Simulation and testing�We have tested our simulation model for louvered fin at different test points and compared the result with designed HE

�Test results obtained from simulation of process of the liquefier and simulation using described numerical model for louvered fins are shown in TABLE-1, 2& 3

�Model was tested both for offset strip fin(fig-5) and louvered fin(fig-6). Test results are compared in TABLE-4

�We tested our simulation model at different cold fluid input temperature with hot fluid input temperature constant at 300k

�Temperature difference between the two stream at two outlet and effectiveness change is shown in fig-7 & fig-8.

�Temperature distribution for hot and cold fluid, metal across different node is shown in Fig-4.

Abstract Turbine based helium liquefier is under development at VECC. The process diagram of the liquefier and refrigerator has been frozen by performing simulation process. The integral part of helium liquefier is plate-fin heat exchanger. Overall design for the plate-fin heat exchangers qualifying the liquefaction and refrigeration process has been done and their requirements have been identified. Numerical simulation for the thermal steady state condition for the heat exchangers has been performed. The axial conduction, fluid property dependence on temperature, parasitic heat transfer etc. have been taken into consideration. Validation for the same is necessary in a simple test setup, which will be cooled by liquid nitrogen and liquid helium. The overall process andinstrumentation diagram of the test setup has already been designed. The process control should be verified using the computational model of the heat exchanger.

ORS

TT

PT

LN2 or LHe

Plate-Fin HE

Finned Tube HECOLD BOX

PT

TT

PT

TT

PT

TT

FT

TTPT

PT

TTValve 1

Valve 2Inference1.Test results for louver fin are better than that for offset strip fin 2.Result obtained from our simulation program is in close proximity of the actual test result3.We have used 3/8-6.06 fin [3] in our simulation, other fin parameters will be tried in future. With the actual fin parameters, that are used in the physical heat exchanger , the simulation result would have been more close to the desired result of the physical heat exchanger4.Test results at different temperature shows that minimum approach decreases at high temperature5.At higher temperature effectiveness increasing

Input parameters

Heat exchanger specifications: L, W, N, th , tc , tm

Fin specifications: , , , ,

Hot and cold side input temperature: Tin,h , Tin,c

Numerical parameters

Number of elements:n

Boundary ConditionsAssume temperature variation as

Setup the equations using equation (1) , (2) and (3)

Solve the differential equations using ODE23t solver

Plot the temperature for hot stream, cold stream and metal wall at different nodes, and calculate the effectiveness

Return to control program

hicinhin

hi Tn

TTT ,1

,,, 1 −+

−−

= 1,,

,,1 −−

−=− n

TTTT cinhin

cici

1,,

,1, −−

−= − n

TTTT cinhin

mimi

hinhi TT ,,1 == cincni TT ,, ==

hinmi TT ,,0 == cinmni TT ,, ==

pLl pF fδ α

Flow chart of the heat exchanger numerical model

Control scheme flow chart

Start with valve 1 full close and valve 2 full open

Increase the valve 1 opening and decrease valve 2 opening

maintaining total flow rate constant

Calculate the Mixing temperature

Calculate the mixing temperature

Call simulation program with mixing temperature as cold side

input

If mixing temperature is greater than set

point

Define the input temperature

Change the valve 1 and valve 2 opening according to error between set point

and mixing temperature

Calculate the mixing temperature

If mixing temperature equal to set

point

YES

NO

NO

YES

Call simulation program with mixing temperature as cold side

input

END

Proposed Numerical Model

)2

)(()

2( ,

,,1,

,1,mi

hihihs

hihih T

TTxA

TTU −

+⋅∆⋅′⋅

+ ++

)2

)(()

2( ,,1

,,,1, cici

micscici

c

TTTxA

TTU

+−⋅∆⋅′⋅

+ ++

)( ,1, mimicmm TTAx

k+−⋅⋅

∆

)( ,,1 mimicmm TTAx

k −⋅⋅∆ −

xTq mi ∆⋅′ )( ,

(Axial conduction)

(Axial conduction) (Heat transfer from hot fluid to metal)

(Heat transfer from metal to cold fluid )

(Parasitic Heat transfer)x∆ cicici

cc TTT

cpm ,1,1, )

2( +

+ ⋅+

⋅cicici

cc TTT

cpm ,,1, )

2( ⋅

+⋅ +

)2

)(()

2( ,,1

,,,1, cici

micscici

c

TTTxA

TTU

+−⋅∆⋅′⋅

+ ++

(Heat transfer from metal to cold fluid )

xTq ci ∆⋅′ )( ,

(Parasitic Heat transfer)

(Enthalpy transfer due to fluid flow)

(Enthalpy transfer due to fluid flow)

x∆

Fig-2 Energy flow in the control volume for the cold stream in the ith element

Fig-1 Energy flow in the control volume for metal in the ith element

cciacciaHe

cicici

micsciacciciciacc

ci VTcpT

xTqTT

TxATUTTTcpmT

⋅⋅

∆⋅′++

−⋅∆⋅′⋅+−⋅⋅=∆

++

)()(

)()2

)(()()()(

,,,,

,,,1

,,,,,,1,,

, ρ

&

From energy flow in ith element of the cold stream,

hhiahhiaHe

himihihi

hshiahhihihiahh

hi VTcpT

xTqTTT

xATUTTTcpmT

⋅⋅

∆⋅′+−+

⋅∆⋅′⋅+−⋅⋅=∆

++

)()(

)()2

)(()()()(

,,,,

,,,,1

,,,,,1,,

, ρ

&

From energy flow in ith element of the hot stream,

mmmmimimicmm

mimicmm

cicimicsciacmi

hihihshiahmi

VcpxTqTTAx

kTTA

x

k

TTTxATUT

TTxATUT

⋅⋅∆⋅′+−⋅⋅∆

−−⋅⋅∆

+

+−⋅∆⋅′⋅−−

+⋅∆⋅′⋅=∆

+−

++

ρ/])()()(

)2

)(()()

2

)(()([

,,1,,,1

,,1,,,,,

,,1,,,,

From energy flow in ith element of metal

All the above equations are implemented in Matlab and ODE23t Matlab solver is used finally to solve initial value problem of first order differential equation for Runga-Kutta method. A control program also developed to control the cold stream input temperature

(3)

(2)

(1)

Test data for HE1chamber 1 2 3

Hot Cold flow rate 9.494 43.035 0mail fin length mm 1500 1450 1050no of layer 26 21 6

In temp. Out temp. In temp. Out temp. In temp. Out temp.Actual designed result 298.02K 224.05K 218.13K 295.9KSimulation result 298.02K 230.27K 218.13K 288.98K

cold side inputtemperature

Hot side inputtemperature

cold side output temperature

Hot side outputtemperature

effectiveness cold side

effectiveness hot side

simulation result for louver fin

with input 77K 298.02K 270.2432 115.2835 0.8743 0.8696

simulation result for strip fin 77K 298.02K 249.0248 132.9657 0.7783 0.7854

Test data for HE2chamber 1 2 3

Hot Cold Coldflow rate(g/s) 45.25 9.494 43.035main fin length(mm) 1475 225 1800no of layer 15 15 15

In temp. Out temp. In temp. Out temp.In temp. Out temp.Actual designed result 224.05 73.52 73.52 57.8 56.13 218.13Simulation result 224.05 93.70 73.52 59.11 56.13 198.60

Test data for HE4

chamber 1 2 3

Hot Cold Cold

flow rate 9.494 43.035 7.577

mail fin length 1800 650 1050

no of layer 6 7 7

In temp. Out temp.In temp. Out temp.In temp.Out temp.

Actual designed result 17.11 7.02 11.06 12.57 4.34 11.06

Simulation result 17.11 7.1481 11.06 12.1026 4.34 10.1153

TABLE-4

Test setup

NomenclatureAcm Cross-sectional area of the metal A’

s Surface area for heat transfer per unit length Aw area for transverse heat conductionkm Thermal conductivity of metalTa Average temperature at ith volume element

Differential length of heat exchanger elementV volume of the element. With subscript h, c, m for hot,

cold and metal side respectively

Future Work1.Our current numerical model in not valid for multi stream HE. The numerical model is to be improved to simulate multistream HE [4].2.We have simulated our numerical model using same flow rate for both the HE stream. With constant flow at one stream and variable flow in the other stream will be considered in future work3.We have not considered flow maldistribution inside HE. With consideration of flow maldistribution for distributor fins the simulation results would have been more accurate and close to the experimental result4.The simulation is also to be performed for different modes of operation like refrigeration, liquefaction with and without LN2 pre cooling . It may be noted that for liquefaction cold return flow is different in comparison to the warm stream flow.

Value of cp is taken from HEPAK. Heat transfer conductance metal to fluid stream, U for louver fin is calculated from the formula

AhAk

t

AU owm

m

⋅⋅+

⋅⋅=

⋅ η1

21

References:

[1] Nellis GF, A heat exchanger model that includes axial consuction, parasitic heat loads, and property variations, Cryogenics 2003:43, 523-538.

[2]Achaichia, A., and T. A. Cowell. "Heat transfer and pressure drop characteristics of flat tube and louvered plate fin surfaces." Experimental Thermal and Fluid Science 1.2 (1988): 147-157

[3] Kays WM, London AL. Compact heat exchangers. 2nd ed. New York: McGraw-Hill; 1964.

[4] Mukesh Goyal, Anindya Chakravarty, M.D. Atrey. Two dimensional model for multistream plate fin heat exchangers, Cryogenics 2014

[5] Maiti TK, Pal Sandip et al Design and optimization of helium iquefaction system with targeted capacity of 50 lph without LN2, ICEC 2016 – ICMC 26, New Delhi, March 8-11, 2016.

h can be calculated from Stanton number[2], mass velocity and cp

Can be calculated from fin dimensions given in fig-3oη

Fig-3: PHFE with louvered fin

Fig-5: Corrugated Fin Geometry (Offset Strip)

Fig-6: Corrugated Fin Geometry (multi-

louvered)

Fig-7: variation of two stream temperature difference

Fig-8: Variation of effectiveness with different cold side inlet temperature

TABLE-3

TABLE-2

TABLE-1

x∆

i = 1,2,......,n-1

i = 2,3,......,n

i = 1,2,......,n-1

Objective: PFHEs after procurement has to be tested in a test set-up before placement in the cold box. It is very difficult to generate the actual conditions to be prevailed inside the cold box of helium liquefier. Therefore, the HEs are to be tested in a condition which can be easily demonstrated. We have designed a test setup to simulate the HE performance .A simulation is done based on the model of PFHE and variable cold inlet temperature. The minimum approach temperature, LMTD & effectiveness are computed and compared with the experimental results. The model will be re-evaluated according to that and will be finally used for the conditions actually prevailed in the liquefier mode of operation.

Fig-4: Temperature at different axial point