Question

Problem 8: Throttling valve for turbine load regulation (adapted from Cravalho & Smith) A throttle valve is used to control the power output of a reversible adiabatic gas turbine as shown in Fig. Q8. The two states 1 and 3 are fixed as follows P 4 x 105 N/m2 7, = 1000 K P3 = 105 N/m? Tg = varies depending upon the load State 1: State 3: The throttle operates by controlling the pressure at the inlet to the turbine (state 2). At full load, there is no pressure drop across the throttle valve and P2- P1. At zero load, the throttle is closed and there is no flow through the turbine so that P2 - P3. For any intermediate load on the turbine, P1 > P2 > P3. Assume that the fluid flowing can be modeled as an ideal gas (air) with c,-715.9 and R = 287-1- kg-K kg-K a) What is the turbine shaft work transfer per unit mass of fluid flowing for full load output (P2 - P1)? b) Determine the pressure in state 2 for a shaft work transfer per unit mass equal to one-half the full load output. c) Sketch the process of (a) and (b) on the T - s and on the h - s diagrams for air State 1 State 2 Throttle valve W. Reversible adiabatic turbine shaft State 3 Figure Q8 Answers: 328 kJ/kg, 187 kPa

Iam looking for the detailed solutions to this question. Absolute answers are given but Im looking for the step by step solutions with every step clearly explained. Thanks In advance..

Answer 1

Throtling Valve Por Turbine Load Relation Fdraing iven Fiqure throtlling valve re2wlated tu bine 왔stem wIrn 29 bine Sstem Glale slale 2 a lve ever W,hart A d iabatic Tarbine state 3 Gtate 5 T varies depending upon load 3 upon load Also Workin luid p proper ies ate

a) Turbine shaft work per unit mass oH full load conditio At Fal load condition 2. es : 4x105 % Also daring throtllin p process, tempe rature ot Plaid before th r t t l ing after throttling ren、ains same h, h APPIxing re lationship between pressure a Hemperature fot re veysble adrabatic process respon sible For shaft wort urbine outlet r birne ouutle r- 스)n 2 For air, n-l-5 1.4-1 I o .. T, : 672.95 At : condilion

Work done du i n ever5bl adiabat toCeSS S OH eVersible adiabatic Steady lo w Shaf こ3 27 998 .415 J shaft W shast 327.993 328 k sure (P) when w W shaft 2 shaft 2. Load Wshaft X 328 ㄅ

T,-T, -163-5257 but Ta-b。ok , thttl . ng process r o Тз : T2-163.5257-lo -(63.5257 T3 836.4742 k usin pressure temperature elation fo eversble adiabalic process h-l ra Ps 14- 836.474 2 2.

T-s& hs di agfam 112 Rever sebl ad iabatic ex pansian ForCb Reverssble adia batic ererssble adiabatic ex pansion xansi on