Comparison of Different Turbulent Models for Backward -facing Step Flow

 

Comparison of Different Turbulent Models for Backward -facing Step Flow 

Abstract

A comparison of different turbulence model for flow over a backward facing Step is presented. A Reynolds number of 36,00 and an averaged velocity of 41.7 m/s was considered. The result was compared with data by Driver and Seegmiller.  The purpose of this paper was to give intuition to the reader that   depending upon the nature of the problem to be solved, one model might be superior in once case whereas the same model might not work at all for different type of flow and when right model is used for the right job, turbulence models yields the reliable result.

Contents

Introduction

Eddy viscosity model

Range of application of viscosity model

RANS Single Equation model: Spalart- Allmaras

RANS Two-Equation Model: (k –
ε
) model

RANS Two-Equation Model: (
k–ω
) model

Limitations of Eddy -viscosity Models

Reynolds Stress Model (RSM): Reynolds Based Models

Range of application of RSM

Shortcoming of RSM

Case Analysis

Background

Near Wall treatment methods

Result and discussion

Conclusion

References

.

Turbulence is the complex type of fluid motion, which makes it definition even more difficult. There are many definitions as for example, the basic definition by Von Karman is “Turbulence is an irregular motion which in general  are seen  in fluids, gaseous or liquid, when they flow past solid surfaces or even when neighboring streams of the same fluid flow past over one another”.(Wilcox) .The Equations for turbulence Fluctuations are obtained by Reynolds de-composition where the flow variables are express in the form of averaged mean value and the fluctuation about the mean .

                                                   
ϕ=ϕ‘+ϕ̃
                                         (1)

Where

is the instantaneous scalar quantity,
∅ ̅
is the mean value and
∅́
is the fluctuation. Substituting the Eq (1) into the Continuity and Navier Strokes Equation one derives what is called Reynolds Average Navier Strokes Equation.

∂U̅i∂x=0
∂U̅i∂t+∂∂xjU̅iU̅j=–1ρ∂P–∂xi+ν∂2U̅i∂xj∂xj–∂∂xjui‘uj‘̅                          (3)

Where
U̅i
is the mean velocity,
Ui‘
is the fluctuating velocity,
ρ
the density of the fluid 
ν
is the kinematic viscosity, while the term
Ui‘Uj‘̅
is the Reynolds-stress tensor.
τij=Ui‘Uj‘̅
   is a symmetric tensor which has six independent components. The number of unknown quantities (3-velocity components and six stresses and pressure is larger than the number of the available equations (continuity and NS) where  no of variables is not equal to no of equations which need to be closed leading  to closure problems .The  method  used to resolve this problem of “closure “ can be done either  by use of Boussinesq eddy -viscosity or the by calculating the of the induvial Reynolds stress using differential transport equation.

Eddy viscosity model

 In eddy viscosity model the Reynolds stress are modelled as follows
τij=Ui‘Uj‘̅=23kδij–νt∂u̅i∂xj+∂Uj̅∂xj
                                                       (4)                                                                                                 
k=12Ui‘Uj‘̅                                       
ω=εk                                             

Where k is the turbulent kinetic energy and
νt=μtρ
is the turbulent or the eddy viscosity,
ω
is the specific dissipation rate
∂u̅i∂t+∂∂xjU̅iU̅j=–1ρ∂P̅∂xi+∂∂xjv+νt∂u̅i∂xj                                          
(5)

 Each turbulent model calculates the
νt
differently, the one equations model considers as a characteristic velocity the square root of the turbulent kinetic energy and assign algebraically the length scale.
νt=Cvkl                                                                                                    (6)

Whereas the two-equation model such as
k–ε
and
k–ω
compute both the characteristic velocity and length and predicts the value of
νt
which is given as

K
–ε
model

vt=CμfμK2ε
                                                                                     (7)
k–ω
model
vt=αkω 
                                                                                           (8)                                                   

Where
Cμ,α
are constant,

being a damping function,
ε
is the turbulent kinetic energy dissipation rate and
ω
the dissipation per unit turbulence kinetic energy

 

Range of application of viscosity model

RANS Single Equation model: Spalart- Allmaras

This one equation model is not memory intensive,  work with poor mesh , stable with good convergence and its application can be found on internal and external flows and boundary layers flow under pressure gradient , but the limitations of the models are they works poorly with 3d flows , flows involving  strong separation , decaying turbulence and shear flows . (engineering.com, n.d.).

RANS Two-Equation Model: (k –
ε
) model

Standard k-epsilon, RNG K-epsilon, Realizable k -epsilon

Standard (k-
ε
) performs poorly for complex flows which includes strong stream line curvature, Adverse pressure gradient and separation. This is suitable for initial screening for alternative design and for initial iterations, whereas the RNG (
k–ε
) can solve complex flows and realizable (
k–ε
) offers a better computational efficiency over RNG (
k–ε
) (www.fluentusers.com, n.d.)

RANS Two-Equation Model: (
k–ω
) model

Standard (
k–ω
), SST (
k–ω
)

This model is appropriate for turbomachinery simulations and where strong vortices are present. This model works for swirling flows and near the wall region but overpredicts separations. converge is difficult as compared to
(k–ε)
model and are sensitive to initial conditions. 
SSTk–ω
model is widely used in aerospace applications. This model can be applied to viscous affected region without any modifications. SST(k-w) is superior on its capability to predict separation and reattachment, better as compared to Standard 
k–ε
and
k–ω
. (www.engineering.com, n.d.)

 

Limitations of Eddy -viscosity Models

Although the eddy viscosity model like 
k–ω
and
k–ε
model is widely used in the engineering applications they have a significant shortcoming when a complex, real-life turbulent flows are encountered. (www.cfd-online.com/wiki/Turbulence _Modeling , n.d.) The Applications of the Boussinesq Approximations leads to failure to predict anisotropy of the normal stresses, to model secondary and swirling flows and to account for streamline curvature effects (Turbulence Modelling for CFD).

Reynolds Stress Model (RSM): Reynolds Based Models

The Reynolds stress model also known as Reynolds Transport Model, are higher level closure problem generally known as second order closure problems. This modelling originates from the work by chou (1935) and Rotta (1951). In this approach the individual Reynolds Stress,
ρui‘uj‘̅
, are calculated. The Reynolds stress model closes the Reynolds Average Navier Stokes equations where the transport equation are solved for Reynolds stresses, along with the equation for the dissipation rate. The exact transport equations for the transport of the Reynolds stress
ρui‘uj‘̅
,  may be written as follows.

       (7)

               

Or 

Local time derivate +
Cij=DTij+DL,ij+Pij+ϕij–ϵij+Fij

Where
Cij
is the Convection term,
DTij
is turbulent diffusion ,
DL,ij
is the Molecular diffusion ,
 Pij
is the stress  production ,
 ϕij
pressure strain
ϵij
is dissipation and
Fij
is the production by the system rotation. Out of these terms
Cij
,
 DL,ij
,
 Pij
,
 Fij
does not require modelling whereas
DTij
,
ϕij
, and
ϵij
requires modelling.

 

Range of application of RSM

The Reynolds stress Model are suitable for complex 3d flows with strong streamline curvature, Strong Swirl Rotation for e.g. rotating flow passage, curved duct, cyclones). Flow with sudden changes in the mean strain rate, secondary flow and Buoyant flow. Reynolds stress model are superior performance compared to eddy viscosity model in these cases, but it comes at the cost of reduced numerical robustness, increased in the computational time.

Shortcoming of RSM

The accuracy of the RSM depends on how accurately the, pressure strain and dissipation is modelled which are complicated, and are often  responsible for compromising the in predictions of RSM. The RSM rely on (
ε or ω
) and inherit deficiencies resulting from the assumption in these equations. The accurate prediction of flow separation is problematic when
ε
– equation model is used. In order to avoid these issues, a Reynold stress model has been implemented a model that uses the
ω
– equation, and it is showed later in this case analysis the Reynolds Stress Omega based model show a better result in predictions of reattachment length as compared to other RSM model.  Although, Reynolds stress model are more suited to complex flows theoretically, however in practical they are often not superior to two-equation model, which will also be proven later in this case analysis.

Background

 Here a case analysis is performed using a Geometry of a backward facing- step where the flow is computationally simulated   with different turbulence models available.  The Plane backward step flow is very complex, even though the geometry is simple it includes recirculation, flow separation, reattachment, Adverse pressure gradient, boundary layer redevelopment  (S.P.YUAN, 1998) . The separated flow , reattachment, promotes to  pressure fluctuation ,structure vibration  and also shows  unsteadiness in  structure with a large scale vortex in the separated shear layer and low frequency motion around the reattachment  with fluctuation of an instantaneous reattachment point (Troutt, 1984).Many investigators have compared their model with (Driver, 1985) which is widely used benchmark to evaluate turbulence model ability to predict reattachment location of  flow

                                                                                            Figure 1 Backward Facing Step

In order to compute the flow over the backward-facing step, (0°) a commercially available CFD, FLUENT, is used. The turbulence model used in this study are standard
k–ε
model, RNG 
k–ε
model, RKE
k–ε
model, RSM, standard
k–ω
model and SST
k–ω
.

Near Wall treatment methods

 The case has been analyzed using both the Enhanced wall treatment and Non -Equilibrium wall function.  The enhanced wall treatment combines a two-layer model with so called enhanced wall function. In two-layer model, the whole domain is subdivided into a viscosity -affected region and fully turbulent region. The near wall mesh is kept at
y+≈1
which is very fine enough to resolve the viscous sublayer. At
y+≈1
,  the enhanced wall treatment is identical to traditional two-layer zonal model. (Fluent ).In Fluent model that uses
ω
, the near wall treatment is not available because the near wall treatment that is used is a
y+
which is an insensitive method that automatically behaves either as a viscous sublayer resolving treatment or as a wall function depending on how fine or coarse the near wall mesh is . (Fluent ). Similarly, the Non-equilibrium wall function is used because of its capability to partly account for effects of pressure gradients. The non- Equilibrium wall functions are recommended for use in complex flow involving separation reattachment and impingement where mean flow and turbulence is subjected to severe pressure gradients and changes rapidly. (Fluent)

Figure 2mesh for backward facing step with 0-degree wall-angle

The mesh used for present computation is quadrilateral mesh with a cell of 21750 and with a minimum orthogonality quality of 1. The average velocity is 41.7 m/s and Reynold’s number are of 36,00. The wall boundaries condition was applied with no slip condition and the flow was assumed to be incompressible

Result and discussion

The reattachment length for different turbulence models are shown in table 1 and is being compared with values by Driver and Seegmiller. (Driver, 1985) also validated with (KIM, GHAJAR, & L.FOUTCH, 2005) .in the above journal the author has also compared results using standard wall function which has been avoided in this report and the comparison has been done using Non-equilibrium wall function and enhanced wall function .

The turbulence model RKE, and RNG with non-equilibrium wall function showed a good result when compared to the experimental data. However, the RSM and SKE underpredicted the reattachment length. For model employing Enhanced wall function all turbulence models of 
k–ε
  overpredicted the reattachment length whereas RSM underpredicted.  Similarly, RSM when modelled using Stress Omega which required no wall treatment showed a good result whereas the SKW and SKE (no wall treatment) overpredicted the reattachment length.

                             Table 1: Comparison of reattachment length.

Turbulence Models

Non- equilibrium wall function

Enhanced wall function

NO-wall treatment

Experiment (1985a)

SKE

5.40

5.28

6.26 ±0.10

RNG

6.07

6.64

6.26 ±0.10

RKE

6.21

6.93

6.26 ±0.10

RSM

4.91

4.79

6.26 ±0.10

SKW

6.79

6.26 ±0.10

SST

6.49

6.26 ±0.10

RSM -Stress omega

6.07

6.26 ±0.10

                                          Figure 3 Reattachment point for different model using enhanced wall treatment.

                                          Figure 4Reattachmnent for different turbulence model using Non- equilibrium wall function

Conclusion

In Practical RSM model are not often superior to two –equation model. Reynolds stress model that implement model (Reynolds Stress Omega) shows a better result in predictions of reattachment length as compared to other RSM model. The two-equation mode is widely used for engineering applications for its robustness some success has been achieved with two -equations models however failure is still common for many applications that involve strong curvature, buoyancy, strong swirl rapid compression and expansion.  Among the difference turbulence model available there always has been a tradeoff between the computational efficiency and solution accuracy and not every model is suitable for every type of flow, so a best judgment should be used.

(n.d.). Retrieved from engineering.com.

(n.d.). Retrieved from www.fluentusers.com.

(n.d.). Retrieved from www.engineering.com.

(n.d.). Retrieved from www.cfd-online.com/wiki/Turbulence _Modeling .

(n.d.). In D. C. Wilcox, Turbulence Modelling for CFD (p. 229). DCW industries.

(n.d.). Retrieved from Fluent .

Driver, D. a. (1985). AIAA journal. Features of reattaching Turbulent Shear Layer in Divergent Channel Flow , 163-171.

KIM, J.-Y., GHAJAR, A. J., & L.FOUTCH, C. T. (2005). Comparsion of near- wall treatment methods for high reynolds number backward-facing step flow . International journal of computational fluid dynamics, 493-500.

S.P.YUAN, R. &. (1998). NEAR-WALL TWO-EQUATION AND REYNOLDS STRESS MODELING OF BACKSTEP FLOW , 283-298.

Troutt, T. S. (1984). Organised Strucutres in a Reattaching Seperated flow field , 413-427.

Wilcox, D. C. (n.d.). Turbulence Modeling For CFD. DCW Industries.

 

Control of the Rough Wall Turbulent Boundary Layer

Introduction
Turbulence is encountered in the various fluid dynamics operations. It is a very undesirable phenomenon that directly affects efficiency. Turbulence is the introduction of the irregularities in the airflow as well as the pressure distribution. This induces the skin friction drag which is known to significantly reduce the efficiency of the device. Turbulence cannot be dismissed completely, it can only be minimized up to a certain amount. Considering the scope in this area, lot of research is conducted in this field. It is very important to minimize the amount of turbulence as much as possible and it can be achieved by modelling the airflow around the device. The process of modelling the airflow around the device to get maximum efficiency is called turbulence modelling. Turbulence modelling is more practiced in the aerospace and automotive sector. This is very important to model a flow around the cars, airplanes to limit the usage of fuel.

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The region closer to the outer surface of the aerodynamic device is considered to be the boundary layer. The boundary layer plays a big part in the behaviour of the turbulence. The boundary layer has a region where the flow is in line or laminar, which is a laminar boundary layer. The region where the flow is disturbed and not linear is called a turbulent boundary layer. The primary reason to study a boundary layer theory is to find the friction drag. The friction drag is calculated by evaluating the pattern of the shear stress distribution over the surface of the wall. Finding the shear stress distribution, velocity profile, and the thickness of the boundary layer are essential for controlling the boundary layer. These terms are calculated for different flows; as mentioned by Hibbeler (2017), for laminar flows by using the Blasius approach and for Turbulent flows by using Prandtl’s one-seventh power law along with a formulation by Prandtl’s and Blasius.
Turbulence modelling is considered to be one of the most difficult topics to study due to its math-heavy basics as well as its dependency on the numerical methods. It may not provide the exact results. It is very important to explore the basic structures before moving to advanced complexities. Considering the difficulties more attention is given to the flow over basics structure, with the less complex flow. Significant research has been conducted on the turbulent boundary layers over a smooth wall surface in the past few years (Kovasznay 1970; Willmarth 1975; Kline 1978; Cantwell 1981; Sreenivasan 1989; Kline and Robinson 1990). Less research has been conducted on the advanced structures where the skin friction is increased due to the introduction of the roughness on the surface (Raupach, Antonia & Rajagopalan 1991).
Based on the results one of the most impressive methods proposed for the control of the flow over a smooth wall was the wall suction method. In this method, region on the wall surface where the turbulent boundary layer formed and then subjected to the wall suction using suction blower. The effect has been studied by comparing the results with or without wall suction. The produced results show that the turbulent boundary layer can be relaminarized by using this method. Limited researchers have tried applying these methods (developed for control of the turbulent boundary layer over the smooth wall) to the rough wall to see the effect.
Boundary Layer Theory
Background
At the beginning of the 20th century, the branch fluid mechanics started getting developed in two directions, theoretical hydrodynamics and hydraulics. The study originated based on application of motion equations to ideal, frictionless and non- viscous fluid. This method always questioned the practicality of the experiments. On the other hand, the science of hydraulics based on the practical approach (Considering all non-ideal factors) to the problems was developed (Schlichting 1960). At the beginning of the current century Ludwig Prandtl worked on the unification of these two branches, and successfully found the co-relation between these two and updated the field of fluid mechanics with the effective amalgamation of these two streams. 
In 1904 Prandtl presented a paper, “On the Motion of Fluids with Very Little Friction” in a Mathematical Congress held at Heidelberg which is considered to be the first document identifying the boundary layer phenomenon. In his eight pages paper, he talked about the theoretical aspects of the boundary layer (Schlichting 1960; Anderson 2005). He showed that the analysis of the much important viscous flows is possible, with some theoretical considerations and with the help of some simplified experiments, he proved that the flow passing over a rigid body can be divided into two different regions, one is the thin layer which sticks to the surface called as boundary layer and the other region away from the body where the effect of friction can be neglected (Anderson 2005).
In 1914 Prandtl showed the results of his famous spheres experiment which depicted the classification of the boundary layer into laminar and turbulent. This discovery was based on the Reynolds founding’s of the classification of flow in fluid dynamics into laminar and 
Turbulent (Schlichting 1960; Dryden 1995). Von Kármán One of the students of the Prandtl in 1921 proposed his well-known equation which involves integration, claiming the computation (approximate) of the boundary layer from the surface (Dryden 1995). After several years of experiments, W. Tollmein was successful in finding the critical value of the Reynolds number, after which the flow starts the transition from the laminar to turbulent. This theory was later verified by H. L. Dryden.
After 1930 the boundary layer theory got popularity and efforts were made by many researchers from all over the world (England, U.S.A, etc.) to understand this important phenomenon directly related to efficiency. At the end of the last century, the rate of papers published on the boundary layer theory is increased by the factor of two.
Boundary layer
Prandtl (1904), proved that fluid flow around the solid body can be divided into two different regions, first one would be the very thin layer close to the solid body which can be called as the boundary layer. The second one would be the region outside this particular layer. In the first region, the friction is considered as its around the surface of the solid body. The second region friction is neglected considering the large distance from the outer surface of the solid body.

Figure 1-1. Boundary-Layer Formation on Smooth Wall (Schlichting 1960).
Figure-1 shows the side view of the boundary layer, where Uꝏ is defined as the free stream velocity. Every fluid particle in the given flow will have its velocity. As the flow proceeds in the X- the direction from the Y-Axis the velocity of the fluid particle increases from the smallest value (Which is 0), when the value of the fluid particle becomes 99% of the free stream velocity that particular point is marked. When all suitable points are marked and drawn in the X-direction, the formed line is called a boundary layer, in figure-1 the boundary line is shown by region below the dotted line. The dotted line is called to be an edge of the boundary layer. δx is defined as the thickness of the boundary layer.
Turbulent Boundary Layer

Figure 1-2. Boundary-Layer Classification (Comsol 2019).
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 of understanding) up to a certain length, the fluid flow is parallel to the surface in an orderly manner. Eventually, the flow begins to get disturbed and changes to a turbulent flow in which the fluid particles jump from 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, a phase occurs where the flow is neither laminar nor turbulent, and this flow/phase is defined to be transitional flow/phase.
In Figure 1-2, the laminar region has particles flow in an orderly manner, and the turbulent region has the fluid particles revolving around their axis. The region in-between the laminar and turbulent is called a transition region where the transition from laminar to turbulent begins. The turbulent boundary layer is the area of interest because it’s the origin of the turbulence. In this work, the objective is to use wall suction just below the turbulent boundary layer region and try to convert the boundary layer into the laminar boundary layer, as much as possible. This can also be called as relaminarization.
The above figure 1-2 is the visual representation of the phases of the boundary layer, but the boundary layer whether it is laminar or turbulent is described using the Reynolds Number. The Reynolds Number is dimensionless quantity gives an idea about the nature of the flow or boundary layer.
Table 1. Boundary-Layer and Reynolds Number (Critical Reynolds Number 2019).

Boundary Layer

Reynolds Number

Laminar

Re

Transitional

2000

Turbulent

Re > 3500

Smooth Wall and Rough Wall
The smooth wall is the flat plate with the plain surface. There are no irregularities introduced. Since the smooth wall comes with no elements that produce roughness on the surface of contact, there is negligible friction with fluid. The rough walls, on the other hand, have irregularities on the surface, which increases the friction and eventually leads to high turbulence. This irregularity could be anything such as cylindrical rods, square-shaped rods, etc. In the last century, a number of researchers has worked on smooth surfaces with very small friction. Rough surfaces were ignored due to the high turbulence introduced by the roughness elements. In which it is very difficult to predict and compute the flow pattern.
The review paper by Raupach, Antonia & Rajagopalan (1991) gives the glimpse of work on turbulent boundary layer in external flows on the smooth wall with a zero pressure gradient (e.g. Kovasznay 1970; Willmarth 1975; Kline 1978; Singh, Radhakrishnan, & Narayan 1988; Antonia, Zhu & Sokolov 1995). The basic turbulence research gives more importance to work on smooth walls, before exploring the advanced complexities such as rough walls or adverse pressure gradient. It is important to study the formation of the boundary layer on smooth surfaces.
The initial hypothesis by Townsend (1976) states that, the outer region of the turbulent boundary layer is the same in both the cases, for a smooth wall as well as for rough wall. The outer region has low shear strength and this is the reason why the outer region is less sensitive to turbulence. Therefore, the outer region is considered to be a region where the turbulence phenomenon is absent. But in the region close to the wall where the shear is large, a significant difference can be observed depending on the smoothness or roughness of the surface. The roughness increases skin friction and alters the structure of the boundary layer (Raupach, Antonia & Rajagopalan 1991).
Krogstad and Antonia (1999) proved that transition from the smooth wall to rough wall causes non- negligible changes in the outer layer. This questions the Townsend (1976) and Raupach, Antonia and Rajagopalan’s (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 (Lee et al. 2009). 
Control of the turbulent boundary layer
In 1976, Furuya, Miyata, and Fujita investigated the turbulent boundary layer formed on the surface introduced to the roughness in the form of the wires which were placed at equal distance. The effect of this advancement on the flow resistance along the boundary layer was observed. The aluminium plate with the small wires of the cementing elements measuring 2 m long and 1m wide fitted with the right angle to the plate at an equal distance throughout. The whole setup was placed in the wind tunnel and measurements performed using a probe. The pressure distribution around the roughness measured, which revealed that the pressure drag acting on the roughness is a major contributor to the surface roughness and the other frictions were observed to be as same as the smooth wall. 
Antonia, Zhu, and Sokolov (1995) relaminarized the wall using the wall suction through the porous strip method, they observed the sufficiently high suction rate causes the pseudo-laminarization of the boundary layer downstream the strip for a very short distance, up to 70 δ0 (δ0 is the boundary layer thickness at the porous strip). Away from the strip, the boundary layer starts to return to the fully turbulent nature. The skin friction coefficient cf decreases in the value below the value of cf obtained when there was no suction. The relaminarization largely depends upon the Reynolds number/suction rate. The required stream wise distance of the full development of the boundary layer decreases with increasing Reynolds Number (Re) for suction rate (σ). The velocity profiles such as mean and RMS longitudinal apart from the undisturbed profiles of Re and σ. The Skewness and flatness factor dont depend upon Re but subject to changes as per the change in turbulence structure. 
The ‘Direct Numerical Simulation’ method was tested by Lee et al. (2009) to understand the structure of the turbulent boundary layer over a wall roughened by rods. The instantaneous flow field obtained by using the DNS was used to inspect the boundary layer over the given surface. The roughness used was two-dimensional rectangular rods placed equidistant from each other with k/δ = 0.05 (where δ boundary layer thickness). The comparison of characteristics of the turbulent boundary layer over a smooth wall and rough wall gives the details about the effect of surface roughness. Friction velocity is affected with the insertion of the roughness on the smooth wall it has very little effect on outer layer vorticity fluctuations.
Later in 2014, Kamruzzaman et al. changed the roughness elements from rectangular to circular. This study was based on the turbulent boundary layer over a circular bar with two-dimensional transverse. The rod with diameter k was arranged with the same spacing of along the line λ/k of 8 (λ is the distance between two circular bars) which resulted in maximum form drag. For measurements of the mean and fluctuating velocities hot wire anemometry was used, to find out the values of drag. The friction velocity is the measure contributing factor to the roughness effect, there is more importance to this value, and it was measured by using the two methods and the results were compared. The first method was to use the momentum integral equation while the other one was based on measuring the distribution of pressure around the rods. The results obtained from both methods showed consistency for friction velocity to within 3%. Further observation revealed that the drag coefficient is independent of the Re, as it didn’t show the change in static pressure over a change in Re. the displacement height also remained unchanged over this range of Re. the mean velocity showed collapse when scaled with friction velocity and thickness. Which explains that these are the better parameters for the scaling of the rough wall.
The recent work in this area is performed by Djenidi, Karuzzaman, and Dostal (2019). Where the two-dimensional rough wall turbulent boundary layer was subjected to the wall suction. The Hot- wire anemometry is used for the measurements such as velocity fluctuations. The wall suction was applied to the turbulent boundary layer through a porous strip. The roughness was of the circular rods, placed in the entire length of the wall in the wind tunnel, with a diameter of k = 1.6 mm and were placed uniformly at the distance of 24 mm which is with the ratio λ/k of 15 (this choice of wavelength by k ratio ensures the roughness of the turbulent boundary layer). This showed that after the impact on the roughness element close to the suction strip, the outer part of the boundary layer was diverted towards the inner part. The formation of the vortices due to the introduction of the roughness elements ultimately results in the increase in drag coefficient, which demands more energy at the input or in other words decreases the efficiency significantly. The relaminarization of the boundary layer was not achieved (which was the key point behind this experiment). Also, not much change was observed in the turbulent boundary layer.
Conclusion
Turbulence reduction is desired in the aerospace and automobile industry as it directly affects the efficiency. Since the discovery of a boundary layer theory, much attention has been given to the flows over a smooth surface. In the present literature review, the aim is to understand the concept of the turbulent boundary layer and to study the control strategies developed for the control of the turbulent boundary layer over a smooth wall. The control strategies developed for the smooth wall will be applied to the rough wall to minimize the effect of turbulence.
References
Akinlade, OG, Bergstrom, DJ, Tachie, MF & Castillo, L 2004, ‘Outer flow scaling of smooth and rough wall turbulent boundary layers’, Experiments in Fluids, vol. 37, no. 4, pp. 604-612.
Anderson, JD 2005, ‘Ludwig Prandtl’s boundary layer’, Physics Today, vol. 58, no.12, pp. 42-48.
Antonia, RA, Zhu, Y & Sokolov, M 1995, ‘Effect of concentrated wall suction on a turbulent boundary layer’, Physics of Fluids, vol. 7,no. 10, pp. 2465-2474.
Cantwell, BJ 1981, ‘Organized motion in turbulent flow’, Annual review of fluid mechanics, vol. 13, no.1, pp.457-515.
Critical Reynolds Number 2019, viewed 11 November 2019, https://www.nuclear-power.net/nuclear-engineering/fluid-dynamics/reynolds-number/critical-reynolds-number/
Djenidi, L, Kamruzzaman, M & Dostal, L 2019 ‘Effects of wall suction on a 2D rough wall turbulent boundary layer’ Experiments in Fluids, vol. 60, no. 3, pp. 43.
Dryden, HL 1995, ‘Fifty years of boundary-layer theory and experiment’, Science, 121(3142), pp.375-380.
Gad-el-Hak, M 1989, ‘Flow control’, Applied mechanics reviews, vol. 42, no. 10, pp. 261-293.
Hibbeler, RC 2017, Fluid Mechanics in SI Units. Pearson Education India.
Kamruzzaman, Md 2016, ‘On The Effects of Non- Homogeneity On Small Scale Turbulence’, The University of Newcastle NSW, Australia.
Katz, Y, Nishri, B & Wygnanski, I 1989, ‘The delay of turbulent boundary layer separation by oscillatory active control’, Physics of Fluids A: Fluid Dynamics, vol. 1, no. 2, pp.179-181.
Kline, SJ 1978, ‘The role of visualization in the study of the structure of the turbulent boundary layer’, Coherent Structure of Turbulent Boundary Layers, pp.1-26.
Kline, SJ & Robinson, SK 1990, ‘Quasi-coherent structures in the turbulent boundary layer’, I-Status report on a community-wide summary of the data, Near-wall turbulence, pp.200-217.
Kovasznay, LS 1970, ‘The turbulent boundary layer’, Annual review of fluid mechanics, 2(1), pp.95-112.
Krogstadt, PÅ & Antonia, RA, 1999, ‘Surface roughness effects in turbulent boundary layers’, Experiments in fluids, vol. 27, no. 5, pp.450-460.
Kumbhar, S 2019, MECH 6840A ‘Control of Rough Wall Turbulent Boundary Layer’, Literature Review 1, Semester 2 2019, The University of Newcastle.
Lee, SH & Sung, HJ, 2007, ‘Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall’, Journal of Fluid Mechanics, vol. 584, pp.125-146.
Lee, JH, Lee, SH, Kim, K & Sung, HJ 2009, ‘Structure of the turbulent boundary layer over a rod-roughened wall’, International Journal of Heat and Fluid Flow, vol. 30, no. 6, pp. 1087-1098.
Leonardi, S, Orlandi, P & Antonia, RA 2007, ‘Properties of d-and k-type roughness in a turbulent channel flow’, Physics of fluids, vol. 19, no. 12, p. 125101.
Oyewola, O, Djenidi, L & Antonia, RA 2003, ‘Combined influence of the Reynolds number and localised wall suction on a turbulent boundary layer’, Experiments in fluids, vol. 35, no. 2, pp.199-206.
Pailhas, G, Cousteix, J, Anselmet, F & Fulachier, L 1991, ‘Influence of suction through a slot on a turbulent boundary layer’, In Symposium on Turbulent Shear Flows, 8th, Munich, Federal Republic of Germany, pp. 18-4.
Turbulence isn’t just a science problem 2019, viewed 7 September 2019, https://phys.org/news/2018-06-turbulence-isnt-science-problem.html/
Raupach, MR, Antonia, RA & Rajagopalan, S 1991, ‘Rough-wall turbulent boundary layers’, Applied mechanics reviews, vol. 44, no. 1, pp. 1-25.
Schlichting, H 1960, Boundary layer theory (Vol. 960), New York: McGraw-Hill.
Singh, P, Narayan, KA & Radhakrishnan, V 1989, ‘Fluctuating flow due to unsteady rotation of a disk’, AIAA journal, vol. 27, no. 2, pp. 150-154.
Sreenivasan, KR 1989, ‘The turbulent boundary layer’, Frontiers in experimental fluid mechanics, Springer, Berlin, pp. 159-209.
Townsend, AA 1976, ‘The structure of turbulent shear flow’, Cambridge University.
Wallis, RA 1950, Some characteristics of a turbulent boundary layer in the vicinity of a suction slot, Aeronautical Research Laboratories.
Willmarth, WW 1975, ‘Structure of turbulence in boundary layers’, In Advances in applied mechanics, Elsevier, Vol. 15, pp. 159-254.