APH

Fixed Tubular Cross-Type Air Preheater

Inline Flow · Inline Pitch · Real-Time Optimizer

Doc Ref:APH-2024-001

CHECK CONSTRAINTS

Q = 239.2 kW · U = 5.18 W/m²·K · A = 163.4 m²

Air Inlet Face Dimensions

Enter inlet face Length (bundle width) and Breadth (tube height) — optimizer auto-adjusts tube count, rows, and height

Inlet Length (L) — Bundle Width Direction[m]

→ N_per_row = ⌊L / S_T⌋ = ⌊1.44 / 0.09⌋ = 16 tubes/row

Bundle width = 1440 mm · S_T = 90 mm (inline pitch)

Inlet Breadth (B) — Tube Height Direction[m]

→ Optimizer selects L_tube ≥ B or as required

Optimized tube height: 2.00 m

Computed Inlet Face Area

2.880m²

A_inlet = 1.44 × 2.00 = 2.880 m²

Free-flow area A_ff

1.2544 m²

N_T × (S_T − D_o) × L_tube

Optimizer Output — Tube Height & Inline Layout

Auto-optimized for minimum tube count · inline pitch · all constraints satisfied

AREA DEFICITVEL OKΔP OK

Tube Height (L_tube)

2.00m

Optimizer selected

Rows (N_rows)

32rows

Depth = 2400 mm

Tubes / Row (N_T)

16tubes

Width = 1440 mm

Total Tubes (N)

512tubes

32 × 16

A_provided

163.4m²

Required: 270.9 m²

Area Surplus

-39.7%

vs A_required

Inline Tube Arrangement (representative view)

ArrangementINLINE (in-line)

Transverse pitch S_T90 mm (P_T/D = 1.77)

Longitudinal pitch S_L75 mm (P_L/D = 1.48)

Bundle width1440 mm

Bundle depth2400 mm

Tube height (L_tube)2.00 m

Zukauskas C / m0.27 / 0.63 (inline)

Optimization Constraint Check

Area adequacy (A_prov ≥ A_req)

163.4 ≥ 270.9 m²FAIL

Shell velocity (5–12 m/s)

V_max = 6.25 m/sPASS

Shell-side Re_s > 2,300

Re_s = 5751PASS

Tube-side Re_t > 2,300

Re_t = 2676PASS

Shell ΔP ≤ 400 Pa

ΔP = 215 PaPASS

Tube ΔP (FD fan)

ΔP = 4.1 PaPASS

Thermal Analysis — Shell & Tube Side

Zukauskas (inline, shell) · Gnielinski (tube) · Resistance network · LMTD

Shell Side — Flue Gas (Cross-Flow, Inline)

ṁ_gas

4.218 kg/s

= 15,183 kg/hr

ρ_gas

0.538 kg/m³

At mean temp ~334°C

A_ff (free-flow)

1.2544 m²

N_T × (S_T−D_o) × L

G_s = ṁ/A_ff

3.363 kg/m²·s

V_max = G_s/ρ

6.250 m/s

✓ 5–12 m/s range

Re_s = G_s·D_o/μ

5751

Turbulent (inline)

Nu_s (Zukauskas inline)

56.5

C=0.27, m=0.63

h_o = Nu·k/D_o

49.70 W/m²·K

ΔP_shell (Euler)

215.2 Pa

≈ 21.9 mmH₂O

Tube Side — Cold Air (Internal Flow)

ṁ_air

1.099 kg/s

= 3,956 kg/hr

N_tubes

512

32 rows × 16/row

A_tube = N·π/4·D_i²

0.8071 m²

G_t = ṁ/A_tube

1.362 kg/m²·s

V_t = G_t/ρ

1.657 m/s

Re_t = G_t·D_i/μ

2676

⚠ Transition

Nu_t (Gnielinski)

8.8

Re > 2,300 valid

h_i = Nu·k/D_i

6.57 W/m²·K

ΔP_tube (D-W)

4.1 Pa

FD fan contribution

Resistance Network (Overall U)

Shell-side film (1/h_o)2.012e-2 · 10.4%

Shell fouling (R_fo)2.000e-4 · 0.1%

Wall conduction6.385e-5 · 0.0%

Tube fouling (R_fi·A_o/A_i)1.134e-4 · 0.1%

Tube-side film (A_o/A_i·1/h_i)1.727e-1 · 89.4%

U = 1/R_total5.18 W/m²·K

LMTD & Heat Duty

T₁ (hot gas in)361°C

T₂ (hot gas out)307°C

t₁ (cold air in)20°C

t₂ (cold air out)247°C

ΔT₁ = T₁ − t₂114°C

ΔT₂ = T₂ − t₁287°C

LMTD_CF187.4°C

F-factor0.91

LMTD_eff = F×LMTD170.5°C

Q = ṁ_g·Cp·ΔT239.2 kW

Fixed Design Parameters & Assumed Standards

All assumed values displayed — TEMA standards · ASME VIII Div.1 · Inline arrangement

Tube Geometry (Fixed)

Tube OD (D_o)	50.8 mm	Fixed per brief
Wall thickness (t)	3.0 mm	Selected optimum
Tube ID (D_i)	44.8 mm	D_o − 2t
Transverse pitch S_T	90 mm	P_T/D = 1.77 (inline)
Longitudinal pitch S_L	75 mm	P_L/D = 1.48 (inline)
Arrangement	INLINE	Zukauskas C=0.27, m=0.63
Wall conductivity k	50 W/m·K	Carbon steel A-106

Fluid Properties (Assumed at Mean T)

ρ_gas (shell)	0.538 kg/m³	~334°C mean
μ_gas	2.97×10⁻⁵ Pa·s	Flue gas
k_gas	0.0447 W/m·K
Pr_gas	0.735
Cp_gas	1050 J/kg·K
ρ_air (tube)	0.822 kg/m³	~134°C mean
μ_air	2.28×10⁻⁵ Pa·s
k_air	0.0336 W/m·K
Pr_air	0.700
Cp_air	1020 J/kg·K

Fouling & Standards (TEMA)

R_fo (shell, flue gas)	2.0×10⁻⁴ m²·K/W	TEMA Class R
R_fi (tube, clean air)	1.0×10⁻⁴ m²·K/W	TEMA Class C
F-factor (cross-flow)	0.91	Single-pass cross
Design FOS	1.5×	Applied to area
Ligament efficiency η	0.430	(90−51.3)/90

Material Zones

Hot-end tubes	A-106 Gr. B	Up to 450°C
Cold-end tubes	Corten A / 316L SS	Below acid dew pt
Tube sheet	A-516 Gr. 70, 20mm	ASME VIII
Expansion	Floating tube sheet	±12 mm axial
T_metal,min (cold end)	~81°C	⚠ Below ADP 110–160°C

Final Optimized Specification

Complete parameter set — updates live with inlet dimensions

Parameter	Value	Notes / Derivation	Status
Heat Duty Q	239.2 kW	= 205641 kcal/hr	INFO
LMTD_eff (F=0.91)	170.5°C	LMTD_CF = 187.4°C	INFO
U (resistance network)	5.18 W/m²·K	1/R_total (inline Zukauskas)	PASS
A_required	270.9 m²	Q / (U × LMTD_eff)	WARN
A_provided	163.4 m²	-39.7% surplus	FAIL
Inlet face L × B	1.44 × 2.00 m	A_inlet = 2.880 m²	INFO
Tube OD / ID	50.8 / 44.8 mm	Fixed OD, t=3mm wall	INFO
Tube arrangement	INLINE	Zukauskas C=0.27, m=0.63	INFO
Tubes per row (N_T)	16	⌊1.44 / 0.09⌋	INFO
Number of rows (N_rows)	32	Optimizer selected	INFO
Total tube count (N)	512	32 × 16	PASS
Tube height (L_tube)	2.00 m	Optimizer selected	INFO
Bundle width	1440 mm	N_T × S_T = 16 × 90	INFO
Bundle depth	2400 mm	N_rows × S_L = 32 × 75	INFO
Shell-side V_max	6.25 m/s	Acceptable: 5–12 m/s	PASS
Shell-side Re_s	5751	Turbulent (inline bank)	PASS
Tube-side V_t	1.66 m/s		INFO
Tube-side Re_t	2676	Gnielinski validity	PASS
h_o (shell-side film)	49.70 W/m²·K	Zukauskas inline	INFO
h_i (tube-side film)	6.57 W/m²·K	Gnielinski	INFO
Shell-side ΔP	215 Pa	≈ 21.9 mmH₂O	PASS
Tube-side ΔP	4.1 Pa	FD fan negligible	PASS
Cold-end material	Corten A / 316L SS	Below acid dew point	WARN
Hot-end material	A-106 Gr. B	Up to 450°C service	PASS
Thermal expansion	Floating tube sheet	±12 mm axial travel	INFO
T_metal,min (cold end)	~81°C	Below H₂SO₄ ADP 110–160°C	FAIL

Inline arrangement · Zukauskas (C=0.27, m=0.63, Re 1,000–2×10⁵) · Gnielinski (tube-side, Re=2,300–10⁶) · Pressure drop: Euler method (inline, Eu=0.32) + Darcy-Weisbach (tube) · LMTD_eff = F×LMTD_CF = 0.91×187.4 = 170.5°C · Fouling: R_fo=2×10⁻⁴, R_fi=1×10⁻⁴ m²·K/W (TEMA) · Standard: ASME Section VIII Div.1 · APH-2024-001