The article proves you are wrong, when you add a smaller throat the shock is expelled into a subcritical condition? what does it mean? simple you have a lower air mass flow ratio as such less air is passing through the narrower throat because the inlet is increasing spillage.
In order to reduce spillage you do the opposite
If the throat area (A2) is too small, corresponding to point c in Figure 2.25, a detached shock will stand ahead of the inlet, as shown in Figure 2.25a. By increasing the throat area, the shock can be moved to the inlet lip. When the operating point a of Figure 2.25 is reached, the shock will reach the inlet lip and
And then what? You are deliberately leaving out the part which mentioned shock is swallowed. Allow me to highlight the part which you have missed:
That citation you gave refers to the process of starting an inlet, not the control of mass flow. An internal/mixed compression inlet does not operate with the normal shock being ahead of the inlet. Furthermore, spillage is independent of throat area:
When the throat area is narrowed, the shock is sucked downstream in the diffuser. This results because the normal shock can no longer be fitted at the throat, and the shock seeks a larger region deep in the inlet to maintain a constant area. Thus, supercritical condition occurs and the mass flow rate is maintained.
Because the engine requieres different mass flows at different speeds and altitude you get contradictions, at the design mach number and cruise flight you can match the air flow needs but at lower speeds you can not, the inlet is just optimized for a speed, otherwise you will need variable throats
At the design cruise speed, inlet throat area and mass flow can be matched to maximize engine efficiency, but "off-design" at transonic and low supersonic speeds the inlet needs a much larger throat area to meet the engine's demand for air. This requires an inlet that can accomodate a wide variation in throat area, otherwise engine efficiency suffers
The purpose of the variable throat is to control the position of the shock, as maximum efficiency can be achieved with the shock sitting right at the throat. It has nothing to do with mass flow.
When the throat is being narrowed, the shock simply shifts downstream into the inlet to maintain a constant area. Since area of the normal shock is what relates to mass flow, then the area being constant means mass flow being constant. Thus, when the throat is too narrowed, the shock sits deeper in the inlet to attain the correct mass flow:
By enlarging the throat area, the shock moves upstream. When the throat area equals to the area of the shock, the shock moves upstream until being positioned right at the throat. Since the mass flow ultimately determines the area of the normal shock, by resizing the throat area to accommodate the normal shock means adjusting the throat to accommodate the mass flow. This is what matching throat area to mass flow means, and throughout this process the mass flow remains unchanged.
By varying the throat size you can increase the air mass supply, that is what they do, at transonic speeds the air mass supply needs to be larger as such a larger throat area is set, the main advantage is a smaller intake but the disadvantage is the extra mechanical systems.
No. Varying the throat size does not increase affect air mass supply. What increases air flow is increase in engine RPM, and what decreases air flow is decrease in engine RPM. The throat size has nothing to do with it.
When the throat is too narrow, your assumption requires that the mass flow cannot be increased any further. Yet, this assumption is false. What really happens is that the normal shock moves deeper into the throat to attain the required mass flow.
When the opposite situation happens, where the throat is wide, your assumption requires that the mass flow must also be high. This assumption is false again, because low engine RPM would cause pressure build up within the inlet, resulting in subcritical condition. With sufficient back pressure, the normal shock gets pushed out of the inlet's mouth, resulting in spillage that results in reduced mass flow.
The above statements are proven here:
Hence, the complete opposite occurs when we look at your assumptions, which means there is no connection between throat area and mass flow. Thus, your claim that variation of throat size being used to control mass flow is incorrect.
Finally, your statement above is a fallacy called
, because you are using "throat size controls mass flow" to prove "throat size controls mass flow".
For typical HSCT-type engines the requiered cruise air flow can be as low as 70% of the required air flow at transonic conditions, To provide for the large airflow rates at transonic condition the inlet throat area must be larger than at the cruise condition, this increased area is provided by the variable inlet geometry
The different throat sizes are consequent of collapsing and expansion of the intake ramps. These ramps are used to control position of shock waves. When the ramps are needed at supersonic speed, they are expanded. When shock waves cannot be generated at subsonic speed, the ramps are collapsed. This is not control of mass flow.
The difference between mass flow at subsonic and at supersonic cruise that your article speaks of is taken care by bypass, as mentioned in the following citation of yours:
And the above source says the following in the next paragraph:
Thus, the reduction in mass flow already has an explanation, and it is not the throat size. This is a fact.
All you have done above is saying throat size variation and mass flow variation occur together in arguing your claim. This is known as
, because
. It is no different than claiming your act of taking a dump causes the sun to rise because you take a dump every morning before sunrise.
Aircraft will only use them if they need to fly at Mach 2.3-8, all the fighters that fly at such speeds have variable geometry throats
This doesn't mean throat area is in control of mass flow. This statement of yours is fallacy of
.
The rest is you usual fallacy, since you have claimed in your initial claim that bernoulli`s principle will allow for no spillage since the flow will accelerate,
Nope. You do not know what a fallacy is. As an example, your statement above constitutes as a fallacy, and it is called
because the statement that Bernoulli's principle does not allow for spillage is manufactured by you, not a claim by me. For the record, I have made clear that spillage occurs on all inlets:
Spillage can occur with inlets with no variable-geometry, such as DSI. You can read about spillage of DSI
. Thus, spill air is not caused by variation in throat area.
Spillage occurs because normal shock wave is outside of inlet's mouth, this is called sub-critical condition. This phenomenon occurs on all inlets, such as DSI.
but because flow is choked and the velocity is choked, the supercritical condition has a choked mass flow
You are using terminologies randomly without considering their meanings. Allow me to provide you with some background:
- Choke condition is related to the fact that maximum flow is limited by area of the normal shock. You incorrectly assume it causes spill. When the shock is inside the inlet, the signal of its existence cannot make it out of the inlet, because the signal propagates at speed-of-sound whereas flow ahead of the shock is supersonic. This means, if we were to exclude the presence of oblique shocks, the normal shock does not cause spillage ahead of itself.
- Supercritical condition means the shock is displaced downstream of the throat. What limits the mass flow is area of normal shock, and this shock shifts downstream to seek a larger area when the throat becomes too narrow. Thus, area of normal shock is conserved, and mass flow rate remains constant.
Super critical mass flow ratio remains a constant because the mass flow through the cowl lip plane is fixed by supersonic conditions .
Mass flow ratio being constant does not mean mass flow is constant. Mass flow ratio refers to the ratio of mass flowing through the stream tube and capture area.
When the two mass flows are 1kg/s, this results in a ratio of 1:1. The ratio remains at 1:1 when the two mass flows are 2kg/s, which is twice the amount as the former example. Your inability to grasp this concept shows you have no fundamental knowledge in proportion.
you even posted this figure
claiming bascily
The conservation of mass (continuity) tells us that the mass flow rate mdot through a tube is a constant and equal to the product of the density r, velocity V, and flow area A:
Eq #1:
mdot = r * V * A
Considering the mass flow rate equation, it appears that for a given area and a fixed density, we could increase the mass flow rate indefinitely by simply increasing the velocity.
but you never said that this happened
because There is a maximum airflow limit that occurs when the Mach number is equal to one. The limiting of the mass flow rate is called choking of the flow. If we substitute M = 1 into Eq #10 we can determine the value of the choked mass flow rate:
thus
The limiting mass flow rate is directly proportional to the stagnation pressure, and inversely proportional to the square root of the stagnation temperature. Thus, if more work is taken out of the flow by the turbine per unit mass, the stagnation pressure drops sharply, and the mass flow and thus the thrust drop sharply as well.
Actually, I said that happens when I told you mass flow is determined by area of normal shock. A normal shock means Mach number is equal to one. What your citation says above is that mass flow is limited by normal shock and not throat size, verifying my statements.
Variation of throat size causes normal shock to shift means that throat size cannot be in control of mass flow. This is because the normal shock maintains the same area as it shifts location, thereby maintaining the same mass flow. When the normal shock shifts downstream to accommodate mass flow, supercritical condition occurs where the flow at the throat goes higher than Mach 1. This is shown in this figure which you have cited:
The flow at the throat is indicated by the small circle, pointed at by the arrow with the flow velocity written right beside. You claimed that flow velocity cannot be higher than Mach 1 at the throat, and the diagrams showed you to be incorrect. Thus, you made the an erroneous claim.
Thus, flow velocity becomes higher to compensate for the restriction at the throat, as according to Benoulli's principle. Mass flow is therefore unaffected by the size of the throat.
