How do I explain the fact that the flow chokes only at the nozzle?
To explain why the flow only chokes at a single point, it is important to remember that for a system at steady state, there can only be a single flow. All of the fluid entering the system must leave. Since there can only be a single flow rate through the system, you must then consider where that maximum flow can occur.
The following equations describe the flow through a frictionless nozzle where the expansion occurs adiabatically and isenthropically. They are from Perry's page 6-23. The actual flow through an orifice is usually handled by a flow coefficient since the flow through an orifice will be less than a frictionless nozzle.
$$
\begin{align}
\frac{p^*}{p_0} &= \left(\frac{2}{k+1}\right)^{k/(k-1)} \\
\frac{T^*}{T_0} &= \frac{2}{k+1} \\
\frac{\rho^*}{\rho_0} &= \left(\frac{2}{k+1}\right)^{1/(k-1)} \\
G^* &= p_0 \sqrt{\left(\frac{2}{k+1}\right)^{(k+1)/(k-1)}\left( \frac{kM_w}{RT_0} \right)} \\
w^* &= G^*A \\
V = V^* = c^* &= \sqrt{\frac{kRT^*}{M_w}}
\end{align}
$$
For the formulas above, the $^*$ represents the condition at choked flow and the $_0$ condition is inlet. The other variables are defined as:
- $p$ = pressure
- $T$ = temperature
- $\rho$ = density
- $G$ = mass velocity (mass flow per unit area)
- $w$ = mass flow
- $A$ = nozzle exit area
- $V, c$ = exit velocity
- $R$ = gas constant
- $M_w$ = molecular weight
Choked flow occurs when the downstream pressure is less than the critical pressure or the pressure ratio is less than the critical ratio. This is shown in equation 1 and repeats your initial question. Once you know the flow will be choked, you can then use the remaining equations. Looking at the equation for the mass velocity, $G^*$, you can see that choked flow is a function of gas composition $(k,M_w)$ and inlet conditions $(T_0,p_0)$ and that changing downstream conditions has no effect on the mass velocity. To get to the mass flow rate $w^*$ you must also consider the orifice area $A$. With those variables known, you can determine which orifice will create the limiting flow rate. This can become an iterative process as changing upstream conditions may then limit downstream components.
I have a pressure regulator bringing an inlet pressure of 150 bar down to 10 bar
Since you have a pressure regulator, this tells you something about the dynamics of the system. The pressure regulator presents a variable sized orifice to the process until it is fully opened. Once it is fully open, it behaves like a fixed orifice size. Since the pressure regulator is able to adjust to maintain a downstream condition, it will not be the limiting component until it is wide open.
When the regulator is partially open, the system has established a steady state condition wherein:
- the flow out of the system (to atmosphere) is the maximum flow through the system
- the position of the regulator (e.g. what % open) is such that its exposed flow area provides exactly the same flow as the outlet to atmosphere; this flow is a function of the temperature, upstream pressure, and composition of the gas at that choke point