Abstract
An industrially applicable nozzle is the subject of this study. The nozzle is an auxiliary equipment of a pneumatic pulsator system for unclogging outlets of silos which store loose materials. The aim is to determine the amount of heat which is generated during one work cycle of the system. Investigation in this field has not been carried out so far, and the present-day designing process is significantly based on heuristic knowledge. The heat is calculated by using results of a numerical simulation. The Finite Volume Method has been used with a thermodynamically ideal gas model. The airflow is assumed to be transient, compressible and supersonic, and it is driven by a time-varying pressure difference. There is an estimation of discretization error of the numerical results carried out in order to confirm the reliability of the solution. The error estimation shows that the results lie in the vicinity of the exact solution of the governing equations. Instantaneous results of the simulation indicate a locally flow which intensifies flow parameters in a similar way as the converging-diverging nozzles do. The value of the total heat generated during gas conversion within the nozzle is negative; thus, the nozzle could be cooled during its functioning.
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Abbreviations
- n :
-
Normal vector (–)
- q :
-
Heat flux vector (W/m2)
- u :
-
Velocity vector (m/s)
- C p :
-
Specific heat at constant pressure (J/kg K)
- C v :
-
Specific heat at constant volume (J/kg K)
- E :
-
Total energy (J)
- e :
-
Internal energy of gas (J/kg)
- h :
-
Mesh size (–)
- k :
-
Turbulent energy (J/kg)
- n :
-
Number of subdivisions (–)
- P :
-
Rank of error (–)
- p :
-
Pressure (Pa)
- Q :
-
Heat transfer rate (W)
- r :
-
Mesh refinement factor (–)
- S :
-
Surface area(m2)
- T :
-
Temperature (K)
- t :
-
Time (s)
- V :
-
Volume (m3)
- ϵ :
-
Error (–)
- λ:
-
Thermal conductivity (W/m K)
- μ :
-
Dynamic viscosity (kg/s m)
- μ t :
-
Turbulent dynamic viscosity (kg/s m)
- \({{\phi}}\) :
-
Mass flow (kg/s)
- ϕ :
-
General quantity (source term) e.g. velocity, pressure, temperature (–)
- ρ :
-
Density (kg/m3)
- ɛ :
-
Turbulent dissipation rate (m2/s3)
- 0:
-
Base mesh
- c:
-
Coarse mesh
- ext:
-
Extrapolated value
- f:
-
Fine mesh
- in:
-
Inlet boundary
- out:
-
Outlet boundary
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Wołosz, K.J., Wernik, J. On the heat in the nozzle of the industrial pneumatic pulsator. Acta Mech 227, 1111–1122 (2016). https://doi.org/10.1007/s00707-015-1502-4
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DOI: https://doi.org/10.1007/s00707-015-1502-4