Plate Fin Heat Exchanger Component

Description

The Plate Fin Heat Exchanger can be used in Compressible and Incompressible (hydraulic and non-hydraulic) simulations. The component has four fluid connections and it models heat exchange between two streams in a network. Heat Exchangers in Flow Simulator come with four hidden chambers representing the four sides of the heat exchanger. The Plate Fin Heat Exchanger uses Orifice elements (Compressible or Incompressible) in the backend to model restriction losses (pressure loss) of both flow paths based on Friction Factor correlations for different Fin Configurations and characteristic flow area. The Heat addition/removal is calculated by the E-NTU method in the PlateFin Hx module, and Q (Heat Addition/Removal) is supplied to Orifice Elements to predict the temperatures of the exiting fluids.

Figure 1.
Figure 2.

Important modeling aspects when using the heat exchanger components include:

  • The Hot Side circuit must be connected to line 1 (red part in the image below) and the Cold Side circuit must be connected to line 2 (the blue part in the image below):
    Figure 3.
  • The Hot/Cold Side circuit line must be connected with either compressible or Incompressible set of elements. Mixing of elements sets for a Hot/Cold side circuit line is not allowed. Plate Fin Heat Exchanges supports following fin configurations. The Heat Transfer Coefficient and Friction factor for various configurations are calculated based on public literature which are provided in theory manual below.

Plate Fin Heat Exchanger Element Inputs

Figure 4. Plate Fin Heat Exchanger Dimension Details
Table 1. Element-Specific Plate Fin Heat Exchanger Component Input Variables
Index Field Description
1 Length in X Direction (L1) Dimensions of Heat Exchanger (Refer Image Above)
2 Length in Y Direction (L2) Dimensions of Heat Exchanger (Refer Image Above)
3 Length in Z Direction (L3) Dimensions of Heat Exchanger (Refer Image Above)
4 Number of Passages (NPASS) Number of Hot Passages
5 Flow Configurations Configuration of Heat Exchanger
  1. Parallel Flow
  2. Counter Flow
  3. Cross Flow
6 Fin Configurations Fin configurations
  1. Plain Rectangular
  2. Plain Triangular
  3. Offset Fins
  4. Wavy Rectangular
  5. Wavy Triangular
  6. Louver Rectangular
  7. Louver Triangular
  8. User-defined Rectangular
  9. User-defined Triangular
7 Fin Material Fin Material. By default, two Standard Materials are listed.
  • Stainless Steel
  • Inco 625

Any Custom Material defined using the Material Manager under the solid category is available for selection apart from the above-mentioned standard materials.

8 Fins per Inch No of Fins per Inch
9 Plate Spacing (H) Distance between Plates
10 Fin Thickness (t) Thickness of Fin (Refer to Image Above)
11 Offset Length (w) Offset Length (Used for Offset Fin Configurations)

(Refer Image in Theory Sections)

12 Wave Length (p) Wavelength (used for Wave Fin Configurations)

(Refer to Image in Theory Sections)

13 Louver Pitch (Lp) Louver Pitch (used for Louver Fin Configurations)

(Refer to Image in Theory Sections)

14 Louver Height (Lh) Louver Height (used for Louver Fin Configurations)

(Refer to Image in Theory Sections)

15 Plate Material Plate Material. By Default, two Standard Materials are listed.
  • Stainless Steel
  • Inco 625

Any Custom Material defined using the Material Manager under the solid category is available for selection apart from the above-mentioned standard materials.

16 Plate Thickness Plate Thickness (Refer to Image Above)
17 Bar/end Plate Thickness End Plate Thickness
18 Colburn J factor coefficient A J_ACOEFF Coefficient A for Colburn J factor (Refer to Equations in Theory Manual)
19 Colburn J factor coefficient B J_BCOEFF Coefficient B for Colburn J factor (Refer to Equations in Theory Manual)
20 Friction factor coefficient A F_ACOEFF Coefficient A for Friction F factor (Refer to Equations in Theory Manual)
21 Friction factor coefficient B F_BCOEFF Coefficient B for Friction F factor (Refer to Equations in Theory Manual)

Plate Fin Heat Exchanger Theory Manual

Nomenclature
H: Plate Spacing P: Wave Length
Tf: Fin Thickness Lp: Louver Pitch
W: Offset Length Lh: Louver Height
Tp: Plate Thickness Dh: Hydraulic Diameter
Fp: Fins per Inch s: Offset Spacing
AO: Free Flow Area m ˙ : Mass flow rate
A: Surface Area ρ : Density
Subscripts
in, up, 1: Upstream station C: Cold
ex, dn, 2: Downstream station H: Hot

Plate Fin Heat Exchanger uses e-NTU method to perform rating problem for a given heat exchanger. The step-by-step procedure is explained below.

Step: 1 -Surface geometrical properties

Determine geometric properties on each fluid side like:

  1. Number of passes on cold side and hot side.

    If Length in Z Direction(L3) is provided, then No of Passages (NPASS) is calculated by

    N P A S S _ H O T = L 3 - H C +   2 * T p H C   +   H H + 2 * T p  

    N P A S S _ C O L D = N P A S S _ H O T +   1

    If No. of passage of hot side is provided, then Length in Z Direction (L3) is calculated from above equation.

  2. Free-flow area

    For Parallel and Counter Flow

    C S E C 1 = H C   * L 1

    C S E C 2 = H h   * L 1

    For Triangular fins Configurations

    A O C = C S E C 1 - ( T f C   * H C   * L 1   *   F p C * T E R C ) * N P A S S _ C O L D

    A O h   = C S E C 2 - ( T f h   * H h   * L 1   *   F p h * T E R H )   * N P A S S _ H O T

    T E R C =   1 + 1 F p C H C 2                                           T E R h =   1 + 1 F p h H h 2

    For Others:

    A O C = C S E C 1 - ( T f C   * H C   * L 1   *   F p C )   -   ( T f C   * L 1 ) * N P A S S _ C O L D

    A O h = C S E C 2 - ( T f h   * H h   * L 1   *   F p h )   -   ( T f h   * L 1 ) * N P A S S _ H O T

    For Cross Flow

    C S E C 1 = H C   * L 1

    C S E C 2 = H h   * L 2

    For Triangular fins Configurations

    A O C = C S E C 1 - ( T f C   * H C   * L 1   *   F p C * T E R C )   * N P A S S _ C O L D

    A O h = C S E C 2 - ( T f h   * H h   * L 2   *   F p h * T E R H )   * N P A S S _ H O T

    T E R C =   1 + 1 F p C H C 2                                                 T E R h =   1 + 1 F p h H h 2

    For Others:

    A O C = C S E C 1 - ( T f C   * H C   * L 1   *   F p C )   -   ( T f C   * L 1 ) * N P A S S _ C O L D

    A O h = C S E C 2 - ( T f h   * H h   * L 2   *   F p h )   -   ( T f h   * L 2 ) * N P A S S _ H O T

    Hydraulic diameter Dh and Heat transfer surface area A:

    D h =   4 * A O * L A

Step: 2 – Mean Temperatures and Fluid Properties

Determine the Tout for hot and cold sides for the first iteration by assuming Heat Exchanger effectiveness ~0.75:

  1. Tmean for hot and cold sides.
  2. Dynamic viscosity for hot and cold sides @ Tmean.
  3. Prandtl number for hot and cold sides @ Tmean.
  4. Specific heat for hot and cold sides @ Tmean.

Step: 3 - Mass Velocities, Reynolds Numbers, and j and f Factors

  1. Core mass velocity (G) = G = m ˙ M i n i m u m   f r e e   f l o w   a r e a   ( A o )
  2. Compute Reynolds number (Re) = R e = G * D h μ
  3. Calculate Colburn factor (j) and Friction factors (f) for various fin configurations.

Plain Rectangular & Triangular channels:

Laminar Developing & Developed Flow Correlations:

Nusselt Number:

NuAZ*=C4fPrZ*m+C2C3fReAZ*135+C1fReA8πϵy5m/51/m

m = 2.27+1.65Pr^ (1/3)

C 3 = 0.409

C 1 = 3.24

C2= 3/2

y = 1/10 for Rectangular & 3/10 for Triangular

f P r =   0.564 1 + ( 1.664 * P r 1 / 6 ) 9 / 2 2 / 9

Friction Factor:

f a p p R e A = 12 ϵ ( 1 + ϵ ) 1 - 192 ϵ π 5 t a n h π 2 ϵ 2 + 3.44 Z + 2 1 / 2

Z * = d i m e n s i o n l e s s   p o s i t i o n   f o r   t h e r m a l l y   d e v e l p i n g   f l o w s   = z/ (L RE PR)

Z + = d i m e n s i o n l e s s   p o s i t i o n   f o r   h y d r o d y n a m i c a l l y   d e v e l p i n g   f l o w s   = z/ (L RE)

L = Characteristic Length Scale

ϵ=aspect ratio=b/a

Re and Nu are based on a characteristic dimension of the square root of the cross section area

Fully developed transitional & Turbulent flows:

Nusselt Number:

N u = f 2 R e - 1000   P r 1 + 12.7   f 2 1 / 2 P r 2 / 3 - 1

Friction Factor:

f = A + B   R e - l m

Where:

A = 0.0054, B = 2.3*10^-8, m = 2/3 for 2100<Re<4000

A = 0.00128, B = 0.1143, m = 3.2154 for 4000<Re<10^7

Offset Fins:

f = f R e D h d h D h R e D h + 1.328 R e D h W d h - 1 / 2 3 + 0.074 R e D h W d h - 1 / 5 + H t + s t / 2 2 W ( H + s ) C D 3 1 / 3

Cd = 0.88, drag coefficient due to blunt leading edges.

s =   1 F p - T f

D h =   4 s ( H - t ) 2 s + 2 ( H - t )

d h =   4 V f r e e A t o t a l =   4 H - t * W * s 2 s W + 2 H - t W + 2 H t + s t

ε = s / H - t

f R e D h = 23.94 - 30.05 ε + 32.27 ε 2 - 12.08 ε 3

j = N u D h d h R e d h P r 1 / 3 D h 5 +   0.641 f R e D h 1 / 3 R e d h 2 / 3 d h 2 D h X 1 / 3 5 7 / 10 + 0.037 R e d h X d h - 1 / 5 7 / 2

N u D h = 7.45 - 16.9 ε + 22.1 ε 2 - 9.75 ε 3

To account for Prandtl Number effects X W = 3.8986 + 9.9473 l o g 10 P r d h W 0.15  

Where:

Dh - hydraulic dia. (4.Ac/Pw)

dh - hydraulic dia. (4.Vf/At)

NuDh - Nusselt number for a rectangular channel for fully developed laminar flow

fReDh - for a rectangular channel with fully developed laminar flow
Figure 5.


Louver Fins:

j = 0.249 R e l p - 0.42 l h 0.33 l l f h 1.1 f h 0.26

R e d h < 900     = >   f = 5.47 R e l p - 0.72 l h 0.37 l l f h 0.89 l 0.2 f h 0.23

R e d h > 900     = >   f = 0.494 R e l p - 0.39 l h 0.33 l l f h 1.1 f h 0.46

Lp - louver pitch

Ll - louver length

Fh - fin height (plate spacing)

Lh - louver height

Figure 6.

Wavy Fins:

10 4 < R e < 10 ^ 5     = >     f = 0.4 8 R e - 0.36 2 b p 1.5 ;     j = 0.4 R e - 0.36 2 b p 0.75

600 < R e < 2300   = >     f = 5 j ;     j = 0.4 R e - 0.4 2 b p 0.75

Figure 7.

User Defined Option:

j=JAReDhJB j = JA R e D h JB

f=FAReDhFB f = FA R e D h FB

Where:

JA, JB, FA, FB are user-defined coefficients.

Step: 4 – HTC, Fin efficiency, Thermal conductance

  1. HTC calculation on hot and cold side:

    j = s t * p r 2 3

    s t = s t a n t o n   n u m b e r = h G c p

    j = h G c p * p r 2 3   h = j * G * c p * p r - 2 3

  2. Fin efficiency:

    η f i n = t a n h ( m l ) m l                 m = 2 h k δ 1 2

  3. Overall surface efficiency:

    η o = 1 - 1 - η f * A f A

  4. Thermal conductance:

    1 U A = 1 η o * h * A C o l d + R w + 1 η o * h * A H o t

Step: 5,6,7 NTU, Exchanger Effectiveness, and Outlet Temperatures

  1. Calculate heat capacity rates, Cmin, NTU.
  2. Calculate effectiveness (ε)
    • Cross Flow

      E f f e c t i v e n e s s = 1 - e 1 C R a t i o N T U 0.22 e - C R a t i o N T U 0.78 - 1

    • Counter Flow

      E f f e c t i v e n e s s =   1 - e - N T U 1 - C R a t i o 1 - C R a t i o e - N T U 1 - C R a t i o

    • Parallel Flow

      E f f e c t i v e n e s s =   1 - e - N T U 1 + C R a t i o 1 + C R a t i o

  3. From the new ε, calculate Heat transfer rate (q) and Tout.
  4. Calculate the fluid properties again with the obtained Tout.
  5. Repeat the steps 2-7 until the Tout equals the previous iteration.

Step-8 -Pressure drop calculations

The total pressure drop across a plate fin Hx is given by

Core pressure drop calculations considering only Skin Friction losses.

PCore=4fLG22gc*dh1ρm

Table 2. Plate Fin Heat Exchanger Component Output Variables
Name Description Units
Flow Configuration Configuration of Heat Exchanger
  1. Parallel Flow
  2. Counter Flow
  3. Cross Flow

(An echo of the user input).

(None)
Plate Material Plate Material (An echo of the user input). (None)
Plate Thickness Thickness of Plate (An echo of the user input). in, m
X_Length Length in X Direction (L1) (An echo of the user input). in, m
Y_Length Length in Y Direction (L2) (An echo of the user input). in, m
Z_Length Length in Z Direction (L3) (An echo of the user input). in, m
Plate Area Plate Area In2, m2
Effectiveness Effectiveness of Heat Exchanger (None)
NTU Number of Transfer Units (None)
Overall Conductance (UA) Overall Conductance BTU/hr.F, W/K
Q Heat Added/Rejected Btu/s, W
Wall Resistance Wall Conductive Resistance BTU/hr.F, W/K
NPASS Number of Passes (An echo of the user input). (None)
Fin Configuration Fin configurations
  1. Plain Rectangular
  2. Plain Triangular
  3. Offset Fins
  4. Wavy Rectangular
  5. Wavy Triangular
  6. Louver Rectangular
  7. Louver Triangular
  8. User-defined Rectangular
  9. User-defined Triangular

(An echo of the user input).

(None)
Fin Material Fin Material (An echo of the user input). (None)
MDOT Mass Flow Rate Lbm/s, kg/s
Plate Spacing Plate Spacing (An echo of the user input). in, m
Fin Thickness Fin Thickness (An echo of the user input). in, m
Fins_Per_In Fins Per Inch (An echo of the user input). in, m
Offset Len Offset Length (An echo of the user input). in, m
Wave_len Wave Length (An echo of the user input). in, m
Louver_pitch Louver Pitch (An echo of the user input). in, m
Louver height Lover Height (An echo of the user input). in, m
JAcoeff Colburn J factor coefficient A (An echo of the user input). (None)
JBcoeff Colburn J factor coefficient B (An echo of the user input). (None)
FAcoeff Friction factor coefficient A (An echo of the user input). (None)
FBcoeff Friction factor coefficient B (An echo of the user input). (None)
Ht_Surf_Area Heat Transfer Surface Area In2, m2
HTC Heat Transfer Coefficient BTU/hr.Ft2.F, W/m2.K
Fanning Friction Fanning Friction Factor (None)
Loss_Coeff Loss Coefficient (K) (None)
PS Static pressure psia, MPa
PT Total pressure psia, MPa
TT Total temperature of fluid deg F, deg K
RE Reynold Number (None)
Rho Density lbm/ft^3, Kg/m^3
CP Specific Heat Btu/(Lbm R), kJ/Kg.K
K Thermal Conductivity Btu/(hr ft R), W/m.K
DVISC Dynamic Viscosity Lbm/(hr ft), N s/m^2
Area Flow Area In2, m2

References

  1. Shah, R. K., & Sekulic, D. P., “Heat Exchangers,” in Handbook of Heat Transfer, Chap. 17.
  2. Muzychka, Y. S., and Yovanovich, M. M., 2004, ‘‘Laminar Forced Convection Heat Transfer in Combined Entry region of Non-Circular Ducts,’’ Journal of Heat Transfer, Transactions of ASME, Vol. 126, pp. 54–61.
  3. M. S. Bhatti and R. K. Shah, "Turbulent and Transition Convective Heat Transfer in Ducts," in Handbook of Single-Phase Convective Heat Transfer, Chapter 4, John Wiley, New York, 1987.
  4. Muzychka, Y.S., and Kenway, G. 2009., “A Model for Thermal-Hydraulic Characteristics of Offset Strip Fin Arrays for Large Prandtl Number Liquids,” Journal of Enhanced Heat Transfer, 16, 73-92.
  5. C. J. Davenport, Correlation for heat transfer and flow friction characteristics of louvered fin, AIChE Syrup. Ser. 79, 19-27 (1983).