ked flow, where the flow expands

2021/05/21

Choked flow, where the flow expands after the nozzle exit (considered non-isentropic). If the exit pressure is sufficiently low to produce sonic flow at the throat, the nozzle is choked and further decreases in exit pressure will not alter the mass flow. Image credit: # Nozzle exit pressure, 1st stage [units: pascal], # Nozzle expansion ratio [units: dimensionless], # Nozzle exit pressure, 2nd stage [units: pascal], # Compute the thrust coeffieicient of the fixed-area nozzle, 1st stage [units: dimensionless], # Compute the thrust coeffieicient of the fixed-area nozzle, 2nd stage [units: dimensionless], # Compute the thrust coeffieicient of a variable-area matched nozzle [units: dimensionless], 'Effect of altitude on nozzle performance', # Compute the characteristic velocity [units: meter second**-1], Smithsonian Institution, National Air and Space Museum. The nozzle accelerates the gas by converting some of the gass thermal energy into kinetic energy. Nozzles are widely used in aerospace propulsion systems. steam compressors ejector tlv mechanism The gas is homogeneous, obeys the ideal gas law, and is calorically perfect. The ratio between them is the back-pressure ratio, which can be used to control flow velocity. As the nozzle area decreases, the flow velocity increases, with the maximum flow velocity occurring at the nozzle throat. pressure ratio and the nozzle total temperature. If you do not see the message in your inbox, please check your "Spam" folder. Image credit: Smithsonian Institution, National Air and Space Museum. If the problem continues, please. Nozzles are commonly used in aircraft and rocket propulsion systems as they offer a simple and effective method to accelerate flow in restricted distances. Here, the pressure at the exit is referred to as the back-pressure, and the pressure at the entry is the stagnation pressure. For an ideal rocket at matched exit pressure, $I_{sp} = v_2 / g_0$. Please click here to view a larger version of this figure. As the inlet flow velocity is increased, flow velocity at the nozzle throat keeps increasing until it reaches Mach 1. Please enter your Institution or Company email below to check. First, flow reaches the choked condition at the throat and decelerates subsonically in the diverging section. Mount the converging nozzle in the center of the nozzle test rig, as shown in. If the flow is both adiabatic and reversible, it is isentropic: the specific entropy. A nozzle begins at the point where the chamber diameter begins to decrease. Schematic of a converging-diverging nozzle. Finally, the plot of MFP shows an increase with decreasing back-pressure ratios, which peaks at 0.5283. Please click here to view a larger version of this figure. On completion of the tests, disconnect all systems and dismantle the nozzle test-rig. A JoVE representative will be in touch with you shortly. FromFigure 8, we observe that as thepB/pOratio decreases(until 0.5283), flow at every section of the nozzle is subsonic and increases with decreasing area. A subscription to JoVE is required to view this content.You will only be able to see the first 20 seconds. You have unlocked a 2-hour free trial now. throat area, chamber pressure, chamber temperature) and its performance (e.g. Please click here to view a larger version of this figure. Therefore, the flow is reversible. Therefore, the flow is adiabatic. b. This result is expected as flow increases up to the choked condition. In this demonstration, the converging and converging-diverging nozzles - two of the most common nozzle types used in aerospace applications - were tested using a nozzle test rig. + Subsonic flow, where there is significantly higher acceleration and the pressure drops. Sorry, your email address is not valid for this offer. from the free stream conditions and the engine This assumption is known as frozen flow. + Inspector General Hotline Choked flow, where any pressure drop does not accelerate the flow. All jet engines have a nozzle which is station 8.

Subscription Required. sets the total mass flow rate through the Make sure to capture data at a back-pressure ratio of 0.5283, which is the theoretical choked flow condition. If the pressure ratio across the nozzle is at least: then the flow at the throat will be sonic ($M = 1$) and the flow in the diverging section will be supersonic. We use cookies to enhance your experience on our website. Once the mass flow rate values are entered, push the 'Record Data' button to record all the readings at the set back-pressure ratio. no thermodynamic work, the total temperature Tt through the nozzle is Under-expanded flow the pressure at the nozzle exit is higher than the ambient pressure and results in similar effects as over-expanded flow. The ideal $c^*$ of the example engine is: Finally, we arrive at specific impulse, the most important performance parameter of a rocket engine. We can determine the nozzle total pressure , ETR. Please click here to view a larger version of this figure. Aeronautical Engineering. We also observed three types of flows that can be obtained after the choked throat depending on the back-pressure ratio of the flow. Analysis of the converging-diverging nozzle provides insight into how supersonic flow velocities can be achieved once flow gets choked at the throat. With a Rotate the valve to adjust the flow rate to obtain a back-pressure ratio (. As the inlet flow velocity increases, flow velocity at the throat also increases until it reaches Mach 1. Measuring Axial Pressure in Converging and Converging-diverging Nozzles. It can be used to compare the efficiency of different nozzle designs on different engines. Decrease the back-pressure ratio in steps of 0.1 until, Replace the converging nozzle with the converging-diverging nozzle and repeat steps 1.2 - 1.8. One of the governing isentropic relations between Mach number (M), nozzle area (A), and velocity (u) is represented by the following equation: where u is the velocity, A is the nozzle area, and M is the Mach number. The nozzles are run for different back-pressure settings to analyze the internal flow in the nozzles under varying flow conditions, identify the various flow regimes, and compare the data to theoretical predictions.

@1m9S6!BhmN-E"7AO?0ZHSvL 1 Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. w6;b(]om*K]D_7S!{'eQjNU"X^@JjLbRZWXqQ1/a84 The most basic type of nozzle, the converging nozzle, is essentially a tube with an area that gradually decreases from the entry to the exit, or throat. As the back-pressure is further reduced, the Mach number at the throat stays constant at one. Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle. Values of $C_F$ are generally between 0.8 and 2.2, with higher values indicating better nozzle performance. The nozzle performance equations work just as well for rocket Then, adjust the flow using the mechanical valve in order to obtain a back-pressure ratio of 0.9. Geometry of converging-diverging nozzle. Subsonic flow that reaches choked condition but does not attain supersonic velocities (considered isentropic). The amount of thrust produced by the nozzle depends on the exit velocity and pressure and the mass flow rate through the nozzle. A comparison of the pressure trends obtained for both the converging and converging-diverging type nozzles with theoretical results was excellent. You have already requested a trial and a JoVE representative will be in touch with you shortly. The stagnation enthalpy $h_0$ is the sum of the static enthalpy and the specific kinetic energy: For a calorically perfect gas, $T = h / c_p$, and the stagnation temperature is: It is helpful to write the fluid properties in terms of the Mach number $M$, instead of the velocity. In jet engines, a nozzle is used to transform energy from a high-pressure source into kinetic energy of the exhaust to produce thrust. the other engine components. thrust equation for the amount of thrust losses in the nozzle, but its value is normally very near 1.0. Recall that the back-pressure measurement was made at port 10. At very low back-pressure ratios, the flow isentropically expands and remains supersonic throughout the diverging nozzle, reaching Mach numbers greater than one. The ratio of the OHwyb[-d- 61g#b^K#Z]ycL`JJdOU@t0UMecQx`m%hnheY/6s* T7m3L5Hl$z)M~6l8Uhbp1Mk3o926Jrofs8qje9V5W+ wc5pc% 8, 14 October 2019 | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. Substituting = 1.4 (specific heat ratio for dry air) in Equation 2, we obtain a back-pressure ratio of: Equation 3 defines the boundary between the non-choked and choked flow regimes. Referring to our station If you need immediate assistance, please email us at subscriptions@jove.com. For the converging-diverging nozzle (Figure 9), subsonic flow is observed untilp/pOat the throat (normalized nozzle distance = 0.68) equals 0.5283 (choked flow condition). 5283, the flow becomes choked and it reaches Mach one before decreasing subsonically. Using this The relation between expansion ratio and pressure ratio can be found from mass conservation and the isentropic relations: This relation is implemented in proptools: Let us plot the effect of expansion ratio on thrust coefficient: The thrust coefficient is maximized at the matched expansion condition, where $p_e = p_a$. Please click here to view a larger version of this figure. For vehicles like rockets and military aircraft, which must travel at and above the speed of sound, a converging-diverging nozzle, as illustrated in Figure 2, is used. Nozzle flow theory can predict the thrust and specific impulse of a rocket engine. Please follow the link in the email to activate your free trial account. pressure, unless the exiting flow is expanded to supersonic We recommend downloading the newest version of Flash here, but we support all versions 10 and above. We can also look at the Mach number across the length of the converging-diverging nozzle to examine flow conditions at varying back-pressure ratios. The expansion ratio is an important design parameter which affects nozzle efficiency. The specific enthalpy, There are no viscous effects or shocks within the gas or at its boundaries. Please enjoy a free 2-hour trial. The mass flow parameter (MFP) is a variable that determines the rate at which mass is flowing through the nozzle and is given by the equation: Here, is the mass flow rate through the nozzle, TO is the stagnation temperature, and AT is the area of the throat, which, in the case of the converging nozzle, is equal to the area at the nozzle exit, AE. engines except that rocket nozzles always expand the flow to some At subsonic speeds, Mach number increases as the area is decreased. nozzle efficiency steam diagram The specific impulse measures the fuel efficiency of a rocket engine. Data collected for the nozzle experiment. We can now show a basic relation between the exit velocity and the combustion conditions of the rocket. There are several different types However, it should be noted that the data at the throat corresponds to port 9, which is slightly before the actual throat.

little algebra which you learned in middle school, and using the Here, the normal shock causes a sudden drop in velocity and an increase in back-pressure, as indicated by the sudden increase in. engine as described on a separate slide. Text Only Site In this experiment, we will study the behavior of nozzles using a nozzle test rig, which consists of a compressed air source that channels the high-pressure air through the nozzles being tested. As shown on this slide, the exit velocity depends on the nozzle Subsonic flow that never reaches choked condition. The total pressure pt across the nozzle is constant as well: The static In order to design nozzles to suit a given application, an understanding of the flow behavior and factors that affect said behavior for a range of flow conditions is essential for designing efficient propulsion systems. + Non-Flash Version ETR depends on the temperature ratio of all the other ratio depends on the exit static pressure and the Now, let's take a look at the converging-diverging nozzle, starting with the plot of pressure ratio and Mach number versus normalized nozzle distance. Subsonic flow that reaches choked condition, with the resulting supersonic flow forming a normal shock, which then experiences subsonic deceleration. Observations of the Mach number variation across the nozzle show subsonic flow until the pressure ratio at the throat equals the choked flow condition of 0.5283. Mach number is the velocity normalized by the local speed of sound, $a = \sqrt{\gamma R T}$. exit flow, a simple convergent nozzle will not. Once the flow becomes choked at the throat of a converging-diverging nozzle (based on Equation 3), three possible flow conditions can occur: subsonic isentropic flow (the flow decelerates after the choked condition), supersonic non-isentropic flow (where the flow accelerates supersonically, forms a shock wave - a thin region of coalesced molecules that forms normal to a certain point on the nozzle and causes a sudden change in flow conditions, generally referred to as a normal shock - and decelerates subsonically after the shock), or supersonic isentropic flow (where the flow accelerates supersonically after the choked condition). Image credit: """Check that the nozzle is choked and find the mass flow. The chemical equilibrium established in the combustion chamber does not change as the gas flows through the nozzle. Please create a free JoVE account to get access, Please login to your JoVE account to get access. Therefore, most rocket nozzles have a convergent-divergent shape. Set state 2 to be the state at the nozzle exit: $p_2 = p_e, v_2 = v_e$. The heat capacity ratio $\gamma$ has a weak effect on exit velocity. We can define another performance parameter which captures the effects of the combustion gas which is supplied to the nozzle. Set state 1 to be the conditions in the combustion chamber: $T_1 = T_c, p_1 = p_c, v_1 \approx 0$. is equal to the static 2159, 2022 American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, Journal of Guidance, Control, and Dynamics, Journal of Thermophysics and Heat Transfer, Source Localization of Crackle-Related Events in Military Aircraft Jet Noise, Coherence Analysis of the Noise from a Simulated Highly Heated Laboratory-Scale Jet, Modelling of jet noise: a perspective from large-eddy simulations. If $p_e \ll p_c$, the pressures have a weak effect on exit velocity. A nozzle is a device that is commonly used in aerospace propulsion systems to accelerate or decelerate flow using its varying cross section. However, the experimental results showed the mass flow parameter decreasing for lower values of back-pressure ratio instead of plateauing once the maximum value was achieved, as predicted by theory. Once the flow is choked, the mass flow rate is fixed, and the MFP remains a constant for decreasing back-pressure ratios. """, # Compute the mass flow [units: kilogram second**-1], 'Thrust vs chamber pressure at $p_e = p_a = {:.0f}$ kPa', 'Thrust vs ambient pressure at $p_c = {:.0f}$ MPa, $p_e = {:.0f}$ kPa', """Map atmospheric pressure [units: kilopascal] to altitude [units: kilometer].

Figure 8. Here, we've plotted the variation in pressure ratio and Mach number versus the normalized nozzle distance for each flow rate in our converging nozzle. Tp6Hl%!$v.Hc&`LX3u0 =9` FB1r~9lSk:!U`>$%@v)030)nI?mk@W` Figure 5. One of the governing isentropic relations between Mach number (. ) Results for the converging-diverging nozzle (from top-right, clockwise) variation in pressure ratio across the nozzle; variation in Mach number across the nozzle; and variation in mass plow parameter with back-pressure ratio. Next, using the data collected, we can calculate the mass flow parameter, MFP, using the equation shown. In summary, we learned how varying cross sections of nozzles accelerate or decelerate flow in propulsion systems. Figure 1. Based on Figure 3, the following are the flow conditions that can be observed in a converging nozzle: Figure 3. sea level) engine has a smaller expansion ratio than the second stage (e.g. Record the data corresponding to Table 1. A convergent-divergent nozzle will have supersonic An efficiency factor nn has been included here to account for all the

Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle. The following constants were used in the analysis: specific heat of dry air,:1.4; reference nozzle area,Ai= 0.0491 in2, and standard atmospheric pressure,Patm= 14.1 psi. Finally, we see that flow continues to accelerate supersonically for the entirety of the diverging section for back-pressure ratios lower than 0.3. """Effect of expansion ratio on thrust coefficient. Under the assumption of isentropic flow and calorically perfect gas, there are several useful relations between fluid states. By continuing to use our website or clicking Continue, you are agreeing to accept our cookies. These assumptions are usually acceptably accurate for preliminary design work. thrust and specific impulse). For the no flow condition, again the Mach number is zero. produced by the nozzle. Figure 4. A nozzle is a device that is commonly used to accelerate or decelerate flow by virtue of its varying cross-section. and Accessibility Certification, + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act, + Budgets, Strategic Plans and Accountability Reports. Please enter an institutional email address. In this experiment, two types of nozzles are mounted on a nozzle test rig, and a pressure flow is created using a compressed air source. JoVE, Cambridge, MA, (2022). Now, take the zero flow condition pressure reading. First, use the conservation of energy to relate the velocity at any two points in the flow: We can replace the enthalpy difference with an expression of the pressures and temperatures, using the isentropic relations. conditions. """, # Compute the expansion ratio and thrust coefficient for each p_e, # Compute the matched (p_e = p_a) expansion ratio, 'matched $p_e = p_a$, $\epsilon = {:.1f}$', '$C_F$ vs expansion ratio at $p_c = {:.0f}$ MPa, $p_a = {:.0f}$ kPa'. The isentropic model along the nozzle is sufficient for a first-order analysis as the flow in a nozzle is very rapid (and thus adiabatic to a first approximation) with very little frictional loses (because the flow is nearly one-dimensional with a favorable pressure gradient, except if shock waves form and nozzles are relatively short). + Freedom of Information Act We can also explore the variation of thrust with ambient pressure for fixed $p_c, p_e$: We can normalize thrust by $A_t p_c$ to give a non-dimensional measure of nozzle efficiency, which is independent of engine size or power level. Connect the ports to the measurement system, then repeat all of the measurements as described previously. EPR depends on the pressure ratio of all Use proptools to plot thrust versus chamber pressure for the example engine: Note that thrust is almost linear in chamber pressure. Decrease the back-pressure ratio in steps of 0.1, down to a ratio of 0.

The trends inMFPfollow theoretical results untilpB/pO= 0.6 but start decreasing instead of plateauing for lower values of back-pressure ratios. definitions shown on the slide, you can solve the energy equation for Flow conditions and regimes in a converging-diverging nozzle (theoretical predictions). gas turbine engines, which are also called For a flow passage to accelerate gas from subsonic to supersonic speeds, it must first decrease in area, then increase in area. We may use this info to send you notifications about your account, your institutional access, and/or other related products. velocity, and the mass flow rate through the engine, we can solve the jet engines. Second, flow accelerates supersonically beyond the throat and then decelerates, in some cases to subsonic velocities.

Please recommend JoVE to your librarian. Note that the first vertical dashed line on the left of the p/pO versus distance along the nozzle plot is the location of the throat, the second vertical dashed line is the location of the nozzle exit, and the horizontal dashed line marks the choked condition. + NASA Privacy Statement, Disclaimer, Compare these curves to the performance of a hypothetical matched nozzle, which expands to $p_e = p_a$ at every altitude. \[\frac{p_1}{p_2} = \left( \frac{\rho_1}{\rho_2} \right)^\gamma = \left( \frac{T_1}{T_2} \right)^{\frac{\gamma}{\gamma - 1}}\], \[T_0 = T \left( 1 + \frac{\gamma - 1}{2} M^2 \right)\], \[p_0 = p \left( 1 + \frac{\gamma - 1}{2} M^2 \right)^{\frac{\gamma}{\gamma - 1}}\], \[v_2 = \sqrt{\frac{2 \gamma}{\gamma - 1} R T_1 \left(1 - \left( \frac{p_2}{p_1} \right)^{\frac{\gamma - 1}{\gamma}} \right) + v_1^2}\], \[\begin{split}v_e &= \sqrt{\frac{2 \gamma}{\gamma - 1} R T_c \left(1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right)} \\ When it reaches Mach 1, the flow at the throat is choked, meaning that any further increase of the inlet flow velocity does not increase the flow velocity at the throat. The specific impulse and propellant mass fraction together determine the delta-v capability of a rocket. The supersonic flow velocities set in the diverging section are a function of the nozzle area ratios after the throat. The stagnation state is the state a moving fluid would reach if it were isentropically decelerated to zero velocity. JoVE, Cambridge, MA, (2022). More. Use proptools to compute the mass flow of the example engine: The thrust force of a rocket engine is equal to the momentum flow out of the nozzle plus a pressure force at the nozzle exit: where $p_a$ is the ambient pressure and $A_e$ is the nozzle exit area. If you have any questions, please do not hesitate to reach out to our customer success team. c. Pattern 3 - Flow continues to accelerate supersonically for the entirety of the diverging section forpB/pOvalues lower than 0.3. The purpose of a rocket is to generate thrust by expelling mass at high velocity. If the pressure at the nozzle exit is higher than the ambient pressure, the flow exhibits similar unstable flow and is called under-expanded. Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle. """, """Compute the expansion ratio for a given pressure ratio. If that doesn't help, please let us know. The fixed-expansion nozzles perform well at their design altitude, but have lower $C_F$ than a matched nozzle at all other altitudes. It depends only on the heat capacity ratio, nozzle pressures, and expansion ratio ($A_e / A_t$). Subsonic flow that reaches choked condition, with the resulting supersonic flow forming a normal shock after the nozzle (considered isentropic in the nozzle). The nozzle sits downstream of the power For this reason, converging nozzles are used to accelerate fluids in the subsonic regime alone. The MFP should then remain constant after 0.6, as the flow is choked at this point and the mass flow cannot increase. Most rocket engines perform within 1% to 6% of the ideal model predictions [RPE]. At and belowpB/pO= 0.5283, the Mach number at the throat (normalized nozzle distance = 0.93) does not exceed one. the nozzle, the specific the exit velocity Ve = V8: V8 = sqrt(2 * nn * cp * Tt8 * [1 - (1 / NPR)^((gam -1 ) / gam)] ). Both of the nozzles tested have 10 ports, enabling pressure measurements throughout the length of the nozzle. Your access has now expired. nozzle simulator program which runs on your browser. Flow conditions and regimes in a converging nozzle (theoretical predictions). Then, use high-pressure PVC tubing to connect the 10 static pressure ports to the pressure measurement system, as well as the stagnation pressure port. of jet engines, but all jet engines have some partsin common. Thank you for taking us up on our offer of free access to JoVE Education until June 15th. When these tests have been completed, turn off the airflow, disconnect the PVC tubing, and replace the converging nozzle with the converging-diverging nozzle. Once flow is choked, any increase in inlet flow velocity did not increase the flow velocity at the throat/exit to supersonic speeds. Increasing the chamber pressure increases the density at the throat, and therefore will increase the mass flow which can fit through the throat. Record the stagnation pressure and atmospheric pressure from the pressure measurement system and the temperature from the temperature sensor. This is why many rockets burn hydrogen and oxygen: they yield a high flame temperature, and the exhaust (mostly H2 and H2O) is of low molar mass. Subsonic flow, where the flow accelerates as area decreases, and the pressure drops. If you would like to continue using JoVE, please let your librarian know as they consider the most appropriate subscription options for your institutions academic community. Over-expanded flow the pressure at the nozzle exit is lower than the ambient pressure, causing the jet exiting the nozzle to be highly unstable with huge variations in pressure and velocity as it travels downstream. This is called over-expanded flow. Please click here to view a larger version of this figure. Results for the converging nozzle tests showed that the maximum limit up to which flow can be accelerated isM= 1, at which point flow at the nozzle throat gets choked. Consider two gas states, 1 and 2, which are isentropically related ($s_1 = s_2$). + Budgets, Strategic Plans and Accountability Reports As the back-pressure decreases, the Mach number increases across the converging section while decreasing across the diverging section. If you do not wish to begin your trial now, you can log back into JoVE at any time to begin. Copyright 2022 MyJoVE Corporation. $c^*$ is independent of the nozzle expansion process. The expansion ratio also allows the nozzle designer to set the exit pressure. supersonic exit velocity. This could be the most likely reason for the incorrect MFP reading. As with the converging nozzle, the MFP should remain constant after reaching the choked flow condition, but we observe a decrease due to the location of the throat pressure tap. nano bubble generator micro introduction