Short answer

When designing for turbulent flow over surfaces with significant roughness, consider the aspect ratio of the roughness elements and prioritize control over the gap width for high aspect ratio features.

Field: Classic Design
Source: Journal of Fluid Mechanics (2018)
Method: Direct numerical simulation (DNS)
Evidence: Strong effect

The perceived roughness of a surface in turbulent flow transitions from being primarily influenced by its height to being dictated by the gap width between roughness elements when the aspect ratio of these elements is sufficiently high. This classic design research insight is drawn from a 2018 study published in Journal of Fluid Mechanics. Using Direct numerical simulation (dns), researchers explored how this design variable affects real-world outcomes. The key design takeaway: When designing for turbulent flow over surfaces with significant roughness, consider the aspect ratio of the roughness elements and prioritize control over the gap width for high aspect ratio features.

Study

Classic DesignHigh ImpactStrong effect

Surface roughness behaviour shifts from height-dependent to width-dependent at high aspect ratios

Journal of Fluid Mechanics · 2018

Key Findings

01Increasing roughness height ($k$) while keeping width (${\mathcal{W}}$) constant in viscous units can lead to non-$k$-type behaviour.
02For deep surfaces with $k/{\mathcal{W}} \gtrsim 3$, the roughness function appears to depend only on ${\mathcal{W}}$ in viscous units, indicating the flow primarily perceives the gap width.

Application

Design takeaway

How to apply

When designing for reduced drag on aircraft wings or optimizing flow through pipes with textured surfaces, consider the geometry of the texture beyond just its height.

Project actions

01When investigating surface textures, consider simulating or testing a range of aspect ratios.
02Document how the perceived effect of a surface feature changes as its proportions vary.

Method & Evidence

AimTo investigate how the aspect ratio of spanwise-aligned bars affects turbulent flow characteristics and the resulting roughness function.

MethodDirect numerical simulation (DNS)

ProcedureSimulated turbulent flow in a minimal-span channel over two-dimensional rectangular bars with varying aspect ratios. Analyzed the roughness function ($\Delta U^{+}$) in relation to roughness height ($k$) and width (${\mathcal{W}}$).

ContextFluid dynamics, surface engineering, aerodynamics

Variables

IVAspect ratio of spanwise-aligned bars (ratio of height to width).

DVRoughness function ($\Delta U^{+}$), which quantifies the effect of roughness on flow velocity.

CVReynolds number, channel geometry (minimal span), viscous units for width.

Strengths & Limitations

Strengths

+Utilizes direct numerical simulation for high fidelity flow analysis.
+Investigates a range of aspect ratios, providing nuanced insights.

Limitations

Simulations are idealised. Real-world surfaces have variations, and flow conditions can be more complex than those modelled.

Reliability & validity

The validity of the findings relies on the accuracy of the DNS method for turbulent flow. Reliability would be assessed by repeating simulations with slight variations in parameters.

Think critically

How might this principle of 'perceived width over height' apply to other design contexts beyond fluid dynamics, such as acoustic dampening or material adhesion?

Design Principles

"The perceived influence of surface roughness on turbulent flow is context-dependent, shifting from height-based to width-based characteristics with increasing aspect ratio."

Understanding this transition is crucial for designers aiming to control surface friction and flow characteristics. It suggests that for certain applications, manipulating the spacing of surface features may be more impactful than simply increasing their height.

What This Means for Your Design

Imagine a comb. If the teeth are very close together, it's the space between the teeth that matters most to how it interacts with something, not just how tall the teeth are.

How to use in your project

1.Reference this study when your design project involves controlling surface friction or flow characteristics, especially if you are considering textured surfaces.

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Quick Cite

Paragraph starter

Research by MacDonald et al. (2018) highlights that the impact of surface roughness on turbulent flow is not solely determined by the height of the roughness elements. Their direct numerical simulations revealed that for high aspect ratio roughness (where height significantly exceeds width), the flow's interaction becomes more sensitive to the width of the gaps between roughness elements rather than their depth. This suggests that for designs incorporating such features, manipulating the spacing could be a more effective strategy for controlling flow characteristics than simply increasing the size of the features.

Source

Journal of Fluid Mechanics

Direct numerical simulation of high aspect ratio spanwise-aligned bars

journal · 2018

View source

Questions About This Research

What does the research say about surface roughness behaviour shifts from height-dependent to width-dependent at high aspect ratios?: When designing for turbulent flow over surfaces with significant roughness, consider the aspect ratio of the roughness elements and prioritize control over the gap width for high aspect ratio features. Evidence: Journal of Fluid Mechanics (2018).
Why does "Surface roughness behaviour shifts from height-dependent to width-dependent at high aspect ratios" matter for design?: Understanding this transition is crucial for designers aiming to control surface friction and flow characteristics. It suggests that for certain applications, manipulating the spacing of surface features may be more impactful than simply increasing their height.
How can designers apply this research?: When designing for turbulent flow over surfaces with significant roughness, consider the aspect ratio of the roughness elements and prioritize control over the gap width for high aspect ratio features.
What were the main findings?: Increasing roughness height ($k$) while keeping width (${\mathcal{W}}$) constant in viscous units can lead to non-$k$-type behaviour.. For deep surfaces with $k/{\mathcal{W}} \gtrsim 3$, the roughness function appears to depend only on ${\mathcal{W}}$ in viscous units, indicating the flow primarily perceives the gap width.
What research method was used?: Direct numerical simulation (DNS).
How strong is the evidence?: Evidence strength is rated Strong effect, based on a 2018 journal from Journal of Fluid Mechanics.
What should I do differently in my next project?: When designing for reduced drag on aircraft wings or optimizing flow through pipes with textured surfaces, consider the geometry of the texture beyond just its height.
What are the limitations?: The study uses minimal-span channels, which may not fully replicate the behaviour of flows over infinitely wide surfaces. The findings are specific to spanwise-aligned bars.