channels 

for two heat exchanging streams. The streams are in a cross flow that correspond to one pass of the multi-

pass WPHE with overall counter-current flow. It is shown that for calculation of heat transfer effectiveness can 

be used the cross flow model where fluid in one channel is mixed, but in another unmixed. The Equations for 

calculation of film heat transfer coefficients and pressure drop are presented, which can be used in earlier 

developed method of WPHE design. The validity of the Equations and developed method of WPHE design is 

confirmed by the data of tests with WPHE installed in ammonia synthesis column at temperature up to 520 °C 

and pressure 32 MPa. 

1. Introduction 

Efficient heat recuperation is of primary importance in resolving the problem of efficient energy usage and 

consequent reduction of fuel consumption and greenhouse gas emissions, as is discussed by Klemes and 

Varbanov (2013). Heat transfer enhancement is substantially facilitate the solution of the problem (Gough et 

al., 2013). Plate Heat Exchanger (PHE) is one of the modern efficient types of compact intensified heat 

transfer equipment. The principles of the construction and design for different types of PHEs are sufficiently 

well described in the literature, e.g. (Klemes et al., 2015). The conventional type is plate-and-frame PHE, 

which was initially developed for the food industry and later proved efficient in many other applications. It is 

confirmed by a number of researchers, as e.g. Hajabdollahi et al. (2016) have found in their study case of 

water to water HE that the comparison of the optimum results for plate-and-frame PHE shown 13 % 

improvement in the total cost compared with shell-and-tube heat exchanger at the same operating conditions. 

Their flexibility allows finding economically viable solutions in different processes of waste heat utilisation, 

asshown by e.g. Arsenyeva et al. (2016). However, due to elastomer gaskets the range of plate-and-frame 

PHE application is limited to pressures up to 25 bar and temperatures up to 180 °C and working fluids friendly 

to gaskets material.  Besides, the cost of the gaskets, especially for severe working conditions, can 

dramatically increase the cost of heat exchanger as a whole unit. To widen the PHE application range by 

excluding elastomer gaskets the brazed (BPHE) and welded (WPHE) types of PHE were developed. In the 

construction of welded PHE the gaskets between plates are eliminated, that allows to widen significantly the 

range of its application on temperatures and pressures. 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1652093 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Tovazhnyanskyy L. L., Kapustenko P. O., Perevertaylenko O. Y., Khavin G. L., Arsenyeva O. P., Arsenyev P. Y., 
2016, Heat transfer and pressure drop in cross-flow welded plate heat exchanger for ammonia synthesis column, Chemical Engineering 
Transactions, 52, 553-558  DOI:10.3303/CET1652093   

553



Nowadays there are a number of different by construction principles types of welded PHEs produced by 

contemporary PHE manufacturers. The comparison of two most widely used types, which are Plate-and-Block 

(Compabloc) HE and Plate-and-Shell HE (PSHE), is presented by Arsenyeva et al. (2016). According to 

analysis published by Andersson et al.(2009) before the year 2009 it was installed more than 750 Compabloc 

HEs only in oil refining industry on different positions worldwide.  

A different design of welded PHE is developed for work at ammonia synthesis process under high temperature 

up to 520 °C and pressure up to 32 MPa. Here the results of experimental research on the heat transfer and 

hydraulic resistance in channels formed by plates of such WPHE are presented. 

The WPHE developed for work in high pressure shell of ammonia synthesis column consist of a stack of round 

plates with special form of corrugations, depicted in Figure 1. The plates are welded together to form a 

number of channels for cold and hot streams exchanging heat.  The welded collectors of special design are 

organizing multi pass movement of both streams with overall counter current flow. The movement of two 

streams in one pass block is cross flow. Compare to the flow of streams in conventional plate-and-frame PHE 

there is significant difference. From hydraulic point of view the stream is entering the channel through almost 

full cross section, while in channels of plate-and-frame PHE it is entering from distribution collector of small 

diameter compare to channel width.  It causes much smaller local hydraulic resistance at the port zone of 

WPHE and ensures even flow distribution across channel width. But for the heat transfer cross flow of streams 

causes the reduction of mean temperature difference compare to counter flow in one pass of plate-and-frame 

PHE. The overall counter flow in WPHE is making this loss in mean temperature difference smaller, but still 

this cross flow feature for individual passes should be accounted in correct PHE design. The available 

literature data are not directly applicable, as the level of fluid mixing across PHE channel is not known. 

2. Experimental model and test rig 

The heat transfer and pressure drop in WPHE were investigated experimentally using the model consisted of 

15 plates representing the block of plates in one pass of WPHE. The plates are forming 14 channels, in 7 of 

which the hot stream is directed and in other 7 channels is directed the cold stream. The geometrical forms of 

the channels for hot and cold fluids are different.  For the cold stream the channel is formed by one plate with 

most of the corrugations (at 2/3 plate area) directed along the main flow direction. The adjacent plate has 

herringbone corrugation direction with angle 60 degrees to main flow direction. Resulting average corrugation 

angle in this area is 30 º.  At the remaining 1/3 of plate area the angle of corrugations to flow direction is 60 º 

on both adjacent plates. The average angle of corrugations to flow direction is β2=40 º.  Such form of 

corrugations is made to facilitate the discharge of possible dust in the synthesis gas stream after catalyser, 

which can appear with catalyser aging. The average angle of corrugations in another channel for hot stream is 

equal to β1=50 º. The main geometrical parameters of the tested model, plate corrugations and inter-plate 

channels are presented in Table 1. 

Table 1: Table title (Style: CET-table-title) 

Total heat transfer surface area, Fa, m2 4.2  

Number of plates, Np 15 

Heat transfer surface area of one plate, Fp,m2 0.32  

Cross section area of one channel, fch, m2 0.0022 

Plate outside diameter, Do, m 0.626 

Plate thickness, δw, m 0.001 

Plate metal AISI 304 

Heat conductivity of the wall, λw, W/(m K) 16 

Corrugations height, b, m 0.004 

Corrugations pitch, S, m 0.018 

Average channel width, Wch, m 0.55 

Equivalent diameter of channel, de, m 0.008 

Average corrugations angle to main flow direction: For 

hot stream, β1, degrees 

For cold stream, β2,degrees 

 

50 

40                   

The width of channel entrance (exit), Wenx, m 0.4 

 

The thermal and hydraulic characteristics of the WPHE model were measured at specially developed test rig 

with water as test fluid for both streams, schematically shown in Figure 2. The testing fluid is distilled water. It 

is pumped from water tank to the tubular heat exchanger, where is heated by steam to required temperature 

554



t11 of hot water inlet to the model. After being cooled in the model to outlet temperature t12, the water is 

entering the PHE, where it is cooled by cooling water from the central cooling water circuit with cooling tower. 

It is cooled to the required temperature t21 of cold stream inlet to the WPHE model. Heated in the model to the 

cold stream outlet temperature t22, water is returning back to the water tank. The flowrate of the coming to the 

model cold water is measured by calibrated orifice meter. The temperatures at heat exchanging streams inlet 

and outlet at the WPHE model were measured with calibrated copper-constantan thermocouples with 

accuracy ±0.05 °C.  Two differential diaphragm-pressure gauges were used to measure pressure differences 

between the inlet and outlet ports of the hot and cold water. The tests were made in stabilized regime when 

the parameters of the process were not changed in consecutive 2 min. The inlet temperature of hot water was 

varied in the range 55 – 85 °C, inlet temperature of cold water 30 – 45 °C. The mass flow rate of water was 

varied in the range from 0.8 kg/s to 4.5 kg/s. 

 

Figure 1: The plate of WPHEFigure 2: Schematic drawing of the test rig for ammonia synthesis column 

3. Results and discussion  

The results of the tests measurements allowed calculate heat load of the test model. The heat load Q for 

further calculations was taken as average between the values calculated for hot Q1 and cold Q2 streams, W: 

1 p1 11 12 2 p 2 22 21 1 2
Q G c (t t ); __ Q G c (t t ); __ Q (Q Q ) / 2,           (1) 

where G is water mass flow rate, kg/s; cp1 and cp2 are specific heat capacities of hot and cold water, J/(kg K).  

The mass flow rates of both streams in the model are equal and heat capacity differ not more than 0.3%, 

hence the mean temperature difference is calculated as: 

 m 11 22 12 21t t t (t t ) / 2      
 (2) 

The experimental value of overall heat transfer coefficient, W/(m2 K): 

ex

m a

Q
U

t F




 
(3) 

 

The results of experiments were compared with predictions by Equations proposed by Arsenyeva et al. 

(2012). For calculating the friction factor in the channels for hot (index i=1) and cold (index i=2) sides by 

following Equation: 

 

1

1212

2

3

2

12 1
8

Re


 
     
     

i
i

i
i i

p

A B

, 

16

5
4 0.9

53

ln
7

0.27 10
Re



  
  
  

   
       
   

i
i i

i

i

p
A p

p

; 
16

1
37530

Re

 
  
 

i
i

i

p
B

 

(4) 

555



 

where p1i, p2i, p3i, p4i, p5iare the parameters defined by channel corrugation form.  

 1 exp 0.15705   i ip ;  
2

2
3

   
 i

i
p

;  
3 2

1
exp

180






 
    

 

i
i

i

p ; 

      
2.63 0.01

4
0.061 0.69 1 1 0.9

i i i i
p tg   



       
;  

5
1

10

i
i

p


 
 

γi=2b/S is the corrugation doubled plate spacing b to corrugation pitch S ratio; βi is the corrugations inclination 

angle, degrees; Rei=widei/ µiis the Reynolds number; de is the equivalent diameter of the channel, de = 2b, 

m; wi is the stream velocity in the channel, m/s; µi is the dynamic viscosity of fluid, Pa∙s; iis the density of the 

fluid, kg/m3. 

The film heat transfer coefficients are estimated using for hot (1) and cold (2) sides the following relation: 

3 0.14
76

7

wi

0.065 Re Pr
  




   
       

   

ci i i
i i i

Nu
F

 (5) 

Where µi and μwi  are the dynamic viscosities for the stream and wall temperatures, Pa∙s; Nu=hide/i is 

the Nusselt number; iis the thermal conductivity of the fluid, W/(m·K); hi  is the film heat transfer coefficient, 

W/(m2·K); Pri is the Prandtl number; ζi is the friction factor accounting for total pressure losses in the channel, 

calculated by Equation (2); ψi is the share of pressure loss due to friction on the wall in total loss of pressure; 

Fx is the coefficient of surface area enlargement due to corrugation.  

The value of ψi is estimated according to relation: 

 
1.75

1
380 / ( )

i i
A tg ;

0.15 sin( )

1 1

1
1 

Re

R

  Re  

e






   

  
  


   

i

i

i
i

i i i

i i

A at A

at A

 
(6) 

The calculated value of overall heat transfer coefficient is determined as: 

1

w
cl

1 2 w

1 1
U

h h







 
   
 

 (7) 

The influence of fluid velocity on overall heat transfer coefficient is shown on graph in Figure 3. There 

presented experimental and calculated values. The calculated values are somewhat higher than experimental 

ones, but the discrepances are not exciding +8 %. Beside some experimental error it can be explained by 

reduction of heat transfer effectiveness due to cross flow. In Figure 4 is presented the dependance of the 

WPHE model heat transfereffectivness ε=(t11-t12)/(t11-t21) from the number of heat transfer units (NTU), 

expressed through calculated overall heat transfer coefficient Ucl by following Equation: 

a cl

p1

F U
NTU

G c






 
(8) 

The ε-NTU experimental values are situated below ε-NTU values calculated by Equation for counter-current 

flow, but can be approximated on a safe side by ε-NTU relation for cross flow with one fluid mixed another 

unmixed (see Shah and Sekulic, 2003): 

 1 exp R NTU
1 exp

R


    
   

 

 (9) 

where R=G1.cp1/( G2.cp2). In our case R=1, but it can be approximated also for other cases with R<1. Using this 

relation (Eq.9) the ε-NTU method proposed by Arsenyeva et al. (2016) can be used for calculation of 

considered multipass WPHEs. 

556



 

 

Figure 3: The influence of flow welocity                         Figure 4: The ε-NTU relation for WPHE                                       

on overall heat transfer coefficient:                                model: 1- experiment; 2 – counter-current;                                             

1 – prediction; 2 – experiment                                       3 – cross flow mixed – unmixed 

 

      

Figure 5: The experimental data for  pressure       Figure 6: The comparison of experimental  losses: 

1 – hot stream; 2 – cold stream                              pressure drop with predicted by Eq.(10): 

                                                                               1 – hot stream; 2 – cold stream 

For correct design of the WPHE the data for pressure drop calculation is required. In Figure 5 are shown the 

experimental data on Eui =ΔPi/(ρi.wi2) number for both hot and cold streams in WPHE model. The data for 

channel with higher corrugation angle β1=50° are demonstrating higher hydraulic losses than for channel with 

β2=40°. For calculation of the pressure losses the division of the channel on main corrugation field and 

distribution zones at the inlet and outlet of the inter-plate channel is used. Arsenyeva et al. (2013) introduced 

the coefficient of local hydraulic resistance in those zones ζDZi, with which the pressure drop inone pass of 

WPHE, represented by the model under investigation, can be calculated by Eq.(10): 

2 2

.

2 2

 
 

 
     i i i enx i

i i DZi

e

w wL
p

d
 (10) 

where wenx.i is the velocity at channel entrance/exit. 

The comparison with experimental data gave following values for coefficient of local hydraulic resistance in 

distribution zones ζDZ1=11 and ζDZ2=17. The comparison of calculation by Eq.(10) with experimental data is 

shown by graph in Fig.6. The error not exceed 10 %. 

557



4. Conclusions 

The experimental study of heat transfer and pressure drop in the model of WPHE has confirmed the validity of 

Equations proposed for PHE channels of different geometry in case of cross flow. It is also estimated the 

dependence of PHE heat transfer effectiveness (ε) from the number of heat transfer units (NTU) in one pass 

of WPHE with cross flow of streams. These Equations can be used in the method for calculation of WPHE 

with overall counter flow and cross flow inside separate passes. 

The validity of the proposed Equations and developed method for WPHE design was confirmed by 

comparison with the data of tests on WPHE installed in ammonia synthesis column at industrial enterprise of 

ammonia production. WPHE was installed in existing synthesis column of ammonia unit instead of shell-and-

tube heat exchanger. The use of WPHE instead shell-and-tube unit enable to cut down the volume occupied 

by heat exchanger in high pressure shell of ammonia synthesis column and allows increase of the volume of 

catalyst. It leads to 15% rise of ammonia output. 

Acknowledgments 

The support of EC Project DISKNET (FP7-PEOPLE-2011-IRSES-294933) and Grant of Education and 

Science Ministry of the Republic Kazakhstan in state program “Grant funding for research”, for sub priority:” 

Power and machine building (Heat and power generation and energy-efficient technologies)”are sincerely 

acknowledged. 

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