Prof. Dr.-Ing. F.-K. Benra. ISE batchelor course

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1 University Duisburg-Essen Campus Duisburg Faculty of engineering Science Department of Mechanical Engineering Examination: Fluid Machines Examiner: Prof. Dr.-Ing. F.-K. Benra Date of examination: Handling time: 120 Minutes ISE batchelor course Designated scores: Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 ( 14 points) ( 24 points) ( 22 points) ( 24 points) ( 16 points) Σ 100 points Permitted utilities: Table of formulas (provided), pocket calculator

2 Exercise 1 (14 points) Part 1: For a single stage, adiabat working, hydraulic turbo machine following data are known: Rotational speed n: 1450 RPM Volume flow rate V & : 110 m /h Outer diameter Da: 0,25 m Pressure coefficient ψ ym : 1,2. The change in state of the turbo machine is approximately polytrop. 1.1 Calculate following characteristics: specific speed, specific diameter and flow coefficient. 1.2 Which type of machine is it according to attached Cordier-diagram? 1.3 Draw a sketch of the impeller in a meridian section and draw in the flow direction. Part 2: In the following a thermal turbo work machine is regarded: 1.4 Draw the polytropic change in state of a thermal turbo work machine in a T,s-diagram. Mark the flow work y, the change in enthalpy Δh and the dissipation j. 1.5 Explain with T,s-diagram, whether the polytropic efficiency or the isentropic efficiency of the machine is greater.

4 Exercise 2 ( 24 points) The first stage of an axial gas turbine is arranged as an impulse turbine. It is a repeating stage r r ( c 0 = c 2 ) with an adiabatic change in state and with an incident flow free of swirl. Following data are given for the mean streamline (at radius rm): Static pressure at stator inlet p 0 : 16,7 bar Pressure ratio of the stage Π Stage : 1.85 Static temperature at stator inlet T 0 : 940 K Polytropic efficiency of the stator η : 0,86 Polytropic efficiency of the stage η: 0,84 Specific gas constant R: 281 J/kgK Constant pressure specific heat c p : 1,186 kj/kgk Rotational speed n: 6500 RPM Mass flow rate m & : 38 kg/s Meridian velocity c m0,m = c m1,m = c m2,m = 120m/s. The turbine is flowed through by an ideal gas with constant specific heat. 2.1 Draw the change in state of the stage in an h,s-diagram and mark following values: - Change in enthalpy for the stage Δh, - Change in enthalpy for stator Δh and for rotor Δh, - Specific work a and - All kinetic energies. 2.2 Calculate the temperature T 1 and the pressure p 1 at the rotor inlet. 2.3 Calculate the isentropic efficiency of the stage and show whether isentropic efficiency is greater or lower than the polytropic efficiency. 2.4 Determine the degree of reaction ρ h of the stage. How does the degree of reaction change for a stage with no pressure change within the rotor? 2.5 Calculate the mean diameter D M and the height h of blade for the plane 1 (at inlet of the rotor).

5 Exercise 3 ( 22 points) An axial turbine stage is designed as repetition stage. The following data are known. Constant through flow coefficient: ϕ 0 = ϕ 1 = ϕ 2 = 0.4 Swirl free outlet flow: α 2 = 90 o Degree of reaction: ρ h = 0.5 Diameter of mean streamline: D m0 = D m1 = D m2 = m Adiabatic change in state q = 0 Rotational speed n = 144 s Which kind of turbine stage is it? 3.2 Draw qualitatively a meridional cut of this stage and indicate the control planes! 3.3 Draw qualitatively correct the appropriate enthalpy-entropy diagram. Show the kinetic energy at each state. Indicate the enthalpy differences Δh, Δh, Δh, Δh t, Δh s and Δh s! 3.4 Draw the velocity triangles of the stage with non-dimensional velocities to scale in the common form of turbines. Show the quantities ϕ, ψ h and ρ h. (Scale: u/u = 5 cm)! 3.5 Give the enthalpy coefficient ψ h and the specific work a of this stage!

6 Exercise 4 ( 24 points) One stage of a radial compressor is composed of an impeller and a stator. The outflow of the impeller is radial (β 2 = 90 o ). The compressor stage is a repetition stage. The fluid can be treated as an ideal gas with constant specific heat capacities. The change in state is adiabatic (q = 0) by approximation. The following data are known: Constant through flow coefficient: ϕ 1 = ϕ 2 = ϕ 3 = 0,4 Ratio of diameters: d 1 /d 2 = 0,55 Circumferential speed at impeller exit: u 2 = 245 m/s Inlet flow angle: α 1 = 60 o 4.1 Outline a meridional and an axis normal view of the stage in a qualitative manner. Enter the correct numbers for the monitoring planes. 4.2 Draw the velocity triangles of the stage with non-dimensional velocities to scale. 4.3 Determine the specific work a, the kinematic degree of reaction ρ h and the work coefficient (or enthalpy coefficient) ψ h of the stage. 4.4 Depict a complete h,s-diagram with all terms in the absolute frame for the stage. Consider the partition of the change in state for the impeller and for the stator in a qualitative correct way (Δh and Δh ). 4.5 Determine the degree of kinematic reaction ρ h for a swirl free through flow to the stage. All other terms remain the same as before.

Exercise 5 ( 16 points) In a non-dimensional

The following assumptions can be made: -

7 Exercise 5 ( 16 points) In a non-dimensional chart [ Ψht =f( ϕ2) ; Ψ yt =f( ϕ2)] the design operating point Aht of a single-stage axial turbomachine is given. The following assumptions can be made: - Repetition stage - Swirl free through flow - Adiabatic change in state

8 5.1 What kind of turbomachine is depicted by the design operating point Aht? Justify your answer. 5.2 Draw into the given diagram the theoretical characteristic (after streamline theory) of the stage Ψht =f( ϕ2). Assumptions: α 1, β 1, ϕ 1 are constant. 5.3 Explain the difference between Ψht ( ϕ2) and Ψ yt ( ϕ2 ) with the help of the Second Law of Thermodynamics. 5.4 Plot into the same diagram the actual operating point A yt for the design operating condition. For the design operating point the following expression 2 is valid: j u A ( )=0, Calculate the total efficiency η ta for the design point. 5.6 Draw into the given diagram the Ψ yt =f( ϕ2)- characteristic of the machine. in a qualitative manner.

Prof. Dr.-Ing. F.-K. Benra. ISE Bachelor Course

Prof. Dr.-Ing. F.-K. Benra. ISE Bachelor Course University Duisburg-Essen Campus Duisburg Faculty of Engineering Science Department of Mechanical Engineering Name Matr.- Nr. Examination: Fluid Machines Examiner: Prof. Dr.-Ing. F.-K. Benra Date of examination: