Question

4.34 Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 4.15 (p. 190). Recall that you fit a first-order model for heat rate (y) as a function of speed (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and air flow rate (x5) to data saved in the GASTURBINE file.

a, Researchers hypothesize that the linear relationship between heat rate (y) and temperature (both inlet and exhaust) depends on air flow rate. Write a model for heat rate that incorporates the researchers’ theories.

b. Use statistical software to fit the interaction model, part a, to the data in the GASTURBINE file. Give the least squares prediction equation.

c. Conduct a test (at α = .05) to determine whether inlet temperature and air flow rate interact to affect heat rate.

d, Conduct a test (at α = .05) to determine whether exhaust temperature and air flow rate interact to affect heat rate.

e. Practically interpret the results of the tests, parts c and d.

Answer 1

(a) The model for heat rate is:

Heart rate = 16,569.8271 - 14.1293*inlet temperature + 20.6848*exhaust temperature

	R²	0.795
	Adjusted R²	0.788
	R	0.891
	Std. Error	733.823
	n	67
	k	2
	Dep. Var.	HeatRate
ANOVA table
Source	SS	df	MS	F	p-value
Regression	13,34,33,406.1993	2	6,67,16,703.0997	123.89	9.87E-23
Residual	3,44,63,802.2484	64	5,38,496.9101
Total	16,78,97,208.4478	66
Regression output				confidence interval
variables	coefficients	std. error	t (df=64)	p-value	95% lower	95% upper
Intercept	16,569.8271
Inlettemp	-14.1293	0.9592	-14.730	3.10E-22	-16.0456	-12.2131
exhtemp	20.6848	2.9865	6.926	2.51E-09	14.7185	26.6510

(b) The model for heat rate is:

Heart rate = 13,696.6672 - 11.7055*inlet temperature + 26.0407*exhaust temperature - 0.0045*inlet temperature*exhaust temperature

	R²	0.795
	Adjusted R²	0.785
	R	0.892
	Std. Error	739.111
	n	67
	k	3
	Dep. Var.	HeatRate
ANOVA table
Source	SS	df	MS	F	p-value
Regression	13,34,81,260.9118	3	4,44,93,753.6373	81.45	1.20E-21
Residual	3,44,15,947.5360	63	5,46,284.8815
Total	16,78,97,208.4478	66
Regression output				confidence interval
variables	coefficients	std. error	t (df=63)	p-value	95% lower	95% upper
Intercept	13,696.6672
Inlettemp	-11.7055	8.2462	-1.419	.1607	-28.1843	4.7733
exhtemp	26.0407	18.3441	1.420	.1607	-10.6172	62.6985
Inlettemp*exhtemp	-0.0045	0.0152	-0.296	.7682	-0.0348	0.0258

(c) The hypothesis being tested is:

H0: β3 = 0

H1: β3 ≠ 0

The p-value from the output is 0.0002.

Since the p-value (0.0002) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that inlet temperature and air flow rate interact to affect heat rate.

	R²	0.751
	Adjusted R²	0.739
	R	0.866
	Std. Error	815.350
	n	67
	k	3
	Dep. Var.	HeatRate
ANOVA table
Source	SS	df	MS	F	p-value
Regression	12,60,15,126.8500	3	4,20,05,042.2833	63.18	5.64E-19
Residual	4,18,82,081.5977	63	6,64,794.9460
Total	16,78,97,208.4478	66
Regression output				confidence 0 0 Add a comment Know the answer? Your Answer: Post as a guest Your Name: What's your source? Earn Coins Coins can be redeemed for fabulous gifts. Log In Sign Up Post as anonymous Post Your Answer Not the answer you're looking for? Ask your own homework help question Similar Questions 4.32: Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and... 4.32: Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 4.13 (p. 188). Recall that you fit a first order model for heat rate (y) as a function of speed (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and air flowrate(x5) to data saved in the GASTURBINE file. (a) Researchers hypothesize that the linear relationship... During periods of high electricity demand, especially during the hot summer months, the power output from... During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated by the Journal of Gas Turbines. One measure of performance is heat rate... 3. (Exercise 4.32, using R) (2 pt) Cooling method for gas turbines. Recall the Journal of... 3. (Exercise 4.32, using R) (2 pt) Cooling method for gas turbines. Recall the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, where we fitted a first-order model for heat rate (y) as a function of speed of the engine (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and air mass flow rate (x5). Now, in this example, a researcher hypothesized that the... 3. (Exercises 8.11, 8.20, using R) (3 pt) Cooling method for gas turbines. Refer to the... 3. (Exercises 8.11, 8.20, using R) (3 pt) Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine. We now consider the interaction model for heat rate (y) of a gas turbine as a function of cycle speed (x1) and cycle pressure ratio (x2), E(y) = β0 + β1x1 + β2x2 + β3x1x2. Import the data from the file “GASTURBINE.txt”... Consider a combined gas-steam power cycle. The topping cycle is a simple Brayton cycle that has... Consider a combined gas-steam power cycle. The topping cycle is a simple Brayton cycle that has a pressure ratio of 7. Air enters the compressor at 15 ºC at a rate of 10 kg/s and the gas turbine at 950 ºC. The bottoming cycle is a reheat Rankine cycle between the pressure limits of 6 MPa and 10 kPa. Steam is heated in a heat exchanger at a rate of 1.15 kg/s by the exhaust gases leaving the gas turbine,... Carbon dioxide gas is compressed at steady state from a pressure of 16 lbf/in2 and a... Carbon dioxide gas is compressed at steady state from a pressure of 16 lbf/in2 and a temperature of 32oF to a pressure of 50 lbf/in2 and a temperature of 110oF. The gas enters the compressor with a velocity of 30 ft/s and exits with a velocity of 80 ft/s. The mass flow rate is 3000 lb/hr. The magnitude of the heat transfer rate from the compressor to its surroundings is 5% of the compressor power input. Use the ideal gas... A fuel gas consists of 75% butane (C4H10), 10% propane (C3H8) and 15% butene (C4H8) by... A fuel gas consists of 75% butane (C4H10), 10% propane (C3H8) and 15% butene (C4H8) by volume. It is to be fed to the combustion chamber in 10% excess air at 25ºC, where it is completely burnt to carbon dioxide and water. The flue gases produced are to be used to generate 5 bar steam from water at 90ºC. (a) Write balanced equations for the combustion of each component of the fuel gas. (b) Explain the need for excess air.... 7.2 A Brayton cycle gas engine is analyzed using the air standard method. Given the conditions... 7.2 A Brayton cycle gas engine is analyzed using the air standard method. Given the conditions at state 1, pressure ratio (rp), and cutoff ratio (rc) determine the efficiency and other values listed below. The specific heat ratio and gas constant for air is given as k=1.4 and R=0.287 kJ/kg-K respectively. T1 (K) = 333 P1 (kPa) = 170 rp = 10.7 rc = 2.54 AV (m3/s) = 1.7 a) Determine the specific enthalpy (kJ/kg) at state 1. b) Determine... I ONLY NEED ANSWERS TO F.) AND G.) I SOLVED THE REST. THANK YOU! The Boeing... I ONLY NEED ANSWERS TO F.) AND G.) I SOLVED THE REST. THANK YOU! The Boeing 747 has a cruising altitude of 45,000 feet and cruising speed of 275 m/s. At this elevation, the temperature and pressure according to the US Standard Atmosphere (air properties as a function of altitude) are 220K and 1.8x104 Pa, respectively. The engines are steady state devices that can be modeled using the 1st Law of Thermodynamics with air (ideal gas) as the working fluid... ADVERTISEMENT Need Online Homework Help? Get Answers For Free Most questions answered within 1 hours. Ask a Question ADVERTISEMENT Active Questions Use Karnaugh maps to design lowest cost circuits for the following functions with NOT, AND and... asked 22 minutes ago c# questions: 24.The counter variable in a for statement must be declared ___________. a.first b.second c.third... asked 27 minutes ago Consider the following hypothesis test: Ho: u = 18 Ha: u ≠ 18 A sample of... asked 27 minutes ago 1. Two students stand x meters apart with a rope stretched between them. One student moves... asked 29 minutes ago An engineer measured the Brinell hardness of 25 pieces of ductile iron from her company, that... asked 34 minutes ago Provide an example of this fallacy in the context of cyberethics. asked 58 minutes ago Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the integrand... asked 58 minutes ago Microwave ovens emit microwave energy with a wavelength of 12.2 cm. What is the energy of... asked 1 hour ago CNNBC recently reported that the mean annual cost of auto insurance is 978 dollars. Assume the... asked 1 hour ago void reverse_in_place(string& s){ int last = s.length() -1; for (int i = 0; i <= last/2;... asked 1 hour ago how has feminist theory contributed to improved commitments to gender equality? asked 1 hour ago SCHEME [2 marks] Define a procedure between? that takes 3 numbers representing a value (x) and... asked 1 hour ago About Contact Terms of Use Privacy Policy Academic Honesty Policy Homework Answer Scanner App Report DMCA © 2022 JustAAA   user contributions licensed under cc by-sa 4.0