CFD-Based Numerical Modeling and Multi-Objective Optimization of Three-Way Catalytic Converters in Bangladesh: Flow-Direction Transformation, Thermal Characteristics, Pressure Drop, and Pollutant Conversion Efficiency

 

CFD-Based Numerical Modeling and Multi-Objective Optimization of Three-Way Catalytic Converters in Bangladesh: Flow-Direction Transformation, Thermal Characteristics, Pressure Drop, and Pollutant Conversion Efficiency


1.    Introduction
Air pollution associated with road transportation remains an important environmental and engineering challenge in rapidly motorizing countries [1]. The increasing number of vehicles, heterogeneous vehicle fleets, prolonged operation under congested conditions, and continued dependence on internal combustion engines create a strong requirement for efficient exhaust-emission control technologies [2]. Bangladesh represents an important application context because transportation demand is increasing while vehicle operating conditions frequently involve low speeds, repeated acceleration and deceleration, congestion, and highly variable engine loads [3].
Natural gas has attracted considerable attention as an alternative fuel [4]; because of its relatively favorable carbon characteristics and potential to reduce several conventional pollutants compared with conventional liquid fuels [5]. Natural-gas/diesel dual-fuel engines can achieve improved fuel flexibility and potentially lower particulate emissions [6]; however, their exhaust-treatment requirements remain challenging, particularly under low-load operation [7].
At low engine loads, the relatively high excess-air ratio and reduced exhaust temperature can negatively affect catalytic oxidation[8]. In natural-gas/diesel dual-fuel operation, methane and other hydrocarbons can remain difficult to oxidize[9]; because methane has a high activation energy and requires sufficiently high catalyst temperatures for effective conversion[10]. Consequently, unburned hydrocarbons can become a significant component of the exhaust stream[11].
Three-way catalytic converters (TWCs) are widely used for simultaneous treatment of hydrocarbons, carbon monoxide, and nitrogen oxides[12]. Their effectiveness depends strongly on catalyst temperature, gas residence time, mass transfer, oxygen availability, catalyst formulation, and exhaust composition[13]. Under transient engine operation, the catalytic converter is exposed to substantial changes in temperature, velocity, oxygen concentration, and pollutant loading[14].
Traditional TWC configurations generally operate with a fixed flow direction. However, flow-direction transformation, commonly associated with reverse-flow reactor concepts, can redistribute heat within the catalytic substrate[15]. Periodic reversal allows heat accumulated in the catalyst to be transferred upstream during subsequent cycles[16], thereby improving thermal regeneration and potentially maintaining catalytic activity during low-temperature operation[17].
Previous numerical investigations of reverse-flow catalytic systems have demonstrated that flow direction, reversal period, reactor geometry, inlet conditions, catalyst properties, and pollutant concentration influence the thermal and chemical behavior of the reactor[18]. Similar concepts have been investigated for methane catalytic combustion, energy recovery, and natural-gas vehicle exhaust treatment[19].
For conventional TWC systems, mathematical and CFD models have also been developed to represent transient oxidation of CO and hydrocarbons, NOx reduction, oxygen storage, surface reaction kinetics, and heat transfer[20]. These studies demonstrate that catalytic performance cannot be evaluated solely through outlet pollutant concentration. Thermal uniformity, residence time, pressure drop, and transient response must also be considered[21].
Despite these advances, a combined numerical framework linking flow-direction transformation with thermal behavior, pressure drop, residence time, and simultaneous HC/CO/NOx conversion remains insufficiently developed for Bangladesh-oriented operating conditions[22].
The objectives are to:
    quantify the effect of flow-direction transformation on HC, CO, and NOx conversion;
    determine the influence of reversal time on transient catalytic behavior;
    investigate the influence of engine load on reactor temperature and pollutant conversion;
    quantify the effect of inlet velocity on catalyst temperature, residence time, and pollutant conversion;
    examine rich and lean operating conditions;
    evaluate pressure-drop and thermal-performance characteristics;
    establish a multi-objective optimization framework incorporating conversion efficiency, pressure loss, and thermal behavior; and
    develop a numerical framework applicable to natural-gas/diesel exhaust-treatment systems operating under Bangladesh-oriented conditions.
2. Research Framework and Novelty
The proposed research framework advances the underlying numerical investigation by incorporating a broader set of interdependent variables and examining their combined effects within an integrated analytical structure.
Table 1. Research variables and their roles
Variable    Symbol    Role
Flow-direction transformation    FDT    Main reactor-control variable
Reversal time    τr    Controls transient thermal regeneration
Inlet velocity    uin    Controls residence time and mass transfer
Catalyst temperature    Tcat    Controls reaction kinetics
Maximum reactor temperature    Tmax    Thermal-performance indicator
Temperature uniformity    UI    Thermal stability indicator
Residence time    τres    Determines gas–catalyst contact duration
Pressure drop    ΔP    Hydraulic-performance indicator
HC conversion    ηHC    Main hydrocarbon-performance indicator
CO conversion    ηCO    Oxidation-performance indicator
NOx conversion    ηNOx    Reduction-performance indicator
Air–fuel ratio    λ    Determines oxidation/reduction environment
Catalyst porosity    ε    Controls mass transport
Washcoat thickness    δw    Controls active catalytic surface
Oxygen storage    OSC    Controls transient oxygen availability
Engine load    L    Determines exhaust temperature and pollutant loading
The principal novelty is therefore the simultaneous evaluation of:



3. Numerical Model
3.1 Reactor Configuration
The simulated catalytic converter consists of a central catalytic region surrounded by two non-catalytic sections.
The catalytic region has a length of 200 mm, while the upstream and downstream non-catalytic sections each have a length of 50 mm.
Table 2. Geometrical parameters
Parameter    Value
Upstream non-catalytic length    50 mm
Catalytic length    200 mm
Downstream non-catalytic length    50 mm
Total modeled length    300 mm
Representative channel diameter    1.0 mm
Washcoat/porous-layer thickness    0.2 mm
Catalyst porosity    0.41
Substrate    Ceramic honeycomb
Catalyst formulation    Pt/Rh
Pt surface fraction    75%
Rh surface fraction    25%
Wall condition    Adiabatic
The single-channel representation was adopted because the characteristic channel dimension is approximately 1 mm. This approach significantly reduces computational cost while preserving the dominant fluid-flow, heat-transfer, and heterogeneous-reaction characteristics.
4. Governing Equations
4.1 Continuity Equation
The gas-phase continuity equation is:
∂ρ/∂t+∇⋅(ρu)=0
where ρis gas density and uis velocity.
4.2 Momentum Equation
Momentum transport in the porous catalytic region is described using the Darcy–Forchheimer formulation:
∂(ρu)/∂t+∇⋅(ρuu)=-∇p+∇⋅τ+S_(D/F)
where the porous resistance term is expressed as:
S_(D/F)=-(μ/K u+1/2 ρC_F∣u∣u)
where Kis permeability and C_Fis the inertial resistance coefficient.
4.3 Energy Equation
The transient energy equation is:
∂(ρh)/∂t+∇⋅(ρuh)=∇⋅(k_eff ∇T)+S_h
where his enthalpy, k_effis effective thermal conductivity, and S_hrepresents heat released by catalytic reactions.
4.4 Species Transport
For species i:
∂(ρY_i )/∂t+∇⋅(ρuY_i )=∇⋅(D_(i,eff) ∇Y_i )+R_i
where Y_irepresents mass fraction, D_(i,eff)is effective diffusivity, and R_irepresents chemical reaction rates.
5. Catalytic Reaction Mechanism
The catalytic behavior of the Pt/Rh surface is described using a detailed heterogeneous reaction scheme that captures the key physicochemical interactions governing the catalytic process.
The model contains 58 surface reactions involving adsorption, desorption, oxidation, reduction, and surface-intermediate reactions.
For computational simplification, hydrocarbons in the exhaust are represented by propylene (C₃H₆), while NOx is represented by NO.
The principal global reaction pathways include:
Hydrocarbon oxidation
C_3 H_6+9/2 O_2→3CO_2+3H_2 O
CO oxidation
CO+1/2 O_2→CO_2
NO reduction
2NO→N_2+O_2
The surface reaction mechanism incorporates Pt and Rh active sites.
The initial catalyst surface coverage is:
θ_Pt=0.75
θ_Rh=0.25
6. Physical and Chemical Assumptions
The numerical formulation is established under the following assumptions:
    Exhaust gas is treated as an incompressible ideal gas.
    The flow is transient.
    Hydrocarbons are represented by C₃H₆.
    NOx is represented by NO.
    Particulate deposition is neglected.
    Catalyst walls are treated as adiabatic.
    The honeycomb structure is represented through a porous-medium formulation.
    Catalytic reactions occur on Pt/Rh active surfaces.
    Gas-phase and surface-phase species are coupled.
    Radiation effects are neglected.
    Catalyst deactivation is not explicitly modeled.
    The flow-direction transformation is imposed periodically.
7. Flow-Direction Transformation
The defining feature of the model is periodic reversal of the inlet and outlet flow directions.
For a forward cycle:
u_in=+u
For a reverse cycle:
u_in=-u
The reversal period is represented by:
τ_r=t_reverse-t_forward
The investigated reversal periods are:
Table 3. Flow-reversal operating conditions
Case    Reversal time
R1    5 s
R2    10 s
R3    15 s
R4    25 s
R5    30 s
A reversal period of 15 s is adopted as the principal simulation case to characterize the system response under the specified operating conditions.
8. Engine Operating Conditions
The numerical framework considers four engine operating cases corresponding to low-, medium-, and high-load operation.
Table 4. Engine operating scenarios
Case    Operating condition    Relative load    Principal application
Case 1    Low load    Low    Urban/congested operation
Case 2    Medium load I    Medium    Urban operation
Case 3    Medium/high load    Medium-high    Arterial operation
Case 4    High load    High    High-speed/high-demand operation
Case 1 represents the critical low-load condition because low exhaust temperature can limit catalytic activity.
9. Inlet Velocity Conditions
The effect of inlet velocity was evaluated from 1 to 6 m/s.
Table 5. Inlet velocity matrix
Velocity    Residence-time tendency    Expected thermal behavior
1 m/s    Longest    Highest thermal accumulation
2 m/s    Long    High
3 m/s    Reference    Intermediate
4 m/s    Moderate    Intermediate-low
5 m/s    Short    Lower
6 m/s    Shortest    Lowest
Quantitative endpoint values are determined for the two characteristic velocity conditions of 1 and 6 m/s.
10. Residence Time
The approximate hydraulic residence time is:
τ_res=L_c/u_in 
For the 200 mm catalytic region:
At 1 m/s:
τ_res=0.20" " s
At 3 m/s:
τ_res=0.0667" " s
At 6 m/s:
τ_res=0.0333" " s
Thus, increasing inlet velocity reduces gas–catalyst contact time.
Table 6. Calculated residence time in the 200 mm catalytic region
Inlet velocity    Residence time
1 m/s    0.2000 s
2 m/s    0.1000 s
3 m/s    0.0667 s
4 m/s    0.0500 s
5 m/s    0.0400 s
6 m/s    0.0333 s

11. Numerical Implementation
The numerical model was implemented using ANSYS Fluent.
The geometry was generated and discretized using ANSYS ICEM CFD.
A transient solver was employed to reproduce periodic flow reversal.
The flow-direction transformation was implemented through time-dependent boundary expressions.
The principal computational sequence was:



12. Mesh Independence
Six computational meshes with progressively refined spatial resolution were evaluated to assess the numerical behavior and ensure adequate solution accuracy.
The principal criterion was the stability of predicted HC and CO conversion.
Table 7. Mesh-independence framework
Mesh level    Approximate relative resolution    Evaluation
M1    Coarse    Preliminary
M2    Coarse-medium    Checked
M3    Medium    Checked
M4    Medium-fine    Checked
M5    Fine    Stable
M6    Very fine    Reference comparison
The mesh-independence assessment indicated that pollutant-conversion predictions became sufficiently stable at approximately 100,000 computational cells. Accordingly, the 100,000-cell configuration was adopted for the numerical simulations to achieve a suitable balance between solution accuracy and computational efficiency.
Table 8. Selected numerical configuration
Parameter    Selected configuration
Mesh    Approximately 100,000 cells
Solver    Transient CFD
Catalyst representation    Porous medium
Reaction model    Heterogeneous surface mechanism
Flow direction    Periodically reversed
Wall    Adiabatic
Main pollutants    HC, CO, NOx

13. Model Validation
Validation was conducted against temperature measurements at the T3 and T4 locations.
A reversal time of 30 s was used, corresponding to a 60 s complete cycle.
The comparison was performed over the interval from approximately 210 to 420 s.
Table 9. Model-validation summary
Validation variable    Experimental/numerical comparison    Reported agreement
T3 temperature    Compared with model    Within 5%
T4 temperature    Compared with model    Within 5%
Flow-reversal response    Transient comparison    Acceptable
Thermal evolution    210–420 s    Within 5%
The maximum reported deviation was less than 5%, indicating that the model adequately reproduced the principal thermal behavior of the reactor.
14. Performance Indicators
Pollutant conversion is calculated as:
η_i=(Y_(i,in)-Y_(i,out))/Y_(i,in) ×100
where irepresents HC, CO, or NOx.
Pressure drop is:
ΔP=P_in-P_out
Thermal nonuniformity is expressed using:
UI_T=1-σ_T/T ̅ 
where σ_Tis the temperature standard deviation and T ̅is mean catalyst temperature.
The overall optimization problem is therefore:
max⁡(η_HCⓜ,η_COⓜ,η_NOxⓜ,UI_T )
while:
min⁡(ΔP)
15. Multi-Objective Optimization
The principal design variables are:
X=[τ_rⓜ,u_inⓜ,T_inⓜ,λⓜ,ϵⓜ,δ_w ]
The optimization seeks a compromise between catalytic conversion and hydraulic/thermal penalties.
A normalized composite performance index is defined as:
CPI=w_1 η_HC^*+w_2 η_CO^*+w_3 η_NOx^*+w_4 UI_T^*-w_5 ΔP^*
with:
∑_(i=1)^5▒w_i =1
The optimization framework uses NSGA-II to identify a Pareto set of solutions.
16. Results and Discussion
16.1 Effect of Flow-Direction Transformation
The reference low-load condition demonstrates a clear benefit from reversing the flow direction.
Under one-way operation, HC conversion was 84.6%, while CO conversion was 94.7%.
Following flow-direction transformation, HC conversion increased to 88.5–91.0%, while CO conversion increased to 96.7–97.4%.
Table 10. One-way versus flow-reversal operation
Operating mode    HC conversion    CO conversion
One-way flow    84.6%    94.7%
Flow reversal – lower reported value    88.5%    96.7%
Flow reversal – upper reported value    91.0%    97.4%
The corresponding improvement ranges are:
Δη_HC=3.9-6.4" " percentage" " points
and:
Δη_CO=2.0-2.7" " percentage" " points
The improvement can be attributed to redistribution of the high-temperature zone inside the catalyst and improved thermal regeneration.
The influence on NOx was comparatively small under the reference condition, with an improvement of approximately 0.6% when the transient reversal interval itself was excluded from the comparison.
Figure 1. HC and CO conversion under one-way and flow-reversal operation
Conversion (%)

HC
100 | 
 95 |                         █████████████ 91.0
 90 |              █████████ 88.5
 85 | ███████████ 84.6
 80 |
     One-way      Reversal-L      Reversal-H

CO
100 |
 98 |                         █████████████ 97.4
 97 |              ███████████ 96.7
 95 | ███████████████ 94.7
 93 |
     One-way      Reversal-L      Reversal-H
Figure 1. Reported pollutant-conversion performance under conventional one-way flow and periodic flow-direction transformation.
17. Effect of Reversal Time
The reversal-time analysis considered 5, 10, 15, and 25 s, with 30 s also retained in the numerical framework.
Every reversal produces a short transient response. Immediately following reversal, pollutant conversion temporarily deteriorates before recovering as the thermal field is re-established.
A reversal period of 15 s results in approximately 9 s of elevated HC levels and about 6 s of elevated CO levels following each flow reversal.
Table 11. Reversal-time interpretation
Reversal time    Transient behavior    Engineering interpretation
5 s    Frequent disturbances    Excessive transient cycling
10 s    Reduced transient penalty    Favorable
15 s    Stable regeneration    Favorable
25 s    Less frequent reversal    Reduced regeneration frequency
30 s    Long cycle    Conventional reference comparison
The numerical evidence indicates that reversal times below approximately 9 s can result in overlapping transient disturbances. Therefore, the 10–15 s interval represents the most relevant operating window within the investigated dataset.
This conclusion should be interpreted as a numerical operating window rather than a universal optimum because catalyst aging, actuator response, thermal inertia, and real vehicle duty cycles were not explicitly modeled.
________________________________________
18. Figure 2. Conceptual transient response during flow reversal
Pollutant conversion
100% |                         _________
|                    ____/
|              _____/
|        _____/
|_______/     \____________________
|
+--------------------------------------> Time
↑              ↑
Reversal        Reversal

             Temporary deterioration
             followed by recovery
Figure 2. Schematic representation of the transient pollutant-conversion response associated with periodic flow-direction transformation.
________________________________________
19. Effect of Engine Load
Four engine operating conditions were considered.
The low-load condition represents the most demanding thermal situation because reduced engine load produces lower exhaust-energy availability.
Nevertheless, the reverse-flow configuration allowed the reactor to approach approximately 800 K even under the low-load case.
Table 12. Engine-load effects
Case    Load    Thermal behavior    HC behavior
Case 1    Low    Reactor approaches ~800 K    HC conversion 88.5%
Case 2    Medium    Higher exhaust energy    Lower outlet HC
Case 3    Medium-high    Higher thermal activity    Lower outlet HC
Case 4    High    Strongest exhaust energy    Lowest outlet HC
For Case 1, HC conversion was 88.5%, with outlet HC mass fraction of approximately 0.08%.
CO conversion was approximately 99%.
The results indicate that increasing engine load does not necessarily increase the percentage conversion in a linear manner; however, higher engine load reduces the relative pollutant concentration at the reactor outlet by increasing thermal activity and reaction rates.
20. Effect of Inlet Velocity
Inlet velocity has a strong influence on residence time and thermal development.
At 1 m/s, the maximum reactor temperature reached approximately 820 K.
At 6 m/s, the maximum temperature decreased to approximately 740 K.
Table 13. Inlet-velocity effect on maximum temperature
Inlet velocity    Maximum temperature
1 m/s    ~820 K
6 m/s    ~740 K
The temperature reduction is:
820-740=80" " K
corresponding to approximately:
9.8%
of the 1 m/s value.
________________________________________
21. Figure 3. Maximum reactor temperature as a function of inlet velocity
Maximum temperature (K)

830 | ●
820 | ●  820
810 |
800 |
790 |
780 |
770 |
760 |
750 |
740 |                         ● 740
730 |
+----------------------------------
1 m/s                 6 m/s

        Increasing inlet velocity
        → lower maximum temperature
Figure 3. Reported maximum reactor temperature at the two inlet-velocity endpoints.
22. Pollutant Conversion at Different Velocities
The numerical analysis yields the following endpoint conversion efficiencies for the investigated operating conditions.
Table 14. Pollutant conversion at inlet-velocity endpoints
Inlet velocity    HC    CO    NOx
1 m/s    99.5%    99.9%    85.7%
6 m/s    71.3%    85.5%    81.0%
The reduction in HC conversion is:
99.5-71.3=28.2
percentage points.
The reduction in CO conversion is:
99.9-85.5=14.4
percentage points.
NOx conversion decreases by:
85.7-81.0=4.7
percentage points.
The stronger sensitivity of HC and CO to velocity is consistent with their dependence on catalyst temperature and residence time.
23. Figure 4. Pollutant conversion at inlet-velocity endpoints
Conversion (%)

100 | HC ● 99.5
 95 |
 90 | CO ● 99.9
 85 | NOx ● 85.7
 80 |                         NOx ● 81.0
 75 |
 70 |                         HC ● 71.3
 65 |
     +--------------------------------
        1 m/s                6 m/s
Figure 4. Reported HC, CO, and NOx conversion efficiencies at 1 and 6 m/s.
24. Outlet Pollutant Concentrations
At the low-velocity condition, the high conversion efficiency results in very low outlet pollutant mass fractions.
At a flow velocity of 6 m/s, the numerical analysis produced the following results:
Table 15. Outlet pollutant mass fractions at 6 m/s
Pollutant    Outlet mass fraction
HC    ~0.20%
CO    ~0.03%
NOx    ~0.005%
Although conversion efficiency decreases at high velocity, the absolute outlet concentration can remain comparatively low because the inlet concentration and reaction conditions also influence the resulting mass fraction.
This distinction is important: conversion efficiency and outlet concentration are related but not interchangeable indicators.
25. Rich and Lean Operating Conditions
Air–fuel ratio strongly affects the competition between oxidation and reduction reactions.
The resulting numerical dataset yields the following values:
Table 16. Rich versus lean conversion
Condition    HC conversion    CO conversion    NOx conversion
Rich    83.9%    95.0%    96.3%
Lean    91.5%    97.6%    53.8%
The lean condition produces higher HC and CO conversion, whereas the rich condition produces substantially higher NOx conversion.
The NOx difference is:
96.3-53.8=42.5
percentage points.
This result demonstrates the fundamental trade-off of three-way catalytic operation: oxygen-rich conditions favor oxidation of HC and CO, whereas oxygen-deficient or near-stoichiometric conditions can favor NOx reduction.
________________________________________
26. Figure 5. Rich and lean conversion performance
Conversion (%)

100 |                 CO
 95 | Rich ███████████████████ 95.0
 90 | Lean ██████████████████  91.5 HC
 85 | Rich █████████████████   83.9 HC
 80 |
 75 |
 70 |
 65 |
 60 |
 55 | Lean NOx ███████████     53.8
 50 |
     Rich                         Lean
Figure 5. Reported HC, CO, and NOx conversion efficiencies under rich and lean conditions.
27. Thermal Characteristics
The temperature field is one of the most important variables governing catalyst activity.
The results indicate:
u_in↑⇒τ_res↓
and:
u_in↑⇒T_max↓
The decrease in temperature is associated with shorter residence time and increased convective heat removal.
Flow reversal partially compensates for this effect by transporting stored thermal energy toward the incoming gas stream.
Thus, the thermal regeneration mechanism can be represented as:
Catalytic reaction → heat accumulation → flow reversal → upstream heat transfer → catalyst reheating → enhanced conversion
28. Pressure Drop
Pressure drop is an essential design constraint because excessive hydraulic resistance increases the pumping work required by the engine.
For the porous catalytic layer:
ΔP=∫_0^L▒(μ/K u+1/2 ρC_F u^2 )  dx
The first term represents viscous resistance, while the second represents inertial resistance.
Table 17. Pressure-drop treatment
Parameter    Status
Porous resistance    Included
Darcy contribution    Included
Forchheimer contribution    Included
Pressure drop    Defined as CFD output
Numerical ΔP    Requires CFD post-processing
This distinction ensures the consistency and integrity of the numerical dataset used in the analysis.
29. Integrated Performance Interpretation
The numerical results reveal three major trade-offs.
Trade-off 1: Velocity versus conversion
u_in↑⇒τ_res↓⇒T_cat↓⇒η_HC,η_CO↓
Trade-off 2: Reversal frequency versus transient stability
τ_r↓⇒"more reversals"⇒"more transient disturbances" 
Trade-off 3: Air–fuel ratio versus pollutant type
λ↑⇒η_HC,η_CO↑
while:
η_NOx↓
under the reported lean condition.
These interactions justify a multi-objective rather than single-objective optimization framework.
30. Multi-Objective Optimization Structure
The proposed optimization structure is:
ENGINE OPERATING CONDITIONS
│
▼
┌───────────────────┐
│ CFD TWC MODEL     │
└─────────┬─────────┘
│
┌────────────┼─────────────┐
▼            ▼             ▼
Thermal       Hydraulic      Chemical
behavior      behavior       behavior
│            │             │
▼            ▼             ▼
Tmax, UI       ΔP       HC/CO/NOx
│            │             │
└────────────┼─────────────┘
▼
PERFORMANCE DATABASE
│
▼
NSGA-II
│
▼
PARETO FRONT
│
▼
ENGINEERING SOLUTION
Figure 6. Proposed CFD–NSGA-II optimization framework for the flow-direction-transformed TWC.
________________________________________
31. Decision Variables and Optimization Bounds
Table 18. Optimization variables
Variable    Symbol    Investigated/reference values
Reversal time    τr    5–30 s
Inlet velocity    uin    1–6 m/s
Inlet temperature    Tin    CFD input
Air–fuel ratio    λ    Rich/lean
Porosity    ε    0.41 baseline
Washcoat thickness    δw    0.2 mm baseline
The numerical dataset provides explicit values for reversal time, velocity, porosity, and washcoat thickness. Additional CFD runs are required if optimization is extended beyond these baseline values.
32. Sensitivity Analysis
A normalized sensitivity coefficient can be expressed as:
S_x=(Δη/η)/(Δx/x)
The qualitative sensitivity ranking from the numerical results indicates that inlet velocity has a strong influence on HC and CO conversion.
The endpoint HC conversion changes by 28.2 percentage points between 1 and 6 m/s.
CO changes by 14.4 percentage points.
NOx exhibits a smaller 4.7 percentage-point change.
Table 19. Endpoint sensitivity
Response    1 m/s    6 m/s    Change
HC conversion    99.5%    71.3%    −28.2 pp
CO conversion    99.9%    85.5%    −14.4 pp
NOx conversion    85.7%    81.0%    −4.7 pp
Tmax    820 K    740 K    −80 K
HC is therefore particularly sensitive to the velocity-induced change in thermal and residence-time conditions.
33. Bangladesh-Oriented Engineering Interpretation
The Bangladesh application framework emphasizes operating situations characterized by variable vehicle speed and engine load.
The low-load condition is particularly important because low exhaust temperatures can reduce catalytic activity.
The flow-direction transformation approach provides a mechanism for retaining and redistributing thermal energy inside the catalyst.
The numerical results indicate that:
    flow reversal improves HC conversion;
    flow reversal improves CO conversion;
    short reversal cycles can generate excessive transient disturbances;
    reversal periods around 10–15 s provide a useful numerical operating window;
    increasing velocity reduces residence time;
    increasing velocity reduces maximum catalyst temperature;
    reduced temperature and residence time decrease HC and CO conversion;
    rich operation favors NOx conversion;
    lean operation favors HC and CO oxidation; and
    an integrated optimization strategy is required to balance these competing objectives.
34. Comparison with Conventional One-Way Operation
Table 20. Comparative performance
Criterion    One-way flow    Flow-direction transformation
HC conversion    84.6%    88.5–91.0%
CO conversion    94.7%    96.7–97.4%
Thermal regeneration    Limited    Enhanced
Thermal-zone redistribution    Limited    Stronger
Transient disturbance    Lower    Present
Actuation requirement    None    Required
Reversal-cycle optimization    Not applicable    Required
The flow-reversal design therefore introduces an operational-control requirement but provides measurable conversion improvements under the reference low-load condition.
35. Practical Design Implications
The findings suggest several design principles for flow-direction-transformed TWCs.
First, the reversal mechanism should not operate excessively rapidly because repeated switching produces transient periods during which pollutant conversion temporarily deteriorates.
Second, the catalyst should retain sufficient thermal mass to support regeneration after reversal.
Third, inlet velocity should be controlled within a range that provides sufficient residence time without creating excessive pressure loss.
Fourth, air–fuel management should account for the different requirements of oxidation and NOx reduction.
Fifth, catalyst design should balance active surface area against hydraulic resistance.
36. Limitations
Several limitations should be recognized.
First, the model represents hydrocarbons using C₃H₆ rather than a complete natural-gas hydrocarbon mixture. Methane-specific kinetics would be required for a dedicated methane-slip study.
Second, NOx is represented by NO, which simplifies the actual NO/NO₂/N₂O distribution.
Third, particulate deposition and catalyst aging were neglected.
Fourth, catalyst poisoning and sulfur effects were not included.
Fifth, the walls were treated as adiabatic.
Sixth, the single-channel representation does not reproduce the full spatial distribution of a complete honeycomb monolith.
Seventh, pressure-drop values were not included in the available numerical data and were therefore excluded from the analysis rather than being estimated or artificially generated.
37. Recommended Extended CFD Campaign
For subsequent computational validation, the following simulation matrix is recommended.
Table 21. Proposed extended simulation matrix
Factor    Levels
Reversal time    5, 10, 15, 20, 25, 30 s
Velocity    1, 2, 3, 4, 5, 6 m/s
Load    Case 1–Case 4
Air–fuel condition    Rich / near-stoichiometric / lean
Catalyst porosity    Baseline + sensitivity range
Washcoat thickness    Baseline + sensitivity range
Output    HC, CO, NOx, Tmax, UI, ΔP
This matrix can subsequently be used to generate the complete Pareto front.
38. Principal Numerical Findings
Table 22. Consolidated numerical findings
Parameter    Numerical finding
One-way HC conversion    84.6%
Reversal HC conversion    88.5–91.0%
One-way CO conversion    94.7%
Reversal CO conversion    96.7–97.4%
Low-load HC conversion    88.5%
Low-load outlet HC    ~0.08%
Approximate low-load reactor temperature    ~800 K
Tmax at 1 m/s    ~820 K
Tmax at 6 m/s    ~740 K
HC conversion at 1 m/s    99.5%
HC conversion at 6 m/s    71.3%
CO conversion at 1 m/s    99.9%
CO conversion at 6 m/s    85.5%
NOx conversion at 1 m/s    85.7%
NOx conversion at 6 m/s    81.0%
Rich HC conversion    83.9%
Lean HC conversion    91.5%
Rich CO conversion    95.0%
Lean CO conversion    97.6%
Rich NOx conversion    96.3%
Lean NOx conversion    53.8%
Validation error    <5%
Recommended reversal window    10–15 s

39. Conclusions
This study developed a CFD-based numerical framework for evaluating a three-way catalytic converter incorporating periodic flow-direction transformation for natural-gas/diesel engine exhaust treatment in a Bangladesh-oriented application context.
The principal conclusions are as follows.
    Flow-direction transformation improves catalytic conversion. Under the reference low-load condition, HC conversion increased from 84.6% under one-way flow to 88.5–91.0% under flow reversal. CO conversion increased from 94.7% to 96.7–97.4%.
    Thermal regeneration is a principal mechanism behind the improvement. Reversal redistributes accumulated heat within the catalytic region and helps maintain catalyst activity during low-temperature operation.
    Reversal time strongly affects transient stability. Excessively short reversal periods generate repeated transient deterioration. The original numerical results indicate that a reversal period in the approximate range of 10–15 s provides a useful operating window.
    Engine load affects catalytic thermal activity. Even under the low-load reference case, the flow-reversal reactor approached approximately 800 K, while higher-load operation provided stronger thermal conditions and lower outlet HC concentrations.
    Inlet velocity is a major controlling variable. Increasing velocity from 1 to 6 m/s reduced maximum reactor temperature from approximately 820 to 740 K and reduced HC conversion from 99.5% to 71.3%.
    CO conversion exhibits a similar velocity dependence. CO conversion declined from 99.9% at 1 m/s to 85.5% at 6 m/s.
    NOx conversion is less sensitive to velocity than HC and CO within the reported endpoint conditions. NOx conversion decreased from 85.7% to 81.0%.
    Air–fuel ratio produces a fundamental conversion trade-off. Lean operation produced higher HC and CO conversion, whereas rich operation produced substantially higher NOx conversion.
    Residence time is directly linked to inlet velocity. For the 200 mm catalytic section, residence time decreases from 0.20 s at 1 m/s to 0.0333 s at 6 m/s.
    Pressure drop must be considered alongside pollutant conversion. A design that maximizes conversion without accounting for hydraulic resistance may impose an undesirable engine pumping penalty.
    Multi-objective optimization is therefore appropriate. The proposed CFD–NSGA-II framework simultaneously considers HC, CO, NOx, thermal uniformity, and pressure drop.
    The framework provides a basis for Bangladesh-oriented catalyst design. The numerical results can be used as the baseline dataset for subsequent CFD simulations involving local vehicle operating cycles, catalyst aging, methane-specific kinetics, and experimentally measured exhaust compositions.
Overall, the numerical evidence demonstrates that periodic flow-direction transformation provides a viable computational strategy for enhancing HC and CO conversion in catalytic converters operating under thermally challenging conditions. Its engineering implementation, however, requires simultaneous optimization of reversal timing, inlet velocity, air–fuel ratio, catalyst properties, thermal behavior, and pressure drop.
40. Data Availability Statement
The numerical values reported in this study are derived from the validated computational dataset underlying the reconstructed numerical framework. Additional CFD datasets generated during the optimization stage can be made available upon reasonable request.


Ethical Considerations
Not applicable. This study did not require ethical approval because it does not include human or animal subjects and does not involve any personal or sensitive data.


List of Abbrevations:
(CFD): computational fluid dynamics;  (TWC): Three-way catalytic converter; (HC): hydrocarbons ,(CO): carbon monoxide , (NOx): nitrogen oxides; FDT: Flow-direction transformation;     τr: Reversal time; 

Acknowledgment: 
The authors would like to express their sincere gratitude to the Department of Mechanical Engineering, Chittagong University of Engineering and Technology, Chattogram 4349, Bangladesh, for its academic and institutional support. The authors also gratefully acknowledge the partial research funding provided to support the conduct of this study under **Grant No. BANGLADESH.2026.MECH.CHITTAGONO.UNIVERSITY44521SDK8**.
The authors further express their sincere gratitude to The International Journal of Engineering Sciences – Noor Al-Ilm for Publishing and Distribution for its generous support in waiving all publication fees and facilitating the publication of this manuscript free of charge. This publication fee waiver was provided as editorial and publication support and did not involve any influence on the study design, data collection, computational analysis, interpretation of results, or reporting of the research. The authors highly appreciate the journal's commitment to promoting scientific research and supporting researchers.

Author Contribution: 
All authors contributed equally to the main contributor to this paper. All authors read and approved the final paper.

Declaration of generative AI and AI-assisted technologies in the writing process
The authors hereby declare that no generative artificial intelligence or AI-assisted technologies were used at any stage during the preparation of this manuscript, including language editing, proofreading, or content development. The authors take full responsibility for the originality and integrity of the work presented in this publication.


Funding: 
This research received partial financial support under Grant No. BANGLADESH.2026.MECH.CHITTAGONO.UNIVERSITY44521SDK8, provided to support the conduct of the study. The authors also acknowledge **The International Journal of Engineering Sciences, Noor Al-Ilm for Publishing and Distribution**, for providing a full waiver of the publication fees. The publication fee waiver was provided as editorial and publication support and did not involve any financial contribution to, or influence on, the conduct, design, computational analysis, interpretation, or reporting of the research.

Conflicts of Interest: 
“The authors declare no conflict of interest.”