Numerical Investigation of the Effect of an Oblique Flow Entry on the Pressure Losses in Square Channels

Callum Samuels; Humberto Medina; Ijhar Rusli; Ran Holtzman; Stephen Benjamin; Svetlana Aleksandrova; Timothy C. Watling

REVIEW 3 major objections 5 minor 12 references

Numerical Investigation of the Effect of an Oblique Flow Entry on the Pressure Losses in Square Channels

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Oblique entry trips turbulence in square channels at Re≈2000

desk verdict Solid engineering CFD paper with a real new finding (length-dependent KObl) and an under-supported causal claim about shear-layer-driven transition. read the letter →

arxiv 2502.07678 v1 pith:CX3OYSQR submitted 2025-02-11 physics.flu-dyn

Callum Samuels , Timothy C. Watling , Svetlana Aleksandrova , Humberto Medina , Ran Holtzman , Ijhar Rusli , Stephen Benjamin This is my paper · ORCID

classification physics.flu-dyn

keywords obliqueflowentrysquarechannelmonolithpressuredroplargeeddysimulationRANStransitiontoturbulenceshear-layerinstabilityleading-edgerounding

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the common engineering assumption—that flow entering a square monolith channel obliquely is laminar at moderate Reynolds numbers—is safe. Using large-eddy simulation, it shows that the shear layer at the channel entrance becomes unstable and sheds eddies that persist downstream even at channel Reynolds numbers around 2000, so the flow is transitional or turbulent well below the usual duct transition threshold. The consequence is that the additional pressure-loss coefficient for oblique entry, KObl, is not a constant or simple function of angle: it depends on Reynolds number, channel length, and the rounding of the leading edge. The paper also shows that sharp-edged LES overpredicts experimental losses, that rounding the edge to a realistic radius (about 3% of the channel width) restores agreement, and that an inexpensive RANS model captures the pressure drop within 5% for most cases. The result matters for the design of catalytic converters, particulate filters, and heat exchangers, where oblique entry is common and pressure drop drives efficiency.

What carries the argument

The central object is the shear layer that forms between the recirculation zone (created by flow separation at the channel entrance) and the freestream jet. Its instability produces coherent vortical structures that shed and persist downstream, acting as a self-sustained turbulence source. The argument is carried by the dimensionless oblique pressure-loss coefficient KObl = ΔPObl / (ρU1²/2), defined by subtracting the axial-entry pressure drop; the paper shows that this subtraction is only valid while both flows are in the same regime. An auxiliary but decisive piece of machinery is the leading-edge rounding radius r/d, which the authors measure from a real cordierite catalytic converter (about 2.9% of channel width) and vary in simulation, showing that it controls the shear-layer instability and therefore KObl.

What would settle it

Measure the pressure drop and velocity fluctuations across a square channel with a 40° oblique entry at Rec ≈ 2000 while systematically increasing the turbulence intensity of the inlet flow from near zero to several percent; if the sharp rise in KObl shifts to lower Reynolds numbers or changes magnitude with inlet turbulence, the claim that the shear layer alone triggers transition is falsified.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that an obliquely entering flow into a square channel is not a laminar flow at moderate channel Reynolds numbers. At entry angles above roughly 20 degrees and Rec around 2000, the recirculation zone at the channel entrance creates a shear layer that becomes unstable and continuously sheds coherent eddies; these persist along the channel and drive a transition to turbulence. This transition is triggered by the shear layer itself, with no turbulence prescribed at the inlet. Because the axial-entry flow at the same Reynolds number remains laminar and developing, subtracting the axial pressure drop (as the definition of KObl does) no longer isolates the entrance loss: KObl then contains the difference between laminar and turbulent friction over the whole channel length, making it length-dependent. The paper further shows that rounding the leading edge, as found in real cordierite monoliths, stabilises the shear layer, delays the transition, and lowers KObl, with a radius of 0.01d bringing LES into agreement with experiments. Laminar flow models, steady or unsteady, fail in the transitional cases, while the k–ω SST RANS model predicts pressure losses within 5% of experiments for most conditions, except where transition occurs (differences up to 40%).

Load-bearing premise

The inlet is a flat, uniform, turbulence-free laminar velocity profile; if real upstream flow contains residual turbulence or pulsation, the shear-layer transition could occur earlier or by a different mechanism, changing both the predicted losses and the comparison with experiments.

Editorial extensions

If this is right

Oblique entry into square channels cannot be treated as laminar at moderate Reynolds numbers: for entry angles above about 20°, the shear layer generates turbulence even at Rec ≈ 2000, so design correlations must include a transition term.
The oblique pressure-loss coefficient KObl depends on channel length when oblique flow is turbulent and axial flow is laminar; a single KObl per angle is not valid.
Sharp-edged simulations overestimate pressure losses at higher Reynolds numbers and angles; rounding the leading edge to realistic values (r ≈ 0.01d–0.05d) reduces losses and brings LES into agreement with experiments.
For engineering pressure-drop predictions, RANS with the k–ω SST model is accurate to within 5% for most conditions; steady or unsteady laminar models are unsuitable for oblique entry even at Rec = 2000.
The turbulence generated by oblique entry could be exploited for enhanced mixing in monolith channels, at the cost of increased pressure drop.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same shear-layer mechanism should appear in channels of other cross-sections (e.g., circular or hexagonal) whenever the inlet flow has a transverse component; the transition threshold likely scales with the ratio of transverse to axial momentum rather than with Reynolds number alone.
The flat, turbulence-free inlet used here probably makes the predicted transition a conservative lower bound: residual upstream turbulence or pulsation in real engines would likely trip the shear layer earlier, so the length-dependence of KObl may be even more pronounced in service.
If KObl is length-dependent, device-level pressure-drop models for monoliths should either resolve the entrance region explicitly or use an entry-loss term that accounts for the distance over which turbulent friction acts, rather than a fixed entry-loss coefficient.
A testable design extension follows directly: vary the inlet chamfer or rounding radius as a design parameter to trade pressure drop against mixing; the paper's data suggest a radius around 1% of channel width already suppresses most of the shear-layer loss.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a useful, competent CFD study that gives the monolith and heat-exchanger community a good reason to stop treating oblique entry as a purely local loss. The strongest new contribution is the demonstration that KObl becomes length-dependent once the oblique-entry shear layer trips transition, so the standard practice of subtracting the axial-entry pressure drop no longer isolates the entrance loss. The edge-rounding explanation is also convincing and well supported by microscope measurements of a real substrate. I believe the paper deserves serious refereeing.

What it does well: the axial-entry cases match the Shah-London developing-flow correlation; the outlet-length check is clean; mesh independence for pressure drop is documented; and the comparison uses external correlations (K-W, Persoons, Quadri) with no constants fitted to the target data. The LES resolution metric (LESIQnu) is reported, and the paper honestly notes the limitation of the KObl subtraction. That is more than many engineering CFD papers do.

The soft spots are real but not fatal. First, the central mechanistic claim—that the shear layer produces continuous shedding of eddies and transition at Rec around 2000—is supported only by flow visualization and resolved fluctuation profiles. The inlet is flat and turbulence-free, so the only perturbations available to seed the instability are numerical. The paper shows pressure-drop convergence with mesh, but not convergence of shedding frequency, spectra, or transition location. If the instability is subcritical, the numerical trigger could affect onset. This does not mean the claim is wrong; it means the causal attribution is underdetermined as presented. Second, the abstract states RANS was within 5% of experiments mostly and up to 40% in transitional cases, but the body never quantifies that; it only says RANS agrees better at some angles. Either substantiate or remove. Third, time-averaging over two residence times is short for statistics, and no uncertainty bars are given for the simulations. Minor: the experiments are from the same group, and the edge profile is representative rather than the actual test specimen, though the authors do acknowledge geometry uncertainty.

The paper is aimed at engineers modeling monolith back-pressure. A referee should push for the missing spectral and mesh checks and the RANS quantification, but the core finding is solid enough to engage with, not to desk-reject.

Referee Report

3 major / 5 minor

Summary. This paper presents CFD simulations of a single square monolith channel with flow entering obliquely. LES (dynamic Smagorinsky), RANS k-omega SST with a transition model, and steady/unsteady laminar models are compared over Rec=500-3000 and alpha=0-70 degrees. The authors report that oblique entry creates a recirculation region and shear layer at the channel entrance, that the shear layer sheds coherent structures and promotes transition to turbulence even at Rec~2000, that this makes the oblique-entry loss coefficient KObl length-dependent, and that sharp-edged simulations overpredict experimental losses because the real leading edges are rounded. The simulations are compared with the Shah-London developing-flow correlation, the K-W, Persoons, and Quadri correlations, and experimental data from Quadri et al. and Mat Yamin.

Significance. If the central transition claim is correct, the paper overturns a common laminar-flow assumption for monolith channels at moderate Reynolds numbers and identifies a physical mechanism (shear-layer shedding from oblique entry) that explains both the Reynolds-number and length dependence of KObl. The study has several genuine strengths: the axial-entry cases are validated against the Shah-London developing-flow correlation; the outlet-length effect is checked; the LES mesh study reports both global pressure-drop convergence and the Celik LESIQnu index; and no constants are fitted to the target pressure-loss data, with the edge-rounding radius being varied and the best-agreeing value identified post hoc. The experimental comparison over four channel lengths is a valuable addition to the literature. However, the central claim rests on LES with a disturbance-free inlet and only two residence times of averaging, and the mesh study does not assess the convergence of the unsteady quantities used to infer shedding. These issues are fixable but currently leave the main physical claim underdetermined.

major comments (3)

[III.A.3 / II.E / II.F] The central claim that the oblique-entry shear layer produces continuous shedding of eddies that persist downstream at Rec~2000 rests on LES in which the inlet is a flat, turbulence-free profile (Sec. II.E). Since no physical disturbances are seeded, the perturbations that initiate the shear-layer instability are numerical in origin. The mesh assessment of Sec. II.F establishes convergence of the s1-s3 pressure drop and LESIQnu, but it does not test convergence of the fluctuation statistics used to support the shedding claim: shedding frequency, spectral content, transition-onset location, or the streamwise evolution of U'_RMS. The observed transition could therefore depend on mesh-dependent numerical noise, particularly in a subcritical regime, and the causal attribution to the oblique-entry shear layer is underdetermined. I recommend either a mesh-4 replicate showing the same shedding frequency and U'_RMS streamwise evolution, or a test with a small controlled inlet disturbance to confirm that the instability is physical rather than triggered by numerical noise.
[II.C / III.A.3 / III.B] All reported time-averaged pressures and fluctuation profiles are averaged over only two residence times of the full domain (Sec. II.C). No convergence check of the running time average is reported for the pressure drop or U'_RMS, and no shedding frequency or Strouhal number is examined. If low-frequency or intermittent transitional behavior is present, two residence times may alias the statistics and materially change KObl. Please report the time-history of the running mean over a longer interval (for example, ten residence times) for a representative transitional case, and quantify the uncertainty of the time-averaged pressure drop used in Figs. 20-26.
[III.B.5 / IV] The conclusion that leading-edge rounding explains the discrepancy with experiments is based on rounded-edge simulations at only alpha=0 and 40 degrees, with the radius varied, and on a single comparison at Rec=1500 and alpha=45 degrees for L=27d. The statement that the r=0.01d case agrees within experimental error is thus not demonstrated across the parameter range over which the discrepancy appears (for example, alpha=30-60 degrees, Rec=2000-3000, and all monolith lengths). Either extend the rounded-edge matrix or temper the conclusion to a demonstration of sensitivity rather than a full quantitative explanation of the experimental differences.

minor comments (5)

[Eq. (22)] In Eq. (22), setting epsilon = 1 for a smooth channel is dimensionally unclear; since epsilon is a roughness height, smooth walls should correspond to epsilon = 0, and the plotted comparison should state the relative roughness used.
[III.A.2] There is a typo in the text near Fig. 13: 'seperation' should be 'separation'.
[III.A.3] Figure 15 defines U'_RMS but does not state the time window over which the root-mean-square is computed; this is important given the two-residence-time averaging stated in Sec. II.C.
[III.B.3 / Figs. 23-26] The experimental data points and error bars in Figs. 23-26 are not described in terms of the number of repeated measurements or the source of uncertainty; a sentence explaining the experimental uncertainty would help the reader judge the agreement.
[II.D.1 / II.D.2] The numerical schemes in Star CCM+ are described only by order of accuracy; specifying the actual discretization schemes (e.g., bounded central differencing for LES, upwind for RANS) would improve reproducibility.

Circularity Check

1 steps flagged · score 2.0 of 10

One post hoc edge-radius selection; central transition and KObl-length claims remain independent.

fitted input called prediction [Section III.B.5, 'Effect of Rounded Walls' (Figs. 31-33)]
"To study the effect of the rounding of the leading edge on the channel pressure losses, three new geometries were produced with the leading edge rounded with a radii of r = 0.01d, 0.025d, and 0.05d ... For the case with r = 0.01d, the agreement with experiments is within the experimental error. This confirms that the presence of a rounded edge in the experimental setup could be the reason for the differences between measured and predicted pressure losses for higher Reynolds numbers and oblique entry angles."

The rounding radius that gives agreement is selected by scanning three candidate values (0.01d, 0.025d, 0.05d) and then the matching case, r = 0.01d, is used to 'confirm' that edge rounding explains the LES/experiment discrepancy. This is a post hoc fit: the agreement is forced by selection, not an independent prediction. Notably, the microscope measurement reported in the same section gives a radius of about 2.92% of channel width (~0.03d), not the 0.01d value that matched the data, reinforcing that the matching radius was chosen by fit rather than by the independent geometric measurement. The paper's central claims about shear-layer shedding and the length dependence of KObl do not depend on this radius choice.

full rationale

The core derivation chain is self-contained. No constants are fitted to the target pressure-loss data: axial-entry cases are validated against Shah-London developing-flow losses and Colebrook turbulent friction, and KObl comparisons use external correlations (K-W, Persoons, Quadri) and experimental datasets (Quadri et al., Mat Yamin) rather than values tuned inside the simulations. The persistent-eddies and transition claims are direct LES observations made with a flat, turbulence-free inlet; they are not defined into existence by the pressure-loss formula. The paper also explicitly acknowledges that Eq. 8 includes downstream laminar/turbulent friction differences, so the length dependence of KObl is a consequence the authors identify and explain rather than a hidden input. Same-group references (Quadri et al., Mat Yamin) are experimental evidence, not load-bearing theoretical authority, so they do not constitute circularity. The only mild circular element is the post hoc selection of the rounded-edge radius that matches experiment, which is secondary to the central claims and therefore warrants only a low score.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The study introduces no new entities and no formally fitted parameters. The central modeling choices are standard incompressible CFD assumptions. The only hand-scanned input is the leading-edge rounding radius, chosen in a three-value sweep, and the averaging window of two residence times; both are mild selection effects rather than fitted constants.

free parameters (2)

Leading-edge rounding radius, r = 0.01d (best agreement with experiments); measured representative radius about 0.029d
Three radii were scanned to explain the sharp-edge overprediction. The smallest radius gave agreement within experimental error, so this is a hand-chosen geometry parameter rather than a formally fitted constant, but it is a post-hoc selection.
Time-averaging window = 2 residence times
Pressure statistics are time-averaged over two residence times of the full domain. No sensitivity study of the averaging window is reported, so the convergence of the reported pressure-loss means is assumed rather than demonstrated.

assumptions (6)

domain assumption Air is modeled as incompressible, isothermal, Newtonian fluid.
Invoked in Section II.D for all simulations; appropriate for the low-Mach flows considered.
domain assumption Flat, uniform, turbulence-free velocity profile at the inlet boundary.
Section II.E specifies no synthetic turbulence, justified by the experimental setups of Quadri et al. and Mat Yamin. The central transition mechanism depends on this laminar inlet condition.
domain assumption Side walls are translational periodic boundaries, representing an infinite array of identical channels.
Section II.E. This removes finite-monolith side effects and assumes each channel behaves identically.
domain assumption Channel walls are smooth with no-slip and zero roughness.
Section II.E. Real catalyst walls can have micro-roughness, which is not included in the model.
domain assumption The measured edge profile from one cordierite monolith is representative of the experimental monoliths used by Quadri et al. and Mat Yamin.
Section III.B.5 uses a focus-variation microscope on one core to infer the rounding in the experiments. The actual test pieces were not measured.
standard math Navier-Stokes, LES-filtered equations, and the Dynamic Smagorinsky SGS model as implemented in Star CCM+ correctly represent the flow physics.
Standard governing equations, Section II.D.1. The implementation is not independently verified by the paper.

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Cite this review

Pith. "Pith review of Numerical Investigation of the Effect of an Oblique Flow Entry on the Pressure Losses in Square Channels." pith.science (2026). https://pith.science/paper/CX3OYSQR

@misc{pith2026250207678,
  author       = {Pith},
  title        = {Pith review of: Numerical Investigation of the Effect of an Oblique Flow Entry on the Pressure Losses in Square Channels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CX3OYSQR}},
  note         = {Machine review of arXiv:2502.07678}
}

read the original abstract

Flows in square channels are common in applications, such as automotive after-treatment systems and heat exchangers. Flows with axial flow entry are well understood, but for oblique flow entry, there is no clarity on the additional pressure loss magnitude or the flow regime. Laminar flow is often assumed, even though flow separation at the channel entrance can cause a transition to turbulence. Here, the impact of oblique flow entry on the flow is investigated using LES (Large Eddy Simulation) and RANS (Reynolds Averaged Navier Stokes) models, and their advantages and limitations are identified. The LES simulations show that the shear layer at the channel entrance produces continuous shedding of eddies that persist downstream even at moderate channel Reynolds numbers (~2000). The predicted pressure losses mostly agree with experimental data. The differences observed for some parameters are attributed to the difficulty of accurately replicating the experimental geometry. It is shown that LES results are susceptible to the rounding of the leading edge (present in experiments). Including edge rounding improves the pressure predictions. RANS simulations predicted pressure losses within 5% of experimental values for most cases, apart from where transitional flow was observed (resulting in differences up to 40%). This study provides insights into the flow structure and sources of pressure losses in square channels and highlights the importance of understanding key flow and geometric features when using LES to predict complex flows involving flow separation and shear layers.

Figures

Figures reproduced from arXiv: 2502.07678 by the authors.

**Figure 1.** FIG. 1. Diagram illustrating formation of recirculation zones and shear layers in a channel with oblique flow entry into the monolith channels [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** FIG. 2. Schematic diagram of the flow domain used for simulations. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 1.** For LES and laminar simulations, a flat velocity pro [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

Figures from the paper (21 more)

**Figure 3.** Figure 3: FIG. 3. Comparison of the dimensional static pressure drop between [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

**Figure 4.** Figure 4: FIG. 4. Comparison of the dimensional static pressure drop between [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Comparison of the dimensional static pressure drop between [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Instantaneous LES [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 9.** Figure 9: FIG. 9. Axial velocity distribution at the entrance of the channel (XY [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: FIG. 10. Time-averaged velocity profiles at the line [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]

**Figure 11.** Figure 11: FIG. 11. Instantaneous velocity magnitude at the entrance of the [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]

**Figure 12.** Figure 12: FIG. 12. Instantaneous vorticity vector magnitude at the entrance of [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]

**Figure 14.** Figure 14: FIG. 14. Isosurfaces of time-averaged, axial velocity, [PITH_FULL_IMAGE:figures/full_fig_p009_14.png]

**Figure 15.** Figure 15: FIG. 15. Distribution of resolved velocity fluctuations averaged in [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]

**Figure 18.** Figure 18: FIG. 18. Pressure distribution along the domain for [PITH_FULL_IMAGE:figures/full_fig_p011_18.png]

**Figure 19.** Figure 19: FIG. 19. Pressure distribution along the domain for [PITH_FULL_IMAGE:figures/full_fig_p011_19.png]

**Figure 20.** Figure 20: FIG. 20. Oblique pressure loss vs [PITH_FULL_IMAGE:figures/full_fig_p012_20.png]

**Figure 22.** Figure 22: FIG. 22 [PITH_FULL_IMAGE:figures/full_fig_p012_22.png]

**Figure 23.** Figure 23: FIG. 23 [PITH_FULL_IMAGE:figures/full_fig_p013_23.png]

**Figure 25.** Figure 25: FIG. 25 [PITH_FULL_IMAGE:figures/full_fig_p013_25.png]

**Figure 26.** Figure 26: FIG. 26 [PITH_FULL_IMAGE:figures/full_fig_p014_26.png]

**Figure 27.** Figure 27: FIG. 27. Comparison of LES and RANS flow models with corre [PITH_FULL_IMAGE:figures/full_fig_p015_27.png]

**Figure 30.** Figure 30: FIG. 30. Mesh at the entrance of the channel with rounding radius [PITH_FULL_IMAGE:figures/full_fig_p015_30.png]

**Figure 32.** Figure 32: shows KObl vs Rec for the sharp and rounded edge cases, correlation from Quadri13, and experimental data by Mat Yamin14 for the 27 mm monolith. KObl is consistently lower for the simulations with the rounded edge than those with a sharp edge ( [PITH_FULL_IMAGE:figure…

**Figure 33.** Figure 33: FIG. 33. Distribution of velocity fluctuations along the channel for [PITH_FULL_IMAGE:figures/full_fig_p016_33.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

[1]

29 The mesh cell size acts as a filter sorting the eddies by size

LES Setup The LES approach segregates the turbulent flow structures (eddies) into those that are sufficiently large to be resolved on the mesh, and the remaining, smaller, eddies which are mod- elled by a sub-grid scale turbulence model. 29 The mesh cell size acts as a filter sorting the eddies by size. Consequently, a more refined mesh results in a small...

work page
[2]

To compare the ac- curacy of different models for the flow in the considered range of Reynolds numbers, a RANS model ( k − ω SST) has been used for several configurations

RANS Setup LES is considered a superior modelling tool for capturing flows with shear; however, RANS models are frequently used because of their computational efficiency. To compare the ac- curacy of different models for the flow in the considered range of Reynolds numbers, a RANS model ( k − ω SST) has been used for several configurations. The RANS gover...

work page
[3]

Laminar Setup Both the LES and RANS models account for turbulence and therefore perform favourably when turbulence is present. Since some simulations are conducted at Reynolds numbers associated with laminar flow transitioning to turbulence, these models may artificially induce turbulence under conditions where it would not develop in reality. To assess w...

work page 2000
[4]

This causes the formation of a vena contracta immediately post-entrance (see Fig

Recirculation Region and Shear Layer In the case of an axial entry, the flow path contracts as it en- ters the channel. This causes the formation of a vena contracta immediately post-entrance (see Fig. 8). For contraction ratios typical to monoliths and catalytic converters ( ≈ 0.75 - 0.9), the effect is not very pronounced, and the separation zones forme...

work page
[5]

Secondary Flow Formation of secondary vortices in non-circular ducts has been observed in many experimental and numerical studies,36–38 and is attributed to the transverse turbulent stress gradients. These vortices play a significant role in shaping the overall flow structure and enhancing mixing within the channel.19,21 At lower Reynolds numbers, the sec...

work page 2000
[6]

Turbulence Development The discussed flow features (flow acceleration due to sepa- ration, shear layer, and secondary flow formation) contribute to the transition of the flow to turbulence with increasing Reynolds number and/or oblique entry angle. Fig. 15 shows the average cross-sectional distribution of resolved velocity Numerical Investigation of the E...

work page 2000
[7]

16 shows the pressure distribution in the domain for axial entry ( α = 0◦) simulations with Rec = 1000, 2000, and

Pressure Drop for Axial Flow Entry Simulations Fig. 16 shows the pressure distribution in the domain for axial entry ( α = 0◦) simulations with Rec = 1000, 2000, and

work page 2000
[9]

18 and 19 show the pressure distribution along the channel for cases with an oblique flow entry for Rec = 1000 and 3000

Pressure Drop for Oblique Flow Entry Simulations Figs. 18 and 19 show the pressure distribution along the channel for cases with an oblique flow entry for Rec = 1000 and 3000. For lower angles, the cross-sectional average pres- sure drops at the entrance to the channel, but recovers from the contraction and separation of the flow back to the developing fl...

work page 2000

Show all 12 references

[10]

Four common correlations used are detailed in Table IV

Comparison with Experimental Data and Existing Correlations The results can be compared with correlations and exper- imental data that exist within the literature. Four common correlations used are detailed in Table IV. Values of A and n for the correlation by Quadri et al.13 ...

2000
[11]

III A that for higher values of Reynolds number and α, large vortical structures form within the shear layer

Effect of Turbulence Model It has been shown in Sec. III A that for higher values of Reynolds number and α, large vortical structures form within the shear layer. This suggests that the shear layer makes a sig- nificant contribution to the total pressure loss, in addition to t...

2000
[12]

Monolith structures, materials, properties and uses,

Effect of Rounded Walls The geometry of the leading edge at the channel entrance plays a crucial role in determining the behaviour of fluid flow around it.4 A rounded edge allows for a gradual change in the flow direction, reducing the adverse pressure gradient and en- abling ...

2001 arXiv
[3000]

To assess the importance of the boundary layer develop- ment, and the effects of the oblique entry, the results are com- pared with the established correlations for frictional losses in a square channel with laminar and turbulent flow. For laminar flow, the fully developed, fr...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

29 The mesh cell size acts as a filter sorting the eddies by size

LES Setup The LES approach segregates the turbulent flow structures (eddies) into those that are sufficiently large to be resolved on the mesh, and the remaining, smaller, eddies which are mod- elled by a sub-grid scale turbulence model. 29 The mesh cell size acts as a filter sorting the eddies by size. Consequently, a more refined mesh results in a small...

work page

[2] [2]

To compare the ac- curacy of different models for the flow in the considered range of Reynolds numbers, a RANS model ( k − ω SST) has been used for several configurations

RANS Setup LES is considered a superior modelling tool for capturing flows with shear; however, RANS models are frequently used because of their computational efficiency. To compare the ac- curacy of different models for the flow in the considered range of Reynolds numbers, a RANS model ( k − ω SST) has been used for several configurations. The RANS gover...

work page

[3] [3]

Laminar Setup Both the LES and RANS models account for turbulence and therefore perform favourably when turbulence is present. Since some simulations are conducted at Reynolds numbers associated with laminar flow transitioning to turbulence, these models may artificially induce turbulence under conditions where it would not develop in reality. To assess w...

work page 2000

[4] [4]

This causes the formation of a vena contracta immediately post-entrance (see Fig

Recirculation Region and Shear Layer In the case of an axial entry, the flow path contracts as it en- ters the channel. This causes the formation of a vena contracta immediately post-entrance (see Fig. 8). For contraction ratios typical to monoliths and catalytic converters ( ≈ 0.75 - 0.9), the effect is not very pronounced, and the separation zones forme...

work page

[5] [5]

Secondary Flow Formation of secondary vortices in non-circular ducts has been observed in many experimental and numerical studies,36–38 and is attributed to the transverse turbulent stress gradients. These vortices play a significant role in shaping the overall flow structure and enhancing mixing within the channel.19,21 At lower Reynolds numbers, the sec...

work page 2000

[6] [6]

Turbulence Development The discussed flow features (flow acceleration due to sepa- ration, shear layer, and secondary flow formation) contribute to the transition of the flow to turbulence with increasing Reynolds number and/or oblique entry angle. Fig. 15 shows the average cross-sectional distribution of resolved velocity Numerical Investigation of the E...

work page 2000

[7] [7]

16 shows the pressure distribution in the domain for axial entry ( α = 0◦) simulations with Rec = 1000, 2000, and

Pressure Drop for Axial Flow Entry Simulations Fig. 16 shows the pressure distribution in the domain for axial entry ( α = 0◦) simulations with Rec = 1000, 2000, and

work page 2000

[8] [9]

18 and 19 show the pressure distribution along the channel for cases with an oblique flow entry for Rec = 1000 and 3000

Pressure Drop for Oblique Flow Entry Simulations Figs. 18 and 19 show the pressure distribution along the channel for cases with an oblique flow entry for Rec = 1000 and 3000. For lower angles, the cross-sectional average pres- sure drops at the entrance to the channel, but recovers from the contraction and separation of the flow back to the developing fl...

work page 2000