Transonic Nozzle
Hello, I am working actually on a numerical simulation of the transonic flow through a choked convergentdivergent nozzle. I'd like to understand how can we classify nozzles geometries : I've seen for instance that we speak about discharge coefficient of the nozzle (which is the real mass flow through the nozzle divided by the ideal one (or 1D approximated)) and also about the nozzle cooling rate. I'd like if possible some explanations about the cooling rate and its variation depending on the geometries. Finally, how can we extend the classification of the nozzles depending on the wall curvature. How can we compute a Reynolds number (at the throat) taking into account, may be, the wall curvature. Because actually, the wall curvature of the nozzle changes the thickness of the boundary layer (and also its behavior, laminar to turbulent), while fixing the throat diameter. How can I compute this thickness ? There are many questions ... ! Thanks for your help, Omar

Re: Transonic Nozzle
(1). The converging part of the nozzle will define the final throat shape and location, which will be different from the 1D straight line, because of the nonuniform flow field. Thus, the mass flow rate will be different from the ideal 1D solution. (2). The nozzle can be straight, conical, or curved walls. This will affect the actual flow field in the supersonic region. (3). In general, there will be shock formation in the supersonic nozzle region, unless the wall is properly shaped to produce a shock free flow field. (4). As a result, there will be shockboundary layer interaction in the supersonic portion of the nozzle. (5). Depending on the operating nozzle pressure ratio, a normal shock and lambda shock will form inside the nozzle. (6). The boundary layer behavior can be computed based on the classical inviscidboundary layer approach, where the inviscid flow is first computed to provide the external condition for the boundary layer flow calculation. The modern approach is to use the NavierStokes code to solve the whole flow field. (7). The laminarturbulent transition is a difficult issue. It will have to be modelled separately. (8). You need to define the nozzle cooling rate first before I can understand it. (I think, the heat transfer part is treated as any convection heat transfer problem. It will be a function of the wall boundary condition.)

Transonic Nozzle
Thank you for your answer, but I'd like to know how is the physics ? Actually, the pressure ratio and the nozzle shape have been chosen to avoid any shock : so the flow is shock free. But, how does the boundary layer behave in the converging and diverging part. (The wall is curved) ? How can I compute its thickness ? In a more general topic, how can we classify nozzles : dimensions, discharge coefficient ... ? How can we make them standardised ISO ?

Re: Transonic Nozzle
(1). All I can say is: the boundary layer is subject to the favorable pressure gradient (the physics), which can be computed from the inviscid flow field at the wall. (the flow is accerating from the converging side to the diverging side) (2).You can start from the inlet (subsonic) and compute the boundary layer by solving the boundary layer equation (parabolic, marching method), with the given inviscid flow solution imposed at the edge of the boundary layer. (3). Or you can simply compute the whole flow field by solving the NavierStokes equations. From the velocity field solution, you can find the edge of the boundary from the wall.(99.5% of the local free stream velocity location) The calculation is rather straight forward, just like any viscous flow calculations. (4). Nozzle can be either subsonic or supersonic, 2D (actually 3D) or axisymmetric, fixed or collapsed, regular or scarfed, solid rocket nozzle vs liquid rocket nozzle (liquid cooled), tiny satellite control thruster vs huge launch vehicle main engine,etc... I am not aware of the ISO standard on the nozzle. (there is an ASME standard of the nozzle for flow metering purpose)

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