Artoza, Christian Jelo R.
2019-01811
BSCHE 3-1
Computer Applications in ChE
Final Project
Sizing of a Plate-Fin Heat Exchanger
Operating Conditions and Geometrical Variables
The goal is to Design a direct-transfer regenerator for an open-cycle gas-turbine plant
operating at an effectiveness of 0.75355 with the following operating conditions and heat
transfer surfaces.
A. Mean Temperature Calculations and Fluid Properties
Since the exchanger effectiveness was specified in the design problem, the definition of
effectiveness was used to calculate the outlet temperature on both fluid sides.
𝜖=
𝐶ℎ 𝑇ℎ,𝑖 − 𝑇ℎ,𝑜
𝐶𝑚𝑖𝑛 𝑇ℎ,𝑖 − 𝑇𝑐,𝑖
=
𝐶𝑐 𝑇𝑐,𝑜 − 𝑇𝑐,𝑖
𝐶𝑚𝑖𝑛 𝑇ℎ,𝑖 − 𝑇𝑐,𝑖
𝐶
For the first iteration, the same heat capacities for both fluid sides were assumed so that 𝐶ℎ =
𝑚ℎ
.
𝑚𝑐
𝑐
The resulting outlet temperatures for the first iteration were then used to calculate the
mean temperature, and the heat capacity on both fluid sides. With the obtained heat
capacity, a number of iterations were carried out to determine the outlet temperatures, and
subsequently, the mean temperatures and the fluid properties were refined accordingly.
B. NTU Calculations
Both fluids were assumed to be unmixed, and the flow arrangement was set to be crossflow.
Hence, the following effectiveness-NTU relationship was used:
𝜖 = 1 − exp
1
𝐶∗
𝑁𝑇𝑈
0.22
{exp −𝐶 ∗ 𝑁𝑇𝑈
0.78
− 1}
Where 𝐶 ∗ is the capacity rate ratio. The number of transfer units for the gas and air fluid
sides, which are needed in the estimation of the mass velocities, were then estimated as
𝑁𝑇𝑈𝑎𝑖𝑟 = 𝑁𝑇𝑈𝑔𝑎𝑠 = 2𝑁𝑇𝑈.
C. Surface Basic Heat Transfer and Flow Friction Characteristics
Heat transfer and flow friction data were retrieved from Kays and London (2018). With these
data, j and f versus Re plots were constructed and appropriate curve fit models were
obtained. Since Re is unknown in the first iteration, an approximate average of the ratio of
the Colburn factor j to the friction factor f over the complete range of Re was obtained.
Subsequently, mass velocities on the two fluid sides were obtained using the core mass
velocity equation provided by Kays and London (2018):
𝐺=
𝑗
𝑓
Δ𝑃
𝑔𝑐
NTU𝑠𝑖𝑑𝑒 𝑣𝑚 Pr 2/3
Re, j and f on both fluid sides were then calculated with the mass velocities and the heat
transfer data; and heat transfer coefficients were obtained using :
ℎ = 𝑗𝐺𝑐𝑝 Pr −2/3
D. Efficiencies and Overall Coefficient
The fin efficiency and the extended surface efficiency on both fluid sides were obtained as
follows, assuming that no heat transfer occurs at the tip of each fin:
𝜂𝑓 =
tanh 𝑚𝑙
,
𝑚𝑙
𝑚=
2ℎ
,
𝑘𝑓𝛿
𝜂𝑜 = 1 − 1 − 𝜂𝑓
𝐴𝑓
𝐴
Where
𝑙=
𝑏
−𝛿
2
Assuming no fouling resistances, the gas side overall heat transfer coefficient for the first
iteration was obtained by:
1
1
=
𝑈𝑔
𝜂𝑜 ℎ
+
𝑔
𝛼𝑔 Τ𝛼𝑎
𝜂𝑜 ℎ 𝑎
The air side overall coefficient was obtained similarly.
E. Areas and Flow Lengths
F. Pressure Drops
OUTPUT
Surface Basic Heat Transfer and Flow Friction
Characteristics
Surface Characteristics
Air Side
6.35
1.11325
0.77
0.152
0.152
840
1204
0.64
0.756
401.0526316
574.8421053
0.446471842
0.442628421
Hydraulic Radius (mm)
Fin Thickness (mm)
Heat transfer area / volume between
2
3
plates (m /m )
Free flow area / frontal area
Air Side
6.35
Plate Spacing (mm)
Fin area / total area
Heat transfer area / total volume
2
3
(m /m )
Gas Side
2
Core Mass Velocity (kg/m -s)
25.14527 14.01787
Reynolds Number
3902.163 1392.759
Colburn Factor
0.007221 0.004843
Friction Factor
0.03722 0.016389
2
Heat Transfer Coefficient (W/m -K)
242.0011 91.54023
Efficiencies, Overall Coefficient, and NTU
Air Side
2
Heat Transfer Area (m )
Gas Side
Gas Side
1626.380616
2331.145549
Fin Efficiency
0.700318 0.854357
0.966384483
1.759503708
Extended Surface Efficiency
0.808203 0.889894
Frontal Area (m )
2
2.164491445
3.975125916
Overall Coefficient (W/m -K)
Flow Length (m)
1.873548523
1.020163848
2
Free Flow Area (m )
2
73.11357 51.00947
NTU
No Flow Length (m)
4.714958724
2.122
Exhanger Dimensions (m X m X m)
Fluid Properties
1.874 X 1.02 X 2.122
Air Side
Gas Side
Mean Temperature (K)
270.8086
336.9218381
Heat Capacity (kJ/kg-K)
1037.853369
1052.511023
Viscosity (Pa-s)
2.86948E-05
3.09997E-05
Thermal Conductivity (W/m-K)
0.043339889
0.047313397
Prandtl Number
0.687150368
0.689603575
0.141359314
1.959535689
0.202567512
1.492797198
0.171963413
1.726166444
3
Inlet Specific Volume (m /kg)
3
Outlet Specific Volume (m /kg)
3
Mean Specific Volume (m /kg)
Fluid_Properties - 1
'================================================================================================
'
A. MEAN TEMPERATURE CALCULATIONS AND FLUID PROPERTIES
'================================================================================================
Sub
Dim
Dim
Dim
T_o(ByVal Thi, ByVal Tci, ByVal Epsilon, ByVal mh, ByVal mc, ByVal cph, ByVal cpc, Tho, Tco)
Ch
Cc
Cmin
Ch = mh * cph
Cc = mc * cpc
Cmin = WorksheetFunction.Min(Ch, Cc)
Tho = Thi - (Epsilon * (Cmin / Ch) * (Thi - Tci))
Tho = Tci + (Epsilon * (Cmin / Cc) * (Thi - Tci))
End Sub
Sub Thermophys(ByVal Tm, cp, Mu, k, Pr)
Dim tempArr(6) As Double
Dim i As Long
For i = 0 To 6
tempArr(i) = (Tm + 273.15) ^ (6 - i)
Next
cp = WorksheetFunction.SumProduct(Range("'Air Thermophysical Properties'!$M$7:$S$7"), tempArr)
k = WorksheetFunction.SumProduct(Range("'Air Thermophysical Properties'!$M$6:$S$6"), tempArr)
Mu = (WorksheetFunction.SumProduct(Range("'Air Thermophysical Properties'!$M$8:$S$8"), tempArr)) * ((1
0) ^ (-7))
Pr = (cp * Mu) / k
End Sub
Sub SpecificVol(ByVal P_i, ByVal DeltaP, ByVal T_i, ByVal T_o, vi, vo, vm)
Dim AirConstant
AirConstant = 287.04
vi = (AirConstant * (T_i + 273.15)) / P_i
vo = (AirConstant * (T_o + 273.15)) / (P_i - DeltaP)
vm = (vi + vo) / 2
End Sub
Function Fluid_Property(ByVal Effectiveness, ByVal AirFlowRate, ByVal FuelAirRatio, ByVal inletTemp_Ai
r, ByVal inletTemp_Gas, ByVal inletPressure_Air, ByVal inletPressure_Gas, ByVal pressureDrop_Air, ByVa
l pressureDrop_Gas, ByVal Output As Boolean)
Dim m_air
Dim m_gas
Dim outletTemp_Air
Dim outletTemp_Gas
Dim meanTemp_Air
Dim meanTemp_Gas
Dim cp_air
Dim cp_gas
Dim trialCp_Air
Dim trialCp_Gas
Dim k_air
Dim k_gas
Dim mu_air
Dim mu_gas
Dim Pr_Air
Dim Pr_Gas
Dim inletSV_Air
Dim inletSV_Gas
Dim outletSV_Air
Dim outletSV_Gas
Dim meanSV_Air
Dim meanSV_Gas
Dim
Dim
Dim
Dim
gasArray(7)
airArray(7)
mainArray()
it_Array(0 To 4, 0 To 7)
m_air = AirFlowRate
m_gas = (1 + FuelAirRatio) * AirFlowRate
Fluid_Properties - 2
'============================================================
'
Iteration 1
'============================================================
If inletTemp_Air > inletTemp_Gas Then
outletTemp_Air = inletTemp_Air - (Effectiveness * (m_air / m_gas) * (inletTemp_Air - inletTemp_Gas
))
outletTemp_Gas = inletTemp_Gas + (Effectiveness * (inletTemp_Air - inletTemp_Gas))
Else
outletTemp_Air = inletTemp_Air + (Effectiveness * (m_air / m_gas) * (inletTemp_Gas - inletTemp_Air
))
outletTemp_Gas = inletTemp_Gas - (Effectiveness * (inletTemp_Gas - inletTemp_Air))
End If
meanTemp_Air = (inletTemp_Air
meanTemp_Gas = (inletTemp_Gas
Call Thermophys(meanTemp_Air,
Call Thermophys(meanTemp_Gas,
it_Array(0,
it_Array(0,
it_Array(0,
it_Array(0,
it_Array(0,
it_Array(0,
it_Array(0,
it_Array(0,
0)
1)
2)
3)
4)
5)
6)
7)
=
=
=
=
=
=
=
=
+ outletTemp_Air) / 2
+ outletTemp_Gas) / 2
cp_air, mu_air, k_air, Pr_Air)
cp_gas, mu_gas, k_gas, Pr_Gas)
1
outletTemp_Air
outletTemp_Gas
meanTemp_Air
meanTemp_Gas
cp_air
cp_gas
"-"
'============================================================
'
Subsequent Iterations
'============================================================
Dim i As Long
Dim j As Long
Dim Ch
Dim Cc
Dim Cmin
i = 1
If inletTemp_Air > inletTemp_Gas Then
Do
trialCp_Air = cp_air
trialCp_Gas = cp_gas
Ch = m_air * cp_air
Cc = m_gas * cp_gas
Cmin = WorksheetFunction.Min(Ch, Cc)
outletTemp_Air = inletTemp_Air - (Effectiveness * (Cmin / Ch) * (inletTemp_Air - inletTemp_Gas
))
outletTemp_Gas = inletTemp_Gas + (Effectiveness * (Cmin / Cc) * (inletTemp_Air - inletTemp_Gas
))
Else
meanTemp_Air = (inletTemp_Air
meanTemp_Gas = (inletTemp_Gas
Call Thermophys(meanTemp_Air,
Call Thermophys(meanTemp_Gas,
If i < 3 Then
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
Else
j = j + 1
End If
0)
1)
2)
3)
4)
5)
6)
7)
=
=
=
=
=
=
=
=
+ outletTemp_Air) / 2
+ outletTemp_Gas) / 2
cp_air, mu_air, k_air, Pr_Air)
cp_gas, mu_gas, k_gas, Pr_Gas)
i + 1
outletTemp_Air
outletTemp_Gas
meanTemp_Air
meanTemp_Gas
cp_air
cp_gas
Abs(trialCp_Gas - cp_gas)
i = i + 1
Loop Until Abs(trialCp_Air - cp_air) < 0.000001 And Abs(trialCp_Gas - cp_gas) < 0.000001
Do
Fluid_Properties - 3
s))
s))
trialCp_Air = cp_air
trialCp_Gas = cp_gas
Cc = m_air * cp_air
Ch = m_gas * cp_gas
Cmin = WorksheetFunction.Min(Ch, Cc)
outletTemp_Air = inletTemp_Air + (Effectiveness * (Cmin / Cc) * (-inletTemp_Air + inletTemp_Ga
outletTemp_Gas = inletTemp_Gas - (Effectiveness * (Cmin / Ch) * (-inletTemp_Air + inletTemp_Ga
meanTemp_Air = (inletTemp_Air
meanTemp_Gas = (inletTemp_Gas
Call Thermophys(meanTemp_Air,
Call Thermophys(meanTemp_Gas,
If i < 3 Then
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
it_Array(i,
Else
j = j + 1
End If
0)
1)
2)
3)
4)
5)
6)
7)
=
=
=
=
=
=
=
=
+ outletTemp_Air) / 2
+ outletTemp_Gas) / 2
cp_air, mu_air, k_air, Pr_Air)
cp_gas, mu_gas, k_gas, Pr_Gas)
i + 1
outletTemp_Air
outletTemp_Gas
meanTemp_Air
meanTemp_Gas
cp_air
cp_gas
Abs(trialCp_Gas - cp_gas)
i = i + 1
Loop Until Abs(trialCp_Air - cp_air) < 0.000001 And Abs(trialCp_Gas - cp_gas) < 0.000001
End If
Call SpecificVol(inletPressure_Air, pressureDrop_Air, inletTemp_Air, outletTemp_Air, inletSV_Air, outl
etSV_Air, meanSV_Air)
Call SpecificVol(inletPressure_Gas, pressureDrop_Gas, inletTemp_Gas, outletTemp_Gas, inletSV_Gas, outl
etSV_Gas, meanSV_Gas)
'Fluid Temperature Calculations Array
Dim k As Long
For k = 0 To 7
it_Array(3, k) = "---"
Next
it_Array(4,
it_Array(4,
it_Array(4,
it_Array(4,
it_Array(4,
it_Array(4,
it_Array(4,
it_Array(4,
0)
1)
2)
3)
4)
5)
6)
7)
=
=
=
=
=
=
=
=
i
outletTemp_Air
outletTemp_Gas
meanTemp_Air
meanTemp_Gas
cp_air
cp_gas
Abs(trialCp_Gas - cp_gas)
'Fluid Properties Array
airArray(0) = meanTemp_Air
airArray(1) = cp_air
airArray(2) = mu_air
airArray(3) = k_air
airArray(4) = Pr_Air
airArray(5) = inletSV_Air
airArray(6) = outletSV_Air
airArray(7) = meanSV_Air
gasArray(0)
gasArray(1)
gasArray(2)
gasArray(3)
gasArray(4)
gasArray(5)
gasArray(6)
gasArray(7)
=
=
=
=
=
=
=
=
meanTemp_Gas
cp_gas
mu_gas
k_gas
Pr_Gas
inletSV_Gas
outletSV_Gas
meanSV_Gas
Fluid_Properties - 4
ReDim mainArray(1)
mainArray(0) = airArray
mainArray(1) = gasArray
If Output = True Then
Fluid_Property = mainArray
Else
Fluid_Property = it_Array
End If
End Function
Module2 - 1
'================================================================================================
'
B. NTU CALCULATIONS
'================================================================================================
Function NTUCalculations(ByVal Epsilon, ByVal c)
Dim itArr(0 To 4, 0 To 4)
Dim trialNTU
Dim i
Dim j
Dim k
Dim a
Dim b
NTU = 10
Do
If i < 3 Then
itArr(i, 0) =
itArr(i, 1) =
itArr(i, 2) =
itArr(i, 3) =
If i = 0 Then
itArr(i, 4) =
Else
itArr(i, 4) =
End If
Else
j = j + 1
End If
i + 1
NTU
2 * NTU
2 * NTU
"-"
Abs(NTU - trialNTU)
trialNTU = NTU
a = c * WorksheetFunction.Ln(1 - Epsilon)
b = Exp(-c * ((NTU) ^ 0.78)) - 1
NTU = (a / b) ^ (1 / 0.22)
i = i + 1
Loop Until Abs(NTU - trialNTU) < (10) ^ (-6)
For k = 0 To 4
itArr(3, k) = "---"
Next
itArr(4,
itArr(4,
itArr(4,
itArr(4,
itArr(4,
0)
1)
2)
3)
4)
=
=
=
=
=
i + 1
NTU
2 * NTU
2 * NTU
Abs(NTU - trialNTU)
NTUCalculations = itArr
End Function
'================================================================================================
'
C. SURFACE BASIC HEAT TRANSFER AND FLOW FRICTION CHARACTERISTICS
'================================================================================================
Sub jOverf(ByVal FinType, ByVal Designation, jOverf)
If FinType = "Plain" Then
If Designation = 2 Then
jOverf = ""
ElseIf Designation = 5.3 Then
jOverf = ""
Else
jOverf = 0.321498799
End If
ElseIf FinType = "Louvered" Then
If Designation = "3/8-6.06" Then
jOverf = 0.200091237
ElseIf Designation = "3/8-8.7" Then
jOverf = ""
Else
jOverf = ""
End If
Else
Module2 - 2
jOverf = 0
End If
End Sub
Sub HeatTransferCoefficient(ByVal plateThickness, ByVal FinType, ByVal Designation, ByVal hydraulicRad
ius, ByVal MassVelocity, ByVal cp, ByVal Pr, ByVal Mu, Re, Colburn, Friction, HCoeff)
'Reynolds Number
Re = (MassVelocity * (4 * (hydraulicRadius * ((10) ^ (-3))))) / Mu
'j and f Factors
If FinType = "Plain" Then
If Designation = 2 Then
Colburn = ""
Friction = ""
ElseIf Deisgnation = 5.3 Then
Colburn = ""
Friction = ""
Else
Colburn = (2.504 / Re) + 0.003045
Friction = (13.388 / Re) + 0.006776
End If
ElseIf FinType = "Louvered" Then
If Designation = "3/8-6.06" Then
Colburn = (5.213 / Re) + 0.005885
Friction = (21.871 / Re) + 0.031615
ElseIf Designation = "3/8-8.7" Then
Colburn = ""
Friction = ""
Else
Colburn = ""
Friction = ""
End If
Else
Colburn = ""
Friction = ""
End If
'Heat Transfer Coefficients
HCoeff = Colburn * cp * MassVelocity * ((Pr) ^ (-2 / 3))
End Sub
'=======================================================
'
ITERATION 1
'=======================================================
'Average j/f
Dim jOverf_Air
Dim jOverf_Gas
Call jOverf(FinType_Air, Designation_Air, jOverf_Air)
Call jOverf(FinType_Gas, Designation_Gas, jOverf_Gas)
'Core Mass Velociy
Dim MassVelocity_Air
Dim MassVelocity_Gas
MassVelocity_Air = ((jOverf_Air) * (pressureDrop_Air / (2 * NTU)) * (1 / (meanSV_Air * ((Pr_Air) ^ (2
/ 3))))) ^ (1 / 2)
MassVelocity_Gas = ((jOverf_Gas) * (pressureDrop_Gas / (2 * NTU)) * (1 / (meanSV_Gas * ((Pr_Gas) ^ (2
/ 3))))) ^ (1 / 2)
'Reynolds Number, j, f, Heat Transfer Coefficient
Dim HydraulicRadius_Air
Dim HydraulicRadius_Gas
Dim Re_Air
Dim Re_Gas
Dim Colburn_Air
Dim Colburn_Gas
Dim Friction_Air
Dim Friction_Gas
Dim HCoeff_Air
Dim HCoeff_Gas
HydraulicRadius_Air = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Ga
Module2 - 3
s, Designation_Air, Designation_Gas), 1, 2)
HydraulicRadius_Gas = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Ga
s, Designation_Air, Designation_Gas), 2, 2)
Call HeatTransferCoefficient(plateThickness, FinType_Air, Designation_Air, HydraulicRadius_Air, MassVe
locity_Air, cp_air, Pr_Air, mu_air, Re_Air, Colburn_Air, Friction_Air, HCoeff_Air)
Call HeatTransferCoefficient(plateThickness, FinType_Gas, Designation_Gas, HydraulicRadius_Gas, MassVe
locity_Gas, cp_gas, Pr_Gas, mu_gas, Re_Gas, Colburn_Gas, Friction_Gas, HCoeff_Gas)
'================================================================================================
'
D. EFFICIENCIES AND OVERALL COEFFICIENT
'================================================================================================
Sub Efficiencies(ByVal HCoeff, ByVal finConductivity, ByVal finThickness, ByVal plateSpacing, ByVal Af
OverA, Etaf, Eta0)
Dim m
Dim l
m = ((2 * HCoeff) / (finConductivity * (finThickness * ((10) ^ (-3))))) ^ (1 / 2)
l = ((plateSpacing / 2) - finThickness) * ((10) ^ (-3))
Etaf = WorksheetFunction.Tanh(m * l) / (m * l)
Eta0 = 1 - ((AfOverA) * (1 - Etaf))
End Sub
'=======================================================
'
ITERATION 1
'=======================================================
'Efficiencies
Dim AfOverA_Air
Dim AfOverA_Gas
Dim finThickness_Air
Dim finThickness_Gas
Dim plateSpacing_Air
Dim plateSpacing_Gas
Dim Etaf_Air
Dim Etaf_Gas
Dim Eta0_Air
Dim Eta0_Gas
plateSpacing_Air = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas,
Designation_Air, Designation_Gas), 1, 1)
AfOverA_Air = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Desig
nation_Air, Designation_Gas), 1, 5)
finThickness_Air = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas,
Designation_Air, Designation_Gas), 1, 3)
plateSpacing_Gas = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas,
Designation_Air, Designation_Gas), 2, 1)
AfOverA_Gas = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Desig
nation_Air, Designation_Gas), 2, 5)
finThickness_Gas = WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas,
Designation_Air, Designation_Gas), 2, 3)
Call Efficiencies(HCoeff_Air, finConductivity, finThickness_Air, plateSpacing_Air, AfOverA_Air, Etaf_A
ir, Eta0_Air)
Call Efficiencies(HCoeff_Gas, finConductivity, finThickness_Gas, plateSpacing_Gas, AfOverA_Gas, Etaf_G
as, Eta0_Gas)
'Overall Coefficient
Dim TResist_Air
Dim TResist_Gas
Dim Alpha_Air
Dim Alpha_Gas
Dim Overallcoeff_Air
Dim OverallCoeff_Gas
Alpha_Air
tion_Air,
Alpha_Gas
tion_Air,
= WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Designa
Designation_Gas), 1, 6)
= WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Designa
Designation_Gas), 2, 6)
TResist_Air = 1 / (Eta0_Air * HCoeff_Air)
TResist_Gas = 1 / (Eta0_Gas * HCoeff_Gas)
Module2 - 4
Overallcoeff_Air = (TResist_Air + ((Alpha_Air / Alpha_Gas) * TResist_Gas)) ^ (-1)
OverallCoeff_Gas = (TResist_Gas + ((Alpha_Gas / Alpha_Air) * TResist_Air)) ^ (-1)
'================================================================================================
'
E. AREAS AND FLOW LENGTHS
'================================================================================================
'=======================================================
'
ITERATION 1
'=======================================================
'Areas
Dim Sigma_Air
Dim Sigma_Gas
Dim HTransferA_Air
Dim HTransferA_Gas
Dim FlowA_Air
Dim FlowA_Gas
Dim FrontalA_Air
Dim FrontalA_Gas
Dim FlowL_Air
Dim FlowL_Gas
Dim NoFlowL
Sigma_Air
tion_Air,
Sigma_Gas
tion_Air,
= WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Designa
Designation_Gas), 1, 7)
= WorksheetFunction.Index(Surface_Geometry(plateThickness, FinType_Air, FinType_Gas, Designa
Designation_Gas), 2, 7)
If C_Air > C_Gas Then
HTransferA_Gas = (C_Gas * NTU) / OverallCoeff_Gas
HTransferA_Air = HTransferA_Gas * (Alpha_Air / Alpha_Gas)
Else
HTransferA_Air = (C_Air * NTU) / Overallcoeff_Air
HTransferA_Gas = HTransferA_Air * (Alpha_Gas / Alpha_Air)
End If
FlowA_Air = AirFlowRate / MassVelocity_Air
FlowA_Gas = ((1 + FuelAirRatio) * AirFlowRate) / MassVelocity_Gas
FrontalA_Air = FlowA_Air / Sigma_Air
FrontalA_Gas = FlowA_Gas / Sigma_Gas
FlowL_Air = ((HydraulicRadius_Air) * ((10) ^ (-3)) * HTransferA_Air) / FlowA_Air
FlowL_Gas = (HydraulicRadius_Gas * ((10) ^ (-3)) * HTransferA_Gas) / FlowA_Gas
NoFlowL = FrontalA_Air / FlowL_Gas
'================================================================================================
'
F. PRESSURE DROP CALCULATIONS
'================================================================================================
Sub PressureDropCalc(ByVal inletPressure, ByVal MassVelocity, ByVal inletSV, ByVal outletSV, ByVal mea
nSV, ByVal Friction, ByVal HTransferA, ByVal FlowA, pressureDrop, MomentumEffect, CoreFriction)
Dim Factor
Factor = (((MassVelocity) ^ 2) / 2) * (inletSV / inletPressure)
MomentumEffect = 2 * ((outletSV / inletSV) - 1)
CoreFriction = Friction * (HTransferA / FlowA) * (meanSV / inletSV)
pressureDrop = inletPressure * Factor * (MomentumEffect + CoreFriction)
End Sub
'=======================================================
'
ITERATION 1
'=======================================================
'Pressure Drop
Dim pressureDrop1_Air
Dim pressureDrop1_Gas
Dim MomentumEffect_AIr
Dim MomentumEFfect_Gas
Dim CoreFriction_Air
Dim CoreFriction_Gas
Call PressureDropCalc(inletPressure_Air, MassVelocity_Air, inletSV_Air, outletSV_Air, meanSV_Air, Fric
Module2 - 5
tion_Air, HTransferA_Air, FlowA_Air, pressureDrop1_Air, MomentumEffect_AIr, CoreFriction_Air)
Call PressureDropCalc(inletPressure_Gas, MassVelocity_Gas, inletSV_Gas, outletSV_Gas, meanSV_Gas, Fric
tion_Gas, HTransferA_Gas, FlowA_Gas, pressureDrop1_Gas, MomentumEFfect_Gas, CoreFriction_Gas)
'================================================================================================
'
G. SUBSEQUENT ITERATIONS
'================================================================================================
Sub PressureDropCalc(ByVal inletPressure, ByVal MassVelocity, ByVal inletSV, ByVal outletSV, ByVal mea
nSV, ByVal Friction, ByVal HTransferA, ByVal FlowA, pressureDrop, MomentumEffect, CoreFriction)
Dim Factor
Factor = (((MassVelocity) ^ 2) / 2) * (inletSV / inletPressure)
MomentumEffect = 2 * ((outletSV / inletSV) - 1)
CoreFriction = Friction * (HTransferA / FlowA) * (meanSV / inletSV)
pressureDrop = inletPressure * Factor * (MomentumEffect + CoreFriction)
End Sub
Sub MassVelocityCalc(ByVal pressureDrop, ByVal inletSV, ByVal outletSV, ByVal meanSV, ByVal HTransferA
, ByVal FlowA, ByVal Friction, MassVelocity)
Dim a
Dim b
Dim c
Dim d
a
b
c
d
=
=
=
=
(2 * pressureDrop) / inletSV
2 * ((outletSV / inletSV) - 1)
Friction * (HTransferA / FlowA) * (meanSV / inletSV)
a / (b + c)
MassVelocity = (d) ^ (1 / 2)
End Sub
Sub OverallCoefficient(ByVal Eta0_1, ByVal Eta0_2, ByVal HTransferCoeff_1, ByVal HTransferCoeff_2, ByV
al HTransferA_1, ByVal HTransferA_2, OverallCoeff)
Dim a
Dim b
Dim c
a = 1 / (Eta0_1 * HTransferCoeff_1)
b = (HTransferA_1 / HTransferA_2) * (1 / (Eta0_2 * HTransferCoeff_2))
c = a + b
OverallCoeff = (c) ^ (-1)
End Sub
Dim trialG_Air
Dim trialG_Gas
Dim i
Do
'Mass Velocity
Call MassVelocityCalc(pressureDrop_Air, inletSV_Air, outletSV_Air, meanSV_Air, HTransferA_Air, Flo
wA_Air, Friction_Air, MassVelocity_Air)
Call MassVelocityCalc(pressureDrop_Gas, inletSV_Gas, outletSV_Gas, meanSV_Gas, HTransferA_Gas, Flo
wA_Gas, Friction_Gas, MassVelocity_Gas)
'Reynolds Number, j, f, Heat Transfer Coefficient
Call HeatTransferCoefficient(plateThickness, FinType_Air, Designation_Air, HydraulicRadius_Air, Ma
ssVelocity_Air, cp_air, Pr_Air, mu_air, Re_Air, Colburn_Air, Friction_Air, HCoeff_Air)
Call HeatTransferCoefficient(plateThickness, FinType_Gas, Designation_Gas, HydraulicRadius_Gas, Ma
ssVelocity_Gas, cp_gas, Pr_Gas, mu_gas, Re_Gas, Colburn_Gas, Friction_Gas, HCoeff_Gas)
'Efficiencies
Call Efficiencies(HCoeff_Air, finConductivity, finThickness_Air, plateSpacing_Air, AfOverA_Air, Et
af_Air, Eta0_Air)
Call Efficiencies(HCoeff_Gas, finConductivity, finThickness_Gas, plateSpacing_Gas, AfOverA_Gas, Et
af_Gas, Eta0_Gas)
'Overall Coefficient
Call OverallCoefficient(Eta0_Air, Eta0_Gas, HCoeff_Air, HCoeff_Gas, HTransferA_Air, HTransferA_Gas
Module2 - 6
, Overallcoeff_Air)
Call OverallCoefficient(Eta0_Gas, Eta0_Air, HCoeff_Gas, HCoeff_Air, HTransferA_Gas, HTransferA_Air
, OverallCoeff_Gas)
'Areas
If C_Air > C_Gas Then
HTransferA_Gas = (C_Gas * NTU) / OverallCoeff_Gas
HTransferA_Air = HTransferA_Gas * (Alpha_Air / Alpha_Gas)
Else
HTransferA_Air = (C_Air * NTU) / Overallcoeff_Air
HTransferA_Gas = HTransferA_Air * (Alpha_Gas / Alpha_Air)
End If
FlowA_Air = AirFlowRate / MassVelocity_Air
FlowA_Gas = ((1 + FuelAirRatio) * AirFlowRate) / MassVelocity_Gas
FrontalA_Air = FlowA_Air / Sigma_Air
FrontalA_Gas = FlowA_Gas / Sigma_Gas
FlowL_Air = ((HydraulicRadius_Air) * ((10) ^ (-3)) * HTransferA_Air) / FlowA_Air
FlowL_Gas = (HydraulicRadius_Gas * ((10) ^ (-3)) * HTransferA_Gas) / FlowA_Gas
NoFlowL = FrontalA_Air / FlowL_Gas
'PressureDrop
Call PressureDropCalc(inletPressure_Air, MassVelocity_Air, inletSV_Air, outletSV_Air, meanSV_Air,
Friction_Air, HTransferA_Air, FlowA_Air, pressureDrop1_Air, MomentumEffect_AIr, CoreFriction_Air)
Call PressureDropCalc(inletPressure_Gas, MassVelocity_Gas, inletSV_Gas, outletSV_Gas, meanSV_Gas,
Friction_Gas, HTransferA_Gas, FlowA_Gas, pressureDrop1_Gas, MomentumEFfect_Gas, CoreFriction_Gas)
i = i + 1
Loop Until Abs(pressureDrop_Air - pressureDrop1_Air) < 0.000001 And Abs(pressureDrop_Gas - pressureDro
p1_Gas) < 0.000001