Control of the Rough Wall Turbulent Boundary Layer: A Literature Review

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Control of the Rough Wall Turbulent Boundary Layer: A Literature Review

The main driving force behind turbulence research is its constant occurrence in the area of fluid dynamics. as the turbulence modelling is considered to be one of the difficult topics to study because of its math-heavy basics as well as it’s dependency on the numerical methods which may not provide the exact results. In the past, in this field, more research has been conducted on the turbulent boundary layers over a smooth wall surface (Cantwell 1981; Kline 1978; Kline and Robinson 1990; Kovasznay 1970; Sreenivasan 1989; Willmarth 1975). Considering the difficulty very few researchers have explored the advanced complexities such as the flows over rough walls, variations in pressure gradient, etc. (Raupach, Antonia & Rajagopalan 1991).

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In the aerospace industry the drag reduction, lift control, and noise level attenuation is very desirable. Hence, the development and use of appropriate control strategies are of much importance. The turbulent boundary layer (TBL) observed in engineering applications such as cars and airplanes become rough. This is due to the TBL thickness reduces with increase in Reynolds number value (Djenidi, Kamruzzaman & Dostal 2019). Understanding and controlling the turbulent boundary layers is a very important phenomenon in order to increase efficiency by reducing the drag (Turbulence isn’t just science problem 2019).

The primary reason to study the boundary layer theory is to find the friction drag. Which is calculated by evaluating how the shear stress is distributed over the surface of the wall. Finding the shear stress distribution, velocity profile and the thickness of the boundary layer is an essential task to control the boundary layer. The terms mentioned here are calculated for different flows as mentioned by Hibbeler (2017), for laminar flows by using Blasius approach and for Turbulent flows by using Prandtl’s one-seventh power law along with a formulation by Prandtl’s and Blasius seem to work well.

Keywords: Boundary layer theory, Turbulent boundary layer, Smooth wall, Rough wall, Control of boundary layer.

Boundary-Layer Theory

In the near-wall region, the fluid adheres to its means, close to the thin layer the forces in the fluid which cause the friction to be delayed. The velocity of the fluid increases in that particular thin layer from the smallest value (which is considered to be 0) near the wall to its final full value which corresponds to the external flow without friction. This particular layer is defined to be the boundary layer. This definition was provided by Schlichting (1960), In his book. This figure of BL formation will help readers to visualize this phenomenon.

Figure 1. Boundary-Layer Formation on Smooth Wall (Schlichting 1960).

Here, the points are connected at each value of “x” where [u (fluid particle velocity) = 0.99 U (free stream velocity)]. The dotted line considered to be the edge of the boundary layer and the region inside the edge is the inner region of the boundary layer.

Boundary-Layer Classification

For the external wall-bounded flows, the nearest thin layer to the surface is considered to be a boundary layer. But the boundary layer is a broad term, as there are several parts/regions of the boundary layer. Whenever the fluid passes over the surface (let’s assume the surface as a smooth wall for ease) up to certain length the fluid flow is parallel to the surface in the orderly manner. There comes a point when the flow begins to get disturbed and changes to a turbulent flow in which the fluid particles jump from the one plane to another. This transition from laminar to turbulent is not sudden, after the demolition of the laminar flow and before the generation of turbulent flow there lies a phase in which the flow is neither laminar nor turbulent, and this flow/phase is defined to be transitional flow/phase.

The Reynolds Number (Re) is the dimensionless quantity which gives the knowledge about the flow pattern whether it is laminar or turbulent. The table below gives information about the flow pattern and the respective Re.

Table 1. Boundary-Layer and Reynolds Number (Critical Reynolds Number 2019).

Boundary Number

Reynold’s Number


Re < 2000


2000 < Re < 3000


Re > 3500

Smooth and Rough Wall

The smooth wall is the one which has no roughness or negligible friction velocity on the contacting surface with the fluid, which means the fluid flow has less resistance as compared to the rough wall, where the rough wall introduces the irregularities on the surface called as roughness. Since the rough surfaces provide more friction and resistance to the flow they induce more turbulence.

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The profoundresearch has been carried out on the turbulent boundary layer in external flows on the smooth wall considering the zero pressure gradient to eliminate the difficulties (e.g. Kovasznay (1970); Willmarth (1975); Kline (1978); Singh, Radhakrishnan and Narayan (1988); Antonia, Zhu & Sokolov (1995)). Studying the TBL’s over the simple structure for better understanding is important, before exploring the complexities of adverse pressure gradient, TBL noise. It is important to explore the turbulence in the wall-bounded region where the wall has roughness, to understand the interaction between the inner and outer layer (Raupach, Antonia & Rajagopalan 1991). In a TBL there are two types of the flow regions, one is an inner layer (the region inside the edge of the TBL) second is an outer layer (the region outside the edge of the TBL) Akinlade et al. (2004).

The wall similarity hypothesis proposed by Townsend (1976), says that the outer region of the TBL in the smooth wall as well as in rough wall is nearly the same, and less sensitive to the turbulence because of low strength of shear in the region.

The smooth wall and rough wall has the same structure in the outer layer where the shear forces are very weak, so the outer region is considered to be a region where the turbulence phenomenon is absent.(based on Townsend (1976)) But, in the inner region close the wall the where the shear is large, significant difference can be observed depending upon the smoothness or roughness of the surface. The roughness increases skin friction and alters the structure of the BL (Raupach, Antonia & Rajagopalan 1991).

Krogstad and Antonia (1999) found the transition from the smooth wall to rough wall causes the non- negligible changes in the outer layer. This challenges the Townsend (1976) and Raupach, Antonia and Rajagopalan (1991) claim on the matter. And explains the unpredictability and uncertainty of results in this field of research.

Lee and Sung (2007) found the normalization of the turbulent quantities by friction velocities, the roughness introduces the turbulent stresses and vertical turbulent transport in the outer layer as well (repeated in Lee et al. (2009) also).

Control of the Turbulent Boundary Layer

In the past experiments done by (Schlichting(1960); Antonia, Zhu and Sokolov (1995); Wallis (1950); Katz, Nishri and Wygnanski (1989); Gad-el Hak (1989); Pailhas et al. (1991); Oyewola, Djenidi and Antonia(2003)) the wall suction reduces the skin friction and delays the flow separation and transition for a smooth wall. (also mentioned by Djenidi, Kamruzzaman and Dostal (2019)).

Antonia, Zhu and Sokolov (1995) worked on a TBL with localized wall suction and used hot wire measurements. The relaminarizing of the layer depends largely upon the Reynolds Number/suction rate. The required streamwise distance for the full development of BL decreases as an increase in Reynold’s Number (Re) for suction rate (σ). The velocity profiles such as mean and RMS longitudinal depart from the undisturbed profiles for all Re and σ. The Skewness and Flatness factor don’t depend on Re but are subjected to changes as per the change in turbulence structure.

Djenidi, Kamruzzaman and Dostal (2019) Performed the wall suction on the rough surface through a porous strip with hot wire measurements for a 2D fully rough wall (k-type roughness, where the square bars of the roughness are introduced on the smooth wall surface). To the downstream of the suction the drag coefficient increases and returns back it’s no suction value. The mean velocity distribution in the region close to suction altered in the outer layer and it shows no relaminarization of BL. Just behind the suction strip due to the suction, the velocity RMS distribution was changed significantly. The less affected velocity factors were flatness and skewness.


The boundary layer separation and it’s negative effects on the efficiency by the introduction of the drag forces and other friction forces needs to be controlled to get better results. Less research is performed in the area of rough walls as compared to smooth walls. this project is planned for optimizing the TBL control strategies of smooth wall on rough walls to get better efficiency by reducing and other friction forces.


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