Mechomatic
Mechanical
- Apr 23, 2013
- 50
I am including specifics to the problem I am currently tackling, though I hope for this to be a more general, qualitative question about nozzles and supersonic flow.
So I've been tasked with developing a "new" product at my company. We create a vapor blending machine using a Convergent-Divergent nozzle to accelerate one vapor into a venturi tube. The gas surrounding the nozzle is drawn into the venturi tube, where the two fluids mix at a specific ratio, exit the venturi tube at an elevated/recovered pressure, and are stored in a receiver tank above ambient pressure. We currently have two sizes of nozzle/venturi tube pairs and want to develop a third, lower capacity nozzle/venturi pair.
Note, subscripts to be used are: i=inlet, o=outlet, n=nozzle, f=frustum, v=venturi, and s=specific OR standard- as appropriate, g=gas, w=vapor.
The relevant fluid details (regarding the nozzle):
Mass Flow Rate (M_dot[sub]n[/sub])= 0.0136 [sup]lb[/sup]/[sub]s[/sub] = 0.00617 [sup]kg[/sup]/[sub]s[/sub]
Inlet Temperature (T[sub]i,n[/sub])= 110[sup]o[/sup]F = 316 K
Inlet Pressure (P[sub]i,n[/sub]) = 40 psig = 377 kPa
Specific Gravity (SG[sub]n[/sub]) = 1.55
Individual Gas Constant (R[sub]s,n[/sub]) = 415 [sup]lb-in[/sup]/[sub]lb.R[/sub] = 186 [sup]J[/sup]/[sub]kg.K[/sub]
Density@STP (rho[sub]s,n[/sub]) = 0.125 [sup]lb[/sup]/[sub]cuft[/sub] = 2.00 [sup]kg[/sup]/[sub]m[sup]3[/sup][/sub]
Moving onward, I am tasked with designing the nozzle and venturi tube dimensions to satisfy both the M_dot[sub]n[/sub] and the required vapor/gas ratio. Using an equation from NASA, I determined the cross-sectional area of the nozzle throat (@ choked velocity, M=c) to be A[sub]t,n[/sub] = 0.00985 in[sup]2[/sup].
The gas enters a frustum section as it approaches the venturi tube, passing through an annular "orifice" with a pressure drop of approximately 0.1 psid (580 Pa) and inlet velocity of v[sub]i,f[/sub] = 0.14 [sup]ft[/sup]/[sub]s[/sub]. The frustum's cross-sectional area decreases from A[sub]i,f[/sub] to the venturi inlet area minus the nozzle's exterior cross-sectional area (A[sub]o,f[/sub] = A[sub]i,v[/sub] = 0.245 in[sup]2[/sup], closely estimated). Given these areas, inlet velocity, and assuming that the gas flow does not approach sonic velocity and, so, may be approximated as incompressible (going for as much reasonable simplification, here), Bernoulli indicates the gas pressure at the venturi opening is P[sub]o,f[/sub] = P[sub]i,v[/sub] = 8.0 psia (velocity of gas = 44.5 [sup]ft[/sup]/[sub]s[/sub]). Obviously the pressure drop is considerable, so my first question is whether others find the value to be reasonable? It doesn't seem unreasonable to me, but I'm going entirely off theory for the moment and this is not something I have really worked on before.
Assuming the "ambient" gas pressure at the venturi inlet, where the nozzle discharges, is reasonable, my understanding is that the next step is to determine the oultet velocity from the nozzle (v[sub]o,n[/sub]). From a separate equation on exit velocity from a De Laval nozzle, I calculate an exit velocity of the vapor to be v[sub]o,n[/sub] = 1476 [sup]ft[/sup]/[sub]s[/sub], or Mach 1.7, according to interpolated gas properties at 32[sup]o[/sup]F and outlet pressure of 8.0 psia.
My understanding is that supersonic flow will decelerate across a sonic shock wave to sonic flow, unless the nozzle is correctly tuned. Ours is not a "proper" nozzle, only having constant slopes across the converging and diverging sections, but the diverging section is a low (12[sup]o[/sup] total angle) taper. My expectation is that the sonic shock should occur at (approximately) the very end of the nozzle, which is coincident with the venturi inlet plane mentioned previously regarding the frustum exit velocity.
In trying to find the density of the vapor exiting the nozzle (in order to utilize conservation of momentum to find the correct dimensions for the venturi opening and throat (to make sure the ratio of vapor to gas is correct, I calculated the exit density of the vapor, based on M_dot[sub]n[/sub] = [rho * A * v][sub]e,n[/sub], to be rho[sub]e,n[/sub] = 0.165 [sup]lb[/sup]/[sub]cuft[/sub], which is significantly above the expected density for the vapor at that pressure- the vapor should liquefy at that pressure and density.
This raises the question of what is actually happening at the nozzle tip. It would seem to me that the vapor is underexpanded at the tip of the nozzle, causing it to billow out significantly. Of course, it's equally (or more) likely that I have made a mistake in applying these equations or that the losses involved with the sonic flow are so great that I need a new approach to try to handle the losses in the calculations.
Any expertise, advice, or suggested ideas for how to move forward with this are appreciated. I should probably add that, while the company I work for has been manufacturing this mixing equipment for years, nobody has really understood or put enough effort into tackling the mechanics involved, so the fact that what we have works at all is just dumb luck.
So I've been tasked with developing a "new" product at my company. We create a vapor blending machine using a Convergent-Divergent nozzle to accelerate one vapor into a venturi tube. The gas surrounding the nozzle is drawn into the venturi tube, where the two fluids mix at a specific ratio, exit the venturi tube at an elevated/recovered pressure, and are stored in a receiver tank above ambient pressure. We currently have two sizes of nozzle/venturi tube pairs and want to develop a third, lower capacity nozzle/venturi pair.
Note, subscripts to be used are: i=inlet, o=outlet, n=nozzle, f=frustum, v=venturi, and s=specific OR standard- as appropriate, g=gas, w=vapor.
The relevant fluid details (regarding the nozzle):
Mass Flow Rate (M_dot[sub]n[/sub])= 0.0136 [sup]lb[/sup]/[sub]s[/sub] = 0.00617 [sup]kg[/sup]/[sub]s[/sub]
Inlet Temperature (T[sub]i,n[/sub])= 110[sup]o[/sup]F = 316 K
Inlet Pressure (P[sub]i,n[/sub]) = 40 psig = 377 kPa
Specific Gravity (SG[sub]n[/sub]) = 1.55
Individual Gas Constant (R[sub]s,n[/sub]) = 415 [sup]lb-in[/sup]/[sub]lb.R[/sub] = 186 [sup]J[/sup]/[sub]kg.K[/sub]
Density@STP (rho[sub]s,n[/sub]) = 0.125 [sup]lb[/sup]/[sub]cuft[/sub] = 2.00 [sup]kg[/sup]/[sub]m[sup]3[/sup][/sub]
Moving onward, I am tasked with designing the nozzle and venturi tube dimensions to satisfy both the M_dot[sub]n[/sub] and the required vapor/gas ratio. Using an equation from NASA, I determined the cross-sectional area of the nozzle throat (@ choked velocity, M=c) to be A[sub]t,n[/sub] = 0.00985 in[sup]2[/sup].
The gas enters a frustum section as it approaches the venturi tube, passing through an annular "orifice" with a pressure drop of approximately 0.1 psid (580 Pa) and inlet velocity of v[sub]i,f[/sub] = 0.14 [sup]ft[/sup]/[sub]s[/sub]. The frustum's cross-sectional area decreases from A[sub]i,f[/sub] to the venturi inlet area minus the nozzle's exterior cross-sectional area (A[sub]o,f[/sub] = A[sub]i,v[/sub] = 0.245 in[sup]2[/sup], closely estimated). Given these areas, inlet velocity, and assuming that the gas flow does not approach sonic velocity and, so, may be approximated as incompressible (going for as much reasonable simplification, here), Bernoulli indicates the gas pressure at the venturi opening is P[sub]o,f[/sub] = P[sub]i,v[/sub] = 8.0 psia (velocity of gas = 44.5 [sup]ft[/sup]/[sub]s[/sub]). Obviously the pressure drop is considerable, so my first question is whether others find the value to be reasonable? It doesn't seem unreasonable to me, but I'm going entirely off theory for the moment and this is not something I have really worked on before.
Assuming the "ambient" gas pressure at the venturi inlet, where the nozzle discharges, is reasonable, my understanding is that the next step is to determine the oultet velocity from the nozzle (v[sub]o,n[/sub]). From a separate equation on exit velocity from a De Laval nozzle, I calculate an exit velocity of the vapor to be v[sub]o,n[/sub] = 1476 [sup]ft[/sup]/[sub]s[/sub], or Mach 1.7, according to interpolated gas properties at 32[sup]o[/sup]F and outlet pressure of 8.0 psia.
My understanding is that supersonic flow will decelerate across a sonic shock wave to sonic flow, unless the nozzle is correctly tuned. Ours is not a "proper" nozzle, only having constant slopes across the converging and diverging sections, but the diverging section is a low (12[sup]o[/sup] total angle) taper. My expectation is that the sonic shock should occur at (approximately) the very end of the nozzle, which is coincident with the venturi inlet plane mentioned previously regarding the frustum exit velocity.
In trying to find the density of the vapor exiting the nozzle (in order to utilize conservation of momentum to find the correct dimensions for the venturi opening and throat (to make sure the ratio of vapor to gas is correct, I calculated the exit density of the vapor, based on M_dot[sub]n[/sub] = [rho * A * v][sub]e,n[/sub], to be rho[sub]e,n[/sub] = 0.165 [sup]lb[/sup]/[sub]cuft[/sub], which is significantly above the expected density for the vapor at that pressure- the vapor should liquefy at that pressure and density.
This raises the question of what is actually happening at the nozzle tip. It would seem to me that the vapor is underexpanded at the tip of the nozzle, causing it to billow out significantly. Of course, it's equally (or more) likely that I have made a mistake in applying these equations or that the losses involved with the sonic flow are so great that I need a new approach to try to handle the losses in the calculations.
Any expertise, advice, or suggested ideas for how to move forward with this are appreciated. I should probably add that, while the company I work for has been manufacturing this mixing equipment for years, nobody has really understood or put enough effort into tackling the mechanics involved, so the fact that what we have works at all is just dumb luck.
