You can find a lot of literature about flow of bluff-body in confined channel, just use some keywords in Google.

Be aware that the Re number in a channel is evalutare using the height while in case of bluff-body the better reference lenght is its characteristic lenght.

Laminar flow occurs when a thin layer of water (such as rainwater drains on a street) flows at a very low speed. The kinematic viscosity of water at a temperature of 20 ∘ C is equal to 1.0 × 10−6 and its average speed in open channels is usually equal to 0.5 m/s.

On the other hand, the hydraulic radius is generally more than 0.1m. Consequently, the Reynolds number for water flowing in an open channel will be greater than 200,000. Therefore, the type of flow is turbulent most of the time. can you send your chanel dimension?

when the Reynolds number is lower than 2300 (about 1000) automatically the flow is laminar but when the pipe contains obstacles it can create some turbulence depending on the geometry of the pipe, the density of the fluid, and the dynamic viscosity of the fluid you can simulate your case study on ANSYS Flent software and see clearly what exactly is happening

The Reynolds number UD/nu=2300 is based on a smooth circular pipe of diameter D, with STEADY mean flow velocity U and fluid of kinematic viscosity nu. Below this critical Reynolds number any perturbation due to an obstacle will not cause persistent turbulence to occur far downstream of the obstacle. Of course locally the wake of a blunt body placed in the pipe can be turbulent, but soon the flow will relaminarize if we travel further downstream. Above Re=2300 the flow does not need to be turbulent. It can be turbulent if there is a sufficiently large initial upstream perturbation. In principle the flow can remain laminar if the inlet is very smooth and care is taken to avoid vibrations. Experimentally fully developed laminar pipe flows have been achieved for Re=500. 000. It is important to realize that this critical Reynolds number does depend on the geometry of the cross-section of the channel. For a rectangular channel of height h and width w >>h, usually one considers a Reynolds number Re=Uh/nu based on the channel heigth. The critical Reynolds number for allowing turbulence is around Re=hU/nu=1100. There is however much less literature on flows through slit shaped channels than circular pipes. If you consider an open channel flow, clearly the critical Reynolds number will be quite different from Re=2300 and of course it does depend on the length scale used in the definition of this Reynolds number!

When the fluid moves in smooth and well-ordered layers, it is referred to as being in a laminar regime. Turbulent flow, on the other hand, occurs when the Reynolds number surpasses a specific value. The presence of obstacles in a channel can disrupt the smooth flow and lead to a transition from laminar to turbulent flow, often at lower Reynolds numbers than in a smooth channel. This is due to the formation of eddies and vortices that increase the level of turbulence. However, the specific conditions under which this transition occurs will depend on a variety of factors such as the size and shape of the obstacle, the viscosity of the fluid, the flow rate, and the geometry of the channel.

I don't have any specific reference for this (this may be relevant: https://doi.org/10.1134/S1995080216030045), but it would be quite straightforward to do the simulation and analyze the results.

When carrying numerical simulations, you will only obtain meaningful information concerning the transition from laminar to turbulent flow if a resolved DNS calculation is carried out. At high Reynolds numbers (order 2000) this is far from trivial. Experiments can be much easier. Using inkt for flow visualization in a water flow you very clearly see the transition from laminar to turbulent flow. This is the original experiment of Reynolds!

to Avraham Hirschberg - Better if you use diluted fluoresceine.

As the writers above point out, this is not new science. Transitional region flows are not amenable to much pure maths. However, when Re < 2000 the flow over obstacles in the flow is usually analysed by "Creeping Flow" (i.e. purely viscous flow) analysis, as the boundary layer is conserved in most cases. There are many classical analytical solutions for this flow regime.

Yes this could change the flow regime from laminar to turbulent as obstacles could create perturbation into the laminar flow, then this perturbation can grow into turbulence..

Yes, the presence of obstacles in a channel can impact the smooth flow and cause a flow transition from laminar to turbulent. Obstacles could introduce perturbation into the flow system and this perturbation increases the turbulence forces.

One should better define what it means turbulence.

The presence of vortices can occur also in laminar flows.

Actually, the idea of introducing undefined concepts "laminar flow" - "turbulent flow" for a channel or pipe flows is based on the replacement of the fundamental equations of fluid mechanics, which are differential analogues of the laws of matter, momentum and energy conservation, by constitutive equations that do not allow experimental verification with accuracy control. It was Stokes, who first noted in a review of Reynolds' first paper on turbulence that the equations of motion are invariant and do not need or do not require the introduction of additional constants.

The possibility of introducing new equations and new variables is explained by several logical, physical and mathematical mistakes that have plagued the theory of fluid flows since the formation of adequate differential models of flows.

Both Euler and Stokes understood and noted in their fundamental articles that all real liquids are "heterogeneous", that is, the density is a variable due to dependence on temperature, pressure, concentration of dissolved substances and suspended particles distributed non-uniformly. Moreover, in the fields of body forces, fluids are stratified and are characterized by continuous or layered profile of density. Variation of density can be small or large and they exist always. In the case of small dissipative coefficients, linearized system of equations can be solved completely applying the theory of singular perturbations.

However, Stokes performed calculations in the approximation of a constant density of the liquid. Such an assumption leads to the degeneration of the equations system.

Consequently, the general properties of the system was not studied during long time, and only regular solutions were found. They describe waves or main stream in a linear approximation . Singular solutions (and their number is more than only one!) were lost. More details about the modern analysis of the system of fundamental equations can be found in [1]. The fundamentals of the surface waves and accompanying ligaments in a liquid theory are given in [2].

A physical error - an attempt to measure the fluid velocity, which is an unobservable physical quantity, is also a consequence of using the homogeneous fluid approximation. In this case the velocity and flow invariant - momentum are indistinguishable. This fact implies the hypothesis of "passive impurity" in which the fields of independent physical quantities - momentum - and distribution of matter or other physical properties of the medium, are identified. This hypothesis has led to the construction of countless methods for implicit measuring flow velocity.

However, I am not aware of works that compared the results of using dissimilar types of flow velocity meters – strain gauge, hot-wire, acoustic and many optical ones. Moreover, results cannot coincide in any case, since ligaments that are the subtle structures of each flow, are individual and manifest themselves in different ways in the patterns of the fields of independent variables.

Once more logical error is the lack of definitions of the general properties of the introduced systems of equations, in particular, calculations of the rank of systems, which define the minimum number of eigenfunctions constituting the complete solution, as well as infinitesimal symmetries, showing the invariants of the system under study.

Summary.

Only equations that correspond to the laws of conservation of matter, energy and momentum are physically justified. Of the three important quantities, one – that is the energy, including internal energy, is practically did not study in hydrodynamics. And, the second one – momentum – is not measured.

Everyone term in the complete solution of the fundamental system of equations is important, both regular and singular. Regular solutions (waves) can be both potential and vortex. Ligaments are always vortex. It is ligaments and the products of their evolution that form the inseparable fine structure of flows observed in experiments with a stratified fluid.

Any flow in a channel or in a tube consist of the main stream and thin submerged longitudinal jets or trickles – ligaments. Trickles are formed at initial conditions and supported by continuous reconstruction of internal energy distribution due to deforming of complexes, clathrats, voids and all other associates of physical and chemical nature.

Moreover, any obstacle changes field of ligaments or internal structure of the flow.

Literature

1. Chashechkin Y.D. Foundations of engineering mathematics applied for fluid flows // Axioms. 2021. V. 10. Iss.4. 286. https://doi.org/10.3390/axioms10040286.

2. Chashechkin Yuli D., Ochirov Artem A. Periodic waves and ligaments on the surface of a viscous exponentially stratified fluid in a uniform gravity field // Axioms.2022. V. 11(8), 402. doi: 10.3390/axioms11080402..

And more in ResearchGate.

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Turbulence is a chaotic essentially unsteady motion in which energy extracted by stretching of large vortical structures is transfeted to lower spatial scale vortical structure in a cascade until the Kolmogorov length scale is reached at which the energy is dissipated by viscosity.

A condition for the occurence of such a chaotic motion is the instability of the main flow and the presence of shear. In a circular pipe the steady flow becomes fully turbulent downstream of a sufficiently large perturbation if the Reynolds number Re=dU/nu based on the pipe diameter and the cross-sctional averaged pipe is larger than Re=2300. For lower Reynolds number the flow can locally be turbulent just downstream of the perturbation or obstacle but with soon become laminar and for sufficiently long smooth pipe reach the Poiseuille flow limit ( at low Mach numbers). If the perturbations are sufficiently small (smooth inlet, no vibrations…) there is no limit for the Reynolds number of a Poiseuille flow in a circulat pipe with smooth rigid walls.

Please note that for a slit flow through a very wide two dimensional channel of height h limited by two plannar smooth walls is always turbulent when Re=hU/nu is above Re=7900 and will not become turbulent below Re=1000 or 1100. The lower limit Re=1000 is less clear than the critical Reynolds number of circular pipes because it also depends on the width of tge channel and there is little experimental information available.

Of course the definition of “channel” and of “ Reynolds number” should be ckarified before drawing a final conclusion. Naybe the above question is for a water flow in a channel with an open upper surface. The the definition of channel height is different!!!! One can also consider a free surface water flow in a channel with circular bottom sgaoe, or triangular shape…

certainly the figure Re=2300 is in such cases completely meaningless.

I think that the discussion should also focus on the blockage ratio. Large values can also prevent the onset of fluctuations at high wavenumbers.

According to my point of view as the obstacle comes in that region velocity changes and Reynolds number must decrease due to this but never pass the 2300 Re value so no impact on the laminar to turbulent region.