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Efficiency of diffuser ● Diffuser efficiency at flow of liquid

Ways for decreasing of sensitivity of flow separation ● Shapes of diffuser according requirements on pressure gradient ● Comparison of diffuser with constant pressure gradient and cone diffuser ● The shape of the diffuser with the lowest sensitivity to boundary layer separation

Non-nominal states of valve with diffuser ● Diffuser blade passage ● Ejectors and injectors ● Ramjet and Scramjet

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The article of online continued resource Transformační technologie; ISSN 1804-8293;

www.transformacni-technologie.cz; Copyright©Jiří Škorpík, 2006-2019. All rights reserved. This work was published without any linguistic and editorial revisions.

www.transformacni-technologie.cz; Copyright©Jiří Škorpík, 2006-2019. All rights reserved. This work was published without any linguistic and editorial revisions.

● 41. Flow of gases and steam through difusers ●

2.723 Change of state quantities inside diffuseri [J·kg^{-1}] specific enthalpy of gas; s [J·kg^{-1}·K^{-1}] specific entropy; t [°C] temperature of gas; p [Pa] pressure of gas. Subscript c denotes stagnation state of gas. |

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● 41. Flow of gases and steam through difusers ●

3.727 Change of state quantities of gas inside the supersonic diffuser |

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6.405 Efficiency of diffuserη [-] Efficiency of diffuser – referred to static state of gas*. |

8.411 Hydraulic efficiency of diffuser |

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● 41. Flow of gases and steam through difusers ●

9.458 Cone diffuserr [m] radius; α [°] angle of diverging; l [m] length of diffuser; x [m] axis scale. |

10.631 Influence angle of diverging of cone diffuser on pressure dropGraph in scale is shown in [1, p. 382]. |

11.418 Principle of flow separation of boundary layer from diffuser wall and developed of recirculationR.P. velocity profile. |

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12.427 Practical solutions of space limited diffusers |

13.428 Development of velocity profile inside throat of diffuserLP laminar flow; PP transition region of flow; TP turbulent flow. x minimum length of diffuser throat for development turbulent flow of boundary layer._{e} |

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Design diffuser of circular cross-section corresponding to requirement *dp/dx=konst.* Parameters at the inlet of diffuser: *80 m·s*^{-1}, *110 kPa*, *20 °C*, dry air. Output parameters: *p=114 kPa*. The required diffuser length is *100 mm* at an input radius of *20 mm*. Calculated flow without losses. The solution of this problem is shown in the Appendix 441.

**Problem 1.**441

Figure at Problem 1.(a) calculated profile of radius; (b) cone diffuser about the same length at α=23,18°. |

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Find profile of pressure gradient inside a cone diffuser with lenght *100 mm*, in let radius *20 mm*, angle of diverging *23,18°*. Inlet and outlet state of gass are the same as in *Problem 1*. Losses at flow are negligable. The solution of this problem is shown in the Appendix 456.

**Problem 2.**456

Figure at Problem 2.Profil of pressure gradient in a cone diffuser. dp/dx [kPa·m^{-1}]; x [mm]. The higher pressure gradient at the beginning of the diffuser is higher than in the case of Problem 1 because there is also a larger angle of expansion. |

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15.430 Diffuser with linear pressure gradientdp/dx [kPa·m^{-1}]; x [mm]. Diffuser on the Figure has parameters: dp/dx=400 kPa·m, ^{-1}R, _{i}=10 mmp._{i}=110 kPa |

16.831 Practical design of diffusers with variable diverging |

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18.554 Influence of input velocity change on subsonic diffuser functionThere are three cases with c<c_{ia}<c_{ib}_{ic}=a. In individual cases, the back pressure also changes, if it were still the same (p), the diffuser would behave like a short diffuser. At less than the critical pressure _{e}=p_{ea}p*, a shock wave arises behind the narrowest cross-section and, in addition, when the back pressure decreases below p the Laval nozzle becomes a diffuser see chapter 40. Flow inside de Laval nozzle at non-nominal states. _{ec}L.T. Laval nozzle function area. |

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19.654 Influence of input velocity change on supersonic diffuser functionThere are three cases with c<c_{ic}<c_{ia}_{ib}>a. In individual cases, the back pressure also changes, if it were still the same (p), the diffuser would behave like a short diffuser. It is changed so that the subsonic parts of the diffuser do not produce a shock wave_{e}=p_{ea}^{(5)}. In the variant c, the convergent part of the diffuser is not able to accommodate such an amount of gas (it will have a high resistance), therefore, before the diffuser a perpendicular shock wave is generated which increases the pressure above the critical and reduces the velocity to subsonic. Thus, the convergent part of the diffuser will function as a nozzle. The divergent portion of the diffuser will function as a Laval nozzle in a non-design state. |

20.110 Valve with diffuser (partially open)There is subsonic flow inside the valve. Flow control is done by changing the flow cross-section using the valve plug RK, which is either retracted (flow cross-section decreases) or extended (flow cross-section increases). At the narrowest point between the plug and the seat, the flow reaches the maximum speed, which again decreases in the diffuser. |

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Condensing turbine about 25 MW at speed 3 000 min^{-1}, one controlled steam extraction at 0,25 MPa for 80 t·h^{-1}, pressure admission steam is 2 MPa at 390 °C, Made in PBS. Figure: [1].

22.745 Geometric similarity of diffuser blade row with symmetrical diffuser |

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23.864 Development of λ-shock wave in blade row of compressorRV shock wave and separtion of flow. |

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Design the basic dimensions of the jet pump for pumping water (injector) from an open tank at a temperature of *90 °C* to a pressure of *0,54 MPa*. The required water flow is *60 kg·h*^{-1}. You consider the efficiency of the diffuser part *80 %*. The efficiency value of the nozzle also includes the efficiency of transferring kinetic energy from the steam to the pumped water and is *10 %*. The steam velocity at the pump inlet is *20 m·s*^{-1}. The water velocity at the pump outlet is *3 m·s*^{-1}. Do not consider pressure losses in the boiler and in the piping. The solution of this problem is shown in the Appendix 410.

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1. DEJČ, Michail. *Technická dynamika plynů*, 1967. Vydání první. Praha: SNTL.

2. MAŠTOVSKÝ, Otakar. *Hydromechanika*, 1964. 2. vydání. Praha: Statní nakladatelství technické literatury.

3. JAPIKSE, David a N BAINES. *Diffuser design technology*. Norwich, VT: Concepts ETI, 1995. ISBN 0933283083.

4. MICHELE, F. a kol. *Historie a současnost Parní turbíny v Brně*, 2010. 3. rozšířené a doplněné vydání. Brno. ISBN: 978-80-902681-3-5.

5. KADRNOŽKA, Jaroslav. *Tepelné turbíny a turbokompresory I*, 2004. 1. vydání. Brno: Akademické nakladatelství CERM, s.r.o., ISBN 80-7204-346-3.

6. NOŽIČKA, Jiří. Osudy a proměny trysky Lavalovy, *Bulletin asociace strojních inženýrů*, 2000, č. 23. Praha: ASI, Technická 4, 166 07.

7. HIBŠ, Miroslav. *Proudové přístroje*, 1981. 2. vydání-přepracované. Praha: SNTL – Nakladatelství technické literatury, n. p., DT 621.694.

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8. KADRNOŽKA, Jaroslav. *Tepelné elektrárny a teplárny*. 1. vyd. Praha: SNTL-Nakladatelství technické literatury, 1984.

9. NECHLEBA, Miroslav, HUŠEK, Josef. *Hydraulické stroje*, 1966. Vydání první. Praha Státní nakladatelství technické literatury.

10. GOROŠČENKO, B. T. *Aerodynamika rychlých letounů*, 1952. Vydalo Technicko-vědecké vydavatelství. Překlad z Ruštiny.

This document is English version of the original in Czech language: ŠKORPÍK, Jiří. Proudění plynů a par difuzory, *Transformační technologie*, 2016-03, [last updated 2018-11-26]. Brno: Jiří Škorpík, [on-line] pokračující zdroj, ISSN 1804-8293. Dostupné z http://www.transformacni-technologie.cz/41.html. English version: Flow of gases and steam through diffusers. Web: http://www.transformacni-technologie.cz/en_41.html.

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previews: pages 8-9, Appendix 404

*Full text is only in Czech language; tip: You can use https://translate.google.com for translate.

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