Week 3 - External flow simulation over an Ahmed body.

Aim: To simulate external flow over an Ahmed body using Ansys fluent.

 

Objectives:

1. To set-up simulation case for velocity of 25 `m/s` with working fluid as air.

2. Simulate various cases with different `Y^+` values (coarse, medium and refined mesh at the boundary).

3. Calculate drag and lift coefficients for the respective cases.

4. Perform grid independency test as a result of drag and lift coeffcient.

 

Project methodology:

In this project, the flow over an Ahmed body is simulated and post-processed in Ansys Fluent. Initially, Ahmed body is imported in SpaceClaim and enclosure is assigned just like a wind tunnel. The Ahmed body is meshed for different `Y^+` values to perform grid dependency test. K-epsilon turbulence model (Realizable with standard wall functions) is used to simulate the flow conditions. The coefficient of drag and lift is calculated for the respective cases and validated with standard reference to compare accuracy of the numerical results.  

 

Introduction:

External aerodynamics over various geometries gives a quick realization of the flow properties. These flow properties acts as case for optimization of the geometry shapes. Such external aerodynamics plays a crucial role in automotive industries. The external car aerodynamics is an important aspect to maximize its stability and lessen the significance of drag over the body. The virtual analysis of such scenarios is developed beforehand to actual development of the product. 

The numerical set-up and CFD codes are validated with standard models to ensure efficient working. Such is the case with Ahmed body, which is used to test CFD set-up or codes before implementing it for any car model. 

Ahmed Body:

The Ahmed body is simplified car model (generically a bluff body) which allows to capture essential flow properties around an automobile. This simplified car body was first defined and characterized in the work of Ahmed [1]. 

It allows to capture the turbulent air flow around an automobile. 

 

                                                           

                                                                                       Fig 1: Ahmed body (CAD Model)

 

The primary aspect of this project is to calculate total drag coefficient, which is a combination of pressure drag and skin-friction drag. The drag coefficient is a function of Reynolds number, frontal/projected area, density of the fluid, aspect ratio, surface roughness, viscosity of the fluid and shape of the geometry. It affects vehicle stability and efficacy in a direct manner. Therefore, it is important to account for drag forces in external aerodynamics.

Geometry Clean-up in SpaceClaim:

1. Dimension of the Ahmed body:

 

 

 

2. Importing Ahmed body in SpaceClaim:

 

3. Creation of Enclosure (wind tunnel):

Enclosure is created to provide constraint volume for the fluid flow over the Ahmed body. It acts like a wind tunnel similar in case of experimental analysis. 

a) Side-view:

b) Back-view:

4. Creation of small enclosure close to Ahmed body:

The significance of small enclosure is to have unconstraint domain near to the Ahmed body to capture flow properties effectively. It segregates flow away from and close to the Ahmed body. Mesh in this region is much more refined as compared to enclosure 1.

a) Side view:

b) Back view:

5. Substantial Ahmed body and windtunnel set-up: 

 

6. Splitting of Ahmed body:

The axisymmetric nature of the Ahmed body gives can an advantage to simulate half portion of the Ahmed body. The remaining half will follow the same results as symmetry boundary conditions will be applied. The Ahmed body is split into half using "split body" command in SpaceClaim. 

The Ahmed body will be used for different case studies with different mesh refinement. 

 

Named Selections:

The patches colored in red serves their respective pupose.

1. Inlet:

2. Outlet:

3. Symmetry:

4. Car-wall: 

 

Fluid properties:

Working fluid = Air at temp of 288.16 K

Velocity of the air = 25 `m/s`

Dynamic viscosity of the air = 1.7894 `(kg)/(m.s)`

Density of the air = 1.225 kg/m^3

 

Geometrical characteristics:

Total length of the Ahmed body (`L_c`)= 1.044 m 

Projected area (A) = 0.06574 `m^2`

Slant angle (`psi`) = `20^0`

 

Calculations:

The Reynolds number for the flow can be given as,

`Re = (rhoVL_C)/(mu)`

`Re = (1.225xx25xx1.044)/(1.7894e-5)`

`Re = 1.7868xx10^6`

The resulted Reynolds number is high, which is efficient to create turbulence and flow separation. The Reynolds number will same for all the case studies as the velocity is not changed.

 

Cases:

The simulation set-up will be using different Y+ values and mesh with K-epsilon turbulence model. Steady-state analysis is performed as the matter of concern is the end result.

Cases	Y+ value	Turbulence model	Mesh
Case 1	250	K-epsilon (Realizable with Standard wall functions)	Coarse
Case 2	175	K-epsilon (Realizable with Standard wall functions)	Medium
Case 3	100	K-epsilon (Realizable with Standard wall functions)	Refined

 

 WHY NOT K-OMEGA AS A TURBULENCE MODEL?

•  The K-omega model is well suited for low Reynolds number which accounts for compressibility and shear flow spreading. 
• However k-omega (SST-Shear Stress Transport) can be used in this case because of it's capability to incorporate high Reynolds number flows. As it uses K-omega in the inner region of the boundary layer and high Reynolds number model i.e K-epsilon in the outer region of the boundary layer.
• The mesh refinement is an important aspect in K-omega model as it accounts for near-wall effects. The `Y^+` values should be in the range between `1leY^+le10`. Mesh refinement should be much fine enough to capture near-wall effects. Accordingly, it uses extensive computation resources for such fine mesh refinement. 
• Therefore it is better to opt for K-epsilon as it uses wall functions to estimate near-wall effects and is well suited for higher Reynolds number flows. Comparatively it is computationally cheap which can work with `30leY^+le30`. This certainly gives mesh refinement flexibility to compute near-wall effects. 

 

Case 1: 

Y+	250
Turbulence model	K- epsilon (Realizable)
Wall functions	Standard wall functions

 

Mesh Details:

Enclosure 1 Mesh Method	Multizone	Element size = 105 mm
Enclosure 2	Sizing (Body sizing)	Element size = 45mm
Car-wall (Leg sizing)	Sizing (Face sizing)	Element size = 5mm
Y value (Height of first cell centroid from the wall)	7mm	--
Number of inflation layers	5	--
Growth rate	1.2	--
Inflation type	Total thickness	52 mm
Total number of cells	1,45,925	Coarse

 

Mesh:

1] Enclosure 1 = hexahedral meshes ; Enclosure 2 = tetrahedral meshes

 

2] Inflation layers over the car the Ahmed body.

 

3] Ahmed body leg sizing (face sizing)

 

Mesh Quality:

Results:

A] Plots

1. Residuals:

2. Drag force (`F_d`):

3. Coefficient of drag (`C_d`)

B] Report Definition:

C] Force Report:

 

D] Contours

1. Pressure:

a) Pressure distribution around Ahmed body:

b) Front pressure distribution:

 

c) Rear pressure distribution:

 

2. Velocity:

3. Velocity vector:

a) Enlarged view:

b) Rear-end of the Ahmed body:

4. Velocity pathlines:

a) Rear-end of the Ahmed body:

b) Enlarged view:

 

 

E] Velocity chart:

 

 

Case 2:

Y+	175
Turbulence model	K- epsilon (Realizable)
Wall functions	Standard wall functions

 

Mesh details:

Enclosure 1 Mesh Method	Multizone	Element size = 105 mm
Enclosure 2	Sizing (Body sizing)	Element size = 33mm
Car-wall (Leg sizing)	Sizing (Face sizing)	Element size = 5mm
Y value (Height of first cell centroid from the wall)	5mm	--
Number of inflation layers	5	--
Growth rate	1.2	--
Inflation type	Total thickness	37.20 mm
Total number of cells	3,21,154	Medium

 

Mesh:

1] Enclosure 1 = hexahedral meshes ; Enclosure 2 = tetrahedral meshes

 

2] Inflation layers over the car the Ahmed body.

 

3] Ahmed body leg sizing (face sizing)

 

Mesh quality:

 

Results: 

A] Plots:

1. Residuals:

2. Drag force (`F_d`):

3. Coefficient of drag (`C_d`):

B] Report Definiton:

 

C] Force Report:

 

D] Contours

1. Pressure:

a) Pressure field around Ahmed body:

b) Front pressure distribution:

 

c) Rear pressure distribution:

 

2. Velocity:

3. Velocity vector:

a) Enlarged view:

b) Rear-end of the Ahmed body:

4. Velocity pathlines:

a) Rear-end of the Ahmed body:

b) Enlarged view:

 

 

 

E] Velocity chart:

 

 

 

Case 3:

Y+	100
Turbulence model	K- epsilon (Realizable)
Wall functions	Standard wall functions

 

Mesh details:

Enclosure 1 Mesh Method	Multizone	Element size = 105 mm
Enclosure 2	Sizing (Body sizing)	Element size = 28 mm
Car-wall (Leg sizing)	Sizing (Face sizing)	Element size = 5 mm
Y value (Height of first cell centroid from the wall)	3mm	--
Number of inflation layers	8	--
Growth rate	1.2	--
Inflation type	Total thickness	50 mm
Total number of cells	5,09,475	Fine mesh

 

Mesh:

1] Enclosure 1 = hexahedral meshes ; Enclosure 2 = tetrahedral meshes

 

 

2] Inflation layers over the car the Ahmed body.

 

3] Ahmed body leg sizing (face sizing)

 

 

Mesh quality:

 

Results: 

A] Plots

1. Residuals:

2. Drag force (`F_d`):

3. Coefficient of drag (`C_d`):

B] Report Definition:

 

C] Force Report:

 

D] Contours

1. Pressure:

a) Pressure field around Ahmed body:

b) Front pressure distribution:

c) Rear pressure distribution:

 

2. Velocity:

3. Velocity vector:

a) Enlarged view:

b) Rear-end of the Ahmed body:

4. Velocity pathlines:

a) Rear-end of the body:

b) Enlarged view:

 

 

E] Animation:

Note: Play-back speed of 0.25x is recommended.

 

 

F] Velocity chart:

 

 

Observation Table:

Cases	Total number of cells	Y+	`F_d (N)`	`C_d`	`C_l`	Pressure drag (N)	Viscous drag (N)	Coefficient of pressure (C_p)
Case 1	1,45,925	250	9.1328	0.3628	0.3123	7.9554	1.1774	0.3161
Case 2	3,21,154	175	8.4460	0.3356	0.2883	7.2571	1.1889	0.2883
Case 3	5,09,475	100	8.0606	0.3202	0.3067	6.8702	1.1904	0.2729

 

The standard reference of drag coefficient taken from W.Meile [2] is approx 0.3125. The resulting numerical solution is C_d = 0.3202, which is close agreement with the standard reference.

Numerical error:

Cases	% Error
Case 1	16.1 %
Case 2	7.4 %
Case 3	2.46 %

 

Mesh independent study:

The K-epsilon turbulence model with varied mesh refinement is used to perform mesh dependent study. The drag coefficient obtained from these case studies though vary in second decimal places but accounts significant for error percentage. It is obvious to have more accurate results with mesh refinement. In drag analysis it is important to have more refined mesh at external surface and in the wake region to capture pressure and viscous effects. Though the case studies shows negligible variation but in terms of drag coeffcient such variation is unfruitful (completely changes the definition of the external body). The study performed can be asserted as "Mesh dependent study", as the approximation varies significantly as a function of mesh refinement. 

 

Technical discussion:

The airflow around Ahmed body possess higher Reynolds number. Initially the airflow will strike the leading edge of the Ahmed body and the velocity of air will reduce significantly. At this point (stagnation point), the pressure acting on the body will be maximum (stagnation pressure). Gradually the flow will accelerate along the leading edge and will driven through favourable pressure gradient. And this motion will cause drop in pressure to the upper leading edge. 

When the airflow experiences sudden geometrical changes (slant length), it will start to detach from the surface of the body. This will subsequently lead to formation of eddies and region of recirculation immediate behind the body. It represents wake region which accounts for low pressure distribution behind the body causing imbalance in the net pressure distribution. The low pressure region will be obtained from flow separation due to adverse pressure gradients. This wake region holds the car body from behind and hence restricts the motion of the body. 

The nature of wake region is completely chaotic and unstable. The flow is completely detached and random. Eddies continuously exchange momentum and energy to another small eddies and grow up as a function of time and space. The eddies immediate behind the body has larger momentum. The region of recirculation is under significant inertial effects. The pressure in that region tries to compensate for the velocity (less velocity, more pressure) however remains ineffective due to momentum and energy exchange due to eddies (energy cascade driven from the wake immediate behind the body to all along the length of windtunnel).  Therefore the pressure in the wake region is unexpectedly lower compared to the stagnation pressure upstream. 

The vortices and wakes behind the body are function of the shape of the body. The slant angle of the rear-body has direct impact on the flow separation. In external aerodynamics, no matter how streamline the body is, once it is set in motion will create disturbance and imbalance in a surrounded fluid medium. Restricting flow separation and formation of wake is inevitable, however it is delayed to reduce adverse impact past a body.   

 

Conclusion:

In this present study, drag and lift coefficient was investigated using numerical simulation and was validated with the standard reference. The numerical results shown good agreement with the standard results with 2.5% error. In external aerodynamic studies it is important to have refined mesh to get more approximate results. The drag and lift analysis holds values between 0 and 1, the deviation in the hundredth place can also affect the problem definition. This type of analysis are quite sensitive and should be executed with refined mesh characteristics to get more approximate results.