Drag (also referred to as air resistance, friction, or fluid resistance) is a force that acts in opposition to any object’s relative motion in relation to the surrounding fluid. A fluid layer (or surface) and a solid surface can both be involved in this phenomenon. The drag force is dependent on velocity, unlike other resistive forces, such as dry friction, which are practically independent of velocity. for low-speed flow, the drag force is directly proportional to the velocity, but for high-speed flow, the drag force is directly proportional to the squared velocity. The turbulent drag is independent of viscosity, despite the fact that viscous friction is the ultimate cause of a drag. The fluid’s velocity relative to the solid object in its passage is always reduced by drag forces.
Examples of drag include the component of the net aerodynamic or hydrodynamic force that acts in the direction that is counter to the movement of a solid object such as cars (the automobile drag coefficient), aircraft, and boat hulls; acting in the same geographical direction of motion as the solid, such as for sails attached to a downwind sailboat; or acting in intermediate directions on a sail depending on the points of sail. In the instance of viscous drag, which occurs when fluid is contained within a pipe, the drag force exerted on the pipe causes a reduction in the fluid’s velocity in comparison to the pipe. When it comes to the physics of sports, the concept of drag force is essential to the explanation of the motion of objects like balls, javelins, arrows, and frisbees, as well as the performance of athletes like runners and swimmers.
A body is subjected to the force from the surrounding fluid when it is placed in a flow. A flat plate is only subjected to a flow in the downstream direction when it is aligned with the flow of the direction. Let’s assume, the pressure is denoted by P, acting on an area dA and friction force per unit area is ????. Due to the pressure P, the force PdA acts normal to dA, where due to stress the force acts tangentially. Therefore, the drag working on the direction of the velocity is called pressure drag or form drag and the drag because of ????dA is called friction drag.
A list of definitions for various types of drag is provided, followed by a classification of drag forces below.
Induced drag: It is the drag that is created when a trailing vortex system is created downstream of a lifting surface that has a finite aspect ratio. To put it another way, this particular kind of drag is brought on by the lift force.
Parasite Drag: The overall drag subtracted from the drag caused by the particle. Therefore, it refers to the resistance that is not immediately connected to the generation of lift. The parasite drag is made up of the drag that is caused by several different aerodynamic components.
Skin Friction Drag: The drag caused by viscous shearing stresses (i.e., friction) on a body’s contact surface (i.e., skin). A skin friction drag is frequently used to describe the drag of a very streamlined shape, such as a thin, flat plate. This drag is proportional to the Reynolds number. The flow in the boundary layer is either entirely laminar or entirely turbulent over the plate in most cases. The Reynolds number is determined by the total length of the object in the velocity direction. In most cases, the boundary layer is laminar near the leading edge of the object, transitioning to a turbulent layer some distance back along the surface.
A laminar boundary layer forms at the leading edge and grows in thickness downstream. The laminar boundary becomes unstable at some distance from the leading edge and is unable to suppress disturbances imposed on it by surface roughness or fluctuations in the free stream. The boundary layer usually transitions to a turbulent boundary layer at a distance. The layer thickens abruptly and is characterized by a mean velocity profile with a random fluctuating velocity component superimposed. The distance between the object’s leading edge and the transition point can be calculated using the transition Reynolds number. Skin friction factor in laminar flow is independent of surface roughness, but it is a strong function of surface roughness in turbulent flow due to the boundary layer.
Form Drag (also known as Pressure Drag): The drag on a body caused by the combined effect of static pressure acting normal to its surface and resolved in the drag direction. Unlike skin friction drag, which is caused by viscous shearing forces tangential to a body’s surface, form drag is caused by pressure distribution normal to the body’s surface. In the extreme case of a flat plate parallel to the flow, the drag is entirely due to a pressure distribution imbalance. Form drags like skin friction drag, is generally proportional to the Reynolds number. The projected frontal area is used to calculate form drag. As a body moves through the air, the vorticity in the boundary layer is shed from the upper and lower surfaces, forming two opposing rotational vortices.
Table 1 provides visual representations of a number of symmetrical structure’s drag values(Cengel and Cimbala, 2013) when moving at low speeds. The numbers for the coefficient of drag that are presented in this table are determined by the inlet area which is the same as our experiment. The flow is coming from the left to the right.
Table 1: The values of the drag coefficient for a variety of geometries and shapes
|
No |
Body |
Status |
Shape |
CD |
|
1 |
Square rod |
Sharp corner |
2.2 |
|
|
Round corner |
1.2 |
|||
|
2 |
Circular rod |
Laminar flow |
1.2 |
|
|
Turbulent flow |
0.3 |
|||
|
3 |
Rectangular rod |
Sharp corner |
L/D= 0.1 |
1.9 |
|
L/D= 0.5 |
2.5 |
|||
|
L/D= 3 |
1.3 |
|||
|
Round front edge |
L/D= 0.5 |
1.2 |
||
|
L/D= 1 |
0.9 |
|||
|
L/D= 4 |
0.7 |
|||
|
4 |
Simi circular rod |
Concave face |
1.2 |
|
|
Flat face |
1.7 |
Interference Drag: The increase in drag caused by bringing two bodies close together. For example, the total drag of a wing-fuselage combination is usually greater than the sum of wing drag, and fuselage drag separately.
Trim Drag: The drag increase is caused by the aerodynamic forces required to trim the shape around its centre of gravity. Trim drag on the horizontal tail is typically a combination of induced and form drag.
Profile Drag: A two-dimensional airfoil section’s form drag is typically understood to refer to the sum of the skin friction drag, and the total form drag.
Cooling Drag: The resistance caused by the loss of momentum incurred by the air as it travels through the power plant installation to fulfil its function of cooling the engine.
Wave Drag: This form of induced drag is unique to supersonic flow and results from non-cancelling static pressure components to either side of a shock wave acting on the surface of the body from which the wave is emanating. Supersonic flow is the only flow regime in which it is observed.
Figure 1. Lift and drag.
The theoretical calculation of drag is critical if the shape of the body is not simple, and the velocity is higher. Therefore, we need to rely on simulation and experimentation. The drag D can be calculated from equation 1.
There are, therefore, two separate forces that affect drag- viscous force and pressure force. The pressure force is called a pressure gradient, and this is always created because of the pressure difference on the surface. The viscous force is because of the friction that works in the opposite direction of the flow. However, depending on the type of flow the magnitude of these two forces may vary. For example, the flow around a bus is often subjugated by the pressure force.
Drag force is the squared velocity for the turbulent flow and is proportional to the velocity of laminar flow. Turbulence is a kind of flow in which the flow goes in a zigzag way. In turbulence flow, the speed of flow changes continuously in both direction and magnitude. In the real world, almost all kinds of flows are turbulent. Common examples of turbulent flow are blood flow in our veins, ocean currents, flow through turbine blades etc. The main tool available for the analysis of turbulence is computational fluid dynamics (CFD). CFD is a branch of engineering that uses programs and algorithms to solve the turbulent problem. Some basic characteristics of turbulent flow are mentioned below-
In this assignment, there are three two-dimensional objects. One is a circle, one semi-circle and the last one trapezoidal. The diameter of the circle and semi-circle is 42.67mm, whereas the diameter of the trapezoid is 42.67 mm on the longer side and 35mm on the shorter side and the provided angle is 30 degrees. The major objectives of the study are written below-
In this section, the methodology of the CFD simulation will be discussed in detail. First, the geometry, then mesh, Fluent interface and finally result section will be analyzed. For the CFD simulation, first three geometries were built with proper dimensions. Then those were imported into the mesh module and proper meshing was done. Further, the mesh file was imported to the setup module and physics, boundary conditions, materials, cell zone conditions etc. were imported to conduct the necessary simulation. Finally, results were obtained and proper comparisons with the experimental results were done.
For creating the geometry ANSYS geometry plugin was used. First, a 2D interface was chosen then the geometry of the first case (circle) was built, a boundary was created around the circle for the air to pass through it. Then the model was saved. The other two model case 2 (semi-circle) and case 3 (trapezoid) were built. Then all three models were imported to mesh one by one and simulation was run.
For meshing ANSYS mesh plugin was used. For conducting the simulation ANSYS student version was used. The student version has limitations with the number of mesh elements, that were taken into consideration and as instructed the mesh elements were below 512,000 in all cases. In the results section details, discussion is provided. For the wall cases (the body) of the body triangular mesh was used. For getting accurate results fine mesh was used near the sphere, semi-sphere and the vertical plate. The reason for providing refinement is to get as much accurate results as possible as this position is very sensitive to velocity. Table 2 shows the number of mesh elements for all three cases.
Table 2. Number of elements for all three cases
|
Cases |
Number of Elements |
Nodes |
|
Case 1 |
78010 |
39807 |
|
Case 2 |
82873 |
42165 |
|
Case 3 |
83547 |
42517 |
The mesh figure for all three cases are shown in figure 2 (a,b and c). In all cases, instruction was followed properly. Because of the high number of nodes and elements the figure is not appropriately visible.
Figure 2. Mesh of three cases (a) Case 1 (b) Case 2 and (c) case 3
This step is done after the mesh section. The mesh file is imported to the setup window. Here, first, the scale of the geometry is corrected. Then Spalart–Allmaras model was selected. This is a one equation model that solves the eddy turbulence viscosity. It was developed for aerospace models to provide good results. The model is very effective for low Reynolds number and where viscosity is involved. The model includes eight closure coefficients and three closure functions.
Inviscid flow: Inviscid flow analyses are appropriate for high-Reynolds-number applications where inertial forces tend to dominate viscous forces. The inviscid flow is appropriate for high-speed aerodynamic analysis because pressure forces on the body will dominate viscous forces. As a result, an inviscid analysis can provide a quick estimate of the primary forces acting on the body. After modifying the body shape to maximize lift forces and minimize drag forces, you can perform a viscous analysis to account for the effects of fluid viscosity and turbulent viscosity on lift and drag forces.
The Euler equations can be solved by ANSYS Fluent for flows that are inviscid. The equation for the conservation of mass is the same as it would be for a laminar flow; however, the equations for the conservation of momentum and energy are simplified because molecular diffusion is not a factor.
The Equation for the Conservation of Mass The equation for the continuity of mass, also known as the equation for the conservation of mass, can be expressed as follows:
Mass added to the continuous phase from the dispersed second and user-defined sources is source Sm.
Momentum Equations: Conservation of momentum:
where p denotes static pressure and g and F denote gravitational and external body forces, respectively. Other model-dependent source terms in F include porous-media and user-defined sources.
By solving two distinct transport equations, two-equation turbulence models make it possible to determine both a turbulent length scale and a turbulent time scale simultaneously. Since it was first proposed by Launder and Spalding, the standard model in ANSYS Fluent, which belongs to this class of models, has become the workhorse of real engineering flow calculations in the time that has passed since it was first introduced (Spalding, 1972).
The prevalence of this method in industrial flow and heat transfer simulations can be attributed to its robustness, economy, and reasonable accuracy across a broad spectrum of turbulent flows. It is a model that depends on phenomenological considerations and empiricism in order to derive its equations, making it a model that is considered to be semi-empirical.
Spalding’s standard k- model is a model that was developed in 1972 and is based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (). The model equation for transporting k is derived from the precise equation, but the model equation for transporting was determined through physical reasoning and has very little in common with its mathematically exact equivalent.
In order to derive the k- model, it was assumed that the flow was completely turbulent and that the effects of molecular viscosity were considered to be insignificant. Because of this, the k- model can only be used to accurately describe fully turbulent flows.
The following set of transport equations can be used to calculate the turbulence kinetic energy, denoted by k, as well as its rate of dissipation, denoted by:
(pk)+ (pkui) = (µ+) +Gk+Gb-PE-YM+Sk
Where Gk represents the generation of turbulence kinetic energy due to mean velocity gradients, Gb represents the generation of turbulence kinetic energy due to buoyancy, and YM represents the contribution of fluctuating dilatation to the overall dissipation rate in compressible turbulence. The turbulent Prandtl numbers for and are and, respectively. Sk and Sx are source terms that have been defined by the user.
A statistical method known as renormalization group theory was utilized in the process of deriving the RNG model. It has the same basic structure as the normal k- model, but it has been improved in the following ways: – The RNG model incorporates an extra term into its equation, which helps to increase its predictive power for flows that are rapidly stretched.
The RNG model incorporates the effect of swirl on turbulence, improving accuracy for swirling flows. The RNG theory provides an analytical formula for turbulent Prandtl numbers, whereas the standard k-model relies on user-specified constant values. Unlike the standard k-model, which has a high Reynolds number, the RNG theory has an analytically derived differential formula for effective viscosity that accounts for low Reynolds number effects. However, the effective use of this feature is dependent on how the near-wall region is treated. These characteristics make the RNG k- model more accurate and reliable than the standard k- model for a broader range of flows.
Using a mathematical technique known as “renormalization group” (RNG) methods, the RNG-based k-turbulence model is derived from the instantaneous Navier-Stokes equations. The analytical derivation yields a model with different constants than the standard k-model, as well as additional terms and functions in the transport equations for k and. More information on RNG theory and its application to turbulence can be found in.
The Reynolds stress model (RSM) offered by ANSYS Fluent is the most intricate variety of the RANS turbulence model that is available. After rejecting the isotropic eddy-viscosity hypothesis, the Reynolds stress model (RSM) completes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses in conjunction with an equation for the dissipation rate. This indicates that there is a need for an additional five transport equations to be solved in 2D flows, as opposed to the additional seven transport equations that must be solved in 3D flows.
The RSM has a better ability to produce correct predictions for complicated flows because it accounts for the impacts of streamlined curvature, swirl, rotation, and rapid variations in strain rate in a more rigorous manner than one-equation and two-equation models do. The closure assumptions that are used to simulate various elements in the exact transport equations for the Reynolds stresses do, however, place certain restrictions on the fidelity of the predictions that can be made using the RSM. The modelling of the pressure-strain and dissipation-rate factors is very difficult, and it is commonly believed that this is the factor that is responsible for lowering the accuracy of RSM predictions.
ANSYS Fluent’s default Reynolds stress model is based on the -equation, and it employs a linear model for the pressure-strain term. Both of these models are linear in nature. A quadratic model can be used to represent the pressure-strain term when the second-based model is utilized.
The two Reynolds stress models that are based on the -equation both use a linear model for the pressure-strain term, but they differ with regard to the scale equation. The stress-omega model is based on the -equation, whereas the stress-BSL model solves the scale equation from the baseline (BSL) k- model and, as a result, eliminates the free-stream sensitivity that was observed with the stress-omega model.
To investigate the drag coefficient in the three distinct geometries at two distinct speeds (5 meters per second and 25 meters per second), six simulations have been conducted using ANSYS Fluent. It is required that the geometry have a total of fewer than or equal to 512,000 mesh elements. Meshing in the computational domain has been done by the Ansys workbench. The velocity profiles can be seen in figure 3. It can be seen from the figures that, by increasing the velocities in the inlet for the shapes, drag forces are increased which can be seen in the velocity profile.
Figure 3: Velocity profile for three different geometries on analysis to investigate drag coefficient. (a)Sphere on a velocity of 5m/s (b) Sphere on a velocity of 25m/s
(c)Semi sphere Circle on a velocity of 5m/s (d)Semi sphere Circle on a velocity of 25m/s
(e)Flat vertical surface on 5m/s (f) Flat vertical surface on 25m/s
It is clear from looking at Table 3 that increasing the velocities in any of the different geometries will result in an increase in the drag forces. In experimental results. Because of its 30-degree slant, the horizontally flat vertical surface generates the greatest amount of drag. With an inlet velocity of 5 meters per second, the flat surface had a drag force of 0.03 newtons. At an inlet velocity of 5 meters per second, the drag force in the sphere was 0 Newtons, while in the semi-sphere it was 0.01 Newtons. The drag forces increase in proportion to the increase in the vehicle’s velocity. The experimental drag force for a sphere was measured at 0.62 N, while the drag force for a semi-sphere was measured at 0.75 N. The force of drag for a horizontally flat and vertical surface that is tilted at a 30-degree angle.
After completing the simulation in ANSYS by drawing geometries based on these given dimensions, the meshing was created, and boundary conditions were applied. In regard to the prerequisite, the geometries are to be examined using inlet velocities of both 5 and 25 meters per second. There is no velocity coming out of the outlet. Because of this, the structure is not particularly complicated. As can be seen from the result of the simulation, the drag forces were significantly greater than the experimental values. At inlet velocities of 5 meters per second, the sphere had a drag force of 0.07 Newtons. However, the result of the experiment was 0N. Again, this can be seen by looking at the graph that, for an inlet velocity of 25 meters per second, the simulation resulted in a drag force of 1.0 Newtons, whereas the actual experimental result was only 0.62 Newtons. For the half-sphere, proceed in the same manner as before. In the experiment, the drag force was measured at 0.75, but in the ANSYS simulation, it showed 1.1N after 500 iterations. These values were calculated based on an inlet velocity boundary condition of 25 meters per second.
After running a simulation for a boundary condition with an inlet velocity of 5 meters per second, the drag force measured experimentally on a vertical flat surface increased from 0.03 N to 0.073 N. The drag force is reduced from 1.25 Newtons to 1.23 Newtons when the inlet boundary condition is set at 25 meters per second. This situation came about as a result of the inclined surface at a 30-degree angle that was present in the flat plate.
There may be several reasons why the simulation overestimates the drag. The conducted simulation was simple in model and there were some assumptions. Further, SA turbulence model was used and the model itself has some limitations. Moreover, the intensity of the air is not mentioned on the problem, therefore an intensity of 10% was assumed. Changing the intensity may change the drag force also as intensity has a direct effect on turbulence. Further, because of using student software and computer, only 500 iterations were done. Increasing the iteration number would have increased the computational cost but could provide better results. However, the obtained CFD results are satisfactory and have the same order of magnitude as the experimental results.
Table 3. Comparison of the experimental and simulation results.
|
Model |
Experimental |
Simulated |
||
|
Sphere |
5 m/s |
25 m/s |
5 m/s |
25 m/s |
|
0N |
0.62N |
0.07N |
1.0N |
|
|
Semi-sphere |
0.01N |
0.75N |
0.07N |
1.1N |
|
Flat vertical surface |
0.03N |
1.25N |
0.073N |
1.23N |
Turbulence increases the drag significantly. In the conducted simulation, the intensity was taken as 10%, therefore the obtained drag is a bit higher than the experimental drag. Increasing the turbulence to 15% or more could increase the drag more. However, a decrease of turbulence could match the experimental results. The meaning of increasing intensity is to increase the zigzag motion of the fluid, which directly affects the drag. The behaviour of drag could be better understood by the Reynolds number. With the increase of the Reynolds number, the drag increases. Increasing the intensity of fluid can increase the Reynolds number, hence turbulence and therefore overall drag.
Meshing also affected the result. In this simulation, Triangular mesh was used. The reason for using this type of meshing model is to simulate the model quickly and get a better result. For the sensitive region, a mesh refinement of “2” was used and an element size of 0.0005 was used for accuracy. However, the limitation of the ANSYS student version was kept in mind.
Discretization is used for continuous function chopping, where on each space and time, solutions values are defined. Therefore, it simply refers to the spacing between each point of the solution space. There are several types of discretization available depending on the problem’s needs and demands. Time discretization, convective discretization, Gradient Discretization, Interpolation. Here, in this problem, time discretization was treated carefully.
Material properties also have a huge impact on drag. The material with which an object is made of affects its mass and also density. An object with a higher density is less affected by drag deceleration. Further, surface texture and shape are also an important factor. However, an exception can occur above the Karman line. In this case, shape and texture do not matter much because of a very thin layer of fluid. Another important factor is the roughness of the object. With the increase of roughness of the object the associated drag increases, and with the decrease of roughness drag decreases. Besides, the properties of air also affect drag. If the property of air changes the drag changes. Properties like mass, viscosity, and compressibility of air affect drag. Velocity and direction of flow also affect drag. With the increase of velocity drag increases, which is visible from our experiment and simulation.
Conclusion
In this study, a simulation has been conducted for three different geometries for computing the drag forces. As well as experiments have been conducted in a wind tunnel. First, three properly sized geometries were developed for CFD simulation. Then, the mesh module was used to do correct meshing. The mesh file was imported to the setup module, and physics, boundary conditions, materials, and cell zone conditions were imported to run the simulation.
References
CENGEL, Y. & CIMBALA, J. 2013. EBOOK: Fluid Mechanics Fundamentals and Applications (SI units), McGraw Hill.
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