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.

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

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	$\dot{m}$ : Mass flow rate
A: Surface Area	$\rho :$ 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

   $NPASS\_HOT=\frac{L3-{\mathrm{H}}_C+\mathrm{ }2\mathrm{*}\mathrm{T}\mathrm{p}}{{\mathrm{H}}_C\mathrm{ }+\mathrm{ }{\mathrm{H}}_H+2\mathrm{*}\mathrm{T}\mathrm{p}}$

   $NPASS\_COLD=NPASS\_HOT+ 1$

   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

   $CSEC1={\mathrm{H}}_C *L1$

   $CSEC2={\mathrm{H}}_h *L1$

   For Triangular fins Configurations

   ${AO}_C=CSEC1-\left({Tf}_C *{\mathrm{H}}_C *L1 * {Fp}_C*{TER}_C\right)$ * $NPASS\_COLD$

   ${AO}_h =CSEC2-\left({Tf}_h *{\mathrm{H}}_h *L1 * {Fp}_h*{TER}_H\right)$ * $NPASS\_HOT$

   ${TER}_C= \sqrt{1+{\left(\raisebox{1ex}{$\left(\frac{1}{{Fp}_C}\right)$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_C$}\right.\right)}^2} {TER}_h= \sqrt{1+{\left(\raisebox{1ex}{$\left(\frac{1}{{Fp}_h}\right)$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_h$}\right.\right)}^2}$

   For Others:

   ${AO}_C=CSEC1-\left({Tf}_C *{\mathrm{H}}_C *L1 * {Fp}_C\right) - \left({Tf}_C *L1\right)$ * $NPASS\_COLD$

   ${AO}_h=CSEC2-\left({Tf}_h *{\mathrm{H}}_h *L1 * {Fp}_h\right) - \left({Tf}_h *L1\right)$ * $NPASS\_HOT$

   For Cross Flow

   $CSEC1={\mathrm{H}}_C *L1$

   $CSEC2={\mathrm{H}}_h *L2$

   For Triangular fins Configurations

   ${AO}_C=CSEC1-\left({Tf}_C *{\mathrm{H}}_C *L1 * {Fp}_C*{TER}_C\right)$ * $NPASS\_COLD$

   ${AO}_h=CSEC2-\left({Tf}_h *{\mathrm{H}}_h *L2 * {Fp}_h*{TER}_H\right)$ * $NPASS\_HOT$

   ${TER}_C= \sqrt{1+{\left(\raisebox{1ex}{$\left(\frac{1}{{Fp}_C}\right)$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_C$}\right.\right)}^2} {TER}_h= \sqrt{1+{\left(\raisebox{1ex}{$\left(\frac{1}{{Fp}_h}\right)$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_h$}\right.\right)}^2}$

   For Others:

   ${AO}_C=CSEC1-\left({Tf}_C *{\mathrm{H}}_C *L1 * {Fp}_C\right) - \left({Tf}_C *L1\right)$ * $NPASS\_COLD$

   ${AO}_h=CSEC2-\left({Tf}_h *{\mathrm{H}}_h *L2 * {Fp}_h\right) - \left({Tf}_h *L2\right)$ * $NPASS\_HOT$

   Hydraulic diameter Dh and Heat transfer surface area A:

   $Dh= \frac{4*AO*L}{A}$

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) = $\mathrm{G}=\frac{\dot{m}}{Minimum\mathrm{ }free\mathrm{ }flow\mathrm{ }area\mathrm{ }\left(A_o\right)}$
2. Compute Reynolds number (Re) = $Re=\left(\frac{G\mathrm{*}{D}_h}{\mu }\right)$
3. Calculate Colburn factor (j) and Friction factors (f) for various fin configurations.

Plain Rectangular & Triangular channels:

Laminar Developing & Developed Flow Correlations:

Nusselt Number:

${Nu}_{\sqrt{A}}\left(Z^{\mathrm{*}}\right)={\left[{\left(\frac{C_{4}f\left(Pr\right)}{\sqrt{Z^{\mathrm{*}}}}\right)}^m+{\left({\left\{{\left(\frac{{C_{2}C}_{3}f\left({Re}_{\sqrt{A}}\right)}{\sqrt{Z^{\mathrm{*}}}}\right)}^{\frac{1}{3}}\right\}}^5+{\left\{\left(\frac{C_{1}f\left({Re}_{\sqrt{A}}\right)}{8\sqrt{\pi }{ϵ}^y}\right)\right\}}^5\right)}^{m/5}\right]}^{1/m}$

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

$C_3=0.409$

$C_1=3.24$

$C_2=\mathrm{ }3/2$

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

$f\left(Pr\right)= \frac{0.564}{{\left(1+{\left(1.664{*Pr}^{1/6}\right)}^{9/2}\right)}^{2/9}}$

Friction Factor:

${f_{app}Re}_{\sqrt{A}}={\left[{\left(\frac{12}{\sqrt{ϵ}(1+ϵ)\left[1-\frac{192ϵ}{{\pi }^5}tanh\left(\frac{\pi }{2ϵ}\right)\right]}\right)}^2+{\left(\frac{3.44}{\sqrt{Z^{+}}}\right)}^2\right]}^{1/2}$

$Z^{\mathrm{*}}=dimensionless\mathrm{ }position\mathrm{ }for\mathrm{ }thermally\mathrm{ }develping\mathrm{ }flows\mathrm{ }$ = z/ (L RE PR)

$Z^{+}=dimensionless\mathrm{ }position\mathrm{ }for\mathrm{ }hydrodynamically\mathrm{ }develping\mathrm{ }flows\mathrm{ }$ = z/ (L RE)

L = Characteristic Length Scale

$ϵ=aspect\mathrm{ }ratio=b/a$

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:

$Nu=\frac{\frac{f}{2}\left(Re-1000\right)\mathrm{ }Pr}{1+12.7\mathrm{ }{\left(\frac{f}{2}\right)}^{1/2}\left({Pr}^{2/3}-1\right)}$

Friction Factor:

$f=A+B\mathrm{ }{Re}^{-\frac{l}{m}}$

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:

$f={\left[{\left\{\frac{\left(f{Re}_{D_h}\frac{d_h}{D_h}\right)}{{Re}_{D_h}}+1.328{\left({Re}_{D_h}\frac{W}{d_h}\right)}^{-1/2}\right\}}^3+{\left\{0.074{\left({Re}_{D_h}\frac{W}{d_h}\right)}^{-1/5}+\frac{\left(Ht+st/2\right)}{2W(H+s)}{C}_D\right\}}^3\right]}^{1/3}$

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

$s= \frac{1}{Fp}-Tf$

$D_h=\mathrm{ }\frac{4s(H-t)}{2s+2(H-t)}$

$d_h=\mathrm{ }\frac{4V_{free}}{A_{total}}=\mathrm{ }\frac{4\left(H-t\right)*W*s}{2sW+2\left(H-t\right)W+2Ht+st}$

$\epsilon =s/\left(H-t\right)$

${fRe}_{D_h}=23.94-30.05\epsilon +32.27{\epsilon }^2-12.08{\epsilon }^3$

$j=\left[{\left\{{\left(\frac{{Nu}_{D_h}{d}_h}{{Re}_{d_h}{Pr}^{1/3}{D}_h}\right)}^5+\mathrm{ }{\left(\left(\frac{0.641f{{Re}_{D_h}}^{1/3}}{{{Re}_{d_h}}^{2/3}}\right){\left(\frac{{d_h}^2}{D_{h}X}\right)}^{1/3}\right)}^5\right\}}^{7/10}+{\left\{0.037{\left({Re}_{d_h}\frac{X}{d_h}\right)}^{-1/5}\right\}}^{7/2}\right]$

${Nu}_{D_h}=7.45-16.9\epsilon +22.1{\epsilon }^2-9.75{\epsilon }^3$

To account for Prandtl Number effects $\frac{X}{W}=3.8986+9.9473{log}_{10}\left(Pr{\left(\frac{d_h}{W}\right)}^{0.15}\right)\mathrm{ }$

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

Louver Fins:

$j=0.249{{Re}_{lp}}^{-0.42}{l_h}^{0.33}{\left(\frac{l_l}{f_h}\right)}^{1.1}{f_h}^{0.26}$

${Re}_{d_h}<900\mathrm{ }\mathrm{ }=>\mathrm{ }f=5.47{{Re}_{lp}}^{-0.72}{l_h}^{0.37}{\left(\frac{l_l}{f_h}\right)}^{0.89}{l^{0.2}{f}_h}^{0.23}$

${Re}_{d_h}>900\mathrm{ }\mathrm{ }=>\mathrm{ }f=0.494{{Re}_{lp}}^{-0.39}{l_h}^{0.33}{\left(\frac{l_l}{f_h}\right)}^{1.1}{f_h}^{0.46}$

Lp - louver pitch

Ll - louver length

Fh - fin height (plate spacing)

Lh - louver height

Wavy Fins:

${10}^4<Re<10^5\mathrm{ }\mathrm{ }=>\mathrm{ }\mathrm{ }f=0.4{8Re}^{-0.36}{\left(\frac{2b}{p}\right)}^{1.5};\mathrm{ }\mathrm{ }j=0.4{Re}^{-0.36}{\left(\frac{2b}{p}\right)}^{0.75}$

$600<Re<2300\mathrm{ }=>\mathrm{ }\mathrm{ }f=5j;\mathrm{ }\mathrm{ }j=0.4{Re}^{-0.4}{\left(\frac{2b}{p}\right)}^{0.75}$

User Defined Option:

$j=\frac{\mathrm{J}\mathrm{A}}{{{Re}_{D_h}}^{\mathrm{J}\mathrm{B}}}$ $j=\frac{\mathrm{JA}}{{{Re}_{D_h}}^{\mathrm{JB}}}$

$f=\frac{\mathrm{F}\mathrm{A}}{{{Re}_{D_h}}^{\mathrm{F}\mathrm{B}}}$ $f=\frac{\mathrm{FA}}{{{Re}_{D_h}}^{\mathrm{FB}}}$

Where:

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

Step: 4 – HTC, Fin efficiency, Thermal conductance

1. HTC calculation on hot and cold side:

   $j=st\mathrm{*}{pr}^{\frac{2}{3}}$

   $st=stanton\mathrm{ }number=\frac{h}{G{c}_p}$

   $j=\frac{h}{G{c}_p}\mathrm{*}{pr}^{\frac{2}{3}}\mathrm{ }\to \mathit{h}=\mathit{j}\mathrm{*}\mathit{G}\mathrm{*}{\mathit{c}}_{\mathit{p}}\mathrm{*}{\mathit{p}\mathit{r}}^{\frac{-2}{3}}$

2. Fin efficiency:

   $\eta fin=\frac{\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(ml\right)}{ml}\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }m=\left(\frac{2h}{k\delta }\right)\frac{1}{2}$

3. Overall surface efficiency:

   ${\mathbf{\eta }}_{\mathrm{o}}=\left[1-\left(1-{\mathbf{\eta }}_{\mathrm{f}}\right)\mathrm{*}\frac{{\mathrm{A}}_{\mathrm{f}}}{\mathrm{A}}\right]$

4. Thermal conductance:

   $\frac{1}{\mathit{U}\mathit{A}}={\left(\frac{1}{{\mathit{\eta }}_{\mathit{o}}\mathrm{*}\mathit{h}\mathrm{*}\mathit{A}}\right)}_{Cold}+{\mathit{R}}_{\mathit{w}}$ + ${\left(\frac{1}{{\mathit{\eta }}_{\mathit{o}}\mathrm{*}\mathit{h}\mathrm{*}\mathit{A}}\right)}_{Hot}$

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

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

     $\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}=1-e^{\left(\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$C_{Ratio}$}\right.\right){NTU}^{0.22}{e}^{\left(-C_{Ratio}{NTU}^{0.78}-1\right)}\right)}$

   • Counter Flow

     $\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}= \frac{1-e^{-NTU\left(1-C_{Ratio}\right)}}{1-C_{Ratio}{e}^{-NTU\left(1-C_{Ratio}\right)}}$

   • Parallel Flow

     $\mathrm{E}\mathrm{f}\mathrm{f}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}= \frac{1-e^{-NTU\left(1+C_{Ratio}\right)}}{1+C_{Ratio}}$

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.

${∆P}_{Core}=\frac{4fL{G}^2}{2g_c\mathrm{*}{d}_h}\left[{\left(\frac{1}{\rho }\right)}_m\right]$

References