The dynamic values are kinetic energy-like terms: The terms dynamic and static are used most commonly with compressible fluids. For flows which have no gravitational or rotational heads, the relative pressure is the gage pressure. For flows with a constant density, the reference density is the constant value. The reference density is calculated at the beginning of the analysis using the reference pressure and temperature. Where the ref subscript refers to reference values, the subscript i refers to the 3 coordinate directions, g is the gravitational acceleration and is the rotational speed. Referring to the relative pressure as Prel, the absolute pressure is calculated as: The absolute pressure adds the gravitational and rotational heads and the reference pressure to that calculated from the pressure equation. It is the part of the pressure that is affected by the velocities in the momentum equation directly. This relative pressure does not contain the gravitational head or the rotational head or the reference pressure. Normally, the solution to the pressure equation is a relative pressure. The term absolute is used in conjunction with pressure. Hypersonic flows cannot be modeled using the Ideal Gas assumption and must consider real gas effects.Ībsolute, Total, Static and Dynamic Values Transonic and supersonic flows can be modeled using the Ideal Gas assumption: Flows with Mach numbers greater than 5 are called hypersonic. Supersonic refers to the Mach number range: 1 ![]() ![]() Transonic, Supersonic and Hypersonic Flow The first term on the right hand side of this equation is referred to as the dynamic temperature. The total temperature is also called the stagnation temperature. Where is the ratio of the constant pressure specific heat to the constant volume specific heat and Rgas is the gas constant for this gas. Where Cp is the mechanical specific heat value calculated using: Assuming an ideal gas, this equation can be written using temperature: Where V is the velocity, and h is the volumetric enthalpy, a measure of energy. In equation form, this can be expressed as: That is, the sum of kinetic and thermal energy is a constant. For this type of flow, total energy is conserved. If there are no heat transfer effects and the fluid is moving below sonic velocities (Mach = 1.0), the flow can be considered adiabatic. Above this value, compressible effects are becoming more influential and must be considered for accurate solutions. For Mach numbers less than 0.3, flows can be assumed to be incompressible. Where a is the speed of sound, gamma is the ratio of the specific heats, R is the Universal Gas Constant and T is the static temperature. One measure of compressibility is the Mach number, defined as the fluid velocity divided by the speed of sound, defined as: For compressible flow, particularly supersonic flows, downstream pressure cannot affect anything upstream and the pressure equation is hyperbolic, requiring only upstream boundary conditions.Äownstream boundaries must be left free of pressure constraints. For incompressible flow, downstream effects are felt everywhere immediately and the pressure equation is mathematically elliptic, requiring downstream boundary conditions. One major difference between compressible and incompressible flow is seen in both the physical nature of pressure and consequently, the mathematical character of the pressure equation. Compressible flows involve gases at very high speeds. If a flow is compressible, changes in fluid pressure affect its density and vice versa. ![]() ![]() The term compressible refers to the relationship between density and pressure.
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