Vector-Scalar Duality

بسم الله الرّحمن الرّحیم

Tensor Notation

بسم اللّه الرّحمن الرّحیم

دریافت
عنوان: Tensor Algebra
حجم: 581 کیلوبایت

Discretization Techniques - گسسته سازی

بسم الله الرّحمن الرّجیم

 

Strain

بسم اللّه الرّحمن الرّحیم 

Nature of Phenomena within a System

Nature of Phenomena within a System (under Study)

1. Time (Variations) (we may consider space too.)
2. Sources and Sinks (internal and external)
3. Transport
4. Reservation
5. Converters, Elements and Medium 

Elements

1. each system element does a task with one of the previous natures listed

Components

1. Energy (and force)
2. Matter: matter serves both as the system(something under study) and also serves as elements, medium and converters

Fluid Force: Effective Parameters

1. Geometry-Angle of Attach
2. Mach number (compressibility effects)
3. Viscous phenomenon: Reynolds, Turbulence, Separation and reattachment and stall, Boundary layer parameters including Pressure gradient 

Remarks: Momentum Equation

REMARK: MOMENTUM EQUATION

The pressure waves that move with the speed of sound are like ambassadors who carry the duty of converting momentum of the fluid to pressure distribution. That is why the momentum of the particles is not directly applied/inserted to the geometry, but firstly converted to pressure and then the pressure will be integrated to calculate the force. 
This is the reason for the Newtonian theory. The flow upstream the Mach waves has not been yet converted to the pressure distribution, hence the flow only senses the momentum. There is no pressure defined and there is no body in the flow behind Mach waves. As Mach number increases, the shock wave gets close enough to the surface that the surface can be approximated by the shock wave shape. Hence, we can directly compute the force by integrating the momentum losses of the flow particles. Because there is no region within which the fluid has felt the presence of the body. 
Around the surface, because the Mach no. has a finite value, no matter how much its value is, there exists a region which encompasses the body and the pressure waves are present there. Because of this, we observe that the physics is ruled so that the flow momentum must be converted to pressure before reaching a body surface. 

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