Midterm Exam Page 1 of 10 Name ______
Energy Simulation in Building Design
MidtermNovember 3, 2016
Open book open notes
Write your name on every page as well as this one. You can use other side of a paper if you need.
Grade
1______/ 15
2______/ 25
3______/ 45
4______/ 60
5 ______/ 35
6______/ 15
7______/ 25
8______/ 30
9______/ 30
Total______/300
Problem:
The Apple Company is famous for their glass store buildings; after developing these stores in New York, Palo Alto, and Santa Monika they are considering a similar structure here in Austin. The first design schematic of this building together with surrounding are provide in the figures below.
Apple hired a designer firm “We Trust our Gutsand Design Accordingly”, which offered you an energy consulting position. You decided NOT to trust your gut, but to “run” some numbers before you provide your feedback. So, you decided to build a simplified energy model that should show the impact of large glass areas on the energy performance of this building.
Since you just need rough numbers that compare glass roof with regular roof, you can simplify this buildign geometry to a sqare box with the geometry provided below. Also, schematics below provide info about the walls, ceiling, and slab structure, as well as the details about the surounding buildings.
To do this analysis, you will need to build an energy model that includes all relevant building components that are major contributors in the heat transfer.I already introduced certain assumptions (simplifications), and most probably you will need to provide more assumptions solve this problem. My assumptions are listed below:
-Roof glass is flat, even though there is a small curvature in the architectural drawings.
-Steel beams that support glass roof do not participate in the heat transfer.
-Side concrete walls span all the way to the front façade (side glass walls are negligibly small).
-The exterior walls of the three surrounding buildings have the same hight as the Apple store and wall temperature of these surrounding building isthe same as the outdoor air temperature.
-The store HVAC system keeps the indoor temperature constant at 23°C.
-Assume that roof glass has no shading.
-The frequent door opening provides constant infiltration of outdoor air that provide 2 ACH.
-Below concrete floor insulation prevent heat transfer to the ground.
-Internal heat source (from occupants, electronics and lighting) are constant equal to 5 kW. Assume that 50% of this energy is convection and 50% is radiation.
-Assume that you know all physical and material properties and the geometry for your model.
-Assume that view factor from sky to the glass roof to the sky is 1.
Part 1)
Identify the external weather parameters and view factors that you need as input for your model.
Part 2)
2a) Rank my assumptions from the most important to the least important (put numbers on the side)
-Roof glass is flat, even though there is a small curvature in the architectural drawings.
-Steel beams that support glass roof do not participate in the heat transfer.
-Side concrete walls span all the way to the front façade (side glass walls are negligibly small).
-The exterior walls of the three surrounding buildings have the same high as the Apple store and wall temperature of these surrounding building is the same as the outdoor air temperature.
-The store HVAC system keeps the indoor temperature constant at 23°C.
-The frequent door opening provides constant infiltration of outdoor air that provide 2 ACH.
-Below concrete floor insulation prevent heat transfer to the ground.
-Internal heat source (from occupants, electronics and lighting) are constant equal to 5 kW. Assume that 50% of this energy is convection and 50% is radiation.
-Assume that you know all physical and material properties as well as geometry parameters needed for your model.
-Assume that view factor from sky to the glass roof to the sky is 1.
Explain your answer for the MOST important and the LEAST important assumption.
2b) List all your assumptions that you introduced to solve the problem. Rank the assumption according to the importance. Justify the 2 most important assumptions you introduced.
Part 3)
Provide a schematic of your model with all building elements that you introduced to the model. Distribute the nodes (discretize the elements that you model) according to your assumptions.
Provide a clear schematicthat shows all the nodes and display heat transfer (connection) between the nodes.
Part 4)
Provide allenergy balance equations for your model in the implicit format. Equations can be in general format. However, 1) roof equation(s), 2) one wall surface equation, and 3) the HVAC equation need to be in the fully developed format (showing all terms).
NOTE: No need to substitute numerical values in equations.
Part 5)
Identify two nonlinear equations and show how to linearize these equations for a linear equation solver.
Show the format ofthe linear equation matrix for the full set of equations you developed for your model. Show the matrix and indicate the positions of nonzero terms in the matrix.
NOTE: You do not need to calculate the matrix coefficients!
Select one equation in the matrix and calculate all the coefficients for that equation (including free vector).
Part 6)
Write thetwo nonlinear equations you identified in part 5 in fully explicit format. Do you need to do linearization when solving these equations? Explain why?
Part 7)
To improve the accuracy of hat transfer calculation for the concrete slab, you can position multiple internal nodes. Also, to improve the model accuracy you can use non-uniform node distribution by positioning more nodes in area closer to the surface (see the figure below).
For the node distribution in the figure, develop the equation for node 3. Assume that you know specific capacity, density and conductivity of concrete. Develop he equation in explicit format
A*T2+ B*T3 + C*T4=F and define coefficient: A, B, C, and F.
Part 8)
I assumed that roof glass has no shading. This is not correct since the three side walls stick above the glass roof. Show how you would correct this assumption. Show the equation that you would use to calculate effect of the shading on the class roof.
Part 9)
I assumed that view factor from sky to the glass roof is 1. Explain why this assumption is not correct. Show how you would calculate the exact view factor. No need to calculate. Just show the geometry and the equation that you would use.