nozzle pressure ratio

The ratio between them is the back-pressure ratio, which can be used to control flow velocity. Please check your Internet connection and reload this page. Please create a free JoVE account to get access, Please login to your JoVE account to get access. No flow condition, where the back-pressure is equal to the total pressure. """, """Compute the expansion ratio for a given pressure ratio. 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. is station 8. This gives the exit velocity: where $\mathcal{R} = 8.314$ J mol -1 K -1 is the universal gas constant and $\mathcal{M}$ is the molar mass of the exhaust gas. 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. If the pressure at the nozzle exit is higher than the ambient pressure, the flow exhibits similar unstable flow and is called under-expanded. The typical converging-diverging shape of rocket nozzles is shown in this cutaway of the Thiokol C-1 engine. Copyright 2022 MyJoVE Corporation. This is called over-expanded flow. Figure 4 shows the following seven profiles in the position versus pressure ratio plot. + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act Small expansion ratios are used for space launch boosters or tactical missiles, which operate at low altitudes (high ambient pressure). Consider two gas states, 1 and 2, which are isentropically related ($s_1 = s_2$). The MFP should then remain constant after 0.6, as the flow is choked at this point and the mass flow cannot increase. We then measured the axial pressure along a converging and a converging-diverging nozzle, to observe variations in Mach number and pressure to deduce the flow patterns. 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. engine as described on a separate slide. For a flow passage to accelerate gas from subsonic to supersonic speeds, it must first decrease in area, then increase in area. The condition at which choked flow occurs can be calculated using the isentropic relation: where is the specific heat ratio of the fluid. If you have any questions, please do not hesitate to reach out to our customer success team. Make sure to capture data at a back-pressure ratio of 0.5283, which is the theoretical choked flow condition. $c^*$ is independent of the nozzle expansion process. This assumption is known as frozen flow. The overall efficiency of the engine ($I_{sp}$) depends on both the combustion gas ($c^*$) and the efficiency of the nozzle expansion process ($C_F$). Nozzle flow theory can predict the thrust and specific impulse of a rocket engine. 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. Most rocket engines perform within 1% to 6% of the ideal model predictions [RPE]. 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 trends inMFPfollow theoretical results untilpB/pO= 0.6 but start decreasing instead of plateauing for lower values of back-pressure ratios. Here, the normal shock causes a sudden drop in velocity and an increase in back-pressure, as indicated by the sudden increase in. For an ideal rocket at matched exit pressure, $I_{sp} = v_2 / g_0$. Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle. If that doesn't help, please let us know. The velocity at the throat is: The mass flow at the sonic throat (i.e. conditions. supersonic exit velocity. Once flow is choked, any increase in inlet flow velocity did not increase the flow velocity at the throat/exit to supersonic speeds. You have unlocked a 2-hour free trial now. 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. If the flow is both adiabatic and reversible, it is isentropic: the specific entropy. constant. Values of $C_F$ are generally between 0.8 and 2.2, with higher values indicating better nozzle performance. One of the governing isentropic relations between Mach number (. ) Figure9. Nozzles are widely used in aerospace propulsion systems. Please check your Internet connection and reload this page. Contact Glenn. 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). JoVE Science Education Database. This result is expected as flow increases up to the choked condition. This result is likely caused by the location of the tap measuring throat pressure, which is slightly before the true nozzle throat. In rockets, propellant that is ejected from the chamber is accelerated through a nozzle to create a reaction force that propels the system. The JoVE video player is compatible with HTML5 and Adobe Flash. exit flow, a simple convergent nozzle will not. Your access has now expired. The specific impulse and propellant mass fraction together determine the delta-v capability of a rocket. Alternatively, the flow can form a shock when it expands in the diverging section. You have already requested a trial and a JoVE representative will be in touch with you shortly. Once the flow exits the nozzle, it undergoes an expansion, due to the sudden increase in area that could lead to (uncontrolled) supersonic flow velocities. Pattern 1 - Flow reaches choked condition at the throat and decelerates subsonically in the diverging section (0.8 $%@v)030)nI?mk@W` This is the characteristic velocity, $c^*$: For an ideal rocket, the characteristic velocity is: The characteristic velocity depends only on the exhaust properties ($\gamma, R$) and the combustion temperature. definitions shown on the slide, you can solve the energy equation for &= \sqrt{\frac{2 \gamma}{\gamma - 1} \mathcal{R} \frac{T_c}{\mathcal{M}} \left(1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right)}\end{split}\], \[\frac{p_e}{p_c} \rightarrow 0 \quad \Rightarrow \quad 1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \rightarrow 1\], \[\frac{A_1}{A_2} = \frac{v_2 \rho_2}{v_1 \rho_1}\], \[\frac{A_1}{A_2} = \frac{M_2}{M_1} \left( \frac{1 + \frac{\gamma - 1}{2} M_1^2}{1 + \frac{\gamma - 1}{2} M_2^2} \right)^{\frac{\gamma + 1}{2 (\gamma - 1)}}\], \[\frac{p_c}{p_e} > \left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma}{\gamma - 1}} \sim 1.8\], \[v_t = \sqrt{\gamma R T_t} = \sqrt{\frac{2 \gamma}{\gamma + 1} R T_c}\], \[\dot{m} = A_t v_t \rho_t = A_t p_c \frac{\gamma}{\sqrt{\gamma R T_c}} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2 (\gamma - 1)}}\], \[F = A_t p_c \sqrt{\frac{2 \gamma^2}{\gamma - 1} \left( \frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{\gamma - 1}} \left(1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right)} + (p_e - p_a) A_e\], \[C_F = \sqrt{\frac{2 \gamma^2}{\gamma - 1} \left( \frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{\gamma - 1}} \left(1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right)} + \frac{p_e - p_a}{p_c} \frac{A_e}{A_t}\], \[\begin{split}\epsilon &= \frac{A_e}{A_t} = \frac{\rho_t v_t}{\rho_e v_e} \\ As the inlet flow velocity increases, flow velocity at the throat also increases until it reaches Mach 1. With a Given that the flow is choked, theMFPshould be constant. ETR depends on the temperature ratio of all the other Please click here to activate your free 2-hour trial. Subsonic flow that reaches choked condition, with the resulting supersonic flow forming a normal shock, which then experiences subsonic deceleration. To begin the experiment, mount the converging nozzle in the center of the nozzle test rig. A convergent-divergent nozzle will have supersonic Larger expansions of the divergent section lead to higher exit Mach numbers. The stagnation state is the state a moving fluid would reach if it were isentropically decelerated to zero velocity. little algebra which you learned in middle school, and using the The expansion ratio also allows the nozzle designer to set the exit pressure. produces the thrust as described on the 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. To analyze our data, first we calculate the pressure ratio across the nozzle using the static pressure measurement at each port. If the problem continues, please. thrust equation slide. As the back-pressure is further reduced, the Mach number at the throat stays constant at one. To conserve mass, the ratio of areas between any two points along the nozzle axis must be: Use the isentropic relations to write the velocity and density in terms of Mach number, and simplify: We can use proptools to plot Mach-Area relation. &= \left( \left( \frac{\gamma + 1}{2} \right)^{\frac{1}{\gamma - 1}} \left( \frac{p_e}{p_c} \right)^{\frac{1}{\gamma}} \sqrt{\frac{\gamma + 1}{\gamma - 1} \left(1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right)} \right)^{-1}\end{split}\], \[c^* = \frac{\sqrt{\gamma R T_c}}{\gamma} \left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma + 1}{2 (\gamma - 1)}}\], """Estimate specific impulse, thrust and mass flow. These relations depend on the heat capacity ratio, $\gamma = c_p /c_v$. In this experiment, we will demonstrate and analyze flow in both a converging and a converging-diverging nozzle. The first stage (e.g. We can define another performance parameter which captures the effects of the combustion gas which is supplied to the nozzle. Next, using the data collected, we can calculate the mass flow parameter, MFP, using the equation shown. Subsonic flow that reaches choked condition, with the resulting supersonic flow forming a normal shock after the nozzle (considered isentropic in the nozzle). When the throat pressure ratio approaches 0. We also observed three types of flows that can be obtained after the choked throat depending on the back-pressure ratio of the flow. 18 May 2020 | AIAA Journal, Vol. 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. Geometry of converging-diverging nozzle. The expansion ratio is an important design parameter which affects nozzle efficiency. For the no flow condition, when the back-pressure ratio is equal to one, the Mach number is obviously zero. Figure 6. The rest of this page derives the nozzle flow theory, and demonstrates other features of proptools.nozzle. + Inspector General Hotline Using this All rights reserved, A nozzle begins at the point where the chamber diameter begins to decrease. 5283, the flow becomes choked and it reaches Mach one before decreasing subsonically. 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. nozzle simulator program which runs on your browser. The gas is homogeneous, obeys the ideal gas law, and is calorically perfect. Please click here to view a larger version of this figure. The flow state varies only in the axial direction of the nozzle. By continuing to use our website or clicking Continue, you are agreeing to accept our cookies. For the no flow condition, again the Mach number is zero. 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. Large expansion ratios are used for second stage or orbital maneuvering engines, which operate in the vacuum of space. """, # Solve for the expansion ratio [units: dimensionless], """Compute the pressure ratio from a given expansion ratio.""". To get started, a verification email has been sent to email@institution.com. 1, recording the measurements at each increment like before. Subsonic flow, where there is significantly higher acceleration and the pressure drops. Results for the converging 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. Record the gauge pressure of each pressure tap, making sure to note the tap number, axial position, and nozzle area ratio for each one based on geometry provided by the manufacturer. It depends only on the heat capacity ratio, nozzle pressures, and expansion ratio ($A_e / A_t$). Therefore, $C_F$ is a figure of merit for the nozzle expansion process. + Freedom of Information Act Please enjoy a free 2-hour trial. The flow is then isentropically expanded to reach supersonic Mach numbers in the diverging section. the nozzle, the specific 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. Referring to our station 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). Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle. If the problem continues, please, An unexpected error occurred. It can be used to compare the efficiency of different nozzle designs on different engines. After this point, three distinct patterns are observed as back-pressure ratio is further reduced. the exit velocity Ve = V8: V8 = sqrt(2 * nn * cp * Tt8 * [1 - (1 / NPR)^((gam -1 ) / gam)] ). Based on the design of the converging-diverging nozzle, the flow velocity after the nozzle throat can either: (i) decrease to subsonic velocities, (ii) become supersonic, cause a normal shock, and then decrease to subsonic velocities at the nozzle exit, or (iii) remain supersonic throughout the diverging section. 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. As back-pressure is decreased, the flow velocity along the converging section increases, as well as the Mach number, with its peak value at the throat. b. Therefore, nozzle designers select the expansion ratio based on the ambient pressure which the engine is expected to operate in. jet engines. The purpose of a rocket is to generate thrust by expelling mass at high velocity. Figure 2. Measuring Axial Pressure in Converging and Converging-diverging Nozzles. through the nozzle) is: Notice that the mass flow does not depend on the exit pressure. velocity, and the mass flow rate through the engine, we can solve the When the stagnation pressure, pO = pB, there is no flow through the nozzle. The first stage (e.g. The typical converging-diverging shape of rocket nozzles is shown in this cutaway of the Thiokol C-1 engine. 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. Temperature and molar mass have the most significant effect on exit velocity. Then, adjust the flow using the mechanical valve in order to obtain a back-pressure ratio of 0.9. A comparison of the pressure trends obtained for both the converging and converging-diverging type nozzles with theoretical results was excellent. All JoVE videos and articles can be accessed for free. the other engine components. The pressure ratio $p_e / p_c$ is usually quite small. Mount the converging nozzle in the center of the nozzle test rig, as shown in. Please click here to view a larger version of this figure. 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. @1m9S6!BhmN-E"7AO?0ZHSvL 1 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). Please click here to view a larger version of this figure. Use proptools to plot thrust versus chamber pressure for the example engine: Note that thrust is almost linear in chamber pressure. turbojet and rocket nozzles with our interactive As the back-pressure is further reduced, the flow after the throat goes supersonic and then subsonic. Based on Figure 3, the following are the flow conditions that can be observed in a converging nozzle: Figure 3. Increasing the chamber temperature increases the throat velocity but decreases the density by a larger amount; the net effect is to decrease mass flow as $1 / \sqrt{T_c}$. thrust and specific impulse). We can also calculate the Mach number at each port using this equation, where gamma is the specific heat. is represented by the following equation: Aeronautical Engineering. a. Please click here to view a larger version of this figure. w6;b(]om*K]D_7S!{'eQjNU"X^@JjLbRZWXqQ1/a84 First, flow reaches the choked condition at the throat and decelerates subsonically in the diverging section. JoVE, Cambridge, MA, (2022). sets the total mass flow rate through the However, based on the location of the tap measuring the throat pressure (tap 9, Figure 6), we see that the measurements are taken slightly before the true nozzle throat that in turn leads to an incorrect measurement of theMFP. You can explore the design and operation of The amount of thrust produced by the nozzle depends on the exit velocity and pressure and the mass flow rate through the nozzle. c. Pattern 3 - Flow continues to accelerate supersonically for the entirety of the diverging section forpB/pOvalues lower than 0.3. When these tests have been completed, turn off the airflow, disconnect the PVC tubing, and replace the converging nozzle with the converging-diverging nozzle. Copyright 2017, Matthew Vernacchia Ideal nozzle flow is a simplified model of the aero- and thermo-dynamic behavior of fluid in a nozzle. Tt8 divided by Tt5 is 1.0. A subscription to JoVE is required to view this content.You will only be able to see the first 20 seconds. Most modern passenger and military aircraft are powered by 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. Please follow the link in the email to activate your free trial account. The nozzle pressure 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. pressure ratio, EPR. When the back-pressure ratio reaches a value of 0.5283, the Mach number at the throat is one and the flow is choked. Record the data corresponding to Table 1. Text Only Site Subsonic flow that never reaches choked condition. We recommend downloading the newest version of Flash here, but we support all versions 10 and above. Geometry of converging nozzle. """, # Exhaust heat capacity ratio [units: dimensionless], # Exhaust molar mass [units: kilogram mole**1], # Thrust coefficient [units: dimensionless], # Characteristic velocity [units: meter second**-1], # Propellant mass flow [units: kilogram second**-1], $\frac{p_0}{p} = \left( \frac{T_0}{T} \right)^{\frac{\gamma}{\gamma - 1}}$, 'Isentropic flow relations for $\gamma={:.2f}$'. Flow after the choked condition is supersonic through the nozzle, and no shock is formed. Here, m-dot is the mass flow rate through the nozzle, T-zero is the stagnation temperature, AT is the area of the throat, and p-zero is the stagnation pressure. A nozzle begins at the point where the chamber diameter begins to decrease. The pressure and Mach number variations across the two nozzles were studied for a wide range of flow conditions. Aeronautical Engineering. When the stagnation pressure equals the back-pressure, there is no flow. Choked flow, where the flow expands after the nozzle exit (considered non-isentropic). engine components. and Accessibility Certification, + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act, + Budgets, Strategic Plans and Accountability Reports. For this reason, converging nozzles are used to accelerate fluids in the subsonic regime alone. 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.

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