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Isentropic Flow of Calorically Perfect Gas

The state of a calorically-perfect gas is represented by a relatively simple model.  If, without increasing entropy, the gas is accelerated to some speed, its thermodynamic energy is exchanged for kinetic energy.  It is customary to characterize the state of such a moving gas in terms of its reservoir (aka stagnation, aka total) state.

This model converts between static and total states.  It incorporates the usual isentropic relations; however, it makes no representations about the spatial scale of the flow or whether it is internal or external (so does not represent the spatial aspects of quasi-1D duct flows, for example the area ratio).  Also, this model solves some special situations where there is incomplete information about both states.

Press «enter» to see the model.  To infer results, try one of the examples below, or your own inputs. To clear results, refresh your browser.

Mach number and static state

  1. Choose a Mach number of 0.5:
    M = 0.5 «enter»
    The model infers temperature ratio, and other ratios if you assert that the state is not a vacuum (which can also be done by asserting pressure as below).
  2. Specify the static state with any two state variables, such as temperature and pressure:
    T = 300 «enter»  P = 1e5 «enter»
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Key results are the total state (Total «enter») and the static state (Static «enter»).

Total state and a static state variable

  1. Choose a total temperature of 2020 K and total density of 5 kg/m³:
    T0 = 2020 «enter» r0 = 5 «enter»
  2. Now choose the desired property for the static state, such as a temperature of 500 K:
    T = 500 «enter»
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Advanced: Mixed states and a branch

  1. Choose a static temperature of 200 K and mass flow rate per unit area of 100 kg/m²/s:
    T = 200 «enter» G = 100 «enter»
  2. Now choose the desired total pressure, such as 10 bar:
    P0 = 1e6 «enter»
  3. Finally, choose which branch of the solution to solve for:
    dP = false «enter»
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