5.3 Calculate the variation with T t4 of exit Mach number, exit velocity, specific thrust, fuel/air ratio, and thrust specific fuel consumption of an ideal turbojet engine for compressor pressure ratios of 10 and 20 at a flight = 2 2 s = = =, , =, , MAE 113 HW3 solution.nb Mach Number - an overview | ScienceDirect Topics The area-Mach number relation (AMR from now on), is important when analyzing nozzle flows. Inlet Mach Number - an overview | ScienceDirect Topics This Air (γ=1.4, R=287 J/KgK) at an inlet Mach number of 0.2 enters a straight duct at 400K and expands isentropically if the exit Mach number is 0.8 determine the following. When this simple modification is performed the exit Area ratio (AR) becomes 2.43 which compares to AR = 2.403 for exact 2-D isentropic flow and represents a 1.124% difference from isentropic theory. Total Mach Number Downstream "of Oblique Shock! Calculate the variation with Tt4 of exit Mach number, exit velocity, specific thrust. Fuel/air ratio, and thrust specific fuel consumption of an ideal turbojet engine for compressor pressure ratios of 10 and 20 at a flight Mach number of 2 and T0= 217K.Perform calculations at Tt4 values of 2400K, 2200K, 2000K and 1800K. Mach number distribution is given by the following output: - For the increase of the characteristic lines from 10 to 200, the nozzle length increases from 0.0856m to 0.0878m and the half of nozzle height appeared first on Brainy Term Papers. Calculate the Mach number at the exit of the nozzle in Prob. A converging-diverging nozzle (supersonic nozzle) is supplied with compressed air from a reservoir at a stagnation pressure and temperature of 1 MPa and 800K. choked condition, the exit Mach number is unity. The procedure is based on the fact that the entrance star pressure ratio can be calculated using . 14 Calculate the Mach number at the exit of the nozzle in Prob. Considering a rocket nozzle, we can set the mass flow rate by setting the area of the throat. 2. Original Article Importance of the vane exit Mach number on the axial clearance-related losses Aki Gro¨nman1, Marc H-O Biester2, Teemu Turunen-Saaresti1, Ahti Jaatinen-Va¨rri1, Jari Backman1 and Jo¨rg R Seume2 Abstract More efficient and physically smaller axial turbine designs are promoted to lower emissions and increase revenue. Calculate the amount of heat per unit mass (in joules per kilogram) necessary to choke the flow at the exit of the duct for an inlet Mach number of M 1 = 0.2. • Mach # at exit keeps rising until flow is choked (Me=1) -pe=p*, max. For all Reynolds numbers, the Mach number in the core flow was slightly below the design value. 6.15. Calculate: (a) the throat pressure, temperature, density, (b) the exit pressure, temperature, density, velocity, (c) the mass flow rate. For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). Critical flow conditions occur when the exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. Noting that =∗1−∗2, the function fL*/D h at the exit state is calculated from The Mach number corresponding to this value of fL*/D is obtained from Table A-16 to be Ma 2 = 0.187 which is the Mach number at the duct exit. Fan Exit Mach Number T 8 =T t8=(1+ g 1 2 M 2 8) Primary Nozzle Exit Temperature A 8 = p gRgT 8 U 8 =M 8A 8 Thrust and TSFC Calculation Thrust = m˙(U8Ua)+am˙(U9Ua) g Calculate Thrust TSFC = m˙ f hc Thrust Fuel Efﬁciency The TSFC, thrust speciﬁc fuel consumption, is an engineering term to describe the fuel efﬁciency of a turbine engine . Solution: The throat must be sonic, and the area ratio at the shock gives the Mach number: Fig. You can also select Mach angle as an input, and see its effect on the other flow variables. The area-Mach number relation is valid for isentropic flows . B. Those data were given for the JT3D-3B. Solution 4. The pressure ratio at the exit plane is easily solved for using flowisentropic. And we can set the exit Mach number by setting the area ratio of the exit to the throat. exit velocity of a projectile as a function of the initial reser-voir pressure. The exit pressure is only equal to free stream pressure at some design condition. If you are an experienced user of this calculator, you can use a sleek version of the program which loads faster . Mach number is the ratio of the gas velocity to the local speed of sound. Determine the mass flow rate through the device. The larger the ratio, the higher the Mach number of the flow that your nozzle will produce (if you set this number very high, say >10) it may be difficult to see all the results clearly on the plots. The Mach number at the nozzle exit is given by a perfect gas expansion expression P c is the pressure in the combustion chamber and P atm is atmospheric pressure, or 14.7 psi. To get started with a simple example (no turbomachinery), we will reexamine the ideal ramjet, picking up where we left off in Section 3.7.3. (b) The Mach number and static pressure at the duct exit. 4. If the exit Mach number is 2.5 determine for adiabatic flow of perfect gas (γ =1.3, R=0.469 KJ/Kg K). a. c. At section 1 of a constant-area combustion chamber the Mach number M. — 0.2 and the stagnation temperature To, - 400 K. What is the amount of heat transfer if the Mach number is 0.7 at the exit? Constant across oblique! The exit Mach number is measured as 0.93 with an exit flow angle of 61.4°. Knowing Te we can use the equation for the speed of sound and the definition of the Mach number to calculate the exit velocity Ve: Ve = Me * sqrt (gam * R * Te) We now have all the information necessary to determine the thrust of a rocket. Naturally, the calculation of the corresponding local or exit Mach number Me is of interest to the propulsion and power generation subdisciplines with particu-lar areas of concentration in nozzle design and optimization. Note that for helium the specific heat ratio is 1.66 and the ideal gas constant is 2077 J/(kg K). (Note that we will continue to use station 5 as the exit station, consistent with . 28. w 1 =w 2 →Mt 1 c 1 =Mt 2 c 2 =M 1 cos(β)c 1 Mt 2 = M 1 cos(β)c 1 c 2 =M 1 cos(β) T 1 T 2 M 2 =Mt 2 2+Mn 2 #$2%& Answer: M=2.94 T = - 98 oC 13.7 At a section in a passage, the pressure is 30 psia, the temperature is 100 oF, and the speed is 1750 ft/s. Exhaust Speed of Sound = 2698 ft/sec. If the Mach number at the nozzle exit is 3, calculate the exit pressure, temperature, and density. 4 The value of the mass flow rate at choked conditions is given by: mdot = (A* * pt/sqrt [Tt]) * sqrt (gam/R) * [ (gam+1)/2]^- [ (gam+1)/ (gam-1)/2] Mach number equal to one is called a sonic condition because the velocity is equal to the speed of sound and we denote the area for the sonic condition by "A*". The Mach number at this location can be found using isentropic ratios for pressure and the given values for pressure. Mach This page shows an interactive Java applet which calculates the speed of sound and the mach number for an input velocity and altitude. Return to Mach number page, or speed of sound page. Either the Mach number can be calculated from a user defined velocity, or the velocity can be calculated from a user defined Mach number. Rocket Propulsion - Supplement #1. • If the actual pressure ratio > critical pressure . At a section downstream the Mach number is 2.5. Calculate API 520 flow rate through a constant diameter pressure relief vent. This variable is only a function of the Mach number of the flow. Sketch the passage shape. the test run were us ed to calculate the e xit Reynolds . The post Calculate the Mach number at the exit of the nozzle in Prob. For a given pipe$\left(\dfrac{4\,f\,L}{D}\right)\$, neither the entrance Mach number nor the exit Mach number are given (sometimes the entrance Mach number is given see the next section). The nozzle is designed to discharge at an exit Mach number of 3.5. MLN Characteristic Mesh For exit Mach number of 2.4 where Inclination angle from sonic line = 0.0 degrees produces AR = 2.43. The Mach angle and Prandtl-Meyer angle are also functions of the Mach number. The reservoir pressure and temperature are 5 atm and 500 K, respectively. the exit pressure and temperature? 2. • The nozzle exit Mach number is given as 2.0. …. In addition, the values of any one of these quantities may be specified and VuCalc will solve for the corresponding Mach number and the remaining . How does that compare with the speed of sound in air at sea level, expressed in feet/sec? Calculate the variation with Tt4 of exit Mach number, exit velocity, specific thrust, fuel-to-air ratio, and thrust specific fuel consumption of an ideal turbojet engine for compressor pressure ratios of 10 and 20 at a flight Mach number of 2 and To = 3900R. Curve (C) represents the case where Mach number just reaches 1.0 at the thro at. Section 4 Homework (cont'd) • Plot the Mach number, pressure, and temperature distribution along the SSME Nozzle for each of the Note that for helium the specific heat ratio is 1.66 and the ideal gas constant is 2077 J/(kg K). For more details on NPTEL visit http://nptel.iitm.ac.in For isothermal flow the critical exit Mach number = √γ. . Solution 4. Determine the pressure at the exit of the converging/diverging nozzle. Use = 18,400 1.4. The specific flow rate can be converted to entrance Mach number and this simplifies the problem. A Boeing 747 is cruising at a velocity of250 m/s at a standard altitude of 13 km. Maximum back pressure to choke the nozzle. Head loss is potential . Use . (c) Thrust A V mV Ans=== ≈ρ eee e 61,100 N 9.10 A certain aircraft flies at the same Mach number regardless of its altitude. Inlet/Diffuser: , (adiabatic, isentropic) Compressor or fan: , . The area ratio for a nozzle with isentropic flow can be expressed in terms of Mach numbers for any points x and y within the nozzle. 6. One side of a mercury manometer is . MAE 5420 - Compressible Fluid Flow. Range of back pressures over which a normal shock will appear in the nozzle. If the velocity of the air leaving the diffuser is 60m/sec, calculate the entrance and exit Mach numbers, the static pressure at exit and the percent change in cross-sectional area between entrance and exit. The default input variable is the Mach number, and by varying Mach number you can see the effect on Mach angle. . Select an input variable by using the choice button and then type in the value of the selected variable. the choked mass flow relation and the equation giving the exit Mach number for cases with an internal normal shock. Consider air entering a heated duct at p 1 = 3.2 atm and T 1 = 212 K. Ignore the effect of friction. Assuming 1-d flow, calculate: (i) Maximum backpressure to choke the nozzle. Problem 4. Mach Number Converging-Diverging Nozzles • Solution of VI.17 (M v. A/A*) VI.6-8 (T/To, p/po, ρ/ . the nozzle exit plane where ε e = (At/Ae)2 represents the square of the so-called area expansion ratio. The area-Mach number relation gives the ratio of local area to throat area as a function of Mach number (or the other way around). The nozzle is supplied from an air reservoir at 5 MPa. Calculate: a) (10 points) Exit Mach Number b) (5 points) Mass flow through the nozzle under ideal condition if throat area is At 0.0025 m2 =. Ans: To find the exit mach number (M2) Sonic velocity at inlet . a. Mach Number The Mach number (Ma) is a dynamic measure of fluid compressibility, and is defined as the ratio of flow velocity (v) to sound speed (a): (1)Ma=v/a.The flow of a compressible fluid like air can be treated as incompressible if the local Mach number is less than 0.3Ma is much smaller in microfluidic systems due to the low flow velocity. COMPROP2. The exit area is 8 times the inlet, and the temperature on the exit is standard atmospheric value. Find also the maximum mass flow rate through the nozzle. The aircraft's Mach numbers are then sea−level: Ma = V a = 400 341 =1.17 15,200 m: Ma = V a = 400 295 =1.36 Note: Although the aircraft speed did not change, the Mach number did change because of the change in the local speed of sound. % Exit loop end end % END: i Loop % Set subsonic Mach number to final M from iterations Msub = M; . For any cascade, given the inlet angle, α 1, the inlet Mach number, M 1, and the exit Mach number, M 2, it is possible to calculate the exit angle, and thus the deviation, if the cascade loss coefficient, Y p, is known. Problem 4. Thus, the problem is reduced to find for given entrance Mach, , and given pressure ratio calculate the flow parameters, like the exit Mach number, . The throat area is 20 cm 2 and the exit Mach number 2. • The exit flow parameters are then defined by the critical parameters. A De Laval Nozzle has to be designed for an exit Mach number of 1.5 with exit diameter of 200mm. P9.57. By Equa-tion 8.1, this can be called K limit at that end. The Mach Angle depends only on the Mach number and is equal to the inverse sin of one over the Mach number is calculated using mach_angle = asin (1/ Mach Number).To calculate Mach Angle, you need Mach Number (M).With our tool, you need to enter the respective value for Mach Number and hit the calculate button. Assumptions and Approximations: The exhaust gas is ideal with γ = 1.33. A convergent-divergent nozzle with an exit-to-throat area ratio of 2.9, works under the condition of: reservoir pressure, temperature and exit pressure are 2 atm, 330 K, and 0.77 atm, respectively. 4.11. Calculate the Mach number of the exit if the diverging duct has an inlet area and velocity of air of 0.5m^2 and 60 m/s respectively. A converging-diverging nozzle is designed to operate with an exit Mach number of 1.75 . Given: The rocket engine shown above, with an exit Mach number of 5. 11. Estimate (a) the tank pressure; and (b) the mass flow. Therefore, flow is not choked and exit Mach number is less than 1. 2. Assuming a calorically perfect gas and isentropic flow, calculate (a) the exit Mach number, (b) the exit velocity, (c) the mass flow through the nozzle, and (d) the area of the exit. Compared to its speed at 12000-m Standard Altitude, it flies 127 km/h faster at sea level. The middle and bottom plots show the Mach number and pressure distributions associated with the flow. Rocket Nozzle Design: Optimizing Expansion for Maximum Thrust. Conical flow calculator by Stephen Krauss, included 5 th January 2014. . Weight flow, thrust, and compressor pressure ratio are taken from the data set mentioned. Shock wave! mass flow rate • What happens as we lower pb (initially =po) x p/po 1 0 pb=po pb<po p*/po pb=p* pb<p* pe=p* . 4.11. What is the speed of sound in the exhaust (feet/sec)? 270 ADIABATIC CoMPRESSIBlE FloW WITH FRICTIoN, USINg MACH NUMBER AS A PARAMETER the Mach number M there and then use Equation 4.16 to find the (fL/D)limit at that end of the duct. 8 2. Calculate: Mass flow rate, stagnation temperature, mach number and stagnation pressure values assuming the flow as compressible and incompressible respectively. 12. Air Speed of Sound = 1115 ft/sec. Determine the pressure at the exit of the converging/diverging nozzle. Therefore the throat Mach number must be 1.0. Mach number distribution is given by the following output: - For the increase of the characteristic lines from 10 to 200, the nozzle length increases from 0.0856m to 0.0878m and the half of nozzle height The exit Mach numbers tested correspond to exit Reynolds numbers of 7.6 × 105, 9.0 × 105, and 1.1 × 106 based on blade true chord. Mach number near the throat (the location of minimum area) is approaching unity. Perform calculations values of 44000R, 40000R, 35000R, and 30000R. In order to compute the sound speed we have to compute the exit temperature . We can compute the exit Mach number where the pressure is the standard atmospheric pressure of 14.696 psia by rearranging equation 11.59 in the text to solve for the Mach number. • To determine whether a nozzle is choked or not, we calculate the actual pressure ratio and then compare this with the critical pressure ratio. The isentropic flow page enables the user to calculate the total temperature ratio, total pressure ratio, total density ratio, area ratio, Mach angle and Prandtl-Meyer function for any Mach number. 1.765 We can find the exit velocity as the product of the Mach number and the sound speed. A normal shock stands in the exit of the nozzle, as shown. A. • Since the inlet velocity is negligible, the stagnation pressure and stagnation temperature are the same as the inlet temperature and pressure, P 0=1.0 MPa and T 0=800 K. 3 ∴ρ 0 =P 0 /RT 0 =4.355kg/m P9.57 2 3 1 11 1 14 10.2Ma A /A* 1.4 , solve Ma 1.76 upstream of the shock 10 1.728Ma + == = ≈ 2 2 1 shock 2 1 2.8(1.76) 0 . This is done using the one-dimensional compressible flow relations for the flow through the cascade. exit = p ambient, we obtain 2 38(1600) . A converging-diverging is designed to operate with an exit Mach number of 1.75. With the help of equation (3.0), Mach number distribution can be defined for the exit flow. b. Determine the pressure at this downstream location for isentropic flow of air. Ans: To find the exit mach number (M2) Sonic velocity at inlet . The exit pressure is 105 KN/m 2 and the exist area is 6.25 cm 2 . 11. The function of the nozzle is to convert the chemical . Knowing Te we can use the equation for the speed of sound and the definition of the Mach number to calculate the exit velocity Ve : Ve = Me * sqrt (gam * R * Te) We now have all the information necessary to determine the thrust of a rocket. Combustor/burner or afterburner: , Turbine: Nozzle: , . QUESTION 2. To do: Calculate the exit -to-throat area ratio. C. Why do you think they are different? For any cascade, given the inlet angle, α 1, the inlet Mach number, M 1, and the exit Mach number, M 2, it is possible to calculate the exit angle, and thus the deviation, if the cascade loss coefficient, Y p, is known. The exit Mach number of the original . Note that downstream of the nozzle exit the pressure distribution shows the back pressure connected to the nozzle exit pressure with a dotted line. If the exit Mach number is 2.5 determine for adiabatic flow of perfect gas (γ =1.3, R=0.469 KJ/Kg K). Calculate the ratio of inlet stagnation pressure to exit static pressure and determine the cascade stagnation pressure loss coefficient. The Mach number increases in the converging part of the nozzle from nearly zero far upstream to 1.0 at the throat, then decreases again in the diverging portion The exit Mach number is 4.54, and the exit velocity is 12,250 feet/sec. Calculate i) Mach number, temperature and velocity at exit ii) Pressure, temperature and velocity at throat iii) Mass flow rate iv) Throat area Ans: To find the exit mach number (M2) Sonic velocity at inlet RMKCET Department of Mechanical Engineering 35 43. Assuming one-dimensional flow, calculate the following: a. Advanced Gas Dynamics by Dr.Rinku Mukherjee,Department of Applied Mechanics, IIT Madras. Mach number= Mach angle= P-M angle= p/p 0 = rho/rho 0 = T/T 0 = p/p*= rho/rho*= T/T*= A/A*= Normal Shock RelationsPerfect Gas, Gamma = INPUT: = M 1 = M 2 = p 02 /p 01 = p 1 /p 02 = p 2 /p 1 = rho 2 /rho 1 = . Type in '4' and press the 'Set' button. 15-2-22 [nozzle-400K] A converging-diverging nozzle has an exit area to throat area ratio of 1.8. 6. nozzle exit Mach number based on nozzle expansion ratio Mjet fully expanded jet Mach number Mach Mach number Meas measured NPR nozzle pressure ratio (P8 / Pamb) N1 fan rotor speed, rpm N2 core rotor speed, rpm OH overhead P1 engine face total pressure, lbf/in 2 Ps3 compressor discharge static pressure, lbf/in 2 PT2.5 fan discharge total . A two-dimensional linear turbine cascade operates in air with an inlet flow angle of 22° and an inlet Mach number of 0.3. These additional variables are used in the design of high speed inlets, nozzles and ducts. With the help of equation (3.0), Mach number distribution can be defined for the exit flow. The exit area of the nozzle is 100 mm2. 11. The Mach number at this location can be found using isentropic ratios for pressure and the given values for pressure. This is done using the one-dimensional compressible flow relations for the flow through the cascade. The speed of sound is calculated from the gas temperature, specific heat ratio and gas specific gravity. Air enters a diffuser at 27 0 C and 1 N / M 2.The approach velocity is 300m/sec, assume the flow to be isentropic. 2. The nozzle area is based on the weight flow given and calculation of an exit Mach number M 7 = 1 according to the stagnation pressures given. Answer to 1 decimal place. for these calculations. A Boeing 747 is cruising at a velocity of250 m/s at a standard altitude of 13 km. . The flow is steady and can be approximated as isentropic, adiabatic, and one -D. Solution . w 1 =w 2 Tangential velocity is! Figure 16 shows Mach number on the exit plane, while the radial coordinate for each curve is normalized with its corresponding exit radius. 3 Ideal Ramjet . Air enters the nozzle with a total pressure of 1100 kPa and a total temperature of 400 K. The throat area is 5 cm 2 .If the velocity at the throat is sonic, and the diverging section acts as a nozzle, determine (a) the mass flow rate, (b) the exit pressure and temperature, (c) the exit Mach number . What is the maximum amount of heat transfer? 4. In the iterative loop, the first thing we do every iteration is calculate the middle Mach number as a simple average of the lower and upper bounds. Find the ratio of throat area to exit area necessary. b. Determine the Mach number outside the wake (region 4). 4 (ii) Range of backpressure over which a normal shock will appear in the nozzle. 18 Consider a low-speed subsonic wind tunnel with a nozzle contraction ratio of 1 : 20. The reservoir conditions are given as P 0 = 1 atm; T 0 = 200C. Critical flow conditions occur when the exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. Figure 3. 2. Fig. Thus the nozzle is choked, and the nozzle area is determined for that . For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). b. The exit area of the nozzle is 100 mm2. The graph on the left shows the shape of the nozzle, chamber on the left, exit on the right. (c) Calculate the exit mass flow If the aircraft descends to an altitude of 8.3km where p 0 =34.5kPa and the exit area is adjusted so as to permit the nozzle to remain in the matched mode: (d) Calculate the exit Mach number M 7 (e)Find the new nozzle exit area A 7 required to attain the maximum gross thrust F possible (f) Calculate the new exit . (Remember that because f and D are constant, K in this context is simply length with a constant coefficient.) Determine its Mach number. Tutorial Problems: 1.The pressure, temperature and Mach number at the entry of a flow passage are 2.45 bar, 26.5° C and 1.4 respectively. Problem 4. Introduction to Flight (8th Edition) Edit edition Solutions for Chapter 4 Problem 31P: Consider the flow of air through a supersonic nozzle. Supplementary Questions I. Determine the Mach number outside the wake (region 4). The peak in Mach number near the centerbody was also present for all cases. Calculate the speed of sound and mach number for an ideal gas. A rocket engine is a device in which propellants are burned in a combustion chamber and the resulting high pressure gases are expanded through a specially shaped nozzle to produce thrust. The nozzle is supplied from an air reservoir at 68bar (abs.). 17 . Solution: At sea level, T 1 = 288.16 K. At 12000 m standard . Solution: = 1.22 is not typically available in the compressible flow tables provided in textbooks. What will be the exit pressure and temperature? 14 . Tutorial Problems: 1.The pressure, temperature and Mach number at the entry of a flow passage are 2.45 bar, 26.5° C and 1.4 respectively. This pair of parameters is the most natural to examine because, in most cases, this information is the only provided information. 17 Calculate the flight Mach number for the supersonic transport in Prob. Determine the mass flow rate through the device. The nozzle is designed to discharge at an exit Mach number of 3.5. 2 Ideal Assumptions. The pressure ratio at the exit plane is easily solved for using flowisentropic.