From SGreen@swri.edu Thu Feb 22 09:14:46 1996 To: Subject: Solar Collector Test Cell I have had a chance to look at your write-up and the data for your solar collector test. You have used the term 'structured convection' in this write-up to describe the heat transfer process in the collector as some new phenomenon. You have said that it as least different from 'normal turbulent convection'. In fact, the heat transfer process in place during most of the time that the data are gathered is simple natural convection that is described in most engineering heat transfer textbooks. We could develop a mathematical model using computational fluid dynamics for your test cell, but I'm not sure that it will tell us anything really new about the flow field. The data you provided, including the smoke pattern description and the 'anomaly', can all be described by a rough engineering analysis. What follows is such a first-order assessment of the data based on my interpretation of the test setup. For natural convection from a vertical surface, only the fluid close to the surface moves under the effect of bouyancy forces caused by the decreased fluid density with respect to the fluid farther away from the surface. The fluid in contact with the wall is stationary and the fluid far away from the wall is approximately stationary. In the region just off the wall, however, the fluid reaches a maximum velocity but decreases to zero at the wall and far away from the wall. While the exact fluid velocity can be obtained by a numerical solution to the appropriate differential equations, an equation which closely approximates the velocity profile for turbulent flow is given as u/umax = 1/0.537 * (y/d)^(1/7) * (1-y/d)^4 where u = local velocity parallel to the wall, umax = maximum velocity in the profile, y = distance from the wall, d = local total boundary layer thickness. By differentiating this equation, we can see that the maximum velocity occurs at about 3.5% of the boundary layer thickness away from the wall. When expressed this way (i.e., dimensionless), the velocity profile is independent of the position along the wall. The boundary layer thickness and the maximum velocity are both functions of the distance along the wall. These have been reported in the literature by a number of workers, but the solution of Eckert and Jackson (NACA TN 2207, 1950) is still a good approximation: umax = 0.636 * mu/x * (Gr)^(1/2) * (1+0.494*Pr^(2/3))^(-1/2) d = 0.565 * x * Gr^(-1/10) * Pr^(-8/15) * (1+0.494*Pr^(2/3))^(1/10) where x = distance up the wall from the bottom, mu = fluid dynamic viscosity, Gr = Grashof Number (a heat transfer parameter), Pr = fluid Prandtl Number We can uses these relationships to get an idea of the velocity and the boundary layer thickness in your collector. From the graphs near noon, I estimate that the wall temperature is 180 F and the air temperature is 100 F at a position about halfway up the wall, which I assume is about 6 ft total height, from these temperatures, the following air properties are taken from a handbook: [PFH ed. Note: measurements were taken at ~3 ft height] 100 F 180 F mean value density = 0.071 0.062 0.067 lb/ft^3 viscosity = 1.285*10^-5 1.409*10^-5 1.347*10^-5 lb/ft*sec B = 1.79*10^-3 1.57*10^-3 1.68*10^-3 1/F (thermal expansion coefficient) Pr = 0.72 0.72 0.72 The Grashof Number, a natural convection heat transfer parameter is Gr = (density)^2*g*B/mu^2 * (Twall-Tair) * x^3 Using the arithmetic mean of the properties, the Grashof Number (a dimensionless value) is Gr = 2.89*10^9 The Gr*Pr product is known as the Rayleigh Number, Ra = Gr*Pr = 2.08*10^9 for this case. If the Rayleigh Number is greater than 1*10^9, the flow is turbulent; so the use of the above equations is warranted. The boundary layer thickness and the maximum velocity are now computed for this position along the wall as d=2.9" and umax=1.9 ft/sec, respectively. The maximum velocity is found at 0.1" from the wall. [PFH ed. Note: observed d<1/2", observed umax=~15 ft/sec] This explains the nature of your smoke patterns. The fluid is relatively quiescent at distances greater than 3 " from the wall, but the velocity increases to almost 2 ft/sec near the surface. The layer of fluid moving near the wall 'pulls' fluid from the bulk so that the boundary layer thickens as it moves up the heated wall. This value of Ra is only 2 times the value for laminar-turbulent transition; so the flow is not strongly turbulent. This is evidenced by the wavy pattern of the smoke as opposed to a more chaotic smoke pattern. The heated fluid spills over the top of the absorber and is replaced by cooler fluid entering at the botteom, thereby setting up a circulating flow in the container - mostly up in the air space along the absorber, mostly down through the rock storage. Because of the limited capated capacity of the rock storage, the top of the rock pile is heated to such a temperature late in the day that the driving force for flow up the storage is nearly as strong as for flow up the wall. In that case the, air will circulate only within the space in front of the absorber which will rapidly heat the volume of air between the glass and the absorber. This is indicated in the data. When the air is heated to a high enough temperature, or the rock pile cools sufficiently, the normal circulation pattern is re-established. I hope this assessment is useful to you. If necessary, I can expand it and make it more formal, but I will have to charge you for that type of effort. Steve Green Southwest Research Institute 210-522-3519 sgreen@swri.edu