On numerical calculation of Lift Force via Potential Flow

Thank you for participating in this discussion.In summary, the conversation discusses computing a potential steady and incompressible flow over an airfoil, with the problem set up as \nabla^2\phi=0. It is mentioned that there should be no normal velocity component on the airfoil surface and that the external flow at large distances is \overline{U_\infty}. The main questions raised are whether it is possible to obtain a steady solution and whether there will be a lift force and why. The summary concludes that a steady solution is possible and the lift force is generated by pressure differences caused by the flow of fluid over the airfoil, dependent on the free stream velocity and airfoil shape.
  • #1
Clausius2
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Imagine:
I want to compute numerically a POTENTIAL STEADY and INCOMPRESSIBLE flow over an airfoil. The set up of the problem is:
[tex] \nabla^2\phi=0[/tex]
[tex]\nabla\phi \cdot \overline{n}\big)_{x=surface}=0[/tex] no normal velocity component on the airfoil surface.
[tex]\nabla \phi=\overline{U_\infty}[/tex] as [tex]x\rightarrow\infty[/tex] external flow at large distances.
The three main questions which arise are the next:
i) Is it possible to obtain an steady solution of this stuff?
ii) Am I going to obtain any Lift force?. Why?
Thanx for participating in this discussion.
 
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  • #2
Yes, it is possible to obtain a steady solution of this problem. The lift force is generated by the pressure differences between the upper and lower surfaces of the airfoil, which are caused by the flow of the fluid over the airfoil. The lift force will depend on the free stream velocity and the shape of the airfoil, among other factors.
 
  • #3


In order to compute the lift force numerically via potential flow, we first need to understand the physical principles behind potential flow. Potential flow is a simplified model of fluid flow that assumes the flow is irrotational and incompressible. This means that the flow has no vorticity and the density of the fluid remains constant throughout the flow. In potential flow, the velocity field can be described by a scalar potential function, denoted as \phi, which satisfies the Laplace equation, \nabla^2\phi=0. This equation governs the flow behavior and can be solved using numerical methods.

In the set up of the problem, we are considering a steady and incompressible flow over an airfoil. This means that the flow remains constant over time and the density of the fluid remains constant as well. The boundary conditions for this problem are \nabla\phi \cdot \overline{n}\big)_{x=surface}=0, which states that there is no normal velocity component on the airfoil surface, and \nabla \phi=\overline{U_\infty} as x\rightarrow\infty, which represents the external flow at large distances.

Now, to address the main questions, yes, it is possible to obtain a steady solution of this problem using numerical methods. The Laplace equation can be solved numerically using techniques such as finite difference or finite element methods. These methods discretize the domain and solve the equation at discrete points, allowing for a numerical solution to be obtained.

As for the lift force, it can be obtained from the pressure distribution on the airfoil surface. According to Bernoulli's principle, there is a relationship between the pressure and velocity of a fluid. In potential flow, the pressure distribution can be calculated using the potential function, and the lift force can be obtained by integrating this pressure distribution over the airfoil surface. This lift force is a result of the difference in pressure between the upper and lower surfaces of the airfoil, creating a net force that acts perpendicular to the flow direction.

In conclusion, potential flow is a useful tool for computing lift force numerically. It allows for a simplified model of fluid flow, which can be solved using numerical methods. The lift force can then be obtained from the pressure distribution on the airfoil surface, providing valuable information for the design and analysis of various aerodynamic systems.
 

1. What is the "Numerical Calculation of Lift Force via Potential Flow" method?

The numerical calculation of lift force via potential flow is a mathematical approach used to estimate the aerodynamic lift force on an object, such as an airfoil or wing, by solving the equations of potential flow around the object. This method is commonly used in the field of aerodynamics to study the lift and drag forces acting on various objects.

2. How does the Potential Flow method work?

The potential flow method is based on the assumption that the fluid flows around an object in a way that can be described by a mathematical function called a potential function. By solving the equations of potential flow using numerical methods, the lift force acting on the object can be calculated.

3. What are the advantages of using the Potential Flow method?

One of the main advantages of using the potential flow method is that it provides a simplified, yet accurate, representation of the flow around an object. This allows for faster and more efficient calculations compared to other methods, making it a popular choice for studying aerodynamic forces.

4. Are there any limitations to the Potential Flow method?

While the potential flow method is a useful tool for estimating lift forces, it does have its limitations. It assumes that the fluid is inviscid (no friction) and incompressible, which may not always be the case in real-world scenarios. Additionally, it cannot accurately predict flow separation and other complex flow phenomena.

5. How is the accuracy of the Potential Flow method evaluated?

The accuracy of the potential flow method can be evaluated by comparing its results to experimental data or more advanced computational methods. It is important to note that the accuracy may vary depending on the complexity of the flow and the assumptions made in the calculations.

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